Infection Spread In Random Geometric Graphs

In this paper we study the speed of infection spread and the survival of the contact process in the random geometric graph G = G (n, r(n), f) of n nodes independently distributed in S = -1/2, 1/2 according to a certain density f(.). In the first part of the paper we assume that infection spreads from one node to another at unit rate and that infected nodes stay in the same state forever. We provide an explicit lower bound on the speed of infection spread and prove that infection spreads in G with speed at least D(1)nr(n)(2). In the second part of the paper we consider the contact process xi(t) on G where infection spreads at rate lambda > 0 from one node to another and each node independently recovers at unit rate. We prove that, for every lambda > 0, with high probability, the contact process on G survives for an exponentially long time; there exist positive constants c(1) and c(2) such that, with probability at least 1 - c(1)/n(4), the contact process xi(1)(t) starting with all nodes infected survives up to time t(n) = exp(c(2)n/log n) for all n.

The Contact Process

Daniel Rodrigues Valesin

This work is a study of three interacting particle systems that are modified versions of the contact process. The contact process is a spin system defined on a graph and is commonly taken as a model for the spread of an infection in a population; transmission of the infection happens by proximity (contact). The first two models we consider – the grass-bushes-trees model and the multitype contact process – are models for competition between species in Ecology. The third model – annealed approximation to boolean networks – approximately describes the transmission of information among genes in a cell. We consider the grass-bushes-trees model on the set of integers, ℤ. Each point of ℤ is a region of space. In the continuous-time dynamics, at each instant each region can be either empty (state 0) or occupied by an individual of one of two existing species (states 1 and 2). Occupants of both species die at rate 1, leaving their regions empty, and send descendents to neighboring regions at rate λ. An individuals of type 1 may be born on a region previously occupied by an individual of type 2, but the converse is forbidden. We take the "heaviside" initial configuration in which all sites to the left of the origin are occupied by type 1 individuals and all sites to the right of the origin are occupied by type 2 individuals. If the birth of new individuals is allowed to occur at sites that are not adjacent to the parent, and if the rate λ is supercritical for the usual contact process on ℤ, we see the formation of an interface region in which both types coexist. Addressing a conjecture of Cox and Durrett (1995), we prove that the size of this region is stochastically tight. The multitype contact process on ℤ is a process identical to the grass-bushes-trees model in every respect except that no births can occur at previously occupied sites; in particular, the model is symmetric for both species. We again start the process from the heaviside configuration and prove that the size of the interface region is tight. In addition, we prove that the position of the interface, when properly rescaled, converges to Brownian motion. Finally, we give necessary and sufficient conditions on the initial configuration so that one of the two species becomes extinct with probability one and also so that both species are present at all times with positive probability. Lastly, we consider a model proposed by Derrida and Pomeau (1986) and recently studied by Chatterjee and Durrett (2009); it is defined as an approximation to S. Kauffman's boolean networks (1969). The model starts with the choice of a random directed graph on n vertices; each node has r input nodes pointing at it. A discrete time threshold contact process is then considered on this graph: at each instant, each site has probability q of choosing to receive input; if it does, and if at least one of its inputs were occupied by a 1 at the previous instant, then it is labeled with a 1; in all other cases, it is labeled with a 0. r and q are kept fixed and n is taken to infinity. Improving a result of Chatterjee and Durrett, we show that if qr > 1, then the time of persistence of the dynamics is exponential in n.

EPFL2011

Error handling in multimodal voice-enabled interfaces of tour-guide robots using graphical models

Plamen Prodanov

Mobile service robots are going to play an increasing role in the society of humans. Voice-enabled interaction with service robots becomes very important, if such robots are to be deployed in real-world environments and accepted by the vast majority of potential human users. The research presented in this thesis addresses the problem of speech recognition integration in an interactive voice-enabled interface of a service robot, in particular a tour-guide robot. The task of a tour-guide robot is to engage visitors to mass exhibitions (users) in dialogue providing the services it is designed for (e.g. exhibit presentations) within a limited time. In managing tour-guide dialogues, extracting the user goal (intention) for requesting a particular service at each dialogue state is the key issue. In mass exhibition conditions speech recognition errors are inevitable because of noisy speech and uncooperative users of robots with no prior experience in robotics. They can jeopardize the user goal identification. Wrongly identified user goals can lead to communication failures. Therefore, to reduce the risk of such failures, methods for detecting and compensating for communication failures in human-robot dialogue are needed. During the short-term interaction with visitors, the interpretation of the user goal at each dialogue state can be improved by combining speech recognition in the speech modality with information from other available robot modalities. The methods presented in this thesis exploit probabilistic models for fusing information from speech and auxiliary modalities of the robot for user goal identification and communication failure detection. To compensate for the detected communication failures we investigate multimodal methods for recovery from communication failures. To model the process of modality fusion, taking into account the uncertainties in the information extracted from each input modality during human-robot interaction, we use the probabilistic framework of Bayesian networks. Bayesian networks are graphical models that represent a joint probability function over a set of random variables. They are used to model the dependencies among variables associated with the user goals, modality related events (e.g. the event of user presence that is inferred from the laser scanner modality of the robot), and observed modality features providing evidence in favor of these modality events. Bayesian networks are used to calculate posterior probabilities over the possible user goals at each dialogue state. These probabilities serve as a base in deciding if the user goal is valid, i.e. if it can be mapped into a tour-guide service (e.g. exhibit presentation) or is undefined – signaling a possible communication failure. The Bayesian network can be also used to elicit probabilities over the modality events revealing information about the possible cause for a communication failure. Introducing new user goal aspects (e.g. new modality events and related features) that provide auxiliary information for detecting communication failures makes the design process cumbersome, calling for a systematic approach in the Bayesian network modelling. Generally, introducing new variables for user goal identification in the Bayesian networks can lead to complex and computationally expensive models. In order to make the design process more systematic and modular, we adapt principles from the theory of grounding in human communication. When people communicate, they resolve understanding problems in a collaborative joint effort of providing evidence of common shared knowledge (grounding). We use Bayesian network topologies, tailored to limited computational resources, to model a state-based grounding model fusing information from three different input modalities (laser, video and speech) to infer possible grounding states. These grounding states are associated with modality events showing if the user is present in range for communication, if the user is attending to the interaction, whether the speech modality is reliable, and if the user goal is valid. The state-based grounding model is used to compute probabilities that intermediary grounding states have been reached. This serves as a base for detecting if the the user has reached the final grounding state, or wether a repair dialogue sequence is needed. In the case of a repair dialogue sequence, the tour-guide robot can exploit the multiple available modalities along with speech. For example, if the user has failed to reach the grounding state related to her/his presence in range for communication, the robot can use its move modality to search and attract the attention of the visitors. In the case when speech recognition is detected to be unreliable, the robot can offer the alternative use of the buttons modality in the repair sequence. Given the probability of each grounding state, and the dialogue sequence that can be executed in the next dialogue state, a tour-guide robot has different preferences on the possible dialogue continuation. If the possible dialogue sequences at each dialogue state are defined as actions, the introduced principle of maximum expected utility (MEU) provides an explicit way of action selection, based on the action utility, given the evidence about the user goal at each dialogue state. Decision networks, constructed as graphical models based on Bayesian networks are proposed to perform MEU-based decisions, incorporating the utility of the actions to be chosen at each dialogue state by the tour-guide robot. These action utilities are defined taking into account the tour-guide task requirements. The proposed graphical models for user goal identification and dialogue error handling in human-robot dialogue are evaluated in experiments with multimodal data. These data were collected during the operation of the tour-guide robot RoboX at the Autonomous System Lab of EPFL and at the Swiss National Exhibition in 2002 (Expo.02). The evaluation experiments use component and system level metrics for technical (objective) and user-based (subjective) evaluation. On the component level, the technical evaluation is done by calculating accuracies, as objective measures of the performance of the grounding model, and the resulting performance of the user goal identification in dialogue. The benefit of the proposed error handling framework is demonstrated comparing the accuracy of a baseline interactive system, employing only speech recognition for user goal identification, and a system equipped with multimodal grounding models for error handling.

EPFL2006

Essays on Capital Calculation in Insurance

Mathieu Jacques David Cambou

In order to be able to bear the risk they are taking, insurance companies have to set aside a certain amount of cushion that can guarantee the payment of liabilities, up to a dened probability, and thus to remain solvent in case of bad events. This amount is named capital. The calculation of capital is a complex problem. To be sustainable, capital must consider all possible risk sources that may lead to losses among assets and liabilities of the insurance company, and it must account for the likelihood and the eect of these bad (and usually extreme) events that could occur to the risk sources. Insurance companies build models and tools in order to perform this capital calculation. For that, they have to collect data, build statistical evidence, build mathematical models and tools in order to eciently and accurately derive capital. The papers exposed in this thesis deal with three major diculties. First, the uncertainty behind the choice of a specic model and the quantication of this uncertainty in terms of additional capital. The use of external scenarios, i.e. opinions on the likelihood of some events happening, allows to build a coherent methodology that make the cushion more robust against wrong model specication. Second, the computational complexity in using these models in an industrialized environment, and numerical methods available for increasing their computational eciency. Most of these models cannot provide an analytical formula of capital. Consequently, one has to approximate it via simulation methods. Considering the high number of risk sources and the complexity of insurance contracts, these methods can be slow to run before providing a reasonable accuracy. This often makes these models unusable in practical cases. Enhancements of classical simulation methods are presented in the aim of making these approximations faster to run for the same level of accuracy. Third, the lack of reliable data and the high complexity of problems with long time horizons, and statistical methods for identifying and building reliable proxies in such cases. A typical example is life-insurance contracts that imply being exposed to multiple risks sources over a long horizon. Such contracts can in fact be approximated wisely by proxies that can capture the risk over time.

EPFL2016