Markov chain comparison

This is an expository paper, focussing on the following scenario. We have two Markov chains, $\mathcal {M}$ and $\mathcal {M}'$. By some means, we have obtained a bound on the mixing time of $\mathcal {M}'$. We wish to compare $\mathcal {M}$ with $\mathcal {M}'$ in order to derive a corresponding bound on the mixing time of $\mathcal {M}$. We investigate the application of the comparison method of Diaconis and Saloff-Coste to this scenario, giving a number of theorems which characterize the applicability of the method. We focus particularly on the case in which the chains are not reversible. The purpose of the paper is to provide a catalogue of theorems which can be easily applied to bound mixing times.Comment: Published at http://dx.doi.org/10.1214/154957806000000041 in the Probability Surveys (http://www.i-journals.org/ps/) by the Institute of Mathematical Statistics (http://www.imstat.org

Exact counting of Euler Tours for Graphs of Bounded Treewidth

In this paper we give a simple polynomial-time algorithm to exactly count the number of Euler Tours (ETs) of any Eulerian graph of bounded treewidth. The problems of counting ETs are known to be #P-complete for general graphs (Brightwell and Winkler, (Brightwell and Winkler, 2005). To date, no polynomial-time algorithm for counting Euler tours of any class of graphs is known except for the very special case of series-parallel graphs (which have treewidth 2).Comment: 16 pages, draf

More than a Match: The Role of Football in Britain’s Deaf Community

The University of Central Lancashire has undertaken a major research project into the role of football within the deaf community in Britain. As well as reconstructing the long history of deaf involvement in football for the first time, the project has also focused on the way in which football has provided deaf people with a means of developing and maintaining social contacts within the community, and of expressing the community’s cultural values. This article will draw on primary data gathered from interviews conducted with people involved in deaf football in a variety of capacities. During the course of these interviews, a number of themes and issues emerged relating to the values and benefits those involved with deaf football place on the game, and it is these which are explored here

The Complexity of Approximately Counting Stable Matchings

We investigate the complexity of approximately counting stable matchings in the $k$-attribute model, where the preference lists are determined by dot products of "preference vectors" with "attribute vectors", or by Euclidean distances between "preference points" and "attribute points". Irving and Leather proved that counting the number of stable matchings in the general case is #P-complete. Counting the number of stable matchings is reducible to counting the number of downsets in a (related) partial order and is interreducible, in an approximation-preserving sense, to a class of problems that includes counting the number of independent sets in a bipartite graph (#BIS). It is conjectured that no FPRAS exists for this class of problems. We show this approximation-preserving interreducibilty remains even in the restricted $k$-attribute setting when $k \geq 3$ (dot products) or $k \geq 2$ (Euclidean distances). Finally, we show it is easy to count the number of stable matchings in the 1-attribute dot-product setting.Comment: Fixed typos, small revisions for clarification, et

Warped Deformed Throats have Faster (Electroweak) Phase Transitions

We study the dynamics of the finite-temperature phase transition for warped Randall-Sundrum(RS)-like throat models related to the Klebanov-Tseytlin solution. We find that, for infrared branes stabilized near the tip of the throat, the bounce action has a mild N^2 dependence, where N(y) \sim [M_5 L(y)]^{3/2} is the effective number of degrees of freedom of the holographic dual QFT, and where L(y) is the local curvature radius, which decreases in the infrared. In addition, the bounce action is not enhanced by large numbers. These features allow the transition to successfully complete over a wider parameter range than for Goldberger-Wise stabilized RS models. Due to the increase of L(y) in the ultraviolet, the throat has a reliable gravitational description even when the number of infrared degrees of freedom is small. We also comment on aspects of the thermal phase transition in Higgsless models, where the gauge symmetry breaking is achieved via boundary conditions. Such models include orbifold-GUT models and the Higgsless electroweak symmetry breaking theories of Csaki et al., with Standard Model gauge fields living in the bulk.Comment: published version, 18 pages, minor typo corrected, reference adde

Deterministic Symmetry Breaking in Ring Networks

We study a distributed coordination mechanism for uniform agents located on a circle. The agents perform their actions in synchronised rounds. At the beginning of each round an agent chooses the direction of its movement from clockwise, anticlockwise, or idle, and moves at unit speed during this round. Agents are not allowed to overpass, i.e., when an agent collides with another it instantly starts moving with the same speed in the opposite direction (without exchanging any information with the other agent). However, at the end of each round each agent has access to limited information regarding its trajectory of movement during this round. We assume that $n$ mobile agents are initially located on a circle unit circumference at arbitrary but distinct positions unknown to other agents. The agents are equipped with unique identifiers from a fixed range. The {\em location discovery} task to be performed by each agent is to determine the initial position of every other agent. Our main result states that, if the only available information about movement in a round is limited to %information about distance between the initial and the final position, then there is a superlinear lower bound on time needed to solve the location discovery problem. Interestingly, this result corresponds to a combinatorial symmetry breaking problem, which might be of independent interest. If, on the other hand, an agent has access to the distance to its first collision with another agent in a round, we design an asymptotically efficient and close to optimal solution for the location discovery problem.Comment: Conference version accepted to ICDCS 201

Oral application of L-menthol in the heat: From pleasure to performance

When menthol is applied to the oral cavity it presents with a familiar refreshing sensation and cooling mint flavour. This may be deemed hedonic in some individuals, but may cause irritation in others. This variation in response is likely dependent upon trigeminal sensitivity toward cold stimuli, suggesting a need for a menthol solution that can be easily personalised. Menthol’s characteristics can also be enhanced by matching colour to qualitative outcomes; a factor which can easily be manipulated by practitioners working in athletic or occupational settings to potentially enhance intervention efficacy. This presentation will outline the efficacy of oral menthol application for improving time trial performance to date, either via swilling or via co-ingestion with other cooling strategies, with an emphasis upon how menthol can be applied in ecologically valid scenarios. Situations in which performance is not expected to be enhanced will also be discussed. An updated model by which menthol may prove hedonic, satiate thirst and affect ventilation will also be presented, with the potential performance implications of these findings discussed and modelled. Qualitative reflections from athletes that have implemented menthol mouth swilling in competition, training and maximal exercise will also be included

Implementing a simple continuous speech recognition system on an FPGA

Speech recognition is a computationally demanding task, particularly the stage which uses Viterbi decoding for converting pre-processed speech data into words or sub-word units. We present an FPGA implementations of the decoder based on continuous hidden Markov models (HMMs) representing monophones, and demonstrate that it can process speech 75 times real time, using 45% of the slices of a Xilinx Virtex XCV100