Transience Properties Research Articles

Hierarchical Two-Stream Growing Self-Organizing Maps With Transience for Human Activity Recognition

The rapid growth in autonomous industrial environments has increased the need for intelligent video surveillance. As a predominant element of video surveillance, recognition of complex human movements is important in a wide range of surveillance applications. However, the current state-of-the-art video surveillance techniques use supervised deep learning pipelines for human activity recognition (HAR). A key shortcoming of such techniques is the inability to learn from unlabeled video streams. To operate effectively in natural environments, video surveillance techniques have to be able to handle huge volumes of unlabeled video data, monitor and generate alerts and insights derived from multiple characteristics such as spatial structure, motion flow, color distribution, etc. Furthermore, most conventional learning systems lack memory persistence capability which can reduce the influence of outdated information in memory-guided decision-making resulting in limiting plasticity and overfitting based on specific past events. In this article, we propose a new adaptation of the Growing Self-Organizing Map (GSOM) to address these shortcomings by 1) adopting two proven concepts of traditional deep learning, hierarchical, and multistream learning, applied into GSOM self-structuring architecture to accommodate learning from unlabeled video data and their diverse characteristics, 2) address overfitting and the influence of outdated information on neural architecture by implementing a transience property in the algorithm. We demonstrate the proposed model using three benchmark video datasets and the results confirm its validity and usability for HAR.

Introducing Temperature-Controlled Phase Transition Elastin-like Polypeptides to Transient Electronics: Realization of Proactive Biotriggered Electronics with Local Transience.

Transient electronics have dramatically changed inner-body therapy in health care. They stand out because of their harmless dissolution in the human body with no lingering electronic trash. However, high-precision biomedical implants require programmable and serial remedy operations, and controlling the whole-device destruction is not proactive and precise. Thus, a novel biotriggered and temperature-controlled transient electronics fabrication method using elastin-like polypeptides (ELPs) as triggers is proposed. Biocompatible ELPs simply mixed with trace silver nanowire (AgNW) can serve as the "switch" for the electronics to respond to local temperature changes in deionized water, exhibiting an agile response time. A ratio gradient experiment of the ELPs and AgNW shows that more programmable and precise transience properties (initial resistance, ready time, response time, and stable resistance) can be achieved by using a designated proportion. Further, we validated that the 3D-printing-based ELP-triggering transient electronics fabrication method is very simple yet effective for preparing transient wireless charging LEDs. Transient devices comprising ELPs-AgNW and PLGA-Ag respond within 160 s below 10 °C and degrade within a certain period.

Recurrence and transience properties of multi-dimensional diffusion processes in selfsimilar and semi-selfsimilar random environments

We consider $d$-dimensional diffusion processes in multi-parameter random environments which are given by values at different $d$ points of one-dimensional $\alpha $-stable or $(r, \alpha )$-semi-stable Levy processes. From the model, we derive some conditions of random environments that imply the dichotomy of recurrence and transience for the $d$-dimensional diffusion processes. The limiting behavior is quite different from that of a $d$-dimensional standard Brownian motion. We also consider the direct product of a one-dimensional diffusion process in a reflected non-positive Brownian environment and a one-dimensional standard Brownian motion. For the two-dimensional diffusion process, we show the transience property for almost all reflected Brownian environments.

On recurrence and transience of two-dimensional Lévy and Lévy-type processes

In this paper, we study recurrence and transience of Lévy-type processes, that is, Feller processes associated with pseudo-differential operators. Since the recurrence property of Lévy-type processes in dimensions greater than two is vacuous and the recurrence and transience of one-dimensional Lévy-type processes have been very well investigated, in this paper we are focused on the two-dimensional case only. In particular, we study perturbations of two-dimensional Lévy-type processes which do not affect their recurrence and transience properties, we derive sufficient conditions for their recurrence and transience in terms of the corresponding Lévy measure and we provide some comparison conditions for the recurrence and transience also in terms of the Lévy measures.

Long-time behavior for a class of Feller processes

In this paper, as a main result, we derive a Chung-Fuchs type condition for the recurrence of Feller processes associated with pseudo-differential operators. In the Lévy process case, this condition reduces to the classical and well-known Chung-Fuchs condition. Further, we also discuss the recurrence and transience of Feller processes with respect to the dimension of the state space and Pruitt indices and the recurrence and transience of Feller-Dynkin diffusions and stable-like processes. Finally, in the one-dimensional symmetric case, we study perturbations of Feller processes which do not affect their recurrence and transience properties, and we derive sufficient conditions for their recurrence and transience in terms of the corresponding Lévy measure. In addition, some comparison conditions for recurrence and transience also in terms of the Lévy measures are obtained.

Ergodic Property of Stable-Like Markov Chains

A stable-like Markov chain is a time-homogeneous Markov chain on the real line with the transition kernel $$p(x,\hbox {d}y)=f_x(y-x)\hbox {d}y$$ , where the density functions $$f_x(y)$$ , for large $$|y|$$ , have a power-law decay with exponent $$\alpha (x)+1$$ , where $$\alpha (x)\in (0,2)$$ . In this paper, under a certain uniformity condition on the density functions $$f_x(y)$$ and additional mild drift conditions, we give sufficient conditions for recurrence in the case when $$0<\liminf _{|x|\longrightarrow \infty }\alpha (x)$$ , sufficient conditions for transience in the case when $$\limsup _{|x|\longrightarrow \infty }\alpha (x)<2$$ and sufficient conditions for ergodicity in the case when $$0<\inf \{\alpha (x):x\in \mathbb {R}\}$$ . As a special case of these results, we give a new proof for the recurrence and transience property of a symmetric $$\alpha $$ -stable random walk on $$\mathbb {R}$$ with the index of stability $$\alpha \ne 1$$ .

Transience of diffusions on Heisenberg and Grushin distributions

In the absence of a general theory of diffusions on non-integrable distributions, an important role is played by the investigation of some particular examples. This paper deals with a couple of these type of examples. The first one is the Heisenberg diffusion, which is a degenerate diffusion with non-holonomic constraints living on the horizontal distribution of the Heisenberg group. The paper proves the transience property of the Heisenberg diffusion for small balls. The second example is the Grushin diffusion, also a degenerate diffusion, which moves in the plane along the Grushin distribution. We prove the transience property of this diffusion.

Escape Rates for Rotor Walks in $\mathbb{Z}^d$

Rotor walk is a deterministic analogue of random walk. We study its recurrence and transience properties on ${\mathbb Z}^d$ for the initial configuration of all rotors aligned. If $n$ particles in turn perform rotor walks starting from the origin, we show that the number that escape (i.e., never return to the origin) is of order $n$ in dimensions $d \geq 3$ and of order $n/\log n$ in dimension $2$.

Recurrence and transience property for a class of Markov chains

We consider the recurrence and transience problem for a time-homogeneous Markov chain on the real line with transition kernel $p(x,\mathrm{d}y)=f_x(y-x)\,\mathrm{d}y$, where the density functions $f_x(y)$, for large $|y|$, have a power-law decay with exponent $\alpha(x)+1$, where $\alpha(x)\in(0,2)$. In this paper, under a uniformity condition on the density functions $f_x(y)$ and an additional mild drift condition, we prove that when $\lim\inf_{|x|\longrightarrow\infty}\alpha(x)>1$, the chain is recurrent. Similarly, under the same uniformity condition on the density functions $f_x(y)$ and some mild technical conditions, we prove that when $\lim\sup_{|x|\longrightarrow\infty}\alpha(x)<1$, the chain is transient. As a special case of these results, we give a new proof for the recurrence and transience property of a symmetric $\alpha$-stable random walk on $\mathbb {R}$ with the index of stability $\alpha\in(0,1)\cup(1,2).$

Long-time behavior of stable-like processes

In this paper, we consider a long-time behavior of stable-like processes. A stable-like process is a Feller process given by the symbol p(x,ξ)=−iβ(x)ξ+γ(x)|ξ|α(x), where α(x)∈(0,2), β(x)∈R and γ(x)∈(0,∞). More precisely, we give sufficient conditions for recurrence, transience and ergodicity of stable-like processes in terms of the stability function α(x), the drift function β(x) and the scaling function γ(x). Further, as a special case of these results we give a new proof for the recurrence and transience property of one-dimensional symmetric stable Lévy processes with the index of stability α≠1.

The Dichotomy of Recurrence and Transience of Semi-Lévy Processes

A semi-Levy process is an additive process with periodically stationary increments. In particular, it is a generalization of a Levy process. The dichotomy of recurrence and transience of Levy processes is well known, but this is not necessarily true for general additive processes. In this paper, we prove the recurrence and transience dichotomy of semi-Levy processes. For the proof, we introduce a concept of semi-random walk and discuss its recurrence and transience properties. An example of semi-Levy process constructed from two independent Levy processes is investigated. Finally, we prove the laws of large numbers for semi-Levy processes.

An Introductory Study of the Hydrogen Atom with Paraquantum Logic

Paraquantum Logics (PQL) has its origins in the fundamental concepts of the Paraconsistent Annotated Logics (PAL) whose main feature is to be capable of treating contradictory information. Based on a class of logics called Paraconsistent Logics with annotations of two values (PAL2v), PQL performs a logical treatment on signals obtained by measurements on physical quantities which are considered Observable Variables in the physical world. In the process of application of the PQL the obtained values are transformed in Evidence Degrees and represented on a Lattice of four Ver- tices where special equations transform these degrees into Paraquantum logical states ψ which propagate. The propagation of Paraquantum logical states provides us with results which can be interpreted and modeled through phenomena studied in physics. Using the paraquantum equations, we investigate the effects of balancing of Energies and the quantization and transience properties of the Paraquantum Logical Model in real Physical Systems. As a demonstration of the usage of the paraquantum equations we perform a numerical comparative study that applies the PQL to the Bohr’s model to find the energy levels of the Hydrogen atom. It is verified that the values of energy in each level of the Paraquantum logical model of the Hydrogen atom are close to the values found by the conventional way. The results through the Paraquantum Logic allow considering other important properties of the atom, as the forecast of number of electrons in each layer.

Jensen Measures in Potential Theory

It is shown that, for open sets in classical potential theory and—more generally—for elliptic harmonic spaces Y, the set J x (Y) of Jensen measures (representing measures with respect to superharmonic functions on Y) for a point x ∈ Y is a simple union of closed faces of the compact convex set $M_x(\mathcal P(Y))$ of representing measures with respect to potentials on Y, a set which has been thoroughly studied a long time ago. In particular, the set of extreme Jensen measures can be immediately identified. The results hold even without ellipticity (thus capturing also many examples for the heat equation) provided a rather weak approximation property for superharmonic functions holds. Equally sufficient are a certain transience property and a weak regularity property. More important, each of these properties turns out to be necessary and sufficient for obtaining (in the classical case) that J x (Y) coincides with the set of all compactly supported probability measures in $M_x(\mathcal P(Y))$ .

Birth and death processes in randomly fluctuating environments

AbstractA birth and death process in a time-dependent random environment is introduced. We will discuss the recurrence and transience properties for the process.

Recurrence and transience properties of some neural networks: an approach via fluid limit models

The subject of the paper is the stability analysis of some neural networks consisting of a finite number of interacting neurons. Following the approach of Dai l5r we use the fluid limit model of the network to derive a sufficient condition for positive Harris-recurrence of the associated Markov process. This improves the main result in Karpelevich et al. l11r and, at the same time, sheds some new light on it. We further derive two different conditions that are sufficient for transience of the state process and illustrate our results by classifying some examples according to positive recurrence or transience.

Equilibria and quasiequilibria for infinite collections of interacting Fleming-Viot processes

In this paper of infinite systems of interacting measure-valued diffusions each with state space P ( [ 0 , 1 ] ) \mathcal {P}\left ( {[0,1]} \right ) , the set of probability measures on [0, 1], is constructed and analysed (Fleming-Viot systems). These systems arise as diffusion limits of population genetics models with infinitely many possible types of individuals (labelled by [0, 1]), spatially distributed over a countable collection of sites and evolving as follows. Individuals can migrate between sites and after an exponential waiting time a colony replaces its population by a new generation where the types are assigned by resampling from the empirical distribution of types at this site. It is proved that, depending on recurrence versus transience properties of the migration mechanism, the system either clusters as t → ∞ t \to \infty , that is, converges in distribution to a law concentrated on the states in which all components are equal to some δ u , u ∈ [ 0 , 1 ] {\delta _u},\ u \in [0,1] , or the system approaches a nontrivial equilibrium state. The properties of the equilibrium states, respectively the cluster formation, are studied by letting a parameter in the migration mechanism tend to infinity and explicitly identifying the limiting dynamics in a sequence of different space-time scales. These limiting dynamics have stationary states which are quasi-equilibria of the original system, that is, change only in longer time scales. Properties of these quasi-equilibria are derived and related to the global equilibrium process for large N N . Finally we establish that the Fleming-Viot systems are the unique dynamics which remain invariant under the associated space-time renormalization procedure.

Markov chains with binomial time change

The effect of a binomial time change on a given Markov chain is studied. Results are obtained for the hitting times, potential operator, and transience and recurrence properties of the time-changed chain. The limiting behavior is considered as the binomial parameter approaches 0 and the time variable approaches∞.

Recurrency of an Oscillating Random Walk

Previous article Next article Recurrency of an Oscillating Random WalkB. A. Rogozin and S. G. FossB. A. Rogozin and S. G. Fosshttps://doi.org/10.1137/1123015PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] J. H. B. Kemperman, The oscillating random walk, Stochastic Processes Appl., 2 (1974), 1–29 10.1016/0304-4149(74)90010-6 MR0362500 0326.60081 CrossrefGoogle Scholar[2] E. A. Pecherskii and , B. A. Rogozin, On joint distributions of random variables associated with fluctuations of a process with independent increments, Theory Prob. Applications, 14 (1969), 410–423 10.1137/1114054 LinkGoogle Scholar[3] B. A. Rogozin, On the distribution of the first jump, Theory Prob. Applications, 9 (1969), 450–465 10.1137/1109060 LinkGoogle Scholar[4] B. A. Rogozin, The distribution of the first ladder moment and height and fluctuation of a random walk, Theory Prob. Applications, 16 (1971), 575–595 10.1137/1116067 0269.60053 LinkGoogle Scholar[5] I. A. Ibragimov and , Yu. V. Linnik, Independent and stationary sequences of random variables, Wolters-Noordhoff Publishing, Groningen, 1971, 443– MR0322926 0219.60027 Google Scholar[6] B. A. Rogozin, Relatively stable walks, Theory Prob. Applications, 21 (1976), 375–379 10.1137/1121041 0381.60043 LinkGoogle Scholar[7] William Feller, An introduction to probability theory and its applications. Vol. II, Second edition, John Wiley & Sons Inc., New York, 1971xxiv+669 MR0270403 0219.60003 Google Scholar Previous article Next article FiguresRelatedReferencesCited byDetails Markov chains with heavy-tailed increments and asymptotically zero driftElectronic Journal of Probability, Vol. 24, No. none Cross Ref Anomalous recurrence properties of many-dimensional zero-drift random walks25 July 2016 | Advances in Applied Probability, Vol. 48, No. A Cross Ref Recurrence and transience property for a class of Markov chainsBernoulli, Vol. 19, No. 5B Cross Ref Series of tail distributions of finitely inhomogeneous random walksJournal of Mathematical Analysis and Applications, Vol. 369, No. 1 Cross Ref On oscillating random walksSiberian Mathematical Journal, Vol. 37, No. 4 Cross Ref Oscillating random walk with a moving boundaryIsrael Journal of Mathematics, Vol. 88, No. 1-3 Cross Ref Making Money From Fair Games Cross Ref Summary of Reports Presented at Sessions of the Seminar on Probability Theory and Mathematical Statistics at the Mathematical Institute of the Siberian Section of the USSR Academy of Sciences ,197928 July 2006 | Theory of Probability & Its Applications, Vol. 25, No. 3AbstractPDF (768 KB) Volume 23, Issue 1| 1978Theory of Probability & Its Applications History Submitted:09 June 1976Published online:17 July 2006 InformationCopyright © 1978 Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI:10.1137/1123015Article page range:pp. 155-162ISSN (print):0040-585XISSN (online):1095-7219Publisher:Society for Industrial and Applied Mathematics