Geometric and Combinatorial Aspects of NonEquilibrium Statistical Mechanics

Non-Equilibrium Statistical Mechanics is a broad subject. Grossly speaking, it deals with systems which have not yet relaxed to an equilibrium state, or else with systems which are in a steady non-equilibrium state, or with more general situations. They are characterized by external forcing and internal fluxes, resulting in a net production of entropy which quantifies dissipation and the extent by which, by the Second Law of Thermodynamics, time-reversal invariance is broken. In this thesis we discuss some of the mathematical structures involved with generic discrete-state-space non-equilibrium systems, that we depict with networks in all analogous to electrical networks. We define suitable observables and derive their linear regime relationships, we discuss a duality between external and internal observables that reverses the role of the system and of the environment, we show that network observables serve as constraints for a derivation of the minimum entropy production principle. We dwell on deep combinatorial aspects regarding linear response determinants, which are related to spanning tree polynomials in graph theory, and we give a geometrical interpretation of observables in terms of Wilson loops of a connection and gauge degrees of freedom. We specialize the formalism to continuous-time Markov chains, we give a physical interpretation for observables in terms of locally detailed balanced rates, we prove many variants of the fluctuation theorem, and show that a well-known expression for the entropy production due to Schnakenberg descends from considerations of gauge invariance, where the gauge symmetry is related to the freedom in the choice of a prior probability distribution. As an additional topic of geometrical flavor related to continuous-time Markov chains, we discuss the Fisher-Rao geometry of nonequilibrium decay modes, showing that the Fisher matrix contains information about many aspects of non-equilibrium behavior, including non-equilibrium phase transitions and superposition of modes. We establish a sort of statistical equivalence principle and discuss the behavior of the Fisher matrix under time-reversal. To conclude, we propose that geometry and combinatorics might greatly increase our understanding of nonequilibrium phenomena.

Lernen mit einer Hybride aus Lernendem Klassifizierendem System und Selbstorganisierender Karte

Im Forschungsgebiet der Künstlichen Intelligenz, insbesondere im Bereich des maschinellen Lernens, hat sich eine ganze Reihe von Verfahren etabliert, die von biologischen Vorbildern inspiriert sind. Die prominentesten Vertreter derartiger Verfahren sind zum einen Evolutionäre Algorithmen, zum anderen Künstliche Neuronale Netze. Die vorliegende Arbeit befasst sich mit der Entwicklung eines Systems zum maschinellen Lernen, das Charakteristika beider Paradigmen in sich vereint: Das Hybride Lernende Klassifizierende System (HCS) wird basierend auf dem reellwertig kodierten eXtended Learning Classifier System (XCS), das als Lernmechanismus einen Genetischen Algorithmus enthält, und dem Wachsenden Neuralen Gas (GNG) entwickelt. Wie das XCS evolviert auch das HCS mit Hilfe eines Genetischen Algorithmus eine Population von Klassifizierern - das sind Regeln der Form [WENN Bedingung DANN Aktion], wobei die Bedingung angibt, in welchem Bereich des Zustandsraumes eines Lernproblems ein Klassifizierer anwendbar ist. Beim XCS spezifiziert die Bedingung in der Regel einen achsenparallelen Hyperquader, was oftmals keine angemessene Unterteilung des Zustandsraumes erlaubt. Beim HCS hingegen werden die Bedingungen der Klassifizierer durch Gewichtsvektoren beschrieben, wie die Neuronen des GNG sie besitzen. Jeder Klassifizierer ist anwendbar in seiner Zelle der durch die Population des HCS induzierten Voronoizerlegung des Zustandsraumes, dieser kann also flexibler unterteilt werden als beim XCS. Die Verwendung von Gewichtsvektoren ermöglicht ferner, einen vom Neuronenadaptationsverfahren des GNG abgeleiteten Mechanismus als zweites Lernverfahren neben dem Genetischen Algorithmus einzusetzen. Während das Lernen beim XCS rein evolutionär erfolgt, also nur durch Erzeugen neuer Klassifizierer, ermöglicht dies dem HCS, bereits vorhandene Klassifizierer anzupassen und zu verbessern. Zur Evaluation des HCS werden mit diesem verschiedene Lern-Experimente durchgeführt. Die Leistungsfähigkeit des Ansatzes wird in einer Reihe von Lernproblemen aus den Bereichen der Klassifikation, der Funktionsapproximation und des Lernens von Aktionen in einer interaktiven Lernumgebung unter Beweis gestellt.

Numerische Integration, angewandt bei der Inferenz in Zustandsraummodellen

In dieser Arbeit werden neuere methodische Entwicklungen aus dem Bereich der Numerischen Integration für die näherungsweise Berechnung von Zustandraummodellen erprobt. Die resultierenden Algorithmen werden bzgl. ihrer Approximationsgüte mit den populären simulationsbasierten Näherungsverfahren verglichen.

Stationary states in random walks on networks

In this thesis we dealt with the problem of describing a transportation network in which the objects in movement were subject to both finite transportation capacity and finite accomodation capacity. The movements across such a system are realistically of a simultaneous nature which poses some challenges when formulating a mathematical description. We tried to derive such a general modellization from one posed on a simplified problem based on asyncronicity in particle transitions. We did so considering one-step processes based on the assumption that the system could be describable through discrete time Markov processes with finite state space. After describing the pre-established dynamics in terms of master equations we determined stationary states for the considered processes. Numerical simulations then led to the conclusion that a general system naturally evolves toward a congestion state when its particle transition simultaneously and we consider one single constraint in the form of network node capacity. Moreover the congested nodes of a system tend to be located in adjacent spots in the network, thus forming local clusters of congested nodes.

Model Predictive Control for Vehicle Stabilization at the Limits of Handling

Recent developments in vehicle steering systems offer new opportunities to measure the steering torque and reliably estimate the vehicle sideslip and the tire-road friction coefficient. This paper presents an approach to vehicle stabilization that leverages these estimates to define state boundaries that exclude unstable vehicle dynamics and utilizes a model predictive envelope controller to bound the vehicle motion within this stable region of the state space. This approach provides a large operating region accessible by the driver and smooth interventions at the stability boundaries. Experimental results obtained with a steer-by-wire vehicle and a proof of envelope invariance demonstrate the efficacy of the envelope controller in controlling the vehicle at the limits of handling.

Enumerating constrained elementary flux vectors of metabolic networks

The concept of elementary vector is generalised to the case where the steady-state space of the metabolic network is not a flux cone but is a general polyhedron due to further inhomogeneous constraints on the flows through some of the reactions. On one hand, this allows to selectively enumerate elementary modes which satisfy certain optimality criteria and this can yield a large computational gain compared with full enumeration. On the other hand, in contrast to the single optimum found by executing a linear program, this enables a comprehensive description of the set of alternate optima often encountered in flux balance analysis. The concepts are illustrated on a metabolic network model of human cardiac mitochondria.

Automated design of self-stabilization

Self-stabilization is a property of a distributed system such that, regardless of the legitimacy of its current state, the system behavior shall eventually reach a legitimate state and shall remain legitimate thereafter. The elegance of self-stabilization stems from the fact that it distinguishes distributed systems by a strong fault tolerance property against arbitrary state perturbations. The difficulty of designing and reasoning about self-stabilization has been witnessed by many researchers; most of the existing techniques for the verification and design of self-stabilization are either brute-force, or adopt manual approaches non-amenable to automation. In this dissertation, we first investigate the possibility of automatically designing self-stabilization through global state space exploration. In particular, we develop a set of heuristics for automating the addition of recovery actions to distributed protocols on various network topologies. Our heuristics equally exploit the computational power of a single workstation and the available parallelism on computer clusters. We obtain existing and new stabilizing solutions for classical protocols like maximal matching, ring coloring, mutual exclusion, leader election and agreement. Second, we consider a foundation for local reasoning about self-stabilization; i.e., study the global behavior of the distributed system by exploring the state space of just one of its components. It turns out that local reasoning about deadlocks and livelocks is possible for an interesting class of protocols whose proof of stabilization is otherwise complex. In particular, we provide necessary and sufficient conditions – verifiable in the local state space of every process – for global deadlock- and livelock-freedom of protocols on ring topologies. Local reasoning potentially circumvents two fundamental problems that complicate the automated design and verification of distributed protocols: (1) state explosion and (2) partial state information. Moreover, local proofs of convergence are independent of the number of processes in the network, thereby enabling our assertions about deadlocks and livelocks to apply on rings of arbitrary sizes without worrying about state explosion.

Multichannel EEG fields during and without visual input: frequency domain model source locations and dimensional complexities

27-Channel EEG potential map series were recorded from 12 normals with closed and open eyes. Intracerebral dipole model source locations in the frequency domain were computed. Eye opening (visual input) caused centralization (convergence and elevation) of the source locations of the seven frequency bands, indicative of generalized activity; especially, there was clear anteriorization of α-2 (10.5–12 Hz) and β-2 (18.5–21 Hz) sources (α-2 also to the left). Complexity of the map series' trajectories in state space (assessed by Global Dimensional Complexity and Global OMEGA Complexity) increased significantly with eye opening, indicative of more independent, parallel, active processes. Contrary to PET and fMRI, these results suggest that brain activity is more distributed and independent during visual input than after eye closing (when it is more localized and more posterior).

Single-dose piracetam effects on global complexity measures of human spontaneous multichannel EEG

Global complexity of 47-channel resting electroencephalogram (EEG) of healthy young volunteers was studied after intake of a single dose of a nootropic drug (piracetam, Nootropil® UCB Pharma) in 12 healthy volunteers. Four treatment levels were used: 2.4, 4.8, 9.6 g piracetam and placebo. Brain electric activity was assessed through Global Dimensional Complexity and Global Omega-Complexity as quantitative measures of the complexity of the trajectory of multichannel EEG in state space. After oral ingestion (1–1.5 h), both measures showed significant decreases from placebo to 2.4 g piracetam. In addition, Global Dimensional Complexity showed a significant return to placebo values at 9.6 g piracetam. The results indicate that a single dose of piracetam dose-dependently affects the spontaneous EEG in normal volunteers, showing effects at the lowest treatment level. The decreased EEG complexity is interpreted as increased cooperativity of brain functional processes.

Chewing-gum flavor affects measures of global complexity of multichannel EEG

Global complexity of spontaneous brain electric activity was studied before and after chewing gum without flavor and with 2 different flavors. One-minute, 19-channel, eyes-closed electroencephalograms (EEG) were recorded from 20 healthy males before and after using 3 types of chewing gum: regular gum containing sugar and aromatic additives, gum containing 200 mg theanine (a constituent of Japanese green tea), and gum base (no sugar, no aromatic additives); each was chewed for 5 min in randomized sequence. Brain electric activity was assessed through Global Omega (Ω)-Complexity and Global Dimensional Complexity (GDC), quantitative measures of complexity of the trajectory of EEG map series in state space; their differences from pre-chewing data were compared across gum-chewing conditions. Friedman Anova (p < 0.043) showed that effects on Ω-Complexity differed significantly between conditions and differences were maximal between gum base and theanine gum. No differences were found using GDC. Global Omega-Complexity appears to be a sensitive measure for subtle, central effects of chewing gum with and without flavor.

Differential dynamic properties of scleroderma fibroblasts in response to perturbation of environmental stimuli.

Diseases are believed to arise from dysregulation of biological systems (pathways) perturbed by environmental triggers. Biological systems as a whole are not just the sum of their components, rather ever-changing, complex and dynamic systems over time in response to internal and external perturbation. In the past, biologists have mainly focused on studying either functions of isolated genes or steady-states of small biological pathways. However, it is systems dynamics that play an essential role in giving rise to cellular function/dysfunction which cause diseases, such as growth, differentiation, division and apoptosis. Biological phenomena of the entire organism are not only determined by steady-state characteristics of the biological systems, but also by intrinsic dynamic properties of biological systems, including stability, transient-response, and controllability, which determine how the systems maintain their functions and performance under a broad range of random internal and external perturbations. As a proof of principle, we examine signal transduction pathways and genetic regulatory pathways as biological systems. We employ widely used state-space equations in systems science to model biological systems, and use expectation-maximization (EM) algorithms and Kalman filter to estimate the parameters in the models. We apply the developed state-space models to human fibroblasts obtained from the autoimmune fibrosing disease, scleroderma, and then perform dynamic analysis of partial TGF-beta pathway in both normal and scleroderma fibroblasts stimulated by silica. We find that TGF-beta pathway under perturbation of silica shows significant differences in dynamic properties between normal and scleroderma fibroblasts. Our findings may open a new avenue in exploring the functions of cells and mechanism operative in disease development.

Differential dynamic properties of scleroderma fibroblasts in response to perturbation of environmental stimuli.

Diseases are believed to arise from dysregulation of biological systems (pathways) perturbed by environmental triggers. Biological systems as a whole are not just the sum of their components, rather ever-changing, complex and dynamic systems over time in response to internal and external perturbation. In the past, biologists have mainly focused on studying either functions of isolated genes or steady-states of small biological pathways. However, it is systems dynamics that play an essential role in giving rise to cellular function/dysfunction which cause diseases, such as growth, differentiation, division and apoptosis. Biological phenomena of the entire organism are not only determined by steady-state characteristics of the biological systems, but also by intrinsic dynamic properties of biological systems, including stability, transient-response, and controllability, which determine how the systems maintain their functions and performance under a broad range of random internal and external perturbations. As a proof of principle, we examine signal transduction pathways and genetic regulatory pathways as biological systems. We employ widely used state-space equations in systems science to model biological systems, and use expectation-maximization (EM) algorithms and Kalman filter to estimate the parameters in the models. We apply the developed state-space models to human fibroblasts obtained from the autoimmune fibrosing disease, scleroderma, and then perform dynamic analysis of partial TGF-beta pathway in both normal and scleroderma fibroblasts stimulated by silica. We find that TGF-beta pathway under perturbation of silica shows significant differences in dynamic properties between normal and scleroderma fibroblasts. Our findings may open a new avenue in exploring the functions of cells and mechanism operative in disease development.

Existence and Uniqueness of Equilibrium in Nonoptimal Unbounded Infinite Horizon Economies

In applied work in macroeconomics and finance, nonoptimal infinite horizon economies are often studied in the the state space is unbounded. Important examples of such economies are single vector growth models with production externalities, valued fiat money, monopolistic competition, and/or distortionary government taxation. Although sufficient conditions for existence and uniqueness of Markovian equilibrium are well known for the compact state space case, no similar sufficient conditions exist for unbounded growth. This paper provides such a set of sufficient conditions, and also present a computational algorithm that will prove asymptotically consistent when computing Markovian equilibrium.

Proceedings of the Sixteenth Annual Biochemical Engineering Symposium

This volume represents the proceedings of the Sixteenth Annual Biochemical Engineering Symposium held at Kansas State University on April 26, 1986. Some of the papers describe the progress of ongoing projects, and others contain the results of completed projects. Only brief summaries are given of many of the papers that will be published in full elsewhere. ContentsEnd-Product Inhibition of the Acetone-Butanol Fermentation—Bob Kuhn, Colorado State University Effect of Multiple Substrates in Ethanal Fermentations from Cheese Whey—C.J. Wang, University of Missouri Extraction and Fermentation of Ensiled Sweet Sorghum—Karl Noah, Colorado State University Removal of Nucleic Acids from Bakers' Yeast—Richard M. Cordes, Iowa State University Modeling the Effects of Plasmid Replication and Product Repression on the Growth Rate of Recombinant Bacteria—William E. Bentley, University of Colorado Indirect Estimates of Cell Concentrations in Mass Cultivation of Bacterial Cells—Andrew Fisher, University of Missouri A Mathematical Model for Liquid Recirculation in Airlift Columns—C.H.Lee, Kansas State University Characterization of Imperfect Mixing of Batch Reactors by Two Compartment Model—Peter Sohn, University of Missouri First Order Breakage Model for the Degradation of Pullalan in the Batch Fermentor—Stephen A. Milligan, Kansas State University Synthesis and Nuclear Magnetic Resonance of 13C-Labeled Amylopectin and Maltooligosaccharides—Bernard Y. Tao, Iowa State University Preparation of Fungal Starter Culture in Gas Fluidized Bed Reactor—Pal Mihaltz, Colorado State University Yeast Flocculation and Sedimentation—David Szlag, University of Colorado Protein Enrichment of Extrusion Cooked Corn by Solid Substrate Fermentation—Lucas Alvarez-Martinez, Colorado State University Optimum Design of a Hollow Fiber Mammalian Cell Reactor—Thomas Chresand, Colorado State University Gas Chromatography and Nuclear Magnetic Resonance of Trifluoroacetylated Carbohydrates—Steven T. Summerfelt, Iowa State University Kinetic and Bioenergetic Considerations for Modeling Photosynthetic Microbial P~ocesses in Producing Biomass and Treating Wastewater—H. Y. Lee, Kansas State University Mathematical Modeling and Simulation of Bicarbonate-Limited Photsynthetic Growth in Continuous Culture—Craig Curless, Kansas State University Data Acquisition and Control of a Rotary Drum Solid State Fermentor—Mnasria A. Habib, Colorado State University Biodegradation of 2,4-Dichlorophenoxyacetic Acid (2,4-D)—Greg Sinton, Kansas State University

Proceedings of the Eighteenth Annual Biochemical Engineering Symposium

The eighteenth annual biochemical engineering symposium was held during April 22–23, 1988 at the YMCA of the Rockies conference center in Estes Park, Colorado, under the sponsorship of the University of Colorado. Previous symposia in this series have been hosted by Kansas State University (1st, 3rd, 5th, 9th, 12th, 16th), University of Nebraska-Lincoln (2nd, 4th), Iowa State University (6th, 7th, l0th, 13th, 17th), University of Missouri–Columbia (8th, 14th), and Colorado State University (11th, 15th). Next year's symposium is scheduled to be held at the University of Missouri-Columbia. The symposia are devoted to talks by students about their ongoing research. Because final publication usually takes place elsewhere, the papers included in the proceedings are brief, and often cover work in progress. ContentsApplications of mass spectrometers in biochemical engineeringJohn P. McDonald, Ayush Gupta, and Lourdes Taladriz, Kansas State University Enzymatic hydrolysis of corn gluten proteinsJulie Hardwick; Iowa State University Improved Acetone-Butanol Fermentation AnalysisZ. Buday; Colorado State University On-Line State Identification for Batch FermentationD. A. Gee and W. F. Ramirez; University of Colorado Role of Spargers in Air-Lift ReactorsPeter U. Sohn and Rakesh K. Bajpai; University of Missouri–Columbia The Interaction of Microcarriers and Turbulence within an Airlift FermenterG. Travis Jones; Kansas State University Oxygen Diffusion in the Inter-Fiber Gel/Cell Matrix of NMR-Compatible Hollow Fiber Bio-ReactorsS. L. Hanson, B. E. Dale, and R. J. Gillies; Colorado State University Characterization of Ca-alginate Gel Beads FormationHorngtwu Su, Rakesh K. Bajpai, and George W. Preckshot; University of Missouri–Columbia Metabolic Effects of Chloramphenicol Resistance in the Recombinant Host/Vector System: E. coli RRl [pBR329]William E. Bentley, Dana C. Andersen, Dhinakar S. Kompala, and Robert H. Davis; University of Colorado Genetic Engineering of Beta-Galactosidase to Aid in Fermentation Product Recovery by Polyelectrolyte PrecipitationD. E. Parker, C. E. Glatz, J. Zhao, C. F. Ford, S. M. Gendel, and M. A. Rougvie; Iowa State University Biodegradation of Organic Compounds in SoilLourdes Taladriz, L. E. Erickson, and L. T. Fan; Kansas State University Effect of Dilution, pH and Nutrient Composition on the Biodegradation of Metalworking FluidsAyush Gupta, L. E. Erickson, and L. T. Fan; Kansas State University Dissolved Hydrogen Correlation with Redox Potential in Acetone-Butanol FermentationXiangdong Zhou; Colorado State University Modeling of Ensiling Fermentation of Sweet SorghumA. K. Hilaly; Colorado State University