Lie symmetry analysis and reductions of a two-dimensional integrable generalization of the Camassa-Holm equation

In this Letter we investigate Lie symmetries of a (2 + 1)-dimensional integrable generalization of the Camassa-Holm (CH) equation. Through the similarity reductions we obtain four different (1 + 1)-dimensional systems of partial differential equations in which one of them turns out to be a (1 + 1)-dimensional CH equation. We establish their integrability by providing the Lax pair for all of them. Further, we present a brief analysis for some types of particular solutions which include the cuspon, peakon and soliton solutions for the two-dimensional generalization of the CH equation. (C) 2000 Published by Elsevier B.V. B.V.

Two-dimensional integrable generalization of the Camassa-Holm equation

In this letter we discuss the (2 + 1)-dimensional generalization of the Camassa-Holm equation. We require that this generalization be, at the same time, integrable and physically derivable under the same asymptotic analysis as the original Camassa-Holm equation. First, we find the equation in a perturbative calculation in shallow-water theory. We then demonstrate its integrability and find several particular solutions describing (2 + 1) solitary-wave like solutions. © 1999 Published by Elsevier Science B.V. All rights reserved.

New doubly periodic waves of the (2+1)-dimensional double sine-Gordon equation

New exact solutions of the (2 + 1)-dimensional double sine-Gordon equation are studied by introducing the modified mapping relations between the cubic nonlinear Klein-Gordon system and double sine-Gordon equation. Two arbitrary functions are included into the Jacobi elliptic function solutions. New doubly periodic wave solutions are obtained and displayed graphically by proper selections of the arbitrary functions.

Superintégrabilité avec séparation de variables en coordonnées polaires et intégrales du mouvement d’ordre supérieur à deux

Dans cette thèse, nous proposons de nouveaux résultats de systèmes superintégrables séparables en coordonnées polaires. Dans un premier temps, nous présentons une classification complète de tous les systèmes superintégrables séparables en coordonnées polaires qui admettent une intégrale du mouvement d'ordre trois. Des potentiels s'exprimant en terme de la sixième transcendante de Painlevé et de la fonction elliptique de Weierstrass sont présentés. Ensuite, nous introduisons une famille infinie de systèmes classiques et quantiques intégrables et exactement résolubles en coordonnées polaires. Cette famille s'exprime en terme d'un paramètre k. Le spectre d'énergie et les fonctions d'onde des systèmes quantiques sont présentés. Une conjecture postulant la superintégrabilité de ces systèmes est formulée et est vérifiée pour k=1,2,3,4. L'ordre des intégrales du mouvement proposées est 2k où k ∈ ℕ. La structure algébrique de la famille de systèmes quantiques est formulée en terme d'une algèbre cachée où le nombre de générateurs dépend du paramètre k. Une généralisation quasi-exactement résoluble et intégrable de la famille de potentiels est proposée. Finalement, les trajectoires classiques de la famille de systèmes sont calculées pour tous les cas rationnels k ∈ ℚ. Celles-ci s'expriment en terme des polynômes de Chebyshev. Les courbes associées aux trajectoires sont présentées pour les premiers cas k=1, 2, 3, 4, 1/2, 1/3 et 3/2 et les trajectoires bornées sont fermées et périodiques dans l'espace des phases. Ainsi, les résultats obtenus viennent renforcer la possible véracité de la conjecture.

Noncommutative integrable field theories in 2d

We study the noncommutative generalization of (Euclidean) integrable models in two dimensions, specifically the sine- and sinh-Gordon and the U(N) principal chiral models. By looking at tree-level amplitudes for the sinh-Gordon model we show that its naive noncommutative generalization is not integrable. on the other hand, the addition of extra constraints, obtained through the generalization of the zero-curvature method, renders the model integrable. We construct explicit nonlocal nontrivial conserved charges for the U(N) principal chiral model using the Brezin-Itzykson-Zinn-Justin-Zuber method. (C) 2003 Elsevier B.V. All rights reserved.

Integrable deformations of strings on symmetric spaces

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Dubrovin Type Equations for Completely Integrable Systems Associated with a Polynomial Pencil

Dubrovin type equations for the N -gap solution of a completely integrable system associated with a polynomial pencil is constructed and then integrated to a system of functional equations. The approach used to derive those results is a generalization of the familiar process of finding the 1-soliton (1-gap) solution by integrating the ODE obtained from the soliton equation via the substitution u = u(x + λt).

Determining process model precision and generalization with weighted artificial negative events

Process mining encompasses the research area which is concerned with knowledge discovery from event logs. One common process mining task focuses on conformance checking, comparing discovered or designed process models with actual real-life behavior as captured in event logs in order to assess the “goodness” of the process model. This paper introduces a novel conformance checking method to measure how well a process model performs in terms of precision and generalization with respect to the actual executions of a process as recorded in an event log. Our approach differs from related work in the sense that we apply the concept of so-called weighted artificial negative events towards conformance checking, leading to more robust results, especially when dealing with less complete event logs that only contain a subset of all possible process execution behavior. In addition, our technique offers a novel way to estimate a process model’s ability to generalize. Existing literature has focused mainly on the fitness (recall) and precision (appropriateness) of process models, whereas generalization has been much more difficult to estimate. The described algorithms are implemented in a number of ProM plugins, and a Petri net conformance checking tool was developed to inspect process model conformance in a visual manner.

Simplified computation and generalization of the refined process structure tree

A business process is often modeled using some kind of a directed flow graph, which we call a workflow graph. The Refined Process Structure Tree (RPST) is a technique for workflow graph parsing, i.e., for discovering the structure of a workflow graph, which has various applications. In this paper, we provide two improvements to the RPST. First, we propose an alternative way to compute the RPST that is simpler than the one developed originally. In particular, the computation reduces to constructing the tree of the triconnected components of a workflow graph in the special case when every node has at most one incoming or at most one outgoing edge. Such graphs occur frequently in applications. Secondly, we extend the applicability of the RPST. Originally, the RPST was applicable only to graphs with a single source and single sink such that the completed version of the graph is biconnected. We lift both restrictions. Therefore, the RPST is then applicable to arbitrary directed graphs such that every node is on a path from some source to some sink. This includes graphs with multiple sources and/or sinks and disconnected graphs.

Mice behaviorally selected for high Pavlovian fear memory exhibit fear generalization, HPA-axis alterations and increased basal activity in cortico-limbic circuits

Biological factors underlying individual variability in fearfulness and anxiety have important implications for stress-related psychiatric illness including PTSD and major depression. Using an advanced intercross line (AIL) derived from C57BL/6 and DBA/2J mouse strains and behavioral selection over 3 generations, we established two lines exhibiting High or Low fear behavior after fear conditioning. Across the selection generations, the two lines showed clear differences in training and tests for contextual and conditioned fear. Before fear conditioning training, there were no differences between lines in baseline freezing to a novel context. However, after fear conditioning High line mice demonstrated pronounced freezing in a new context suggestive of poor context discrimination. Fear generalization was not restricted to contextual fear. High fear mice froze to a novel acoustic stimulus while freezing in the Low line did not increase over baseline. Enhanced fear learning and generalization are consistent with transgenic and pharmacological disruption of the hypothalamic-pituitary-adrenal axis (HPA-axis) (Brinks, 2009, Thompson, 2004, Kaouane, 2012). To determine whether there were differences in HPA-axis regulation between the lines, morning urine samples were collected to measure basal corticosterone. Levels of secreted corticosterone in the circadian trough were analyzed by corticosterone ELISA. High fear mice were found to have higher basal corticosterone levels than low line animals. Examination of hormonal stress response components by qPCR revealed increased expression of CRH mRNA and decreased mRNA for MR and CRHR1 in hypothalamus of high fear mice. These alterations may contribute to both the behavioral phenotype and higher basal corticosterone in High fear mice. To determine basal brain activity in vivo in High and Low fear mice we used manganese-enhanced magnetic resonance imaging (MEMRI). Analysis revealed a pattern of basal brain activity made up of amygdala, cortical and hippocampal circuits that was elevated in the High line. Ongoing studies also seek to determine the relative balance of excitatory and inhibitory tone in the amygdala and hippocampus and the neuronal structure of its neurons. While these heterogeneous lines are selected on fear memory expression, HPA-axis alterations and differences in hippocampal activity segregate with the behavioral phenotypes. These differences are detectable in a basal state strongly suggesting these are biological traits underlying the behavioral phenotype (Johnson et al, 2011).

A Literary Turn : Rethinking the Roles of Generalization and Theory in Anglo-American Moral Philosophy

This work investigates the role of narrative literature in late-20th century and contemporary Anglo-American moral philosophy. It aims to show the trend of reading narrative literature for purposes of moral philosophy from the 1970 s and early 80 s to the present day as a part of a larger movement in Anglo-American moral philosophy, and to present a view of its significance for moral philosophy overall. Chapter 1 provides some preliminaries concerning the view of narrative literature which my discussion builds on. In chapter 2 I give an outline of how narrative literature is considered in contemporary Anglo-American moral philosophy, and connect this use to the broad trend of neo-Aristotelian ethics in this context. In chapter 3 I connect the use of literature to the idea of the non-generalizability of moral perception and judgment, which is central to the neo-Aristotelian trend, as well as to a range of moral particularisms and anti-theoretical positions of late 20th century and contemporary ethics. The joint task of chapters 2 and 3 is to situate the trend of reading narrative literature for the purposes of moral philosophy in the present context of moral philosophy. In the following two chapters, 4 and 5, I move on from the particularizing power of narrative literature, which is emphasized by neo-Aristotelians and particularists alike, to a broader under-standing of the intellectual potential of narrative literature. In chapter 4 I argue that narrative literature has its own forms of generalization which are enriching for our understanding of the workings of ethical generalizations in philosophy. In chapter 5 I discuss Iris Murdoch s and Martha Nussbaum s respective ways of combining ethical generality and particularity in a philosophical framework where both systematic moral theory and narrative literature are taken seriously. In chapter 6 I analyse the controversy between contemporary anti-theoretical conceptions of ethics and Nussbaum s refutation of these. I present my suggestion for how the significance of the ethics/literature discussion for moral philosophy can be understood if one wants to overcome the limitations of both Nussbaum s theory-centred, equilibrium-seeking perspective, and the anti-theorists repudiation of theory. I call my position the inclusive approach .

Profiling k-Iteration Paths : A Generalization of the Ball-Larus Profiling Algorithm

The Ball-Larus path-profiling algorithm is an efficient technique to collect acyclic path frequencies of a program. However, longer paths -those extending across loop iterations - describe the runtime behaviour of programs better. We generalize the Ball-Larus profiling algorithm for profiling k-iteration paths - paths that can span up to to k iterations of a loop. We show that it is possible to number suchk-iteration paths perfectly, thus allowing for an efficient profiling algorithm for such longer paths. We also describe a scheme for mixed-mode profiling: profiling different parts of a procedure with different path lengths. Experimental results show that k-iteration profiling is realistic.

Generalization of Dynkin's Identity and Some Applications

Let X(t) be a right continuous temporally homogeneous Markov pro- cess, Tt the corresponding semigroup and A the weak infinitesimal genera- tor. Let g(t) be absolutely continuous and r a stopping time satisfying E.( S f I g(t) I dt) < oo and E.( f " I g'(t) I dt) < oo Then for f e 9iJ(A) with f(X(t)) right continuous the identity Exg(r)f(X(z)) - g(O)f(x) = E( 5 " g'(s)f(X(s)) ds) + E.( 5 " g(s)Af(X(s)) ds) is a simple generalization of Dynkin's identity (g(t) 1). With further restrictions on f and r the following identity is obtained as a corollary: Ex(f(X(z))) = f(x) + k! Ex~rkAkf(X(z))) + n-1E + (n ) )!.E,(so un-1Anf(X(u)) du). These identities are applied to processes with stationary independent increments to obtain a number of new and known results relating the moments of stopping times to the moments of the stopped processes.

Analysis,Insights and Generalization of a Fast Decentralized Relay Selection Mechanism

Relay selection for cooperative communications has attracted considerable research interest recently. While several criteria have been proposed for selecting one or more relays and analyzed, mechanisms that perform the selection in a distributed manner have received relatively less attention. In this paper, we analyze a splitting algorithm for selecting the single best relay amongst a known number of active nodes in a cooperative network. We develop new and exact asymptotic analysis for computing the average number of slots required to resolve the best relay. We then propose and analyze a new algorithm that addresses the general problem of selecting the best Q >= 1 relays. Regardless of the number of relays, the algorithm selects the best two relays within 4.406 slots and the best three within 6.491 slots, on average. Our analysis also brings out an intimate relationship between multiple access selection and multiple access control algorithms.