Influence of the driving mechanism on the response of systems with athermal dynamics: The example of the random-field Ising model

We investigate the influence of the driving mechanism on the hysteretic response of systems with athermal dynamics. In the framework of local mean-field theory at finite temperature (but neglecting thermally activated processes), we compare the rate-independent hysteresis loops obtained in the random field Ising model when controlling either the external magnetic field H or the extensive magnetization M. Two distinct behaviors are observed, depending on disorder strength. At large disorder, the H-driven and M-driven protocols yield identical hysteresis loops in the thermodynamic limit. At low disorder, when the H-driven magnetization curve is discontinuous (due to the presence of a macroscopic avalanche), the M-driven loop is reentrant while the induced field exhibits strong intermittent fluctuations and is only weakly self-averaging. The relevance of these results to the experimental observations in ferromagnetic materials, shape memory alloys, and other disordered systems is discussed.

Probability Theory. Stochastic Processes And Their Applications Probabilistic Analysis Of Some Queueing And Inventory Models

In this thesis we attempt to make a probabilistic analysis of some physically realizable, though complex, storage and queueing models. It is essentially a mathematical study of the stochastic processes underlying these models. Our aim is to have an improved understanding of the behaviour of such models, that may widen their applicability. Different inventory systems with randon1 lead times, vacation to the server, bulk demands, varying ordering levels, etc. are considered. Also we study some finite and infinite capacity queueing systems with bulk service and vacation to the server and obtain the transient solution in certain cases. Each chapter in the thesis is provided with self introduction and some important references

On the Noise Model of Support Vector Machine Regression

Support Vector Machines Regression (SVMR) is a regression technique which has been recently introduced by V. Vapnik and his collaborators (Vapnik, 1995; Vapnik, Golowich and Smola, 1996). In SVMR the goodness of fit is measured not by the usual quadratic loss function (the mean square error), but by a different loss function called Vapnik"s $epsilon$- insensitive loss function, which is similar to the "robust" loss functions introduced by Huber (Huber, 1981). The quadratic loss function is well justified under the assumption of Gaussian additive noise. However, the noise model underlying the choice of Vapnik's loss function is less clear. In this paper the use of Vapnik's loss function is shown to be equivalent to a model of additive and Gaussian noise, where the variance and mean of the Gaussian are random variables. The probability distributions for the variance and mean will be stated explicitly. While this work is presented in the framework of SVMR, it can be extended to justify non-quadratic loss functions in any Maximum Likelihood or Maximum A Posteriori approach. It applies not only to Vapnik's loss function, but to a much broader class of loss functions.

Thermal Noise Behavior of the Bridge Circuit

This paper considers a connection between the deterministic and noisy behavior of nonlinear networks. Specifically, a particular bridge circuit is examined which has two possibly nonlinear energy storage elements. By proper choice of the constitutive relations for the network elements, the deterministic terminal behavior reduces to that of a single linear resistor. This reduction of the deterministic terminal behavior, in which a natural frequency of a linear circuit does not appear in the driving-point impedance, has been shown in classical circuit theory books (e.g. [1, 2]). The paper shows that, in addition to the reduction of the deterministic behavior, the thermal noise at the terminals of the network, arising from the usual Nyquist-Johnson noise model associated with each resistor in the network, is also exactly that of a single linear resistor. While this result for the linear time-invariant (LTI) case is a direct consequence of a well-known result for RLC circuits, the nonlinear result is novel. We show that the terminal noise current is precisely that predicted by the Nyquist-Johnson model for R if the driving voltage is zero or constant, but not if the driving voltage is time-dependent or the inductor and capacitor are time-varying

Monitoring procedures in environmental geochemistry and compositional data analysis theory

First discussion on compositional data analysis is attributable to Karl Pearson, in 1897. However, notwithstanding the recent developments on algebraic structure of the simplex, more than twenty years after Aitchison’s idea of log-transformations of closed data, scientific literature is again full of statistical treatments of this type of data by using traditional methodologies. This is particularly true in environmental geochemistry where besides the problem of the closure, the spatial structure (dependence) of the data have to be considered. In this work we propose the use of log-contrast values, obtained by a simplicial principal component analysis, as LQGLFDWRUV of given environmental conditions. The investigation of the log-constrast frequency distributions allows pointing out the statistical laws able to generate the values and to govern their variability. The changes, if compared, for example, with the mean values of the random variables assumed as models, or other reference parameters, allow defining monitors to be used to assess the extent of possible environmental contamination. Case study on running and ground waters from Chiavenna Valley (Northern Italy) by using Na+, K+, Ca2+, Mg2+, HCO3-, SO4 2- and Cl- concentrations will be illustrated

TU Graz: Course: 707.000 Web Science and Web Technology: Lecture 3: Network Theory and Terminology

In this class, we will discuss network theory fundamentals, including concepts such as diameter, distance, clustering coefficient and others. We will also discuss different types of networks, such as scale-free networks, random networks etc. Readings: Graph structure in the Web, A. Broder and R. Kumar and F. Maghoul and P. Raghavan and S. Rajagopalan and R. Stata and A. Tomkins and J. Wiener Computer Networks 33 309--320 (2000) [Web link, Alternative Link] Optional: The Structure and Function of Complex Networks, M.E.J. Newman, SIAM Review 45 167--256 (2003) [Web link] Original course at: http://kmi.tugraz.at/staff/markus/courses/SS2008/707.000_web-science/

Conceptuals Mentefactos as a Didactic-Pedagogical Strategy of the Basic Concepts in the Sampling Theory Applyed to the Health Research

In populational sampling it is vitally important to clarify and discern: first, the design or sampling method used to solve the research problem; second, the sampling size, taking into account different components (precision, reliability, variance); third, random selection and fourth, the precision estimate (sampling errors), so as to determine if it is possible to infer the obtained estimates from the target population. The existing difficulty to use concepts from the sampling theory is to understand them with absolute clarity and, to achieve it, the help from didactic-pedagogical strategies arranged as conceptual “mentefactos” (simple hierarchic diagrams organized from propositions) may prove useful. This paper presents the conceptual definition, through conceptual “mentefactos”, of the most important populational probabilistic sampling concepts, in order to obtain representative samples from populations in health research.

Fronts from complex two-dimensional dispersal kernels: theory and application to Reid's paradox

Bimodal dispersal probability distributions with characteristic distances differing by several orders of magnitude have been derived and favorably compared to observations by Nathan [Nature (London) 418, 409 (2002)]. For such bimodal kernels, we show that two-dimensional molecular dynamics computer simulations are unable to yield accurate front speeds. Analytically, the usual continuous-space random walks (CSRWs) are applied to two dimensions. We also introduce discrete-space random walks and use them to check the CSRW results (because of the inefficiency of the numerical simulations). The physical results reported are shown to predict front speeds high enough to possibly explain Reid's paradox of rapid tree migration. We also show that, for a time-ordered evolution equation, fronts are always slower in two dimensions than in one dimension and that this difference is important both for unimodal and for bimodal kernels

Sudden stratospheric warmings as noise-induced transitions

Sudden stratospheric warmings (SSWs) are usually considered to be initiated by planetary wave activity. Here it is asked whether small-scale variability (e.g., related to gravity waves) can lead to SSWs given a certain amount of planetary wave activity that is by itself not sufficient to cause a SSW. A highly vertically truncated version of the Holton–Mass model of stratospheric wave–mean flow interaction, recently proposed by Ruzmaikin et al., is extended to include stochastic forcing. In the deterministic setting, this low-order model exhibits multiple stable equilibria corresponding to the undisturbed vortex and SSW state, respectively. Momentum forcing due to quasi-random gravity wave activity is introduced as an additive noise term in the zonal momentum equation. Two distinct approaches are pursued to study the stochastic system. First, the system, initialized at the undisturbed state, is numerically integrated many times to derive statistics of first passage times of the system undergoing a transition to the SSW state. Second, the Fokker–Planck equation corresponding to the stochastic system is solved numerically to derive the stationary probability density function of the system. Both approaches show that even small to moderate strengths of the stochastic gravity wave forcing can be sufficient to cause a SSW for cases for which the deterministic system would not have predicted a SSW.

Mapping and controlling molecular processes: The application of control theory and system identification algorithms to ASOPS and other fast pulse spectroscopies

Asynchronous Optical Sampling (ASOPS) [1,2] and frequency comb spectrometry [3] based on dual Ti:saphire resonators operated in a master/slave mode have the potential to improve signal to noise ratio in THz transient and IR sperctrometry. The multimode Brownian oscillator time-domain response function described by state-space models is a mathematically robust framework that can be used to describe the dispersive phenomena governed by Lorentzian, Debye and Drude responses. In addition, the optical properties of an arbitrary medium can be expressed as a linear combination of simple multimode Brownian oscillator functions. The suitability of a range of signal processing schemes adopted from the Systems Identification and Control Theory community for further processing the recorded THz transients in the time or frequency domain will be outlined [4,5]. Since a femtosecond duration pulse is capable of persistent excitation of the medium within which it propagates, such approach is perfectly justifiable. Several de-noising routines based on system identification will be shown. Furthermore, specifically developed apodization structures will be discussed. These are necessary because due to dispersion issues, the time-domain background and sample interferograms are non-symmetrical [6-8]. These procedures can lead to a more precise estimation of the complex insertion loss function. The algorithms are applicable to femtosecond spectroscopies across the EM spectrum. Finally, a methodology for femtosecond pulse shaping using genetic algorithms aiming to map and control molecular relaxation processes will be mentioned.

Noise, predation risk compensation and vigilance in the chaffinch Fringilla coelebs

Background noise should in theory hinder detection of auditory cues associated with approaching danger. We tested whether foraging chaffinches Fringilla coelebs responded to background noise by increasing vigilance, and examined whether this was explained by predation risk compensation or by a novel stimulus hypothesis. The former predicts that only inter-scan interval should be modified in the presence of background noise, not vigilance levels generally. This is because noise hampers auditory cue detection and increases perceived predation risk primarily when in the head-down position, and also because previous tests have shown that only interscan interval is correlated with predator detection ability in this system. Chaffinches only modified interscan interval supporting this hypothesis. At the same time they made significantly fewer pecks when feeding during the background noise treatment and so the increased vigilance led to a reduction in intake rate, suggesting that compensating for the increased predation risk could indirectly lead to a fitness cost. Finally, the novel stimulus hypothesis predicts that chaffinches should habituate to the noise, which did not occur within a trial or over 5 subsequent trials. We conclude that auditory cues may be an important component of the trade-off between vigilance and feeding, and discuss possible implications for anti-predation theory and ecological processes

High signal to noise ratio THz spectroscopy with ASOPS and signal processing schemes for mapping and controlling molecular and bulk relaxation processes

Asynchronous Optical Sampling has the potential to improve signal to noise ratio in THz transient sperctrometry. The design of an inexpensive control scheme for synchronising two femtosecond pulse frequency comb generators at an offset frequency of 20 kHz is discussed. The suitability of a range of signal processing schemes adopted from the Systems Identification and Control Theory community for further processing recorded THz transients in the time and frequency domain are outlined. Finally, possibilities for femtosecond pulse shaping using genetic algorithms are mentioned.

Neural networks for identification of nonlinear systems under random piecewise polynomial disturbances

The problem of identification of a nonlinear dynamic system is considered. A two-layer neural network is used for the solution of the problem. Systems disturbed with unmeasurable noise are considered, although it is known that the disturbance is a random piecewise polynomial process. Absorption polynomials and nonquadratic loss functions are used to reduce the effect of this disturbance on the estimates of the optimal memory of the neural-network model.