Random Walks

After a review of recent psychogeographical practice and publications, this talk addresses the challenges for contemporary psychogeography from a multiplicitous and invasive global Spectacle that has shifted beyond its former 'integrated' state. The talk proposes that psychogeography make its own shifts in relation to a shorter and more flexible situational-'dérive' (and away from the ideal of the 'permanent 'dérive''), embracing the principle of disturbance and the practice of encoding and re-encoding space. It also discusses the uses of fictional totalities in psychogeography, experiment, and the uses for the 'mess' of the situationist milieu.

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.

This study explores the weak-form efficiency of the Philippine Stock Exchange (PSE) and its different sectoral markets using modern inference techniques with robust statistical properties. The research is motivated by the lack of consensus in the literature on the informational efficiency of the country’s stock market and the apparent scarcity of studies on the same issue using data covering the period of massive modernization of the exchange, geared toward transparent disclosures and integrity of transactions. The study may also be considered a fitting assessment of why the PSE is setting the pace over most stock exchanges in Asia in terms of growth levels across key stock market indicators, culminating in a highly successful year 2012 when it ranked ninth among the ten best-performing stock markets of the world. Evidence presented by the results of the study suggests the presence of overall informational efficiency in the Philippine Stock Exchange during the period under review.

Stochastic components such as random walks have become an intrinsic part of modern metaheursitic algorithms. The efficiency of a metaheuristic algorithm may implicitly depend on the appropriate use of such randomization. In this paper, we provide some basic analysis and observations about random walks, Lévy flights, step sizes and efficiency using Markov theory. We show that the reason why Lévy flights are more efficient than Gaussian random walks, and the good performance of Eagle Strategy. Finally, we use bat algorithm to design a PID controller and have achieved equally good results as the classic Ziegler-Nichols tuning scheme.

"It is demonstrated that the conventional monetary model of exchange rates can (irrespective of the specification, estimation method or the forecasting horizon) outperform the random walk in out-of-sample forecasting if forecasting power is measured by direction accuracy and profitability. Claims of outperforming the random walk in terms of the root mean square error are false because they are typically based on the introduction of dynamics,
hence a random walk component, commonly without testing for the statistical significance of the difference between root mean square errors. And even if proper hypothesis testing reveals that a dynamic model outperforms the random walk, this amounts to beating the random walk by a random walk with the help of some explanatory variables. The failure of conventional macroeconomic models to outperform the random walk in terms of the root mean square error should be expected rather than considered to be a puzzle. "

Connectedness of random walk segmentation is examined, and novel properties are discovered, by considering electrical circuits equivalent to random walks. A theoretical analysis shows that earlier conclusions concerning connectedness of random walk segmentation results are incorrect, and counterexamples are demonstrated.

We quantify the effectiveness of random walks for searching and construction of unstructured peer-to-peer (P2P) networks. We have identified two cases where the use of random walks for searching achieves better results than flooding: a) when the overlay topology is clustered, and b) when a client re-issues the same query while its horizon does not change much. For construction, we argue that an expander can be maintained dynamically with constant operations per addition. The key technical ingredient of our approach is a deep result of stochastic processes indicating that samples taken from consecutive steps of a random walk can achieve statistical properties similar to independent sampling (if the second eigenvalue of the transition matrix is bounded away from 1, which translates to good expansion of the network; such connectivity is desired, and believed to hold, in every reasonable network and network model). This property has been previously used in complexity theory for construction of pseudorandom number generators. We reveal another facet of this theory and translate savings in random bits to savings in processing overhead.

— La région des Trois-Lacs, à l'ouest du plateau suisse, est très bien documentée pour la période comprise entre 3850 et 3350 av. J.-C. environ. Deux cultures archéologiques différentes de part et d'autre du Jura sont avérées. Elles sont mêlées dans le site de Concise fouillé entre 1996 et 2000. Les variations des styles céramiques y semblent liées à des mouvements de populations. Nous avons cherché à modéliser la dynamique de ces mouvements à l'aide d'un graphe et sur la base d'hypothèses ethno-archéologiques. Notre stratégie visait, d'une part, à rendre compte de la diffusion de ces cultures par une marche aléatoire (destinée à restituer la notion de diffusion technologique par le mariage) et, d'autre part, à qualifier chaque site avec des indicateurs topologiques. Au final, nous avons confronté les résultats archéologiques avec ceux du modèle. Cette approche nous permet de proposer des pistes de réflexions quant aux types de relations entretenues entre communautés. Graphes • Marche aléatoire • Modélisation spatiale • Néolithique moyen • Peuplement • Plateau suisse • Styles céramiques • Topologie Abstract.— Spatial modeling of the settlement process of the Swiss Plateau during the Middle Neolithic.— The region of Three Lakes, to the west of the Swiss Plateau, is highly documented for the period between roughly 3850 and 3350 before J.-C. It appears that two different archeological cultures existed on either side of the Jura. Both figured at the Concise site, excavated between 1996 and 2000. Variations in pottery styles seem to be linked to population movements. We sought to model the dynamics of these movements with a graph and on the basis of ethno-archaeological hypotheses. Our strategy was to first account for the spread of these cultures through the random walk of individuals (in an attempt to restore the concept of technology diffusion through marriage) and, secondly, to characterize each site with topological indicators. Finally, we compared the archaeological results with those of the model. This approach allows us to suggest ways of approaching the types of relations maintained between communities. Ceramic Styles • Graphs • Middle Neolithic • Random Walk • Settlement • Spatial Modeling • Swiss Plateau • Topology Resumen.— Modelización espacial de la dinámica de poblamiento de la meseta suiza en el Neolítico medio.— La región de los Tres-Lagos, al oeste de la meseta suiza, esta muy documentada para el periodo aproximadamente entre 3850 y 3350 a.J.-C. Dos culturas arqueológicas distintas existen de lado y otro del Jura, pero se han mezclado en el sitio Concise, excavado entre 1996 y 2000. Las variaciones de los estilos cerámicos parecen ligadas a movimientos poblacionales. Hemos tratado una modelización de estos movimientos con la ayuda de un grafo y con la base de hipótesis etno-arqueológicas. Nuestra estrategia trataba de abarcar, de un lado, la difusión de estas culturas usando de un itinerario aleatorio (con el fin de restituir la noción de difusión tecnológica a través del matrimonio) y, de otro lado, calificando cada sitio con indicadores topológicos. Al final, se han confrontado los resultados arqueológicos con los del modelo. Este acercamiento permite proponer direcciones de reflexiones sobre los tipos de relaciones llevadas entre comunidades. Estilos cerámicos • Grafos • Itinerario aleatorio • Meseta suiza • Modelización espacial • Neolítico medio • Poblamiento • Topología

This paper describes a framework to support the electricity distribution system operator (DSO) in identifying the appropriate control strategy in a system due to the stochastic nature of the integrated intermittent distributed generation. A distributed optimization and control algorithm is applied in order to determine the look-ahead allocation of distributed resources for risk mitigation, as well as real-time controls to attempt to ensure that the electrical distribution system (DS) is managed in a reliable and cost-effective manner. The management of these active resources will thus ensure that the DS can be optimized to operate in an efficient manner while providing adequate security

To offer a view into the rapidly developing theory of fractional diffusion processes we describe in some detail three topics of present interest: (i) the well-scaled passage to the limit from continuous time random walk under power law assumptions to space-time fractional diffusion, (ii) the asymptotic universality of the Mittag-Leffler waiting time law in time-fractional processes, (iii) our method of parametric subordination for generating particle trajectories.

"The Martingale properties of the floating exchange rates of the
ASEAN+3 region are analyzed in this study using contemporary
(2000 to 2012) weekly data of inter-bank call rates. The main goal of the analysis is to see if informational efficiency is a feature floating (managed or independently floating) currencies in this coalition of countries still possess despite the current credit crisis and other economic shocks during the period. Employing relevant state-of-the art econometric techniques, the study set to empirically determine the presence of two important ingredients of informationally efficient market – the existence of the unit root component and the presence of uncorrelated increments within each exchange rate series. To address the unit root problem, a battery of tests catering to heterogeneous panel data is used while variance ratio tests robust to the occurrence of conditional volatilities are implemented. "

We describe a system for robustly estimating synthetic depth maps in unconstrained images and videos, for semi-automatic conversion into stereoscopic 3D. Currently, this process is automatic or done manually by rotoscopers. Automatic is the least labor intensive, but makes user intervention or error correction difficult. Manual is the most accurate, but time consuming and costly. Noting the merits of both, a semi-automatic method blends them together, allowing for faster and accurate conversion.

A fuzzy overlapping community is an important kind of overlapping community in which each node belongs to each community to different extents. It exists in many real networks but how to identify a fuzzy overlapping community is still a challenging task. In this work, the concept of local random walk and a new distance metric are introduced. Based on the new distance measurement, the dissimilarity index between each node of a network is calculated firstly. Then in order to keep the original node distance as much as possible, the network structure is mapped into low-dimensional space by the multidimensional scaling (MDS). Finally, the fuzzy c-means clustering is employed to find fuzzy communities in a network. The experimental results show that the proposed algorithm is effective and efficient to identify the fuzzy overlapping communities in both artificial networks and real- world networks.

Einkaufen-Gehen ist etwas, was allein in der Stadt wirklich geht. lm Dorf kann man nur Besorgungen machen, und in der Kleinstadt kann man darüber hinaus höchstens zum Einkaufen fahren. lch gehe Einkaufen meint im urbanen Kontext etwas anderes als Ich mache Besorgungen. Gehen und Kaufen sind beim Einkaufen-Gehen in dieselbe flache, in sich selbst ein wenig verschobene Gegenwart verfügt, und diese Gegenwart lässt kaum Ansatzpunkte für eine Zäsurierung des Gehens erkennbar werden, an denen man eine Kauf-Handlung von der Geh-Bewegung abtrennen könnte.

En el contexto académico que nos proporciona el Máster de Gestión y Producción artística de la Universidad de Murcia –y en particular la asignatura Estéticas Migratorias en el Arte Contemporáneo impartida por la Dra. Aurora Alcaide Ramírez- en el curso 2012/2013 tuvo lugar una conferencia homónima a este artículo. A lo largo de dicha charla se intentaron vincular dos tipos distintos de desplazamientos, el físico y el virtual, con el fin de estudiar cómo el arte ha abordado los recorridos virtuales como estrategia procesual o tema de reflexión en su praxis. Con tales objetivos, se comenzó el hilo discursivo de la conferencia con una breve introducción acerca de los orígenes del hipertexto y la Red. Una vez establecido el contexto mediático, se expusieron, en un trabajo de asociación de conceptos, las características fundamentales tanto de los paseos físicos como de los desplazamientos online, haciendo un especial hincapié en la función que desarrolla el cuerpo en ambas prácticas. Finalmente, tras una imprescindible vinculación de estas nociones con la producción artística, nos centramos en cómo la práctica del Net.art ha estado explotando las posibilidades de la arquitectura hipertextual tanto antes como después de la aparición de la Web 2.0, ejemplificando, todo ello, a través de obras paradigmáticas.

This report presents a very simple algorithm for overlaping
community-detection in large graphs under constraints such
as the minimum and maximum number of members allowed.
The algorithm is based on the simulation of random walks
and measures the entropy of each random walk to detect the
discovery of a community.

Competitive learning is an important machine learning approach which is widely employed in artificial neural networks. In this paper, we present a rigorous definition of a new type of competitive learning scheme realized on large-scale networks. The model consists of several particles walking within the network and competing with each other to occupy as many nodes as possible, while attempting to reject intruder particles. The particle's walking rule is composed of a stochastic combination of random and preferential movements. The model has been applied to solve community detection and data clustering problems. Computer simulations reveal that the proposed technique presents high precision of community and cluster detections, as well as low computational complexity. Moreover, we have developed an efficient method for estimating the most likely number of clusters by using an evaluator index that monitors the information generated by the competition process itself. We hope this paper will provide an alternative way to the study of competitive learning..

We examine the proposition that the random walk without drift is more powerful in predicting exchange rates than the random walk with drift. It is demonstrated that there is no theoretical reason why the random walk without drift always outperforms the random walk with drift and that this is an empirical issue. The results show that while the random walk without drift can outperform the random walk with drift in terms of the RMSE, it fails to do so in terms of the ability to predict the direction of change, measures that take into account magnitude and direction, and in terms of profitability. If the drift factor is allowed to change over time by estimating the model in time-varying parameter terms, the random walk with drift performs even better.

As increasingly large volumes of sophisticated options are traded in world financial markets, determining a "fair" price for these options has become an important and difficult computational problem. Many valuation codes use the binomial pricing model, in which the stock price is driven by a random walk. In this model, the value of an n-period option on a stock is the expected time-discounted value of the future cash flow on an n-period stock price path. Path-dependent options are particularly difficult to value since the future cash flow depends on the entire stock price path rather than on just the final stock price. Currently such options are approximately priced by Monte Carlo methods with error bounds that hold only with high probability and which are reduced by increasing the number of simulation runs.

Öz Küreselleşme ile birlikte finansal etkinlik teorisi de önemi artan bir konu haline gelmiştir. Bu durumun en önemli nedenlerinden biri hisse senedinden elde edilen getirilerin piyasadaki mevcut tüm bilgiyi tamamen yansıttığına inanılmasıdır. Zayıf etkinlik varsayımları altındaki piyasada geçmiş fiyat performansının tümü var olan fiyatlara yansımış olup geçmiş fiyat performansı kullanılarak normalden fazla getiri elde edilemez. Çalışmada Borsa İstanbul için zayıf formda piyasa etkinliği banka indeksi ve seçilmiş banka hisseleri ile test edilmiştir. Ampriki analiz boyunca rassal yürüyüş hipotezi göz önünde bulundurulmuştur. Çıkan sonuçlara göre seçilen seriler seviyede birim köke sahip olup rassal yürüyüş modelinin varlığı kanıtlanmıştır. Anahtar Kelimeler: Borsa Istanbul, Rassal Yürüyüş, Bankacılık Sektörü. Abstract Bye the globalization, the theory of financial efficiency has become an important issue among market actors. The most important reason of this situation is to be believed that Markets which returns of share are reflected all information. Under the weak-form efficiency assumptions all past price were reflected with current price and it isn't acquiring upon the normal return to use with past price activity in markets. In this paper, weak form efficiency was tested for Borsa Istanbul by using Bankıng Index and selected bankıng shares. During the empirical analysis, random walk hypothesis was considered. According to findings, selected time series have a unit root at level which means existence of random walk theory was proven. Giriş Ekonomi ile finansal piyasalar etkileşimi, bir çok araştırmacı ve akademisyenin üzerinde önemli durduğu bir konudur. Özellikle küreselleşmenin de etkisiyle gelişen menkul kıymetler borsaları, hisse senetlerinin gelecekte ulaşacakları fiyatların tahmin edilip edilemeyeceği sorusunu da beraberinde getirmiştir. Özellikle gelişmekte olan ülkelere akan sermaye hareketlerindeki keskin artışlar, bu ülke piyasalarının etkinliği konusundaki tartışmaları da beraberinde getirmiştir. Borsa İstanbul istatistiklerine göre yabancı payının % 64 oranında olması, gelişen ülkele borsalarına kanalize olan yabancı sermayenin önemli bir göstergesidir. Ekonomi literatüründe Samuelson (1965) 'a kadar sermaye piyasalarında mevcut fiyat hareketleri ile ilgili herhangi bir teori geliştirilmemiştir. Fama'nın 1970 yılında ortaya attığı etkin piyasa hipotezi, bilinen tüm bilgiler ile ilave gelir elde edemeyeceğimizi iddia etmektedir. Bu durumun geçerli olduğu hisse senedi piyasalarına sermayenin yönelmesi, gelişmekte olan ülkelerde etkin piyasalar hipotezini sorgulatır hale getirmiştir. Özellikle de finansal piyasaların önemli aktörlerinden olan yatırımcıların bilgisel etkinliğe önem vermeleri, bilginin ve riskin taraflar arasında farklı seviyede olduğuna inanmaları etkin piyasa hipotezinin önemini daha da arttırmıştır. Çalışmada öncelikli olarak konuyla ilgili yapılan yerli ve yabancı literatür araştırmasına yer verilecektir. Daha sonra zayıf formda piyasa etkinliği, Borsa İstanbul XBN10 endeksi ve seçilmiş 8 farklı banka hisse senedi kullanılarak rassal (tesadüfi) yürüyüş hiptezi çerçevesinde test edilecektir.

A Digital image is a two dimensional numeric representation. They are composed of picture elements called pixels, and of it represent the intensity information at a single point in the image. Thus digital images with such a massive data are mostly prone to attacks and forgeries. The term tampering or image forgery relates to the image modification by adding or removing certain regions in the image. This easy-to-tamper target i.e. the digital images are modified for various intentions, mostly for illegal activities. Analysis and investigation of this process is the Digital Image Forensics (DIF). Detecting and localizing such tampering in digital images are posing a great challenge and to face it, an effective method is proposed. With the widespread usage of digital images in storage and transfer of visual information, vulnerabilities against them are also increasing. MERW, Maximal Entropy Random Walk, method is taken for conforming to the aforementioned analysis. The input images are initially over segmented using the SLIC algorithm, Simple Linear Iterative Clustering. Features are extracted from each blocks based on Scale Invariant feature extraction algorithm (SIFT). From the extracted features the forgery is detected based on MERW method, applied in co-alliance with the block matching and labeled feature point matching. The performance of the process is measured with the help of values of Precision, Recall and F-Measure related to the input image.

A dynamic one-dimensional model of Marine Protected Areas (MPAs) along a coastline has been developed to investigate their impact on fish stocks and landings over time. The model is basically a cellular automaton implemented with a spreadsheet and is used to trace stocks and landings from the initiation of the MPA for several years under a set of three different scenarios for the allocation of fishing effort. In all cases landings decline as soon as part of the coastline is protected, but in every case they recover to their original level and above. The time it takes for landings to recover ranges from four to nine years and with two small MPAs (several small) the recovery is faster than with one large one of the same spatial extent (single large). These results indicate that although fishery closures through an MPA will undoubtedly have an immediate adverse impact on the fishing industry, the chances of full recovery after several years are good, and both the fishery and the fish stocks will benefit in the long run. Further, our model provides a null model on the impacts over time of MPAs that may iteratively be compared with real cases that have biological and social variables.

We present a continuous time generalization of a random walk with complete memory of its history [Phys. Rev. E 70, 045101(R) (2004)] and derive exact expressions for the first four moments of the distribution of displacement when the number of steps is Poisson distributed. We analyze the asymptotic behavior of the normalized third and fourth cumulants and identify new transitions in a parameter regime where the random walk exhibits superdiffusion. These transitions, which are also present in the discrete time case, arise from the memory of the process and are not reproduced by Fokker-Planck approximations to the evolution equation of this random walk.

We model the time series of the S&P500 index by a combined process, the AR+GARCH process, where AR denotes the autoregressive process which we use to account for the short-range correlations in the index changes and GARCH denotes the generalized autoregressive conditional heteroskedastic process which takes into account the long-range correlations in the variance. We study the AR+GARCH process with an initial distribution of truncated LÃ evy form. We ÿnd that this process generates a new probability distribution with a crossover from a LÃ evy stable power law to a power law with an exponent outside the LÃ evy range, beyond the truncation cuto . We analyze the sum of n variables of the AR+GARCH process, and ÿnd that due to the correlations the AR+GARCH process generates a probability distribution which exhibits stable behavior in the tails for a broad range of values n-a feature which is observed in the probability distribution of the S&P500 index. We ÿnd that this power-law stability depends on the characteristic scale in the correlations. We also ÿnd that inclusion of short-range correlations through the AR process is needed to obtain convergence to a limiting Gaussian distribution for large n as observed in the data.

The structure of animal movement paths at varying spatial scales allows insight into the importance of habitat distribution and their response to scale in heterogeneous landscapes. Home-ranging animals typically exhibit constrained random movements at large spatial scales, with small-scale orientation reflecting responses to sensory stimuli. The southern stingray Dasyatis americana is an abundant demersal elasmobranch found in coastal systems throughout the Caribbean, yet very little is known of its movement ecology. Twelve southern stingrays were manually tracked at Glovers Reef (Belize) for up to 32 non-continuous hours to evaluate movement structure and activity space. Response to spatial scale was analysed using fractal analysis, and domains of scale were compared to habitat spatial characteristics. Mean stingray activity space was relatively small (< 0.5 km 2 ) with daytime activity space significantly larger than nighttime activity space. Movement paths showed significant straightening correlated with increasing size in females. Stingray movement structure exhibited 2 distinct domains: at scales of <100 m, paths were more dispersed than a correlated random walk (CRW), and at scales >100 m, paths were more constrained than CRW, indicating directed movement at scales up to 100 m. Nearest neighbour spatial analysis of lagoon patch reefs showed mean spacing of 100 m (± 4.5), equivalent to orientation distance seen in rays. Random walk movements at large scales are consistent with a home-ranging animal; however, larger scale orientation than expected and patch reef spacing equalling 100 m suggests that patch reefs represent important spatial and ecological networks, strongly influencing stingray movement, habitat use, and dispersal.

As the economic malaise lingers on and mainstream active managers increasingly fail to deliver on “over-performance” expectations, institutional asset owners are switching to passive in droves. World Pension Council (WPC) experts estimate that the relative share of passive investments could double in the next five years, reaching up to 40% of pension and insurance assets by 2020.
Pension funds are collectively losing out on billions of dollars every year because of artificially low interest rates while the governments lower the debt servicing bills, resulting in a transfer of wealth from the future income of pensioners to enrich the Treasury department and a handful of financiers. . .

We present a new approach to the calculation of first passage statistics for correlated random walks on one-dimensional discrete systems. The processes may be non-Markovian and also nonstationary. A number of examples are used to demonstrate the theory.

Conventional saliency detection approaches are human fixation detection and single dominant region detection. However, real-world photographs usually consist of multiple dominant regions. We propose a saliency detection method with the aim to highlight the whole object and distinguish objects with different saliency levels. It combines the bottom-up approach and top-down approach via two nested levels of hierarchical segmentations -the coarse level objects and fine level details. We first calculate a preliminary saliency on the fine patches with a random walk model. Then two mid-level cues and one object-level cue are fused to refine the preliminary saliency to emphasize the objects against the background. At last, the object-level saliency map is synthesized via a heat diffusion process restricted by the coarse level patches to enhance object saliency and distinguish saliency between different objects. Extensive evaluation on a publicly available database verifies that our method outperforms the state-ofthe-art algorithms.

Nodes in the real world networks organize in the form of network communities. A community (also referred
to as module or cluster)is defined as where the links are denser inside the nodes and sparser outside the
nodes in the network. Communities in the networks also overlap because the nodes may belong to different
clusters at once. The task of detecting communities in networks becomes an open problem because of lack
of reliable algorithms. In practice all the existing community detection methods work good for nonoverlapping
communities and fail to detect communities with dense overlaps. We developed a novel method
for detecting communities by considering a single seed node. This method successfully captures the
overlapping networks ranging from social to information and from biological to citation networks. We
believe that the proposed system works well for the overlapping communities.

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.

We quantify the effectiveness of random walks for searching and construction of unstructured peer-to-peer (P2P) networks. We have identified two cases where the use of random walks for searching achieves better results than flooding: (a) when the overlay topology is clustered, and (b) when a client re-issues the same query while its horizon does not change much. Related to the simulation of random walks is also the distributed computation of aggregates, such as averaging. For construction, we argue that an expander can be maintained dynamically with constant operations per addition. The key technical ingredient of our approach is a deep result of stochastic processes indicating that samples taken from consecutive steps of a random walk on an expander graph can achieve statistical properties similar to independent sampling. This property has been previously used in complexity theory for construction of pseudorandom number generators. We reveal another facet of this theory and translate savings in random bits to savings in processing overhead.

New developments in global positioning systems (GPS) and related satellite tracking technologies have facilitated the collection of highly accurate data on moving objects, far surpassing the ability to analyze them. Within geographic information science, 'movement pattern analysis' (MPA) has developed as a subfield that addresses concepts and theories used to explore the spatio-temporal structure in data, although the methodological and analytical framework associated with MPA is new and still evolving. Interactions between individuals can be considered a second order property of movement and have been far less studied. The nature of interactions between individuals in a population is a fundamental aspect of a species' behavioral ecology and information on the frequency and duration of these interactions is vital to understanding mating and territorial behavior, resource use, and infectious disease epidemiology. The focus of this work was to explore how spatially explicit simulated data can be used to analyse dynamic interactions between individuals. Five different techniques that have been used to quantify dynamic interactions based on GPS data of pairs of individuals were utilised, and all were compared in the context of spatially explicit simulated data intended to represent biologically realistic null models for individual movement, and subsequently paired interactions.

Semantic networks have been used extensively in psychology to describe how humans organize facts and knowledge in memory. Numerous methods have been proposed to construct semantic networks using data from memory retrieval tasks, such as the semantic fluency task (listing items in a category). However these methods typically generate group-level networks, and sometimes require a very large amount of participant data. We present a novel computational method for estimating an individual’s semantic network using semantic fluency data that requires very little data. We establish its efficacy by examining the semantic relatedness of associations estimated by the model.

Nodes in the real world networks organize in the form of network communities. A community (also referred  to  as  module  or  cluster)is  defined  as  where  the  links  are  denser  inside  the  nodes  and  sparser  outside the  nodes in the network. Communities in the networks also overlap because the nodes may belong to different  clusters at once. The task of detecting communities  in networks becomes an open problem because of lack  of  reliable  algorithms.  In  practice  all  the  existing  community  detection  methods  work  good  for  non-overlapping communities and fail to detect communities with dense overlaps. We developed a novel method  for  detecting  communities  by  considering  a  single  seed  node.  This  method  successfully  captures  the overlapping  networks  ranging  from  social  to  information  and  from  biological  to  citation  networks.  We  believe that the proposed system works well for the overlapping communities.

We quantify the effectiveness of random walks for searching and construction of unstructured peer-to-peer (P2P) networks. We have identified two cases where the use of random walks for searching achieves better results than flooding: (a) when the overlay topology is clustered, and (b) when a client re-issues the same query while its horizon does not change much. Related to the simulation of random walks is also the distributed computation of aggregates, such as averaging. For construction, we argue that an expander can be maintained dynamically with constant operations per addition. The key technical ingredient of our approach is a deep result of stochastic processes indicating that samples taken from consecutive steps of a random walk on an expander graph can achieve statistical properties similar to independent sampling. This property has been previously used in complexity theory for construction of pseudorandom number generators. We reveal another facet of this theory and translate savings in random bits to savings in processing overhead.

In this article, we propose a distributed scheme to compute distance-based clusters. We first present a mechanism based on the  flow of distributed tokens called walkers, circulating randomly between a source and a sink to compute a shortest path. This mechanism is a discrete emulation of the slime mould (Physarum polycephalum) dynamics presented in [16]: each node observes the flow of walkers going through each adjacent edge and uses this flow to compute the probabilities with which it sends the walkers through each edge. Then, based on this mechanism, we show how several sources compute a shortest path DAG to a given sink. Finally, given some clusterheads acting like sinks, we prove that this process converges to  distance-based clusters (i.e. nodes join the clusterhead to which they are closest) with shortest-path DAGs. The algorithm is designed with a special focus on dynamic networks: the
ow locally adapts to the appearance and disappearance of links and nodes, including clusterheads.

The factors influencing the movement and recruitment of settlement stage larvae are investigated using random walk models. Individual-based sensing and orientating abilities are included explicitly in the model. We consider 2 simple reef environment models consisting of a simple circular reef with and without a constant cross-current. The sensing ability of the larvae is modelled as either fixed or spatially dependent, together with a fixed orientating ability. The survival probability is found to be highly sensitive to both the sensing and orientating abilities of the larvae, as well as to the properties of the reef environment itself.

The traditional way of studying temporal networks is to aggregate the dynamics of the edges to create a static weighted network. This implicitly assumes that the edges are governed by Poisson processes, which is not typically the case in empirical temporal networks. Consequently, we examine the effects of non-Poisson inter-event statistics on the dynamics of edges, and we apply the concept of a generalized master equation to the study of continuous-time random walks on networks. We show that the equation reduces to the standard rate equations when the underlying process is Poisson and that the stationary solution is determined by an effective transition matrix whose leading eigenvector is easy to calculate. We discuss the implications of our work for dynamical processes on temporal networks and for the construction of network diagnostics that take into account their nontrivial stochastic nature.