IDENTIFICATION OF EMG FREQUENCY PATTERNS IN RUNNING BY WAVELET ANALYSIS AND SUPPORT VECTOR MACHINES

The purpose of this study was to identify EMG pattern of running at different speed and incline based on a trial-to-trial analysis. Eight subjects performed treadmill running at five different conditions (4, 5 and 6 m/s, 5m/s at 5° incline, 5m/s at 2° decline). EMG data of eight leg muscles were recorded and transformed by a wavelet analysis (van Tscharner, 2000). Ten subsequent steps of each subject and condition were classified by support vector machines. Between 93 and 100% of all EMG patterns were assigned correctly to the individual. According to the different running conditions recognition rates ranged between 78 and 88%. Hence, support vector machines can be considered as powerful nonlinear tool for the classification of dynamic EMG patterns

Pair Contact Process with Diffusion: Failure of Master Equation Field Theory

We demonstrate that the `microscopic' field theory representation, directly derived from the corresponding master equation, fails to adequately capture the continuous nonequilibrium phase transition of the Pair Contact Process with Diffusion (PCPD). The ensuing renormalization group (RG) flow equations do not allow for a stable fixed point in the parameter region that is accessible by the physical initial conditions. There exists a stable RG fixed point outside this regime, but the resulting scaling exponents, in conjunction with the predicted particle anticorrelations at the critical point, would be in contradiction with the positivity of the equal-time mean-square particle number fluctuations. We conclude that a more coarse-grained effective field theory approach is required to elucidate the critical properties of the PCPD.Comment: revtex, 8 pages, 1 figure include

Primary Structure and Catalytic Mechanism of the Epoxide Hydrolase from Agrobacterium radiobacter AD1

The epoxide hydrolase gene from Agrobacterium radiobacter AD1, a bacterium that is able to grow on epichlorohydrin as the sole carbon source, was cloned by means of the polymerase chain reaction with two degenerate primers based on the N-terminal and C-terminal sequences of the enzyme. The epoxide hydrolase gene coded for a protein of 294 amino acids with a molecular mass of 34 kDa. An identical epoxide hydrolase gene was cloned from chromosomal DNA of the closely related strain A. radiobacter CFZ11. The recombinant epoxide hydrolase was expressed up to 40% of the total cellular protein content in Escherichia coli BL21(DE3) and the purified enzyme had a kcat of 21 s-1 with epichlorohydrin. Amino acid sequence similarity of the epoxide hydrolase with eukaryotic epoxide hydrolases, haloalkane dehalogenase from Xanthobacter autotrophicus GJ10, and bromoperoxidase A2 from Streptomyces aureofaciens indicated that it belonged to the α/β-hydrolase fold family. This conclusion was supported by secondary structure predictions and analysis of the secondary structure with circular dichroism spectroscopy. The catalytic triad residues of epoxide hydrolase are proposed to be Asp107, His275, and Asp246. Replacement of these residues to Ala/Glu, Arg/Gln, and Ala, respectively, resulted in a dramatic loss of activity for epichlorohydrin. The reaction mechanism of epoxide hydrolase proceeds via a covalently bound ester intermediate, as was shown by single turnover experiments with the His275 → Arg mutant of epoxide hydrolase in which the ester intermediate could be trapped.

Reaction-controlled diffusion: Monte Carlo simulations

We study the coupled two-species non-equilibrium reaction-controlled diffusion model introduced by Trimper et al. [Phys. Rev. E 62, 6071 (2000)] by means of detailed Monte Carlo simulations in one and two dimensions. Particles of type A may independently hop to an adjacent lattice site provided it is occupied by at least one B particle. The B particle species undergoes diffusion-limited reactions. In an active state with nonzero, essentially homogeneous B particle saturation density, the A species displays normal diffusion. In an inactive, absorbing phase with exponentially decaying B density, the A particles become localized. In situations with algebraic decay rho_B(t) ~ t^{-alpha_B}, as occuring either at a non-equilibrium continuous phase transition separating active and absorbing states, or in a power-law inactive phase, the A particles propagate subdiffusively with mean-square displacement ~ t^{1-alpha_A}. We find that within the accuracy of our simulation data, \alpha_A = \alpha_B as predicted by a simple mean-field approach. This remains true even in the presence of strong spatio-temporal fluctuations of the B density. However, in contrast with the mean-field results, our data yield a distinctly non-Gaussian A particle displacement distribution n_A(x,t) that obeys dynamic scaling and looks remarkably similar for the different processes investigated here. Fluctuations of effective diffusion rates cause a marked enhancement of n_A(x,t) at low displacements |x|, indicating a considerable fraction of practically localized A particles, as well as at large traversed distances.Comment: Revtex, 19 pages, 27 eps figures include

Waldschmidt Constant for Squarefree Monomial Ideals

Given a squarefree monomial ideal I ⊆ R = k[x1, . . . , xn], we show that α(I), the Waldschmidt constant of I, can be expressed as the optimal solution to a linear program constructed from the primary decomposition of I. By applying results from fractional graph theory, we can then express α(I) in terms of the fractional chromatic number of a hypergraph also constructed from the primary decomposition of I. Moreover, expressing α(I) as the solution to a linear program enables us to prove a Chudnovsky-like lower bound on α(I), thus verifying a conjecture of Cooper-Embree- Ha`-Hoefel for monomial ideals in the squarefree case. As an application, we compute the Waldschmidt constant and the resurgence for some families of squarefree monomial ideals. For example, we determine both constants for unions of general linear subspaces of Pn with few components compared to n, and we find the Waldschmidt constant for the Stanley-Reisner ideal of a uniform matroid

Nonequilibrium critical dynamics of the relaxational models C and D

We investigate the critical dynamics of the $n$-component relaxational models C and D which incorporate the coupling of a nonconserved and conserved order parameter S, respectively, to the conserved energy density rho, under nonequilibrium conditions by means of the dynamical renormalization group. Detailed balance violations can be implemented isotropically by allowing for different effective temperatures for the heat baths coupling to the slow modes. In the case of model D with conserved order parameter, the energy density fluctuations can be integrated out. For model C with scalar order parameter, in equilibrium governed by strong dynamic scaling (z_S = z_rho), we find no genuine nonequilibrium fixed point. The nonequilibrium critical dynamics of model C with n = 1 thus follows the behavior of other systems with nonconserved order parameter wherein detailed balance becomes effectively restored at the phase transition. For n >= 4, the energy density decouples from the order parameter. However, for n = 2 and n = 3, in the weak dynamic scaling regime (z_S <= z_rho) entire lines of genuine nonequilibrium model C fixed points emerge to one-loop order, which are characterized by continuously varying critical exponents. Similarly, the nonequilibrium model C with spatially anisotropic noise and n < 4 allows for continuously varying exponents, yet with strong dynamic scaling. Subjecting model D to anisotropic nonequilibrium perturbations leads to genuinely different critical behavior with softening only in subsectors of momentum space and correspondingly anisotropic scaling exponents. Similar to the two-temperature model B the effective theory at criticality can be cast into an equilibrium model D dynamics, albeit incorporating long-range interactions of the uniaxial dipolar type.Comment: Revtex, 23 pages, 5 eps figures included (minor additions), to appear in Phys. Rev.

Theory of Branching and Annihilating Random Walks

A systematic theory for the diffusion--limited reaction processes $A + A \to 0$ and $A \to (m+1) A$ is developed. Fluctuations are taken into account via the field--theoretic dynamical renormalization group. For $m$ even the mean field rate equation, which predicts only an active phase, remains qualitatively correct near $d_c = 2$ dimensions; but below $d_c' \approx 4/3$ a nontrivial transition to an inactive phase governed by power law behavior appears. For $m$ odd there is a dynamic phase transition for any $d \leq 2$ which is described by the directed percolation universality class.Comment: 4 pages, revtex, no figures; final version with slight changes, now accepted for publication in Phys. Rev. Let

The Waldschmidt constant for squarefree monomial ideals

Given a squarefree monomial ideal $I \subseteq R =k[x_1,\ldots,x_n]$, we show that $\widehat\alpha(I)$, the Waldschmidt constant of $I$, can be expressed as the optimal solution to a linear program constructed from the primary decomposition of $I$. By applying results from fractional graph theory, we can then express $\widehat\alpha(I)$ in terms of the fractional chromatic number of a hypergraph also constructed from the primary decomposition of $I$. Moreover, expressing $\widehat\alpha(I)$ as the solution to a linear program enables us to prove a Chudnovsky-like lower bound on $\widehat\alpha(I)$, thus verifying a conjecture of Cooper-Embree-H\`a-Hoefel for monomial ideals in the squarefree case. As an application, we compute the Waldschmidt constant and the resurgence for some families of squarefree monomial ideals. For example, we determine both constants for unions of general linear subspaces of $\mathbb{P}^n$ with few components compared to $n$, and we find the Waldschmidt constant for the Stanley-Reisner ideal of a uniform matroid.Comment: 26 pages. This project was started at the Mathematisches Forschungsinstitut Oberwolfach (MFO) as part of the mini-workshop "Ideals of Linear Subspaces, Their Symbolic Powers and Waring Problems" held in February 2015. Comments are welcome. Revised version corrects some typos, updates the references, and clarifies some hypotheses. To appear in the Journal of Algebraic Combinatoric

Critical Behavior of O(n)-symmetric Systems With Reversible Mode-coupling Terms: Stability Against Detailed-balance Violation

We investigate nonequilibrium critical properties of $O(n)$-symmetric models with reversible mode-coupling terms. Specifically, a variant of the model of Sasv\'ari, Schwabl, and Sz\'epfalusy is studied, where violation of detailed balance is incorporated by allowing the order parameter and the dynamically coupled conserved quantities to be governed by heat baths of different temperatures $T_S$ and $T_M$, respectively. Dynamic perturbation theory and the field-theoretic renormalization group are applied to one-loop order, and yield two new fixed points in addition to the equilibrium ones. The first one corresponds to $\Theta = T_S / T_M = \infty$ and leads to model A critical behavior for the order parameter and to anomalous noise correlations for the generalized angular momenta; the second one is at $\Theta = 0$ and is characterized by mean-field behavior of the conserved quantities, by a dynamic exponent $z = d / 2$ equal to that of the equilibrium SSS model, and by modified static critical exponents. However, both these new fixed points are unstable, and upon approaching the critical point detailed balance is restored, and the equilibrium static and dynamic critical properties are recovered.Comment: 18 pages, RevTeX, 1 figure included as eps-file; submitted to Phys. Rev.