Downloads & Free Reading Options - Results

An adaptive network model using SIS epidemic propagation with link-type dependent link activation and deletion is considered. Bifurcation analysis of the pairwise ODE approximation and the network-based stochastic simulation is carried out, showing that three typical behaviours may occur; namely, oscillations can be observed besides disease-free or endemic steady states. The oscillatory behaviour in the stochastic simulations is studied using Fourier analysis, as well as through analysing the exact master equations of the stochastic model. A compact pairwise approximation for the dynamic network case is also developed and, for the case of link-type independent rewiring, the outcome of epidemics and changes in network structure are concurrently presented in a single bifurcation diagram. By going beyond simply comparing simulation results to mean-field models, our approach yields deeper insights into the observed phenomena and help better understand and map out the limitations of mean-field models.

Applied Stochastic Models and Data Analysis 1989: Volume 5 , Issue CONTENTS. Digitized from IA1534624-02 . Previous issue: sim_applied-stochastic-models-in-business-and-industry_1988-12_4_4 . Next issue: sim_applied-stochastic-models-in-business-and-industry_1989-03_5_1 .

Applied Stochastic Models and Data Analysis 1989: Volume 5 , Issue CONTENTS. Digitized from IA1534624-02 . Previous issue: sim_applied-stochastic-models-in-business-and-industry_1988-12_4_4 . Next issue: sim_applied-stochastic-models-in-business-and-industry_1989-03_5_1 .

Applied Stochastic Models and Data Analysis 1989: Volume 5 , Issue CONTENTS. Digitized from IA1534624-02 . Previous issue: sim_applied-stochastic-models-in-business-and-industry_1988-12_4_4 . Next issue: sim_applied-stochastic-models-in-business-and-industry_1989-03_5_1 .

We investigate the dynamics of large-scale interacting neural populations, composed of conductance based, spiking model neurons with modifiable synaptic connection strengths, which are possibly also subjected to external noisy currents. The network dynamics is controlled by a set of neural population probability distributions ($\mathrm{PPD}$)which are constructed along the same lines as in the Klimontovich approach to the kinetic theory of plasmas. An exact non-closed, nonlinear, system of integro-partial differential equations is derived for the $\mathrm{PPD}$s. As is customary, a closing procedure leads to a mean field limit. The equations we have obtained are of the same type as those which have been recently derived using rigorous techniques of probability theory. The numerical solutions of these so called McKean-Vlasov-Fokker-Planck equations, which are only valid in the limit of infinite size networks, actually shows that the statistical measures as obtained from $\mathrm{PPD}$s are in good agreement with those obtained through direct integration of the stochastic dynamical system for large but finite size networks. Although numerical solutions have been obtained in the case of Fitzhugh-Nagumo model neurons, the theory can be readily applied to systems of Hodgkin-Huxley type model neurons of arbitrary dimension.

Reynolds Averaged Navier Stokes (RANS) models represent the workhorse for studying turbulent flows in industrial applications. Such single-point turbulence models have limitations in accounting for the influence of the non-local physics and flow history on the evolution of the turbulent flow. In this context, we investigate the sensitivity inherent to single-point models due to their characterization of the internal structure of homogeneous turbulent flows solely by the means of the Reynolds stresses. For a variety of mean flows, we study the prediction intervals engendered due to this coarse-grained description. The nature of this variability and its dependence on parameters such as the mean flow topology, the initial Reynolds stress tensor and the normalized strain rate is identified, analyzed and explicated. The ramifications of this variability on the formulation of classical RANS closure models are highlighted.

This paper deals with the analysis of closed boundaries of arbitrary shape in a plane. Specifically, it is concerned with the problems of representation and reconstruction. We first set up a one to one correspondence between the given closed boundary and a univariate or multivariate sequence of real numbers. Univariate or multivariate circular autoregressive models are suggested for the representation of the sequence of numbers derived from the closed boundary. The stochastic model representing the closed boundary is invariant to transformations of the boundary such as scaling, rotation and choice of the starting point. Methods for estimating the unknown parameters of the model are given and a decision rule for choosing the appropriate order of the model is included. Constraints on the estimates are derived so that the estimates are invariant to transformations of the boundaries. The specific stochastic model used enables us to reconstruct a closed boundary with less computational effort using FFT algorithms. Results of simulations are included and applications to contour coding are discussed. In a subsequent paper we will consider the classification problem. (Author)

A new approach to the study of stochastic Lanchester processes based on diffusion approximations is presented. The distribution of the two force levels over time is shown to be well approximated by a nonstationary bivariate Gaussian diffusion process with specified mean and covariance structure. The approximation is based on an asymptotic analysis which assumes the initial force levels are large. Numerical studies are presented, however, which show surprising accuracy for force levels as small as 30. A wide variety of attrition structures are discussed including the linear and square law cases, Helmbold's general attrition structure, Karr's engagement model, and heterogeneous models. The development of tractable mathematical expressions for the time evolution of complicated Lanchester-type attrition processes makes possible the introduction and analysis of decision theoretic aspects to the problem such as force level decisions, combat tactics, reinforcement decisions, and the value of information about the opponent's strengths, weaknesses, and strategies. (Author)

In this paper we introduce a method for exploiting entities from the emerging Web of Data for enhancing various Information Retrieval (IR) services. The approach is based on named-entity recognition applied in a set of search results, and on a graph of documents and identified entities that is constructed dynamically and analyzed stochastically using a Random Walk method. The result of this analysisis exploited in two different contexts: for automatic query expansion and for re-ranking a set of retrieved results. Evaluation results in the 2015 TREC Clinical Decision Support Track illustrate that query expansion can increase recall by retrieving more relevant hits, while re-ranking can notably improve the ranked list of results by moving relevant but low-ranked hits in higher positions.

This report summarizes the activities in the second phase of a three-year program of research and development directed toward the analysis and evaluation of myoelectric signals (MES) as indicators of operator alertness, and potentially workload in aircraft piloting tasks. The purpose of the study is to investigate the efficiency of stochastic models such as autoregressive (AR), autoregressive-moving-average (ARMA) and autoregressive integrated moving average (ARIMA) models in characterizing the MES under different levels of task imposed burden. The specific objectives of this effort are: (1) to develop/adapt state-of-the-art stochastic models for characterizing myoelectric signal patterns; (2) To investigate under controlled experimental conditions if meaningful repeatable quantitative relationships can be identified between MES patterns and operator loading; (3) To experimentally identify muscle sites that provide reliable MES signatures; (4) To develop methods and procedures for tuning the models and possibly filtering out pattern variations due to variables in electrode locations and individual biases; and (5) To develop guidelines for automatically assessing operator alertness level from the MES temporal signature in piloting tasks. (Author)

This report summarizes the activities in the second phase of a three-year program of research and development directed toward the analysis and evaluation of myoelectric signals (MES) as indicators of operator alertness, and potentially workload in aircraft piloting tasks. The purpose of the study is to investigate the efficiency of stochastic models such as autoregressive (AR), autoregressive-moving-average (ARMA) and autoregressive integrated moving average (ARIMA) models in characterizing the MES under different levels of task imposed burden. The specific objectives of this effort are: (1) to develop/adapt state-of-the-art stochastic models for characterizing myoelectric signal patterns; (2) To investigate under controlled experimental conditions if meaningful repeatable quantitative relationships can be identified between MES patterns and operator loading; (3) To experimentally identify muscle sites that provide reliable MES signatures; (4) To develop methods and procedures for tuning the models and possibly filtering out pattern variations due to variables in electrode locations and individual biases; and (5) To develop guidelines for automatically assessing operator alertness level from the MES temporal signature in piloting tasks. (Author)

Delivery of broadcast messages among vehicles for safety purposes, which is known as one of the key ingredients of Intelligent Transportation Systems (ITS), requires an efficient Medium Access Control (MAC) that provides low average delay and high reliability. To this end, a Geo-Location Based Access (GLOC) for vehicles has been proposed for Vehicle-to-Vehicle (V2V) communications, aiming at maximizing the distance of co-channel transmitters while preserving a low latency when accessing the resources. In this paper we analyze, with the aid of stochastic geometry, the delivery of periodic and non-periodic broadcast messages with GLOC, taking into account path loss and fading as well as the random locations of transmitting vehicles. Analytical results include the average interference, average Binary Rate (BR), capture probability, i.e., the probability of successful message transmission, and Energy Efficiency (EE). Mathematical analysis reveals interesting insights about the system performance, which are validated thought extensive Monte Carlo simulations. In particular, it is shown that the capture probability is an increasing function with exponential dependence with respect to the transmit power and it is demonstrated that an arbitrary high capture probability can be achieved, as long as the number of access resources is high enough. Finally, to facilitate the system-level design of GLOC, the optimum transmit power is derived, which leads to a maximal EE subject to a given constraint in the capture probability.

We analyze a semi-discrete splitting method for conservation laws driven by a semilinear noise term. Making use of fractional $BV$ estimates, we show that the splitting method produces a compact sequence of approximate solutions converging to the exact solution, as the time step $\Delta t \rightarrow 0$. Under the assumption of a homogenous noise function, and thus the availability of $BV$ estimates, we provide an $L^1$ error estimate. Bringing into play a generalization of Kruzkov's entropy condition, permitting the "Kruzkov constants" to be Malliavin differentiable random variables, we establish an $L^1$ convergence rate of order $\frac13$ in $\Delta t$.

We consider the problem of influence maximization in fixed networks, for both stochastic and adversarial contagion models. The common goal is to select a subset of nodes of a specified size to infect so that the number of infected nodes at the conclusion of the epidemic is as large as possible. In the stochastic setting, the epidemic spreads according to a general triggering model, which includes the popular linear threshold and independent cascade models. We establish upper and lower bounds for the influence of an initial subset of nodes in the network, where the influence is defined as the expected number of infected nodes. Although the problem of exact influence computation is NP-hard in general, our bounds may be evaluated efficiently, leading to scalable algorithms for influence maximization with rigorous theoretical guarantees. In the adversarial spreading setting, an adversary is allowed to specify the edges through which contagion may spread, and the player chooses sets of nodes to infect in successive rounds. Both the adversary and player may behave stochastically, but we limit the adversary to strategies that are oblivious of the player's actions. We establish upper and lower bounds on the minimax pseudo-regret in both undirected and directed networks.

This volume was digitized and made accessible online due to deterioration of the original print copy.

This volume was digitized and made accessible online due to deterioration of the original print copy.

This volume was digitized and made accessible online due to deterioration of the original print copy.

Model-based prediction of stochastic noise in biomolecular reactions often resorts to approximation with unknown precision. As a result, unexpected stochastic fluctuation causes a headache for the designers of biomolecular circuits. This paper proposes a convex optimization approach to quantifying the steady state moments of molecular copy counts with theoretical rigor. We show that the stochastic moments lie in a convex semi-algebraic set specified by linear matrix inequalities. Thus, the upper and the lower bounds of some moments can be computed by a semidefinite program. Using a protein dimerization process as an example, we demonstrate that the proposed method can precisely predict the mean and the variance of the copy number of the monomer protein.

This paper focuses on the performance and the robustness analysis of stochastic jump linear systems. The state trajectory under stochastic jump process becomes random variables, which brings forth the probability distributions in the system state. Therefore, we need to adopt a proper metric to measure the system performance with respect to stochastic switching. In this perspective, Wasserstein metric that assesses the distance between probability density functions is applied to provide the performance and the robustness analysis. Both the transient and steady-state performance of the systems with given initial state uncertainties can be measured in this framework. Also, we prove that the convergence of this metric implies the mean square stability. Overall, this study provides a unifying framework for the performance and the robustness analysis of general stochastic jump linear systems, but not necessarily Markovian jump process that is commonly used for stochastic switching. The practical usefulness and efficiency of the proposed method are verified through numerical examples.

Applied Stochastic Models and Data Analysis 1994: Volume 10 , Issue CONTENTS. Digitized from IA1534624-02 . Previous issue: sim_applied-stochastic-models-in-business-and-industry_1993-12_9_4 . Next issue: sim_applied-stochastic-models-in-business-and-industry_1994-03_10_1 .

This paper presents three new computational methods for calculating design sensitivities of statistical moments and reliability of high-dimensional complex systems subject to random input. The first method represents a novel integration of polynomial dimensional decomposition (PDD) of a multivariate stochastic response function and score functions. Applied to the statistical moments, the method provides mean-square convergent analytical expressions of design sensitivities of the first two moments of a stochastic response. The second and third methods, relevant to probability distribution or reliability analysis, exploit two distinct combinations built on PDD: the PDD-SPA method, entailing the saddlepoint approximation (SPA) and score functions; and the PDD-MCS method, utilizing the embedded Monte Carlo simulation (MCS) of the PDD approximation and score functions. For all three methods developed, the statistical moments or failure probabilities and their design sensitivities are both determined concurrently from a single stochastic analysis or simulation. Numerical examples, including a 100-dimensional mathematical problem, indicate that the new methods developed provide not only theoretically convergent or accurate design sensitivities, but also computationally efficient solutions. A practical example involving robust design optimization of a three-hole bracket illustrates the usefulness of the proposed methods.

This paper presents three new computational methods for calculating design sensitivities of statistical moments and reliability of high-dimensional complex systems subject to random input. The first method represents a novel integration of polynomial dimensional decomposition (PDD) of a multivariate stochastic response function and score functions. Applied to the statistical moments, the method provides mean-square convergent analytical expressions of design sensitivities of the first two moments of a stochastic response. The second and third methods, relevant to probability distribution or reliability analysis, exploit two distinct combinations built on PDD: the PDD-SPA method, entailing the saddlepoint approximation (SPA) and score functions; and the PDD-MCS method, utilizing the embedded Monte Carlo simulation (MCS) of the PDD approximation and score functions. For all three methods developed, the statistical moments or failure probabilities and their design sensitivities are both determined concurrently from a single stochastic analysis or simulation. Numerical examples, including a 100-dimensional mathematical problem, indicate that the new methods developed provide not only theoretically convergent or accurate design sensitivities, but also computationally efficient solutions. A practical example involving robust design optimization of a three-hole bracket illustrates the usefulness of the proposed methods.

This is the second in a series of technical reports developing the most modern procedures of time series analysis and forecasting for use in engineering, the physical sicences, and the social sciences. The exposition of methodology is based on a succinct presentation of the theoretical background and is illustrated with appropriate examples from engineering, maintenance and reliability economics, and other physical and social sciences. This report is concerned with linear statistical models, especially autoregressive processes.

This report summarizes the research conducted in the second phase of this three-year research and development program directed toward the analysis and evaluation of myoelectric signals (MES) is indicators of operator alertness and piloting workload. The purpose of the study was to investigate the efficiency of stochastic models such as autoregressive (AR), autoregressive-moving-average (ARMA), and autoregressive integrated moving average (ARIMA) models in characterizing the MES under different levels of task-imposed burden. The implications from this three-year research program are two-fold. Surface myoelectric activity is not a reliable measure of operator alertness. During Phase I, the first autoregressive coefficient of the ARIMA model revealed a significant correlation with task difficulty level. During Phase III, the pi weights did not show the same trend. Intramuscular electrodes, on the other hand, that do pick up more reliable signatures have obvious drawbacks. Post hoc analysis of the experimental data revealed that the total number of experimental subjects which were constrained by program scope and size were inadequate in terms of producing a statistically significant difference in perceived stress between the single and dual-task groups.

Applied Stochastic Models and Data Analysis 1987: Volume 3 , Issue CONTENTS. Digitized from IA1534624-02 . Previous issue: sim_applied-stochastic-models-in-business-and-industry_1987_3_index . Next issue: sim_applied-stochastic-models-in-business-and-industry_1987-03_3_1 .

In many combinatorial domains, simple stochastic algorithms often exhibit superior performance when compared to highly customized approaches. Many of these simple algorithms outperform more sophisticated approaches on difficult benchmark problems; and often lead to better solutions as the algorithms are taken out of the world of benchmarks and into the real-world. Simple stochastic algorithms are often robust, scalable problem solvers. This thesis explores methods for combining sets of heuristics within a single stochastic search. The ability of stochastic search to amplify heuristics is often a key factor in its success. Heuristics are not, however, infallible and in most domains no single heuristic dominates. It is therefore desirable to gain the collective power of a set of heuristics; and to design a search control framework capable of producing a hybrid algorithm from component heuristics with the ability to customize itself to a given problem instance. A primary goal is to explore what can be learned from quality distributions of iterative stochastic search in combinatorial optimization domains; and to exploit models of quality distributions to enhance the performance of stochastic problem solvers. We hypothesize that models of solution quality can lead to effective search control mechanisms, providing a general framework for combining multiple heuristics into an enhanced decision-making process. These goals lead to the development of a search control framework, called QD-BEACON that uses online-generated statistical models of search performance to effectively combine search heuristics. A prerequisite goal is to develop a suitable stochastic sampling algorithm for combinatorial search problems. This goal leads to the development of an algorithm called VBSS that makes better use, in general, of the discriminatory power of a given search heuristic as compared to existing sampling approaches.

This volume was digitized and made accessible online due to deterioration of the original print copy.

We discuss prospects for direct measurement of stochastic gravitational wave background around 0.1-1Hz with future space missions. It is assumed to use correlation analysis technique with the optimal TDI variables for two sets of LISA-type interferometers. The signal to noise for detection of the background and the estimation errors for its basic parameters (amplitude, spectral index) are evaluated for proposed missions.

We discuss prospects for direct measurement of stochastic gravitational wave background around 0.1-1Hz with future space missions. It is assumed to use correlation analysis technique with the optimal TDI variables for two sets of LISA-type interferometers. The signal to noise for detection of the background and the estimation errors for its basic parameters (amplitude, spectral index) are evaluated for proposed missions.

We discuss prospects for direct measurement of stochastic gravitational wave background around 0.1-1Hz with future space missions. It is assumed to use correlation analysis technique with the optimal TDI variables for two sets of LISA-type interferometers. The signal to noise for detection of the background and the estimation errors for its basic parameters (amplitude, spectral index) are evaluated for proposed missions.

This talk will be a survey of some recent developments in average-case analysis of algorithms for combinatorial problems. I will focus on random distributions which seem to yield computationally challenging problems and where to find the 'easiest hard problems' and the 'hardest easy problems'. As a detailed example, I will describe the modular subset sum problem, where you are given n numbers, a modulus M, and a target number T, and the goal is to find a subset of the numbers which sum to T (mod M). Though this is a classic NP-hard problem, many particular instances are not too challenging computationally. When the n numbers are selected uniformly at random from {0, 1, ... , M-1}, the difficulty depends critically on the size of M (as a function of n). I will describe what is known about this complicated relationship, including results from [Flaxman and Przydatek, STACS 2005] which describe an algorithm that succeeds in expected polynomial time when M = n O(log n) . I will also talk about another combinatorial problem, which related to the minimum spanning tree. When the cost of the edges between n nodes are selected independently and uniformly from [0,1], the cost of the minimum spanning tree converges to a constant, and the constant is ζ(3) = 1/1 3 + 1/2 3 + 1/3 3 + ... [Frieze, Discrete Appl. Math.1985]. In the two-stage stochastic programming version of this problem [Flaxman, Frieze, and Krivelevich, SODA 2005/Random Structures Algorithms 2006], you know the costs of each edge on Monday and the distribution of the costs of each edge on Tuesday. The goal is to select a set of edges to buy on Monday so that when the tree is completed on Tuesday, the expected total cost is minimized. When the Monday and Tuesday costs are all selected independently and uniformly from [0,1], a simple threshold heuristic produces a solution with expected cost ζ(3) - 1/2. This is not the optimal two-stage solution, however. ©2006 Microsoft Corporation. All rights reserved.

This article is from PLoS ONE , volume 9 . Abstract We propose a new framework for rigorous robustness analysis of stochastic biochemical systems that is based on probabilistic model checking techniques. We adapt the general definition of robustness introduced by Kitano to the class of stochastic systems modelled as continuous time Markov Chains in order to extensively analyse and compare robustness of biological models with uncertain parameters. The framework utilises novel computational methods that enable to effectively evaluate the robustness of models with respect to quantitative temporal properties and parameters such as reaction rate constants and initial conditions. We have applied the framework to gene regulation as an example of a central biological mechanism where intrinsic and extrinsic stochasticity plays crucial role due to low numbers of DNA and RNA molecules. Using our methods we have obtained a comprehensive and precise analysis of stochastic dynamics under parameter uncertainty. Furthermore, we apply our framework to compare several variants of two-component signalling networks from the perspective of robustness with respect to intrinsic noise caused by low populations of signalling components. We have successfully extended previous studies performed on deterministic models (ODE) and showed that stochasticity may significantly affect obtained predictions. Our case studies demonstrate that the framework can provide deeper insight into the role of key parameters in maintaining the system functionality and thus it significantly contributes to formal methods in computational systems biology.

Data and Extended Materials

Data and Extended Materials

Stochastic variance reduction algorithms have recently become popular for minimizing the average of a large, but finite number of loss functions. The present paper proposes a Riemannian stochastic quasi-Newton algorithm with variance reduction (R-SQN-VR). The key challenges of averaging, adding, and subtracting multiple gradients are addressed with notions of retraction and vector transport. We present a global convergence analysis and a local convergence rate analysis of R-SQN-VR under some natural assumptions. The proposed algorithm is applied to the Karcher mean computation on the symmetric positive-definite manifold and low-rank matrix completion on the Grassmann manifold. In all cases, the proposed algorithm outperforms the Riemannian stochastic gradient descent and the Riemannian stochastic variance reduction algorithms.

Stochastic variance reduction algorithms have recently become popular for minimizing the average of a large, but finite number of loss functions. The present paper proposes a Riemannian stochastic quasi-Newton algorithm with variance reduction (R-SQN-VR). The key challenges of averaging, adding, and subtracting multiple gradients are addressed with notions of retraction and vector transport. We present a global convergence analysis and a local convergence rate analysis of R-SQN-VR under some natural assumptions. The proposed algorithm is applied to the Karcher mean computation on the symmetric positive-definite manifold and low-rank matrix completion on the Grassmann manifold. In all cases, the proposed algorithm outperforms the Riemannian stochastic gradient descent and the Riemannian stochastic variance reduction algorithms.

A formulation of the problem of making decisions concerning the state of nonstationary stochastic processes is given. An optimal decision rule, for the case in which the stochastic process is independent of the decisions made, is derived. It is shown that this rule is a generalization of the Bayesian likelihood ratio test; and an analog to Wald's sequential likelihood ratio test is given, in which the optimal thresholds may vary with time.

We investigate Markov property of rough surfaces. Using stochastic analysis we characterize the complexity of the surface roughness by means of a Fokker-Planck or Langevin equation. The obtained Langevin equation enables us to regenerate surfaces with similar statistical properties compared with the observed morphology by atomic force microscopy.

We investigate Markov property of rough surfaces. Using stochastic analysis we characterize the complexity of the surface roughness by means of a Fokker-Planck or Langevin equation. The obtained Langevin equation enables us to regenerate surfaces with similar statistical properties compared with the observed morphology by atomic force microscopy.

We consider stochastic networks with pairwise transition rates of the exponential form where the temperature T is a small parameter. Such networks arise in physics and chemistry and serve as mathematically tractable models of complex systems. Typically, such networks contain large numbers of states and widely varying pairwise transition rates. We present a methodology for spectral analysis and clustering of such networks that takes advance of the small parameter T and consists of two steps: (1) computing zero-temperature asymptotics for eigenvalues and the collection of quasi-invariant sets, and (2) finite temperature continuation. Step (1) is re- ducible to a sequence of optimization problems on graphs. A novel single-sweep algorithm for solving them is introduced. Its mathematical justification is provided. This algorithm is valid for both time-reversible and time-irreversible networks. For time-reversible networks, a finite temperature continuation technique combining lumping and truncation with Rayleigh quotient iteration is developed. The proposed methodology is applied to the network representing the energy landscape of the Lennard-Jones-75 cluster containing 169,523 states and 226,377 edges. The transition process between its two major funnels, is analyzed. The corresponding eigenvalue is shown to have a kink at the solid-solid phase transition temperature.

This volume was digitized and made accessible online due to deterioration of the original print copy.

We tightly analyze the sample complexity of CCA, provide a learning algorithm that achieves optimal statistical performance in time linear in the required number of samples (up to log factors), as well as a streaming algorithm with similar guarantees.

We tightly analyze the sample complexity of CCA, provide a learning algorithm that achieves optimal statistical performance in time linear in the required number of samples (up to log factors), as well as a streaming algorithm with similar guarantees.

This paper presents a new approach to congestion management at traffic-light intersections. The approach is based on controlling the relative lengths of red/green cycles in order to have the congestion level track a given reference. It uses an integral control with adaptive gains, designed to provide fast tracking and wide stability margins. The gains are inverse-proportional to the derivative of the plant-function with respect to the control parameter, and are computed by infinitesimal perturbation analysis. Convergence of this technique is shown to be robust with respect to modeling uncertainties, computing errors, and other random effects. The framework is presented in the setting of stochastic hybrid systems, and applied to a particular traffic-light model. This is but an initial study and hence the latter model is simple, but it captures some of the salient features of traffic-light processes. The paper concludes with comments on possible extensions of the proposed approach to traffic-light grids with realistic flow models.

In this paper, we analyze the behavior of stochastic approximation schemes with set-valued maps in the absence of a stability guarantee. We prove that after a large number of iterations if the stochastic approximation process enters the domain of attraction of an attracting set it gets locked into the attracting set with high probability. We demonstrate that the above result is an effective instrument for analyzing stochastic approximation schemes in the absence of a stability guarantee, by using it obtain an alternate criteria for convergence in the presence of a locally attracting set for the mean field and by using it to show that a feedback mechanism, which involves resetting the iterates at regular time intervals, stabilizes the scheme when the mean field possesses a globally attracting set, thereby guaranteeing convergence. The results in this paper build on the works of V.S. Borkar, C. Andrieu and H. F. Chen , by allowing for the presence of set-valued drift functions.

We investigate coarse equilibrium states of a fine-scale, stochastic agent-based model of consumer lock-in in a duopolistic market. In the model, agents decide on their next purchase based on a combination of their personal preference and their neighbours' opinions. For agents with independent identically-distributed parameters and all-to-all coupling, we derive an analytic approximate coarse evolution-map for the expected average purchase. We then study the emergence of coarse fronts when spatial segregation is present in the relative perceived quality of products. We develop a novel Newton-Krylov method that is able to compute accurately and efficiently coarse fixed points when the underlying fine-scale dynamics is stochastic. The main novelty of the algorithm is in the elimination of the noise that is generated when estimating Jacobian-vector products using time-integration of perturbed initial conditions. We present numerical results that demonstrate the convergence properties of the numerical method, and use the method to show that macroscopic fronts in this model destabilise at a coarse symmetry-breaking bifurcation.

Dense cellular networks (DenseNets) are fast becoming a reality with the rapid deployment of base stations (BSs) aimed at meeting the explosive data traffic demand. In legacy systems however this comes with the penalties of higher network interference and energy consumption. In order to support network densification in a sustainable manner, the system behavior should be made 'load-proportional' thus allowing certain portions of the network to activate on-demand. In this work, we develop an analytical framework using tools from stochastic geometry theory for the performance analysis of DenseNets where load-awareness is explicitly embedded in the design. The model leverages on a flexible cellular network architecture where there is a complete separation of the data and signaling communication functionalities. Using the proposed model, we identify the most energy- efficient deployment solution for meeting certain minimum service criteria and analyze the corresponding power savings through dynamic sleep modes. Based on state-of-the-art system parameters, a homogeneous pico deployment for the data plane with a separate layer of signaling macro-cells is revealed to be the most energy-efficient solution in future dense urban environments.

Dense cellular networks (DenseNets) are fast becoming a reality with the rapid deployment of base stations (BSs) aimed at meeting the explosive data traffic demand. In legacy systems however this comes with the penalties of higher network interference and energy consumption. In order to support network densification in a sustainable manner, the system behavior should be made 'load-proportional' thus allowing certain portions of the network to activate on-demand. In this work, we develop an analytical framework using tools from stochastic geometry theory for the performance analysis of DenseNets where load-awareness is explicitly embedded in the design. The model leverages on a flexible cellular network architecture where there is a complete separation of the data and signaling communication functionalities. Using the proposed model, we identify the most energy- efficient deployment solution for meeting certain minimum service criteria and analyze the corresponding power savings through dynamic sleep modes. Based on state-of-the-art system parameters, a homogeneous pico deployment for the data plane with a separate layer of signaling macro-cells is revealed to be the most energy-efficient solution in future dense urban environments.