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API module¶

This module provides wrapper functions for the core functions provided in the C++-module _tacoma.

tacoma.api.aggregated_network(temporal_network)[source]

Measures the static network composed.

Parameters: temporal_network (_tacoma.edge_changes, _tacoma.edge_lists, _tacoma.edge_changes_with_histograms, or _tacoma.edge_lists_with_histograms) – An instance of a temporal network. aggregated_network – Keys represent edges and values represent the aggregated time spent together (in units of time provided by the temporal network dict where keys are pairs of ints and values are floats
tacoma.api.bin(temporal_network, dt=0.0, N_time_steps=0, verbose=False)[source]

Bins a temporal network for each dt (after each step, respectively, if N_time_steps was provided).

Parameters: temporal_network (_tacoma.edge_changes, _tacoma.edge_lists, _tacoma.edge_changes_with_histograms, or _tacoma.edge_lists_with_histograms) – An instance of a temporal network. dt (float) – The demanded bin size. default : 0.0 N_time_steps (int) – Number of time bins (use either this or dt). default : 0 verbose (bool, optional) – Be chatty. An edge_lists instance with one edge list describing the network as a list of all edges that were present in the last time bin. _tacoma.edge_lists
tacoma.api.binned_social_trajectory(temporal_network, node, dt=0.0, N_time_steps=0, verbose=False)[source]

Computes the binned social trajectory of node node in temporal_network, i.e. the groups it was part of and pairs of times (t0, t1) when it was part of a certain group. In this case, binning makes it easier to, e.g. see the days where a group was active.

Parameters: temporal_network (_tacoma.edge_changes, _tacoma.edge_lists, _tacoma.edge_changes_with_histograms, or _tacoma.edge_lists_with_histograms) – An instance of a temporal network. node (int) – The node for which to compute the social trajectory dt (float) – The demanded bin size. default : 0.0 N_time_steps (int) – Number of time bins (use either this or dt). default : 0 verbose (bool, optional) – Be chatty. A list, one entry for each dt. Each entry is a list of group ids. list of list of int
tacoma.api.concatenate(list_of_temporal_networks, verbose=False)[source]

Concatenates a list of either _tacoma.edge_changes or _tacoma.edge_lists to a single instance of _tacoma.edge_changes or _tacoma.edge_lists, respectively.

Parameters: temporal_network (list of _tacoma.edge_changes, _tacoma.edge_lists, _tacoma.edge_changes_with_histograms, or _tacoma.edge_lists_with_histograms) – A list of a temporal networks. verbose (bool, default : False) – Be chatty. A single instance of the format provided in the lists.
tacoma.api.convert(temporal_network, verbose=False)[source]

Converts either an instance of _tacoma.edge_changes to an instance of _tacoma.edge_lists or vice versa.

Parameters: temporal_network (_tacoma.edge_changes, _tacoma.edge_lists, _tacoma.edge_changes_with_histograms, or _tacoma.edge_lists_with_histograms) – An instance of a temporal network. verbose (bool, optional) – Be chatty. An instance of the other format.
tacoma.api.convert_edge_trajectories(traj)[source]

Convert an instance of _tacoma.edge_trajectories to an instance of _tacoma.edge_changes. Note that there’s no method to convert to _tacoma.edge_lists directly.

Parameters: traj (_tacoma.edge_trajectories) – The temporal network which has to be converted. temporal_network – The converted temporal network. _tacoma.edge_changes
tacoma.api.convert_to_edge_trajectories(temporal_network, return_edge_similarities=False, verbose=False)[source]

Converts a temporal network to an instance of _tacoma.edge_trajectories.

Parameters: temporal_network (_tacoma.edge_changes, _tacoma.edge_lists, _tacoma.edge_changes_with_histograms, or _tacoma.edge_lists_with_histograms) – An instance of a temporal network. return_edge_similarities (bool, optional) – If this is True, compute the similarity between edges, too. default : False verbose (bool, optional) – Be chatty. traj – The converted temporal network. _tacoma.edge_trajectories
tacoma.api.degree_distribution(temporal_network)[source]

Measures the time-averaged degree distribution.

Parameters: temporal_network (_tacoma.edge_changes, _tacoma.edge_lists, _tacoma.edge_changes_with_histograms, or _tacoma.edge_lists_with_histograms) – An instance of a temporal network. P_k – A list of N entries where the k-th entry is the time-averaged probability of finding a node with degree k. list of float
tacoma.api.edge_counts(temporal_network)[source]

Returns the number of edge events and total edge count (In this order: m_in, m_out, and m).

Parameters: temporal_network (_tacoma.edge_changes, _tacoma.edge_lists, _tacoma.edge_changes_with_histograms, or _tacoma.edge_lists_with_histograms) – A list of a temporal networks. list of int – Number of edges coming into the network at the corresponding times. list of int – Number of edges leaving the network at the corresponding times. list of int – Number of edges existent in the network at the corresponding times.
tacoma.api.get_edge_trajectories(temporal_network, return_edge_similarities=False, verbose=False)[source]

Computes a list of time intervals in which each edge existed and optionally the similarity between edges.

Parameters: temporal_network (_tacoma.edge_changes, _tacoma.edge_lists, _tacoma.edge_changes_with_histograms, _tacoma.edge_lists_with_histograms or _tacoma.edge_trajectories) – An instance of a temporal network. return_edge_similarities (bool, optional) – If this is True, return the similarity between edges. default : False verbose (bool, optional) – Be chatty. trajectories (_tacoma.edge_trajectories.trajectories) – a list of edge_trajectory_entry objects, which contain the .time_pairs attributes, a list of time pairs (t0, t1) for time t0 <= t <= t1 in which the edge existed and .edge a pair of node integers. similarities (_tacoma.edge_trajectories.edge_similarities) – a list of triples ( u, v, similarity ) where u and v refer to the edge indices in edge_trajectories.trajectories and similarity is the integrated time both edges were switched on while being connected to the same node.
tacoma.api.gillespie_SI(temporal_network, SI, is_static=False, verbose=False)[source]

Simulates an SI process on the provided temporal network using the Gillespie stochastic simulation algorithm.

Parameters: temporal_network (_tacoma.edge_changes, _tacoma.edge_lists, _tacoma.edge_changes_with_histograms, or _tacoma.edge_lists_with_histograms) – An instance of a temporal network. SI (_tacoma.SI) – An initialized SI object. is_static (bool, default : False) – The algorithm works a bit differently if it knows that the network is actually static. It works only with instances of _tacoma.edge_lists. verbose (bool, optional) – Be chatty. But the observables are saved in the _tacoma.SI object. None
tacoma.api.gillespie_SIR(temporal_network, SIR, is_static=False, verbose=False)[source]

Simulates an SIR process on the provided temporal network using the Gillespie stochastic simulation algorithm.

Parameters: temporal_network (_tacoma.edge_changes, _tacoma.edge_lists, _tacoma.edge_changes_with_histograms, or _tacoma.edge_lists_with_histograms) – An instance of a temporal network. SIR (_tacoma.SIR) – An initialized SIR object. is_static (bool, default : False) – The algorithm works a bit differently if it knows that the network is actually static. It works only with instances of _tacoma.edge_lists. verbose (bool, optional) – Be chatty. But the observables are saved in the _tacoma.SIR object. None
tacoma.api.gillespie_SIRS(temporal_network, SIRS, is_static=False, verbose=False)[source]

Simulates an SIRS process on the provided temporal network using the Gillespie stochastic simulation algorithm.

Parameters: temporal_network (_tacoma.edge_changes, _tacoma.edge_lists, _tacoma.edge_changes_with_histograms, or _tacoma.edge_lists_with_histograms) – An instance of a temporal network. SIRS (_tacoma.SIRS) – An initialized SIRS object. is_static (bool, default : False) – The algorithm works a bit differently if it knows that the network is actually static. It works only with instances of _tacoma.edge_lists. verbose (bool, optional) – Be chatty. But the observables are saved in the _tacoma.SIRS object. None
tacoma.api.gillespie_SIS(temporal_network, SIS, is_static=False, verbose=False)[source]

Simulates an SIS process on the provided temporal network using the Gillespie stochastic simulation algorithm.

Parameters: temporal_network (_tacoma.edge_changes, _tacoma.edge_lists, _tacoma.edge_changes_with_histograms, or _tacoma.edge_lists_with_histograms) – An instance of a temporal network. SIS (_tacoma.SIS) – An initialized SIS object. is_static (bool, default : False) – The algorithm works a bit differently if it knows that the network is actually static. It works only with instances of _tacoma.edge_lists. verbose (bool, optional) – Be chatty. But the observables are saved in the _tacoma.SIS object. None
tacoma.api.gillespie_epidemics(temporal_network_or_model, epidemic_object, is_static=False, reset_simulation_objects=True, verbose=False)[source]

Simulates an epidemic process on the provided temporal network using the Gillespie stochastic simulation algorithm.

Parameters: temporal_network_or_model (_tacoma.edge_changes, _tacoma.edge_lists, _tacoma.edge_changes_with_histograms, _tacoma.edge_lists_with_histograms, _tacoma.EdgeActivityModel, or _tacoma.FlockworkPModel.) – An instance of a temporal network or network model. epidemic_object (_tacoma.SI, _tacoma.SIS, _tacoma.SIR, _tacoma.SIRS, _tacoma.node_based_SIS, _tacoma.eSIS) – An initialized epidemic object. is_static (bool, default : False) – The algorithm works a bit differently if it knows that the network is actually static. It works only with instances of _tacoma.edge_lists. reset_simulation_objects (bool, default : True) – Whether or not the simulation objects should be reset in the beginning. verbose (bool, optional) – Be chatty. But the observables are saved in the _tacoma epidemic object. None
tacoma.api.gillespie_node_based_SIS(temporal_network, SIS, is_static=False, verbose=False)[source]

Simulates a node-based SIS process on the provided temporal network using the Gillespie stochastic simulation algorithm.

Parameters: temporal_network (_tacoma.edge_changes, _tacoma.edge_lists, _tacoma.edge_changes_with_histograms, or _tacoma.edge_lists_with_histograms) – An instance of a temporal network. SIS (_tacoma.SIS_node_based) – An initialized node-based SIS object. is_static (bool, default : False) – The algorithm works a bit differently if it knows that the network is actually static. It works only with instances of _tacoma.edge_lists. verbose (bool, optional) – Be chatty. But the observables are saved in the _tacoma.SIS object. None
tacoma.api.markov_epidemics(temporal_network_or_model, epidemic_object, max_dt, is_static=False, reset_simulation_objects=True, verbose=False)[source]

Integrates an epidemic markov process on the provided temporal network.

Parameters: temporal_network_or_model (_tacoma.edge_changes, _tacoma.edge_lists, _tacoma.edge_changes_with_histograms, _tacoma.edge_lists_with_histograms, _tacoma.EdgeActivityModel, or _tacoma.FlockworkPModel.) – An instance of a temporal network or network model. epidemic_object (_tacoma.MARKOV_SIS) – An initialized epidemic object. max_dt (float) – The maximally allowed integration step. is_static (bool, default : False) – The algorithm works a bit differently if it knows that the network is actually static. It works only with instances of _tacoma.edge_lists. reset_simulation_objects (bool, default : True) – Whether or not the simulation objects should be reset in the beginning. verbose (bool, optional) – Be chatty. But the observables are saved in the _tacoma epidemic Markov-object. None
tacoma.api.mean_degree(temporal_network)[source]

Computes the time dependent mean degree of the temporal network.

Parameters: temporal_network (_tacoma.edge_changes, _tacoma.edge_lists, _tacoma.edge_changes_with_histograms, or _tacoma.edge_lists_with_histograms) – A list of a temporal networks. numpy array – t containing the time points. numpy array – k containing the mean degree at the corresponding times.
tacoma.api.measure_group_sizes_and_durations(temporal_network, ignore_size_histogram=False, verbose=False)[source]

Measures aggregated group size distribution, group size histogram for each time point, contact durations, inter-contact durations, durations of each group size, and the aggregated social network.

Parameters: temporal_network (_tacoma.edge_changes, _tacoma.edge_lists, _tacoma.edge_changes_with_histograms, or _tacoma.edge_lists_with_histograms) – An instance of a temporal network. ignore_size_histogram (bool, optional) – Don’t compute the single time point group size histograms (save time and memory). default : False verbose (bool, optional) – Be chatty. The result of the measurements. Note that inter-contact durations is just durations of groups of size 1 and hence correspond to the first entry of _tacoma.group_sizes_and_durations.group_durations. _tacoma.group_sizes_and_durations
tacoma.api.sample(temporal_network, dt=0.0, N_time_steps=0, sample_aggregates=False, verbose=False)[source]

Samples a temporal network after each dt (after each step, respectively, if N_time_steps was provided).

Parameters: temporal_network (_tacoma.edge_changes, _tacoma.edge_lists, _tacoma.edge_changes_with_histograms, or _tacoma.edge_lists_with_histograms) – An instance of a temporal network. dt (float) – The demanded bin size. default : 0.0 N_time_steps (int) – Number of time bins (use either this or dt). default : 0 sample_aggregates (bool, optional) – If this is True, the following happens. If an edge is active during a time bin, it will appear in the final graph at the end of this time bin. It will then exist until the ende of the coming time bin. (This is different from the binning procedure). This does not seem to make very much sense so maybe just don’t use it. default : False verbose (bool, optional) – Be chatty. An edge_lists instance with one edge list describing the network states after each discrete time step. _tacoma.edge_lists
tacoma.api.slice(temporal_network, new_t0, new_tmax, verbose=False)[source]

Get a slice of a temporal network for times new_t0 <= t < new_tmax.

Parameters: temporal_network (_tacoma.edge_changes, _tacoma.edge_lists, _tacoma.edge_changes_with_histograms, or _tacoma.edge_lists_with_histograms) – An instance of a temporal network. new_t0 (float) – Where the slice should begin. new_t0 – Where the slice should end. verbose (bool, optional) – Be chatty. default : False Sliced network (type depending on input type).
tacoma.api.social_trajectory(temporal_network, node, verbose=False)[source]

Computes the social trajectory of node node in temporal_network, i.e. the groups it was part of and pairs of times (t0, t1) when it was part of a certain group.

Parameters: temporal_network (_tacoma.edge_changes, _tacoma.edge_lists, _tacoma.edge_changes_with_histograms, or _tacoma.edge_lists_with_histograms) – An instance of a temporal network. node (int) – The node for which to compute the social trajectory verbose (bool, optional) – Be chatty.
tacoma.api.verify(temporal_network, verbose=False)[source]

Checks wether the temporal network is compliant with the demanded formats for analyses. Writes remarks on violations to stdout.

Parameters: temporal_network (_tacoma.edge_changes, _tacoma.edge_lists, _tacoma.edge_changes_with_histograms, or _tacoma.edge_lists_with_histograms) – An instance of a temporal network. verbose (bool, optional) – If this is True, cout all errors that were found. default : False Number of found errors. int


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# At the rate of 3,000 revolutions per minute, how many revolu

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At the rate of 3,000 revolutions per minute, how many revolu [#permalink]  04 Aug 2018, 10:46
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At the rate of 3,000 revolutions per minute, how many revolutions will a wheel make in k seconds?

A. $$3,000k$$

B. $$50k$$

C. $$\frac{50}{k}$$

D. $$\frac{3,000}{k}$$

E. $$\frac{180,000}{k}$$
[Reveal] Spoiler: OA

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Re: At the rate of 3,000 revolutions per minute, how many revolu [#permalink]  04 Aug 2018, 18:10
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At the rate of 3,000 revolutions per minute, how many revolutions will a wheel make in k seconds?

A. $$3,000k$$

B. $$50k$$

C. $$\frac{50}{k}$$

D. $$\frac{3,000}{k}$$

E. $$\frac{180,000}{k}$$

As the wheel makes 3000 revolutions in a minute or 60 seconds time,

So in 1 second it will make =$$\frac{3000}{60} = 50 rev$$

Therefore, in k seconds, the wheel will make = $$50 * k = 50k rev$$
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Re: At the rate of 3,000 revolutions per minute, how many revolu   [#permalink] 04 Aug 2018, 18:10
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# Math playpen

$$\mathcal{P}e^{i \oint_C A_\mu dx^\mu} \to g(x) \mathcal{P}e^{i \oint_C A_\mu dx^\mu} g^{-1}(x)\,$$

Numbers, woo!

Can I bork the page? Trying to bork the page… 3

asdf

Parents:

• Mathematics

Mathematics is the study of numbers and other ideal objects that can be described by axioms.


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# Modified energy method for transformed Fokker-Planck equation (tricky integration by parts…)

I came across Villani's paper titled "Hypocoercive diffusion operators" and couldn't figure out a computation that is skipped in that paper. Specifically, consider the following transformed Fokker-Planck equation, where $$h(t,x,v)$$ is the unknown, $$(x,v) \in \mathbb{R}^n \times \mathbb{R}^n$$, $$V(x)$$ is some potential force: $$\partial_t h + v\cdot \nabla_x h - \nabla V(x)\cdot \nabla_v h = \Delta_v h - v\cdot \nabla_v h.$$ Notice that the Laplacian $$\Delta_v$$ is only a partial Laplacian in the sense that it only acts on the velocity variables $$v$$, and for the usual $$L^2$$ energy $$\int h^2 d\mu$$, where $$d\mu = f_\infty(x,v) dxdv$$ and $$f_\infty(x,v) = \frac{\mathrm{e}^{-\left(V(x)+\frac{|v|^2}{2}\right)}}{Z}$$ with $$Z$$ a normalization constant making $$f_\infty$$ a probability density in $$(x,v) \in \mathbb{R}^n \times \mathbb{R}^n$$, and we easily have $$\frac{1}{2} \frac{d}{dt} \int h^2 d\mu = -\int |\nabla_v h|^2 d\mu$$. Then the author says under suitable assumptions on $$V$$, we can find suitable constants $$a,c, K>0$$ so that $$\frac{d}{dt}\left(\int h^2 d\mu + a\int |\nabla_x h|^2 d\mu + c\int |\nabla_v h|^2 d\mu \right) \leq -K\left(\int |\nabla_v h|^2 d\mu + \int |\nabla_v\nabla_x h|^2 d\mu + \int |\nabla_v\nabla_v h|^2 d\mu\right).$$ However, I have no clue why the above inequality holds (and justifying it in 1D should be enough for me, i.e., in the case $$(x,v) \in \mathbb{R}\times\mathbb{R}$$). What I did is the following (in 1D setting). Set $$I(t):=\left(a\int |\nabla_x h|^2 d\mu + c\int |\nabla_v h|^2 d\mu \right).$$ Then \begin{align*} \frac 12\frac{dI}{dt} &= -a\int |\partial_v\partial_x h|^2 d\mu - c\int |\partial_v\partial_v h|^2 d\mu - c\int |\partial_v h|^2 d\mu\\ &\quad \color{red}{+ a\int \partial_x h \partial_x\left(V'(x)\partial_v h\right) - v\partial_xh\partial_{xx}h~d\mu} \\ &\quad \color{red}{+c\int V'(x)\partial_vh\partial_{vv}h - \partial_vh\left(\partial_x h+v\partial_v\partial_xh\right)~d\mu} \end{align*} But I have no clue as to the treatment of the terms in red. Any help would be greatly appreciated!


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# MIT-Harvard-MSR Combinatorics Seminar

## Schedule 1995 Fall

Organizer: Jim Propp

### Wednesday, September 20, 4:35 p.m.; MIT, room 2-338

Joseph Bonin (GWU and MIT)

Matroids with no (q+2)-point-line minors

We are concerned with U(q), the class of matroids containing no minor isomorphic to the (q+2)-point line. This class is of interest in part because of its connections with representability questions and its role in extremal matroid theory, in particular, in connection with size functions.

For any prime power q, L(q) is a subset of U(q), where L(q) is the class of matroids representable over GF(q). In 1958, Tutte proved that L(2) = U(2). We will give a new proof of Tutte's theorem and sketch several other applications of the techniques used.

For prime powers q>2, the (q+2)-point line is not the only excluded minor for GF(q)-representability. However, we show that with enough points in a geometry, the (q+2)-point line is the only minor one must exclude to guarantee that the geometry is representable over GF(q). Indeed, such geometries are uniquely representable over GF(q). We will apply these ideas to bound the size function of U(q) and to obtain a simple counting characterization of affine space.

### Friday, September 22, 4:35 p.m.; MIT, room 2-338

William Jockusch

Antisymmetric monotone triangles and domino tilings of quartered Aztec diamonds

In earlier work it was shown that the Aztec diamond of order n has 2^{n(n+1)/2} domino-tilings, and connections were established with monotone triangles and alternating sign matrices. In this talk I will describe follow-up work that establishes formulas for the number of domino-tilings of a quarter'' of an Aztec diamond of order n, with different formulas depending on exactly how the quartering is done as well as on the residue of n mod 4.

This turns out to be a special case of a more general enumeration problem, where the number of domino-tilings of a certain kind of region is always equal to a power of 2 times the dimension of a particular representation of a Lie algebra. Our method of proof uses a weighted count of certain sorts of monotone triangles. Interestingly, if one considers other enumeration problems for these monotone triangles, one gets conjectural product-formulas that generalize earlier conjectures of Mills, Robbins and Rumsey.

This is joint work with Jim Propp.

### Friday, September 29, 4:35 p.m.; MIT, room 2-338

Karen Collins (Wesleyan)

Symmetry breaking in graphs

A classic elementary problem with a surprise answer is the following: if a circular key ring holds n identically shaped keys, and in order to tell them apart, we plan to affix to each one a colored label, what is the minimum number of different colors needed to distinguish the keys? The surprise is that if n is at least 6, there need only be 2 different colors of labels; but if there are three, four, or five keys on the ring, there must be 3 different colors of labels. If we consider the keys as vertices in the n-cycle, then the effect of the labels on the vertices is to destroy every symmetry of the n-cycle.

Define a labeling of a graph G, l:V(G) --> {1,2,...,r}, to be _r-distinguishing_ if no automorphism of G preserves all of the vertex labels. Then a natural question is, for any graph G, what is the minimum r such that G is r-distinguished? For an n-cycle, the answer is 3 if n=3,4,5 and 2 if n is at least 6. For a complete graph on m vertices, the answer is m. We give a bound on the minimum distinguishing number of a graph in terms of the order of its automorphism group, as well as finding the distinguishing numbers of graphs whose automorphism groups are abelian, dihedral, S_3, or S_4.

This is joint work with Michael Albertson.

### AMS meeting at Northeastern, October 7 & 8

Participants in the MIT combinatorics seminar may be interested in attending the special session on "Representation Theory and Combinatorics" that will be held at Northeastern University as part of the AMS regional meeting on October 7 and 8.

SPECIAL SESSION ON REPRESENTATION THEORY AND COMBINATORICS

            Saturday, October 7

8:30 am   C. Kenneth Fan (Harvard University)
9:00 am   Peter Magyar (University of Utrecht)
9:30 am   Mark Shimozono (Massachusetts Institute of Technology)
10:00 am   Francesco Brenti (University of Perugia)
10:30 am   J. Matthew Douglass (University of North Texas)

2:30 pm   Philip Hanlon (University of Michigan)
3:00 pm   Daniel Rockmore (Dartmouth College)
3:30 pm   David  Grabiner (Hebrew University)
4:00 pm   Curtis Greene (Haverford College)

4:45 pm   John Stembridge (University of Michigan)
5:15 pm   Robert Proctor (University of North Carolina)
5:45 pm   Adriano Garsia (University of California at San Diego)

Sunday, October 8

8:30 am    Sheila Sundaram (University of Miami)
9:00 am    Michelle Wachs (University of Miami)
9:30 am    Victor Reiner (University of Minnesota)
10:00 am   William  Doran (California Institute of Technology)
10:30 am   Mark Haiman (University of California at San Diego)

2:30 pm   Alexander Kirillov, Jr. (Yale University)
3:00 pm   Pavel Etingof (Yale University)
3:30 pm   Bernard Leclerc (University of Paris VII)

4:15 pm   Toshiki Nakashima (University of Osaka)
4:45 pm   Yan Soibelman (Kansas State University)
5:15 pm   Eugene Stern (University of California at Berkeley)

SPECIAL SESSION ON ERGODIC THEORY

            Saturday Morning

8:30    Bruce Kitchens
Dynamics of Markov groups
Topological conjugacy of endomorphisms of the 2-torus
9:30    Jane Hawkins
Characterizing mildly mixing actions using ratio sets and orbit equivalence.
10:00   Aimee S.A. Johnson
Loosely Bernoulli in $Z^d$
10:30   Cesar Silva
Relatively weak mixing and infinite skew product entropy
Dyadic equivalence to actions of completely positive entropy
4:00    Janet Whalen Kammeyer
Restricted Orbit Equivalence for Actions of Discrete Amenable Groups
4:30    Jonthan King
Interrelations between determinism, zero-entropy and orbit separation
5:00    Andres del Junco
Construction of simple measure-preserving maps with prescribed automorphism group
5:30    Nicholas S. Ormes
Strong Orbit Realization for Minimal Homeomorphisms

Sunday Morning

8:30    Robbie Robinson
Finite type property and topoloogical dynamics for polyominoe tiling dynamical systems
9:00    Boris Solomyak
Ergodic theory of non-periodic tilings.
Ergodic theory and the symmetry of tilings
10:00   James Propp
A law of large numbers for the random domino tiling process
2:30    Geoff Goodson
$G$-Maps in the Centralizer of Compact Abelian Group Extensions.
The Mean-Ergodic Theorem and Spectral
Decomposition of Complete isometries
Comparison of Generalizations of the Hopf Decomposition.

SPECIAL SESSION ON GEOMETRIC AND HYPERBOLIC DYNAMICS

            Organizers: Zbigniew Nitecki,   ZNitecki(at-sign)Tufts.edu, Tufts University Boris Hasselblatt,  BHasselb(at-sign)Tufts.edu, Tufts University

Current information about  this session  is available  on the  Worldwide  Web under  the  URL  http://www.tufts.edu/~bhasselb/amsmtg.html,   and  from  the organizers.

Saturday, October 7

9:30   Juan Tolosa (Stockton College of New Jersey)
Pattern families
10:00   Marco Martens (SUNY Stony Brook)
Hyperbolicity of Circle Renormalization
10:30   Mark Levi (Rensselaer Polytechnic Institute)
Deterministic randomness with positive probability
2:40   Michael Shub (IBM)
Stable Ergodicity and Partial Hyperbolicity (40 minutes)
3:30   Slobodan Simic (UC Berkeley)
Synchronization of Anosov flows
4:00   Cymra Haskell (SUNY Stony Brook)
The Infinite Periodic Lorentz Gas is Space-Time Bernoulli
4:30   Amie Wilkinson (UC Berkeley)
Stable ergodicity of maps arising from geodesic flows
5:00   Fern Hunt (National Institute of Standards and Technology)
Approximation of Attractors by Ulam's Method

Sunday, October 8

KAM theory and the Fermi-Pasta-Ulam string model
9:30    Tasso Kaper (Boston University)
Hyperbolicity in near-integrable N degrees-of-freedom Hamiltonian systems
10:00   Pau Atela (Smith College)
A remarkable global bifurcation diagram in a Hamiltonian system
10:30   Dmitri Kleinbock (Yale University)
Nondense orbits of flows on homogeneous spaces
2:30    Andrei Torok and Viorel Nitica (Princeton U. & Indiana U. Bloomington)
Regularity of solutions for cocycle equations
3:00    Alexei Kononenko (Pennsylvania State University)
Cohomologies of group actions and their applications
3:30    Nantian Qian (Yale University)
Smooth conjugacy for Anosov diffeomorphisms and rigidity of
Anosov actions of higher rank lattices
4:00    Henk Bruin (Universitat Erlangen)
Cantor-attractors for interval maps

Stan Eigen would like to invite all participants to the following event:

Ig Nobel Award Ceremony
October 6, 1995, 7:30 PM
Lowell Hall, Harvard University

(Tickets need to be bought in advance; contact info(at-sign)improb.com.)

SPECIAL SESSION ON GEOMETRIC AND GRAPH THEORY

            Saturday, Oct. 7, 1995

8:30   Nancy Eaton, Univ. of Rhode Island
9:00   C. Zhang, W. Virginia University
9:30   Ruth Haas, Smith College
10:00  Claude Tardif, University of Montreal
10:30  Gena Hahn,  University of Montreal

2:30   Gara Pruesse, University of Vermont
3:00   Lenwood Heath, Virginia Polytech Inst. & State Univ.
3:30   Kathy McKeon, Conn. College

4:00  BREAK

4:30   Linda Lesniak, Drew University
5:00   Daniel Kleitman, MIT
5:30   Seth Chaiken, SUNY Albany

Sunday, Oct. 8, 1995

8:30   Lauren Rose, Wellesley College
9:00   Brigitte Servatius, WPI
9:30   Herman Servatius, MIT
10:00  Karen Collins, Wesleyan Univ.
10:30  Michael Albertson, Smith College

2:30   Ann Trenk, Wellesley College
3:00   Ken Bogart, Dartmouth College
3:30   Ross McConnell, Amherst College

4:00 BREAK

4:30   Dave Berman, Univ. of New Orleans
5:00   Emily Petrie, Arizona State Univ.
5:30   Kathleen Romanik, DIMACS

### The NOETHERIAN RING at MIT, Friday, October 6, 5:00pm in room 2-136, MIT

Biweekly half-hour talks given by women in mathematics followed by a half-hour for socializing and refreshments.

Professor Lynne M. Butler, Haverford College

An example of the topological perspective in combinatorics

Many beautiful theorems in algebraic topology have analogues in the theory of partially ordered sets. For example, Stanley discovered an Alexander duality theorem for Eulerian posets. In this talk we show how an observation of Matveev's, on how to compute the M\"obius number of a poset from edge coverings of its incomparability graph, may be quickly deduced from Stanley's Alexander duality theorem.

### Wednesday, October 11, 4:35 p.m.; MIT, room 2-338

Joseph Bonin (George Washington University and MIT)

A survey of Dowling lattices

Dowling lattices arose in connection with the theory of linear codes and as q-analogs of partition lattices, and they were quickly seen to be of use for studying arrangements of hyperplanes. These geometric lattices also provided the motivation for biased graphs, and, like projective spaces and free matroids, they are the universal models for one of the five types of varieties of combinatorial geometries. This talk will provide an introduction to these lattices and will outline several recent advances in the theory.

The first class of results to be treated brings out similarities between Dowling lattices and projective spaces. This includes an axiom scheme for Dowling lattices, analogs of Desargues' and Pappus' theorems, and a coordinatization theory analogous to that for projective spaces. We will also present an application of the automorphism theory for Dowling lattices.

The second collection of results to be discussed involves the Tutte polynomial, the matroid counterpart of the dichromatic polynomial of graph theory. The Tutte polynomial of any matroid contains much information about the matroid, and this is especially true for Dowling lattices. We will explore exactly how much information about a Dowling lattice is reflected in its Tutte polynomial.

### Friday, October 13, 4:15 p.m.; MIT, room 2-338

Tal Kubo (Harvard)

Conway's recursive sequence

Sequences obeying a(n) = a(a(n-1))+a(n-a(n-1)) have been explored by Conway, Hofstadter, Mallows, Kleitman and others. They have beautiful and intricate properties: combinatorial (symmetry, self-similarity), analytic (asymptotics related to the Gaussian distribution), and arithmetic (e.g., a(2^n)=2^{n-1}). We will show that a(n) can be viewed not as a complicated sequence, but as a simple compression operation on finite sets. Combinatorial structures including trees, Fibonacci and Catalan numbers, refinements of Pascal's triangle, and a mysterious appearance of Nim-like games, are encountered on the way. (These results were obtained in collaboration with R. Vakil.)

### Wednesday, October 18, 4:35 p.m.; MIT, room 2-338

Thomas Sundquist (Dartmouth)

Pfaffians and theta functions

The classical theory of Elliptic Functions gives rise to many interesting theta function identities such as P(b+e) P(b-e) P(c+d) P(c-d) - P(b+d) P(b-d) P(c+e) P(c-e) + q^(c-d) P(b+c) P(b-c) P(d+e) P(d-e) = 0, where P is a rescaled version of Jacobi's third theta function. The proofs of these identities typically are analytic, or rely on invoking standard facts about the finite dimensional space of modular forms of a given weight. Other theta function identities, like Jacobi's Triple Product which factors a theta function into three infinite products, have nice combinatorial interpretations and proofs. In this talk I will discuss a simple "symmetric function theory" proof of a generalization of the former identity. The technique involves expressing the combination of theta functions as the Pfaffian of a 4 by 4 skew-symmetric matrix, and then expanding the Pfaffian as a (vanishing) sum of alternants. Finally, we generalize the proof to give interesting expansions for Pfaffians of other "theta-like" functions.

### Friday, October 20, 4:15 p.m.; MIT, room 2-338

Ruth Haas (Smith)

Decomposing graphs into trees

The original characterization for when a graph can be decomposed into k spanning forests was given by Nash-Williams in 1964. In this talk we give several old and new characterizations for the following two classes of graphs: (i) graphs for which adding _some_ m edges produces a graph which is decomposable into k spanning trees, i.e., the graph has arboricity k; and (ii) graphs for which adding _any_ m edges produces a graph which is decomposable into k spanning trees.

The study of the second of these is motivated by some results in combinatorial rigidity. In particular, a graph is rigid in the plane if it can be "constructed" using rigid bars for the edges and rotatable joints for the vertices so that the only possible motions in the plane are translation and rotation. Lovasz and Yemini showed that a graph is minimally rigid in the plane (removal of any edge would make it not rigid) if and only if adding any edge to the graph, including a multiple edge results in a graph which is decomposable into 2 spanning trees. A recent paper of Crapo gives another characterization of this class and it is this characterization that we extend to other cases.

### Wednesday, October 25, 4:15 p.m.; MIT, room 2-338

C. Kenneth Fan (MIT):

Matchings and canonical forms for symmetric tensors

Let V be a q-dimensional vector space. Fix a set B of q(q-1) monomials in S^p(V) of the form x^I where i_k>0 for all k. The generic element of S^p(V) is conjugate under a suitable linear transformation to an element with support off of B. We prove this by showing the existence of a perfect matching with a unique weight in a certain weighted bipartite graph. Such a perfect matching corresponds to the non-vanishing of an appropriate determinant.

This is joint work with Jozsef Losonczy.

### Friday, October 27, 4:15 p.m.; MIT, room 2-338

Greg Kuperberg (Yale)

Alternating-sign matrices and the Yang-Baxter equation

Robbins conjectured, and Zeilberger recently proved, that there are

             1!4!7!...(3n-2)!
------------------
n!(n+1)!...(2n-1)!

alternating sign matrices of order n. We will discuss a new proof of this result using an analysis of the six-vertex state model (also called square ice) based on the Yang-Baxter equation.

### Friday, November 3, 4:15 p.m.; MIT, room 2-338

Richard Stanley (MIT)

Hyperplane arrangements, interval orders, and trees

Abstract: A (real) hyperplane arrangement is a finite set of affine hyperplanes in R^n. A central problem in the theory of hyperplane arrangements is to count the number of regions into which the hyperplanes subdivide R^n. For instance, the number of regions of the arrangement (known as the _braid_arrangement_) consisting of all hyperplanes x_i = x_j, i<j, is easily seen to be n!. We will consider some modifications (deformations) of the braid arrangement and show some surprising connections with such topics as interval orders and the enumeration of trees. In particular, there is an explicit conjecture for the number of regions of the arrangement x_i - x_j=1, i<j. Much of this work was done in collaboration with Nati Linial, Igor Pak, Alexander Postnikov, and Schmulik Ravid.

The cost will be $7 for grad students and undergraduates (not counting alcoholic beverages), with the rest of us making up the difference. ### Wednesday, November 8, 4:35 p.m.; MIT, room 2-338 Ira Gessel (Brandeis) Counting binary trees by ascents and descents The number of unlabeled binary trees on n vertices is the Catalan number C_n={1 \over n+1}{2n \choose n}, so the number of labeled binary trees is n! C_n. We call a vertex of a labeled binary tree (with totally ordered vertices) a _left_ascent_ if it is a left child and is greater than its parent, and we define right ascents and left and right descents similarly. In this talk I will count labeled binary trees by left and right ascents and descents. Special cases yield Eulerian numbers and the number (n+1)^{n-1} of labeled rooted forests. There are also some non-obvious symmetries: There is a symmetry that switches left ascents with right descents, and by allowing repeated labels we obtain symmetric functions which I conjecture to be Schur-positive. ### Seventeenth One Day Conference on Combinatorics and Graph Theory Saturday, November 11, 1995 10 a.m. to 4:30 p.m. at Smith College Northampton MA 01063 10:00 Esther Tesar (Drew University) Some Extensions of the Genus Distribution of Closed-End Ladders Laszlo Lovasz (Yale University) The Matching Structure of Graphs Lunch Joe Bonin (George Washington University) A Survey of Dowling Lattices Ileana Streinu (Smith College) Visibility in Pseudo-Polygons and Vertex-Edge Pseudo-Visibility Graphs Our Web page site has directions to Smith College, abstracts of speakers, dates of future conferences, and other information. The address is: http://math.smith.edu/~rhaas/coneweb.html We have received an NSF grant to support these conferences. This will allow us to provide a modest transportation allowance to those attendees who are not local. ### Wednesday, November 15, 4:35 p.m.; MIT, room 2-338 Miklos Bona (MIT) Permutations avoiding certain patterns It is a long-studied, hard problem to determine how many permutations in S_n avoid a certain pattern q. The general conjecture claims that less than K^n, where K is a constant. Efforts to prove this have been unsuccessful for most patterns. (For two permutations a and b, it is NP-complete to decide whether a is a pattern of b; the problem of counting permutations in S_n avoiding q is #P-complete. Thus in general all we can expect is an upper bound or an asymptotical formula, not an exact formula). The only important cases in which the conjecture is known to be true were when k = 3 or when the pattern is monotonic. We improve these results showing that the_conjecture_on_the_exponential_ upper_bound_is_true_for_all_patterns_of_length_4. A conjecture states that if S_n(q_1) < S_n(q_2) for some n, then this inequality holds for all N > n. We prove this conjecture for patterns of length 4. These are the first results proving that one pattern is more likely to occur in a random permutation than another one. (Even in the asymptotical sense). Finally, we prove a lemma which allows us to extend our results to some longer patterns. ### Friday, November 17, 4:15 p.m.; MIT, room 2-338 David Jackson (Waterloo) The genus series for monopoles and the Euler characteristic for the moduli spaces of real algebraic curves This question was solved for the complex case in 1986 by Harer and Zagier. A later argument was given by Penner. The real case, however, has remained open. In this talk I will give two arguments, that are combinatorial ones, which appeal 2-cell embeddings of graphs. The first argument is based on determining the genus series for monopoles (these are maps with one vertex) in locally orientable surfaces. This is of interest in its own right. The moduli space question can be expressed as a particular monopole problem (joint work with Goulden and Harer). This second problem can be treated by a classical theorem about multivariate integrals, to give a very simple explicit expression for the Euler characteristic. The integral representation for the case of orientable surfaces can also be given, and this gives a proof of the original result of Harer and Zagier that is direct. ### APPLIED MATHEMATICS COLLOQUIUM Monday, November 20, 4:15pm, 2-105 Gil Kalai, Institute for Advanced Study and Hebrew University All Monotone Graph Properties Have Sharp Thresholds In their seminal work which initiated random graph theory Erd\"os and R\'enyi discovered that many graph properties have sharp thresholds as the number of vertices tends to infinity. That is, if every edge of the graph is chosen with probability$p$, then when$p\$ increases, the transition from a property being very unlikely to its being very likely is very swift.

We prove a conjecture of Linial that every monotone graph property has a sharp threshold. This result applies to random subgraphs of arbitrary symmetric graphs. We will discuss the relation between the symmetry group and the length of the transition interval.

### Wednesday, November 29, 4:35 p.m.; MIT, room 2-338

All of Us (from All Over the Boston Area)

Open Mike Session / Combinatorial Free-for-All

Here's another chance to share partial results, open questions, and nice ideas that aren't suited to the 50-minute talk format. Presenters will include Gian-Carlo Rota, Dan Kleitman, and Christos Athanasiadis. Let Jim Propp know ahead of time what you're bringing, if you plan on presenting something that will take longer than five minutes.

### Wednesday, December 6, 4:35 p.m.; MIT, room 2-338 *and* Friday, December 8, 4:15 p.m.; MIT, room 2-338

Gian-Carlo Rota (MIT)

A formal theory of resultants

Part I: The Cliffordization of Hopf algebras

Part II: Explicit formulas for resultants

A formula for the resultant of n homogoneous polynomials will be given. This formula can be used to derive all known properties of resultants without recourse to elimination theory.

Those who attend are expected to know basic notation of Hopf algebras.

### Wednesday, December 13, 4:35 p.m.; MIT, room 2-338

Heidi Burgiel (Geometry Center)

Symmetric embeddings of regular maps: regular skew polyhedra

The label "regular polytope" can be applied to objects ranging from Platonic solids to simplicial complexes. The object of this talk is to describe methods of taking regular maps --- regularly tiled 2-manifolds --- and embedding the vertices of the tilings in Euclidean space to form objects called regular skew polyhedra. These polyhedra have all the symmetries dictated by the automorphism group of the underlying manifold, but may not have planar faces. They need not even lie in three dimensional space!

For example, a sphere can be regularly tiled with pentagons. One realization of this map is the dodecahedron. More interestingly, a torus can be tiled with squares. As Coxeter and Petrie discovered in 1926, this map can be realized in four dimensions as a polyhedral surface with square faces and "skew square" vertex figures.

In my talk I will describe more skew polyhedra, and review the methods I used to discover them. These methods, involving association schemes and representation theory, can be extended to provide symmetric realizations of any graph or polytope whose automorphism group is vertex-transitive.

## Archive

All announcements since Fall 2007 are in the Google Calendar


text:
# Question 398ac

Apr 4, 2016

A few ideas below...

#### Explanation:

Not to sure on the context of this, but if you are using the laws of Simple Harmonic Motion to determine say, gravity, using T=2pisqrt((L/g)#
Then:

1. A pendulum only exhibits SHM for small displacements (systematic error if too large)
2. You should measure the period by determining the time of as large a number of oscillations as possible (reducing random errors)


text:
# Change UUID of VirtualBox vdi

Looking for quick way to reuse a vdi I preped with Windows XP SP3 and recent updates, I decided to duplicate the vdi with Windows Explorer. Of course, this was too simple. After attempting to create a new virtual machine which used the newly created vdi, I was presented with a nasty error along the lines of  “Failed to open the hard disk ….” and “Cannot register the hard disk C:\path\to\new\vdi with UUID {xxxx} because a hard disk C:\path\to\old\vdi already exists in the media registry (C:\path to VirtualBox.xml)

Luckily there is a simple fix for this…

Lauch a command prompt and browse to where VBoxManager.exe is located (for me this is C:\Program Files\Oracle\VirtualBox) and run the comand below

VBoxManage.exe internalcommands setvdiuuid "C:\path\to\new\vdi"

NOTE: the command has been changed to sethduuid in version 4.0.4 (thanks Isaac!). So the commad in 4.0.4 would be…

VBoxManage.exe internalcommands sethduuid "C:\path\to\new\vdi"

Which should return something similar to “UUID Changed to …”

{ 47 comments… add one }

• Isaac W. March 17, 2011, 8:57 pm

With version 4.0.4, use “sethduuid” instead of “setvdiuuid.”

Reply
• Shaik June 8, 2011, 6:30 am

Its Working fine.
Thanks a Lotttttttt

Reply
• M.Back June 17, 2011, 10:43 am

thanks a lot fot that good description!

Reply
• Mostafa July 1, 2011, 1:37 am

Extreme big hug thank u !!!
the manual really sucks and u give it like a glance :d

Reply
• Amyo Rahman July 6, 2011, 3:42 pm

Thanks!!

Reply
• MS July 22, 2011, 2:15 pm

Thanks for sharing, this helped for sure!

Reply
• Dave K August 29, 2011, 4:45 am

Genius! What a life saver! Many Thanks

Reply
• Neeraj Pansari September 29, 2011, 7:17 am

Thanks for the detailed info.
It is easy and it works fine

Reply
• Asadi October 24, 2011, 1:03 am

Thanks, I used “sethduuid” instead of “setvdiuuid.”

Reply
• Sergey November 28, 2011, 10:22 am

Thanks a lot! It’s helped me on 4.1.6 version, I uses “sethduuid”

Reply
• Ricky November 30, 2011, 3:34 am

It solved my problem, thank you very much.

Reply
• Jim December 2, 2011, 12:40 pm

Worked on a VMDK (VMWare) disk as well (that I’m using under VirtualBox). I pulled many hairs over the last few days until I found your post – thank you.

Reply
• liming December 5, 2011, 8:16 am

thank you ! 终于知道解决方法了……（NOTE: the command has been changed to sethduuid in version 4.0.4 (thanks Isaac!). So the commad in 4.0.4 would be…）

Reply
• Richard Hundhausen March 6, 2012, 2:31 pm

Thanks Randall. You saved me some time today!

Reply
• sammi April 24, 2012, 7:30 am

Thanks alot

Reply
• LazerFX April 30, 2012, 11:30 am

Thanks, you just saved me a load of time This blog-post is going in my bookmarks for sure. Like others, I used the new (sethduuid) command format, with VirtualBox 4.1.12

Reply
• Adam May 4, 2012, 1:38 pm

When I try to run sethduuid on 4.1.14 using this command:

vboxmanage internalcommands setheuuid “E:\vm.vdi”

I get the following error:

VERR_FILE_NOT_FOUND at D:\tinderbox\win-4.1\src\VBox\Storage\VD.cpp(4484) in function VDOpen
VBoxManage.exe : error: Cannot open the image : VERR_FILE_NOT_FOUND

I have no D: drive and have nothing to do with tinderbox. Help!

Reply
• R. Kent May 7, 2012, 2:03 pm

Adam -

Can you confirm your .virtualbox file is pointing to the correct location of the vdi?

Reply
• Adam May 7, 2012, 2:33 pm

Yes, and no reference anywhere to a D: drive.

Reply
• Adam May 7, 2012, 3:43 pm

SOLVED – turns out vboxmanage is case sensitive when looking at path and file names.

Simple solution!

Reply
• hamid May 10, 2012, 8:50 am

thanks a lot !
Good answer

Reply
• Arnold June 5, 2012, 5:33 am

Its works great ! Thx

Reply
• Thodoris June 25, 2012, 2:22 pm

thank you…. It was just driving me crazy

Reply
• Jason September 1, 2012, 1:10 am

Thanks a lot!
That’s so easy

Reply
• Alex November 2, 2012, 6:01 pm

Thanks a lot! Resetting the uuid via cmd totally fixed my problem. You’re the man!!

Reply
• Jun November 24, 2012, 1:39 pm

Thanks a lot ! My problem was solved!

Reply
• Taher December 13, 2012, 11:39 am

Thx a mil

Reply
• Rahul December 27, 2012, 1:37 am

Thanks a lot!
It was really useful for me to save my time….

Reply
• Tamil Astrology January 16, 2013, 9:41 am

Thank you very much. I knew there was a solution and it was in the back of my mind. Your link was the first entry when I searched for the solution.

I had copied a cloned image into a different location (instead of the default C: drive), which, when I tried to use, caused this error.

Reply
• Vito April 3, 2013, 9:45 am

I have use the command and I do not have any error but when i try to import the Virtual Machine Definiton file I obtain the same error. There is another way to solve the problem? Thanks.

Reply
• R. Kent June 18, 2013, 4:26 pm

Vito –

Check out @thegeekprophet’s reply with the reminder to update the UUID in the .vbox file. Let us know if that works!

Reply
• thegeekprophet April 10, 2013, 10:32 am

If it still complains, dont forget to update the UUID in the .vbox file for the drives you updated…

Reply
• Alex June 24, 2013, 11:57 pm

Thanks for posting this, worked perfectly for me! I needed to transfer a VBOX hard drive image to a different drive to save space which ought to be a common/easy function in VirtualBox, but isn’t. I copied the file and then changed the UUID with the command you posted. If you’re in Linux (Ubuntu, in my case), this is the command you’ll want to use:

vboxmanage internalcommands sethduuid pathto.vdi

Reply
• odeklas November 7, 2013, 11:01 am

Thanks a lot , saves me a headache

Reply
• sgk August 5, 2013, 3:21 am

Thanks man.. it worked perfectly..!!

Reply
• Mahdi August 19, 2013, 1:46 am

Thanks Thousands

Reply
• j September 27, 2013, 12:50 am

for version 4.2.18 what should i use instead of setvdiuuid and sethduuid

Reply
• Nick October 11, 2013, 9:04 am

Thanks.! It worked with “VirtualBox 4.2.18″

Reply
• Joakim Olsson October 15, 2013, 4:24 pm

BIG thanks for easy fix to super frustrating problem.. MAN that was one whiny moron of a hurdle…

Reply
• Henry November 8, 2013, 1:01 pm

Hey I’m trying to use this with a vhd file and I’m getting invalid UUid parameter….does this work with vhd files? I see you guys are using a vdi file…please help
Henry

Reply
• jk December 19, 2013, 1:46 am

thanks a lot!

Reply
• Mario Roberto December 19, 2013, 5:13 pm

Very useful info. Thanks a lot.

Reply
• FreyrLin January 3, 2014, 11:26 pm

Very thanks, it do helpful !
Solved my same problem on virualbox : )

Reply
• Pawblosky January 10, 2014, 11:50 am

Muchísimas gracias, me ayudó (;

Reply
• Pawblosy January 10, 2014, 11:55 am

Yo tengo la versión 4.3.6 y me sirvió con sethduuid

Reply
• Jerry March 8, 2014, 5:03 pm

Was trying to move a hard drive file and ran into this issue. Thanks for the information. Worked like a charm.

Reply
• Wild August 8, 2014, 4:50 am

Thank you. It works

Reply

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Last edited by Tojamuro
Tuesday, April 14, 2020 | History

2 edition of Sphere cells and surfaces. found in the catalog.

Sphere cells and surfaces.

Essential Structures Research Association.

# Sphere cells and surfaces.

Written in English

Edition Notes

Sponsored by Doulton Glass Industries Ltd.

The Physical Object ID Numbers Contributions Doulton Glass Industries. Pagination 32p. Number of Pages 32 Open Library OL20234396M

Biology Experiments On Cells Surface Area To Volume Ratio. Surface area / Volume ratio Experiment Introduction: The surface area to volume ratio in living organisms is very important. Nutrients and oxygen need to diffuse through the cell membrane and into the cells are no longer than 1mm in diameter because small cells enable nutrients and oxygen to diffuse . This is hardly a rigorous proof, but I think it's pretty obvious from the equations, that if you hold the volumes equal, the surface area of the torus keeps getting BIGGER, relative to the surface area of the sphere, as the major radius (R) gets bigger and bigger. So clearly, for at least these two cases, the sphere has a smaller surface area. Volume of a sphere of radius r = $$\frac{4}{3}\pi r^{3}$$ Alternatively, the formula for the volume of a sphere can also be derived as follows. Consider a sphere of radius r and divide it into pyramids. In this way, we see that the volume of the sphere is the same as the volume of all the pyramids of height, r and total base area equal to the.

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### Sphere cells and surfaces. by Essential Structures Research Association. Download PDF EPUB FB2

The book was made into the film Sphere (), directed by Barry Levinson, with a cast including Dustin Hoffman (Norman Johnson, renamed Norman Goodman), Samuel L.

Jackson (Harry Adams), Peter Coyote (Harold Barnes), Liev Schreiber (Ted Fielding), and Sharon Stone (Beth Halpern, renamed Beth Halperin).Author: Michael Crichton. A sphere (from Greek σφαῖρα —sphaira, "globe, ball") is a geometrical object in three-dimensional space that is the surface of a ball (viz., analogous to the circular objects in two dimensions, where a "circle" circumscribes its "disk").

Like a circle in a two-dimensional space, a sphere is defined Sphere cells and surfaces. book as the set of points that are all at the same distance r from a given.

A larger sphere has a relatively smaller surface area for its interior volume than does a smaller sphere, because surface area increase with size at a lower rate volume than volume does. Diffusion would be more efficient in the smaller sphere.

COVID Resources. Reliable information about the coronavirus (COVID) is available from the World Health Organization (current situation, international travel).Numerous and frequently-updated resource results are available from this ’s WebJunction has pulled together information and resources to assist library staff as they consider how to handle.

Although surface tension is present at all interfaces, it is most important for small ﬂuid bodies. At length scales where surface tension does come into play the shape of an inter-face bears little relation to the gravitational equipotential surfaces that dominate the static shapes of large-scale systems analyzed in the preceding Size: KB.

A Dyson sphere is a hypothetical megastructure that completely encompasses a star and captures a large percentage of its power output. The concept is a thought experiment that attempts to explain how a spacefaring civilization would meet its energy requirements once those requirements exceed what can be generated from the home planet's resources alone.

Only a. Thin silicon solar cells are distinguished from traditional silicon solar cells that are composed of ～mm-thick wafers or sheets of silicon. The common defining feature of a thin silicon solar cell is a relatively thin.

The primary function of red blood cells is to transport oxygen to body cells and deliver carbon dioxide to the lungs. A red blood cell has what is known as a biconcave shape. Both sides of the cell's surface curve inward like the interior of a : Regina Bailey.

A sphere is a perfectly round geometrical 3-dimensional object. It can be characterized as the set of all points located distance.

r (radius) away from a given point (center). It is perfectly symmetrical, and has no edges or vertices. A sphere has several interesting properties, one of which is that, of all shapes with the same surface area.

set of vertices (0-cells), edges (1-cells) and faces (2-cells) of the cell complex G are denoted by V, E and F. Moreover, we assume that interior v ertices Sphere cells and surfaces. book of even degree, that is, the. Essentially, a large number of adhesive receptors and ligands are randomly distributed on the surfaces of a rigid sphere and a planar wall, with individual molecules modeled as linear springs.

The motions of the cell and of each molecular bond between the cell and surface are recorded as the cell rolls over or moves relative to the other Cited by: 1.

Surface Area and Volume of a sphere. STUDY. PLAY. sphere. any spherically shaped artifact. volume of a sphere. The set of points in a space that are equidistant from a given point known as the center of the sphere.

surface area of a sphere. Unlike the surfaces of Kapouleas and Yang, these new embeddings are not symmetric with respect to any isometries of the 3-sphere exchanging.

In addition, uPAR(+) cells could differentiate into CD56(+)cells, CK(+) cells, and uPAR(-) cells. These data support the existence of a population of tumor sphere-forming cells with stem cell properties in the H SCLC cell line.

Furthermore, the stem cell population may be enriched in cells expressing the uPAR cell surface by: Surface area of a sphere is given by the formula.

Surface Area of sphere = 4πr 2. where r is the radius of the sphere. Example: Calculate the surface area of a sphere with radius cm. Solution: Surface area of sphere = 4π r 2 = 4π () 2 = 4 × × × = cm 2. Worksheet to calculate the surface area of spheres.

How to. Intrinsic Geometry of Surfaces. This note covers the following topics: The Fundamental Form of a Surface, Normal Curvature, Gaussian Curvature and The Poincare Half-Plane. Author(s): Jeff Knisley, Dept. of Math, East Tennessee State University.

Specific Surface Area of a sphere Solve. Add to Solver. Description. The surface area relative to the mass of a sphere is called the specific surface area and can be calculated by the area, the volume and the ratio of mass to volume (density) Related formulas.

Variables. SSA: Specific Surface Area (m 2 /kg) A. In general, surface area is the sum of all the shapes that cover the surface of an object.

To calculate the surface area of a sphere we multiply 4 by pi by the radius of the sphere squared. Given this formula, we can find the surface area of a sphere when given the radius.

Similarly, we can find the radius of a sphere is we are given the. One of the principle difficulties is to separate the effect of the internal contents of the cell from that of the cell surface.

In the case of red blood cells which are more simple in structure this can be done with some surity but in most other cells some uncertainty by: 1. The surface area of a sphere is cm a. Find the radius of the sphere. Round to the nearest hundredth. Find the volume of the sphere. Round to the nearest hundredth.

The surface area of a sphere is cm a. Find the radius of the sphere. Round to the nearest hundredth. Find the volume of the sphere. Round to the nearest 2. 2 File Size: 98KB. Contact between a sphere and an elastic half-space. As showed in Figure 1, an elastic sphere of radius R indents an elastic half-space to depth u, and thus creates a contact area of radius 𝑎≅(3 2 𝑅𝐹 𝐸 ∗) 1/3.

Fig. Contact stress. The depth of indentation u is given by: 𝑢≅(2𝐹. 𝐸 ∗ 2. 𝑅) 1/3. where 1 𝐸. Volume and Surface Area of Spheres (no rating) 0 customer reviews. Author: Created by rach Preview. Created: | Updated: May 7, Observation lesson which I split into 2 parts.

First Volume which has Sheet A and B attached, B is the harder of the two. Second Surface area which uses sheets C and D again the latter is harder. Sphere Example: Case 1: Find the volume and curved surface area of a Sphere with the given radius 3.

Step 1: Find the volume. Volume = (4/3)πr³ = (4/3) * * 3³ = * * 27 = Step 2: Find the curved surface area(CSA). Curved Surface Area(CSA) = 4πr² = 4 * * 3² = * 9 = The above example will clearly. This task shows how to create surfaces in the shape of a sphere. The spherical surface is based on a center point, an axis-system defining the meridian & parallel curves orientation, and angular limits.

Open the t document. Click. A radius of a sphere is a segment from the center to a point on the sphere. Sample answer: $(5 Sample answer: a diameter 62/87,21 A diameter of a sphere is a chord that contains the center.$(5 a tangent 62/87,21 A tangent to a sphere is a line that intersects the sphere in exactly one point.

Line l intersects the sphere at A. $(5File Size: 1MB. Fig. 1 illustrates a model of interfacial attachment between two spheres of radius R 1 and R 2 [].The center, O, of the local spatial frame is located at the point of minimum separation and on the surface of sphere 2. The surface of the spheres bind onto each other due to the presence of adherent elastic binders (which are polymer strands with sticky heads) attached on the floc Cited by: 5. In the book: "The Works of Archimedes", Chapter: "On the Sphere and Cylinder I" Proposition 33 is a proof of contradiction based on the previous propositions dealing with circumscribed and inscribed polyhedra surfaces. Archimedes did his Pi approximations the same way with polygons and the circle. A sort of geometry Calculus. Covers the design, production, evaluation and application of surfaces having high absorptance in the solar spectrum and low emittance at the operating temperature of the solar collection system. Presents current, significant data on the enhancement of solar collector efficiency by the use of selective surfaces. In studying spherical submanifolds as submanifolds of a round sphere, it is more relevant to consider the spherical Gauss map rather than the Gauss map of those defined by the oriented Grassmannian manifold induced from their ambient Euclidean space. In that sense, we study ruled surfaces in a three-dimensional sphere with finite-type and pointwise 1-type spherical Author: Sun Mi Jung, Young Ho Kim, Jinhua Qian. of the Sphere David Garber and Boaz Tsaban 1. INTRODUCTION. In the beginning of the twelfth century CE, an interesting new geometry book appeared: The Book of Mensuration of the Earth and its Division,by Rabbi Abraham Bar Hiya (acronym RABH), a Jewish philosopher and scientist. This book is interesting both historically and mathematically. The small sphere initially has a positive charge q, and the larger one is initially uncharged. Now the spheres are connected using a thin wire. What is the ratio of the final surface charge density of sphere 1 to that of sphere 2. The book says the answer is 2. Objective: I know how to calculate the surface area of a sphere. The surface area of a sphere is given by the formula: V = 4πr 2. If you are given the diameter, remember to first divide the diameter by 2 to get the radius before using the formula. Read this lesson on the surface area of spheres if you need additional help. Geometry Surface Area and Volume of Spheres and Hemispheres Riddle Worksheet This is a 15 question Riddle Practice Worksheet designed to practice and reinforce the concepts of finding the Surface Area and Volume of Spheres and Hemispheres. Note: This worksheet is written at a /5(23). Journal of Materials Chemistry A Platinum nanoparticles partially-embedded into carbon sphere surfaces: a low metal-loading anode catalyst with superior performance for direct methanol fuel cells † Kui Li, abc Zhao Jin, ac Junjie Ge,* ac Changpeng Liu * ac and Wei Xing * acdCited by: Spheres Date_____ Period____ Find the surface area of each figure. Round your answers to the nearest tenth, if necessary. 1) 3 ft 2) 12 cm 3) in 4) 7 cm 5) 8 in 6) 10 mi 7) A sphere with a diameter of in. 8) A sphere with a radius of 10 mi ©B E2r0b1 w26 jK Fu htLau rSzoTf nt9w eaar Hek ZLYLACz.o T QA zl al H prCiHgh6t sv drre gs File Size: 32KB. This is a stupid question, but are human cells roughly flat/planar or spherical in shape. Biology I was under the assumption that the lipid bi-layer of the plasma membrane was roughly planar due to the roughly cylindrical shape of the double-tail phospholipid molecule (as opposed to the spherical shape formed by lipid micelles due to the single. Then use three$1$-cells.$\endgroup$– Joe Johnson Nov 7 '12 at$\begingroup$@JoeJohnson With regards to your first comment, why can't I start with one$0$- cell. Because in the quotient space there is only one$0$- cell. Biological Interactions on Materials Surfaces Understanding and Controlling Protein, Cell, and Tissue Responses depends on molecular-level events that determine subsequent responses of cells and tissues. This book presents the latest developments and state-of-the-art knowledge regarding protein, cell, and tissue interactions with both. This website and its content is subject to our Terms and Conditions. Tes Global Ltd is registered in England (Company No ) with its registered office at 26 Red Lion Square London WC1R 4HQ/5(7). Muscle cells are elongated, squamous epithelial cell are flat, sperm cells are tadpole-shaped, macrophage and neutrophil white blood cells are amoeboid. Cells come in all shapes and sizes. Look at a scanning electron micrograph of almost any cell (the 3D false-colour microscope ones) and you will see that they look miniature explosions. b. Cells are the basic units of structure and function in an organism. c. Cells come only from the replication of existing cells. CELL DIVERSITY Not all cells are alike. Even cells within the same organism show enormous diversity in size, shape, and internal organization. Your body contains around to cells of around different cell.uniform area quadrilateral element surfaces, produced for example from voxel data, involves a preliminary mapping to a sphere. This is followed by optimization of the mapping by moving points on the sphere surface. The method of Gu et al. requires pre-editing of the surface, which for our application is not desirable.Count the number of spheres required given two sphere sizes?$\endgroup$– JamalS Sep 22 '14 at$\begingroup$To place them on the surface.$\endgroup$– bitted Sep 22 '14 at$\begingroup\$ What do you mean by "cover"?


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# How do you write the following in interval notation: x>3 and x ≤ 7?

$x > 3$ and $x \le 7$ would be written as: $\left(3 , 7\right]$


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# American Dream

• News
quantumcarl
I'm not too sure about what the American Dream is... I think it has to do with recognizing and actualizing opportunity. And the fact that anyone can do it.

I think its a really grand idea!

It seems to have sprouted from the suppressive effect of the Feifdoms and Landlords of the English, German and Italian traditions. America offered an escape from the tyranny of these traditions and people went for it.

What's your idea of the American Dream?

Mentor
Originally posted by quantumcarl
I'm not too sure about what the American Dream is... I think it has to do with recognizing and actualizing opportunity. And the fact that anyone can do it.

What's your idea of the American Dream?
Thats pretty much it. The main problem with it is that it is such an extrordinary thing that many (most?) people don't believe it is possible and make that a self-fulfilling prophecy.

Dissident Dan
I'm going to try to live the American Dream. I think that I have the skills to do it. However, I think that it's not possible for everyone to "live the American Dream", because that usually involves being famous or having well above average wealth..which, both of which, by definition, cannot apply to everyone.

For some of us, wealth has nothing to do with living the American Dream. In retrospect, the financial worst of times was the best of times(Apologies to Dickens).

Rgeards

Mentor
Originally posted by Dissident Dan
However, I think that it's not possible for everyone to "live the American Dream", because that usually involves being famous or having well above average wealth..which, both of which, by definition, cannot apply to everyone.
I don't believe that being famous is part of the American Dream. And if everyone were a millionaire, "average wealth" would be a million dollars.

My idea of the American dream consisted of;
Owning your own house, being able to comfortably support a family, and having the opportunity to create your own business, be your own boss, and make lots of money.

Rage Against The Machine, on the other hand, says;
Hypocrisy, Brutality, the Elite... all of which are American Dreams.

quantumcarl
Originally posted by russ_watters
I don't believe that being famous is part of the American Dream. And if everyone were a millionaire, "average wealth" would be a million dollars.

this is not unbelievable to me.

Each person is worth an infinite amount to each other person... in terms of their potential.

A factory worker can come up with the extreme best way to do something that saves the factory owner millions of dollars. It is in the owner's best interest to foster that relationship with all people. And, of course, a good relationship is recognizable in the presence of equal pay for equal efficiancy and contribution. Rewarding ingenuity only fosters more ingenuity and this can only lead to better products and production.

The woman at home with the kids can become the next Oprah or the next big Jewlery designer... or contract out her tutoring skils as a Sculptor or musician.

This type of condition was never possible under the Old World Kingdoms. People were classified and stamped and sent off to dig the coal or the field or the fresh dung.

In the American Dream a person can get a start as a coal miner or a McDonalds employee... and concentrate on a goal that they are assured of getting if they are persistant. There won't be some dark figure telling them their family belongs to it... that they owe the Landlord another 3 generations of farming to pay their great great great great granddaddies debts.

Todays economy works a little better... it is a science and it is intticately woven with the science of sociology. This is where Democracy works its way in. Tolerance of religion, creed, tradition...and this tolerance is what the american dream is founded on... the tolerance is metamorphized by the american dream where each individual has so much to offer to its Country that the Country, by way of Democratic rule, no longer must "tolerate" these various types of peoples... but will profit, as a whole, by experiencing this variety of ideas and cultures/peoples.

Thanks.

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The American Dream is a compelling myth. If you want to measure its accuracy, I guess it's fairly accurate if you are talking about the opportunites for improvement from the level at which you are at. But it's not accurate if you try to describe America as a level playing field where everyone has a fair and equal opportunity to become president, the next Michael Jordan or Michael Jackson. Then it's more like a handicap race with the most privileged starting well ahead of the pack.

Mentor
Originally posted by N_Quire
The American Dream is a compelling myth. If you want to measure its accuracy, I guess it's fairly accurate if you are talking about the opportunites for improvement from the level at which you are at. But it's not accurate if you try to describe America as a level playing field where everyone has a fair and equal opportunity to become president, the next Michael Jordan or Michael Jackson. Then it's more like a handicap race with the most privileged starting well ahead of the pack.
If you replaced the word "privileged" with "able," we'd be in near complete agreement. Though "myth" is a little strong of a word too.

Many people seem to think the American Dream should simply be handed out stapled to your US birth certificate. Thats not the way it works. You have to EARN it. Some people are not smart enough, motivated enough, or tenacious enough to earn it. But that doesn't mean it isn't available to them. Certainly some people have more obstacles to overcome than others, but that does NOT mean that there is a level of obstruction that can't be overcome. People have realized the American Dream from the worst possible starting point.

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kat
"The American Dream is "that dream of a land in which life should be better and richer and fuller for everyone, with opportunity for each according to ability or achievement. It is a difficult dream for the European upper classes to interpret adequately, and too many of us ourselves have grown weary and mistrustful of it. It is not a dream of motor cars and high wages merely, but a dream of social order in which each man and each woman shall be able to attain to the fullest stature of which they are innately capable, and be recognized by others for what they are, regardless of the fortuitous circumstances of birth or position." -James Truslow Adams, The Epic of America

Russ, I don't think that starting with wealthy, famous or in other way privileged parents has anything to do with the children's ability. The child of such parents has a head start and that head start can even compensate for a lack of ability. Just look at George W Bush.

quantumcarl
Originally posted by russ_watters
If you replaced the word "privileged" with "able," we'd be in near complete agreement. Though "myth" is a little strong of a word too.

Many people seem to think the American Dream should simply be handed out stapled to your US birth certificate. Thats not the way it works. You have to EARN it. Some people are not smart enough, motivated enough, or tenacious enough to earn it. But that doesn't mean it isn't available to them. Certainly some people have more obstacles to overcome than others, but that does NOT mean that there is a level of obstruction that can't be overcome. People have realized the American Dream from the worst possible starting point.

I agree, the proof is all over the place.

There's this guy who's been whacked with a brain hemmorage and heart failure... for whatever reasons... who is easily making 30 - 40 grand a year driving around in his little custom wheelchair... He's sold space on the thing to all the local bussinesses for advertising. Each space brings him 300 bucks a year... he's got room for about 50 ads. This guy is having fun, meeting people and raking in the cash... and he's not ripping anyone off.

He's simply living the dream

The Canadian Dream, however, is slightly different. I think it involves images of Don Cherry in a plaid, pleated miniskirt on a can of beer... and a frozen muckluck for lunch. Don't ask.

The American Dream is... you can appear on a show called Fear Factor, eat some cockroaches and worms and win $100,000 or you can go to a good graduate school, do a masters and phd in physics and then join the unemployment line. quantumcarl Originally posted by N_Quire The American Dream is... you can appear on a show called Fear Factor, eat some cockroaches and worms and win$100,000 or you can go to a good graduate school, do a masters and phd in physics and then join the unemployment line.

Why would anyone join the unemployment line (whatever that is)?

No telling for taste... or imagination (or lack thereof), I guess.

Some people would lie to you(and themselves), and claim that ability and hard work are all it takes to get teh 'American dream.' They are[//i] wrong, though, because so much of attainuing sucess depends on factors out of our hands. To claim otherwise is short-sighted, and frankly false. Who your parents are, what economic class you are born into, etc, play a HUGE role in your adult acheivements.

The people who believe otherwise are just wrong.

Dissident Dan
I would also add to that list: the intelligence that you are born with, along with other factors that are out of your control (at least, partially) that are still part of you, stuff as physical abilities and attributes.

This American Dream, is it for each individual to decide, or is it for another to tell him about?

Most wealthy Americans can truthfully say they had a very poor great grand parent.

Each of us aspires to fulfill our own dream.

Regards

quantumcarl
Originally posted by GENIERE
Most wealthy Americans can truthfully say they had a very poor great grand parent.

Each of us aspires to fulfill our own dream.

Regards

Yes, this is a natural tendency that is less prohibited in America than it is in some other countries. Cuba, on the other hand is still working on the theory that handing out food vouchers and artificially limiting incomes if people like it or not is a good, evolutionary social policy. Kind of like a worrisome nannie.

Originally posted by GENIERE
Most wealthy Americans can truthfully say they had a very poor great grand parent.

Each of us aspires to fulfill our own dream.

Regards

What I find is ironic is that those great grandparents would credit things like opportunities and luck as much as their own hard work...while their great grandchildren, who never worked for anything, would claim that people are poor simply because they aren't trying hard enough.

quantumcarl
Originally posted by Zero
What I find is ironic is that those great grandparents would credit things like opportunities and luck as much as their own hard work...while their great grandchildren, who never worked for anything, would claim that people are poor simply because they aren't trying hard enough.

Some people like being poor... that's the opportunity they've seen and that they've gone for.

Robert DeNero was a security guard at Penn Station or another. Not a big wage... Obviously his idea was not to remain in that wage category or that profession. He dreamed... he made good on his dreams... that's the American Dream... something like 20 million per picture!

My compatriot Brian Adams used to serve burgers at a restaurant that my wife almost had my first kid in... not his dream... there in poverty... there in the grease pit.

Today, Brian has met the Queen, Paul McCartney, EVERYBODY in the music buz... and has many gold records. That is the manifestation of his dreams... and he did this by seizing the opportunities available to him... that are available to everyone.

Look at Stephan Hawkings. Most people would have stayed in their hospital room and given up... (taking that opportunity over all others)... Now look at the guy!... he's even chasing his secretary around... (not that I know... simple gossip)!

quantumcarl
American Dream:

does this imply that America is asleep? A "sleeping giant"?

It could. But, originally, the term was coined by some pretty experienced and bright people. If I had the time I'd find out who exactly coined the phrase and developed the concept. If any of you by the glory of the dawning of the coming of the light dudes or dudettes know off hand who started this snowball, the american dream, please illuminate this thread with your info. Thank you very much!

kat
Originally posted by quantumcarl
American Dream:

does this imply that America is asleep? A "sleeping giant"?

It could. But, originally, the term was coined by some pretty experienced and bright people. If I had the time I'd find out who exactly coined the phrase and developed the concept. If any of you by the glory of the dawning of the coming of the light dudes or dudettes know off hand who started this snowball, the american dream, please illuminate this thread with your info. Thank you very much!

Originally posted by kat
"The American Dream is "that dream of a land in which life should be better and richer and fuller for everyone, with opportunity for each according to ability or achievement. It is a difficult dream for the European upper classes to interpret adequately, and too many of us ourselves have grown weary and mistrustful of it. It is not a dream of motor cars and high wages merely, but a dream of social order in which each man and each woman shall be able to attain to the fullest stature of which they are innately capable, and be recognized by others for what they are, regardless of the fortuitous circumstances of birth or position." -James Truslow Adams, The Epic of America

quantumcarl
Originally posted by kat

Yes, I wondered if that quote was from the originator or
an expansion on the existing idea.

Do you know which it is?
Is the statement 200 years old or more?

Obviously not since it mentions motor cars.

Did the American Dream start at the same time as Ford?

kat
Originally posted by quantumcarl
Yes, I wondered if that quote was from the originator or
an expansion on the existing idea.

Do you know which it is?
Is the statement 200 years old or more?

Obviously not since it mentions motor cars.

Did the American Dream start at the same time as Ford?

The term was first coined in Adams novel, The Epic of America. The book was published in the early 193o's during the worst of the depression. I believe Adams expressed that the "American Dream" had always existed, that in fact it was the ideal that our country was built upon. I think Ford's automobile production started a few decades before that.

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Dissident Dan
It looks like we have a way to go, then. Hopefully, we can continue to make progress.

quantumcarl
Originally posted by kat
The term was first coined in Adams novel, The Epic of America. The book was published in the early 193o's during the worst of the depression. I believe Adams expressed that the "American Dream" had always existed, that in fact it was the ideal that our country was built upon. I think Ford's automobile production started a few decades before that.

Thank you kat...

that's pretty wild... James Truslow Adams... identifier of a certain, very healthy quality of the United States of America. Excellent!

Canadian Dream? The return of the fashionablity of shag carpets and black light posters. (not really) actually, I couldn't tell ya.

Could be more something like Gold Fever.. we had quite a bout of that back before the depression... it was a big boom for the Cnd Northwest.
We learned a bit of independence then.

People left their Landloards and Kingdomes and Servitile existences and struck out to become independent prospectors and dream-makers. The Gold Rush could have been the seed of our dream. As nightmarish as it may have been! Thanks again

Originally posted by quantumcarl
Some people like being poor... that's the opportunity they've seen and that they've gone for.

This is one of the most ignorant things I have ever read...pretty impressive! How do you explain poor people with two jobs? I know ALOT of them.

Mentor
Originally posted by Zero
This is one of the most ignorant things I have ever read...pretty impressive! How do you explain poor people with two jobs? I know ALOT of them.
They should get better jobs. Not enough school or training? Get some. There is no excuse for an able-bodied/unburdoned person being poor in the US.

kat
Originally posted by russ_watters
They should get better jobs. Not enough school or training? Get some. There is no excuse for an able-bodied/unburdoned person being poor in the US.

There are just too many possible impacting factors in life that could undermine this outlook, even for the able bodied and highly educated. I know people here in Maine who have worked hard all their lives, lost their jobs through the closing of so many of the mills here, many of them with college educations and still unable to get jobs, competing with 100's for jobs in positions on the level of a cashier at a pizza place. Often hard working people with multiple jobs can't afford to stop working in order to get further education, and today more then ever perhaps..it is very clear that a degree isn't the key to success it used to be.

Originally posted by kat
There are just too many possible impacting factors in life that could undermine this outlook, even for the able bodied and highly educated. I know people here in Maine who have worked hard all their lives, lost their jobs through the closing of so many of the mills here, many of them with college educations and still unable to get jobs, competing with 100's for jobs in positions on the level of a cashier at a pizza place. Often hard working people with multiple jobs can't afford to stop working in order to get further education, and today more then ever perhaps..it is very clear that a degree isn't the key to success it used to be.

All good points...and to me, sometimes it seems like people who ignore these points want to maintain the illusion that everything they have is based solely on hard work, and want to discount things like their parent's ability to help, luck, being in the right place at the right time, etc.

quantumcarl
Originally posted by Zero
All good points...and to me, sometimes it seems like people who ignore these points want to maintain the illusion that everything they have is based solely on hard work, and want to discount things like their parent's ability to help, luck, being in the right place at the right time, etc.

I think its all about recognizing opportunity.

If you don't know how to recognize opportunity... you will miss out on it. So... if you're in the right place at the right time... if you have parents willing to help you or educate you... if you have a large lump of quartz impregnated with gold in front of you... and you are unable to recognized these gifts and opportunities (for whatever reason)... then... yer screwed.

That's why its a good idea to get a well rounded education or to offer one to your children. Education is the key to recognizing a good opportunity as opposed to a stinky one.

One thing evident in the past in America is the opportunity for people to advance their education. This, perhaps, is the foundation of the American Dream. Mind you... the europeans who came to this continent... with a ruck sack and a family of 18... would say the foundation of the American Dream was the large amounts of free land being offered. But, it still took some education to recognize this offer as a good thing.

Originally posted by quantumcarl

That's why its a good idea to get a well rounded education or to offer one to your children. Education is the key to recognizing a good opportunity as opposed to a stinky one.

One thing evident in the past in America is the opportunity for people to advance their education. This, perhaps, is the foundation of the American Dream. Mind you... the europeans who came to this continent... with a ruck sack and a family of 18... would say the foundation of the American Dream was the large amounts of free land being offered. But, it still took some education to recognize this offer as a good thing.

On teh other hand, if a kid only gets one meal a day, and lives in poverty, how good of an education can he get?

quantumcarl
Originally posted by Zero
On teh other hand, if a kid only gets one meal a day, and lives in poverty, how good of an education can he get?

In this case, your right... the basic needs are to be met for your children. This helps to build a strong constitution upon which to build a strong education. This is where parents... practical and experienced or educated parents come in handy.

However, the children who learn to survive on one meal a day and still enjoy life are often the ones that learn, early on, what a good opportunity looks like. It looks like two meals a day, maybe... or a tricycle with wheels that work. Whatever. Kids are smart. If they don't get what their body is asking for... they go out and find it.

There are a ton of success stories out of America that speak of children who had nothing growing up. This condition made them hungry for the things they didn't have. It also made them appreciate the little things. Consider Elvis, for example. If you're American you probably know more stories than me.

The other factor... glaringly obvious... is the parenting of the child. In some cases the parents had no scruples... were too drunk... too hung up on their own trips... to get down and provide a good example for their children. The provision of good examples of values, respect of others... etc... seem to help the impoverished or any child grow up and succeed in their "American Dream".

Values, good manners and respect don't cost squat. These are perhaps some of the other components of the American Dream. Why is it that they are beginning to become extinct? Who knows... perhaps its natural for all things to go the way of the Pteridactyl.

Raven
The American dream is simply that -- a dream.

It just doesn't add for me. There are no gains with no losses. When someone rises another falls. All are taught to strive for the highest gains, but it is never mentioned how many will suffer. The hierarchy that exists in a capitalistic society is built on an elite top with a huge bottom base of low and medium range wage workers who support them. Without this structure it may collapse.

Everyone will strive to rise, but in reality the system can only allow a few to actually move up. In time the base will increase the the top will shrink. Dismal thinking I know, but that's how I see it.

Needless to say, the opportunities that exist in America are abundant, unfortunately the greed that feeds it tends to be self-destructive to the country and the world in general. This country's wealth in my opinion has prospered on other countries means as well as on its own citizens. I personally think the dream should be revised to take what you need and make sure to contribute back what you can. Capitalism in itself isn't the problem but like all systems it has its flaws. The death of a capitalistic system will be caused by those who horde (that could probably to all systems).


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# Operators

Even though the Observable is the foundation, reactive extensions is mostly useful because of its operators. Operators are the essential pieces that allow complex asynchronous code to be easily composed in a declarative manner.

## What are operators?

There are two kinds of operators:

## Pipeable operators

Pipeable Operators are the kind that can be piped to Observables using the syntax source |> operator(). These include the filter() and map() operators. When called, operators do not change the existing Observable instance. Instead, they return a new Observable, whose subscription logic is based on the first Observable.

Note

A Pipeable Operator is a function that takes an Observable as its input and returns another Observable. It is a pure operation: the previous Observable remains unmodified.

A Pipeable Operator is essentially a pure callable object that accepts one Observable as input and returns another Observable as output. Subscribing to the output Observable will also subscribe to the input Observable.

For example, the operator called map() is analogous to the Array method of the same name. Just like the array method map((d) -> d ^ 2, [ 1, 2, 3 ]) yields [ 1, 4, 9 ], the Observable emits 1, 4, 9:

source = from([ 1, 2, 3 ])
subscribe!(source |> map(Int, (d) -> d ^ 2), lambda(
on_next = (d) -> println(d)
))

// Logs:
// 1
// 4
// 9

Another useful operator is first():

source = from([ 1, 2, 3 ])
subscribe!(source |> first(), lambda(
on_next     = (d) -> println(d),
on_complete = ()  -> "Completed"
))

// Logs:
// 1
// Completed

## Creation operators

Distinct from pipeable operators, creation operators are functions that can be used to create an Observable with some common predefined behavior or by joining other Observables. For example: from([ 1, 2, 3 ]) creates an observable that will sequentially emit 1, 2, and 3.

source = from([ 1, 2, 3 ])
subscribe!(source, lambda(
on_next     = (d) -> println("Value: $d"), on_error = (e) -> println("Oh no, error:$e")
on_complete = ()  -> println("Completed")
))

// Logs:
// Value: 1
// Value: 2
// Value: 3
// Completed

## Operators piping

Pipeable operators are special objects that can be used like ordinary functions with on_call!(operator, source). In practice however they tend to accumulate and quickly grow unreadable: on_call!(operator1, on_call!(operator2, on_call!(operator3, source))). Therefore, Rocket.jl overloads |> for operators and Observables:

using Rocket

source = from(1:100) |> filter((d) -> d % 2 === 0) |> map(Int, (d) -> d ^ 2) |> sum()

subscribe!(source, logger())

// Logs
// [LogActor] Data: 171700
// [LogActor] Completed

It is also possible to create an operator composition with + or |>. It might be useful to create an alias for some often used operator chain

using Rocket

mapAndFilter = map(Int, d -> d ^ 2) + filter(d -> d % 2 == 0)

source = from(1:5) |> mapAndFilter

subscribe!(source, logger())

// Logs
// [LogActor] Data: 4
// [LogActor] Data: 16
// [LogActor] Completed

mapAndFilterAndSum = mapAndFilter + sum()

source = from(1:5) |> mapAndFilterAndSum

subscribe!(source, logger())

// Logs
// [LogActor] Data: 20
// [LogActor] Completed

For stylistic reasons, on_call!(operator, source) is never used in practice - even if there is only one operator. Instead, source |> operator() is generally preferred.


text:
# Arithmetic progression of rationals

We know that the set of rational numbers is countable. For which $n$ can we order all rational numbers as $a_1,a_2,\dots$ so that every subsequence of length $n$ is not an arithmetic progression?

For $n=1,2$ this is trivially impossible. If $n=3$, then the subsequence $a_1,a_2,2a_2-a_1$ forms an arithmetic progression, so it is also impossible. For large enough $n$ it should be possible, though.

To put in other words (thanks to Greg Martin), for which $n$ does there exist an enumeration $a_1,a_2,\dots$ of all rationals such that any time $a_{j_1},a_{j_2},\dots,a_{j_n}$ forms an arithmetic progression of length $n$, the indices $j_1,\dots,j_n$ are not in increasing order?

• Your question is unclear. When you say "any subsequence" do you mean "some subsequence" or "every subsequence"? – Rob Arthan Oct 16 '16 at 2:26
• In your $n=3$ case, you seem to be assuming that there is an index $i \geq 3$ such that $a_i = 2 a_2 - a_1$? Certainly we can design a sequence such that this fails. – erfink Oct 16 '16 at 2:26
• I mean every subsequence. There must exist $i$ with $a_i=2a_2-a_1$ since all rational numbers appear in the sequence. – pi66 Oct 16 '16 at 2:31
• In other words, the OP wants an enumeration $a_1,a_2,\dots$ of the rationals with the following property: any time $a_{j_1}, a_{j_2}, \dots, a_{j_n}$ forms an arithmetic progression in $\Bbb Q$ of length $n$, then the indices $j_1,\dots,j_n$ must not be in increasing order. – Greg Martin Oct 16 '16 at 3:13


text:
# Topology by Simmons Problem 1.3.3

Tags:
1. Feb 27, 2017

### Figaro

1. The problem statement, all variables and given/known data
Let $X$ and $Y$ be non-empty sets, $i$ be the identity mapping, and $f$ a mapping of $X$ into $Y$. Show the following

a) $f$ is one-to-one $~\Leftrightarrow~$ there exists a mapping $g$ of $Y$ into $X$ such that $gf=i_X$
b) $f$ is onto $~\Leftrightarrow~$ there exists a mapping $h$ of $Y$ into $X$ such that $fh=i_Y$

2. Relevant equations

3. The attempt at a solution
a) $~\Rightarrow~$ Since $f$ is one-to-one, there exist $y \in Y$ such that $y=f(x)$ for some $x\in X$, this shows that there exist at least some mapping $g$ that maps $Y$ into $X$ such that $x=g(y)=g(f(x))=(gf)(x)$ for some $y$, and also $gf=i_X$.

b) $~\Rightarrow~$ Since $f$ is onto, for all $y\in Y$ there exist some $x\in X$ such that $y=f(x)$, this shows that there exist some mapping $h$ of $Y$ into $X$ such that $x=h(y)$ and $y=f(x)=f(h(y))=(fh)(y)$ which implies $fh=i_Y$.

I have done the forward proof but I just want to know if my proof here is correct.

2. Feb 27, 2017

### Dick

I'm sure you have the right idea. In the injective case you can simply define what $g$ is. For the surjective case you need to show there exists such a function $h$. What you need for a formal statement is the axiom of choice.

Last edited: Feb 27, 2017
3. Feb 27, 2017

### Figaro

So you mean in a) I should state it as,
Since $f$ is one-to-one and suppose that there exist a mapping $g$ of $Y$ into $X$, then $x=g(y)=g(f(x))=(gf)(x)$ which implies $gf=i_X$.

In b) didn't I already show that there exist a mapping $h$ since for every $y$ there is always an $x$ such that $y=f(x)$? If not, what do you mean by using the axiom of choice? How should I use it to formalize the proof?

4. Feb 27, 2017

### Dick

Well, no. You need to define what the mapping $g$ is for ALL $y$ in $Y$. You can't just suppose there is one. For the onto case you need to do the same thing for $h$. If these are infinite sets you'll find you may have to make an infinite number of choices. The assumption you can do this is called the axiom of choice. It's a little technical and if you haven't talked about it just assume you can do that.