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Sep 23, 2013
09/13

by
Aljaž Zalar

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A linear polyomial non-negative on the non-negativity domain of finitely many linear polynomials can be expressed as their non-negative linear combination. Recently, under several additional assumptions, Helton, Klep, and McCullough extended this result to matrix polynomials. The aim of this paper is to study which of these additional assumptions are really necessary.

Source: http://arxiv.org/abs/1012.5420v2

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8.0

Jun 27, 2018
06/18

by
Aljaž Zalar

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The matrix Fej\'er-Riesz theorem characterizes positive semidefinite matrix polynomials on the real line $\mathbb{R}$. We extend a characterization to arbitrary closed semialgebraic sets $K\subseteq \mathbb{R}$ by the use of matrix preorderings from real algebraic geometry. In the compact case a denominator-free characterization exists, while in the non-compact case there are counterexamples. However, there is a weaker characterization with denominators in the non-compact case. At the end we...

Topics: Algebraic Geometry, Mathematics

Source: http://arxiv.org/abs/1503.06034

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47

Sep 23, 2013
09/13

by
Aljaz Godec; Franci Merzel

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The hydrophobic effect (HE) is commonly associated with the demixing of oil and water at ambient conditions and plays the leading role in determining the structure and stability of biomolecular assembly in aqueous solutions. On the molecular scale HE has an entropic origin. It is believed that hydrophobic particles induce order in the surrounding water by reducing the volume of con- figuration space available for hydrogen bonding. Here we show with computer simulation results that this...

Source: http://arxiv.org/abs/1202.1228v1

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43

Sep 22, 2013
09/13

by
Aljaz Godec; Ralf Metzler

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We study the ergodic properties of superdiffusive, spatiotemporally coupled Levy walk processes. For trajectories of finite duration, we reveal a distinct scatter of the scaling exponents of the time averaged mean squared displacement delta**2 around the ensemble value 3-alpha (1

Source: http://arxiv.org/abs/1210.4418v1

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17

Jun 27, 2018
06/18

by
Aljaz Godec; Ralf Metzler

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The kinetics of a variety of transport-controlled processes can be reduced to the problem of determining the mean time needed to arrive at a given location for the first time, the so called mean first passage time (MFPT) problem. The occurrence of occasional large jumps or intermittent patterns combining various types of motion are known to outperform the standard random walk with respect to the MFPT, by reducing oversampling of space. Here we show that a regular but spatially heterogeneous...

Topics: Condensed Matter, Statistical Mechanics

Source: http://arxiv.org/abs/1503.00558

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17

Jun 26, 2018
06/18

by
Aljaz Godec; Ralf Metzler

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In biological cells and novel diagnostic devices biochemical receptors need to be sensitive to extremely small concentration changes of signaling molecules. The accuracy of such molecular signaling is ultimately limited by the counting noise imposed by the thermal diffusion of molecules. Many macromolecules and organelles transiently bind to molecular motors and are then actively transported. We here show that a random albeit directed delivery of signaling molecules to within a typical...

Topics: Subcellular Processes, Biological Physics, Quantitative Biology, Physics

Source: http://arxiv.org/abs/1501.02941

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Jun 27, 2018
06/18

by
Henning Krusemann; Aljaz Godec; Ralf Metzler

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We study the first passage dynamics of an ageing stochastic process in the continuous time random walk (CTRW) framework. In such CTRW processes the test particle performs a random walk, in which successive steps are separated by random waiting times distributed in terms of the waiting time probability density function $\psi(t) \simeq t^{-1-\alpha}$) ($0\le \alpha \le 2$). An ageing stochastic process is defined by the explicit dependence of its dynamic quantities on the ageing time $t_a$, the...

Topics: Condensed Matter, Statistical Mechanics

Source: http://arxiv.org/abs/1503.09028

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Oct 24, 2014
10/14

by
PogaCnik, Aljaz; Pozar, Tomaz; Kalin, Mitjan; Mozina, Janez

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This article is from Sensors (Basel, Switzerland) , volume 13 . Abstract We report on the successful realization of a contactless, non-perturbing, displacement-measuring system for characterizing the surface roughness of polymer materials used in tribological applications. A single, time-dependent, scalar value, dubbed the collective micro-asperity deformation, is extracted from the normal-displacement measurements of normally loaded polymer samples. The displacement measurements with a...

Source: http://www.ncbi.nlm.nih.gov/pmc/articles/PMC3574698