Stochastic Properties Research Articles

CMOS-compatible wafer-scale Si subulate array for superb switching uniformity of RRAM with localized nanofilaments

Resistive switching random access memory (RRAM) is one of the most promising candidates with high-density three-dimensional integration characteristics for next-generation nonvolatile memory technology. However, the poor uniformity issue caused by the stochastic property of the conductive filament (CF) impedes the large-scale manufacture of RRAM chips. Subulate array has been introduced into the RRAM to minimize the CF randomness, but the methods are cumbersome, expensive, or resolution-limited for large-scale preparation. In this work, Si subulate array (SSA) substrates with different curvature radii prepared by a wafer-scale and nanoscale-controllable method are introduced for RRAM fabrication. The SSA structure, which induces a quasi-single CF or a few CFs formed in the tip region (TR) of the device as evidenced by the high-resolution transmission electron microscopy and energy dispersive spectroscopy characterization, dramatically improves the cycle-to-cycle and device-to-device uniformity. Decreasing the curvature radius of the TR significantly improves the device performance, including switching voltages, high/low resistance states, and retention characteristics. The improved uniformity can be attributed to the enhanced local electric field in the TR. The proposed SSA provides a low-cost, uniform, CMOS-compatible, and nanoscale-controllable optimization strategy for the large-scale integration of highly uniform RRAM devices.

Spectrum of the Laplace operator on closed surfaces

AbstractA survey is given of classical and relatively recent results on the distribution of the eigenvalues of the Laplace operator on closed surfaces. For various classes of metrics the dependence of the behaviour of the second term in Weyl’s formula on the geometry of the geodesic flow is considered. Various versions of trace formulae are presented, along with ensuing identities for the spectrum. The case of a compact Riemann surface with the Poincaré metric is considered separately, with the use of Selberg’s formula. A number of results on the stochastic properties of the spectrum in connection with the theory of quantum chaos and the universality conjecture are presented.Bibliography: 51 titles.

Sparse Bayesian long short-term memory networks for computationally efficient stochastic modeling of plasma etch processes

As the required feature size of microelectronic devices continues to shrink, stringent process control of plasma etch process has become a critical issue in semiconductor manufacturing. In order to design a high-performance controller and its verification, there have been increasing needs for a high-fidelity model. This study proposes a probabilistic surrogate modeling method, named sparse Bayesian long short-term memory networks (SBLSTM). In SBLSTM, all the neural weights are given by parameterized Gaussian distributions, and the resulting distributional parameters are trained to maximize the posterior probability of the dataset. By imparting stochastic property to versatile neural network models, the proposed method allows modeling plasma etch processes’ complex behaviors. In order to find an optimal model structure, we propose a posteriori dropout, which eliminates insignificant weights after training based on their relative importance. The effectiveness of the proposed method is demonstrated through experimental data and compared with three conventional surrogate modeling techniques.

Dynamics of a Rumor Propagation Model With Stochastic Perturbation on Homogeneous Social Networks

Abstract The rapid development of information society highlights the important role of rumors in social communication, and their propagation has a significant impact on human production and life. The investigation of the influence of uncertainty on rumor propagation is an important issue in the current communication study. Due to incomprehension about others and the stochastic properties of the users' behavior, the transmission rate between individuals on social network platforms is usually not a constant value. In this paper, we propose a new rumor propagation model on homogeneous social networks from the deterministic structure to the stochastic structure. First, a unique global positive solution of the rumor propagation model is obtained. Then, we verify that the extinction and persistence of the stochastic rumor propagation model are restricted by some conditions. If R̂0*<1 and the noise intensity σi(i=1,2,3) satisfies some certain conditions, rumors will extinct with a probability one. If R0*>1, rumor-spreading individuals will persist in the system, which means the rumor will prevail for a long time. Finally, through some numerical simulations, the validity and rationality of the theoretical analysis are effectively verified. The numerical results show that (1) on the premise that other parameters are determined, the increase of noise intensity can effectively control the spread of rumors; (2) cut off the way of spreading rumors and reduce the contact between ignorant and rumor-spreading individuals (i.e., reduce the value of α); popularize scientific knowledge, reducing the attraction of rumors (i.e., increase the value of β) or replacing rumors of emergencies with other hot topics (i.e., increase the value of η) can effectively curb rumor propagation.

Selective transfer learning with adversarial training for stock movement prediction

Stock movement prediction is a critical issue in the field of financial investment. It is very challenging since a stock usually shows highly stochastic property in price and has complex relationships with other stocks. Most existing approaches cannot jointly take the above two issues into account and thus cannot yield satisfactory prediction result. This paper contributes a new stock movement prediction model, Selective Transfer Learning with Adversarial Training (STLAT). Our STLAT method advances existing solutions in two major aspects: (i) tailoring the pre-trained and fine-tuned method for stock movement prediction and (ii) introducing the data selector module to select the more relevant training samples. More specifically, we pre-train the shared base model using three different tasks. The predictor task is constructed to measure the performance of the shared base model with source domain data and target domain data. The adversarial training task is constructed to improve the generalisation of the shared base model. The data selector task is introduced to select the most relevant and high-quality training samples from stocks in source domain. All three tasks are jointly trained with a loss function. As a result, the pre-trained shared base model can be fine-tuned with the stock data in target domain. To validate our method, we perform the back-testing on the historical data of two public datasets and a newly constructed dataset. Extensive experiments demonstrate the superiority of our STLAT method. It outperforms state-of-the-art stock prediction solutions on ACC evaluation of 3.76%, 4.12%, 4.89% on ACL18, KDD17 and CN50, respectively.

On the stability of recovering two sources and initial status in a stochastic hyperbolic-parabolic system

Consider an inverse problem of determining two stochastic source functions and the initial status simultaneously in a stochastic thermoelastic system, which is constituted of two stochastic equations of different types, namely a parabolic equation and a hyperbolic equation. To establish the conditional stability for such a coupling system in terms of some suitable norms revealing the stochastic property of the governed system, we first establish two Carleman estimates with regular weight function and two large parameters for stochastic parabolic equation and stochastic hyperbolic equation, respectively. By means of these two Carleman estimates, we finally prove the conditional stability for our inverse problem, provided the source in the elastic equation be known near the boundary and the solution be in an a priori bounded set. Due to the lack of information about the time derivative of wave field at the final time, the stability index with respect to the wave field at final time is found to be halved, which reveals the special characteristic of our inverse problem for the coupling system.

Optimal Power Flow Considering Global Voltage Stability Based on a Hybrid Modern Heuristic Technique

Integrating large renewable energy to grid complicates power systems’ steady-state operation which leads to the high risk of voltage instability due to its intermittent and stochastic properties. The steady-state voltage stability margin (VSM) can be measured by the smallest singular value (SSV) of the load flow Jacobian matrix. Unlike other voltage stability indices such as L-index which shows the probability of voltage collapse for a particular bus, namely, local stability index, SSV represents the global voltage stability and the smaller the value is, the riskier the whole system's stability is. Voltage stability constrained-optimal power flow (VSC-OPF) is an effective tool to stabilize system voltage. Yet VSC-OPF is a highly non-linear and non-convex problem because of AC power flow and implicit SSV constraints. Such challenge is tackled, in this work, by a novel hybrid heuristic method, differential evolutionary particle swarm optimization (DEEPSO) which can easily formulate explicit constraints and objective functions to obtain near-optimal solutions efficiently. Several case studies are conducted on the IEEE 30-bus system, and they demonstrate the effectiveness of the hybrid technique and presents some insights on voltage profiles under various system operating condition.

Stochastic Properties and Pricing of Bitcoin Using a GJR-GARCH Model with Conditional Skewness and Kurtosis Components

Stochastic Properties and Pricing of Bitcoin Using a GJR-GARCH Model with Conditional Skewness and Kurtosis Components

Phase and Amplitude Synchronization in Power-Grid Frequency Fluctuations in the Nordic Grid

Monitoring and modelling the power grid frequency is key to ensuring stability in the electrical power system. Many tools exist to investigate the detailed deterministic dynamics and especially the bulk behaviour of the frequency. However, far less attention has been paid to its stochastic properties, and there is a need for a cohesive framework that couples both short-time scale fluctuations and bulk behaviour. Moreover, commonly assumed uncorrelated stochastic noise is predominantly employed in modelling in energy systems. In this publication, we examine the stochastic properties of the Nordic Grid, focusing on the increments of the frequency recordings. We show that these increments follow non-Gaussian statistics and display spatial and temporal correlations. Furthermore, we report two different physical synchronisation phenomena: a very short timescale phase synchronisation (< 2 s) followed by a slightly larger timescale amplitude synchronisation (2 s–5 s). Overall, these results show that modelling of fluctuations in power systems should not be restricted to Gaussian white noise.

Observation-driven models for discrete-valued time series

Statistical inference for discrete-valued time series has not been developed like traditional methods for time series generated by continuous random variables. Some relevant models exist, but the lack of a homogenous framework raises some critical issues. For instance, it is not trivial to explore whether models are nested and it is quite arduous to derive stochastic properties which simultaneously hold across different specifications. In this paper, inference for a general class of first order observation-driven models for discrete-valued processes is developed. Stochastic properties such as stationarity and ergodicity are derived under easy-to-check conditions, which can be directly applied to all the models encompassed in the class and for every distribution which satisfies mild moment conditions. Consistency and asymptotic normality of quasi-maximum likelihood estimators are established, with the focus on the exponential family. Finite sample properties and the use of information criteria for model selection are investigated throughout Monte Carlo studies. An empirical application to count data is discussed, concerning a test-bed time series on the spread of an infection.

Reliability Analysis of the Proportional Mean Departure Time Model

In this article, the mean lifetime of an individual whose lives lost based on a function of the time before which the individual has passed away is considered. The measure is used to construct a semi‐parametric model called proportional mean departure time model. Examples are given and evidences are gathered to show that the model is a proper alternative for the proportional mean past lifetime model. Closure properties of the model concerning several stochastic orders and a number of reliability properties are established. Finally, the model is extended to entertain random amounts of the parameter and establish a proportional mean departure time frailty model. Further stochastic properties using several stochastic orders are developed in the context of the frailty model.

Elastic-net Regularized High-dimensional Negative Binomial Regression: Consistency and Weak Signal Detection

We study a sparse negative binomial regression (NBR) for count data by showing the non-asymptotic advantages of using the elastic-net estimator. Two types of oracle inequalities are derived for the NBR's elastic-net estimates by using the Compatibility Factor Condition and the Stabil Condition. The second type of oracle inequality is for the random design and can be extended to many $\ell_1 + \ell_2$ regularized M-estimations, with the corresponding empirical process having stochastic Lipschitz properties. We derive the concentration inequality for the suprema empirical processes for the weighted sum of negative binomial variables to show some high--probability events. We apply the method by showing the sign consistency, provided that the nonzero components in the true sparse vector are larger than a proper choice of the weakest signal detection threshold. In the second application, we show the grouping effect inequality with high probability. Third, under some assumptions for a design matrix, we can recover the true variable set with a high probability if the weakest signal detection threshold is large than the turning parameter up to a known constant. Lastly, we briefly discuss the de-biased elastic-net estimator, and numerical studies are given to support the proposal.

Tempered positive Linnik processes and their representations

This paper analyzes various classes of processes associated with the tempered positive Linnik (TPL) distribution. We provide several subordinated representations of TPL Lévy processes and in particular establish a stochastic self-similarity property with respect to negative binomial subordination. In finite activity regimes we show that the explicit compound Poisson representations give raise to innovations following Mittag-Leffler type laws which are apparently new. We characterize two time-inhomogeneous TPL processes, namely the Ornstein-Uhlenbeck (OU) Lévy-driven processes with stationary distribution and the additive process determined by a TPL law. We finally illustrate how the properties studied come together in a multivariate TPL Lévy framework based on a novel negative binomial mixing methodology. Some potential applications are outlined in the contexts of statistical anti-fraud and financial modelling.

Signal Analysis via the Stochastic Geometry of Spectrogram Level Sets

Spectrograms are fundamental tools in time-frequency analysis, being the squared magnitude of the so-called short time Fourier transform (STFT). Signal analysis via spectrograms has traditionally explored their peaks, i.e. their maxima. This is complemented by a recent interest in their zeros or minima, following seminal work by Flandrin and others, which exploits connections with Gaussian analytic functions (GAFs). However, the zero sets (or extrema) of GAFs have a complicated stochastic structure, complicating any direct theoretical analysis. Standard techniques largely rely on statistical observables from the analysis of spatial data, whose distributional properties for spectrograms are mostly understood only at an empirical level. In this work, we investigate spectrogram analysis via an examination of the stochastic geometric properties of their level sets. We obtain rigorous theorems demonstrating the efficacy of a spectrogram level sets based approach to the detection and estimation of signals, framed in a concrete inferential set-up. Exploiting these ideas as theoretical underpinnings, we propose a level sets based algorithm for signal analysis that is intrinsic to given spectrogram data, and substantiate its effectiveness via extensive empirical studies. Our results also have theoretical implications for spectrogram zero based approaches to signal analysis. To our knowledge, these results are arguably among the first to provide a rigorous statistical understanding of signal detection and reconstruction in this set up, complemented with provable guarantees on detection thresholds and rates of convergence.

Algorithm for control and forecasting of the functional stability of complex information-technical systems

The characteristics of the behavior of complex technical systems that realize the property of functional stability of these systems were studied. One of the possible statements of the problems of planning the operation of complex technical systems arising within the functional-parametric direction of risk theory is considered. It is shown that on the basis of the developed algorithms of the minimax assessment of the technical condition using the idea of ellipsoidal assessment, it is possible to implement a guaranteeing strategy for managing the risks of unauthorized influences. The proposed approach allows forecasting even with a small number of parameter measurements, does not require information about the stochastic properties of measurement errors and other obstacles, and has adaptive properties. The conditions for ensuring the functional stability of the technological process are given and practical recommendations for applying these conditions for decision-making in the practical implementation of production processes are described. Ensuring the functional stability of production processes is one of the most important tasks today. Currently, many different methods have been proposed to ensure a high level of functional stability, but this problem requires constant improvement and development of new approaches. In order to improve and develop methods of organizing production processes that ensure the functional stability of technological processes thanks to the implementation of an individual strategy for the operation of technical systems, an approach to the formation of an operation management strategy that ensures the functional stability of the relevant systems is proposed. An individual strategy for planning the operation of technical systems was studied, depending on their actual state, taking into account the features of this specific system. The proposed approach is advisable to use when planning the functionally stable operation of complex technical systems of responsible purpose, the failure of which is associated with significant material losses or catastrophic consequences.

繊維配向角を考慮した一方向繊維強化複合材料の素材の材料定数変動に対するマルチスケール確率応力解析

Multiscale stochastic stress analysis of unidirectional fiber reinforced composites considering microscopic randomness has been reported in recent, but most of them consider the fiber direction or transverse direction loading. On the other hand, unidirectional fiber reinforced composites are used at arbitrary orientation angles in forms such as laminated materials, so it is necessary to consider influence of fiber orientation when analyzing the stochastic problem. In this report, the influence of fiber orientation angle on the stochastic properties of microscopic stresses is investigated with using multiscale stochastic stress analysis considering the variation of elastic properties component materials of a unidirectional fiber reinforced composite material for various fiber orientation, and the effectiveness of a perturbation-based approach for this problem is investigated.

On Stochastic ISS of Time-Varying Switched Systems With Generic Lévy Switching Signals

Switched systems in which switching among subsystems occurs at random time instants find numerous applications in engineering. Stability analysis of such systems, however, is quite challenging. This letter investigates the stochastic input-to-state stability of this class of switched systems. The random switching instants are modeled by a non-decreasing, positive, and real-valued L&#x00E9;vy process, which, at every time instant, selects the active subsystem from a family of deterministic systems. No assumption on the stability of subsystems is presumed; they can be stable or unstable. Stochastic properties of the switching signal are coupled with a family of Lyapunov-like functions to obtain a sufficient condition for stochastic input-to-state stability.

Stochastic sequential supply chain management system: with a solution approach using the systematic sampling evolutionary method

Supply chain management describes a complex sequence of strategies implemented by multiple decision makers to transform raw materials into products and deliver to the market. Mathematical formulations of such problems involve hierarchical games with some form of stochastic properties in the problem definition. Such kind of mathematical problems are generally known to be NP-hard and are challenging to solve. This paper considers a general form of supply chain management problem with various forms of model formulations and analysis. Moreover, a solution approach based on a systematic sampling evolutionary method is also proposed to solve any form of such problem definitions to obtain a Stackelberg equilibrium or Stackelberg-Nash equilibrium solution. The convergence of the solution approach is shown. The reliability of the proposed method is checked. In addition to this, the algorithm is implemented on carefully constructed stochastic supply chain management problems and solutions to these problems are presented.

Inverse stereographic hyperbolic secant distribution: a new symmetric circular model by rotated bilinear transformations

The inverse stereographic projection (ISP), or equivalently, bilinear transformation, is a method to produce a circular distribution based on an existing linear model. By the genesis of the ISP method, many important circular models have been provided by many researchers. In this study, we propose a new symmetric unimodal/bimodal circular distribution by the rotated ISP method considering the hyperbolic secant distribution as a baseline distribution. Rotation means that fixing the origin and rotating all other points the same amount counterclockwise. Considering the effect of rotation on the circular distribution to be obtained with the bilinear transformation, it is seen that it actually induces a location parameter in the obtained circular probability distribution. We analyze some of the stochastic properties of the proposed distribution. The methods for the parameter estimation of the new circular model and the simulation-based compare results of these estimators are extensively provided by the paper. Furthermore, we compare the fitting performance of the new model according to its well-known symmetric alternatives, such as Von-Misses, and wrapped Cauchy distributions, on a real data set. From the information obtained by the analysis on the real data, we say that the fitting performance of the new distribution is better than its alternatives according to the criteria frequently used in the literature.

Stochastic and deterministic responses of an asymmetric quad-stable energy harvester

In this paper, stochastic and deterministic dynamical properties of an asymmetric quad-stable energy harvester are explored for improving the energy harvesting performance. Firstly, the harmonic balance method is utilized to explicitly derive the coupled relationship of the displacement amplitude, the constant term, and the output voltage amplitude. By means of direct numerical results, the existence of the multi-valued phenomenon of the asymmetric quad-stable energy harvester is found. Especially, the constant term is asymmetric due to the asymmetric characteristics. In addition, the influence of the depth of different potential wells on the highest orbit of inter-well oscillations is discussed. Finally, it is found that the symbol change of the largest Lyapunov exponent (LLE) of the harvester is consistent with the results derived by bifurcation diagrams, which verify the effectiveness of the LLE. The existence of noise can induce the harvester to transform from period motions to chaotic motions. The transition of the probability density function (PDF) of the harvester is influenced by the potential distribution and depth.