Stochastic Frame Research Articles

Preprocessing for Keypoint-Based Sign Language Translation without Glosses

While machine translation for spoken language has advanced significantly, research on sign language translation (SLT) for deaf individuals remains limited. Obtaining annotations, such as gloss, can be expensive and time-consuming. To address these challenges, we propose a new sign language video-processing method for SLT without gloss annotations. Our approach leverages the signer's skeleton points to identify their movements and help build a robust model resilient to background noise. We also introduce a keypoint normalization process that preserves the signer's movements while accounting for variations in body length. Furthermore, we propose a stochastic frame selection technique to prioritize frames to minimize video information loss. Based on the attention-based model, our approach demonstrates effectiveness through quantitative experiments on various metrics using German and Korean sign language datasets without glosses.

Analytical heat conduction model of particle reinforced tertiary composite materials based on complete spatial randomness of fillers in base matrix and its application in the development of cryosorption pump

In this article, we propose an analytical heat conduction model within a stochastic frame work which estimates the thermal conductivity (TC) value of particle reinforced composite materials comprising of three parent elements i.e. a base matrix along with two different filler element particles randomly distributed in it. The spatial distribution of the filler particles in a sample of specific dimension has been estimated by applying bivariate Poisson distribution. This distribution is then used to arrive at the TC value of the composite. This concept has been applied to predict the TC of the tertiary composite comprised of epoxy as the base matrix, aluminium and zinc particles as filler elements. The TC values obtained from this model for different volume fractions of fillers were extensively compared with experimental results. The model is found to predict the results fairly well with less aberrations up to the total filler volume fraction of ∼20%. The developed model for TC prediction has been used in the design of high efficiency cryosorption pump where the adhesive material used is Epoxy-Aluminium -Zinc composite.

Stochastic quantization and holographic Wilsonian renormalization group of scalar theories with arbitrary mass

We have studied a mathematical relationship between holographic Wilsonian renormalization group(HWRG) and stochastic quantization(SQ) of scalar field with arbitrary mass in AdS spacetime. In the stochastic theory, the field is described by an equation with a form of harmonic oscillator with time dependent frequency and its Euclidean action also shows explicit time dependent kernel in it. We have obtained the stochastic 2-point correlation function and demonstrate that it reproduces the radial evolution of the double trace operator correctly via the suggested relation given in arXiv:1209.2242. Moreover, we justify our stochastic procedure with time dependent kernel by showing that it can be mapped to a new stochastic frame with a standard kernel without time dependence. Finally, we consider more general boundary conditions for the stochastic field to reproduce the radial evolution of the holographic boundary effective action when alternative quantization is allowed. We extensively study the Neumann boundary condition case and confirm that even in this case, the relation between HWRG and SQ is precisely hold.

An Ornstein-Uhlenbeck Process-Driven Power System Dynamics

In electrical power system dynamics, the single machine-infinite bus system is studied widely. This paper presents an analysis of the evolution of the state trajectories of a stochastic single machine-infinite bus system. The dynamical equation of single machine-infinite bus (SMIB) system is called swing equation. That assumes the structure of a second-order ordinary differential equation. In this paper first, we add random fluctuations as the Ornstein-Uhlenbeck process noise in the dynamical equation of the SMIB system and then, we develop conditional mean and variance evolution equations. Finally, we simulate the resulting equations with a set of data. This paper will be of interest to power system dynamists, control theorists, electrical engineers, especially power systems Researchers looking for power systems and their control system under noise influence involving formal stochastic frame works.

Spatial coherence properties of one dimensional exciton-polariton condensates.

In this work, we combine a systematic experimental investigation of the power- and temperature-dependent evolution of the spatial coherence function, g^{(1)}(r), in a one dimensional exciton-polariton channel with a modern microscopic numerical theory based on a stochastic master equation approach. The spatial coherence function g^{(1)}(r) is extracted via high-precision Michelson interferometry, which allows us to demonstrate that in the regime of nonresonant excitation, the dependence g^{(1)}(r) reaches a saturation value with a plateau, which is determined by the intensity of the pump and effective temperature of the crystal lattice. The theory, which was extended to allow for treating incoherent excitation in a stochastic frame, matches the experimental data with good qualitative and quantitative agreement. This allows us to verify the prediction that the decay of the off-diagonal long-range order can be almost fully suppressed in one dimensional condensate systems.

Uncertainty in applying the temperature time-series method to the field under heterogeneous flow conditions

summary Due to the irregular distributions of aquifer hydraulic properties, the detail on the characterization of flow field cannot be anticipated. There can be a great degree of uncertainty in the prediction of heat transport processes anticipated in applying the traditional deterministic transport equation to field situations. This article is therefore devoted to quantification of uncertainty involving predictions over larger scales in terms of the temperature variance. A stochastic frame of reference is adopted to account for the spatial variability in hydraulic conductivity and specific discharge. Within this framework, the use of the firstorder perturbation approximation and spectral representation leads to stochastic differential equations governing the mean behavior and perturbation of the temperature field in heterogeneous aquifers. It turns out that the mean equation developed in this sense is equivalent to the traditional deterministic transport equation and the temperature variance gives a measure of the prediction uncertainty from the traditional transport equation. The closed-form expression for the temperature variance developed here indicates that the controlling parameters such as the correlation scale of specific discharge, which measures the spatial persistence of the flow field, and the periodicity of the source term tend to increase the variability in temperature field in heterogeneous aquifers. The uncertainty of the traditional heat transport model increases as the penetration depth of thermal front through the aquifer increases. This suggests that prediction of temperature distribution using the traditional heat transport model in heterogeneous aquifers is expected to be subject to large uncertainty at a large depth (in the downstream region). For the management purpose, the variance of temperature could serve as a calibration target when applying the traditional model to field situations. It may be more reasonable to make conclusions from, say, the mean temperature with one or two standard deviations rather than only the mean temperature drawn from the traditional heat transport equation.

Green’s Function Method for Stability Analysis of Stochastic Structures

AbstractThe governing equations for the stability analysis of stochastic frame structures with small variations of the material and geometry parameters are established for the means and deviations of responses by including first-order terms. Taking advantage of the similarity between these equations and the governing equations for static analysis, a new Green’s function method based on the fundamental solutions for static problems is proposed for the stability analysis of stochastic structures in conjunction with multidomain techniques. The numerical examples presented show that there is good agreement between the results of the proposed method and those from Monte Carlo simulation for small variation situations, and that the new approach is more efficient than the perturbation stochastic FEM. Based on the numerical results, the effects of the covariance type, correlation scale parameter, coefficient of variation, and discretization of random fields, as well as the location of fictitious loads, are invest...

Dual estimation of partially observed nonlinear structural systems: A particle filter approach

Dual estimation consists of tracking the whole state of partially observed systems, and simultaneously estimating unknown model parameters. In case of nonlinearly evolving systems, standard filtering procedures may provide unreliable model calibrations, either because of estimates affected by bias or due to diverging filter response. In this paper, we propose a particle filter (PF) wherein particles, i.e. system realizations evolving in a stochastic frame, are first sampled from the current probability density function of the system and then moved towards the region of high probability by an extended Kalman filter. We show that the proposed filter works much better than a standard PF, in terms of accuracy of the estimates and of computing time.

A Stochastic Framework for Rate-Distortion Optimized Video Coding Over Error-Prone Networks

This paper proposes a complete stochastic framework for RD optimal encoder design for video over error-prone networks, which applies to any motion-compensated predictive video codec. The distortion measure has been taken as the mean square error over an ensemble of channels given an estimate of the instantaneous packet loss probability. We show that 1) the optimal motion compensated prediction, in the MSE sense, requires computation of the expected value of the reference frames, and 2) calculation of the MSE (distortion measure) requires computation of the second moment of the reference frames. We propose a recursive procedure for the computation of both the expected value and second moment of the reference frames, which are together called the stochastic frame buffer. Furthermore, we propose a stochastic RD optimization method for selection of the optimal macroblock mode and motion vectors given the instantaneous packet loss probability. If available, channel feedback can also be incorporated into the proposed stochastic framework. However, the proposed framework does not require a feedback channel to exist, and when it exists, it does not have to be lossless. In the absence of any packet losses, the proposed stochastic framework reduces to the well-known deterministic RD optimization procedures. One possible application of the optimal stochastic framework would be for multicast streaming to an ensemble of receivers. Experimental results indicate that the proposed framework outperforms other available error tracking and control schemes.

Response variability of stochastic frame structures using evolutionary field theory

The integral form for the variance of the response of stochastic statically indeterminate structural systems involving the so-called variability response function (VRF) and the spectral density function of the stochastic field modelling the uncertain system properties is established for the first time in this paper using evolutionary spectra theory. The VRF is a function depending on deterministic parameters related to the geometry, boundary conditions, (mean) material properties and loading of the structural system. No approximations are involved in the derivation of the integral form. However, a conjecture has to be made that is validated using Monte Carlo simulations. The uncertain system property considered is the inverse of the elastic modulus (flexibility). Closed-form expressions can be derived in principle for the VRF of any statically determinate or indeterminate frame system using a flexibility-based formulation. Alternatively, a fast Monte Carlo simulation approach is provided to numerically evaluate the VRF. It is shown in closed-form and numerically that the VRF for statically indeterminate structures is a function of the standard deviation σ ff of the stochastic field modeling the inverse of the elastic modulus. Although the VRF depends on σ ff , it appears to be independent of the functional form of the spectral density function of the stochastic field modeling the uncertain system properties. For statically determinate structures, the VRF is independent of σ ff . The integral form can be used to compute the variance of the system response as well as its upper bound with minimal computational effort. It also provides an excellent insight into the mechanisms controlling the response variability. The upper bounds for the response variance are spectral- and probability-distribution-free requiring knowledge of only the variance of the inverse of the elastic modulus. The proposed bounds are realizable in the sense that it is possible to determine the probabilistic characteristics of the stochastic field that produces them. Several numerical examples are provided demonstrating the capabilities of the methodology.

Dynamic Response Analysis of Stochastic Frame Structures Under Nonstationary Random Excitation

A new method (random factor method) for the dynamic response analysis of linear stochastic frame structures under nonstationary random excitation is presented. From the expressions of structural random response of the frequency domain, the computational expressions of the mean value, variance, and variation coefficient of the mean square value of the structural nonstationary random displacement and stress response are developed by means of the random variable's functional moment method and the algebra synthesis method, in which the randomness of the structural physical parameters is considered. The influences of the randomness of the structural physical parameters on the randomness of the mean square value of the structural displacement and stress response are inspected via an engineering example.

Risk of Sediment Erosion and Suspension in Turbulent Flows

It is shown how some basic probability tools may help in the characterization of the turbulent processes involved in the mechanics of sediment transport. Both the initiation of sediment motion and the threshold for sediment suspension are analyzed in a stochastic frame of work. Isorisk curves are constructed based upon some minimum experimental information. The well-known Shields' curve is shown to correspond to an erosion risk of approximately 40%. These concepts are believed to be of importance for the design of movable-bed channels as well as for future experimental investigations, which are indeed necessary for computing the risk for higher values of the particle Reynolds number. Finally, an approximate methodology is proposed for computing the risk of erosion.

Mean convergence behavioural analysis of IIR adaptive filters

In spite of having several advantages, IIR adaptive filters have not been getting their due share in applications because of the need for stability monitoring during adaptation and uncertainty in convergence time for stochastic inputs which can be mainly attributed to the involved nonquadratic criterion function. Because of this type of criterion function, it has been very difficult to estimate the nature of convergence in the stochastic frame work. Recently, it is shown that the ensemble mean parameter updating equations of the IIR adaptive algorithms can be represented by the associated ordinary differential equations (ODEs). In this paper a method of solving the ODEs in order to analyse the mean convergence behaviour of these filters, given the mean description of the input in the form of power spectral density is presented. Further, this procedure is applied to study the convergence behaviour of general IIR adaptive filters. Effectiveness of this method is shown through several analytical and simulation results obtained from two adaptive filtering examples.

Mean-Convergence behavior of Adaptive Identification Algorithms for Pole-Zero Systems

Adaptive methods for the estimation of unknown system parameters has the advantage of tracking time-varying systems. Identification algorithms for recursive systems produce nonquadratic performance functions. In such problems it is very difficult to estimate the nature of convergence in a stochastic frame work. Recently, it has been shown that the ensemble mean parameter updating equations of IIR adaptive algorithm can be represened by associated ordinary differential equations (ODEs). A method of solving the ODEs in order to analyze the mean- convergence behavior of these algorithms, given the mean description of the input in the form of power spectral density, has been presented recently. In this paper, this procedure is applied to study the convergence behavior of recursive adaptive algorithms applied for the identification of pole-zero systems. Effectiveness of this method is shown through analytical and simulation results.

Flow in Heterogeneous Media Displaying a Linear Trend in the Log Conductivity

The purpose of this study is to derive a general solution for the problem of flow in nonstationary geological formations where the nonstationarity manifests itself in the form of a spatial trend in the mean log conductivity. A stochastic frame of reference is adopted to account for the spatial variability of the hydraulic conductivity. For a complete stochastic description we derive the expected values and spatial covariances of the hydraulic head and the fluid flux vector, as well as a relation between the expected values of the head and the fluxes. These expressions are obtained using a perturbation expansion of the log conductivity about its nonstationary mean, and they are correct to the first order in the variance of the log conductivity. The expressions we derive are applicable for any space dimensionality and for arbitrary orientation of the trend in space. A general methodology is outlined for derivation of these expressions for any type of spatial covariance; and for demonstration, explicit results are obtained for a Gaussian isotropic covariance.

A Synthesis of Approaches to Upscaling of Hydraulic Conductivities

Simulation of flow through heterogeneous media often requires discretizing the flow domain into blocks and assigning an equivalent block conductivity value to each one of them. The process of defining block conductivities from point values is termed upscaling. A number of approaches to upscaling are available, most of which consider the uncertainty associated with any natural property, so that they cast the problem in a stochastic frame. Recently, Indelman and Dagan (1993a, b) provided a general stochastic methodology to upscaling in heterogeneous anisotropic formations by means of the dissipation energy function; unfortunately, they did not provide any “practical” method to compute block values from point ones. The objective of this work is twofold: First, we analyze different practical approaches to compute block conductivities and find that all of them provide very similar results in terms of actual computed values; second, we check that all approaches verify approximately a number of conditions stated by Indelman and Dagan (1993a). Specifically, we show analytically that for regular blocks, the methodologies of both Rubin and Gómez‐Hernández (1990) and Desbarats (1992) (which we call “practical” methodologies) satisfy the condition that the effective conductivity obtained from a field where the elementary conductivities are defined over a certain support (we call this the actual formation) is identical to that obtained from the same field with conductivities defined at a larger support (upscaled formation). The analysis is carried out by working with the logarithm of block conductivities and using a small‐perturbation expansion and thus is strictly valid for small variances. On the other hand, we show numerically that the two methodologies satisfy approximately an important condition stated in terms of the dissipation energy: that block‐averaged dissipation values computed are indeed very close to the true dissipation values in each block. The agreement is even better if we consider statistical moments instead of point values. As an important conclusion we should note that all practical methodologies considered in this work perform equally well and, more important, constitute a simple way to treat an otherwise very complex problem.

Weighted Integral Method. II: Response Variability and Reliability

After obtaining in a companion paper an exact expression of the stochastic stiffness matrix in terms of random variables called weighted integrals, the response variability and the safety index of stochastic frame structures are calculated in this paper. The response variability is calculated using a first‐order Taylor's expansion and the safety index using the advanced first‐order second‐moment approach. It is concluded that the potential energy and virtual work approaches produce identical results for the mean value and the variance of nodal displacements and internal forces. On the contrary, the two approaches produce different values for the safety index of both nodal displacements and internal forces. These values for the safety index obtained using the two approaches compare very well. It is noted that the stochastic stiffness matrix obtained using the potential energy approach is an approximation of the corresponding one obtained using the virtual work approach. Finally, the effect of statistical dependence or independence among the stochastic fields of different elements is examined.