Semi-algebraic methods for symbolic analysis of complex reaction networks

The identification of chemical mechanism that can exhibit oscillatory phenomena in reaction networks are currently of intense interest. In particular, the parametric question of the existence of Hopf bifurcations has gained increasing popularity due to its relation to the oscillatory behavior around the fixed points. However, the detection of oscillations in high-dimensional systems and systems with constraints by the available symbolic methods has proven to be difficult. The development of new efficient methods are therefore required to tackle the complexity caused by the high-dimensionality and non-linearity of these systems. In this thesis, we mainly present efficient algorithmic methods to detect Hopf bifurcation fixed points in (bio)-chemical reaction networks with symbolic rate constants, thereby yielding information about their oscillatory behavior of the networks. The methods use the representations of the systems on convex coordinates that arise from stoichiometric network analysis. One of the methods called HoCoQ reduces the problem of determining the existence of Hopf bifurcation fixed points to a first-order formula over the ordered field of the reals that can then be solved using computational-logic packages. The second method called HoCaT uses ideas from tropical geometry to formulate a more efficient method that is incomplete in theory but worked very well for the attempted high-dimensional models involving more than 20 chemical species. The instability of reaction networks may lead to the oscillatory behaviour. Therefore, we investigate some criterions for their stability using convex coordinates and quantifier elimination techniques. We also study Muldowney's extension of the classical Bendixson-Dulac criterion for excluding periodic orbits to higher dimensions for polynomial vector fields and we discuss the use of simple conservation constraints and the use of parametric constraints for describing simple convex polytopes on which periodic orbits can be excluded by Muldowney's criteria. All developed algorithms have been integrated into a common software framework called PoCaB (platform to explore bio- chemical reaction networks by algebraic methods) allowing for automated computation workflows from the problem descriptions. PoCaB also contains a database for the algebraic entities computed from the models of chemical reaction networks.

Relatedness in Evidence Networks

Einhergehend mit der Entwicklung und zunehmenden Verfügbarkeit des Internets hat sich die Art der Informationsbereitstellung und der Informationsbeschaffung deutlich geändert. Die einstmalige Trennung zwischen Publizist und Konsument wird durch kollaborative Anwendungen des sogenannten Web 2.0 aufgehoben, wo jeder Teilnehmer gleichsam Informationen bereitstellen und konsumieren kann. Zudem können Einträge anderer Teilnehmer erweitert, kommentiert oder diskutiert werden. Mit dem Social Web treten schließlich die sozialen Beziehungen und Interaktionen der Teilnehmer in den Vordergrund. Dank mobiler Endgeräte können zu jeder Zeit und an nahezu jedem Ort Nachrichten verschickt und gelesen werden, neue Bekannschaften gemacht oder der aktuelle Status dem virtuellen Freundeskreis mitgeteilt werden. Mit jeder Aktivität innerhalb einer solchen Applikation setzt sich ein Teilnehmer in Beziehung zu Datenobjekten und/oder anderen Teilnehmern. Dies kann explizit geschehen, indem z.B. ein Artikel geschrieben wird und per E-Mail an Freunde verschickt wird. Beziehungen zwischen Datenobjekten und Nutzern fallen aber auch implizit an, wenn z.B. die Profilseite eines anderen Teilnehmers aufgerufen wird oder wenn verschiedene Teilnehmer einen Artikel ähnlich bewerten. Im Rahmen dieser Arbeit wird ein formaler Ansatz zur Analyse und Nutzbarmachung von Beziehungsstrukturen entwickelt, welcher auf solchen expliziten und impliziten Datenspuren aufbaut. In einem ersten Teil widmet sich diese Arbeit der Analyse von Beziehungen zwischen Nutzern in Applikationen des Social Web unter Anwendung von Methoden der sozialen Netzwerkanalyse. Innerhalb einer typischen sozialen Webanwendung haben Nutzer verschiedene Möglichkeiten zu interagieren. Aus jedem Interaktionsmuster werden Beziehungsstrukturen zwischen Nutzern abgeleitet. Der Vorteil der impliziten Nutzer-Interaktionen besteht darin, dass diese häufig vorkommen und quasi nebenbei im Betrieb des Systems abfallen. Jedoch ist anzunehmen, dass eine explizit angegebene Freundschaftsbeziehung eine stärkere Aussagekraft hat, als entsprechende implizite Interaktionen. Ein erster Schwerpunkt dieser Arbeit ist entsprechend der Vergleich verschiedener Beziehungsstrukturen innerhalb einer sozialen Webanwendung. Der zweite Teil dieser Arbeit widmet sich der Analyse eines der weit verbreitetsten Profil-Attributen von Nutzern in sozialen Webanwendungen, dem Vornamen. Hierbei finden die im ersten Teil vorgestellten Verfahren und Analysen Anwendung, d.h. es werden Beziehungsnetzwerke für Namen aus Daten von sozialen Webanwendungen gewonnen und mit Methoden der sozialen Netzwerkanalyse untersucht. Mithilfe externer Beschreibungen von Vornamen werden semantische Ähnlichkeiten zwischen Namen bestimmt und mit jeweiligen strukturellen Ähnlichkeiten in den verschiedenen Beziehungsnetzwerken verglichen. Die Bestimmung von ähnlichen Namen entspricht in einer praktischen Anwendung der Suche von werdenden Eltern nach einem passenden Vornamen. Die Ergebnisse zu der Analyse von Namensbeziehungen sind die Grundlage für die Implementierung der Namenssuchmaschine Nameling, welche im Rahmen dieser Arbeit entwickelt wurde. Mehr als 35.000 Nutzer griffen innerhalb der ersten sechs Monate nach Inbetriebnahme auf Nameling zu. Die hierbei anfallenden Nutzungsdaten wiederum geben Aufschluss über individuelle Vornamenspräferenzen der Anwender. Im Rahmen dieser Arbeit werden diese Nutzungsdaten vorgestellt und zur Bestimmung sowie Bewertung von personalisierten Vornamensempfehlungen verwendet. Abschließend werden Ansätze zur Diversifizierung von personalisierten Vornamensempfehlungen vorgestellt, welche statische Beziehungsnetzwerke für Namen mit den individuellen Nutzungsdaten verknüpft.

Growing through Connections – A Multi-Case Study of Two Alternative Food Networks in Cluj-Napoca, Romania

In a context of urgent global socio-ecological challenges, the aim of this paper has been to explore the potential of localised and socially connected food systems. More specifically, through a multi-case study of two alternative food networks in the city of Cluj-Napoca, Romania, their contribution to a sustainable food paradigm has been explored. An important synergy within the networks is how good food is equated with peasant produce, but issues regarding quantity, delivery arrangement, power relations and inclusiveness constitute potential conflicts. Although challenged by unfavourable trends on national and EU levels, the networks are becoming more embedded horizontally, through an intrinsic focus on community in one case and through quality food stimulating good relations in the other case. The networks contribute to a sustainable food paradigm by promoting agroecology, by reclaiming socio-cultural factors of food provisioning and by being part of a (re)-peasantisation process. Exploring how these kinds of initiatives can emerge, be sustained and be developed is of relevance, especially considering their potential for improving the prospects of environmentally sustainable and socially just futures in Romania and beyond.

Optimal Unsupervised Learning in Feedforward Neural Networks

We investigate the properties of feedforward neural networks trained with Hebbian learning algorithms. A new unsupervised algorithm is proposed which produces statistically uncorrelated outputs. The algorithm causes the weights of the network to converge to the eigenvectors of the input correlation with largest eigenvalues. The algorithm is closely related to the technique of Self-supervised Backpropagation, as well as other algorithms for unsupervised learning. Applications of the algorithm to texture processing, image coding, and stereo depth edge detection are given. We show that the algorithm can lead to the development of filters qualitatively similar to those found in primate visual cortex.

Using Recurrent Networks for Dimensionality Reduction

This report explores how recurrent neural networks can be exploited for learning high-dimensional mappings. Since recurrent networks are as powerful as Turing machines, an interesting question is how recurrent networks can be used to simplify the problem of learning from examples. The main problem with learning high-dimensional functions is the curse of dimensionality which roughly states that the number of examples needed to learn a function increases exponentially with input dimension. This thesis proposes a way of avoiding this problem by using a recurrent network to decompose a high-dimensional function into many lower dimensional functions connected in a feedback loop.

Safe Distributed Coordination of Heterogeneous Robots through Dynamic Simple Temporal Networks

Research on autonomous intelligent systems has focused on how robots can robustly carry out missions in uncertain and harsh environments with very little or no human intervention. Robotic execution languages such as RAPs, ESL, and TDL improve robustness by managing functionally redundant procedures for achieving goals. The model-based programming approach extends this by guaranteeing correctness of execution through pre-planning of non-deterministic timed threads of activities. Executing model-based programs effectively on distributed autonomous platforms requires distributing this pre-planning process. This thesis presents a distributed planner for modelbased programs whose planning and execution is distributed among agents with widely varying levels of processor power and memory resources. We make two key contributions. First, we reformulate a model-based program, which describes cooperative activities, into a hierarchical dynamic simple temporal network. This enables efficient distributed coordination of robots and supports deployment on heterogeneous robots. Second, we introduce a distributed temporal planner, called DTP, which solves hierarchical dynamic simple temporal networks with the assistance of the distributed Bellman-Ford shortest path algorithm. The implementation of DTP has been demonstrated successfully on a wide range of randomly generated examples and on a pursuer-evader challenge problem in simulation.

Online Learning of Non-stationary Sequences

We consider an online learning scenario in which the learner can make predictions on the basis of a fixed set of experts. The performance of each expert may change over time in a manner unknown to the learner. We formulate a class of universal learning algorithms for this problem by expressing them as simple Bayesian algorithms operating on models analogous to Hidden Markov Models (HMMs). We derive a new performance bound for such algorithms which is considerably simpler than existing bounds. The bound provides the basis for learning the rate at which the identity of the optimal expert switches over time. We find an analytic expression for the a priori resolution at which we need to learn the rate parameter. We extend our scalar switching-rate result to models of the switching-rate that are governed by a matrix of parameters, i.e. arbitrary homogeneous HMMs. We apply and examine our algorithm in the context of the problem of energy management in wireless networks. We analyze the new results in the framework of Information Theory.

Probabilistic Independence Networks for Hidden Markov Probability Models

Graphical techniques for modeling the dependencies of randomvariables have been explored in a variety of different areas includingstatistics, statistical physics, artificial intelligence, speech recognition, image processing, and genetics.Formalisms for manipulating these models have been developedrelatively independently in these research communities. In this paper weexplore hidden Markov models (HMMs) and related structures within the general framework of probabilistic independencenetworks (PINs). The paper contains a self-contained review of the basic principles of PINs.It is shown that the well-known forward-backward (F-B) and Viterbialgorithms for HMMs are special cases of more general inference algorithms forarbitrary PINs. Furthermore, the existence of inference and estimationalgorithms for more general graphical models provides a set of analysistools for HMM practitioners who wish to explore a richer class of HMMstructures.Examples of relatively complex models to handle sensorfusion and coarticulationin speech recognitionare introduced and treated within the graphical model framework toillustrate the advantages of the general approach.

Neural Networks

We present an overview of current research on artificial neural networks, emphasizing a statistical perspective. We view neural networks as parameterized graphs that make probabilistic assumptions about data, and view learning algorithms as methods for finding parameter values that look probable in the light of the data. We discuss basic issues in representation and learning, and treat some of the practical issues that arise in fitting networks to data. We also discuss links between neural networks and the general formalism of graphical models.

Fast Learning by Bounding Likelihoods in Sigmoid Type Belief Networks

Sigmoid type belief networks, a class of probabilistic neural networks, provide a natural framework for compactly representing probabilistic information in a variety of unsupervised and supervised learning problems. Often the parameters used in these networks need to be learned from examples. Unfortunately, estimating the parameters via exact probabilistic calculations (i.e, the EM-algorithm) is intractable even for networks with fairly small numbers of hidden units. We propose to avoid the infeasibility of the E step by bounding likelihoods instead of computing them exactly. We introduce extended and complementary representations for these networks and show that the estimation of the network parameters can be made fast (reduced to quadratic optimization) by performing the estimation in either of the alternative domains. The complementary networks can be used for continuous density estimation as well.

Forecasting Global Temperature Variations by Neural Networks

Global temperature variations between 1861 and 1984 are forecast usingsregularization networks, multilayer perceptrons and linearsautoregression. The regularization network, optimized by stochasticsgradient descent associated with colored noise, gives the bestsforecasts. For all the models, prediction errors noticeably increasesafter 1965. These results are consistent with the hypothesis that thesclimate dynamics is characterized by low-dimensional chaos and thatsthe it may have changed at some point after 1965, which is alsosconsistent with the recent idea of climate change.s

Belief Propagation and Revision in Networks with Loops

Local belief propagation rules of the sort proposed by Pearl(1988) are guaranteed to converge to the optimal beliefs for singly connected networks. Recently, a number of researchers have empirically demonstrated good performance of these same algorithms on networks with loops, but a theoretical understanding of this performance has yet to be achieved. Here we lay the foundation for an understanding of belief propagation in networks with loops. For networks with a single loop, we derive ananalytical relationship between the steady state beliefs in the loopy network and the true posterior probability. Using this relationship we show a category of networks for which the MAP estimate obtained by belief update and by belief revision can be proven to be optimal (although the beliefs will be incorrect). We show how nodes can use local information in the messages they receive in order to correct the steady state beliefs. Furthermore we prove that for all networks with a single loop, the MAP estimate obtained by belief revisionat convergence is guaranteed to give the globally optimal sequence of states. The result is independent of the length of the cycle and the size of the statespace. For networks with multiple loops, we introduce the concept of a "balanced network" and show simulati.

A Unified Framework for Regularization Networks and Support Vector Machines

Regularization Networks and Support Vector Machines are techniques for solving certain problems of learning from examples -- in particular the regression problem of approximating a multivariate function from sparse data. We present both formulations in a unified framework, namely in the context of Vapnik's theory of statistical learning which provides a general foundation for the learning problem, combining functional analysis and statistics.