Polarization and Ideology: Partisan Sources of Low Dimensionality in Scaled Roll Call Analyses

2014 ◽  
Vol 22 (4) ◽  
pp. 435-456 ◽  
Author(s):  
John H. Aldrich ◽  
Jacob M. Montgomery ◽  
David B. Sparks
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Simulations ◽  
Dimensional Space ◽  
Roll Call ◽  
Policy Space ◽  
Policy Conflict ◽  
Party Polarization ◽  
Misleading Evidence ◽  
Low Dimensionality ◽  
Low Dimensional

In this article, we challenge the conclusion that the preferences of members of Congress are best represented as existing in a low-dimensional space. We conduct Monte Carlo simulations altering assumptions regarding the dimensionality and distribution of member preferences and scale the resulting roll call matrices. Our simulations show that party polarization generates misleading evidence in favor of low dimensionality. This suggests that the increasing levels of party polarization in recent Congresses may have produced false evidence in favor of a low-dimensional policy space. However, we show that focusing more narrowly on each party caucus in isolation can help researchers discern the true dimensionality of the policy space in the context of significant party polarization. We re-examine the historical roll call record and find evidence suggesting that the low dimensionality of the contemporary Congress may reflect party polarization rather than changes in the dimensionality of policy conflict.

A Test of Randomness for Finite Spatial Distributions

1994 ◽  
Vol 78 (3) ◽  
pp. 707-714 ◽  
Author(s):  
Frank O'brien
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Simulations ◽  
Null Hypothesis ◽  
Nearest Neighbor ◽  
Dimensional Space ◽  
Spatial Distributions ◽  
Two Dimensional ◽  
Model Extension ◽  
Spatially Distributed ◽  
Test Of Randomness

A statistical method is presented for determining randomness of points spatially distributed in two-dimensional space. The procedure is based on a distance-to-particle (nearest neighbor) model derived from an elementary Poisson process. In a previous derivation of the method, an extension to the model was proposed and used without adequate empirical justification. Herein the test is derived in detail and its performance evaluated with Monte Carlo simulations. Results indicate that the model extension provides adequate representations when the null hypothesis is true.

An Investigation of Solar Trees for Effective Sunlight Capture Using Monte Carlo Simulations of Solar Radiation Transport

2014 ◽  
Author(s):  
Navni N. Verma ◽  
Sandip Mazumder
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Simulations ◽  
Radiation Flux ◽  
Radiation Transport ◽  
Dimensional Space ◽  
Global Radiation ◽  
Three Dimensional ◽  
Capture Efficiency ◽  
Solar Photovoltaic ◽  
Three Dimensional Space

Solar photovoltaic cells arranged in complex three-dimensional leaf-like configurations — referred to as a solar tree — can potentially collect more sunlight than traditionally used flat configurations. It is hypothesized that this could be because of two reasons. First, the three-dimensional space can be utilized to increase the overall surface area over which the sunlight may be captured. Second, as opposed to traditional flat panel configurations where the capture efficiency decreases dramatically for shallow angles of incidence, the capture efficiency of a solar tree is hampered little by shallow angles of incidence due to the three-dimensional orientation of the solar leaves. In this paper, high fidelity Monte Carlo simulation of radiation transport is conducted to gain insight into whether the above hypotheses are true. The Monte Carlo simulations provide local radiation flux distributions in addition to global radiation flux summaries. The studies show that except for near-normal solar incidence angles, solar trees capture sunlight more effectively than flat panels — often by more than a factor of 5. The Monte Carlo results were also interpolated to construct a daily sunlight capture profile both for mid-winter and mid-summer for a typical North American city. During winter, the solar tree improved sunlight capture by 227%, while in summer the improvement manifested was 54%.

scholarly journals SpHMC: Spectral Hamiltonian Monte Carlo

2019 ◽  
Vol 33 ◽  
pp. 5516-5524
Author(s):  
Haoyi Xiong ◽  
Kafeng Wang ◽  
Jiang Bian ◽  
Zhanxing Zhu ◽  
Cheng-Zhong Xu ◽  
...  
Keyword(s):  
Monte Carlo ◽  
Probability Distribution ◽  
Real World ◽  
Dimensional Space ◽  
Probability Distributions ◽  
Superior Performance ◽  
High Dimensional ◽  
Hamiltonian Monte Carlo ◽  
Real World Datasets ◽  
Low Dimensional

Stochastic Gradient Hamiltonian Monte Carlo (SGHMC) methods have been widely used to sample from certain probability distributions, incorporating (kernel) density derivatives and/or given datasets. Instead of exploring new samples from kernel spaces, this piece of work proposed a novel SGHMC sampler, namely Spectral Hamiltonian Monte Carlo (SpHMC), that produces the high dimensional sparse representations of given datasets through sparse sensing and SGHMC. Inspired by compressed sensing, we assume all given samples are low-dimensional measurements of certain high-dimensional sparse vectors, while a continuous probability distribution exists in such high-dimensional space. Specifically, given a dictionary for sparse coding, SpHMC first derives a novel likelihood evaluator of the probability distribution from the loss function of LASSO, then samples from the high-dimensional distribution using stochastic Langevin dynamics with derivatives of the logarithm likelihood and Metropolis–Hastings sampling. In addition, new samples in low-dimensional measuring spaces can be regenerated using the sampled high-dimensional vectors and the dictionary. Extensive experiments have been conducted to evaluate the proposed algorithm using real-world datasets. The performance comparisons on three real-world applications demonstrate the superior performance of SpHMC beyond baseline methods.

scholarly journals Legislators’ roll-call voting behavior increasingly corresponds to intervals in the political spectrum

2020 ◽  
Vol 10 (1) ◽  
Author(s):  
David Schoch ◽  
Ulrik Brandes
Keyword(s):  
Voting Behavior ◽  
Dimensional Space ◽  
Political Orientation ◽  
Interval Order ◽  
Roll Call ◽  
Roll Call Voting ◽  
One Dimensional ◽  
Political Actors ◽  
Political Spectrum ◽  
Low Dimensional

Abstract Scaling techniques such as the well known NOMINATE position political actors in a low dimensional space to represent the similarity or dissimilarity of their political orientation based on roll-call voting patterns. Starting from the same kind of data we propose an alternative, discrete, representation that replaces positions (points and distances) with niches (boxes and overlap). In the one-dimensional case, this corresponds to replacing the left-to-right ordering of points on the real line with an interval order. As it turns out, this seemingly simplistic one-dimensional model is sufficient to represent the similarity of roll-call votes by U.S. senators in recent years. In a historic context, however, low dimensionality represents the exception which stands in contrast to what is suggested by scaling techniques.

scholarly journals Robustness of Magic and Symmetries of the Stabiliser Polytope

Quantum ◽  
2019 ◽  
Vol 3 ◽  
pp. 132 ◽  
Author(s):  
Markus Heinrich ◽  
David Gross
Keyword(s):  
Monte Carlo ◽  
Fault Tolerant ◽  
Dimensional Space ◽  
Convex Polytope ◽  
Approximate Solutions ◽  
Monte Carlo Algorithm ◽  
Sign Problem ◽  
Clifford Group ◽  
Low Dimensional ◽  
Complex Projective

We give a new algorithm for computing therobustness of magic- a measure of the utility of quantum states as a computational resource. Our work is motivated by themagic state modelof fault-tolerant quantum computation. In this model, all unitaries belong to the Clifford group. Non-Clifford operations are effected by injecting non-stabiliser states, which are referred to asmagic statesin this context. Therobustness of magicmeasures the complexity of simulating such a circuit using a classical Monte Carlo algorithm. It is closely related to the degree negativity that slows down Monte Carlo simulations through the infamoussign problem. Surprisingly, the robustness of magic issub- multiplicative. This implies that the classical simulation overhead scales subexponentially with the number of injected magic states - better than a naive analysis would suggest. However, determining the robustness ofncopies of a magic state is difficult, as its definition involves a convex optimisation problem in a 4n-dimensional space. In this paper, we make use of inherent symmetries to reduce the problem tondimensions. The total run-time of our algorithm, while still exponential inn, is super-polynomially faster than previously published methods. We provide a computer implementation and give the robustness of up to 10 copies of the most commonly used magic states. Guided by the exact results, we find a finite hierarchy of approximate solutions where each level can be evaluated in polynomial time and yields rigorous upper bounds to the robustness. Technically, we use symmetries of the stabiliser polytope to connect the robustness of magic to the geometry of a low-dimensional convex polytope generated by certainsigned quantum weight enumerators. As a by-product, we characterised the automorphism group of the stabiliser polytope, and, more generally, of projections onto complex projective 3-designs.

Low-voltage EDS of magnesium ferrite Dendrites in a FEG-SEM

1996 ◽  
Vol 54 ◽  
pp. 478-479
Author(s):  
Matthew T. Johnson ◽  
Ian M. Anderson ◽  
Jim Bentley ◽  
C. Barry Carter
Keyword(s):  
Monte Carlo ◽  
Quantitative Analysis ◽  
Monte Carlo Simulations ◽  
Cross Section ◽  
Spatial Resolution ◽  
Low Voltage ◽  
Magnesium Ferrite ◽  
X Ray ◽  
Interaction Volume ◽  
Ferrite Spinel

Energy-dispersive X-ray spectrometry (EDS) performed at low (≤ 5 kV) accelerating voltages in the SEM has the potential for providing quantitative microanalytical information with a spatial resolution of ∼100 nm. In the present work, EDS analyses were performed on magnesium ferrite spinel [(MgxFe1−x)Fe2O4] dendrites embedded in a MgO matrix, as shown in Fig. 1. spatial resolution of X-ray microanalysis at conventional accelerating voltages is insufficient for the quantitative analysis of these dendrites, which have widths of the order of a few hundred nanometers, without deconvolution of contributions from the MgO matrix. However, Monte Carlo simulations indicate that the interaction volume for MgFe2O4 is ∼150 nm at 3 kV accelerating voltage and therefore sufficient to analyze the dendrites without matrix contributions.Single-crystal {001}-oriented MgO was reacted with hematite (Fe2O3) powder for 6 h at 1450°C in air and furnace cooled. The specimen was then cleaved to expose a clean cross-section suitable for microanalysis.

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