Deterministic Part Research Articles

Statistics of Correlations and Fluctuations in a Stochastic Model of Wealth Exchange.

In our recently proposed stochastic version of discretized kinetic theory, the exchange of wealth in a society is modelled through a large system of Langevin equations. The deterministic part of the equations is based on non-linear transition probabilities between income classes. The noise terms can be additive, multiplicative or mixed, both with white or Ornstein–Uhlenbeck spectrum. The most important measured correlations are those between Gini inequality index G and social mobility M, between total income and G, and between M and total income. We describe numerical results concerning these correlations and a quantity which gives average stochastic deviations from the equilibrium solutions in dependence on the noise amplitude.

Modeling the Phase Correlation of Effective Diffuse Scattering From Surfaces for Radio Propagation Prediction With Antennas at Refined Separation

Diffuse scattering (DS), mostly caused by macroscopically rough surfaces, can be modeled by an effective roughness (ER) approach. In the ER approach, the object surface is divided into tiles, and the DS field amplitude associated with each tile is given. Assuming that the transmit antenna (or emitted field) is fixed and the phases associated with different tiles are independent, this paper proposes a phase evolution model based on the relative spatial locations of the receive antenna (Rx) to each tile. The proposed model contains two parts: the deterministic part that depends on the variation of the distance from Rx to tile center, and the correlated random part that depends on the variation of the angle between the Rx and the normal vector of tile. The correlation of the tile field phases resulting from the angular variation is modeled by the exponentially damped cosine correlation function. The proposed phase evolution model is evaluated by being applied to the ER approach to predict the DS component of radio channel transfer function (CTF). The predicted DS-CTF is compared with the reference (simulated data by physical optics and measured data in well-controlled environment) in terms of the spatial autocorrelation as well as the spatial Doppler spectrum.

Stochastic mixed-mode oscillations in a three-species predator-prey model

The effect of demographic stochasticity, in the form of Gaussian white noise, in a predator-prey model with one fast and two slow variables is studied. We derive the stochastic differential equations (SDEs) from a discrete model. For suitable parameter values, the deterministic drift part of the model admits a folded node singularity and exhibits a singular Hopf bifurcation. We focus on the parameter regime near the Hopf bifurcation, where small amplitude oscillations exist as stable dynamics in the absence of noise. In this regime, the stochastic model admits noise-driven mixed-mode oscillations (MMOs), which capture the intermediate dynamics between two cycles of population outbreaks. We perform numerical simulations to calculate the distribution of the random number of small oscillations between successive spikes for varying noise intensities and distance to the Hopf bifurcation. We also study the effect of noise on a suitable Poincaré map. Finally, we prove that the stochastic model can be transformed into a normal form near the folded node, which can be linked to recent results on the interplay between deterministic and stochastic small amplitude oscillations. The normal form can also be used to study the parameter influence on the noise level near folded singularities.

A Pitch-Synchronous Simultaneous Detection-Estimation Framework for Speech Enhancement

Speech enhancement methods formulated in the short-time Fourier transform (STFT) domain vary in the statistical assumptions made on the STFT coefficients, in the optimization criteria applied or in the models of the signal components. Recently, approaches relying on a stochastic-deterministic speech model have been proposed. The deterministic part of the signal corresponds to harmonically related sinusoids, often used to represent voiced speech. The stochastic part models signal components that are not captured by the deterministic components. In this paper, we consider this scenario under a new perspective yielding three main contributions. First, a pitch-synchronous signal representation is considered and shown to be advantageous for the estimation of the harmonic model parameters. Second, we model the harmonic amplitudes in voiced speech as random variables with frequency bin dependent Gamma distributions. Finally, distinct estimators for the different models of voiced speech, unvoiced speech, and speech absence are derived. To select from the arising estimates, we take into account the mutual impact of detection and estimation by proposing a binary decision framework that is derived from a Bayesian risk function. The resulting pitch-synchronous stochastic-deterministic estimator outperforms several benchmark methods in terms of speech intelligibility and perceived quality predicted by instrumental measures for various noise types and different signal-to-noise ratios.

On the noise characteristics of time series recorded with nearby located GPS receivers and superconducting gravity meters

The inter-comparison of ground gravity measurements and vertical surface displacements enables to better understand the structure, dynamics and evolution of the Earth’s system. Within this research we analyzed the Global Positioning System vertical position time series acquired in the vicinity of the superconducting gravimeters. We estimated of noise character of GPS and SG by comparison of the satellite and terrestrial measurements collected at 18 globally distributed neighboring sites. The comparable results were provided by applying the appropriate and corresponding models of geophysical phenomena to obtain residual time series, and by unifying the sampling rate since the noise characteristics may depend on it. The deterministic part of the series was assumed to follow the Polynomial Trend Model and was subtracted prior to noise analysis. Then, a combination of power-law and white noise was presumed and the Maximum Likelihood Estimation implemented in the Hector software to investigate the stochastic part was applied. Within the paper, we show that the spectral indices for all SG time series fall in the area of fractional Brownian motion (− 2 < κ < − 1), while GPS data are best characterized by fractional Gaussian noises (− 1 < κ < 0). The estimated ratio between spectral indices of GPS and SG is stable worldwide with a global median value of about 0.5. Concerning the power-law amplitudes, these are very consistent worldwide for the GPS position time series and fluctuate around 15 mm/year−κ/4, while in the case of SG records they spread between 60 and 300 nm/s2/year−κ/4. The fraction of power-law noise employed in the assumed combination is equal to 100% for almost all SG stations, while in case of GPS it varies between 26.1 and 99.9%. The main finding of this research is that the assumption of power-law noise is much more preferred for SG data than the assumption of a pure white noise being used until now.

Calculating State-Dependent Noise in a Linear Inverse Model Framework

Abstract The most commonly used version of a linear inverse model (LIM) is forced by state-independent noise. Although having several desirable qualities, this formulation can only generate long-term Gaussian statistics. LIM-like systems forced by correlated additive–multiplicative (CAM) noise have been shown to generate deviations from Gaussianity, but parameter estimation methods are only known in the univariate case, limiting their use for the study of coupled variability. This paper presents a methodology to calculate the parameters of the simplest multivariate LIM extension that can generate long-term deviations from Gaussianity. This model (CAM-LIM) consists of a linear deterministic part forced by a diagonal CAM noise formulation, plus an independent additive noise term. This allows for the possibility of representing asymmetric distributions with heavier- or lighter-than-Gaussian tails. The usefulness of this methodology is illustrated in a locally coupled two-variable ocean–atmosphere model of midlatitude variability. Here, a CAM-LIM is calculated from ocean weather station data. Although the time-resolved dynamics is very close to linear at a time scale of a couple of days, significant deviations from Gaussianity are found. In particular, individual probability density functions are skewed with both heavy and light tails. It is shown that these deviations from Gaussianity are well accounted for by the CAM-LIM formulation, without invoking nonlinearity in the time-resolved operator. Estimation methods using knowledge of the CAM-LIM statistical constraints provide robust estimation of the parameters with data lengths typical of geophysical time series, for example, 31 winters for the ocean weather station here.

Modulating Function Based Fault Detection for Parabolic Systems with Polynomial Faults

This paper presents an algebraic approach to the fault detection for parabolic systems. It is assumed that the unknown time-varying faults are of polynomial type. In addition to the fault, the system is subject to a disturbance that can be separated into a polynomial deterministic part and a remaining bounded part. While the deterministic part is isolated from the fault, the bounded part is taken into account by introducing a threshold. For this setup, the modulating function approach is utilized to determine a directly implementable algebraic equation for the fault detection, which depends only on measurements. The results of the paper are illustrated for a faulty diffusion-reaction system.

Achieving New Upper Bounds for the Hypergraph Duality Problem through Logic

The hypergraph duality problem DUAL is defined as follows: given two simple hypergraphs $\mathcal{G}$ and $\mathcal{H}$, decide whether $\mathcal{H}$ consists precisely of all minimal transversals of $\mathcal{G}$ (in which case we say that $\mathcal{G}$ is the dual of $\mathcal{H}$). This problem is equivalent to deciding whether two given non-redundant monotone DNFs are dual. It is known that non-DUAL, the complementary problem to DUAL, is in $\mathrm{GC}(\log^2 n,\mathrm{PTIME})$, where $\mathrm{GC}(f(n),\mathcal{C})$ denotes the complexity class of all problems that after a nondeterministic guess of $O(f(n))$ bits can be decided (checked) within complexity class $\mathcal{C}$. It was conjectured that non-DUAL is in $\mathrm{GC}(\log^2 n,\mathrm{LOGSPACE})$. In this paper we prove this conjecture and actually place the non-DUAL problem into the complexity class $\mathrm{GC}(\log^2 n,\mathrm{TC}^0)$ which is a subclass of $\mathrm{GC}(\log^2 n,\mathrm{LOGSPACE})$. We here refer to the logtime-uniform version of $\mathrm{TC}^0$, which corresponds to $\mathrm{FO(COUNT)}$, i.e., first order logic augmented by counting quantifiers. We achieve the latter bound in two steps. First, based on existing problem decomposition methods, we develop a new nondeterministic algorithm for non-DUAL that requires to guess $O(\log^2 n)$ bits. We then proceed by a logical analysis of this algorithm, allowing us to formulate its deterministic part in $\mathrm{FO(COUNT)}$. From this result, by the well known inclusion $\mathrm{TC}^0\subseteq\mathrm{LOGSPACE}$, it follows that DUAL belongs also to $\mathrm{DSPACE}[\log^2 n]$. Finally, by exploiting the principles on which the proposed nondeterministic algorithm is based, we devise a deterministic algorithm that, given two hypergraphs $\mathcal{G}$ and $\mathcal{H}$, computes in quadratic logspace a transversal of $\mathcal{G}$ missing in $\mathcal{H}$.

Semi-analytical stochastic analysis of the generalized van der Pol system

The paper is motivated by a series of wind tunnel experiments, which deal with aeroelastic Single Degree of Freedom (SDOF) and Two Degrees of Freedom (TDOF) section models. Most of them can be mathematically expressed by van der Pol-Duffing type equations or their combination. Excitation due to aeroelastic forces consists mostly of a deterministic periodic part and random components, both of them are applied as additive processes. The lock-in state represents an auto-synchronization of the vortex shedding and basic eigen-frequency of the system. This problem seems to be very polymorphous and, therefore, several isolated regimes have been outlined together with their characterization. Parameter setting with solely random excitation is further investigated in the paper. The strategy of stochastic averaging is then employed to formulate normal form of stochastic system for partial amplitudes of harmonic approximates of the response. The random part of excitation is considered as a Gaussian process with significantly variable spectral density. Hence, a conventional way of investigation based on an idea of white noise excitation is no more applicable. Therefore, the general formulation of diffuse and drift coefficients should be used to construct the relevant Fokker-Planck equation (FPE). Semi-analytical solution of FPE is deduced in the exponential form by means of a probability potential. It is later used for stochastic stability investigation together with consideration about the stationary probability distribution existence. Open problems and further research steps are outlined.

What you always wanted to know about the deterministic part of the International Planning Competition (IPC) 2014 (but were too afraid to ask)

AbstractThe International Planning Competition (IPC) is a prominent event of the artificial intelligence planning community that has been organized since 1998; it aims at fostering the development and comparison of planning approaches, assessing the state-of-the-art in planning and identifying new challenging benchmarks. IPC has a strong impact also outside the planning community, by providing a large number of ready-to-use planning engines and testing pioneering applications of planning techniques.This paper focusses on the deterministic part of IPC 2014, and describes format, participants, benchmarks as well as a thorough analysis of the results. Generally, results of the competition indicates some significant progress, but they also highlight issues and challenges that the planning community will have to face in the future.

LSM-harmonic analysis of bi-periodic nonstationary vibration signals

The estimators of parameters of bi-periodic nonstationary vibration signal deterministic part, obtained with using the least squares method (LSM), are analyzed. LSM estimation allows avoiding aliasing effects. The formulas for estimators of variance and bias, which describe their dependences on realization length and signal covariance components, are derived. The results are specified for the quadrature model of the signal. LSM has shown its efficiency for separation of harmonics with close frequencies, so it should be considered as the main method for vibration signals analysis. It is shown that its usage allows one to obtain unbiased estimators of bi-periodic nonstationary vibration signal deterministic part regardless of realization length and harmonic frequencies.

Geometric integrator for Langevin systems with quaternion-based rotational degrees of freedom and hydrodynamic interactions.

We introduce new Langevin-type equations describing the rotational and translational motion of rigid bodies interacting through conservative and non-conservative forces and hydrodynamic coupling. In the absence of non-conservative forces, the Langevin-type equations sample from the canonical ensemble. The rotational degrees of freedom are described using quaternions, the lengths of which are exactly preserved by the stochastic dynamics. For the proposed Langevin-type equations, we construct a weak 2nd order geometric integrator that preserves the main geometric features of the continuous dynamics. The integrator uses Verlet-type splitting for the deterministic part of Langevin equations appropriately combined with an exactly integrated Ornstein-Uhlenbeck process. Numerical experiments are presented to illustrate both the new Langevin model and the numerical method for it, as well as to demonstrate how inertia and the coupling of rotational and translational motion can introduce qualitatively distinct behaviours.

Stochastic models in the DORIS position time series: estimates for IDS contribution to ITRF2014

This paper focuses on the investigation of the deterministic and stochastic parts of the Doppler Orbitography and Radiopositioning Integrated by Satellite (DORIS) weekly time series aligned to the newest release of ITRF2014. A set of 90 stations was divided into three groups depending on when the data were collected at an individual station. To reliably describe the DORIS time series, we employed a mathematical model that included the long-term nonlinear signal, linear trend, seasonal oscillations and a stochastic part, all being estimated with maximum likelihood estimation. We proved that the values of the parameters delivered for DORIS data are strictly correlated with the time span of the observations. The quality of the most recent data has significantly improved. Not only did the seasonal amplitudes decrease over the years, but also, and most importantly, the noise level and its type changed significantly. Among several tested models, the power-law process may be chosen as the preferred one for most of the DORIS data. Moreover, the preferred noise model has changed through the years from an autoregressive process to pure power-law noise with few stations characterised by a positive spectral index. For the latest observations, the medians of the velocity errors were equal to 0.3, 0.3 and 0.4 mm/year, respectively, for the North, East and Up components. In the best cases, a velocity uncertainty of DORIS sites of 0.1 mm/year is achievable when the appropriate coloured noise model is taken into consideration.

Forced oscillations of cracked beam under the stochastic cyclic loading

Abstract An analysis of forced oscillations of cracked beam using statistical methods for periodically correlated random processes is presented. The oscillation realizations are obtained on the basis of numerical solutions of differential equations of the second order, for the case when applied force is described by a sum of harmonic and stationary random process. It is established that due to crack appearance forced oscillations acquire properties of second-order periodical non-stationarity. It is shown that in a super-resonance regime covariance and spectral characteristics, which describe non-stationary structure of forced oscillations, are more sensitive to crack growth than the characteristics of the oscillation’s deterministic part. Using diagnostic indicators formed on their basis allows the detection of small cracks.

THE IMPACT OF TAXES ON THE CONSUMPTION TO INCOME RATIO

This article, in the statistical analysis of possible cointegration relationships among the variables from the expenditure approach to the GDP formula, explains how taxes affect the consumption to income ratio. A causal relationship that defines investment as the leading factor in GDP formation was rearranged and applied for the study of taxation effects under various income levels. The technique that was used for the estimation of taxation effects was based on the deterministic part of causal relationship, though the results must be interpreted very carefully. This analysis demonstrates that, when taken to the extreme, higher taxes have a huge negative effect on consumption and a very small effect on savings; in addition, these effects depend on the level of income. The higher the incomes are, the more deteriorating the effects of taxes on consumption can be observed; therefore, an economy cannot afford a high level of taxes, even when the income level is also high. As taxes have negative effects on consumption and, with lesser extent, on savings, tax-based fiscal consolidation has to be avoided at any cost, and governments should rely on tax-based fiscal consolidation only if no other option is available.

Demographic-noise-induced fixation in subdivided populations with migration

We investigate the stochastic dynamics of a model which consists of subdivided populations of individuals confined to a set of islands. In subdivided populations, migration acts with selection and genetic drift to determine the evolutionary dynamics. The individuals are assumed to be haploid with two types. They reproduce according to their fitness values, die at random, and migrate between the islands. The evolutionary dynamics of an individual-based model is formulated in terms of a master equation and is approximated as the multidimensional Fokker–Planck equation (FPE) and the coupled non-linear stochastic differential equations (SDEs) with multiplicative noise. We first analyze the deterministic part of the SDEs, to obtain the fixed points and determine the stability of each fixed point. We find that there is a continuous phase transition in the population distribution when the migration rate is equal to the selection strength in the antisymmetric selection scheme. Next, we take demographic stochasticity into account, and analyze the FPE by eliminating the fast variable to reduce the coupled two-variable FPE to the single-variable FPE. We derive a quasi-stationary distribution of the reduced FPE, and predict the fixation probabilities and the mean fixation times to absorbing states. We also carry out numerical simulations, in the form of the Gillespie algorithm, and find that the results of simulations are consistent with the analytic predictions.

Green\u2019s function for elliptic systems: existence and Delmotte\u2013Deuschel bounds

This paper is divided into two parts: In the main deterministic part, we prove that for an open domain D subset mathbb {R}^d with d ge 2, for every (measurable) uniformly elliptic tensor field a and for almost every point y in D, there exists a unique Green’s function centred in y associated to the vectorial operator -nabla cdot anabla in D. This result implies the existence of the fundamental solution for elliptic systems when d>2, i.e. the Green function for -nabla cdot anabla in mathbb {R}^d. In the second part, we introduce a shift-invariant ensemble langle cdot rangle over the set of uniformly elliptic tensor fields, and infer for the fundamental solution G some pointwise bounds for langle |G(cdot ; x,y)|rangle , langle |nabla _x G(cdot ; x,y)|rangle and langle |nabla _xnabla _y G(cdot ; x,y)|rangle . These estimates scale optimally in space and provide a generalisation to systems of the bounds obtained by Delmotte and Deuschel for the scalar case.

Evolutionary dynamics with migration by using the fast-mode elimination method

We investigate the evolutionary dynamics of a Moran model which consists of subdivided populations of individuals confined to a set of islands. In subdivided populations, migration acts with selection and genetic drift to determine the evolutionary dynamics. The individuals are assumed to be haploid with two types. They reproduce according to their fitness values, die at random, and migrate between the islands. The evolutionary dynamics of an individual based model is formulated in terms of a master equation and is approximated as the multidimensional Fokker-Planck equation (FPE) and the coupled non-linear stochastic differential equations (SDEs) with multiplicative noise. We first analyze the deterministic part of the SDEs to obtain the fixed points and determine the stability of each fixed point. We find that there is only one stable fixed point to which all populations started from any initial distribution other than the unstable absorbing points will evolve in both the symmetric and antisymmetric selection schemes. Next, we take demographic stochasticity into account and analyze the FPE by eliminating the fast variable to reduce the coupled two-variable FPE to the single-variable FPE. We derive a quasi-stationary distribution of the reduced FPE and predict the fixation probabilities and the mean fixation times to absorbing states. We also carry out numerical simulations in the form of the Gillespie algorithm and find that the results of simulations are consistent with the analytic predictions.

Information Transfer of Control Strategies: Dualities of Stochastic Optimal Control Theory and Feedback Capacity of Information Theory

The control-coding capacity of stochastic control systems is introduced, and its operational meaning is established using randomized control strategies, which simultaneously control output processes encode information, and communicate information from control processes to output processes. The control-coding capacity is the analog Shannon's coding-capacity of noisy channels. Furthermore, duality relations to stochastic optimal control problems with deterministic and randomized control strategies are identified including the following. First, extremum problems of stochastic optimal control with directed information payoff are equivalent to feedback capacity problems of information theory, in which the control system act as a communication channel. Second, for Gaussian linear decision models with average quadratic constraints, it is shown that optimal randomized strategies are Gaussian, and decompose into a deterministic part and a random part. The deterministic part is precisely the optimal strategy of the linear quadratic Gaussian stochastic optimal control problem, whereas the random part is the solution of an water-filling information transmission problem that encodes information, which is estimated by a decoder.

Conditional Granger causality of diffusion processes

The statistical concept of Granger causality is defined by prediction improvement, i.e. the causing time series contains unique information about the future of the caused one. Recently we proposed extending this concept to bivariate diffusion processes by defining Granger causality for each point of the state space as the Granger causality of a process obtained by local linearisation. This provides a Granger causality map, well-defined at least in the vicinity of stable fixed points of the deterministic part of the dynamics. This extension has convenient properties, but carries several important limitations. In the current paper we show how the Granger causality of diffusion processes can be further generalized, incorporating in particular the concept of conditional causality. Moreover, we demonstrate the application potential to systems with a more complex attractor structure such as limit cycles or bistability of fixed points.