arXiv subjects

Thomas Richardson

Publications and source records attributed to Thomas Richardson.

26 records · Page 2Linked to original sources

arXiv2014

On the dark matter profile in Sculptor: Breaking the $β$ degeneracy with Virial shape parameters

We present a new method for studying tracers in gravitational systems where higher moments of the line-of-sight velocity distribution are introduced via Virial equations rather than the Jeans equations. Unlike the fourth order Jeans equations, the fourth order Virial equations can simply be added to the standard second order Jeans equation without introducing a new anisotropy parameter $β^{\prime}$. We introduce two new global shape parameters $ζ_A$ and $ζ_B$ which replace the kurtosis as a more statistically robust measure of the shape of the line of sight velocity distribution. We show that in the case of stars in dwarf spheroidal galaxies these new parameters can significantly reduce the range of density profiles that are otherwise consistent with the observed stellar kinematics (a problem sometimes known as the $β$ degeneracy). Specifically, we find that $ζ_A$ focuses tightly on a subset of solutions where cusped density profiles are degenerate with more concentrated cored dark matter halos. If the number density of stars $ν(r)$ is fixed, then introducing $ζ_B$ can further reduce the space of solutions by constraining the outer slope of the dark matter density profile. Assuming a Plummer profile for $ν(r)$ we recover the surprising result that the dark matter in Sculptor may be cuspy after all, in contrast to the conclusions of other approaches.

astro-ph.GA↗

arXiv2014

Plan beta: Core or Cusp?

The inner profile of Dark Matter (DM) halos remains one of the central problems in small-scale cosmology. At present, the problem can not be resolved in dwarf spheroidal galaxies due to a degeneracy between the DM profile and the velocity anisotropy beta of the stellar population. We discuss a method which can break the degeneracy by exploiting 3D positions and 1D line-of-sight (LOS) velocities. With the full 3D spatial information, we can determine precisely what fraction of each stars LOS motion is in the radial and tangential direction. This enables us to infer the anisotropy parameter beta directly from the data. The method is particularly effective if the galaxy is highly anisotropic. Finally, we argue that such a test could be applied to Sagittarius and potentially other dwarfs with RR Lyrae providing the necessary depth information.

astro-ph.GA↗

arXiv2014

Analytical Solutions to the Mass-Anisotropy Degeneracy with Higher Order Jeans Analysis: A General Method

The Jeans analysis is often used to infer the total density of a system by relating the velocity moments of an observable tracer population to the underlying gravitational potential. This technique has recently been applied in the search for Dark Matter in objects such as dwarf spheroidal galaxies where the presence of Dark Matter is inferred via stellar velocities. A precise account of the density is needed to constrain the expected gamma ray flux from DM self-annihilation and to distinguish between cold and warm dark matter models. Unfortunately the traditional method of fitting the second order Jeans equation to the tracer dispersion suffers from an unbreakable degeneracy of solutions due to the unknown velocity anisotropy of the projected system. To tackle this degeneracy one can appeal to higher moments of the Jeans equation. By introducing an analog to the Binney anisotropy parameter at fourth order, beta' we create a framework that encompasses all solutions to the fourth order Jeans equations rather than those in the literature that impose unnecessary correlations between anisotropy of second and fourth order moments. The condition beta' = f(beta) ensures that the degeneracy is lifted and we interpret the separable augmented density system as the order-independent case beta'= beta. For a generic choice of beta' we present the line of sight projection of the fourth moment and how it could be incorporated into a joint likelihood analysis of the dispersion and kurtosis. Having presented the mathematical framework, we then use it to develop a statistical method for the purpose of placing constraints on dark matter density parameters from discrete velocity data. The method is tested on simulated dwarf spheroidal data sets leading to results which motivate study of real dwarf spheroidal data sets.

astro-ph.CO↗

arXiv2013

Cores in Classical Dwarf Spheroidal Galaxies? A Dispersion-Kurtosis Jeans Analysis Without Restricted Anisotropy

We attempt to measure the density of dark matter in the two Dwarf Spheroidal Galaxies Fornax and Sculptor using a new method which employs Jeans equations based on both the second and fourth moment of the Collisionless Boltzmann Equation (i.e. variance and kurtosis of line of sight stellar velocities). Unlike previous related efforts, we allow the anisotropy of the radial and tangential second and fourth order moments to vary independently of each other. We apply the method to simulated data and establish that to some degree it appears to be able to break the degeneracies associated with second order only Jeans analyses. When we apply the technique to real data, we see no huge improvement in our understanding of the inner density of Fornax, which can still be fit by either a quite cuspy or cored density profile. For Sculptor however we find that the technique suggests that the data is incompatible with a steep profile and a cored profile seems more consistent. As well as presenting these new results and comparing them to other estimates in the literature, we try to understand why the technique is more effective in one system than the other.

astro-ph.GA↗

arXiv2013

Large Scale Distributed Acoustic Modeling With Back-off N-grams

The paper revives an older approach to acoustic modeling that borrows from n-gram language modeling in an attempt to scale up both the amount of training data and model size (as measured by the number of parameters in the model), to approximately 100 times larger than current sizes used in automatic speech recognition. In such a data-rich setting, we can expand the phonetic context significantly beyond triphones, as well as increase the number of Gaussian mixture components for the context-dependent states that allow it. We have experimented with contexts that span seven or more context-independent phones, and up to 620 mixture components per state. Dealing with unseen phonetic contexts is accomplished using the familiar back-off technique used in language modeling due to implementation simplicity. The back-off acoustic model is estimated, stored and served using MapReduce distributed computing infrastructure. Speech recognition experiments are carried out in an N-best list rescoring framework for Google Voice Search. Training big models on large amounts of data proves to be an effective way to increase the accuracy of a state-of-the-art automatic speech recognition system. We use 87,000 hours of training data (speech along with transcription) obtained by filtering utterances in Voice Search logs on automatic speech recognition confidence. Models ranging in size between 20--40 million Gaussians are estimated using maximum likelihood training. They achieve relative reductions in word-error-rate of 11% and 6% when combined with first-pass models trained using maximum likelihood, and boosted maximum mutual information, respectively. Increasing the context size beyond five phones (quinphones) does not help.

cs.CL↗

arXiv2010

Community Structure in Time-Dependent, Multiscale, and Multiplex Networks

Network science is an interdisciplinary endeavor, with methods and applications drawn from across the natural, social, and information sciences. A prominent problem in network science is the algorithmic detection of tightly-connected groups of nodes known as communities. We developed a generalized framework of network quality functions that allowed us to study the community structure of arbitrary multislice networks, which are combinations of individual networks coupled through links that connect each node in one network slice to itself in other slices. This framework allows one to study community structure in a very general setting encompassing networks that evolve over time, have multiple types of links (multiplexity), and have multiple scales.

physics.data-an↗

arXiv2009

Spectral tripartitioning of networks

We formulate a spectral graph-partitioning algorithm that uses the two leading eigenvectors of the matrix corresponding to a selected quality function to split a network into three communities in a single step. In so doing, we extend the recursive bipartitioning methods developed by Newman [Proc. Nat. Acad. Sci. 103, 8577 (2006); Phys. Rev. E 74, 036104 (2006)] to allow one to consider the best available two-way and three-way divisions at each recursive step. We illustrate the method using simple "bucket brigade" examples and then apply the algorithm to examine the community structures of the coauthorship graph of network scientists and of U. S. Congressional networks inferred from roll-call voting similarities.

physics.data-an↗

arXiv2008

Spherical grand-canonical minority games with and without score discounting

We present a spherical version of the grand-canonical minority game (GCMG), and solve its dynamics in the stationary state. The model displays several types of transitions between multiple ergodic phases and one non-ergodic phase. We derive analytical solutions, including exact expressions for the volatility, throughout all ergodic phases, and compute the phase behaviour of the system. In contrast to conventional GCMGs, where the introduction of memory-loss precludes analytical approaches, the spherical model can be solved also when exponential discounting is taken into account. For the case of homogeneous incentives to trade epsilon and memory loss rates rho, an efficient phase is found only if rho=epsilon=0. Allowing for heterogeneous memory-loss rates we find that efficiency can be achieved as long as there is any finite fraction of agents which is not subject to memory loss.

physics.soc-ph↗