Asymptotics of the Farey Fraction Spin Chain Free Energy at the Critical Point

We consider the Farey fraction spin chain in an external field $h$. Using ideas from dynamical systems and functional analysis, we show that the free energy $f$ in the vicinity of the second-order phase transition is given, exactly, by $$f \sim \frac t{\log t}-\frac1{2} \frac{h^2}t \quad \text{for} \quad h^2\ll t \ll 1 .$$ Here $t=\lambda_{G}\log(2)(1-\frac{\beta}{\beta_c})$ is a reduced temperature, so that the deviation from the critical point is scaled by the Lyapunov exponent of the Gauss map, $\lambda_G$. It follows that $\lambda_G$ determines the amplitude of both the specific heat and susceptibility singularities. To our knowledge, there is only one other microscopically defined interacting model for which the free energy near a phase transition is known as a function of two variables. Our results confirm what was found previously with a cluster approximation, and show that a clustering mechanism is in fact responsible for the transition. However, the results disagree in part with a renormalisation group treatment

A note on the algebraic growth rate of Poincar\'e series for Kleinian groups

In this note we employ infinite ergodic theory to derive estimates for the algebraic growth rate of the Poincar\'e series for a Kleinian group at its critical exponent of convergence.Comment: 8 page

Coupling a model of human thermoregulation with computational fluid dynamics for predicting human-environment interaction

This paper describes the methods developed to couple a commercial CFD program with a multi-segmented model of human thermal comfort and physiology. A CFD model is able to predict detailed temperatures and velocities of airflow around a human body, whilst a thermal comfort model is able to predict the response of a human to the environment surrounding it. By coupling the two models and exchanging information about the heat transfer at the body surface the coupled system can potentially predict the response of a human body to detailed local environmental conditions. This paper presents a method of exchanging data, using shared files, to provide a means of dynamically exchanging simulation data with the IESD-Fiala model during the CFD solution process. Additional code is used to set boundary conditions for the CFD simulation at the body surface as determined by the IESD-Fiala model and to return information about local environmental conditions adjacent to the body surface as determined by the CFD simulation. The coupled system is used to model a human subject in a naturally ventilated environment. The resulting ventilation flow pattern agrees well with other numerical and experimental work

Parameterizing by the Number of Numbers

The usefulness of parameterized algorithmics has often depended on what Niedermeier has called, "the art of problem parameterization". In this paper we introduce and explore a novel but general form of parameterization: the number of numbers. Several classic numerical problems, such as Subset Sum, Partition, 3-Partition, Numerical 3-Dimensional Matching, and Numerical Matching with Target Sums, have multisets of integers as input. We initiate the study of parameterizing these problems by the number of distinct integers in the input. We rely on an FPT result for ILPF to show that all the above-mentioned problems are fixed-parameter tractable when parameterized in this way. In various applied settings, problem inputs often consist in part of multisets of integers or multisets of weighted objects (such as edges in a graph, or jobs to be scheduled). Such number-of-numbers parameterized problems often reduce to subproblems about transition systems of various kinds, parameterized by the size of the system description. We consider several core problems of this kind relevant to number-of-numbers parameterization. Our main hardness result considers the problem: given a non-deterministic Mealy machine M (a finite state automaton outputting a letter on each transition), an input word x, and a census requirement c for the output word specifying how many times each letter of the output alphabet should be written, decide whether there exists a computation of M reading x that outputs a word y that meets the requirement c. We show that this problem is hard for W[1]. If the question is whether there exists an input word x such that a computation of M on x outputs a word that meets c, the problem becomes fixed-parameter tractable

On vertex coloring without monochromatic triangles

We study a certain relaxation of the classic vertex coloring problem, namely, a coloring of vertices of undirected, simple graphs, such that there are no monochromatic triangles. We give the first classification of the problem in terms of classic and parametrized algorithms. Several computational complexity results are also presented, which improve on the previous results found in the literature. We propose the new structural parameter for undirected, simple graphs -- the triangle-free chromatic number $\chi_3$. We bound $\chi_3$ by other known structural parameters. We also present two classes of graphs with interesting coloring properties, that play pivotal role in proving useful observation about our problem. We give/ask several conjectures/questions throughout this paper to encourage new research in the area of graph coloring.Comment: Extended abstrac

Global Conformational Dynamics of a Y-Family DNA Polymerase during Catalysis

High-resolution analysis of protein, and DNA conformational changes during DNA polymerization, established relationships between the enzymatic function and conformational dynamics of individual domains for a DNA polymerase

Transition from Townsend to glow discharge: subcritical, mixed or supercritical

The full parameter space of the transition from Townsend to glow discharge is investigated numerically in one space dimension in the classical model: with electrons and positive ions drifting in the local electric field, impact ionization by electrons ($\alpha$ process), secondary electron emission from the cathode ($\gamma$ process) and space charge effects. We also perform a systematic analytical small current expansion about the Townsend limit up to third order in the total current that fits our numerical data very well. Depending on $\gamma$ and system size pd, the transition from Townsend to glow discharge can show the textbook subcritical behavior, but for smaller values of pd, we also find supercritical or some intermediate ``mixed'' behavior. The analysis in particular lays the basis for understanding the complex spatio-temporal patterns in planar barrier discharge systems.Comment: 12 pages, 10 figures, submitted to Phys. Rev.

Reactive direction control for a mobile robot: A locust-like control of escape direction emerges when a bilateral pair of model locust visual neurons are integrated

Locusts possess a bilateral pair of uniquely identifiable visual neurons that respond vigorously to the image of an approaching object. These neurons are called the lobula giant movement detectors (LGMDs). The locust LGMDs have been extensively studied and this has lead to the development of an LGMD model for use as an artificial collision detector in robotic applications. To date, robots have been equipped with only a single, central artificial LGMD sensor, and this triggers a non-directional stop or rotation when a potentially colliding object is detected. Clearly, for a robot to behave autonomously, it must react differently to stimuli approaching from different directions. In this study, we implement a bilateral pair of LGMD models in Khepera robots equipped with normal and panoramic cameras. We integrate the responses of these LGMD models using methodologies inspired by research on escape direction control in cockroaches. Using ‘randomised winner-take-all’ or ‘steering wheel’ algorithms for LGMD model integration, the khepera robots could escape an approaching threat in real time and with a similar distribution of escape directions as real locusts. We also found that by optimising these algorithms, we could use them to integrate the left and right DCMD responses of real jumping locusts offline and reproduce the actual escape directions that the locusts took in a particular trial. Our results significantly advance the development of an artificial collision detection and evasion system based on the locust LGMD by allowing it reactive control over robot behaviour. The success of this approach may also indicate some important areas to be pursued in future biological research

Semi-Automated Reconstruction of Neural Processes from Large Numbers of Fluorescence Images

We introduce a method for large scale reconstruction of complex bundles of neural processes from fluorescent image stacks. We imaged yellow fluorescent protein labeled axons that innervated a whole muscle, as well as dendrites in cerebral cortex, in transgenic mice, at the diffraction limit with a confocal microscope. Each image stack was digitally re-sampled along an orientation such that the majority of axons appeared in cross-section. A region growing algorithm was implemented in the open-source Reconstruct software and applied to the semi-automatic tracing of individual axons in three dimensions. The progression of region growing is constrained by user-specified criteria based on pixel values and object sizes, and the user has full control over the segmentation process. A full montage of reconstructed axons was assembled from the ∼200 individually reconstructed stacks. Average reconstruction speed is ∼0.5 mm per hour. We found an error rate in the automatic tracing mode of ∼1 error per 250 um of axonal length. We demonstrated the capacity of the program by reconstructing the connectome of motor axons in a small mouse muscle