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# GAM with categorical variables - interpretation

I want to use GAM to analyze my experimental data. In my experiment, participants basically play a game for 40 experimental years. In total I have 6 different conditions and I have a between-subject design: one participant only experiences one condition.

I want to analyze a variable which is the output of participants' annual decisions. What I want to show is that:

1. Year has an impact on this output variable for all the conditions.
2. The path of this output variable over 40 experimental years is significantly different across 6 conditions.

To this end, I run the following model and get this result:

Abbr is my categorical variable which has 6 levels. My question is mostly on the interpretation. The "Approximate significance of smooth terms" part of the table tells me that Year has a significant effect on pr in all conditions. Is it correct?

What does the "Parametric coefficients" part tell me? How can I compare these 6 conditions and tell that the paths are significantly different?

And this is the plot of GAM:

Thank you for the great reply! It is much more clear now in terms of smooths.

What I try to do is to test that the smooths are significantly different from each other for my 6 categories. To this end, I followed your blog post and end up with ordered factors with the following model and the results, where OC is my ordered categorical variable:

Now, I can say that there is a significant difference between the smooths of F-G1P1 and F-G5P1. And when I plot, I get the following: The first plot gives me the smooth for my category F (reference category), while others are the difference smooths. How should I interpret them?

Now, I would like to extend this analysis to have a pairwise comparison between my 6 categories. To do this, I try to follow this post but I didn't succeed. Do all my categories need to have the same number of observations for these comparisons?

In a factor by variable smooth, like other simple smooths, the bases for the smooths are subject to identifiability constraints. If you just naively computed the basis of the required dimension, and given the defaults for s(), you'd get 2 basis functions that are in the null space of the smoothness penalty:

1. a flat, horizontal function, and
2. a linear functions

Both are perfectly smooth and not penalised by the smoothness penalty as a result. The flat function is the same thing as the model intercept. The identifiability issues arises because you could add any value to the estimated coefficient for the intercept (constant) term and subtract the same value from the coefficient for the flat, horizontal basis function, and get the same fit but via a new model. As there are an infinite set of numbers you could add to the intercept you have an infinity of models.

This is not good, so to alleviate the issue an identifiability constraint is used. There are several such constraints but the one that leads to good confidence interval coverage properties is the sum-to-zero constraint. Over the range of the covariate, the smooth is constrained to sum to zero. This means it is centred about zero and this means the flat function is deleted from the basis of the smooth.

Now, in the case of factor by variables, because each smooth is centred about zero, the smooth itself contains no easy way to control for differences between the levels in terms of the mean response; say samples from condition F were on average having larger values of pr than condition G1. We'd want the spline for F to be shifted up by some constant amount relative to G1. That's what the parametric terms are and they come from the + as.factor(Abbr) term in the model formula. The parametric terms represent the deviation of the indicated group from the mean of the reference group (in your case the level not listed, F). If you didn't include this term in the model, then the smooths may become more wiggly as they try to account for the mean shifts of the groups, which is not something you want.

The other main type of smooth you might use for this kind of model is the random factor smooth basis bs = "fs". This basis/smooth includes intercepts for each level of the grouping factor and as such doesn't need the parametric terms.

The approximate significance of the smooths actually represents a test that the indicated smooth is actually a flat, zero, function. Or put another way, it is the smooth equivalent of a t or Wald Z test of the null hypothesis that a coefficient in a linear model or GLM is equal to zero (i.e. has no effect). There is strong evidence against the null for each of your smooths, which is reflected in the strong non-linearity of the estimated smooths and that the confidence intervals for the smooths do not include 0 for most of the range of Year.

• Thank you for the great reply! It is much more clear now in terms of smooths. – bgencer Jun 4 '18 at 13:00


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# Show that $v_1, v_2, \cdots , v_r$ span $R^n$ if and only if $v_1+\alpha *v_2, v_2, \cdots, v_r$ span $R^n$

In our textbook I've seen this claim:

$v_1, v_2, \cdots , v_r$ span $R^n$ if and only if $v_1+\alpha *v_2, v_2, \cdots, v_r$ span $R^n$ for some $\alpha \in \mathbb{R}$

Now I've tried to prove it to myself and I'm having some difficulty with the left-to-right direction.

For the first direction I assumed: $v_1+\alpha *v_2, v_2, \cdots, v_r$ span $R^n$ so every vector in $R^n$ can be represented as a linear combination of those vectors, meaning a general vector $w$ in $R^n$ can be written as:

$\alpha_1 *(v_1 + \alpha*v_2 ) + \alpha_2 *v_2 + \cdots + \alpha_r*v_r = w$

$\Rightarrow \alpha_1 * v_1 + (\alpha_1*\alpha + \alpha_2)*v_2 + \cdots + \alpha_r*v_r = w$

meaning that $v_1, v_2, \cdots , v_r$ also span $R^n$

For the other direction I assumed that $v_1, v_2, \cdots , v_r$ span $R^n$ so for some $w \in R^n$ :

$\alpha_1 * v_1 + \alpha_2 * v_2 +\cdots+\alpha_r*v_r = w$

$\Rightarrow \alpha_1 *v_1 + (a+b)*v_2 +\cdots+\alpha_r*v_r = w$

$\Rightarrow \alpha_1 * v_1 +a*v_2 + b*v_2 +\cdots+\alpha_r*v_r = w$

$\Rightarrow \alpha_1 * (v_1 + \frac{a}{\alpha_1}*v_2) + b*v_2 + \cdots+\alpha_r*v_r = w$

which would prove that $v_1+\alpha *v_2, v_2, \cdots, v_r$ span $R^n$ but I have no guarantee that $\alpha_1\ne0$ or that such a combination where $\alpha_1\ne0$ even exists (as far as I know, maybe that's what I'm missing here)

any guidance would be appreciated!

• The other implication is wrong unless $v_1+\alpha v_2\neq 0$. So you just have to chose one $\alpha$ such that it is true and call $v'_1=v_1+\alpha v_2$. – Tom-Tom Jun 25 '14 at 12:22
• could you elaborate? what do you mean by the other implication (I'm not familiar with the word implication in this context)? If you're referring to the last lines as I wrote they are what I tried to assume but as I said couldn't since I have no guarantee that $\alpha_1\ne0$ – byentropy Jun 25 '14 at 12:27

Clearly $$\langle v_{1} + \alpha v_{2}, v_{2}, \dots , v_{r} \rangle \subseteq \langle v_{1}, v_{2}, \dots , v_{r} \rangle,$$ where $\langle \cdots \rangle$ denotes the linear span.
Conversely $$v_{1} = (v_{1} + \alpha v_{2}) - \alpha v_{2} \in \langle v_{1} + \alpha v_{2}, v_{2}, \dots , v_{r} \rangle,$$ so the other inclusion also holds.
• Thanks, this certainly helped me see I was going at it the other way around, but I'm still wondering could I have also proved it as I tried? by reaching to $\alpha_1 * (v_1+\frac{\alpha}{\alpha_1}v_2)$ could I have known or assured that $\alpha_1\ne0$ as well? – byentropy Jun 25 '14 at 13:02
• @byentropy, following your approach, if you can write an arbitrary $v$ as $c_1 v_1 + c_2 v_2 + \dots$, then you can also write it as $v = c_1 (v_1 + \alpha v_2) + (c_2 - c_1 \alpha) v_2 + \dots$. – Andreas Caranti Jun 25 '14 at 17:58

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# Problems of the possible worlds account of conditionals

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## The sequent calculus G3cp

The sequent calculus G3cp for classical propositional logic closely resembles Gentzen’s original sequent calculus in [32], and was introduced in [102]. For p atomic formula, A and B formulas of the language, the set of formulas of classical propositional logic is generated by the following grammar: p j ? j :A j A ^ B j A _ B j A ! B. To de ne a system of sequent calculus we introduce the notion of sequent, specify its interpretation in the language of the logic and provide the set of initial sequents and inference rules2. De nition 2.2.1. A G3cp sequent is an expression of the form For a treatment of natural deduction, refer to [74]. We shall here treat only sequent calculus. the consequent of the sequent. Both antecedent and consequent can possibly be empty or constituted of just one formula occurrence. A sequent ) is interpreted in the language of classical propositional logic as follows:
^ _ ( ) )int = ! .
The symbol ) represents in the object language the metalinguistic notion of con-sequence relation, describing how some formulas (the assumptions) entail some other formulas (the conclusions). The comma in the antecedent represents conjunction at the meta-level, while the comma in the consequent represents disjunction. Thus, a se-quent can be read as: \from the conjunction of formulas in the antecedent follows the disjunction of formulas in the consequent ».
An empty antecedent is a conjunction of empty formulas (which conventionally stands for the truth >) and an empty consequent is a disjunction of empty formu-las (which conventionally stands for a generic contradiction ?). A sequent with both antecedent and consequent empty stands for a generic contradiction (> ! ?).

### Desirable properties of sequent calculus

Given a well-formed formula we are interested in knowing whether this formula is valid in a certain system of logic L. If we have a sequent calculus S which is sound and complete with respect to L, we can decide the validity of the formula by trying to construct a derivation for it. Thus, a system of sequent calculus can be fruitfully employed to provide a decision procedure for the logic. One of the main interests of a proof theorist is to obtain – where possible – rules which facilitate the de nition of an e cient and automated decision procedure. Thus, it is useful to consider derivations bottom-up, in what is called root- rst proof search. The formula to be checked is placed at the root, and one tries to construct a derivation for it applying the inference rules of the system. There are several desirable require-ments allowing an e cient root- rst proof search. Here follows a non-exhaustive list of properties.
Analyticity. This property – de ned in the previous section – is essential for root- rst proof search: if the calculus is analytic, each formula occurring in a derivation is a subformula of the formulas occurring lower in the derivation branch. Thus, at each step of the derivation no new formulas are introduced, and all formulas can be ultimately traced down to the root of the derivation tree. All the (analytic) logical rules of G3cp are straightforwardly applicable bottom-up: it su ces to \decompose » the main formula of each rule into its active (sub)formulas. Conversely, applying bottom-up the cut rule requires to perform a guess on what formula should be chosen as cut-formula.
Avoidance of backtrack. In root- rst proof search, \backtracking » is the action of going back to a certain sequent and apply a di erent rule to it. In some calculi the order of application of the rules, or the formula to which a certain rule is applied, can determine the derivability of the formula at the root. In such calculi, to check the derivability of a formula we have to check all possible derivation trees – for if we end up with a failed proof search, it might be that we applied the wrong rules, or in the wrong order, to the sequents.
Usually, it is possible to avoid backtracking by means of an attentive de nition of the inference rules. If there is no need to backtrack, construction of just one derivation tree is enough to decide derivability of a sequent. Sequent calculi composed only of invertible rules avoid backtrack. If a rule is invertible, no pieces of information are lost when going from the conclusion to the premiss(es). For this reason, the invertible version of rule R_ (on the left) is preferred over its non-invertible version (on the right, composed of a pair of rules)7. ) ;A;B ) ; A R_0 ) ; B R_00 R_ ) ; A _ B ) ; A _ B ) ; A _ B. Observe that, if we were to apply root- rst rule R_0, we would loose formula B, which could have been the formula allowing to obtain an initial sequent. As explained in [70], invertible inference rules preserve both the validity and the refutability of sequents, allowing to construct only one derivation tree to asses the derivability of the sequent placed at the root. Conversely, non-invertible inference rules preserve only the validity of the sequent and thus possibly lead to a division of the proof search tree into multiple derivation trees, which are all to be tested in order to ascertain the refutability of the endsequent.

READ  SEMANTIC TECHNOLOGY: TERMS AND TOOLS

#### Preferential conditional logic

The preferential conditional logic PCL was rst studied by Burgess in [18] and Halpern and Friedman in [28]. This logic is weaker than Lewis’ systems, and it can be adapted to capture non-monotonic conditionals: as explained in Chapter 1, the non-monotonic logic P introduced by Kraus, Lehman and Magidor corresponds to the at fragment of PCL. De nition 3.1.1. The set of well formed formulas of PCL and its extensions is de ned by means of the following grammar, for p 2 Atm propositional variable and A; B 2 F>: F> ::= p j ? j A ^ B j A _ B j A ! B j A > B.
The conditional operator > can be read as expressing either a non-monotonic con-ditional, a counterfactual or a deontic conditional, depending on the system under con-sideration. When treating logics of Lewis’ family we will add to the language the com-parative plausibility operator, 4, where for A; B 2 F> the well-formed formula A 4 B reads \A is at least as plausible as B ».
The semantics of preferential conditional logics is usually de ned in terms of prefer-ential models, introduced in De nition 1.4.3 of Chapter 1. De nition 3.1.2. Extensions of preferential models are de ned by specifying the fol-lowing conditions [28]:
Normality: For all x 2 W , Wx is non-empty.
Total re exivity: For all x 2 W it holds that x 2 Wx.
Weak centering: For all x 2 W , for all y 2 Wx, it holds that x x y.
Centering: For all x 2 W , for all y 2 Wx, it holds that x x y and if there is w 2 Wx such that for all y 2 Wx, w x y, then w = x.
Local uniformity: For all x 2 W , for all y 2 Wx it holds that Wy = Wx.
Local absoluteness: For all x 2 W , for all y 2 Wx it holds that Wy = Wx and for all w1; w2 2 Wx we have w1 x w2 if and only if w1 y w2. Connectedness: For all x 2 W , for all w1; w2 2 Wx it holds that w1 x w2 or w2 x w1.

Introduction
1 Conditional logics: a gentle introduction
1.1 Conditionals in natural language
1.2 Truth-functional implication
1.3 Possible worlds account of conditionals
1.4 A semantic account
1.5 An axiomatic account
1.6 Conditional logics and modal logics
1.7 Problems of the possible worlds account of conditionals
1.A Appendix: Modal logics
2 Proof methods for modal and conditional logics
2.1 Structural proof theory
2.2 The sequent calculus G3cp
2.3 Desirable properties of sequent calculus
2.4 Sequent calculi for modal logics
2.5 A semantic approach
2.6 A syntactic approach
2.7 To conclude
2.8 State of the art
3 Labelled sequent calculi for PCL and extensions
3.1 Preferential conditional logic
3.2 From preferential models to neighbourhood models (and back)
3.3 A family of labelled sequent calculi
3.4 Structural properties
3.5 Termination
3.6 Semantic completeness
3.7 Nesting
3.8 Absoluteness
3.9 To conclude
3.A Appendix: derivations of the axioms
4 Internal calculi for Lewis’ conditional logics
4.1 Lewis’ family of conditional logics
4.2 Nested sequent calculi for basic systems
4.3 Cut elimination for IV
4.4 An invertible version: Ii Base
4.5 Semantic completeness
4.6 Logic VTU and extensions
4.7 Hypersequent calculi SHi Strong
4.8 Semantic completeness of SHi VTU, SHi VWU and SHi VCU
4.9 Head-hypersequents calculi HHi StrongA
4.10 Semantic completeness of HHi StrongA
4.11 To sum up
5 Relations between proof systems
5.1 A case study
5.2 Sequent calculi G3V and Ii
5.3 From the internal to the labelled sequent calculus
5.4 From the labelled to the internal calculus
5.5 To conclude
6 Conditional epistemic logics
6.1 Multi-agent modal epistemic logic
6.2 Axiomatization and semantics
6.3 Adequacy of the axiomatization
6.4 Sequent calculus G3CDL
6.5 Termination and completeness
6.6 Relating the old and the new
6.7 Other epistemic and doxastic modalities
6.8 To conclude
Conclusions
Bibliography

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Location of Repository

## Measurement of the Absolute Branching Fractions $B \to D\pi$, $D*\pi$, $D**\pi$ with a Missing Mass Method

### Abstract

8 pages, 6 postscript figures, submitted to ICHEP2006 submitted to Phys. Rev. D (Rapid communications)We present branching fraction measurements of charged and neutral B decays to Dpi-, D*pi- and D**pi- with a missing mass method, based on a sample of 231 million Y(4S)-->BBar pairs collected by the BaBar detector at the PEP-II e+e- collider. One of the B mesons is fully reconstructed and the other one decays to a reconstructed charged pion and a companion charmed meson identified by its recoil mass, inferred by kinematics. Here D** refers to the sum of all the non-strange charm meson states with masses in the range 2.2-2.8 Gev/c2

Topics: 13.25.Hw, 12.15.Hh, 11.30.Er, [PHYS.HEXP] Physics [physics]/High Energy Physics - Experiment [hep-ex]
Publisher: American Physical Society
Year: 2006
DOI identifier: 10.1103/PhysRevD.74.111102
OAI identifier: oai:HAL:in2p3-00115178v1
Provided by: Hal-Diderot


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# Hochschild (co)homology of differential operators

I googled the title on the internet, and arrived at the following result

$$HH_k(D)\cong H_{DR}^{2n-k}(M).$$

Here $M$ is a smooth manifold of dimension $n$, and $D$ is the ring of differential operators on $M$. My first question is

(A): is there a known chain map realizing the above isomorphism?

I think the above isomorphism remains true if we replace $D$ by the ring of differential operators on $M$ with coefficients in a vector bundle $E$. But I am not so sure. If this is indeed the case, my second question is

(B): question (A) with coefficients in $E$?

-
If I remember right this was computed in Wodzicki's paper "Cyclic homology of differential operators", but I don't have access right now to know if there is an explicit chain map. The way I think about this for Hochschild cohomology is via deformation quantization for the cotangent bundle, namely the Hochschild cohomology should be (T_poly(T^*(X), [\omega*,) which is Poisson cohomology with a symplectic form. It is then fairly easy to see gives the same thing as cohomology by using the Poisson structure to turn differential forms into polyvector fields. Maybe that can help construct your map? –  Daniel Pomerleano Mar 11 '12 at 6:25
Hi Daniel, I have the paper with me. The argument there was indeed along your comments. But this is exactly where the problem is: to reduce to the cotangent bundle, one uses the spectral sequence associated to the order filtration on D, which does not hint on a chain level map. –  tu_junwu Mar 11 '12 at 8:17
Do you care whether the chain map goes (Hochschild -> de Rham) or (de Rham -> Hochschild)? Or would it be useful to have a third complex with quasi-isomorphisms to (or from) both? The homology isomorphism is natural with respect to open embeddings (in particular diffeomorphisms), but a nontrivial chain map cannot be natural, at least in the direction (de Rham -> Hochschild). You can see this by letting $n=1$, $M=\mathbb R$, and considering the subcomplexes of chains invariant under affine motions of the line. –  Tom Goodwillie Mar 11 '12 at 13:08
Actually I was even expecting maps in both directions, but this is a good example to know. –  tu_junwu Mar 11 '12 at 18:32


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# Electric bell symbol

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Remove the motor connector from the end bell outlet. Set meter to ohms, and place …
What can you do with simple electric bell?
How to make electric bell model kit?
Step 1: Fix the Bell to the Card board with the help of long bolt …
How does an electromagnet work in an electric bell?
They are found in electric motors and loudspeakers. Electric bells like the ones used in …
How does an electric bell work for class 7?
The electric circuit is completed by installing a push switch which you can press to …
How to make electric bell easy to cook?
How to Roast Bell Peppers – Easy methods for cooking and charring bell peppers for …
How is the circuit of an electric bell completed?
The electric circuit is completed by installing a push switch which you can press to …
Describe how an electric bell works and provide a diagram?
Describe the construction and working of an electric bell with the help of a diagram. …
What symbol is used for electric diapole?
An electric dipole is denoted by the symbol $$\vec{p}$$. We know that electric dipole is …
How to play jingle bell rock on electric guitar?
Jingle Bell Rock | How to play it on a guitar! - YouTube.
What is the symbol for emerson electric company in the nyse?
The symbol for Emerson Electric Company in the NYSE is: EMR.
What is the symbol for general electric company in the nyse?
The symbol for General Electric Company in the NYSE is: GE.
How to make an electric bell working model?
Step 1: Fix the Bell to the Card board with the help of long bolt …
What is the symbol for general electric capital corporation in the nyse?
The symbol for General Electric Capital Corporation in the NYSE is: GEH.


text:
# WebDeploy Gets Even More Awesome – Profile Specific Transforms

I love WebDeploy – I have ever since I read Scott Hanselman’s post “Web Deploy Made Awesome: If You’re Using XCopy, You’re Doing It Wrong”. Whenever I’m helping teams that build web applications improve their ALM processes, invariable I end up moving them onto Web Deploy. Not only is it an easier and cleaner way to deploy, but you get the bonus of being able to manage configuration files (Web.config) in your project.

## Config as Code

Maturing in ALM means that you need to head towards continuous deployment. You need to be able to deploy your application with a single click of a button. However, one challenge with this is managing configurations. How do you manage Web.config files in dev, UAT and Production environments? Do you find yourself copying config files out the way before you deploy? That’s BAD. You should be managing your configs as if they were code. They need to be source controlled.

Fair enough, I hear you say. So you’ll just copy all your config files from all your servers into a folder and manage them from there. Better – but still lots of pain. A far better approach is to use config transforms.

Config transforms came into web applications in VS 2010. With the latest release of VS 2013, not only are they also available for web sites (NOTE: please don’t use websites – always use web applications!) but you can new preview your transforms from VS and there’s now support for profile-specific transforms.

Let’s have a look at a config transform in a newly created MVC web application. You can see that the Web.config file expands to show 2 other files – one per project configuration:

If you add project configurations, then you can right-click the Web.config and select “Add config Transforms” and VS will create a new transform file for you.

Let’s have a look at the Web.Release.config (I’ve removed the comments that are auto-generated):

<configuration xmlns:xdt="http://schemas.microsoft.com/XML-Document-Transform">
<system.web>
<compilation xdt:transform="RemoveAttributes(debug)">
</compilation></system.web>
</configuration>

You can see that in the  tag there’s an xdt:Transform to remove the debug attribute. When applied, the transform uses the structure of the transform file to find the correct element and perform the necessary transforms – whether it’s an insert, a remove or some other transform. You can read about the syntax for transforms here. Note that when you debug out of VS, your application will use the Web.config file irrespective of if you’re running in Debug or Release – the transforms only happen when you publish or package your web app.

This is all existing “2012” stuff. What’s new in the latest release?

## Preview and Profile Specific Transforms

You can now preview your transform by right-clicking on the transform file (Web.Release.config, for example) and selecting “Preview Transform”. This immediately shows a diff – the original Web.config on the left and the transformed config on the right:

Now you can debug your transforms!

So let’s imagine you have a UAT environment. You want to publish your site, so you create a new project configuration called UAT. You then copy the release transforms and put in your UAT connection strings and so on. After doing some testing in UAT, you realize that you actually need to debug, so you’ll have to update your Web.UAT.config file again, or create a UAT-DEBUG project configuration. Soon you’ll get lots of project configurations, and that’s just a mess.

However, you can now create a profile-specific transform on top of the project configuration transforms! Let’s create a publish profile. I’ll right-click the web project and select “Publish”. I’ll create a new profile called “UAT-Debug” and give it whatever settings I need to. On the “Configuration” page, I’ll change the configuration from Release to Debug.

Then I’ll click on “Close” to save the profile without publishing. That will create a pubxml file for me. I’ll repeat the process and create a publish profile called “UAT-Release”. Looking under the Properties of my project I’ll see the pubxml files:

Now I can right-click a pubxml and select “Add Config Transform” – which creates a new transform for me that’s tied to this publish profile.

I’ll create one for each profile. You’ll see that I now have 4 transforms (but still only 2 project configurations – hooray!)

Let’s insert an attribute in both of the new config files:

<appsettings>

I’ve also removed the debug attribute from the compilation tag on the UAT-Release config and removed that transform from the debug one:

Now when I right-click Web.UAT-Release.config and select “Preview Transform” I can see the diff. Note that the right-hand file tells me that it has actually applied 2 transforms: first the Release transform (since the profile specifies Release for the project configuration) and secondly the Web.UAT-Release.config transforms themselves.

Voila! I can now maintain 2 project configurations (Debug and Release) and have a publish profile and transform config per project config and environment. Awesome!

If you’re using Release Management, don’t forget to check out my post about how to use config transforms for parameterizing releases!

Happy transforming!


text:
Infoscience

Report

# Evaluating the Complexity of Databases for Person Identification and Verification

For the development and evaluation of methods for person identification, verification, and other tasks, databases play an important role. Despite this fact, there exists no measure whether a given database is sufficient to train and/or to test a given algorithm. This paper proposes a method to grade'' the complexity of a database, respectively to validate whether a database is appropriate for the simulation of a given application. Experiments support the argumentation that the complexity of a data set is not equivalent to its size. The first nearest neighbor'' method applied to image vectors is shown to perform reasonably well for person identification, respectively the mean square distance for person verification. This suggests to use them as a minimal performance measure for other algorithms.

Keywords: vision

#### Reference

• EPFL-REPORT-82491

Record created on 2006-03-10, modified on 2017-05-10


text:
Formats
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### Abstract

We explore some similarities between the theory of D-modules and that of quasi-coherent sheaves of categories. The original motivation is to better understand several results on the literature that relates vanishing cycles with some invariants of the category of matrix factorizations like its periodic cyclic homology or its etale cohomology. We propose the following explanation: given a function f:X---> A^1, the category of matrix factorizations MF(X,f) can be thought as a higher categorical version of vanishing cycles for the sheaf of categories corresponding to Perf(X). Here, the 2-periodic structure on matrix factorizations corresponds to the monodromy of vanishing cycles. A second goal is to find the general phenomena behind the work of A. Preygel that uses~derived algebraic geometry to construct MF(X,f) from a cohomological operation of degree 2 on Coh(X_0). We interpret this as the microlocalization of Perf(X) over T^*_0A^1 and extend it to arbitrary quasi-coherent sheaves of categories over smooth schemes. To realize the above we need the theory of quasi-coherent sheaves of categories developed by D.Gaitsgory, J.Lurie, B.Toen and G.Vessozzi. The basic formalism is quite recent and contains pushforward and pullback. We slightly modify it to get an extraordinary pullback for complete intersection morphisms. We also introduce the matrix factorizations functor. The main result of this thesis is a comparison between the usual and the extraordinary pullback. In rough terms, via Koszul duality, the extraordinary pullback localize over a conormal bundle and the usual pullback correspond to the part supported on the zero section. We study the case of the closed immersion of a point in a smooth scheme. This defines for every quasi-coherent sheaf of categories its punctual singular support, analogous to the singular support of a D-module. In the end we give a deformation theory interpretation. This is part of joint work with G. Stefanich. In future work we will define and study the global singular support of a quasi-coherent sheaf of categories. This is a closed conical subset of the cotangent bundle that measures the directions on which the sheaf is proper and smooth.

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text:
# Why the optical gap is not identical to the charge gap?

The optical gap is the photon energy required to create an exciton (in a solar cell for example). The charge gap (aka electrical gap) is the energy (voltage) required to create a photon (in an LED for example). Why are these two gaps not identical?

Ref:

Undoped (neutral) conjugated polymers are semiconductors, with optical gaps of ~ 2-3 eV and charge (or band) gaps typically ~ 0.5-1.0 eV higher in energy, reflecting the large exciton binding energies in polymers. (source: Barford, 2013)

(source)

• The usual definition of "optical band gap" (at least in the field of photonic crystals which is where I have heard it used most often) is not what you described in your first paragraph, and has nothing to do with photon absorption, electrons, holes, or excitons. – The Photon Aug 6 '15 at 4:47
• Given that, could you share how "optical band gap" or "optical gap" is defined in the text you cited? – The Photon Aug 6 '15 at 4:49
• The reason is given clearly in your reference: the bound excition state is 0.5-1.0 eV below the conduction band edge. – Jon Custer Aug 6 '15 at 16:53
• @JonCuster can you explain that? i.e. how exciton state is related etc. – Sparkler Aug 6 '15 at 17:53
• The existence of exictons makes an asymmetry between absorption (you don't absorb into an exciton state) and emission (you can emit from the excition state). So, no, the two are distinct. – Jon Custer Aug 6 '15 at 19:41

The difference between the fundamental gap (following IUPAC definitions - and your diagram ) (this is what you refer to as your electronic gap in your question) exists because the optical gap corresponds to the energy of the lowest electronic transition accessible via absorption of a single photon. The optical gap is generally substantially lower than the fundamental gap.

The reason for this is that that in the excited state the electron and the hole remain electrostatically bound to one another. This means the magnitude difference between the fundamental gap and the optical gap is related to the binding energy.

The fundamental gap corresponds to the different energy caused due to the sharp bound between eigenvalues in the Schrodinger operator.

So in the diagram you have provided, the fundamental gap is labelled $E_{fund}$, the electron-hole pair binding energy $E_{B}$ is given by $E_{fund}-E_{opt}$.

## Non Technical Summary

The optical gap only lists an electron over the band gap and you must account for the electrostatic effects between your hole and the electron.

The fundamental/electronic gap is the proper quantum energy difference between the energy levels..

The optical or vertical bandgap is the minimum separation between the valence and the conduction band at constant k-value, or electron momentum. The charge bandgap is the separation of the conduction and valence states where these may have different k-values. The optical bandgap is always larger than the charge band gap. Exciton states have an energy somewhat smaller than the optical band gap. The difference is the binding energy, a fraction of the optical band gap.


text:
Integration of probability density

Let g be a map: g: $[0,1] \rightarrow \mathbb R$ and U a random variable uniformly distributed on [0,1]. Then my lecture notes say that the following holds:

E[g(U)] = $\int_{-\infty}^{\infty} g(x) f_{U}(x)dx = \int_{0}^{1}g(x)dx$

where "E" stands for the expected value. What I don't understand is the part

$\int_{-\infty}^{\infty} g(x) f_{U}(x)dx = \int_{0}^{1}g(x)dx$

though. I understand the changes of the boundaries of the integral, but not why $f_{U}(x)$ "disappears".

-
Since the uniform distribution density function on $[0,1]$ is $f_U(x)=1,x\in [0,1]$ – user60610 Feb 15 '13 at 23:23
..of course, thanks! – user62487 Feb 15 '13 at 23:35

Recall that $$f_{U}(x):= 1_{[0,1]}(x) = \begin{cases} {} 1, & \text{ if } x \in [0,1] \\ 0 , &\text{ else} \end{cases}$$
$$\int_{-\infty}^{\infty} g(x) f_{U}(x)dx = \int_{0}^{1}g(x) \cdot 1 \, dx + \int_{- \infty}^0 g(x) \cdot 0 \, dx + \int_1^{\infty} g(x) \cdot 0 \, dx = \int_{0}^{1}g(x)dx$$
shouldn't $\int_{0}^{\infty}g(x)*0dx$ be $\int_{1}^{\infty}g(x)*0dx$ instead? – user62487 Feb 15 '13 at 23:40


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Shortcuts using aliases

There are some steps in there that we should just be doing all the time. What about making a single command alias that will cycle through all these commands just so we know things are always in good shape? Yup, we can do that.

In Bash

Using Git and Bash is like using a zipper and pants. They just go together. Creating a Bash alias is extremely simple. From your Terminal, enter

\$ open ~/.bash_profile

This will open a hidden file in a default text editor. If you have a shortcut command for opening in an editor like Sublime Text, use that to open the file. In the file add the following:

alias refresh="git checkout master && dskil && git pull && git fetch -p"

The alias dskil is useful for removing annoying .DS_Store files. You should have a .gitignore file that keeps these out of version control, but I like to keep a clean house too. To make that work, add the following:

alias dskil="find . -name '*.DS_Store' -type f -delete"

With this in your .bash_profile, you simply need to enter refresh in the command line and POW!

In Powershell

If you are on Windows and using Powershell, you can use the same aliases, but the set up is different. The article Windows PowerShell Aliases is a good tutorial of the process.


text:
XMM-Newton Science Analysis System

hello (hello-1.17.2) [xmmsas_20070308_1802-6.6.0]

Meta Index / Home Page / Macro reference / SAS Latex Environments

A SAS specific LaTeX Environment
synopsis
\begin{taskparameters}

description
Parameters, whether mandatory or optional, are described here. Please use the macros supplied, that guarantee uniformity of look. Here's how the next three parameter descriptions appear in the source. Note that the parameters are described in a special environment. This is why these comments seem to be at the wrong place. Refer to the documentation of the param package for a list of allowed types.

example
\begin{taskparameters}

\mandparm{mandatoryparam}{default value}{type}{constraints}{
description for mandatory parameter
}
\optparm{optionalparam}{default value}{type}{constraints}{
description for optional parameter
}
\optparm{set}{set.ds}{set}{}{
the value of this parameter is printed out}


text:
5. Process Improvement
5.5.9. An EDA approach to experimental design

## Cumulative residual standard deviation plot

Purpose The cumulative residual sd (standard deviation) plot answers the question:
What is a good model for the data?
The prior 8 steps in this analysis sequence addressed the two important goals:
1. Factors: determining the most important factors that affect the response, and
2. Settings: determining the best settings for these factors.
In addition to the above, a third goal is of interest:
1. Model: determining a model (that is, a prediction equation) that functionally relates the observed response Y with the various main effects and interactions.
Such a function makes particular sense when all of the individual factors are continuous and ordinal (such as temperature, pressure, humidity, concentration, etc.) as opposed to any of the factors being discrete and non-ordinal (such as plant, operator, catalyst, supplier).

In the continuous-factor case, the analyst could use such a function for the following purposes.

1. Reproduction/Smoothing: predict the response at the observed design points.
2. Interpolation: predict what the response would be at (unobserved) regions between the design points.
3. Extrapolation: predict what the response would be at (unobserved) regions beyond the design points.
For the discrete-factor case, the methods developed below to arrive at such a function still apply, and so the resulting model may be used for reproduction. However, the interpolation and extrapolation aspects do not apply.

In modeling, we seek a function f in the k factors X1, X2, ..., Xk such that the predicted values

$$\hat{Y} = f(X_{1}, X_{2}, \ldots , X_{k})$$
are "close" to the observed raw data values Y. To this end, two tasks exist:
1. Determine a good functional form f;
2. Determine good estimates for the coefficients in that function f.
For example, if we had two factors X1 and X2, our goal would be to
1. determine some function f(X1,X2); and
2. estimate the parameters in f
such that the resulting model would yield predicted values $$\hat{Y}$$ that are as close as possible to the observed response values Y. If the form f has been wisely chosen, a good model will result and that model will have the characteristic that the differences ("residuals" = Y - $$\hat{Y}$$) will be uniformly near zero. On the other hand, a poor model (from a poor choice of the form f) will have the characteristic that some or all of the residuals will be "large".

For a given model, a statistic that summarizes the quality of the fit via the typical size of the n residuals is the residual standard deviation:

$$s_{res} = \sqrt{\frac{\sum_{i=1}^{n}{r_{i}^{2}}}{n-p}}$$
with p denoting the number of terms in the model (including the constant term) and r denoting the ith residual. We are also assuming that the mean of the residuals is zero, which will be the case for models with a constant term that are fit using least squares.

If we have a good-fitting model, sres will be small. If we have a poor-fitting model, sres will be large.

For a given data set, each proposed model has its own quality of fit, and hence its own residual standard deviation. Clearly, the residual standard deviation is more of a model-descriptor than a data-descriptor. Whereas "nature" creates the data, the analyst creates the models. Theoretically, for the same data set, it is possible for the analyst to propose an indefinitely large number of models.

In practice, however, an analyst usually forwards only a small, finite number of plausible models for consideration. Each model will have its own residual standard deviation. The cumulative residual standard deviation plot is simply a graphical representation of this collection of residual standard deviations for various models. The plot is beneficial in that

1. good models are distinguished from bad models;
2. simple good models are distinguished from complicated good models.
In summary, then, the cumulative residual standard deviation plot is a graphical tool to help assess
1. which models are poor (least desirable); and
2. which models are good but complex (more desirable); and
3. which models are good and simple (most desirable).
Output The outputs from the cumulative residual standard deviation plot are
1. Primary: A good-fitting prediction equation consisting of an additive constant plus the most important main effects and interactions.

2. Secondary: The residual standard deviation for this good-fitting model.
Definition A cumulative residual sd plot is formed by
1. Vertical Axis: Ordered (largest to smallest) residual standard deviations of a sequence of progressively more complicated fitted models.

2. Horizontal Axis: Factor/interaction identification of the last term included into the linear model:

1 indicates factor X1;
2 indicates factor X2;
...
12 indicates the 2-factor X1*X2 interaction
123 indicates the 3-factor X1*X2*X3 interaction
etc.

3. Far right margin: Factor/interaction identification (built-in redundancy):

1 indicates factor X1;
2 indicates factor X2;
...
12 indicates the 2-factor X1*X2 interaction
123 indicates the 3-factor X1*X2*X3 interaction
etc.

If the design is a fractional factorial, the confounding structure is provided for main effects and 2-factor interactions.

The cumulative residual standard deviations plot is thus a Pareto-style, largest to smallest, graphical summary of residual standard deviations for a selected series of progressively more complicated linear models.

The plot shows, from left to right, a model with only a constant and the model then augmented by including, one at a time, remaining factors and interactions. Each factor and interaction is incorporated into the model in an additive (rather than in a multiplicative or logarithmic or power, etc. fashion). At any stage, the ordering of the next term to be added to the model is such that it will result in the maximal decrease in the resulting residual standard deviation.

Motivation This section addresses the following questions:
Plot for defective springs data Applying the cumulative residual standard deviation plot to the defective springs data set yields the following plot.

How to interpret As discussed in detail under question 4 in the Motivation section, the cumulative residual standard deviation "curve" will characteristically decrease left to right as we add more terms to the model. The incremental improvement (decrease) tends to be large at the beginning when important factors are being added, but then the decrease tends to be marginal at the end as unimportant factors are being added.

Including all terms would yield a perfect fit (residual standard deviation = 0) but would also result in an unwieldy model. Including only the first term (the average) would yield a simple model (only one term!) but typically will fit poorly. Although a formal quantitative stopping rule can be developed based on statistical theory, a less-rigorous (but good) alternative stopping rule that is graphical, easy to use, and highly effective in practice is as follows:

Keep adding terms to the model until the curve's "elbow" is encountered. The "elbow point" is that value in which there is a consistent, noticeably shallower slope (decrease) in the curve. Include all terms up to (and including) the elbow point (after all, each of these included terms decreased the residual standard deviation by a large amount). Exclude any terms after the elbow point since all such successive terms decreased the residual standard deviation so slowly that the terms were "not worth the complication of keeping".
From the residual standard deviation plot for the defective springs data, we note the following:
1. The residual standard deviation (rsd) for the "baseline" model

$$\hat{Y} = \bar{Y} = 71.25$$

is sres = 13.7.

2. As we add the next term, X1, the rsd drops nearly 7 units (from 13.7 to 6.6).

3. If we add the term X1*X3, the rsd drops another 3 units (from 6.6 to 3.4).

4. If we add the term X2, the rsd drops another 2 units (from 3.4 to 1.5).

5. When the term X3 is added, the reduction in the rsd (from about 1.5 to 1.3) is negligible.

6. Thereafter to the end, the total reduction in the rsd is from only 1.3 to 0.
In step 5, note that when we have effects of equal magnitude (the X3 effect is equal to the X1*X2 interaction effect), we prefer including a main effect before an interaction effect and a lower-order interaction effect before a higher-order interaction effect.

In this case, the "kink" in the residual standard deviation curve is at the X2 term. Prior to that, all added terms (including X2) reduced the rsd by a large amount (7, then 3, then 2). After the addition of X2, the reduction in the rsd was small (all less than 1): 0.2, then 0.8, then 0.5, then 0.

The final recommended model in this case thus involves p = 4 terms:

1. the average
2. factor X1
3. the X1*X3 interaction
4. factor X2
The fitted model thus takes on the form
$$\hat{Y} = \bar{Y} + B_{1}X_{1} + B_{13}X_{1}X_{3} + B_{2}X_{2}$$
The least-squares estimates for the coefficients in this model are
$$\hat{Y}$$ = 71.25
B1 = 11.5
B13 = 5
B2 = -2.5
The B1 = 11.5, B13 = 5, and B2 = -2.5 least-squares values are, of course, one half of the estimated effects E1 = 23, E13 = 10, and E2 = -5. Effects, calculated as $$\hat{Y}$$(+1) - $$\hat{Y}$$(-1), were previously derived in step 7 of the recommended 10-step DOE analysis procedure.

The final fitted model is thus

$$\hat{Y} = 71.25 + 11.5 X_{1} + 5 X_{1}X_{3} - 2.5 X_{2}$$
Applying this prediction equation to the 8 design points yields: predicted values $$\hat{Y}$$ that are close to the data Y, and residuals (Res = Y - $$\hat{Y}$$) that are close to zero:
X1 X2 X3 Y $$\hat{Y}$$ Res
- - - 67 67.25 -0.25
+ - - 79 80.25 -1.25
- + - 61 62.25 -1.25
+ + - 75 75.25 -0.25
- - + 59 57.25 +1.75
+ - + 90 90.25 -0.25
- + + 52 52.25 -0.25
+ + + 87 85.25 +1.75
Computing the residual standard deviation:
$$s_{res} = \sqrt{ \frac{\sum_{i=1}^{n}{r_{i}^{2}}} {n-p} }$$
with n = 8 data points, and p = 4 estimated coefficients (including the average) yields
sres = 1.54 (or 1.5 if rounded to 1 decimal place)
The detailed sres = 1.54 calculation brings us full circle, for 1.54 is the value given above the X3 term on the cumulative residual standard deviation plot.
Conclusions for the defective springs data The application of the Cumulative Residual Standard Deviation Plot to the defective springs data set results in the following conclusions:
1. Good-fitting Parsimonious (constant + 3 terms) Model:

$$\hat{Y} = 71.25 + 11.5 X_{1} + 5 X_{1}X_{3} - 2.5 X_{2}$$

2. Residual Standard Deviation for this Model (as a measure of the goodness-of-fit for the model):

sres = 1.54


text:
# Algebraic definition of a residual from a regression

Can anyone give some advice on how to start proving this algebraically?

Define the residual from a regression (one independent variable) algebraically and show that:

1. the mean of the residuals is zero
2. the correlation of the residuals and the independent variable is zero
-
 I presume this is homework? What have you tried so far? – csgillespie Mar 1 '11 at 13:50 can you give a more explicit statement of the model you're considering? I ask because, in general, the first thing you're asked to prove is false! – cardinal Mar 1 '11 at 13:50

Suppose you have the following regression model:

$$y_i=\alpha+\beta x_i+\varepsilon_i$$

Least squares problem looks for $\alpha$ and $\beta$ which minimize the following function:

$$g(\alpha,\beta)=\sum_{i=1}^n(y_i-\alpha-\beta x_i)^2$$

Solution for this problem will satisfy

$$\frac{\partial g}{\partial \alpha}=0, \quad \frac{\partial g}{\partial \beta}=0.$$

Try differencing and look hard at the resulting expressions. You will see that this answers your problem.

Note that @cardinal is right, if you do not include $\alpha$, your first statement is false.

Update This is might be considered non-algebraic solution, so please state more clearly what do you mean by algebraic. If this is not helpful, I will retract my answer, which really is a long comment.

-
 Well I am supposed to have an algebraic proof that the mean of the residuals is zero. I assumed that by showing that the sum of the residuals is zero, then one could state that the mean is similarly zero, but I am not sure if that is accurate. I feel that something is missing.. – user3487 Mar 1 '11 at 19:21 @cassetete, did you try to differentiate $g$? You are right mean will be zero when sum will be zero. – mpiktas Mar 1 '11 at 19:33 It finally became clear to me. I just worked it out, many thanks to all! – user3487 Mar 1 '11 at 19:51 @cassetete, congratulations! It would be good if you posted your solution as an answer. So that somebody can find it by googling it. Or you can accept my answer, wink, wink, hint, hint, if it was the proverbial push over the cliff. – mpiktas Mar 1 '11 at 20:01


text:
#### Volume 13, issue 2 (2009)

 Recent Issues
 The Journal About the Journal Editorial Board Editorial Interests Editorial Procedure Submission Guidelines Submission Page Subscriptions Author Index To Appear Contacts ISSN (electronic): 1364-0380 ISSN (print): 1465-3060
Tutte chromatic identities from the Temperley–Lieb algebra

### Paul Fendley and Vyacheslav Krushkal

Geometry & Topology 13 (2009) 709–741
##### Abstract

This paper introduces a conceptual framework, in the context of quantum topology and the algebras underlying it, for analyzing relations obeyed by the chromatic polynomial $\chi \left(Q\right)$ of planar graphs. Using it we give new proofs and substantially extend a number of classical results concerning the combinatorics of the chromatic polynomial. In particular, we show that Tutte’s golden identity is a consequence of level-rank duality for $SO\left(N\right)$ topological quantum field theories and Birman–Murakami–Wenzl algebras. This identity is a remarkable feature of the chromatic polynomial relating $\chi \left(\varphi +2\right)$ for any triangulation of the sphere to ${\left(\chi \left(\varphi +1\right)\right)}^{2}$ for the same graph, where $\varphi$ denotes the golden ratio. The new viewpoint presented here explains that Tutte’s identity is special to these values of the parameter $Q$. A natural context for analyzing such properties of the chromatic polynomial is provided by the chromatic algebra, whose Markov trace is the chromatic polynomial of an associated graph. We use it to show that another identity of Tutte’s for the chromatic polynomial at $Q=\varphi +1$ arises from a Jones–Wenzl projector in the Temperley–Lieb algebra. We generalize this identity to each value $Q=2+2cos\left(2\pi j∕\left(n+1\right)\right)$ for $j positive integers. When $j=1$, these $Q$ are the Beraha numbers, where the existence of such identities was conjectured by Tutte. We present a recursive formula for this sequence of chromatic polynomial relations.

##### Keywords
chromatic polynomial, Temperley–Lieb algebra, level-rank duality, Tutte golden identity, planar graph, Beraha number
##### Mathematical Subject Classification 2000
Primary: 57M15
Secondary: 05C15, 57R56, 81R05


text:
Circular distributions Kolmogorov-Smirnov vs. Watson test vs. Rayleigh test

I am interested in assessing whether my angular data distribution is satisfactorily described by a von Mises distribution.

In scale data, one can potentially use a Kolmogorov-Smirnov test. However, with circular data, it is usual to use the Watson test. The Rayleigh, Watson or Rao Spacing tests are used if a uniform distribution on the circle is suspected.

Question: Why is a Kolmogorov-Smirnov test not appropriate?

Also, I notice differences when plotting Probability and Quantile plots in routine software packages, e.g., Mathematica etc. vs. dedicated software for circular data? How are PP and QQ plots distorted in the circular data setting?

For circular data, it is not as straightforward to define the CDF. With circular data, we have to choose a reference point $0^\circ$, arbitrarily. If we rotate the data, say by $180^\circ$, we should find the same answer as to whether the von Mises distribution is an appropriate distribution. However, the maximum difference between the empirical and theoretical CDF (which is the Kolmogorov-Smirnov test) depends on the arbitrary reference point, and will change when we rotate the data.


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# NEN-EN-ISO 19232-3

## Non-destructive testing - Image quality of radiographs - Part 3: Image quality classes

active, Most Current
 Organization: NEN Publication Date: 1 June 2013 Status: active Page Count: 22 ICS Code (Non-destructive testing): 19.100
##### scope:

This part of ISO 19232 specifies the minimum image quality values to ensure a uniform radiographic quality. It applies to the two types of image quality indicator as detailed in ISO 19232-1 for wire-type IQI and ISO 19232-2 for step/hole-type IQI and for the two techniques described in ISO 5579. Values are specified for the two classes of radiographic technique specified in ISO 5579.

### Document History

NEN-EN-ISO 19232-3
June 1, 2013
Non-destructive testing - Image quality of radiographs - Part 3: Image quality classes
This part of ISO 19232 specifies the minimum image quality values to ensure a uniform radiographic quality. It applies to the two types of image quality indicator as detailed in ISO 19232-1 for...
June 1, 2011
Non-destructive testing - Image quality of radiographs - Part 3: Image quality classes for ferrous metals
This part of ISO 19232 specifies the minimum image quality values to ensure a uniform radiographic quality. It applies to the two types of image quality indicator as detailed in ISO 19232-1 for...


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# Building a Model

The first and most important thing to do before anything else is to think about model design, structure, layout, and planning. These steps play a key role in the quality and success of modeling project.

For finance-related modelers, designing can sometimes be the most difficult part of building a financial model. A well-designed model will be so straightforwardly logical that it will simply speak for itself. Also, the layout and structure of the model relate to the look and feel of the model, and how users navigate through the model. Let’s say you are creating a high-level five-year sales forecasts. We expect that number to increase by 5 percent every year.

So there are a few golden rules for model design in my experience.

• Separate inputs, calculations, and results. They can be on separate worksheets or separate places on a given worksheet but make sure that the user knows exactly what each section is for. Colour coding is also another solution.
• Use each Column for the same purpose. This is extremely important when dealing with time series data.
• Use one formula per Row or Column. This forms the basis of the best-practice principle in order to keep formulas consistent when in a block of data.
• Refer to the Left and Above. The model should read logically, like a book. Calculations, inputs, and outputs should flow logically to avoid circular referencing.
• Use multiple worksheets. Avoid putting everything on one sheet.
• Include documentation sheets. A documentation sheet is where assumptions and source data are stored. Also, a model should not have too much documentation.

There are also 4 key issues we need to think about before starting a model:

• Time series. Time series data are the most popular type in most financial models. We need to pay attention heavily on the frequency of the data.
• Data collection. Often the majority of time is spent not in building a model but rather collecting, interpreting, analyzing and manipulating data to put into the model.
• Model purpose. Think about what outputs we expect the model to show.
• Model audience. No need to build a fancy model for you. In otherwise, you should make a really user-friendly model as possible.

Unless a model is very small, there should be a dedicated tab worksheet for each major components of the model.

• Cover sheet contains many details about the model. Some details as shining examples are:

• Flow chart of the model structure
• Instructions on how to use the model
• The purpose of the model
• Key assumptions integral to the use of the model.
• Input sheet is the place where hard-coded data is permissible.

• Output, summary, and scenario sheets present the final outcomes.
• Calculation or working sheets should be split logically and set up consistently.
• Error check sheet contains links to all error checks in the model. It should include a sheet of the summary of all error checks so that the modelers can quickly check to see if any of the error checks have been triggered.

Although planning in advance is very important for successful modeling, it is unrealistic to expect a detailed project plan prior to starting to build it. The first question is how long or the time it takes to build a financial model. And certainly, the answer is never straightforward. It depends on how much time the modeler has (in most cases, there is never enough time :)) ) and how much detail the user(s) needs. And the second is how to use the permitted time wisely and efficiently. Do not waste time on validating minor assumptions that are not material to the outcome of the model is one of my tips for time-saving.

Besides, for BIG models that will be viewed or reviewed by external parties, a flow chart that maps the model’s structure and how it solves the problem might be useful. Not only does this assist in building the model, it also helps users to better understand and follow the model’s logic, design, purpose, and can be used as a presentation tool when explaining the model. One flow chart that I have recently obtained from the Internet is an illustrative example as follow:

Once the aforementioned factors have been determined, we can begin to create our model. If you are working as the sole financial modeler then we might be able to follow a less formal process, called The Streamlined Version by some practitioners. If you are a member of a team of financial modelers, the steps shall be more detailed, as it is more important to follow a documented and structured process, called The Team Version.

There are mainly 7 steps in the streamlined version1 as follow:

• Design the high-level structure:
• Design outputs: summaries, charts, and reports
• Plan calculations by breaking larger problems into smaller ones
• Finalize outputs
• Design sensitivities and scenario analysis
• Assumptions documentation

For the team version [1], we have 12 steps which have been split into 2 categories: planning and building. The planning stage should include:

1. Scope out the project: purpose, problem we need to solve, time frame
2. Assign project tasks based on specific skills
3. Determine the users of the model
4. Design the high-level structure
5. Create a data collection plan

The building stage should include:

1. Build inputs
2. Build calculations and working
3. Build outputs: summaries, charts, and reports
4. Peer and Client review of draft model
5. Design sensitivities and scenario analysis
6. Formal model quality assurance check: includes stress test, check some Excel errors like #DIV/0!, sensitivity tests of outputs
7. Maintain and/or Update the model

In reality, several necessary inputs rely solely on information from other parties, whether internal or external to the organization. This leads to the fact that the receipt of timely and accurate information is much important. Therefore, you may consider creating a formalized information request procedure.

For more efficiency, you should also design the file structure where you can find:

• Models: a list of the model with version-control nomenclature applied.
• Project planning: documents relating to the project plan, resource allocation, and timelines.
• Source data

The best example might be shown as follow:

Next chapter, I will show you some best practice principles of modeling which I have been collecting for several years.

Please leave some comments if there are any questions or recommendations. Thank you!

1. Danielle Stein Fairhurst, 2015. Using Excel for Business Analysis. Revised Edition. Wiley↩


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# Are homodesmotic reactions isodesmic reactions?

Dec 26, 2014

Yes, homodesmotic reactions are a subset of isodesmic reactions.

An isodesmic reaction is a reaction that has the same number and type of bonds in the reactants and in the products.

An example of an isodesmic reaction is

Homodesmotic reactions are a subclass of isodesmic reactions.

Here, the reactants and products are even more similar. They must contain equal numbers of

• atoms in the same state of hybridization
• groups containing the same number of H atoms.

An example of a homodesmotic reaction is

The reactants and products contain equal numbers of bonds between carbons in the same state of hybridization and hydrogens bound to identical atom types.

${C}_{s {p}^{3}} \text{-} {O}_{s {p}^{3}}$ = 1

${C}_{s {p}^{3}} \text{-} {C}_{s {p}^{2}}$ = 1

${C}_{s {p}^{2}} \text{-} {O}_{s {p}^{3}}$ = 1

${C}_{s {p}^{2}} \text{-} {C}_{s {p}^{2}}$ = 7

${C}_{s {p}^{2}} \text{=} {C}_{s {p}^{2}}$ = 6

${C}_{s {p}^{3}} {H}_{3}$ = 2

${C}_{s {p}^{2}} {H}_{2}$ = 2

${C}_{s {p}^{2}} H$ = 9


text:
Home OALib Journal OALib PrePrints Submit Ranking News My Lib FAQ About Us Follow Us+
 Title Keywords Abstract Author All
Search Results: 1 - 10 of 100 matches for " "
 Page 1 /100 Display every page 5 10 20 Item
 International Journal of Stochastic Analysis , 1998, DOI: 10.1155/s1048953398000239 Abstract: The following paper, first written in 1974, was never published other than as part of an internal research series. Its lack of publication is unrelated to the merits of the paper and the paper is of current importance by virtue of its relation to the relaxation time. A systematic discussion is provided of the approach of a finite Markov chain to ergodicity by proving the monotonicity of an important set of norms, each measures of egodicity, whether or not time reversibility is present. The paper is of particular interest because the discussion of the relaxation time of a finite Markov chain [2] has only been clean for time reversible chains, a small subset of the chains of interest. This restriction is not present here. Indeed, a new relaxation time quoted quantifies the relaxation time for all finite ergodic chains (cf. the discussion of Q1(t) below Equation (1.7)]. This relaxation time was developed by Keilson with A. Roy in his thesis [6], yet to be published.
 Mathematics , 2015, Abstract: Motivated by a model presented by S. Gudder, we study a quantum generalization of Markov chains and discuss the relation between these maps and open quantum random walks, a class of quantum channels described by S. Attal et al. We consider processes which are nonhomogeneous in time, i.e., at each time step, a possibly distinct evolution kernel. Inspired by a spectral technique described by L. Saloff-Coste and J. Z\'u\~niga, we define a notion of ergodicity for nonhomogeneous quantum Markov chains and describe a criterion for ergodicity of such objects in terms of singular values. As a consequence we obtain a quantum version of the classical probability result concerning the behavior of the columns (or rows) of the iterates of a stochastic matrix induced by a finite, irreducible, aperiodic Markov chain. We are also able to relate the ergodic property presented here with the notions of weak and uniform ergodicity known in the literature of noncommutative $L^1$-spaces.
 Mathematics , 2008, DOI: 10.1214/07-AAP486 Abstract: We introduce a new property of Markov chains, called variance bounding. We prove that, for reversible chains at least, variance bounding is weaker than, but closely related to, geometric ergodicity. Furthermore, variance bounding is equivalent to the existence of usual central limit theorems for all $L^2$ functionals. Also, variance bounding (unlike geometric ergodicity) is preserved under the Peskun order. We close with some applications to Metropolis--Hastings algorithms.
 Richard C. Bradley Mathematics , 2014, Abstract: It is well known that for a strictly stationary, reversible, Harris recurrent Markov chain, the $\rho$-mixing condition is equivalent to geometric ergodicity and to a "spectral gap" condition. In this note, it will be shown with an example that for that class of Markov chains, the "interlaced" variant of the $\rho$-mixing condition fails to be equivalent to those conditions.
 Mathematics , 2015, Abstract: We study properties of the Laplace transforms of non-negative additive functionals of Markov chains. We are namely interested in a multiplicative ergodicity property used in [18] to study bifurcating processes with ancestral dependence. We develop a general approach based on the use of the operator perturbation method. We apply our general results to two examples of Markov chains, including a linear autoregressive model. In these two examples the operator-type assumptions reduce to some expected finite moment conditions on the functional (no exponential moment conditions are assumed in this work).
 Mathematics , 2011, DOI: 10.1214/11-AAP800 Abstract: We consider a bivariate stationary Markov chain $(X_n,Y_n)_{n\ge0}$ in a Polish state space, where only the process $(Y_n)_{n\ge0}$ is presumed to be observable. The goal of this paper is to investigate the ergodic theory and stability properties of the measure-valued process $(\Pi_n)_{n\ge0}$, where $\Pi_n$ is the conditional distribution of $X_n$ given $Y_0,...,Y_n$. We show that the ergodic and stability properties of $(\Pi_n)_{n\ge0}$ are inherited from the ergodicity of the unobserved process $(X_n)_{n\ge0}$ provided that the Markov chain $(X_n,Y_n)_{n\ge0}$ is nondegenerate, that is, its transition kernel is equivalent to the product of independent transition kernels. Our main results generalize, subsume and in some cases correct previous results on the ergodic theory of nonlinear filters.
 Computer Science , 2010, Abstract: We apply Doeblin's ergodicity coefficient as a computational tool to approximate the occupancy distribution of a set of states in a homogeneous but possibly non-stationary finite Markov chain. Our approximation is based on new properties satisfied by this coefficient, which allow us to approximate a chain of duration n by independent and short-lived realizations of an auxiliary homogeneous Markov chain of duration of order ln(n). Our approximation may be particularly useful when exact calculations via first-step methods or transfer matrices are impractical, and asymptotic approximations may not be yet reliable. Our findings may find applications to pattern problems in Markovian and non-Markovian sequences that are treatable via embedding techniques.
 系统科学与数学 , 1996, Abstract: By the comparison of transition matrices of two nonhomogeneous Markov chains, we discuss the relations of ergodicity for the two chains and obtain some sufficient conditions for a nonhomogeneous Markov chain to be strongly ergodic. The relations of uniformstrong ergodicity and ulilform weall ergodicity for a nonhomogeneous Markov chain are analysedand some sufficient conditions of uniform strong ergodicity for a nonhomogeneous Markov chainare obtained.
 Witold Bednorz Mathematics , 2013, Abstract: In this paper we prove a sharp quantitative version of the Kendall's Theorem. The Kendal Theorem states that under some mild conditions imposed on a probability distribution on positive integers (i.e. probabilistic sequence) one can prove convergence of its renewal sequence. Due to the well-known property - the first entrance last exit decomposition - such results are of interest in the stability theory of time homogeneous Markov chains. In particular the approach may be used to measure rates of convergence of geometrically ergodic Markov chains and consequently implies estimates on convergence of MCMC estimators.
 Mathematics , 2013, Abstract: We consider a population with non-overlapping generations, whose size goes to infinity. It is described by a discrete genealogy which may be time non-homogeneous and we pay special attention to branching trees in varying environments. A Markov chain models the dynamic of the trait of each individual along this genealogy and may also be time non-homogeneous. Such models are motivated by transmission processes in the cell division, reproduction-dispersion dynamics or sampling problems in evolution. We want to determine the evolution of the distribution of the traits among the population, namely the asymptotic behavior of the proportion of individuals with a given trait. We prove some quenched laws of large numbers which rely on the ergodicity of an auxiliary process, in the same vein as \cite{guy,delmar}. Applications to time inhomogeneous Markov chains lead us to derive a backward (with respect to the environment) law of large numbers and a law of large numbers on the whole population until generation $n$. A central limit is also established in the transient case.
 Page 1 /100 Display every page 5 10 20 Item


text:
## Find the network’s poles and zeros

A certain network having an input voltage function x(t) andoutput voltage function y(t) is described by the followingdifferential equation:
find the network’s poles and zeros


text:
R Dataset / Package boot / calcium

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Documentation

Calcium Uptake Data

Description

The calcium data frame has 27 rows and 2 columns.

Howard Grimes from the Botany Department, North Carolina State University, conducted an experiment for biochemical analysis of intracellular storage and transport of calcium across plasma membrane. Cells were suspended in a solution of radioactive calcium for a certain length of time and then the amount of radioactive calcium that was absorbed by the cells was measured. The experiment was repeated independently with 9 different times of suspension each replicated 3 times.

Usage

calcium

Format

This data frame contains the following columns:

time

The time (in minutes) that the cells were suspended in the solution.

cal

The amount of calcium uptake (nmoles/mg).

Source

The data were obtained from

Rawlings, J.O. (1988) Applied Regression Analysis. Wadsworth and Brooks/Cole Statistics/Probability Series.

References

Davison, A.C. and Hinkley, D.V. (1997) Bootstrap Methods and Their Application. Cambridge University Press.

--

Dataset imported from https://www.r-project.org.

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