Random Walks

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• We use the evolution of distributions to characterize normal or anomalous diffusion. • We considered space and time dynamics to test different regimes of diffusion. • The width of the distribution is related to the parameters of the random walk. • This analysis is independent of the mechanism responsible for the diffusion. • The technique is specially useful in superdiffusion, where the variance diverges.

We theoretically study the trapping time distribution and the efficiency of the excitation energy transport in dendritic systems. Trapping of excitations, created at the periphery of the dendrimer, on a trap located at its core, is used as a probe of the efficiency of the energy transport across the dendrimer. The transport process is treated as incoherent hopping of excitations between nearest-neighbor dendrimer units and is described using a rate equation. We account for radiative and nonradiative decay of the excitations while diffusing across the dendrimer. We derive exact expressions for the Laplace transform of the trapping time distribution and the efficiency of trapping, and analyze those for various realizations of the energy bias, number of dendrimer generations, and relative rates for decay and hopping. We show that the essential parameter that governs the trapping efficiency is the product of the on-site excitation decay rate and the trapping time (mean first passage tim...

We find the solution of the partial difference equation subject to the absorbing boundary conditions at x = 0 and x = m+1. Green's function will be determined using random walk techniques applying the reflective and inclusion-exclusion principles.

We find the solution of the partial difference equation subject to the absorbing boundary conditions at x = 0 and x = m+1. Green's function will be determined using random walk techniques applying the reflective and inclusion-exclusion principles.

We apply new image processing tools and computer modeling of DSB formation to analyze new experimental data on DSB (DNA doublestrand break) yield (#DSB per base pair per Gray). There is LET-dependent DSB clustering within the nucleus volume, and clustering of DSBs along the DNA length, which we show through modeling the whole set of human chromosomes. In recent experiments, DSBs are imaged as phosphorylation sites of the histone protein H2AX, denoted as H2AX foci, and it is suggested that foci images indicate the spatial distribution of DSBs. For high-LET radiation, DSBs should be located closer to the track center or grouped around ionization sites leading to clustered DSBs as described theoretically, and as can be seen in images. We describe the successful segmentation of foci images and determine foci statistics that will relate models of DSB spatial correlation and clustering along DNA length to the experimental data. The foci data can be used to analyze high-LET effects on DNA fragment sizes and DSB distributions.

Bu kitabın Türkiye'deki her türlü yayın hakkı Gazi Kitabevi Tic. Ltd. Şti'ne aittir, tüm hakları saklıdır. Kitabın tamamı veya bir kısmı 5846 sayılı yasanın hükümlerine göre, kitabı yayınlayan firmanın ve yazarlarının önceden izni olmadan elektronik, mekanik, fotokopi ya da herhangi bir kayıt sistemiyle çoğaltılamaz, yayınlanamaz, depolanamaz.

In human perception, convex surfaces have a strong tendency to be perceived as the "figure". Convexity has a stronger influence on figural organization than other global shape properties, such as symmetry ([9]). And yet, there has been very little work on convexity properties in computer vision. We present a model for figure/ground segregatation which exhibits a preference for convex regions as the figure (i.e., the foreground). The model also shows a preference for smaller regions to be selected as figures, which is also known to hold for human visual perception (e.g., Koffka [11]). The model is based on the machinery of Markov random fields/random walks/diffusion processes, so that the global shape properties are obtained via local and stochastic computations. Experimental results demonstrate that our model performs well on ambiguous figure/ground displays which were not captured before. In particular, in ambiguous displays where neither region is strictly convex, the model shows preference to the "more convex" region, thus offering a continuous measure of convexity in agreement with human perception.

In human perception, convex surfaces have a strong tendency to be perceived as the "figure". Convexity has a stronger influence on figural organization than other global shape properties, such as symmetry ([9]). And yet, there has been very little work on convexity properties in computer vision. We present a model for figure/ground segregatation which exhibits a preference for convex regions as the figure (i.e., the foreground). The model also shows a preference for smaller regions to be selected as figures, which is also known to hold for human visual perception (e.g., Koffka [11]). The model is based on the machinery of Markov random fields/random walks/diffusion processes, so that the global shape properties are obtained via local and stochastic computations. Experimental results demonstrate that our model performs well on ambiguous figure/ground displays which were not captured before. In particular, in ambiguous displays where neither region is strictly convex, the model shows preference to the "more convex" region, thus offering a continuous measure of convexity in agreement with human perception.

The pursuit of a unified theory that captures the intricacies of the brain and mind continues to be a significant challenge in theoretical neuroscience. This paper presents a novel, triune framework that utilizes the concept of collective biased random walk (cBRW). Our approach strives to transcend biological specifics, offering a high-level abstraction that remains general and applicable across various neural phenomena. Despite the solid traditional foundation of computational neuroscience, the intricate delicacy of neural processes calls for a renewed probabilistic approach. We aim to utilize the intuitive nature of probability concepts —such as the probability of localization and state, and uniform probability distribution— to study the stochastic organization of electric charges and signals in the brain. This electrophysiological intricacy emerges from the seemingly paradoxical reality that tiny electric events, while random, collectively give rise to predictable, long-range oscillations. These oscillations manifest in three groups of activation states. Our framework categorizes the brain as a triune system, accommodating classical, semiclassical, and non-classical interpretations of both probabilistic phenomena and cBRW models, alongside three groups of states. We conclude that by appreciating, rather than overlooking, the tiny random walks of electric charges and signals in the brain, we can gain a triune mathematical foundation for theoretical brain science, the powerful capabilities of this organ, and the electromagnetic interfaces we can develop. Manuscript received: 30-10-2023. Revised: 19-06-2024. Accepted: 21-08-2024. RESEARCH ARTICLE. Keywords. Brain States, Brain Theory, Brain Electrophysiology, Neural Computations, Electroencephalography, Non-Classic Brains. MAIN Abbreviations: BRW: Biased Random Walks, cBRW: Collective Random Walks, P(.): Probability, Pl(x): Probability of localization at x, Ps(b): Probability of state b, RW: Random Walk. OTHER Abbreviations: 1D: one Dimension, 2D: two Dimensions, DWI: diffusion weighted imaging, E(.): Expectancy, EEG: Electroencephalography, MEG: Magnetoencephalography, MRI: Magnetic Resonance Imaging, NIRS: near-infrared spectroscopy, TES/TMS: electric/magnetic stimulation, Var(.): Variance. International Group of Neuroscience, Neuroengineering and Neurophilosophy, IGN(S,E,P). Colombia, US, India, Europe.

As this century unfolds we will witness the rise of the quantum computer. A quantum computer is a device that utilizes the laws of one of the most fundamental theories of physics -quantum mechanics. By utilizing properties of quantum mechanics a quantum computer is able to perform certain information processing tasks much more efficiently than an ordinary classical computer. The last century of modern society was revolutionized by some of the simplest ideas in quantum mechanics like energy quantization and quantum tunnelling, which led to technologies like the laser and the transistor. We can expect to see additional technological revolutions occur in this century since we are beginning to build technologies with some of the more complex properties of quantum mechanics such as quantum entanglement and quantum superposition. These quantum effects make more radical technologies like the quantum computer possible. This thesis is based upon the work I have done during my PhD candidature at Macquarie University. In this work we develop quantum technologies that are directed towards realising a quantum computer. Specifically, we have made many theoretical advancements in a type of quantum information processing protocol called B S . This device efficiently simulates the interaction of quantum particles called bosons, which no classical computer can efficiently simulate. In this thesis we explore quantum random walks, which are the basis of how the bosons in B S interfere with each other. We explore implementing B -S using the most readily available photon source technology. We invented a completely new architecture which can implement B S in time rather than space and has since been used to make the worlds largest B S experiment ever performed. We look at variations to the traditional B S architecture by considering other quantum states of light. We show a worlds first application inspired by B S in quantum metrology where measurements may be made more accurately than with any classical method. Lastly, dealing with B S , we look at reformulating the formalism of B S using a quantum optics approach. In addition, but not related to B S , we show a protocol for efficiently generating large-photon Fock states, which are a type of quantum state of light, that are useful for quantum computation. Also, we show a method for generating a specific quantum state of light that is useful for quantum error correction -an essential component of realising a quantum computer -by coupling together light and atoms.

Este trabajo intenta presentar una metodología que pueda suministrar señales anticipadas de intervención en el mercado cambiario, en función de los niveles de volatilidad del tipo de cambio observados durante el Régimen de Flotación vigente entre febrero de 2002 y enero de 2003. Para alcanzar este fin, se hace uso del enfoque del Valor en Riesgo ( Value at Risk) y del Modelos de Volatilidad Condicionada del Tipo GARCH (1,1). Este modelo define los movimientos en la cotización de la divisa que no estén asociados con los fundamentos macroeconómicos, y requieran la intervención en el mercado cambiario por parte de la autoridad monetaria.

Random walks on general graphs play an important role in the understanding of the general theory of stochastic processes. Beyond their fundamental interest in probability theory, they arise also as simple models of physical systems. A brief survey of the physical relevance of the notion of random walk on both undirected and directed graphs is given followed by the exposition of some recent results on random walks on randomly oriented lattices. It is worth noticing that general undirected graphs are associated with (not necessarily Abelian) groups while directed graphs are associated with (not necessarily Abelian) C * -algebras. Since quantum mechanics is naturally formulated in terms of C * -algebras, the study of random walks on directed lattices has been motivated lately by the development of the new field of quantum information and communication. * Extended version of the talk given by at the Workshop "Random walks and geometry" held

Network embedding approaches are gaining momentum to analyse a large variety of networks. Indeed, these approaches have demonstrated their effectiveness in tasks such as community detection, node classification, and link prediction. However, very few network embedding methods have been specifically designed to handle multiplex networks, i.e. networks composed of different layers sharing the same set of nodes but having different types of edges. Moreover, to our knowledge, existing approaches cannot embed multiple nodes from multiplex-heterogeneous networks, i.e. networks composed of several multiplex networks containing both different types of nodes and edges. In this study, we propose MultiVERSE, an extension of the VERSE framework using Random Walks with Restart on Multiplex (RWR-M) and Multiplex-Heterogeneous (RWR-MH) networks. MultiVERSE is a fast and scalable method to learn node embeddings from multiplex and multiplex-heterogeneous networks. We evaluate MultiVERSE on several b...

The XX0 Heisenberg model on a cyclic chain is considered. The representation of the Bethe wave functions via the Schur functions allows to apply the well-developed theory of the symmetric functions to the calculation of the thermal correlation functions. The determinantal expressions of the form-factors and of the thermal correlation functions are obtained. The q-binomial determinants enable the connection of the form-factors with the generating functions both of boxed plane partitions and of self-avoiding lattice paths. The asymptotical behavior of the thermal correlation functions is studied in the limit of low temperature provided that the characteristic parameters of the system are large enough.

The linear relation between Kemeny's constant, a graph metric directly linked with random walks, and the effective graph resistance in a regular graph has been an incentive to calculate Kemeny's constant for various networks. In this paper we consider complete bipartite graphs, (generalized) windmill graphs and tree networks with large diameter and give exact expressions of Kemeny's constant. For non-regular graphs we propose two approximations for Kemeny's constant by adding to the effective graph resistance term a linear term related to the degree heterogeneity in the graph. These approximations are exact for complete bipartite graphs, but show some discrepancies for generalized windmill and tree graphs. However, we show that a recently obtained upper-bound for Kemeny's constant in Wang et al. (2017) based on the pseudo inverse Laplacian gives the exact value of Kemeny's constant for generalized windmill graphs. Finally, we have evaluated Kemeny's constant, its two approximations and its upper bound, for 243 real-world networks. This evaluation reveals that the upper bound is tight, with average relative error of only 0.73%. In most cases the upper bound clearly outperforms the other two approximations.

The issue of long memory, though has important theoretical and practical implications, has not received much attention in India. This article examines the issue of long memory in mean of the stock returns by employing a set of sophisticated time-series tests including a bias reduced log periodogram test of Andrews and Guggenberger. The study used daily values of 29 major indices including sectoral indices traded on the National Stock Exchange and Bombay Stock Exchange from April 2003 to March 2012, which provide insights into relation between composition of indices and long memory. The findings of the study suggest significant presence of long memory in mean returns of the medium-and small-sized indices and weaker evidences for large cap indices. Further, the study identifies a relationship between presence of long memory and market structure variables. The use of linear models in the presence of long memory would result in incorrect inferences, and this calls for investigation of appropriate long memory model to generate profits in Indian stock market.

This study uses "event study" and "identification through heteroscedasticity" methodology to study the impact of Indian monetary policy announcements on stock indices during 2004-14. Although stock indices decline after announcement of policy tightening, the results are statistically insignificant. Unanticipated policy announcements have weakly significant impact, particularly on banking stocks. Dominance of the banking channel and ineffectiveness of the asset price channel in monetary transmission could have contributed to this non-confirmative result. Finally, UMP announcements of the US Fed also do not impact Indian stock returns except for a few events of LSAP in 2008 and Operation Twist in 2011.

We address the problem of building and maintaining a forest of spanning trees in highly dynamic networks, in which topological events can occur at any time and any rate, and no stable periods can be assumed. In these harsh environments, we strive to preserve some properties such as cycle-freeness or existence of a unique root in each fragment regardless of the events, so as to keep these fragments functioning uninterruptedly to a possible extent. Our algorithm operates at a coarse-grain level, using atomic pairwise interactions akin to population protocol or graph relabeling systems. The algorithm relies on a perpetual alternation of topology-induced splittings and computation-induced mergings of a forest of trees. Each tree in the forest hosts exactly one token (also called root) that performs a random walk inside the tree, switching parentchild relationships as it crosses edges. When two tokens are located on both sides of a same edge, their trees are merged upon this edge and one token disappears. Whenever an edge that belongs to a tree disappears, its child endpoint regenerates a new token instantly. The main features of this approach is that both merging and splitting are purely localized phenomenons. This paper presents the algorithm and establishes its correctness in arbitrary dynamic networks. We also discuss aspects related to the implementation of this general principle in fine-grain models, as well as embryonic elements of analysis. The characterization of the algorithm performance is left open, both analytically and experimentally.

We study the price dynamics of 24 publicly traded companies in the New York Stock Exchange (NYSE) during the years 1926-1933 using data from the Wharton Research Data Service (WRDS) database. We find evidence against the hypothesis of random walks in stock prices. There was a bubble during the years 1927-29, which begins in the fall of 1927. Companies introducing new technologies, such as Radio Corporation of America (RCA), had their price peak first, and led the boom. Companies in traditional sectors had their peaks last, and were followers. In addition, there is significant price undershooting in the aftermath of the crash, in contrast to the typical experimental bubble a la Vernon Smith.

A numerical solution for the simulation of chemical vapor infiltration of ceramic matrix composites is presented. This computational model requires a 3D representation of the preform. Gas transport and chemical reaction are simulated by a Monte Carlo random walk technique. The developed algorithm can also be used for determination of effective transport and reaction properties in a porous medium. It is firstly validated by considering the simple case of diffusion and reaction in a flat pore. Results of infiltration of an actual fiber 2 arrangement are described and discussed. Extension to deposition on a thin substrate with asperities is also studied.

The probability distribution for the number of top to bottom spanning clusters in Directed percolation in two and three dimensions appears to be universal and is of the form $P(n) \sim \exp(-\alpha n^2)$. We argue that $\alpha$ is a new critical quantity vanishing at the upper critical dimension. The probability distribution of the individual masses of the spanning clusters is found to have a Pearson distribution with a lower cutoff. Various properties of the clusters are reported.

Since some important variables are axial in weather study such as turbulent wind direction, the study of variance gamma distribution in case of circular data can be an amiable perspective; as such the ”Wrapped variance gamma” distribution along with its probability density function has been derived. Some of the other wrapped distributions have also been unfolded through proper specification of the concern parameters. Explicit forms of trigonometric moments, related parameters and some other properties of the same distribution are also obtained. As an example the methods are applied to a data set which consists of the wind directions of a Black Mountain ACT.

Openness to experience-the enjoyment of novel experiences and ideas-has many connections to cognitive processes. People high in openness to experience, for example, tend to be more creative and have broader general knowledge than people low in openness to experience. In the current study, we use a network science approach to examine if the organization of semantic memory differs between high and low groups of openness to experience. A sample of 516 adults completed measures of openness to experience (from the NEO Five-Factor Inventory-3 and Big Five Aspect Scales) and a semantic verbal fluency task. Next, the sample was split into half to form high (n = 258) and low (n = 258) openness to experience groups. Semantic networks were then constructed on the basis of their verbal fluency responses. Our results revealed that the high openness to experience group's network was more interconnected, flexible, and had better local organization of associations than the low openness to experience group. We also found that the high openness to experience group generated more responses on average and provided more unique responses than the low openness to experience group. Taken together, our results indicate that openness to experience is related to semantic memory structure.

Semantic distance plays an important role in the creative process: The farther one 'moves away' from a conventional idea, the more creative the new idea will likely be. Although intuitive, the role of semantic distance in creativity has been only indirectly examined due to the challenge of its measurement. Recent studies have started applying quantitative measures of semantic distance in creativity research. Such studies complement standard subjective measures of creativity; provide objective measures of the creative output; and also allow to more directly examine the role of semantic memory, and distance, in creativity. An overview of the main approaches that are being used will be described and the advantages of using such quantitative measures in creativity will be discussed.

The creative process involves several cognitive processes, such as working memory, controlled attention and task switching. One other process is cognitive search over semantic memory. These search processes can be controlled (e.g., problem solving guided by a heuristic), or uncontrolled (e.g., mind wandering). However, the nature of this search in relation to creativity has rarely been examined from a formal perspective. To do this, we use a random walk model to simulate uncontrolled cognitive search over semantic networks of low and high creative individuals with an equal number of nodes and edges. We show that a random walk over the semantic network of high creative individuals "finds" more unique words and moves further through the network for a given number of steps. Our findings are consistent with the associative theory of creativity, which posits that the structure of semantic memory facilitates search processes to find creative solutions.

Compatibility among suppliers is an effective approach to manage the dependencies between members of supply chain. These members often try to achieve their respective goal, disregarding the objective of the complete supply chain for a new product development and at last, the supply chain converges towards higher supply chain cost, greater leading times and a large variance between supply and demands. Kim and Wagner (2012) suggested compatibility among suppliers is necessary for new product development (NPD). On the basis of literature survey, compatibility among suppliers can be defined as the joint efforts of the suppliers towards mutually defined goals. Compatibility involves the interaction within as well as outside of the organizations/firms.Outside interaction of theorganization and supplier management is considered as a critical success factor for any organizations. In the modern global manufacturing environment, the most important factors for the compatibility between the sup...

on large deviations for sums of i.i.d. regularly varying random variables to partial sum processes of i.i.d. regularly varying vectors. The results are stated in terms of a heavy-tailed large deviation principle on the space of càdlàg functions. We illustrate how these results can be applied to functionals of the partial sum process, including ruin probabilities for multivariate random walks and long strange segments. These results make precise the idea of heavy-tailed large deviation heuristics: in an asymptotic sense, only the largest step contributes to the extremal behavior of a multivariate random walk.

This paper introduces a method for the automatic conversion of the 3D mesh models into a set of the 2D patterns for producing physical copy-models. We consider the models that can be segmented into the near-developable parts. Each part is regenerated into the 2D patterns by decomposing it into a set of triangle strips and mapping them onto the 2D print plane. Mapping strips are done in two steps: 1) mapping onto the fixed plane in 3D; 2) mapping the flattened strips onto a print plane. The resulting strips are assembling in the flattened patches, or patterns, located in a common plane. A paper copy-model is produced by cutting and gluing the printed patterns. The paper presents a set of the developed algorithms which allow us to achieve the desired goal. To demonstrate the practicality of the proposed method we show the 2D patterns of several mesh models and their copy-models. Our research is connecting to producing the paper prototypes based on unfolding the given 3D computer models. The art of origami is the type of paper modeling. For this reason, we call our system "Origami 3D printer".

The increase of the capacity of processing units and the growth of distributed computing make easy to collect and process information of Internet traffic flows. This information, however, can be used to perform attacks in anonymous communications that could compromise privacy. With the aim of preventing these attacks, we propose a scheme that implements a multimodal behavior using the random walk theory and crypto-types. The random walk mechanism is responsible for generating network patterns, and the cryptotype performs the micro-encryption tasks using series of quantum-resistant cryptography methods through the anonymous channel. The result shows that using this technique, we can prevent network analysis attacks by means of the generation of a different pattern in each execution for the same set of data. Namely, the experiments we have developed indicate that the average rate of true detections of application behaviors made by intruders does not exceed 24%. Thus, this multimodal pattern gives a high level of immunity against data analysis attacks because the intruders could consider the generated patterns as the typical patterns.

The random walk to be considered takes place in the δ-spherical dual of the group U(n + 1), for a fixed finite dimensional irreducible representation δ of U(n). The transition matrix comes from the three-term recursion relation satisfied by a sequence of matrix valued orthogonal polynomials built up from the irreducible spherical functions of type δ of SU(n + 1). One of the stochastic models is an urn model and the other is a Young diagram model.

A new area is coming with intelligent materials able to provide diverse functionalities to users all along the product lifecycle, during the design, manufacturing, use and dismantling phases. These materials can track their own evolution all along the product lifetime, gather helpful information and thus allow information continuum at all time and everywhere. Usually, these functionalities are fulfilled via the integration of specific electronic components into the material (wireless sensors nodes, RFID tags). The present paper forms part of this framework in considering that thousands of microsensor nodes are integrated into a concrete precast. All nodes store different information of precast properties in their memory requiring designing a specific Wireless Sensor Network (WSN) protocol to extract this information. The proposed protocol employs three mechanisms. First, the random walk is used as multi-hop process to forward the request to further nodes. Then, the pull gossip mechanism is added to interrogate the neighbor nodes in each hop. Finally, a mechanism called farthest neighbors selection is added. Only the farthest and most powerful neighbor is selected as next hop for improving the reliability of the original random walk process.

In a coalescing random walk, a set of particles make independent random walks on a graph. Whenever one or more particles meet at a vertex, they unite to form a single particle, which then continues the random walk through the graph. Coalescing random walks can be used to achieve consensus in distributed networks, and is the basis of the self-stabilizing mutual exclusion algorithm of Israeli and Jalfon [11]. Let G = (V, E), be an undirected, connected n vertex graph. Let C(n) be the expected time for all particles to coalesce, when initially one particle is located at each vertex of an n vertex graph. We study the problem of bounding the coalescence time C(n) for general classes of graphs. For d-regular graphs with expansion parameterized by the eigenvalue gap 1 − λ2, where λ2 is the second eigenvalue of the transition matrix of the random walk, we establish that C(n) = O(n/(1 − λ2)). This result also extends of near regular graphs; where a graph is near regular if the ratio of the maximum and minimum degrees ∆/δ is constant. Our general result is, that C(n) = O(n/(ν(1 − λ2))), where ν = (d 2 (v))/(d 2 n), and d is the average node degree. The parameter ν is an indicator of the variability of node degrees: 1 ≤ ν = O(n), with ν = 1 for regular graphs. The result holds provided the maximum node degree is O(m 1−ǫ). A system of coalescing particles where initially one particle is located at each vertex, corresponds to a voter model. Initially each vertex has a distinct opinion, and at each step each vertex changes its opinion to that of a random neighbour. The voting process can be used for leader election in a distributed context. Let E(Cv) be the expected time for voting to complete, i.e. for a unique opinion to emerge. It is known that E(Cv) = C(n), so our results imply that E(Cv) = O(n/(ν(1 − λ2))). We also investigate how the voting time improves when a vertex elicits more than one opinion at each step. In a model which we call min-voting, each vertex initially holds an opinion from {1, 2, ..., n}. At each step each vertex takes the opinions of two random neighbours and keeps the smaller. We show that for regular graphs with very good expansion properties, voting is completed in O(log n) time with high probability. This result can be viewed as an example for the "power of two choices" in distributed voting.

In a coalescing random walk, a set of particles make independent discrete-time random walks on a graph. Whenever one or more particles meet at a vertex, they unite to form a single particle, which then continues a random walk through the graph. Let G = (V, E), be an undirected and connected graph, with n vertices and m edges. The coalescence time, C(n), is the expected time for all particles to coalesce, when initially one particle is located at each vertex. We study the problem of bounding the coalescence time for general connected graphs, and prove that

I would like to thank my committee members, colleagues, and family for their help, support, and guidance in this work. First of all I want to express my special appreciation and thanks to my advisor Professor Cox for the continuous support of my study and for his patience, motivation, enthusiasm, and immense knowledge, and to Professor Zachos for his guidance and encouragement. I acknowledge and thank the other members of my Thesis Advisory and Defense Committee: Professor Nelly Fazio and Professor Noson Yanofsky for their support and encouragement during the course of my work. I want to thank all of my family. I could not have completed this work without their constant support and encouragement. Finally, I give special thanks and love to my daughter Cindy.

Reingold has shown that L = SL, that s-t connectivity in a poly-mixing digraph is complete for promise-RL, and that s-t connectivity for a poly-mixing out-regular digraph with known stationary distribution is in L. Several properties that bound the mixing times of random walks on digraphs have been identified, including the digraph conductance and the digraph spectral expansion. However, rapidly mixing digraphs can still have exponential cover time, thus it is important to specifically identify structural properties of digraphs that effect cover times. We examine the complexity of random walks on a basic parameterized family of unbalanced digraphs called Strong Chains (which model weakly symmetric logspace computations), and a special family of Strong Chains called Harps. We show that the worst case hitting times of Strong Chain families vary smoothly with the number of asymmetric vertices and identify the necessary condition for non-polynomial cover time. This analysis also yields ...

The advent of omics technologies have enabled the generation of huge, complex, heterogeneous, and highdimensional omics data. Imposing numerous challenges in data integration, these data could lead to a better understanding of the organism's cellular system. Omics data are typically represented as networks to study relations between biological entities, such as protein-protein interaction, gene regulation, and signal transduction. To this end, network embedding approaches allow us to learn latent feature representations for nodes of a graph structure. In this study, we propose a new methodology to learn embeddings by modeling the underlying interactions among biological entities (nodes) with exponential family distributions from a well chosen set of omics modalities. We evaluate our proposed method based on the gene regulatory network (GRN) inference problem. As the ground truth for evaluation, we use GRN available in public databases and demonstrate its effectiveness by comparing to other network integration approaches.

The paths animals take while moving through their environments affect their likelihood of encountering food and other resources; thus, models of foraging behavior abound. To collect movement data appropriate for comparison with these models, we used time-lapse photography to track movements of a small, hardy, and easy-to-obtain organism, Aquilonastra anomala sea stars. We recorded the sea stars in a tank over many hours, with and without a food cue. With food present, they covered less distance, as predicted by theory; this strategy would allow them to remain near food. We then compared the paths of the sea stars to three common models of animal movement: Brownian motion, Lévy walks, and correlated random walks; we found that the sea stars' movements most closely resembled a correlated random walk. Additionally, we compared the search performance of models of Brownian motion, a Lévy walk, and a correlated random walk to that of a model based on the sea stars' movements. We found that the behavior of the modeled sea star walk was similar to that of the modeled correlated random walk and the Brownian motion model, but that the sea star walk was slightly more likely than the other walks to find targets at intermediate distances. While organisms are unlikely to follow an idealized random walk in all details, our data suggest that comparing the effectiveness of an organism's paths to those from theory can give insight into the organism's actual movement strategy. Finally, automated optical tracking of invertebrates proved feasible, and A. anomala was revealed to be a tractable, 2D-movement study system.

Benjamini, Häggström, Peres and Steif introduced the model of dynamical random walk on d [2]. This is a continuum of random walks indexed by a parameter t. They proved that for d = 3, 4 there almost surely exist t such that the random walk at time t visits the origin infinitely often, but for d ≥ 5 there almost surely do not exist such t. Hoffman showed that for d = 2 there almost surely exists t such that the random walk at time t visits the origin only finitely many times [5]. We refine the results of [5] for dynamical random walk on 2 , showing that with probability one the are times when the origin is visited only a finite number of times while other points are visited infinitely often.

We present an algorithm by which nodes arranged in a tree, with each node initially knowing only its parent and children, can construct a fault-tolerant communication structure (an expander graph) among themselves in a distributed and scalable way. The tree overlayed with this logical expander is a useful structure for distributed applications that require the intrinsic "treeness" from the topology but cannot afford any obstruction in communication due to failures. At the core of our construction is a novel distributed mechanism that samples nodes uniformly at random from the tree. In the event of node joins, node departures or node failures, the expander maintains its own fault tolerance and permits the reformation of the tree. We present simulation results to quantify the convergence of our algorithm to a fault tolerant network having both good vertex connectivity and expansion properties.

In this work, deep reinforcement learning methodology takes advantage of transfer learning methodology to achieve a reasonable trade-off between environmental impact and operating costs in the activated sludge process of Wastewater treatment plants (WWTPs). WWTPs include complex nonlinear biological processes, high uncertainty, and climatic disturbances, among others. The dynamics of complex real processes are difficult to accurately approximate by mathematical models due to the complexity of the process itself. Consequently, model-based control can fail in practical application due to the mismatch between the mathematical model and the real process. Control based on the model-free reinforcement deep learning (RL) methodology emerges as an advantageous method to arrive at suboptimal solutions without the need for mathematical models of the real process. However, convergence of the RL method to a reasonable control for complex processes is data-intensive and time-consuming. For this ...

Empresas que fazem distribuição de produtos no atacado normalmente têm grande quantidade de itens comercializados de diversos fabricantes em seu portfólio de produtos. Assim, encontrar e recomendar produtos ao cliente entre milhares de possibilidades se caracteriza num desafio para a equipe de vendas. O objetivo deste artigo é mostrar uma arquitetura de sistema de recomendação para implantação em ferramentas de sistema de automação de força de vendas e suportado por Inteligência Artificial que possa recomendar produtos online a cada interação no processo de venda. Foram usados os seguintes os métodos e materiais: revisão sistemática da literatura, pesquisa exploratória quali-quantitativa, experimentos computacionais, estudo de caso, prova de conceito do sistema e pesquisa com o método Delphi junto a especialistas com aplicação de questionários. A arquitetura foi aplicada construindo-se uma prova de conceito numa empresa de distribuição de autopeças na qual o sistema foi capaz de for...

In this paper we establish the cover time of a random graph G(d) chosen uniformly at random from the set of graphs with vertex set [n] and degree sequence d. We show that under certain restrictions on d, the cover time of G(d) is with high probability asymptotic to d−1 d−2 θ d n log n. Here θ is the average degree and d is the effective minimum degree. The effective minimum degree is the first entry in the sorted degree sequence which occurs order n times.

Recently, Lévy walks have been put forward as a new paradigm for animal search and many cases have been made for its presence in nature. However, it remains debated whether Lévy walks are an inherent behavioural strategy or emerge from the animal reacting to its habitat. Here, we demonstrate signatures of Lévy behaviour in the search movement of mud snails (Hydrobia ulvae) based on a novel, direct assessment of movement properties in an experimental set-up using different food distributions. Our experimental data uncovered clusters of small movement steps alternating with long moves independent of food encounter and landscape complexity. Moreover, size distributions of these clusters followed truncated power laws. These two findings are characteristic signatures of mechanisms underlying inherent Lévy-like movement. Thus, our study provides clear experimental evidence that such multi-scale movement is an inherent behaviour rather than resulting from the animal interacting with its en...