A new methodology is developed to calculate density of states of interstellar and atmospheric clusters that takes account of their loosely bound nature and incorporates kinetically important angular momentum constraints explicitly. The method is based on classical phase space integration for the intermonomer modes of the cluster with imposition of the constraints of selected total energy and total angular momentum. It achieves considerable efficiency via essentially analytic evaluation of the momentum space integrals coupled with efficient Monte Carlo sampling of configurations. The derivation for the equation for the density of states is outlined and all steps in the simplification of the accessible momentum space volume are detailed. The method is tested rigorously against an entirely analytic result obtained for the ideal case of a dimer with spherical top fragments and no interaction potential. Interstellar applications of the new approach are presented for (HCN)2 and (CO)2. The new intermononmer density of states has been integrated over metastable states to obtain the intermonomer partition function, which in turn is used to calculate the metastable equilibrium constants for interstellar clusters, which in turn is used tocalculate the second order rate constant of overall dimer formation in the interstellar environment. Atmospheric applications of the new approach are presented for (H2O)2. The new intermonomer density of states is convoluted with the intramonomer density of states to obtain the convoluted density of states. This convoluted density of states is then integrated over total energy and angular momentum to obtain the anharmonic partition function, which in turn is used to calculate the equilibrium constant for atmospheric clusters, which in turn is used to calculate the third order rate constant for overall dimer formation in the atmospheric environment. Kinetic quantities are also calculated with the intermonomer and convoluted density of states for interstellar and atmospheric clusters, respectively. These densities of states are combined with RRKM theory to compute unimolecular dissociation rate constants, which are then averaged with respect to the thermal capture flux distribution to compute average lifetimes as a function of temperature.

A new methodology is developed to calculate density of states of interstellar and atmospheric clusters that takes account of their loosely bound nature and incorporates kinetically important angular momentum constraints explicitly. The method is based on classical phase space integration for the intermonomer modes of the cluster with imposition of the constraints of selected total energy and total angular momentum. It achieves considerable efficiency via essentially analytic evaluation of the momentum space integrals coupled with efficient Monte Carlo sampling of configurations. The derivation for the equation for the density of states is outlined and all steps in the simplification of the accessible momentum space volume are detailed. The method is tested rigorously against an entirely analytic result obtained for the ideal case of a dimer with spherical top fragments and no interaction potential. Interstellar applications of the new approach are presented for (HCN)2 and (CO)2. The new intermononmer density of states has been integrated over metastable states to obtain the intermonomer partition function, which in turn is used to calculate the metastable equilibrium constants for interstellar clusters, which in turn is used tocalculate the second order rate constant of overall dimer formation in the interstellar environment. Atmospheric applications of the new approach are presented for (H2O)2. The new intermonomer density of states is convoluted with the intramonomer density of states to obtain the convoluted density of states. This convoluted density of states is then integrated over total energy and angular momentum to obtain the anharmonic partition function, which in turn is used to calculate the equilibrium constant for atmospheric clusters, which in turn is used to calculate the third order rate constant for overall dimer formation in the atmospheric environment. Kinetic quantities are also calculated with the intermonomer and convoluted density of states for interstellar and atmospheric clusters, respectively. These densities of states are combined with RRKM theory to compute unimolecular dissociation rate constants, which are then averaged with respect to the thermal capture flux distribution to compute average lifetimes as a function of temperature.

A new methodology is developed to calculate density of states of interstellar and atmospheric clusters that takes account of their loosely bound nature and incorporates kinetically important angular momentum constraints explicitly. The method is based on classical phase space integration for the intermonomer modes of the cluster with imposition of the constraints of selected total energy and total angular momentum. It achieves considerable efficiency via essentially analytic evaluation of the momentum space integrals coupled with efficient Monte Carlo sampling of configurations. The derivation for the equation for the density of states is outlined and all steps in the simplification of the accessible momentum space volume are detailed. The method is tested rigorously against an entirely analytic result obtained for the ideal case of a dimer with spherical top fragments and no interaction potential. Interstellar applications of the new approach are presented for (HCN)2 and (CO)2. The new intermononmer density of states has been integrated over metastable states to obtain the intermonomer partition function, which in turn is used to calculate the metastable equilibrium constants for interstellar clusters, which in turn is used tocalculate the second order rate constant of overall dimer formation in the interstellar environment. Atmospheric applications of the new approach are presented for (H2O)2. The new intermonomer density of states is convoluted with the intramonomer density of states to obtain the convoluted density of states. This convoluted density of states is then integrated over total energy and angular momentum to obtain the anharmonic partition function, which in turn is used to calculate the equilibrium constant for atmospheric clusters, which in turn is used to calculate the third order rate constant for overall dimer formation in the atmospheric environment. Kinetic quantities are also calculated with the intermonomer and convoluted density of states for interstellar and atmospheric clusters, respectively. These densities of states are combined with RRKM theory to compute unimolecular dissociation rate constants, which are then averaged with respect to the thermal capture flux distribution to compute average lifetimes as a function of temperature.

A new methodology is developed to calculate density of states of interstellar and atmospheric clusters that takes account of their loosely bound nature and incorporates kinetically important angular momentum constraints explicitly. The method is based on classical phase space integration for the intermonomer modes of the cluster with imposition of the constraints of selected total energy and total angular momentum. It achieves considerable efficiency via essentially analytic evaluation of the momentum space integrals coupled with efficient Monte Carlo sampling of configurations. The derivation for the equation for the density of states is outlined and all steps in the simplification of the accessible momentum space volume are detailed. The method is tested rigorously against an entirely analytic result obtained for the ideal case of a dimer with spherical top fragments and no interaction potential. Interstellar applications of the new approach are presented for (HCN)2 and (CO)2. The new intermononmer density of states has been integrated over metastable states to obtain the intermonomer partition function, which in turn is used to calculate the metastable equilibrium constants for interstellar clusters, which in turn is used tocalculate the second order rate constant of overall dimer formation in the interstellar environment. Atmospheric applications of the new approach are presented for (H2O)2. The new intermonomer density of states is convoluted with the intramonomer density of states to obtain the convoluted density of states. This convoluted density of states is then integrated over total energy and angular momentum to obtain the anharmonic partition function, which in turn is used to calculate the equilibrium constant for atmospheric clusters, which in turn is used to calculate the third order rate constant for overall dimer formation in the atmospheric environment. Kinetic quantities are also calculated with the intermonomer and convoluted density of states for interstellar and atmospheric clusters, respectively. These densities of states are combined with RRKM theory to compute unimolecular dissociation rate constants, which are then averaged with respect to the thermal capture flux distribution to compute average lifetimes as a function of temperature.

We review equivariant localization and through the Feynman formalism of quantum mechanics motivate its role as a tool for calculating partition functions. We also consider a specific supersymmetric theory of one boson and two fermions and conclude that by applying localization to its partition function we may arrive at a known result that has previously been derived using different approaches. This paper follows a similar article by Levent Akant.

Nous étudions le modèle de la marche aléatoire branchante. Nous obtenons d'abord des résultats concernant le processus ponctuel formé par les particules extrémales, résolvant ainsi une conjecture de Brunet et Derrida 2010 [36]. Ensuite, nous établissons la dérivée au point critique de la limite des martingales additives complétant ainsi l'étude initiée par Biggins [23]. Ces deux travaux reposent sur les techniques modernes de décompositions épinales de la marche aléatoire branchante, originairement développées par Chauvin, Rouault et Wakolbinger [41], Lyons, Pemantle et Peres [74], Lyons [73] et Biggins et Kyprianou [24]. Le dernier chapitre de la thèse porte sur un champ Gaussien log-correle introduit par Kahane 1985 [61]. Via de récents travaux comme ceux de Allez, Rhodes et Vargas [11], Duplantier, Rhodes, Sheeld et Vargas [46] [47], ce modèle a connu un important regain d'intérêt. La construction du chaos multiplicatif Gaussien dans le cas critique a notamment été prouvée dans [46]. S'inspirant des techniques utilisées pour la marche aléatoire branchante nous résolvons une conjecture de [46] concernant le maximum de ce champ Gaussien. / We study the model of the branching random walk. First we obtain some results concerning thepoint process formed by the extremal particles, proving a Brunet and Derrida's conjecture [36] as well. Thenwe establish the derivative of the additive martingale limit at the critical point, completing the study initiatedby Biggins [23]. These two works rely on the spinal decomposition of the branching random walk, originallyintroduced by Chauvin, Rouault and Wakolbinger [41], Lyons, Pemantle and Peres [74], Lyons [73] and Bigginsand Kyprianou [24].The last chapter of the thesis deals with a log-correlated Gaussian field introduced by Kahane [61]. Thismodel was recently revived in particular by Allez, Rhodes and Vargas [11], and Duplantier, Rhodes, Shefield andVargas [46] [47]. Inspired by the techniques used for branching random walk we solved a conjecture of Duplantier,Rhodes, Shefield and Vargas [46], on the maximum of this Gaussian field.

This thesis introduces normal factor graphs under a new semantics, namely, the exterior function semantics. Initially, this work was motivated by two distinct lines of research. One line is ``holographic algorithms,'' a powerful approach introduced by Valiant for solving various counting problems in computer science; the other is ``normal graphs,'' an elegant framework proposed by Forney for representing codes defined on graphs. The nonrestrictive normality constraint enables the notion of holographic transformations for normal factor graphs. We establish a theorem, called the generalized Holant theorem, which relates a normal factor graph to its holographic transformation. We show that the generalized Holant theorem on one hand underlies the principle of holographic algorithms, and on the other reduces to a general duality theorem for normal factor graphs, a special case of which was first proved by Forney. As an application beyond Forney's duality, we show that the normal factor graphs duality facilitates the approximation of the partition function for the two-dimensional nearest-neighbor Potts model. In the course of our development, we formalize a new semantics for normal factor graphs, which highlights various linear algebraic properties that enables the use of normal factor graphs as a linear algebraic tool. Indeed, we demonstrate the ability of normal factor graphs to encode several concepts from linear algebra and present normal factor graphs as a generalization of ``trace diagrams.'' We illustrate, with examples, the workings of this framework and how several identities from linear algebra may be obtained using a simple graphical manipulation procedure called ``vertex merging/splitting.'' We also discuss translation association schemes with the aid of normal factor graphs, which we believe provides a simple approach to understanding the subject. Further, under the new semantics, normal factor graphs provide a probabilistic model that unifies several graphical models such as factor graphs, convolutional factor graphs, and cumulative distribution networks.

Background: RNA has been recognized as a key player in cellular regulation in recent years. In many cases, non-coding RNAs exert their function by binding to other nucleic acids, as in the case of microRNAs and snoRNAs. The specificity of these interactions derives from the stability of inter-molecular base pairing. The accurate computational treatment of RNA-RNA binding therefore lies at the heart of target prediction algorithms. Methods: The standard dynamic programming algorithms for computing secondary structures of linear single-stranded RNA molecules are extended to the co-folding of two interacting RNAs. Results: We present a program, RNAcofold, that computes the hybridization energy and base pairing pattern of a pair of interacting RNA molecules. In contrast to earlier approaches, complex internal structures in both RNAs are fully taken into account. RNAcofold supports the calculation of the minimum energy structure and of a complete set of suboptimal structures in an energy band above the ground state. Furthermore, it provides an extension of McCaskill's partition function algorithm to compute base pairing probabilities, realistic interaction energies, and equilibrium concentrations of duplex structures.

京都大学 / 0048 / 新制・論文博士 / 博士(理学) / 乙第12910号 / 論理博第1546号 / 新制||理||1590(附属図書館) / 32120 / ソウル大学大学院数学科 / (主査)教授 中島 啓, 教授 小野 薫, 教授 向井 茂 / 学位規則第4条第2項該当 / Doctor of Science / Kyoto University / DFAM

Because of the huge amounts of data made available by the technology boom in the late twentieth century, new methods are required to turn data into usable information. Much of this data is categorical in nature, which makes estimation difficult in highly multivariate settings. In this thesis we review various multivariate statistical methods, discuss various statistical methods of natural language processing (NLP), and discuss a general class of models described by Erosheva (2002) called generalized mixed membership models. We then propose extensions of the information partition function (IPF) derived by Engler (2002), Oliphant (2003), and Tolley (2006) that will allow modeling of discrete, highly multivariate data in linear models. We report results of the modified IPF model on the World Health Organization's Survey on Global Aging (SAGE).