text:
Copied to
clipboard

## G = C3×C33⋊C4order 324 = 22·34

### Direct product of C3 and C33⋊C4

Aliases: C3×C33⋊C4, C3C4, AΣL1(𝔽81), C342C4, C336C12, C337Dic3, C322(C32⋊C4), C324(C3×Dic3), C3⋊(C3×C32⋊C4), C3⋊S3.(C3×S3), (C3×C3⋊S3).2S3, (C3×C3⋊S3).5C6, (C32×C3⋊S3).2C2, SmallGroup(324,162)

Series: Derived Chief Lower central Upper central

 Derived series C1 — C33 — C3×C33⋊C4
 Chief series C1 — C3 — C33 — C3×C3⋊S3 — C32×C3⋊S3 — C3×C33⋊C4
 Lower central C33 — C3×C33⋊C4
 Upper central C1 — C3

Generators and relations for C3×C33⋊C4
G = < a,b,c,d,e | a3=b3=c3=d3=e4=1, ab=ba, ac=ca, ad=da, ae=ea, bc=cb, bd=db, ebe-1=bc-1, cd=dc, ece-1=b-1c-1, ede-1=d-1 >

Subgroups: 424 in 96 conjugacy classes, 14 normal (all characteristic)
C1, C2, C3, C3, C4, S3, C6, C32, C32, Dic3, C12, C3×S3, C3⋊S3, C3×C6, C33, C33, C3×Dic3, C32⋊C4, S3×C32, C3×C3⋊S3, C3×C3⋊S3, C34, C3×C32⋊C4, C33⋊C4, C32×C3⋊S3, C3×C33⋊C4
Quotients: C1, C2, C3, C4, S3, C6, Dic3, C12, C3×S3, C3×Dic3, C32⋊C4, C3×C32⋊C4, C33⋊C4, C3×C33⋊C4

Permutation representations of C3×C33⋊C4
On 12 points - transitive group 12T131
Generators in S12
(1 9 8)(2 10 5)(3 11 6)(4 12 7)
(1 9 8)(2 5 10)(3 6 11)(4 12 7)
(1 8 9)(3 11 6)
(1 9 8)(2 5 10)(3 11 6)(4 7 12)
(1 2 3 4)(5 6 7 8)(9 10 11 12)

G:=sub<Sym(12)| (1,9,8)(2,10,5)(3,11,6)(4,12,7), (1,9,8)(2,5,10)(3,6,11)(4,12,7), (1,8,9)(3,11,6), (1,9,8)(2,5,10)(3,11,6)(4,7,12), (1,2,3,4)(5,6,7,8)(9,10,11,12)>;

G:=Group( (1,9,8)(2,10,5)(3,11,6)(4,12,7), (1,9,8)(2,5,10)(3,6,11)(4,12,7), (1,8,9)(3,11,6), (1,9,8)(2,5,10)(3,11,6)(4,7,12), (1,2,3,4)(5,6,7,8)(9,10,11,12) );

G=PermutationGroup([[(1,9,8),(2,10,5),(3,11,6),(4,12,7)], [(1,9,8),(2,5,10),(3,6,11),(4,12,7)], [(1,8,9),(3,11,6)], [(1,9,8),(2,5,10),(3,11,6),(4,7,12)], [(1,2,3,4),(5,6,7,8),(9,10,11,12)]])

G:=TransitiveGroup(12,131);

On 18 points - transitive group 18T123
Generators in S18
(1 3 6)(2 4 5)(7 13 18)(8 14 15)(9 11 16)(10 12 17)
(1 7 9)(3 13 11)(6 18 16)
(1 7 9)(2 8 10)(3 13 11)(4 14 12)(5 15 17)(6 18 16)
(1 6 3)(2 4 5)(7 18 13)(8 14 15)(9 16 11)(10 12 17)
(1 2)(3 4)(5 6)(7 8 9 10)(11 12 13 14)(15 16 17 18)

G:=sub<Sym(18)| (1,3,6)(2,4,5)(7,13,18)(8,14,15)(9,11,16)(10,12,17), (1,7,9)(3,13,11)(6,18,16), (1,7,9)(2,8,10)(3,13,11)(4,14,12)(5,15,17)(6,18,16), (1,6,3)(2,4,5)(7,18,13)(8,14,15)(9,16,11)(10,12,17), (1,2)(3,4)(5,6)(7,8,9,10)(11,12,13,14)(15,16,17,18)>;

G:=Group( (1,3,6)(2,4,5)(7,13,18)(8,14,15)(9,11,16)(10,12,17), (1,7,9)(3,13,11)(6,18,16), (1,7,9)(2,8,10)(3,13,11)(4,14,12)(5,15,17)(6,18,16), (1,6,3)(2,4,5)(7,18,13)(8,14,15)(9,16,11)(10,12,17), (1,2)(3,4)(5,6)(7,8,9,10)(11,12,13,14)(15,16,17,18) );

G=PermutationGroup([[(1,3,6),(2,4,5),(7,13,18),(8,14,15),(9,11,16),(10,12,17)], [(1,7,9),(3,13,11),(6,18,16)], [(1,7,9),(2,8,10),(3,13,11),(4,14,12),(5,15,17),(6,18,16)], [(1,6,3),(2,4,5),(7,18,13),(8,14,15),(9,16,11),(10,12,17)], [(1,2),(3,4),(5,6),(7,8,9,10),(11,12,13,14),(15,16,17,18)]])

G:=TransitiveGroup(18,123);

Polynomial with Galois group C3×C33⋊C4 over ℚ
actionf(x)Disc(f)
12T131x12-69x10-72x9+1566x8+2466x7-14530x6-27216x5+49953x4+102474x3-21636x2-43272x+9616220·334·59·292·592·4992·6012·32394292

36 conjugacy classes

 class 1 2 3A 3B 3C 3D 3E 3F ··· 3W 4A 4B 6A 6B 6C 6D 6E 12A 12B 12C 12D order 1 2 3 3 3 3 3 3 ··· 3 4 4 6 6 6 6 6 12 12 12 12 size 1 9 1 1 2 2 2 4 ··· 4 27 27 9 9 18 18 18 27 27 27 27

36 irreducible representations

 dim 1 1 1 1 1 1 2 2 2 2 4 4 4 4 type + + + - + image C1 C2 C3 C4 C6 C12 S3 Dic3 C3×S3 C3×Dic3 C32⋊C4 C3×C32⋊C4 C33⋊C4 C3×C33⋊C4 kernel C3×C33⋊C4 C32×C3⋊S3 C33⋊C4 C34 C3×C3⋊S3 C33 C3×C3⋊S3 C33 C3⋊S3 C32 C32 C3 C3 C1 # reps 1 1 2 2 2 4 1 1 2 2 2 4 4 8

Matrix representation of C3×C33⋊C4 in GL4(𝔽7) generated by

 2 0 0 0 0 2 0 0 0 0 2 0 0 0 0 2
,
 3 2 4 3 4 5 5 6 3 3 6 1 0 0 0 1
,
 0 5 2 6 0 2 0 2 3 3 6 1 0 0 0 4
,
 3 6 3 2 6 3 4 2 0 0 2 0 0 0 0 4
,
 5 3 5 3 1 1 0 4 2 5 6 3 6 6 1 2
G:=sub<GL(4,GF(7))| [2,0,0,0,0,2,0,0,0,0,2,0,0,0,0,2],[3,4,3,0,2,5,3,0,4,5,6,0,3,6,1,1],[0,0,3,0,5,2,3,0,2,0,6,0,6,2,1,4],[3,6,0,0,6,3,0,0,3,4,2,0,2,2,0,4],[5,1,2,6,3,1,5,6,5,0,6,1,3,4,3,2] >;

C3×C33⋊C4 in GAP, Magma, Sage, TeX

C_3\times C_3^3\rtimes C_4
% in TeX

G:=Group("C3xC3^3:C4");
// GroupNames label

G:=SmallGroup(324,162);
// by ID

G=gap.SmallGroup(324,162);
# by ID

G:=PCGroup([6,-2,-3,-2,-3,3,-3,36,1443,111,1444,376,7781]);
// Polycyclic

G:=Group<a,b,c,d,e|a^3=b^3=c^3=d^3=e^4=1,a*b=b*a,a*c=c*a,a*d=d*a,a*e=e*a,b*c=c*b,b*d=d*b,e*b*e^-1=b*c^-1,c*d=d*c,e*c*e^-1=b^-1*c^-1,e*d*e^-1=d^-1>;
// generators/relations

׿
×
𝔽


text:
# GMAT Challenging Question 2 | Inequalities in Exponents

###### GMAT Sample Questions | Data Sufficiency Practice

The concept tested in this GMAT hard math question is tested quite often in the GMAT - especially as the data sufficiency variant. The relation between two exponents vary depending on whether the numbers are negative or positive or greater than 1 or less than -1.

This data sufficiency problem consists of a question and two statements, labeled (1) and (2), in which certain data are given. You have to decide whether the data given in the statements are sufficient for answering the question. Using the data given in the statements, plus your knowledge of mathematics and everyday facts (such as the number of days in a leap year or the meaning of the word counterclockwise), you must indicate whether -

1. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.
2. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.
3. BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question asked.
5. Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.
##### Numbers

All numbers used are real numbers.

##### Figures

A figure accompanying a data sufficiency question will conform to the information given in the question but will not necessarily conform to the additional information given in statements (1) and (2)

Lines shown as straight can be assumed to be straight and lines that appear jagged can also be assumed to be straight

You may assume that the positions of points, angles, regions, etc. exist in the order shown and that angle measures are greater than zero.

All figures lie in a plane unless otherwise indicated.

##### Note

In data sufficiency problems that ask for the value of a quantity, the data given in the statement are sufficient only when it is possible to determine exactly one numerical value for the quantity.

Question 2: Is x3 > x2 ?

Statement 1: x > 0
Statement 2: x < 1

## GMAT Live Online Classes

### Explanatory Answer | GMAT Inequalities DS

#### Step 1: Decode the Question Stem and Get Clarity

Q1: What kind of an answer will the question fetch?
An "Is" question will fetch an "Yes" or a "No" as an answer.
The data provided in the statements will be considered sufficient if the question is answered with a conclusive Yes or a conclusive No.

Q2: When is the answer yes?
If x3 > x2, the answer to the question is a conclusive Yes.

Q3: When is the answer yes?
If x3 ≤ x2, the answer to the question is a conclusive No.
Note: When x3 = x2, the answer is No.

It pays rich dividend to note down the answer to questions 2 and 3 mentioned above in your scratch paper while solving DS questions.

#### Step 2: Key concepts of Statement 1:

x3 is greater than x2 for certain values of x and will not be greater for other values of x.
There are 4 intervals to keep in mind while evaluating the relation between two different exponents of x.
Interval 1: -∞ < x < -1 x3 is negative in this interval and x2 is positive in this interval. So, x3 < x2.
Interval 2: -1 < x < 0 x3 is negative in this interval and x2 is positive in this interval. So, x3 < x2.
Interval 3: 0 < x < 1 x3 is positive and so is x2.
Sep 21, 2020

## GMAT Sample Questions | Topicwise GMAT Questions

##### Where is Wizako located?

Wizako - GMAT, GRE, SAT Prep
An Ascent Education Initiative
48/1 Ramagiri Nagar
Velachery, Chennai 600 042. India

##### How to reach Wizako?

Phone: (91) 44 4500 8484
Mobile: (91) 95000 48484
WhatsApp: WhatsApp Now
Email: learn@wizako.com

format: plain


text:
Translational Spring

Ideal spring in mechanical translational systems

Library

Mechanical Translational Elements

Description

The Translational Spring block represents an ideal mechanical linear spring, described with the following equations:

$F=Kx$

$x={x}_{init}+{x}_{R}-{x}_{C}$

$v=\frac{dx}{dt}$

where

 F Force transmitted through the spring K Spring rate x Relative displacement (spring deformation) xinit Spring initial displacement (initial deformation); the spring can be initially compressed (xinit > 0) or stretched (xinit < 0) xR,xC Absolute displacements of terminals R and C, respectively v Relative velocity t Time

The block positive direction is from port R to port C. This means that the force is positive if it acts in the direction from R to C.

Dialog Box and Parameters

Parameters Tab

Spring rate

Spring rate. The default value is 1000 N/m.

Variables Tab

Use the Variables tab in the block dialog box (or the Variables section in the block Property Inspector) to set the priority and initial target values for the block variables prior to simulation. For more information, see Set Priority and Initial Target for Block Variables.

Ports

The block has the following ports:

R

Mechanical translational conserving port.

C

Mechanical translational conserving port.


text:
# Are number of photons in an incident radiation proportional to its intensity?

Does number of photos emitted depends upon frequency of light source (or light color)?

I don't think so but one of the questions I attempted today suggests so. When the number of photons is proportional to the frequency of the radiation?

I think it should only depend on intensity of light. How can one relate the number of photons in an incident radiation to its intensity ?

Intensity is the total amount of energy falling on (or going through) a surface/region per unit area $$A$$ per unit time $$t$$ and therefore measured in $$\rm J/(m^2\,s)$$.

For monochromatic radiation, the total energy emitted equals the number of photons $$n$$ times the energy of one photon, $$h\nu$$.

Hence intensity $$I$$ is given by $$I=\frac{hn\nu}{At}$$

For constant area and time, $$I \propto n\cdot\nu$$

This is a very important result. You can increase the intensity of the radiation by either increasing the number of photons in it or increasing energy of each photon, or both.

The number of photons does not necessarily increase when the frequency of the radiation increases; only the energy of each photon increases.

However, for constant intensity, $$n \propto \frac{1}{\nu}$$

Light intensity is a classical measure , proportional to the square of the electric field in the electromagnetic wave equation.

Photons are elementary particles which carry $$E=h{\nu}$$ and build up in confluence the classical wave.

The number of photons comes from dividing the classical energy by the single photon energy. For the same classical beam energy, the higher the frequency the fewer the photons, from this simple algebra.


text:
### DIMACS/CCICADA Workshop on Risk-Averse Algorithmic Decision Making

#### May 9 - 11, 2011 DIMACS Center, CoRE Building, Rutgers University

`
Organizers:
Melike Baykal-Gursoy, Rutgers University, gursoy at rci.rutgers.edu
David Brown, Duke University, dbbrown at duke.edu
Aleksandar Pekec, Duke University, pekec at duke.edu
Andrzej Ruszczynski, Rutgers University, rusz at business.rutgers.edu
Dharmashankar Subramanian, IBM Watson Labs dharmash at us.ibm.com
Presented under the auspices of the Special Focus on Algorithmic Decision Theory and The Homeland Security Center for Command, Control, and Interoperability Center for Advanced Data Analysis (CCICADA).

#### Abstracts:

David Brown, Duke University

Title: Dynamic Portfolio Optimization with Transaction Costs: Heuristics and Dual Bounds

We study dynamic portfolio choice with transaction costs. This problem is naturally formulated as a dynamic program that is very difficult to solve when there are more than just a few assets. We explore some limited-look-ahead heuristic trading strategies and develop information-relaxation-based dual bounds that provide an upper bound on the performance of an optimal trading strategy. Extensive numerical results suggest that these easy-to-compute heuristic strategies are often nearly optimal.

Ozlem Cavus, Rutgers University

Title: Risk-Averse Optimal Path Problems for Markov Models

We use Markov risk measures to formulate a risk-averse version of the undiscounted stochastic shortest or longest path problems in an absorbing controlled Markov chain. We derive risk-averse dynamic programming equations and we show that a randomized policy may be strictly better than deterministic policies, when risk measures are employed.

This is a joint work with Andrzej Ruszczynski

Ricardo A. Collado, New York University

Title: Scenario decomposition of risk-averse multistage stochastic programming problems

In the last decade the theory of coherent risk measures established itself as an alternative to expected utility models of risk averse preferences in stochastic optimization. Recently, increased attention is paid to dynamic measures of risk, which allow for risk-averse evaluation of streams of future costs or rewards.

When used in stochastic optimization models, dynamic risk measures lead to a new class of problems, which are significantly more complex than their risk-neutral counterparts. Decomposition, an established and efficient approach to risk-neutral multistage stochastic optimization problems, cannot be directly applied to risk-averse models. With dynamic risk measures, the main feature facilitating decomposition, the integral form of the objective function, is absent.

Our main objective is to overcome this difficulty by exploiting specific structure of dynamic risk measures, and to develop new decomposition methods that extend the ideas of earlier approaches to risk-neutral problems.

In this work we develop generalizations of scenario decomposition methods, in the spirit of J.M. Mulvey and A. Ruszczynski, "A new scenario decomposition method for large-scale stochastic optimization", Operations Research 43, 1995. The key to success is the use of dual properties of dynamic measures of risk to construct a family of risk-neutral approximations of the problem. First, we define and analyze a two-stage risk-averse stochastic optimization problem. Next, we develop methods to solve efficiently this problem. Later, we formally define a multistage risk-averse stochastic optimization problem and we discuss its properties. We also develop efficient methods to solve the multistage problem and apply these to an inventory planning and assembly problem.

Finally, we analyze and compare the results of our computational experiments.

Peng Dai, SUNY Stony Brook

Title: Extension of Lyapunov's Convexity Theorem to Subranges

Consider a measurable space with a finite vector measure. This measure defines a mapping of the $\sigma$-field into a Euclidean space.

According to Lyapunov's convexity theorem, the range of this mapping is compact and, if the measure is atomless, this range is convex.

Similar ranges are also defined for measurable subsets of the space.

We show that the union of the ranges of all subsets having the same given vector measure is also compact and, if the measure is atomless, it is convex. We further provide a geometrically constructed convex compactum in the Euclidean space that contains this union.

We show that, for two-dimensional measures, among all the subsets having the same given vector measure, there exists a set with the maximal range of the vector measure (maximal subset). Furthermore, for two-dimensional measures, the maximal subset, the above-mentioned union, and the above-mentioned compactum are equal sets. We also give counterexamples showing that, in three or higher dimensions, the maximal subset may not exist and these equalities may not hold.

We use the existence of maximal subsets to strengthen the Dvoretzky-Wald-Wolfowitz purification theorem for the case of two measures. We show that there are no similar results for three or higher dimensions.

Dan Iancu, IBM Research Center Yorktown Heights

Title: Tight Dynamically Consistent Approximations of Inconsistent Distortion Risk Measures

A proper framework for measuring and mitigating risk in dynamic settings is of utmost importance, on both a practical, as well as a theoretical level. In recent years, coherent risk measures have emerged as a viable alternative to classical frameworks involving expected utility theory; their properties and axiomatic representation theorems are well understood in static settings, and have recently been extended to dynamic decision problems. In practice, however, since the specification of the resulting dynamic risk measures is typically much more involved, single-period static risk metrics are often used to assess dynamic risk, due to their conciseness and ease of interpretability. This can lead to an over or under-estimation of the true dynamic risk, as well as potentially inconsistent behavior.

In this paper, we investigate two different frameworks for assessing the risk in a multi-period decision process: a dynamically inconsistent formulation (whereby a single, static risk measure is applied to the entire sequence of future costs), and a dynamically consistent one, obtained by suitably composing one-step risk mappings. We characterize the class of dynamically consistent measures that provide a tight approximation for a given inconsistent measure, and discuss how the approximation factors can be computed. For the case where the consistent measures are given by Average Value-at-Risk, we derive a polynomial-time algorithm for approximating an arbitrary inconsistent distortion measure. We also present exact analytical bounds for the case where the dynamically inconsistent measure is also given by Average Value-at-Risk. Our theoretical and algorithmic constructions exploit interesting connections between the study of risk measures and the theory of submodularity and lattice programming, which may be of independent interest.

This is joint work with Pu Huang, Marek Petrik and Dharmashankar Subramanian.

Marco Laumanns, IBM Research Center Zurich

Title: Multi-Period Production Planning Under Non-Compliance Risk

This paper addresses a production planning setting for pharmaceutical companies under the risk of failing quality inspections that are undertaken by the regulatory authorities to ensure good manufacturing practices. We consider a staged decision model where the regulatory authority is considered an adversary with limited inspection budget, and the chosen inspections themselves have uncertain outcomes, depending on the set of products at a given production site. After reviewing the single-period problem of maximizing the worst-case revenue and the worst-case expectation, we discuss and compare different stochastic programming and dynamic programming formulations for the multi-period version. In particular, the problem of handling decision-dependent probabilities is highlighted, which requires solving a MINLP for each state in the multi-period DP.

This is joint work with Alwin Haensel, Ban Kawas, Eleni Pratsini, Steve Prestwich and Catalin-Stefan Tiseanu.

Warren B. Powell, Department of Operations Research and Financial Engineering, Princeton University

Title: An Integrated Framework for Stochastic Programming, Dynamic Programming, Stochastic Search and Simulation-Optimization

Stochastic programming, dynamic programming, stochastic search and simulation-optimization have evolved to a large degree in separate communities (with some overlap), characterized by cosmetic differences in notation and problem representation, and more substantive differences in applications. In this talk, I will present a perspective on policies that brings these fields under a single umbrella, exposing common algorithmic strategies that cut across fields. At the same time, I will describe how differences in problem characteristics lead to fundamentally different algorithmic strategies. Key issues are the dimensionality of the decision variable, and the complexity of the state variable. I will describe why problems with discrete actions or low-dimensional vectors can be "hard" while very high-dimensional decision vectors can be "easy." I will describe the exploration vs. exploitation problem, when it is important and the challenges that arise in high-dimensional problems. Finally, I will close by discussing how advanced machine learning methods can help bridge the gap between dynamic programming and scenario trees.

Werner Römisch, Humboldt University Berlin

Title: Multistage stochastic optimization with extended polyhedral risk measures

Extended polyhedral risk measures (EPRMs) are introduced and discussed. Examples of EPRMs are provided for the one- and multi-period situation. It is also argued that they are time consistent and information monotone . It is shown that EPRM represents a suitable concept to be incorporated into (linear) multistage stochastic optimization models. After their incorporation linearity of the optimization model, stability properties and decomposition structures are preserved. Finally, we show that the risk averse dynamic programming equations may be used within sampling-based decomposition methods.

Andrzej Ruszczynski, Rutgers University

Title: Dynamic Risk-Averse Optimization

We present the concept of a dynamic risk measure and discuss its important properties. In particular, we focus on time-consistency of risk measures. Next, we focus on dynamic optimization problems for Markov models. We introduce the concept of a Markov risk measure and we use it to formulate risk-averse control problems for two Markov decision models: a finite horizon model and a discounted infinite horizon model. For both models we derive risk-averse dynamic programming equations and a value iteration method. For the infinite horizon problem we also develop a risk-averse policy iteration method and we prove its convergence. We propose a version of the Newton method to solve a non-smooth equation arising in the policy iteration method and we prove its global convergence. Finally, we discuss relations to Markov games.

Alexander Shapiro, Georgia Institute of Technology

Title: Risk averse dynamic optimization

In recent years a theory of the so-called coherent risk measures had emerged. Its application to static (two-stage) stochastic programming is well established and generally accepted by the scientific community. The multistage case, on the other hand, is much more delicate. In this talk we discuss various approaches to multistage risk averse stochastic programming. In particular, we discuss the concept of time consistency and the Stochastic Dual Dynamic Programming approach to solving multistage risk averse stochastic programs.

Previous: Program
Workshop Index
DIMACS Homepage
Contacting the Center


text:
## Auxiliary Programs — EnergyPlus 8.6

### Auxiliary Programs

We developed a utility for the E/E format to read standard weather service file types such as SAMSON and newer ‘typical year’ weather files such as TMY2, WYEC2, and IWEC. The utility also reads ESP-r (CLM format), DOE-2 (fmt format), BLAST (Ascii format) files and other files.

The utility translates and extends typical weather data into the E/E format. The processor makes the calculations necessary for supplying data (when data is missing) and calculates the Horizontal Infrared Radiation Intensity values-not typically currently an observed value reported by the meteorological offices through the world. The utility also prepares an statistical summary of the weather data set as part of the processing. An additional “output format” from the utility is a comma-delimited file that can easily be imported into a spreadsheet program such as Excel™ for further user perusal, charting and/or editing.

The utility consists of two parts: a user interface that executes on standard Wintel systems and a DLL that does the work of the processing. The DLL interface is described in a later section for those developers who might wish to access it directly.

The user front end is a simple to use program with standard graphical user interface menus. It is executed from the Start Menu programs using the specific folder where the EnergyPlus program was installed. (e.g., Start Menu -> EnergyPlus <version> -> WeatherConverter). For convenience, it automatically opens with the “convert” option.

EP-Launch can also be used to run the weather utility program. Weather is one of the options on the Utilities tab in EP-Launch. See the section on EP-Launch in this document for more information on how to use EP-Launch with the weather utility program.

The file menu has four options:

### Fix Out of Range Data[LINK]

This is a toggle option that once selected is saved in the registry with other options (for example, screen size) for the program. As shown in the IDD type description of the Weather Data, there are minimum and maximum values for several of the fields. The weather converter program can ignore these (and just report them) or it can try to fix them with appropriate values. If the option is “checked”, then the processor will try to fix the data; if it is blank, the processor will not fix the data though it will report any out of range data that it finds.

Depending on the quality control and accuracy of the weather data collection, time period (usually hour to hour) changes in some data values may make the data suspect for that time period. This selection brings up the screen shown below and will allow the user some control over the actual value reporting. Note that this data is not “fixed”, merely reported by the program in the audit output file.

Though only one “trigger” value is selected from this screen, consecutive values of dry-bulb temperature, dew-point temperature and wind speed are reported using appropriate calculated values. Both dew-point and wind speed use a calculated value based on mean of their values over the entire data period and standard deviation from that mean, heuristically derived.

An excerpt from the audit file is illustrative:

Average Delta DB Change = 0.78°C ; Std Dev = 0.83°C

Average Delta DP Change = 0.68°C ; Std Dev = 0.78°C

Average Delta Relative Humidity Change = 4.02% ; Std Dev = 4.22%

Average Delta Wind Speed Change = 0.91m/s ; Std Dev = 0.88m/s

Hourly Dry Bulb temperature change trigger = minimum of 12.13°C and 10.°C

12.13°C = calculated trigger based on mean change in dry-bulb temperature and standard deviation shown above

10.°C = trigger set by user

Here the calculated DB trigger would be 12.13°C, but the user chosen trigger is 10°C. Changes > = 10°C will be reported.

• Delta DB/DP Range Triggered for Apr 30

• Change in DB = 11.60°C, Hour = 14

Such detail allows the user to hand edit the incoming data, if desired.

You may use this menu option to browse your computer and delete files.

### Input Folder = > Output Folder[LINK]

Choosing this option (a check will show and will carry over from one use to the next) sets the output folder for saving files to be the same as the input folder where the original files are located.

This choice exits the program.

This screen is automatically shown when you start the program - it will allow you to select raw data for processing, change the default type (based on file extension), select the kind of conversion you want, select where and what name to store for the processed data, and process the data. An “almost” completed screen shows:

The screen is navigated by choosing the following buttons on the left portion of the screen. Interpretation from the program is shown in the status boxes on the right portion of the screen.

Selecting this command button brings up a common dialog interface that allows you to select a file for conversion from a specific set of default file extensions. These are shown in the following table. Note that you can (mostly) override the default file extension by the use of a simple DEF file and change the input file type.

Input File Extensions with implied Data types
File Extension Implicit Data File Type
LST Processing List of Files
< any > or CST Custom - must have “def” file as specified below
EPW EnergyPlus E/E
CSV Comma Delimited File (EPW Format) Note: special EnergyPlus CSV format. For other CSV files use the DEF file and describe the format.
TM2 TMY2
TMY TMY
IWC IWEC
WY2 WYEC2
DAT SAMSON
FMT DOE-2 Formatted File
CLM ESP-r Climate Formatted File
ASC BLAST ASCII
SWE SWERA
WEA Ecotect WEA file

Of course, the “all files” (*.*) may be used as well. If the file selected is not one of the above types, you will be cautioned to use the “override default type” button to select the correct type before proceeding. Most of the data file types are described in other publications and won’t be described in detail here.

Note on the input CSV format: It is the EPW CSV format. The CSV format must mirror the output CSV format very closely. The processor expects a Location header record and the headers for the data fields as a minimum (as well as the data that supports those header fields). If you have a differently formatted file, possible comma delimited, investigate the “custom” format option.

The LST data type allows you to specify a list of files to be “batch processed”. The format of this file is very simple (however, the default extensions from the preceding table must be used or you must include a “def” file - see below for details).

Each line of the LST file can have a columnar structure as shown in the following table or can have the input file separated from the output file with a TAB character.

LST File Structure
Columns Contents
1-45 Name of Input File to be Processed
46-105 (or follow the first name with a {TAB}) Output File with: EPW - same as output type “EPW” CSV - same as output type “CSV” Both - same as output type “both” Rpt - same as output type “rpt”
106-end (or follow the second name with a {TAB}) URL for KML output

An auxiliary file, the Definitions File (extension .def) can be used to specify additional or replacement characteristics for the incoming data. This file is fully described in the section “Definitions File & Custom File Processing” later in this document.

This button is used as described above to select the correct data type for a file that might have one of the standard “default” extensions but may, in fact, be a data file of an entirely different type. For example, the BLAST ASCII files as they exist on the BLAST CD have extensions of .dat - our default type for the SAMSON data. You must select the proper data type for your data or the processor probably won’t work anywhere near what you expect.

You may select from four options of output format:

• EPW Format – both an epw file and a statistical report file are produced

• CSV Format - both a csv file and a statistical report file are produced

• Both EPW and CSV - epw, csv, and statistical report files are produced

• Rpt only - only a statistical report file is produced (output extension is “stat”)

Note that the CSV file is very similar to the EPW format file but is ready to be imported into a spreadsheet program such as Excel™ and has some additional “header” records in front of each EPW style header record


text:
# Mixed effects model with splines

I am fitting a mixed effects model with a spline term in an application where the trend over time is known to be curvi-linear. However, what I would like to assess is whether the curvi-linear trend occurs due to individual deviation from linearity, or is it an effect at the group level that makes a group level fit appear curvi-linear. I give a reproducible example boring a dataset from the JM package.

library(nlme)
library(JM)
data(pbc2)

fitLME1 <- lme(log(serBilir) ~ ns(year, 2), random = ~ year | id, data = pbc2)
fitLME2 <- lme(log(serBilir) ~ year, random = ~ ns(year, 2) | id, data = pbc2)

Essentially I want to know which one of these better fits my data. However comparison by anova gives me an ominous warning:

        Model df      AIC      BIC    logLik   Test  L.Ratio p-value
fitLME1     1  7 3063.364 3102.364 -1524.682
fitLME2     2  9 2882.324 2932.472 -1432.162 1 vs 2 185.0399  <.0001
Warning message:
In anova.lme(fitLME1, fitLME2) :
fitted objects with different fixed effects. REML comparisons are not meaningful.

Now I am aware that there are difficulties making these kinds of comparisons via maximum likelihood methods - but what is the alternative?

• Try re-fitting with method = "ML" or whatever the correct phrase is and see if the warning goes away. – mdewey Dec 4 '16 at 14:17

The next issues is that the models are not nested so the F-test presumably does not makes sense. You could look at the information criteria. Both favor fitLME2.


text:
Nominations are open for the RationalWiki 2022 Board of Trustees election.

# Difference between revisions of "Talk:Andrea Dworkin"

## "Slander"?

How can you slander someone who says "Under patriarchy, every woman's son is ... the inevitable rapist or exploiter of another woman." as being a misandrist? Do the "hate speech test": change "woman's son" to "black man" or "muslim" and see how it sounds. She clearly was misandrist. --Toffeeman 12:32, 17 December 2008 (EST)

Er, yeah. When you completely change the words it is offensive. Saying "black man" or "Muslim" instead of "woman's son" completely changes the meaning and social connotation. However, with the qualifier under patriarchy, her statement is completely true. --194.80.32.9 07:12, 26 February 2009 (EST)
Most people do not dispute this. However, there were certain right-wing smears on her that used false or out-of-context quotes to make this conclusion. Although the conclusion was arguably true, the false quotes constituted slander. (That quote might itself be false; I could not find any neutral or pro-Dworkin source confirming that she said it, hence the qualifier, "She was supposed to have said.") ListenerXTalkerX 12:49, 17 December 2008 (EST)
There is a reference to the source here. (The joys of Googlebooks)--Toffeeman 13:01, 17 December 2008 (EST)
I have inserted this reference and removed the qualifier. ListenerXTalkerX 13:05, 17 December 2008 (EST)

## Moonbat v Wingnut

Can you acutally be both? ArmondikoVpathetic 12:53, 17 December 2008 (EST)

I added her to both categories because she was an extreme moonbat herself, but extreme wingnuts latched on to her anti-pornography crusade. ListenerXTalkerX 12:53, 17 December 2008 (EST)
Thanks for the clarification. I was getting extremely confused. ArmondikoVpathetic 13:06, 17 December 2008 (EST)
Lyndon LaRouche can. Harmonic bastard Phantom Hoover!

## Quote mine

My initial reaction to this is it might be a bit quote-miney. I started to try to put some sense into the article but it is all over the place jumping from one topic to the next could someone who knows this women's views well put it into some semblance of a prose. - User ${\displaystyle \pi }$ 23:00, 17 December 2008 (EST)

## I'm not expert on this woman...

But doesn't it seem that most of her arguments remove all agency from a woman? Pornography, even if all involved are female, is an assault on the women involved. Marriage is a shackling of the woman in it, no matter how much she wants in. It seems (to this liberal feminist) that Dworkin's arguments recycle a lot more of many anti-feminist ideas about women and sex than this article shows. Am I missing something? (And I mean this sincerely--what do I not get about her?) Researcher 23:40, 17 December 2008 (EST)

No. The patriarchy removes all agency from a woman. Dworkin was just pointing this out. --194.80.32.9 08:20, 26 February 2009 (EST)
Susie Bright, individualist feminists, and Andrew Sullivan said roughly the same thing, that anti-feminists and Dworkin both wanted the State and society to coddle and protect women like weak, helpless creatures --- just to different ends. Several of her friends remarked that Dworkin was "a weak, vulnerable person." ListenerXTalkerX 23:57, 17 December 2008 (EST)
Individualist feminists should admit they are anti-feminist to their core. --194.80.32.9 08:20, 26 February 2009 (EST)
In other words, they are not Red methodologically post-Marxist enough to satisfy the likes of Dworkin... ListenerXTalkerX 11:15, 26 February 2009 (EST)
No, everything they say is completely anti-feminist. The founders of their ideology are anti-feminist, but just refuse to admit it. You can't be a Libertarian and a feminist. They used the word 'feminist' and co-opted it for their own movement. --89.243.240.113 08:09, 27 February 2009 (EST)
"You can't be a Libertarian and a feminist" — why, because you have to be a collectivist to be one? ListenerXTalkerX 11:03, 27 February 2009 (EST)
I think the argument would work like this: libertarianism is focused on the individual, and assumes that social/economic justice is best served by having each individual pursue her self-interest with as few limits as possible in her way. Feminism starts from the position that that is not possible for the half of the people in a given society that are saddled with structural barriers based on their sex/gender; therefore, libertarianism has fundamental tenets which conflict with the fundamentals of feminism. TheoryOfPractice 11:11, 27 February 2009 (EST) PS you say collectivist like it's a dirty word. TheoryOfPractice 11:18, 27 February 2009 (EST)
That is only a certain sort of feminism, though. The feminism of old time focused on issues such as giving women the rights to own property and vote and have equal protection under the law, and those goals are very much compatible with individualism. ListenerXTalkerX 11:23, 27 February 2009 (EST)
No, the "feminism of old time" (I don't know to what you are referring, even) did not just focus on "equal rights". You can only have (even the concept of being "given" rights by the ruling classes is problematic) equals rights on a level playing field, which does not exist within a patriarchy. Individualist "feminism" and Libertarianism ignores the concept of society and completely forgets about the massive patriarchy all around us that oppresses us, restricts us, and takes away our agency (and by 'us', I mean 'oppressed classes'.) Any so-called feminist who thinks that women are restricted only by the written law, and the only way to counteract the massive social and economic injustices against women is through individual perseverance, needs to take a harder look at the patriarchy. --194.80.32.9 11:57, 27 February 2009 (EST)
To put it into your lingo, "first-wave feminism."
You seem to think that one has to be a collectivist (more specifically, someone who adopts a Marxist theory of "class") to be a feminist. I disagree. The first-wave feminists, just for starters, did not generally adopt such beliefs. ListenerXTalkerX 12:33, 27 February 2009 (EST)
Except they did. They understood that women as a class were oppressed politically, economically, and socially. They understood that women as a class ('class' is not a purely Marxist concept) did not control their own lives, bodies, or destinies in any way. They did not stop at getting women the vote; they knew that many oppressive systems existed, such as inequalities in higher education and the workplace, and they went on to change those as well. Second-wave feminism expanded on this and moved on to fight for equality beyond the written law, definitely, but to say that first wave feminists didn't believe in class is ridiculous. A good deal of first-wave feminists were Marxists or Anarchists. Individualists can't be feminists; they're the ones saying it's the oppressed's fault that they're oppressed. --81.151.236.108 16:21, 27 February 2009 (EST)
I did not say that first-wave feminists did not believe in class, period; only that they were not all collectivists.
Although obviously "class" is not a Marxist idea per se, emphasizing as you do a conflict between two distinct classes of rulers and ruled, in the context of making a change in society, is a distinctly Marxist idea.
Since first-wave feminism had its beginnings before the birth of Marx, and was a full-blown movement before most of his theory (or the theory of collectivist anarchism, which owes much to Marx) was developed, obviously some first-wave feminists did not share these ideas. Mary Wollstonecraft, in particular, was of the liberal sort; she was the wife of an individualist and, if not one herself, was certainly not hostile to his views. Lucretia Mott was a Quaker minister.
Also, you are making a straw man characterization of individualism. I do not believe that being on the short end of social inequality is any "fault" of the people concerned; there are many ways in which people can make a living, and if one is not qualified for employment on good terms in one time and place, that is no indicator that s/he will not at some other time and different place be thus qualified. Not to mention that there is also a strong element of luck in where one winds up on the social ladder.
The sort of people who state that one's position on the social ladder is due entirely to his/her merit or demerit are often not individualists at all; they welcome individual initiative and achievement only when it brings benefit to some favored collective of theirs, like a corporation or a State. Hence, the contempt that this sort of person often shows for, e.g., artists and other such "free spirits" who show much individual initiative and achievement but have no truck with "the system."
That is one of the good things about individualism: it allows different people and groups to have different standards of what constitutes one's place on a social ladder. Look at this Wiki and Conservapedia, for examples in miniature — noting that we are more individualist and that Conservapedia is more collectivist. ListenerXTalkerX 02:29, 28 February 2009 (EST)
First-wave feminists did see 'men and women' as two distinct classes of rulers and ruled, respectively. Otherwise there could be no basis for feminism. Furthermore, Wollstonecraft and Mott were deemed feminists after the fact. --81.151.236.108 08:17, 28 February 2009 (EST)
"Otherwise there could be no basis for feminism" — Ah, I see; we are not arguing from facts, but from dogma. That might go over well some places, but it is not an acceptable sort of argument for proving facts on this Wiki.
Many of the arguments made by first-wave feminists were not laid on the basis of class, but on the basis of a consistent application of liberal ideals — simply the idea that when liberals spoke of all people being equal, that should include women as well. ListenerXTalkerX 02:30, 1 March 2009 (EST)
And that is misguided, because men as a class oppress women as a class. Voltairine de Cleyre and Emma Goldman understood this. Returning to my original point, "Individualist Femnists" are not feminists; they have co-opted the word to suit their own anti-feminist ideals. This happens a lot. --81.151.236.108 06:54, 1 March 2009 (EST)
You might think such arguments are misguided, but the first-wave feminists who made them obviously did not. ListenerXTalkerX 17:52, 1 March 2009 (EST)
And many of these first-wave feminists didn't think a woman had much place outside of the home and were very much for traditional gender roles. Mary Wollstonecraft herself even held men as the golden standard to which women should aspire. Again, if you don't think such a thing as the patriarchy exists, or that men and women have in every way except the law a level playing field, and that there can be such a thing as institutionalized sexism against men, they are barely feminists. --81.151.236.108 18:37, 1 March 2009 (EST)
But this is an article about Dworkin. Guess what kind of feminist she was. TheoryOfPractice 11:25, 27 February 2009 (EST)
The argument is not whether Dworkin was an individualist feminist or not, but whether that designator is an oxymoron or not. ListenerXTalkerX 11:35, 27 February 2009 (EST)
I think what you don't get is historical context--I think her arguments needed to be made when they were made as a sort of base-line from which to begin to explore, from a tabula rasa, the ways in which women have worked within and around unequal power relationships in order to exercise agency and create politics/power and meaning. Dworkin's work is unsettling, and it forces us to confront some ugly truths about male/female relationships. But a lot of feminist scholars have moved beyond Dworkin in just the ways you describe--and while porn-positive feminism, for example, may have been an oxymoron in Dworkin's time, I don't think it could have happened without her interventions. PFoster 00:03, 18 December 2008 (EST)
See, that makes perfect sense to me (and was something I was mulling in my head earlier, before I forgot about it and typed the above.) Can someone who actually knows more about this topic get this conversation (both what Listener and PFoster said) into the article? Or more into the article? Also, Listener...love the Mjollner in your sig. Researcher 00:06, 18 December 2008 (EST)
I am in the middle of re-working the article right now, although it will probably need some input from the other side of the spectrum when I am done with it. ListenerXTalkerX 00:11, 18 December 2008 (EST)

## Dworkin was a left-winger

1. Before she became a radical feminist, Dworkin was an anarchist and active in the 1960s anti-war protests. This was how she met her first husband.
2. Dworkin's colleague, Catharine MacKinnon, once described her and Dworkin's sort of feminism as "methodologically post-Marxist;" as I understand it, this is because it views women approximately how classical Marxism views the proletariat.

ListenerXTalkerX 14:52, 6 February 2009 (EST)

## Have you all read her?

I'm curious because many people who have opinions on Dworkin tend to have not read her, but rather have read comments by others (on either side of the argument) about what she had to say. I find, having read Mercy, Right wing women, and Intercourse, that the typical arguments found on sites like this rather polarize her more complex arguments. Just my two cents. I didn't really enjoy her writing, so I never read beyond what was assigned in class.--En attendant Godot"«Lo-lee-ta: the tip of the tongue taking a trip of three steps down the palate to tap, at three, on the teeth. Lo. Lee. Ta. V.Nabokov» 11:26, 27 February 2009 (EST)

I have read some of her rav — er, works; besides having frankly frightening sentence structure (which worsened as she got older and crazier), their complex arguments mostly just mixed lurid and contemptuous descriptions of men and sex with historical-materialist conspiracy theories. ListenerXTalkerX 11:33, 27 February 2009 (EST)
Listener, again with the grammar and the "anything not mainstream capitalist" is loony Marxism. At least you're a two-trick pony, I suppose. TheoryOfPractice 11:38, 27 February 2009 (EST)
You are overgeneralizing again. ListenerXTalkerX 11:47, 27 February 2009 (EST)
(Edit Conflict)::I am curious what's so crazy about the idea that for 2000+ years, women's value as breeder and sexual object forces her into a position of "wife" with all the lack of independence it holds; that sexuality was and has been throughout patriarchal cultures, something to hide for women, something not to be enjoyed by women, something dirty and shameful for women (though not always for men - depended on the culture); that women knowingly used sex as a way to get things in life, in society, and in their marriage, and that when you have limited voice to say "I'm going out into the world to make my own way", marriage and all sexual relations become a mere aspect of rape even *if* you happen to like it; that when the sexually produced materials are made by men, and for men, in a culture where women act *still* as objects though they may now be paid for it; when they are not included in the pay as writers, creative consultants; when the very act of having a porn industry reinforces the idea that women are predominantly just boobs and holes for male members; when our advertisement industry reinforces this position; where our children's fairy tales still insist that women are both weak and exist to be married to men - dream of it, and only it; I just don't see where these ideas are "bat shit crazy". We've moved on, we've modified and tweaked them, but they are sound ideas based on a patriarchal culture that continues to define women in its own terms and in relation to men's sexuality, and not on our own terms and in relation to our sexuality. --En attendant Godot"«Lo-lee-ta: the tip of the tongue taking a trip of three steps down the palate to tap, at three, on the teeth. Lo. Lee. Ta. V.Nabokov» 11:51, 27 February 2009 (EST)
(EC) Uh, not exactly what I was thinking about. I was thinking more about when she said that the 1960s counterculture only came about because men found it a handy way to bring their oppression into girls' pants, and lost its steam when it ceased thus to be handy. ListenerXTalkerX 12:06, 27 February 2009 (EST)
You know that Dworkin wasn't the only person saying this, right? Steinem has said the same thing; the 60's free-love movement was for men, not women. --81.151.236.108 16:24, 27 February 2009 (EST)
You criticize people a lot around here for not being "good" writers in your concept. If this idea of Dworkin is the idea you were criticizing about Dworkin, don't you think a "good writer" would be specific about that one *very minor* aspect of her writing? Also, I believe you misconstrue what she is saying. She is saying that the feminist movement of the day isn't going far enough, and becomes a tool used by the political male, to divert from other far more important issues about women's identity. Something I would say we are quite good at today. the "pro-choice" movement is NOT a women's movement, it's a men's movement. And it's done to distract women from dealing with real issues like "being an equal participant in humanity", or you know "stopping the government from stealing every bit of money we have and giving it to their rich (male) buddies". Just cause an issue is "about" things a woman can or cannot do, does not mean it's a women's issue.--En attendant Godot"«Lo-lee-ta: the tip of the tongue taking a trip of three steps down the palate to tap, at three, on the teeth. Lo. Lee. Ta. V.Nabokov» 12:14, 27 February 2009 (EST)
By the "very minor" aspect of her writing, do you mean her sentence structure? (And I dispute your statement about the "pro-choice" movement.) ListenerXTalkerX 12:45, 27 February 2009 (EST)

I see where the pro-choice arguement comes from: discourses about abortion serve to reproduce/reinforce women's subject position as reproducers/receptacles. Interesting. TheoryOfPractice 12:49, 27 February 2009 (EST)

My dispute was that it is a conspiracy theory ("THEY'RE JUST MAKING THIS DEBATE TO DISTRACT US!"), hence is worthy of as much consideration as any other conspiracy theory.
As to your remarks about how "society says this, society says that" — society does not say those things, as society is an abstract concept; individuals within a society say them, and those listening would do well to remember what Aesop said on that subject.
"...we criminalize and politicize being female..." Since when has being a woman been a crime?
"...my body is not a valid place for you to make political hay..." This sounds as if you, being (presumably) for legal abortion, are trying to close down the debate on the question. ListenerXTalkerX 13:34, 27 February 2009 (EST)
The point is that the debate over when life starts, what's moral, what's just etc. does distract from the real issue: that either women are people deserving of bodily sovereignty or they are just tools for reproduction. There would be no debate if a woman's humanity wasn't in question. This is why it's a crime to be female; your humanity comes into question every damn day. Your society comment, by the way, makes me laugh. People are never arranged into groups or anything, and no one specific group has been in power forever. "There is no society, just individuals and families". Wait, no. That was Margaret Thatcher. --81.151.236.108 16:28, 27 February 2009 (EST)
(1) It is one thing to speak of certain tangential effects of a debate, and another to say, as WaitingforGodot did, that the entire debate is being made with the intention of producing said effects.
(2) Nobody says that women are subhuman, except perhaps for Fall down, and nobody listens to him anyway.
(3) The choice you postulate of "freedom or babies" is a false dichotomy; if for some incomprehensible reason a woman should like to have children, she can have both.
(4) I dispute the claim that the abortion debate would be over but for the question of women's humanity. Although a minority of pro-lifers might be motivated to oppose abortion due to a belief that women should be baby-machines, very few of them actually argue for laws against abortion based on that idea; if this were the only argument pro-lifers were making, the debate would have been over a long time ago. So you could say that speaking of "women's humanity being in question" is distracting from the issue of whether or not a fetus is human or not.
(5) Let us assume for the purposes of argument that women are subhuman. Does that mean being a woman is a crime? It does not, any more than being a cat or a dog is a crime.
(6) The reductio ad Thatcherum aside, I reiterate that society has no mouth and therefore cannot say anything. Everything that is said is said by some individual or other; perhaps some of those individuals are claiming to speak for society, but they are not, any more than the President speaks for all Americans. ListenerXTalkerX 17:21, 27 February 2009 (EST)
I don't know if you intentionally misunderstood everything I said or are just so blinded by your rampant individualism that you can't see the forest through the trees. Probably both? Society has been constructed in a way to take human rights away from women. Therefore, society regards women as subhuman. It makes no difference if a fetus is human or not. Again, that distracts from the real point: do women have to give up their bodies to anyone against their will, or do they have control over it? (Note: the former is the basis of rape culture.) I never said "freedom or babies". I said "freedom" or "forced babies, because you are a tool for the patriarchy and nothing more." I've already explained the logic behind "it is a crime to be female", so I'm not going to reiterate it. Same with society. Oh I forgot that there's no such thing as dominant discourse or culture. I forgot we aren't arranged into groups. I forgot that no specific group is in power, and how that specific group doesn't have significant advantages over other, disadvantaged groups. I forgot that there are no disadvantaged groups! I forgot that specific groups don't dictate culture. My mistake! There is no society! So laughable. I laugh at your individualism.
This is over. I gave up arguing with people who didn't understand the finer points of feminism and patriarchy long ago. --81.151.236.108 18:19, 27 February 2009 (EST)
Laugh on, laugh on; no amount of laughing will change the fact of your stated abandonment of this debate. Perhaps I do not understand your position, but you do not understand mine, either; see my remarks above on individualism. Yet I am willing to continue, and you are withdrawing.
(1) My apologies about my mischaracterization of your freedom vs. forced-baby dichotomy; I had assumed that you, like Dworkin, believed that in the phrase "forced babies" the adjective was redundant. This was obviously incorrect.
(2) I still think the question of the fetus being human is very relevant in the abortion case. Let us assume that a certain woman has become pregnant in some way that she could not have expected, and does not want the baby. Let us assume further that if she is prevented from having an abortion, she will, as you say, be giving up her body to another's service.
Now if the fetus is human, there is a choice to be made: disallow the abortion and condemn the woman to servitude, or allow the abortion and condemn the fetus to be murdered, through no possible fault of the fetus's. Those who believe that it is acceptable to murder people in furtherance of human rights have much arguing to do.
(3) I did not say, nor do I believe, that there are no such things as groups or classes or society; there is no need to overgeneralize my statement about things that "society says." ListenerXTalkerX 02:29, 28 February 2009 (EST)
I'm still laughing. Again, by saying that it's not okay for a woman to assert her bodily sovereignty when something that is arguably human is inside her, then you are saying that a woman is also arguably human. That somehow, a creature whose status is completely unknown has more right to a woman's body than she does. Disgusting. And babies vs. freedom is not a false dichotomy, if you are a woman. And again, I forgot that there is no society. There's no such thing as dominant discourse or anything. Society doesn't have a mouth, because television, literature, art, advertising, politics, etc. don't exist. You really need to brush up on your Feminist theory. --81.151.236.108 08:06, 28 February 2009 (EST)
(1) My fetus argument was made under two assumptions, which I stated: firstly, that the mother is a person with bodily sovereignty, and secondly, that the fetus is also a person. The fetus's being a person is a case that has to be considered, since you think the question of the fetus's personhood irrelevant.
The mother's body is not exactly the only body involved there; the fetus has a body as well, and if the fetus is a person then by your own arguments it has certain rights to its own body, such as the right not to have it ground up and chucked out with the trash. If you believe that the fetus's right not to be killed in this manner is trumped by the mother's right to bodily sovereignty, then you believe that murder is acceptable in upholding the latter right. Although this position may by some stretch of the imagination be logically consistent, you will have considerable difficulty convincing most other people of the merits of these ideas, if you believe that.
(2) "babies vs. freedom is not a false dichotomy" — it is such for women who want to have them; indeed, to deprive these women of their children is a violation of their freedom, as Lucy Stone remarked in the case of slave women who had their children taken away.
(3) I have now placed in bold type my above response to your continued ravings about my "society" remarks. ListenerXTalkerX 02:30, 1 March 2009 (EST)
So another "person" (we would have a long argument over what 'personhood' requires, but for the sake of argument I'll bite) has more right to a woman's body than herself. Got it. So, should we have forced organ donation as well? Should a woman give up all of her other organs in service to other people? Is rape OK too? Just seeing how logically consistent you are here. I'll have some difficulty convincing most other people of the merits of these ideas because most people start from the position that women are sub-human or sub-person. There would be no opposition from so-called "pro life" (I call them anti-woman, which is what they are) groups if they had any idea of a woman's humanity.
If a woman wants to have a child she is voluntarily giving up her freedom. Who said I was "depriving women of their children"? I was merely pointing out the lifelong no-pay, no-thanks drudgery that it is to be a housewife with no public voice or public respect. And if she's a working mother, well then she has two jobs.
And I still consider your society remarks to be amazingly shortsighted. Still laughing, by the way. --81.151.236.108 07:03, 1 March 2009 (EST)
<DISCLAIMER>I do not believe fetuses to be human.</DISCLAIMER> So, hang on... A woman's decision as to what happens to her body is more important than allowing another human to live? Evil harmonic Hoover! 08:59, 1 March 2009 (EST)
Surprisingly, yes. I honestly don't see why this is such a radical idea. --81.151.236.108 09:35, 1 March 2009 (EST)
Because you think that your ideals are more important than the life of a human being? Which do you think is the higher cost: a woman having a child, at great inconvenience, or that fetus being killed, at arguably infinite cost? If you really think that the woman comes out worse in the first scenario than the fetus does in the second, you really need to sort out your ethics. Evil harmonic Hoover! 10:48, 1 March 2009 (EST)
Ditto to everything said below, and, "my ideals" are not what is at stake. It is the humanity of women. Please tell me that someone forced to do something for someone else against their will is not a slave. Tell me that a woman's body is free game if anyone wants to use it for their own benefit against her will. Tell me that in earnest, and at least you will have the benefit of being logically consistent. --81.151.236.108 11:37, 1 March 2009 (EST)
If a child or another human has to use my body to survive, then I and only I must be able to give approval, and it cannot be a one time thing. I must be able to stop giving approval at any time, or I literally become a slave to that other person. I hate when people talk about pregnancy as some mere "inconvenience". I've been pregnant twice. It's not "inconvenient", it's life changing, it's all demanding, it's emotionally overwhelming. I like to talk about the woman who is in the Air Force academy. One stupid night with a fellow junior, and she is faced with losing everything you work for. You cannot be a cadet and be pregnant, it's not allowed. Also, if you leave school for any reason, you cannot come back. Now, if a child is more important than your career, you'll drop out, but if not, that's 3 years of very hard work flushed down the toilet *for every* cause someone else thinks you should act as a womb. A drinker who doesn't want to give up drinking can do serious harm to a fetus. Should she have to give up her drink for a child she doesn't want? 1 in 10,000 women in the US will die due to complications of pregnancy. 1 in 100 will suffer serious long term or permanent damage (heart attacks, strokes, loss of sensation in the lower body, diabetes that was only "supposed" to be gestational, bone density loss, etc), 1 in 1 women will be in serious pain for at least a few hours. It's an "inconvenience" when it's someone else's body. It's not a mere inconvenience when it's your body. — Unsigned, by: WaitingforGodot / talk / contribs

(UNINDENT) (1) "Please tell me that someone forced to do something for someone else against their will is not a slave." I do say this, in the case when not doing the said something results in the death of the said "someone else." Doctors are not slaves on account of being required by law to perform operations to save the lives of emergency-room patients. People are not slaves on account of being required by law to save someone else's life, suffering legal penalties if they do not. And if a fetus is a person, a woman is not a slave on account of being required by law to sustain a fetus's life until it no longer has an absolute dependency upon her.

(2) "Tell me that a woman's body is free game if anyone wants to use it for their own benefit against her will." I am only speaking of the hypothetical rights of a fetus here; no person who has "wants" of that sort is a fetus that is absolutely dependent on the woman for its life, and therefore one can consistently say that a woman's body is not "free game" to such people, while maintaining that the fetus, which has no such wants, has a right to its life.

(3) "I was merely pointing out the lifelong no-pay, no-thanks drudgery that it is to be a housewife..." Your personal disdain for housewifery is: (a) not shared by all women; (b) based on false premises, since many women who perform those tasks have hearty thanks from their families in return.

(4) As your position on abortion is becoming more clear, let me put out some questions.

(a) Suppose you live in an isolated area. One day a woman comes to your door gravely injured, begging a bed to recuperate. She cannot safely be moved to any hospital or any other house, and if she is to survive you will have to feed her and care for her for some months. If for some reason you did not want to do this, would you have the right to blast her brains out with a shotgun?
(b) In pagan Iceland, they had abortion as well: they would wait until winter and then pitch the baby out the window. If this were the best available way to get rid of a baby and save the mother from the fabled misery of motherhood, would it be acceptable to you?

ListenerXTalkerX 17:52, 1 March 2009 (EST)

Nice. You give two examples which are (a) not comparable to pregnancy and (b) not comparable to abortion. Well done! --Kels 18:45, 1 March 2009 (EST)
Ditto to the above.
So you do believe that people should be forced to donate their organs and blood to the needy. (Being a doctor is a profession that requires the saving of a life; it is not comparable.) How disgustingly honest. So a woman's body is free game to some people, but not to others? You still operate under the assumption that a woman has less rights to her body than others.
I take issue to the idea that I have a personal disdain for housewives. I do not. I am merely pointing out the conditions most housewives face. I think it is horrible that women must face these conditions (domestic slavery) if they choose to have children. Even hearty thanks as you put them does not detract from the tremendous load women have to bear for the sake of the institution of "family".
As for your hypothetical and not-comparable-to-abortion situation, no, I would not find it acceptable, as material possessions may be used by anyone. However, if a woman came to me and by some method attached herself to my organs in order to sustain her own life, and my body and future was thus compromised by this intruder, then yes I would cut her off. Even if that removal caused her death.
No, they didn't have abortions in pagan Iceland. Abortions are the termination of a pregnancy. (I like your snide remark disparaging all mothers' struggles everywhere, by the way, very chauvinistic and dismissive). And no, it would not be acceptable to me as anyone may take care of a born child. Should they raise that child willingly? Absolutely. You cannot force anyone to adopt a child. Similarly, you should not be able to force a woman to bear a child. Your implication that a 12 week old fetus is comparable to a born, independent baby is very humorous. --Astrophilia 19:01, 1 March 2009 (EST) (Yes, I made an account.)

### Old branch of the thread

Godot, I pretty much agree with you--somewhere above, a long tiome ago, I made a comment about how feminism has moved beyond a lot of what Dworkin wrote about, but this doesn't make her interventions any less crucial. And I think that people who pile on her do so sometimes because they want her to be more "objective"--which was not at all her goal. TheoryOfPractice 11:56, 27 February 2009 (EST)
Anyone who reads philo of any kind realizes that philosophy (and religious writing, and probably political writings) are creations of their time. I love reading de Beauvoir, her french is just delicious, but what was offensive and groundbreaking in the 1930s, is today so common and understood, that most girls reading her today go... "um, and this is a good philosopher, why? She's just stating the obvious" Dworkin asks of men and women, is there something implicit in the act of being the penitrator vs., the penitratee that makes the sexual act a power play? and if so, what must the social repercussions be, and how do you change that? I'd be curious to talk with a gay male able this, who can (and does?) take on both aspects of the sexual act. Viewing women's sexuality from the eyes of someone who "lives" (as far as teh sexual act) in both worlds - penitrator and penetratee. --En attendant Godot"«Lo-lee-ta: the tip of the tongue taking a trip of three steps down the palate to tap, at three, on the teeth. Lo. Lee. Ta. V.Nabokov» 12:04, 27 February 2009 (EST)


text:
Copyright (c) 2015 Ghent University – INTEC with offices at Sint-Pietersnieuwstraat 25, 9000 Ghent, Belgium and company number 0248.015.142. Contact:  Bart Moeneclaey:    This email address is being protected from spambots. You need JavaScript enabled to view it.
document.getElementById('cloak23de5ba1c1a65ddf602bc0c937ffa0b1').innerHTML = '';
var prefix = 'ma' + 'il' + 'to';
var path = 'hr' + 'ef' + '=';
var addy23de5ba1c1a65ddf602bc0c937ffa0b1 = 'bart.moeneclaey' + '@';
var addy_text23de5ba1c1a65ddf602bc0c937ffa0b1 = 'bart.moeneclaey' + '@' + 'analogdesign' + '.' + 'be';document.getElementById('cloak23de5ba1c1a65ddf602bc0c937ffa0b1').innerHTML += '<a ' + path + '\'' + prefix + ':' + addy23de5ba1c1a65ddf602bc0c937ffa0b1 + '\'>'+addy_text23de5ba1c1a65ddf602bc0c937ffa0b1+'<\/a>';

/* <![CDATA[ */!function(){try{var t="currentScript"in document?document.currentScript:function(){for(var t=document.getElementsByTagName("script"),e=t.length;e--;)if(t[e].getAttribute("cf-hash"))return t[e]}();if(t&&t.previousSibling){var e,r,n,i,c=t.previousSibling,a=c.getAttribute("data-cfemail");if(a){for(e="",r=parseInt(a.substr(0,2),16),n=2;a.length-n;n+=2)i=parseInt(a.substr(n,2),16)^r,e+=String.fromCharCode(i);e=document.createTextNode(e),c.parentNode.replaceChild(e,c)}}}catch(u){}}();/* ]]> */
/* <![CDATA[ */!function(){try{var t="currentScript"in document?document.currentScript:function(){for(var t=document.getElementsByTagName("script"),e=t.length;e--;)if(t[e].getAttribute("cf-hash"))return t[e]}();if(t&&t.previousSibling){var e,r,n,i,c=t.previousSibling,a=c.getAttribute("data-cfemail");if(a){for(e="",r=parseInt(a.substr(0,2),16),n=2;a.length-n;n+=2)i=parseInt(a.substr(n,2),16)^r,e+=String.fromCharCode(i);e=document.createTextNode(e),c.parentNode.replaceChild(e,c)}}}catch(u){}}();/* ]]> */       This email address is being protected from spambots. You need JavaScript enabled to view it.
document.getElementById('cloak17b68591909c4dafa293809a4fd61a6e').innerHTML = '';
var prefix = 'ma' + 'il' + 'to';
var path = 'hr' + 'ef' + '=';
var addy17b68591909c4dafa293809a4fd61a6e = 'bart.moeneclaey' + '@';
addy17b68591909c4dafa293809a4fd61a6e = addy17b68591909c4dafa293809a4fd61a6e + 'intec' + '.' + 'ugent' + '.' + 'be';
var addy_text17b68591909c4dafa293809a4fd61a6e = 'bart.moeneclaey' + '@' + 'intec' + '.' + 'ugent' + '.' + 'be';document.getElementById('cloak17b68591909c4dafa293809a4fd61a6e').innerHTML += '<a ' + path + '\'' + prefix + ':' + addy17b68591909c4dafa293809a4fd61a6e + '\'>'+addy_text17b68591909c4dafa293809a4fd61a6e+'<\/a>';

/* <![CDATA[ */!function(){try{var t="currentScript"in document?document.currentScript:function(){for(var t=document.getElementsByTagName("script"),e=t.length;e--;)if(t[e].getAttribute("cf-hash"))return t[e]}();if(t&&t.previousSibling){var e,r,n,i,c=t.previousSibling,a=c.getAttribute("data-cfemail");if(a){for(e="",r=parseInt(a.substr(0,2),16),n=2;a.length-n;n+=2)i=parseInt(a.substr(n,2),16)^r,e+=String.fromCharCode(i);e=document.createTextNode(e),c.parentNode.replaceChild(e,c)}}}catch(u){}}();/* ]]> */
/* <![CDATA[ */!function(){try{var t="currentScript"in document?document.currentScript:function(){for(var t=document.getElementsByTagName("script"),e=t.length;e--;)if(t[e].getAttribute("cf-hash"))return t[e]}();if(t&&t.previousSibling){var e,r,n,i,c=t.previousSibling,a=c.getAttribute("data-cfemail");if(a){for(e="",r=parseInt(a.substr(0,2),16),n=2;a.length-n;n+=2)i=parseInt(a.substr(n,2),16)^r,e+=String.fromCharCode(i);e=document.createTextNode(e),c.parentNode.replaceChild(e,c)}}}catch(u){}}();/* ]]> */Jochen Verbrugghe:  This email address is being protected from spambots. You need JavaScript enabled to view it.
document.getElementById('cloakb2444dc0086aae384b8e68f9888ff98b').innerHTML = '';
var prefix = 'ma' + 'il' + 'to';
var path = 'hr' + 'ef' + '=';
var addyb2444dc0086aae384b8e68f9888ff98b = 'jochen.verbrugghe' + '@';
var addy_textb2444dc0086aae384b8e68f9888ff98b = 'jochen.verbrugghe' + '@' + 'analogdesign' + '.' + 'be';document.getElementById('cloakb2444dc0086aae384b8e68f9888ff98b').innerHTML += '<a ' + path + '\'' + prefix + ':' + addyb2444dc0086aae384b8e68f9888ff98b + '\'>'+addy_textb2444dc0086aae384b8e68f9888ff98b+'<\/a>';

/* <![CDATA[ */!function(){try{var t="currentScript"in document?document.currentScript:function(){for(var t=document.getElementsByTagName("script"),e=t.length;e--;)if(t[e].getAttribute("cf-hash"))return t[e]}();if(t&&t.previousSibling){var e,r,n,i,c=t.previousSibling,a=c.getAttribute("data-cfemail");if(a){for(e="",r=parseInt(a.substr(0,2),16),n=2;a.length-n;n+=2)i=parseInt(a.substr(n,2),16)^r,e+=String.fromCharCode(i);e=document.createTextNode(e),c.parentNode.replaceChild(e,c)}}}catch(u){}}();/* ]]> */
/* <![CDATA[ */!function(){try{var t="currentScript"in document?document.currentScript:function(){for(var t=document.getElementsByTagName("script"),e=t.length;e--;)if(t[e].getAttribute("cf-hash"))return t[e]}();if(t&&t.previousSibling){var e,r,n,i,c=t.previousSibling,a=c.getAttribute("data-cfemail");if(a){for(e="",r=parseInt(a.substr(0,2),16),n=2;a.length-n;n+=2)i=parseInt(a.substr(n,2),16)^r,e+=String.fromCharCode(i);e=document.createTextNode(e),c.parentNode.replaceChild(e,c)}}}catch(u){}}();/* ]]> */     This email address is being protected from spambots. You need JavaScript enabled to view it.
document.getElementById('cloakbf963a6d12f9ca2be0033b0bd365c34d').innerHTML = '';
var prefix = 'ma' + 'il' + 'to';
var path = 'hr' + 'ef' + '=';
var addybf963a6d12f9ca2be0033b0bd365c34d = 'jochen.verbrugghe' + '@';
addybf963a6d12f9ca2be0033b0bd365c34d = addybf963a6d12f9ca2be0033b0bd365c34d + 'intec' + '.' + 'ugent' + '.' + 'be';
var addy_textbf963a6d12f9ca2be0033b0bd365c34d = 'jochen.verbrugghe' + '@' + 'intec' + '.' + 'ugent' + '.' + 'be';document.getElementById('cloakbf963a6d12f9ca2be0033b0bd365c34d').innerHTML += '<a ' + path + '\'' + prefix + ':' + addybf963a6d12f9ca2be0033b0bd365c34d + '\'>'+addy_textbf963a6d12f9ca2be0033b0bd365c34d+'<\/a>';

/* <![CDATA[ */!function(){try{var t="currentScript"in document?document.currentScript:function(){for(var t=document.getElementsByTagName("script"),e=t.length;e--;)if(t[e].getAttribute("cf-hash"))return t[e]}();if(t&&t.previousSibling){var e,r,n,i,c=t.previousSibling,a=c.getAttribute("data-cfemail");if(a){for(e="",r=parseInt(a.substr(0,2),16),n=2;a.length-n;n+=2)i=parseInt(a.substr(n,2),16)^r,e+=String.fromCharCode(i);e=document.createTextNode(e),c.parentNode.replaceChild(e,c)}}}catch(u){}}();/* ]]> */
/* <![CDATA[ */!function(){try{var t="currentScript"in document?document.currentScript:function(){for(var t=document.getElementsByTagName("script"),e=t.length;e--;)if(t[e].getAttribute("cf-hash"))return t[e]}();if(t&&t.previousSibling){var e,r,n,i,c=t.previousSibling,a=c.getAttribute("data-cfemail");if(a){for(e="",r=parseInt(a.substr(0,2),16),n=2;a.length-n;n+=2)i=parseInt(a.substr(n,2),16)^r,e+=String.fromCharCode(i);e=document.createTextNode(e),c.parentNode.replaceChild(e,c)}}}catch(u){}}();/* ]]> */Prof. Johan Bauwelinck:                                   This email address is being protected from spambots. You need JavaScript enabled to view it.
document.getElementById('cloak4be6e4a7c4643c5750938d74e8924af1').innerHTML = '';
var prefix = 'ma' + 'il' + 'to';
var path = 'hr' + 'ef' + '=';
var addy4be6e4a7c4643c5750938d74e8924af1 = 'johan.bauwelinck' + '@';
addy4be6e4a7c4643c5750938d74e8924af1 = addy4be6e4a7c4643c5750938d74e8924af1 + 'intec' + '.' + 'ugent' + '.' + 'be';
var addy_text4be6e4a7c4643c5750938d74e8924af1 = 'johan.bauwelinck' + '@' + 'intec' + '.' + 'ugent' + '.' + 'be';document.getElementById('cloak4be6e4a7c4643c5750938d74e8924af1').innerHTML += '<a ' + path + '\'' + prefix + ':' + addy4be6e4a7c4643c5750938d74e8924af1 + '\'>'+addy_text4be6e4a7c4643c5750938d74e8924af1+'<\/a>';

/* <![CDATA[ */!function(){try{var t="currentScript"in document?document.currentScript:function(){for(var t=document.getElementsByTagName("script"),e=t.length;e--;)if(t[e].getAttribute("cf-hash"))return t[e]}();if(t&&t.previousSibling){var e,r,n,i,c=t.previousSibling,a=c.getAttribute("data-cfemail");if(a){for(e="",r=parseInt(a.substr(0,2),16),n=2;a.length-n;n+=2)i=parseInt(a.substr(n,2),16)^r,e+=String.fromCharCode(i);e=document.createTextNode(e),c.parentNode.replaceChild(e,c)}}}catch(u){}}();/* ]]> */
/* <![CDATA[ */!function(){try{var t="currentScript"in document?document.currentScript:function(){for(var t=document.getElementsByTagName("script"),e=t.length;e--;)if(t[e].getAttribute("cf-hash"))return t[e]}();if(t&&t.previousSibling){var e,r,n,i,c=t.previousSibling,a=c.getAttribute("data-cfemail");if(a){for(e="",r=parseInt(a.substr(0,2),16),n=2;a.length-n;n+=2)i=parseInt(a.substr(n,2),16)^r,e+=String.fromCharCode(i);e=document.createTextNode(e),c.parentNode.replaceChild(e,c)}}}catch(u){}}();/* ]]> */Permission is hereby granted, free of charge, to any person obtaining a copy of this software and associated documentation files (the "Software"), to deal in the Software for non-commercial educational and research use, including without limitation the rights to use, copy, modify, merge, publish, distribute and/or sublicense copiesof the Software, and to permit persons to whom the Software is furnished to do so,subject to the following conditions:1. The above copyright notice and this permission notice shall be included in all copies of the Software.2. Permission is restricted to non-commercial educational and research use: the use of the Software is allowed for teaching purposes and academic research. Usage by non-academic parties is allowed in a strict research environment only. The use of the results of the research for commercial purposes or inclusion in commercial activities requires the permission of Ghent University. 3. Until 31 December 2015 all usage is restricted to the Software code in compiled form. Until that date, it is not permitted to disassemble, decompile or otherwise reverse engineer the Software and all non-compiled Software code needs to be treated as strictly confidential. This clause expires as of the mentioned date.4. THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.3rd parties--------------------------------------------------------------------------------------This software uses Numpy.    Numpy code is covered by following notice:        Copyright © 2005-2013, NumPy Developers.    All rights reserved.        Redistribution and use in source and binary forms, with or without modification,     are permitted provided that the following conditions are met:            Redistributions of source code must retain the above copyright notice, this         list of conditions and the following disclaimer. Redistributions in binary         form must reproduce the above copyright notice, this list of conditions and         the following disclaimer in the documentation and/or other materials provided         with the distribution. Neither the name of the NumPy Developers nor the names         of any contributors may be used to endorse or promote products derived from         this software without specific prior written permission.        THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS “AS IS” AND     ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED     WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED.     IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT,    INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED    TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR    BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT,    STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF    THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.This software uses libpsf    libpsf code is covered by following notice:    libpsf is available at https://github.com/henjo/libpsf/blob/master    GNU LESSER GENERAL PUBLIC LICENSE    Version 3, 29 June 2007    Copyright (C) 2007 Free Software Foundation, Inc. <http://fsf.org/>    Everyone is permitted to copy and distribute verbatim copies    of this license document, but changing it is not allowed.    This version of the GNU Lesser General Public License incorporates    the terms and conditions of version 3 of the GNU General Public    License, supplemented by the additional permissions listed below.    0. Additional Definitions.    As used herein, "this License" refers to version 3 of the GNU Lesser    General Public License, and the "GNU GPL" refers to version 3 of the GNU    General Public License.    "The Library" refers to a covered work governed by this License,    other than an Application or a Combined Work as defined below.    An "Application" is any work that makes use of an interface provided    by the Library, but which is not otherwise based on the Library.    Defining a subclass of a class defined by the Library is deemed a mode    of using an interface provided by the Library.    A "Combined Work" is a work produced by combining or linking an    Application with the Library. The particular version of the Library    with which the Combined Work was made is also called the "Linked    Version".    The "Minimal Corresponding Source" for a Combined Work means the    Corresponding Source for the Combined Work, excluding any source code    for portions of the Combined Work that, considered in isolation, are    based on the Application, and not on the Linked Version.    The "Corresponding Application Code" for a Combined Work means the    object code and/or source code for the Application, including any data    and utility programs needed for reproducing the Combined Work from the    Application, but excluding the System Libraries of the Combined Work.    1. Exception to Section 3 of the GNU GPL.    You may convey a covered work under sections 3 and 4 of this License    without being bound by section 3 of the GNU GPL.    2. Conveying Modified Versions.    If you modify a copy of the Library, and, in your modifications, a    facility refers to a function or data to be supplied by an Application    that uses the facility (other than as an argument passed when the    facility is invoked), then you may convey a copy of the modified    version:    a) under this License, provided that you make a good faith effort to    ensure that, in the event an Application does not supply the    function or data, the facility still operates, and performs    whatever part of its purpose remains meaningful, or    b) under the GNU GPL, with none of the additional permissions of    this License applicable to that copy.    3. Object Code Incorporating Material from Library Header Files.    The object code form of an Application may incorporate material from    a header file that is part of the Library. You may convey such object    code under terms of your choice, provided that, if the incorporated    material is not limited to numerical parameters, data structure    layouts and accessors, or small macros, inline functions and templates    (ten or fewer lines in length), you do both of the following:    a) Give prominent notice with each copy of the object code that the    Library is used in it and that the Library and its use are    covered by this License.    b) Accompany the object code with a copy of the GNU GPL and this license    document.    4. Combined Works.    You may convey a Combined Work under terms of your choice that,    taken together, effectively do not restrict modification of the    portions of the Library contained in the Combined Work and reverse    engineering for debugging such modifications, if you also do each of    the following:    a) Give prominent notice with each copy of the Combined Work that    the Library is used in it and that the Library and its use are    covered by this License.    b) Accompany the Combined Work with a copy of the GNU GPL and this license    document.    c) For a Combined Work that displays copyright notices during    execution, include the copyright notice for the Library among    these notices, as well as a reference directing the user to the    copies of the GNU GPL and this license document.    d) Do one of the following:    0) Convey the Minimal Corresponding Source under the terms of this    License, and the Corresponding Application Code in a form    suitable for, and under terms that permit, the user to    recombine or relink the Application with a modified version of    the Linked Version to produce a modified Combined Work, in the    manner specified by section 6 of the GNU GPL for conveying    Corresponding Source.    1) Use a suitable shared library mechanism for linking with the    Library. A suitable mechanism is one that (a) uses at run time    a copy of the Library already present on the user's computer    system, and (b) will operate properly with a modified version    of the Library that is interface-compatible with the Linked    Version.    e) Provide Installation Information, but only if you would otherwise    be required to provide such information under section 6 of the    GNU GPL, and only to the extent that such information is    necessary to install and execute a modified version of the    Combined Work produced by recombining or relinking the    Application with a modified version of the Linked Version. (If    you use option 4d0, the Installation Information must accompany    the Minimal Corresponding Source and Corresponding Application    Code. If you use option 4d1, you must provide the Installation    Information in the manner specified by section 6 of the GNU GPL    for conveying Corresponding Source.)    5. Combined Libraries.    You may place library facilities that are a work based on the    Library side by side in a single library together with other library    facilities that are not Applications and are not covered by this    License, and convey such a combined library under terms of your    choice, if you do both of the following:    a) Accompany the combined library with a copy of the same work based    on the Library, uncombined with any other library facilities,    conveyed under the terms of this License.    b) Give prominent notice with the combined library that part of it    is a work based on the Library, and explaining where to find the    accompanying uncombined form of the same work.    6. Revised Versions of the GNU Lesser General Public License.    The Free Software Foundation may publish revised and/or new versions    of the GNU Lesser General Public License from time to time. Such new    versions will be similar in spirit to the present version, but may    differ in detail to address new problems or concerns.    Each version is given a distinguishing version number. If the    Library as you received it specifies that a certain numbered version    of the GNU Lesser General Public License "or any later version"    applies to it, you have the option of following the terms and    conditions either of that published version or of any later version    published by the Free Software Foundation. If the Library as you    received it does not specify a version number of the GNU Lesser    General Public License, you may choose any version of the GNU Lesser    General Public License ever published by the Free Software Foundation.    If the Library as you received it specifies that a proxy can decide    whether future versions of the GNU Lesser General Public License shall    apply, that proxy's public statement of acceptance of any version is    permanent authorization for you to choose that version for the    Library.This software uses logging.    logging code is covered by following notice:    Copyright 2001-2010 by Vinay Sajip. All Rights Reserved.    Permission to use, copy, modify, and distribute this software and its    documentation for any purpose and without fee is hereby granted,    provided that the above copyright notice appear in all copies and that    both that copyright notice and this permission notice appear in    supporting documentation, and that the name of Vinay Sajip    not be used in advertising or publicity pertaining to distribution    of the software without specific, written prior permission.    VINAY SAJIP DISCLAIMS ALL WARRANTIES WITH REGARD TO THIS SOFTWARE, INCLUDING    ALL IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL    VINAY SAJIP BE LIABLE FOR ANY SPECIAL, INDIRECT OR CONSEQUENTIAL DAMAGES OR    ANY DAMAGES WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER IN    AN ACTION OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT OF OR    IN CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE.This software uses lapack.    lapack code is covered by following notice:    Copyright (c) 1992-2013 The University of Tennessee and The University                            of Tennessee Research Foundation.  All rights                            reserved.    Copyright (c) 2000-2013 The University of California Berkeley. All                            rights reserved.    Copyright (c) 2006-2013 The University of Colorado Denver.  All rights                            reserved.    $COPYRIGHT$    Additional copyrights may follow    $HEADER$    Redistribution and use in source and binary forms, with or without    modification, are permitted provided that the following conditions are    met:    - Redistributions of source code must retain the above copyright      notice, this list of conditions and the following disclaimer.    - Redistributions in binary form must reproduce the above copyright      notice, this list of conditions and the following disclaimer listed      in this license in the documentation and/or other materials      provided with the distribution.    - Neither the name of the copyright holders nor the names of its      contributors may be used to endorse or promote products derived from      this software without specific prior written permission.    The copyright holders provide no reassurances that the source code    provided does not infringe any patent, copyright, or any other    intellectual property rights of third parties.  The copyright holders    disclaim any liability to any recipient for claims brought against    recipient by any third party for infringement of that parties    intellectual property rights.    THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS    "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT    LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR    A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT    OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,    SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT    LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,    DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY    THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT    (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE    OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.


text:
## Tuesday, April 3, 2018

### Geometry Lesson: find point closest to set of lines

In [1] a simple optimization problem is posted:

Find a single point $$q$$ in 3d space that is closest to a number of given lines. Each line $$L_j$$ is defined by two points $$p_{j,a}$$ and $$p_{j,b}$$.

This looks like a problem for which specialized algorithms have been developed. Let's just ignore that and see if we can use standard mathematical programming models to tackle this. My geometry is a bit rusty, but the necessary formulas can be found in [2]. To recap, the squared distance $$d^2$$ between a point $$q$$ and a single line through $$p_a$$ and $$p_b$$ is given by:$d^2=\frac{|p_a-q|^2 |p_b-p_a|^2 - \left[(p_a-q)\cdot (p_b-p_a) \right]^2}{|p_b-p_a|^2}$ where $$\cdot$$ indicates the dot product.

Actually just finding the shortest distance between a given line and a given point can be interpreted as an optimization problem:

 Shortest distance between a line and a point

We have multiple lines and the position of the point is not given. An optimization model to find the best place for our point $$q$$ can be formulated as:
$\min_q\>\sum_j \frac{|p_{j,a}-q|^2 |p_{j,b}-p_{j,a}|^2 - \left[(p_{j,a}-q)\cdot (p_{j,b}-p_{j,a}) \right]^2}{|p_{j,b}-p_{j,a}|^2}$ After simplifying some constants we have: $\min_q\>\sum_j \frac{|\alpha_j-q|^2 |\beta_j|^2 - \left[(\alpha_j-q)\cdot \beta_j \right]^2}{|\beta_j|^2}$ This thing is convex, so it is somewhat easy to solve as a QP (Quadratic Programming) problem.

 2D example: Minimize sum of squared distances

Actually I cheated a bit: I minimized the sum of the squared distances. When really minimizing the sum of the distances we need to minimize: $\min_q\>\sum_j \sqrt{\frac{|\alpha_j-q|^2 |\beta_j|^2 - \left[(\alpha_j-q)\cdot \beta_j \right]^2}{|\beta_j|^2}}$ This can be solved as an NLP (Nonlinear Programming) model. Of course the objective with the quadratic distances will put more weight on the larger distances.

How do results compare?  For a 3D problem with 10 random lines I see:

----     54 PARAMETER results

x           y           z         obj

squared dist       0.015      -0.069      -0.282       4.087
dist               0.050      -0.142      -0.413       5.634

Here the $$x,y,z$$ values are the coordinates of $$q$$. The column marked obj indicates the objective function value. In our 2D example we can see the differences more clearly:

 Minimization of sum of distances

The differences are a little bit more pronounced than I would have predicted.

#### Minimax Model

A different objective can be formed by minimizing the maximum distance:\begin{align} \min\> & z\\ &z \ge d_i\end{align} We get the same solution if we minimize the maximum of the squared distance: \begin{align} \min\> & z\\ &z \ge d^2_i\end{align} This means we have a convex quadratic model. This model puts all the emphasis on the largest distance and thus will shift our location to the right:

 Minimize maximum of distances

A 3d visualization would be interesting.

#### SOCP Model

In the comments it is suggested to use a Second Order Cone Programming (SOCP) model. This would allow us to solve the minimum sum of distance problem using solvers like Cplex, Gurobi, Mosek and Xpress. There is no need to resort to a general purpose NLP solver. In [3] I have some results.


text:
## Delayed Connectivity in Random Graphs

### Aside

I presented a poster at the Oxford SIAM Student Chapter Conference on Friday. It was nice to win the prize for best poster, but mainly I enjoyed putting it together. For once it meant ignoring the technical details and anything requiring displayed formulae, and focusing only on aspects that could be conveyed with bullet points and images. Anyway, this is what I came up with. The real thing is sitting safely in a tube in my office, ready for the next time it is needed in a hurry!

Delayed Connectivity Poster

## DBEs and stationary distributions

### Aside

The most recent Applied Probability assignment sheet featured various aspects of Detailed Balance Equations for continuous-time Markov chains. We discussed the advantages and disadvantages of using DBEs rather than solving for an equilibrium distribution directly. The equations used in this second case are often called Full Balance Equations.

Briefly, the advantages of DBEs are that they are easy to solve. After all, each one contains only two components of the equilibrium distribution, so generally you can solve one-at-a-time. The disadvantage is that an equilibrium distribution might not satisfy the DBEs. The deductive structure is:

$\text{Solves DBEs}\quad \stackrel{\Rightarrow}{\not\Leftarrow}\quad\text{Equilibrium distribution}$

Usually, the chain will be irreducible, so the equilibrium distribution is unique. This means that if we can solve the DBEs, the result is the unique equilibrium distribution.

The DBEs are soluble only if the situation is reversible. This is probably the best definition to use in practice, but informally we can say that this means that the behaviour looks qualitatively the same if we reverse time. For example, as in Q1:

$Q=\begin{pmatrix}-1 &1&0\\ 0& -1&1\\1&0&-1\end{pmatrix},$

gives the Q-matrix which equilibrium distribution $(\frac13,\frac13,\frac13)$, which does not satisfy DBEs. The chain is not reversible because sample paths always go clockwise, so if we reversed time they would go anti-clockwise (or vice-versa depending on how you’ve drawn the diagram).

What I wanted to say in the class, and made a mess of explaining was this, about why it was inappropriate to use DBEs to find stationary distributions in Q3d):

Reversibility is not just a function of the chain. It is a function of the chain AND the initial distribution. This is only in practice a concern when the chain is reducible, but in this case it really can lead you astray. Let’s consider an example, like

$Q=\begin{pmatrix}-3&2&0&0&1&0\\ 0&-4&3&1&0&0\\ 0&1&-4&3&0&0\\ 0&3&1&-4&0&0\\ 0&0&0&0&-5&5\\ 0&0&0&0&5&-5\end{pmatrix}.$

Then by solving as in the problem sheet, the invariant distributions are given by:

$\lambda(0,\frac13,\frac13,\frac13,0,0)+\mu(0,0,0,0,\frac12\frac12),\quad \lambda+\mu=1.$

If you attempted to solve the DBEs, you would succeed, but the only solution would be

$(0,0,0,0,\frac12,\frac12).$

The explanation is fairly simple in the end. Reversibility is a class property, and only one of the communicating classes, $\{5,6\}$ in this example admits a reversible initial distribution, so to solve the DBEs we must assign zero mass on the other class.

Anyway, I hope that clears up any residual confusion from the class.

## An obvious remark

### Aside

An obvious remark:

If a sequence of independent random variables $X_n$ converge almost surely to some limit $X$, this limit must be a constant (almost surely).

I’ve been thinking about the Central Limit Theorem about related Large Deviations results this afternoon, and wasted almost an hour worrying about situations which were effectively well-disguised special cases of the above.

Why is it true? Well, suppose each $X_n$ is $\mathcal{F}_n$-measurable. But by independence, we might as well take $\mathcal{F}_n=\sigma(X_n)$. Then the limit variable $X$ is independent of $\mathcal{F}_n$ for all $n$, and thus independent of $\cup F_n=\mathcal{F}\supset \sigma(X)$. If $X$ is independent of itself, it must be almost surely constant.