A subset solution to the sign problem in random matrix simulations

We present a solution to the sign problem in dynamical random matrix simulations of a two-matrix model at nonzero chemical potential. The sign problem, caused by the complex fermion determinants, is solved by gathering the matrices into subsets, whose sums of determinants are real and positive even though their cardinality only grows linearly with the matrix size. A detailed proof of this positivity theorem is given for an arbitrary number of fermion flavors. We performed importance sampling Monte Carlo simulations to compute the chiral condensate and the quark number density for varying chemical potential and volume. The statistical errors on the results only show a mild dependence on the matrix size and chemical potential, which confirms the absence of sign problem in the subset method. This strongly contrasts with the exponential growth of the statistical error in standard reweighting methods, which was also analyzed quantitatively using the subset method. Finally, we show how the method elegantly resolves the Silver Blaze puzzle in the microscopic limit of the matrix model, where it is equivalent to QCD.Comment: 18 pages, 11 figures, as published in Phys. Rev. D; added references; in Sec. VB: added discussion of model satisfying the Silver Blaze for all N (proof in Appendix E

Technological advances relevant to transport – understanding what drives them

Transport policy makers are increasingly perplexed by the pace of change in their sector and by the increasing influence of external actors. This leads to a variety of responses, including “business as usual”, technological optimism, technological fatalism and technological ignorance. To explore this perplexity and its justification, we examine four areas of technological advance relevant to transport: mobility as a service; unmanned aerial vehicles (drones); automated vehicles; and telehealth. In each case, we identify the principal underlying shifts which are driving these technological advances, concluding that there is considerable overlap: three of the advances rely on ubiquitous sensing and on artificial intelligence and all four rely, to some degree, on connectedness. We then explore these three “drivers”, finding that progress is steadier than may be generally thought. We discuss the implications for our set of transport-related technological developments, concluding that policy makers could approach the future with greater confidence than is currently typical. They could also draw on the concepts of anticipatory governance to support their management of emerging technology and, at the same time, of the influence of external actors

ClassTR: Classifying Within-Host Heterogeneity Based on Tandem Repeats with Application to Mycobacterium tuberculosis Infections.

Genomic tools have revealed genetically diverse pathogens within some hosts. Within-host pathogen diversity, which we refer to as "complex infection", is increasingly recognized as a determinant of treatment outcome for infections like tuberculosis. Complex infection arises through two mechanisms: within-host mutation (which results in clonal heterogeneity) and reinfection (which results in mixed infections). Estimates of the frequency of within-host mutation and reinfection in populations are critical for understanding the natural history of disease. These estimates influence projections of disease trends and effects of interventions. The genotyping technique MLVA (multiple loci variable-number tandem repeats analysis) can identify complex infections, but the current method to distinguish clonal heterogeneity from mixed infections is based on a rather simple rule. Here we describe ClassTR, a method which leverages MLVA information from isolates collected in a population to distinguish mixed infections from clonal heterogeneity. We formulate the resolution of complex infections into their constituent strains as an optimization problem, and show its NP-completeness. We solve it efficiently by using mixed integer linear programming and graph decomposition. Once the complex infections are resolved into their constituent strains, ClassTR probabilistically classifies isolates as clonally heterogeneous or mixed by using a model of tandem repeat evolution. We first compare ClassTR with the standard rule-based classification on 100 simulated datasets. ClassTR outperforms the standard method, improving classification accuracy from 48% to 80%. We then apply ClassTR to a sample of 436 strains collected from tuberculosis patients in a South African community, of which 92 had complex infections. We find that ClassTR assigns an alternate classification to 18 of the 92 complex infections, suggesting important differences in practice. By explicitly modeling tandem repeat evolution, ClassTR helps to improve our understanding of the mechanisms driving within-host diversity of pathogens like Mycobacterium tuberculosis

Algebraic Properties of Valued Constraint Satisfaction Problem

The paper presents an algebraic framework for optimization problems expressible as Valued Constraint Satisfaction Problems. Our results generalize the algebraic framework for the decision version (CSPs) provided by Bulatov et al. [SICOMP 2005]. We introduce the notions of weighted algebras and varieties and use the Galois connection due to Cohen et al. [SICOMP 2013] to link VCSP languages to weighted algebras. We show that the difficulty of VCSP depends only on the weighted variety generated by the associated weighted algebra. Paralleling the results for CSPs we exhibit a reduction to cores and rigid cores which allows us to focus on idempotent weighted varieties. Further, we propose an analogue of the Algebraic CSP Dichotomy Conjecture; prove the hardness direction and verify that it agrees with known results for VCSPs on two-element sets [Cohen et al. 2006], finite-valued VCSPs [Thapper and Zivny 2013] and conservative VCSPs [Kolmogorov and Zivny 2013].Comment: arXiv admin note: text overlap with arXiv:1207.6692 by other author

A Solvable Model for Many Quark Systems in QCD Hamiltonians

Motivated by a canonical, QCD Hamiltonian we propose an effective Hamiltonian to represent an arbitrary number of quarks in hadronic bags. The structure of the effective Hamiltonian is discussed and the BCS-type solutions that may represent constituent quarks are presented. The single particle orbitals are chosen as 3-dimensional harmonic oscillators and we discuss a class of exact solutions that can be obtained when a subset of single-particle basis states is restricted to include a certain number of orbital excitations. The general problem, which includes all possible orbital states, can also be solved by combining analytical and numerical methods.Comment: 24 pages, 2 figures, research articl

Efficiency of feedback process in cavity quantum electrodynamics

Utilizing the continuous frequency mode quantization scheme, we study from first principle the efficiency of a feedback scheme that can generate maximally entangled states of two atoms in an optical cavity through their interactions with a single input photon. The spectral function of the photon emitted from the cavity, which will be used as the input of the next round in the feedback process, is obtained analytically. We find that the spectral function of the photon is modified in each round and deviates from the original one. The efficiency of the feedback scheme consequently deteriorates gradually after several rounds of operation.Comment: 11 pages, 5 figures, accepted for publication in Journal of Physics

Creep Evaluation of (Orthotic) Cast Materials During Simulated Clubfoot Correction

The Ponseti method is a widely accepted and highly successful conservative treatment of pediatric clubfoot that relies on weekly manipulations and cast applications. However, the material behavior of the cast in the Ponseti technique has not been investigated. The current study sought to characterize the ability of two standard casting materials to maintain the Ponseti corrected foot position by evaluating creep response. A dynamic cast testing device (DCTD) was built to simulate a typical pediatric clubfoot. Semi-rigid fiberglass and rigid fiberglass casting materials were applied to the device, and the rotational creep was measured at various constant torques. The movement was measured using a 3D motion capture system. A 2-way ANOVA was performed on the creep displacement data at a significance level of 0.05. Among cast materials, the rotational creep displacement was found to be significantly different (p-values ≪ 0.001). The most creep displacement occurs in the semi-rigid fiberglass (approximately 1.0 degrees), then the rigid fiberglass (approximately 0.4 degrees). There was no effect of torque magnitude on the creep displacement. All materials maintained the corrected position with minimal change in position over time

Large Magnetic Fields and Motions of OH Masers in W75 N

We report on a second epoch of VLBA observations of the 1665 and 1667 MHz OH masers in the massive star-forming region W75 N. We find evidence to confirm the existence of very strong (~40 mG) magnetic fields near source VLA 2. The masers near VLA 2 are dynamically distinct and include a very bright spot apparently moving at 50 km/s relative to those around VLA 1. This fast-moving spot may be an example of a rare class of OH masers seen in outflows in star-forming regions. Due to the variability of these masers and the rapidity of their motions, tracking these motions will require multiple observations over a significantly shorter time baseline than obtained here. Proper motions of the masers near VLA 1 are more suggestive of streaming along magnetized shocks rather than Keplerian rotation in a disk. The motions of the easternmost cluster of masers in W75 N (B) may be tracing slow expansion around an unseen exciting source.Comment: 7 pages including 4 figures (2 color) & 3 tables, to appear in Ap

Rendezvous of Two Robots with Constant Memory

We study the impact that persistent memory has on the classical rendezvous problem of two mobile computational entities, called robots, in the plane. It is well known that, without additional assumptions, rendezvous is impossible if the entities are oblivious (i.e., have no persistent memory) even if the system is semi-synchronous (SSynch). It has been recently shown that rendezvous is possible even if the system is asynchronous (ASynch) if each robot is endowed with O(1) bits of persistent memory, can transmit O(1) bits in each cycle, and can remember (i.e., can persistently store) the last received transmission. This setting is overly powerful. In this paper we weaken that setting in two different ways: (1) by maintaining the O(1) bits of persistent memory but removing the communication capabilities; and (2) by maintaining the O(1) transmission capability and the ability to remember the last received transmission, but removing the ability of an agent to remember its previous activities. We call the former setting finite-state (FState) and the latter finite-communication (FComm). Note that, even though its use is very different, in both settings, the amount of persistent memory of a robot is constant. We investigate the rendezvous problem in these two weaker settings. We model both settings as a system of robots endowed with visible lights: in FState, a robot can only see its own light, while in FComm a robot can only see the other robot's light. We prove, among other things, that finite-state robots can rendezvous in SSynch, and that finite-communication robots are able to rendezvous even in ASynch. All proofs are constructive: in each setting, we present a protocol that allows the two robots to rendezvous in finite time.Comment: 18 pages, 3 figure