Monte Carlo limit cycle characterization

The fixed point implementation of IIR digital filters usually leads to the appearance of zero-input limit cycles, which degrade the performance of the system. In this paper, we develop an efficient Monte Carlo algorithm to detect and characterize limit cycles in fixed-point IIR digital filters. The proposed approach considers filters formulated in the state space and is valid for any fixed point representation and quantization function. Numerical simulations on several high-order filters, where an exhaustive search is unfeasible, show the effectiveness of the proposed approach

Shift in critical temperature for random spatial permutations with cycle weights

We examine a phase transition in a model of random spatial permutations which originates in a study of the interacting Bose gas. Permutations are weighted according to point positions; the low-temperature onset of the appearance of arbitrarily long cycles is connected to the phase transition of Bose-Einstein condensates. In our simplified model, point positions are held fixed on the fully occupied cubic lattice and interactions are expressed as Ewens-type weights on cycle lengths of permutations. The critical temperature of the transition to long cycles depends on an interaction-strength parameter $\alpha$. For weak interactions, the shift in critical temperature is expected to be linear in $\alpha$ with constant of linearity $c$. Using Markov chain Monte Carlo methods and finite-size scaling, we find $c = 0.618 \pm 0.086$. This finding matches a similar analytical result of Ueltschi and Betz. We also examine the mean longest cycle length as a fraction of the number of sites in long cycles, recovering an earlier result of Shepp and Lloyd for non-spatial permutations.Comment: v2 incorporated reviewer comments. v3 removed two extraneous figures which appeared at the end of the PDF

Design Principles for High-Capacity Mn-Based Cation-Disordered Rocksalt Cathodes

Mn-based Li-excess cation-disordered rocksalt (DRX) oxyfluorides are promising candidates for next-generation rechargeable battery cathodes owing to their large energy densities, the earth abundance, and low cost of Mn. In this work, we synthesized and electrochemically tested four representative compositions in the Li-Mn-O-F DRX chemical space with various Li and F content. While all compositions achieve higher than 200 mAh g−1 initial capacity and good cyclability, we show that the Li-site distribution plays a more important role than the metal-redox capacity in determining the initial capacity, whereas the metal-redox capacity is more closely related to the cyclability of the materials. We apply these insights and generate a capacity map of the Li-Mn-O-F chemical space, LixMn2-xO2-yFy (1.167 ≤ x ≤ 1.333, 0 ≤ y ≤ 0.667), which predicts both accessible Li capacity and Mn-redox capacity. This map allows the design of compounds that balance high capacity with good cyclability

Walking dynamics are symmetric (enough)

Many biological phenomena such as locomotion, circadian cycles, and breathing are rhythmic in nature and can be modeled as rhythmic dynamical systems. Dynamical systems modeling often involves neglecting certain characteristics of a physical system as a modeling convenience. For example, human locomotion is frequently treated as symmetric about the sagittal plane. In this work, we test this assumption by examining human walking dynamics around the steady-state (limit-cycle). Here we adapt statistical cross validation in order to examine whether there are statistically significant asymmetries, and even if so, test the consequences of assuming bilateral symmetry anyway. Indeed, we identify significant asymmetries in the dynamics of human walking, but nevertheless show that ignoring these asymmetries results in a more consistent and predictive model. In general, neglecting evident characteristics of a system can be more than a modeling convenience---it can produce a better model.Comment: Draft submitted to Journal of the Royal Society Interfac

Improving Sensitivity to Weak Pulsations with Photon Probability Weighting

All gamma-ray telescopes suffer from source confusion due to their inability to focus incident high-energy radiation, and the resulting background contamination can obscure the periodic emission from faint pulsars. In the context of the Fermi Large Area Telescope, we outline enhanced statistical tests for pulsation in which each photon is weighted by its probability to have originated from the candidate pulsar. The probabilities are calculated using the instrument response function and a full spectral model, enabling powerful background rejection. With Monte Carlo methods, we demonstrate that the new tests increase the sensitivity to pulsars by more than 50% under a wide range of conditions. This improvement may appreciably increase the completeness of the sample of radio-loud gamma-ray pulsars. Finally, we derive the asymptotic null distribution for the H-test, expanding its domain of validity to arbitrarily complex light curves.Comment: 10 pages, 11 figures, published by ApJ; v2 fixes an error in Eq.

Path-integral Monte Carlo and the squeezed trapped Bose-Einstein gas

Bose-Einstein condensation has been experimentally found to take place in finite trapped systems when one of the confining frequencies is increased until the gas becomes effectively two-dimensional (2D). We confirm the plausibility of this result by performing path-integral Monte Carlo (PIMC) simulations of trapped Bose gases of increasing anisotropy and comparing them to the predictions of finite-temperature many-body theory. PIMC simulations provide an essentially exact description of these systems; they yield the density profile directly and provide two different estimates for the condensate fraction. For the ideal gas, we find that the PIMC column density of the squeezed gas corresponds quite accurately to that of the exact analytic solution and, moreover, is well mimicked by the density of a 2D gas at the same temperature; the two estimates for the condensate fraction bracket the exact result. For the interacting case, we find 2D Hartree-Fock solutions whose density profiles coincide quite well with the PIMC column densities and whose predictions for the condensate fraction are again bracketed by the PIMC estimates.Comment: 2 pages, 3 figure

Probabilistic Reachability Analysis for Large Scale Stochastic Hybrid Systems

This paper studies probabilistic reachability analysis for large scale stochastic hybrid systems (SHS) as a problem of rare event estimation. In literature, advanced rare event estimation theory has recently been embedded within a stochastic analysis framework, and this has led to significant novel results in rare event estimation for a diffusion process using sequential MC simulation. This paper presents this rare event estimation theory directly in terms of probabilistic reachability analysis of an SHS, and develops novel theory which allows to extend the novel results for application to a large scale SHS where a very huge number of rare discrete modes may contribute significantly to the reach probability. Essentially, the approach taken is to introduce an aggregation of the discrete modes, and to develop importance sampling relative to the rare switching between the aggregation modes. The practical working of this approach is demonstrated for the safety verification of an advanced air traffic control example