Field Driven Thermostated System : A Non-Linear Multi-Baker Map

In this paper, we discuss a simple model for a field driven, thermostated random walk that is constructed by a suitable generalization of a multi-baker map. The map is a usual multi-baker, but perturbed by a thermostated external field that has many of the properties of the fields used in systems with Gaussian thermostats. For small values of the driving field, the map is hyperbolic and has a unique SRB measure that we solve analytically to first order in the field parameter. We then compute the positive and negative Lyapunov exponents to second order and discuss their relation to the transport properties. For higher values of the parameter, this system becomes non-hyperbolic and posseses an attractive fixed point.Comment: 6 pages + 5 figures, to appear in Phys. Rev.

List decoding of noisy Reed-Muller-like codes

First- and second-order Reed-Muller (RM(1) and RM(2), respectively) codes are two fundamental error-correcting codes which arise in communication as well as in probabilistically-checkable proofs and learning. In this paper, we take the first steps toward extending the quick randomized decoding tools of RM(1) into the realm of quadratic binary and, equivalently, Z_4 codes. Our main algorithmic result is an extension of the RM(1) techniques from Goldreich-Levin and Kushilevitz-Mansour algorithms to the Hankel code, a code between RM(1) and RM(2). That is, given signal s of length N, we find a list that is a superset of all Hankel codewords phi with dot product to s at least (1/sqrt(k)) times the norm of s, in time polynomial in k and log(N). We also give a new and simple formulation of a known Kerdock code as a subcode of the Hankel code. As a corollary, we can list-decode Kerdock, too. Also, we get a quick algorithm for finding a sparse Kerdock approximation. That is, for k small compared with 1/sqrt{N} and for epsilon > 0, we find, in time polynomial in (k log(N)/epsilon), a k-Kerdock-term approximation s~ to s with Euclidean error at most the factor (1+epsilon+O(k^2/sqrt{N})) times that of the best such approximation

Fracture toughness and fatigue-crack propagation in a Zr–Ti–Ni–Cu–Be bulk metallic glass

The recent development of metallic alloy systems which can be processed with an amorphous structure over large dimensions, specifically to form metallic glasses at low cooling rates (similar to 10 K/s), has permitted novel measurements of important mechanical properties. These include, for example, fatigue-crack growth and fracture toughness behavior, representing the conditions governing the subcritical and critical propagation of cracks in these structures. In the present study, bulk plates of a Zr41.2Ti13.8Cu12.5Ni10Be22.5 alloy, machined into 7 mm wide, 38 mm thick compact-tension specimens and fatigue precracked following standard procedures, revealed fracture toughnesses in the fully amorphous structure of K(lc)similar to 55 MPa root m, i.e., comparable with that of a high-strength steel or aluminum ahoy. However, partial and full crystallization, e.g., following thermal exposure at 633 K or more, was found to result in a drastic reduction in fracture toughness to similar to 1 MPa root m, i.e., comparable with silica glass. The fully amorphous alloy was also found to be susceptible to fatigue-crack growth under cyclic loading, with growth-rate properties comparable to that of ductile crystalline metallic alloys, such as high-strength steels or aluminum alloys; no such fatigue was seen in the partially or fully crystallized alloys which behaved like very brittle ceramics. Possible micromechanical mechanisms for such behavior are discussed

Algorithmic linear dimension reduction in the l_1 norm for sparse vectors

This paper develops a new method for recovering m-sparse signals that is simultaneously uniform and quick. We present a reconstruction algorithm whose run time, O(m log^2(m) log^2(d)), is sublinear in the length d of the signal. The reconstruction error is within a logarithmic factor (in m) of the optimal m-term approximation error in l_1. In particular, the algorithm recovers m-sparse signals perfectly and noisy signals are recovered with polylogarithmic distortion. Our algorithm makes O(m log^2 (d)) measurements, which is within a logarithmic factor of optimal. We also present a small-space implementation of the algorithm. These sketching techniques and the corresponding reconstruction algorithms provide an algorithmic dimension reduction in the l_1 norm. In particular, vectors of support m in dimension d can be linearly embedded into O(m log^2 d) dimensions with polylogarithmic distortion. We can reconstruct a vector from its low-dimensional sketch in time O(m log^2(m) log^2(d)). Furthermore, this reconstruction is stable and robust under small perturbations

Non-equilibrium Lorentz gas on a curved space

The periodic Lorentz gas with external field and iso-kinetic thermostat is equivalent, by conformal transformation, to a billiard with expanding phase-space and slightly distorted scatterers, for which the trajectories are straight lines. A further time rescaling allows to keep the speed constant in that new geometry. In the hyperbolic regime, the stationary state of this billiard is characterized by a phase-space contraction rate, equal to that of the iso-kinetic Lorentz gas. In contrast to the iso-kinetic Lorentz gas where phase-space contraction occurs in the bulk, the phase-space contraction rate here takes place at the periodic boundaries

Knowing your neighbourhood: local ecology and personal experience predict neighbourhood perceptions in Belfast, Northern Ireland

Evolutionary theory predicts that humans should adjust their life-history strategies in response to local ecological threats and opportunities in order to maximize their reproductive success. Cues representing threats to individuals' lives and health in modern, Western societies may come in the form of local ages at death, morbidity rate and crime rate in their local area, whereas the adult sex ratio represents a measure of the competition for reproductive partners. These characteristics are believed to have a strong influence over a wide range of behaviours, but whether they are accurately perceived has not been robustly tested. Here, we investigate whether perceptions of four neighbourhood characteristics are accurate across eight neighbourhoods in Belfast, Northern Ireland. We find that median age at death and morbidity rates are accurately perceived, whereas adult sex ratios and crime rates are not. We suggest that both neighbourhood characteristics and personal experiences contribute to the formation of perceptions. This should be considered by researchers looking for associations between area-level factors

Quantising on a category

We review the problem of finding a general framework within which one can construct quantum theories of non-standard models for space, or space-time. The starting point is the observation that entities of this type can typically be regarded as objects in a category whose arrows are structure-preserving maps. This motivates investigating the general problem of quantising a system whose `configuration space' (or history-theory analogue) is the set of objects \Ob\Q in a category \Q. We develop a scheme based on constructing an analogue of the group that is used in the canonical quantisation of a system whose configuration space is a manifold $Q\simeq G/H$, where $G$ and $H$ are Lie groups. In particular, we choose as the analogue of $G$ the monoid of `arrow fields' on \Q. Physically, this means that an arrow between two objects in the category is viewed as an analogue of momentum. After finding the `category quantisation monoid', we show how suitable representations can be constructed using a bundle (or, more precisely, presheaf) of Hilbert spaces over \Ob\Q. For the example of a category of finite sets, we construct an explicit representation structure of this type.Comment: To appear in a volume dedicated to the memory of James Cushin

Parity-Projected Shell Model Monte Carlo Level Densities for fp-shell Nuclei

We calculate parity-dependent level densities for the even-even isotopes 58,62,66 Fe and 58 Ni and the odd-A nuclei 59 Ni and 65 Fe using the Shell Model Monte Carlo method. We perform these calculations in the complete fp-gds shell-model space using a pairing+quadrupole residual interaction. We find that, due to pairing of identical nucleons, the low-energy spectrum is dominated by positive parity states. Although these pairs break at around the same excitation energy in all nuclei, the energy dependence of the ratio of negative-to-positive parity level densities depends strongly on the particular nucleus of interest. We find equilibration of both parities at noticeably lower excitation energies for the odd-A nuclei 59 Ni and 65 Fe than for the neighboring even-even nuclei 58 Ni and 66 Fe.Comment: 5 pages, 4 figures, submitted to Phys. Rev.

Phase Coherent Precessional Magnetization Reversal in Micro-scopic Spin Valve Elements

We study the precessional switching of the magnetization in microscopic spin valve cells induced by ultra short in-plane hard axis magnetic field pulses. Stable and highly efficient switching is monitored following pulses as short as 140 ps with energies down to 15 pJ. Multiple application of identical pulses reversibly toggles the cell's magnetization be-tween the two easy directions. Variations of pulse duration and amplitude reveal alter-nating regimes of switching and non-switching corresponding to transitions from in-phase to out-of-phase excitations of the magnetic precession by the field pulse. In the low field limit damping becomes predominant and a relaxational reversal is found allowing switching by hard axis fields below the in-plane anisotropy field threshold.Comment: 17 pages, 4 figure

Integrated cost-benefit analysis of tsetse control and herd productivity to inform control programs for animal African trypanosomiasis

Animal African trypanosomiasis (AAT) and its tsetse vector are responsible for annual losses estimated in billions of US dollars ($). Recent years have seen the implementation of a series of multinational interventions. However, actors of AAT control face complex resource allocation decisions due to the geographical range of AAT, diversity of ecological and livestock systems, and range of control methods available. The study presented here integrates an existing tsetse abundance model with a bio-economic herd model that captures local production characteristics as well as heterogeneities in AAT incidence and breed. These models were used to predict the impact of tsetse elimination on the net value of cattle production in the districts of Mambwe, in Zambia, and Faro et Déo in Cameroon. The net value of cattle production under the current situation was used as a baseline, and compared with alternative publicly funded control programmes. In Zambia, the current baseline is AAT control implemented privately by cattle owners (Scenario Z0). In Cameroon, the baseline (Scenario C0) is a small-scale publicly funded tsetse control programme and privately funded control at farm level. The model was run for 10 years, using a discount rate of 5%