scholarly journals Space mapping-based optimization with the macroscopic limit of interacting particle systems

Author(s):  
Jennifer Weißen ◽  
Simone Göttlich ◽  
Claudia Totzeck

AbstractWe propose a space mapping-based optimization algorithm for microscopic interacting particle dynamics which are infeasible for direct optimization. This is of relevance for example in applications with bounded domains for which the microscopic optimization is difficult. The space mapping algorithm exploits the relationship of the microscopic description of the interacting particle system and a corresponding macroscopic description as partial differential equation in the “many particle limit”. We validate the approach with the help of a toy problem that allows for direct optimization. Then we study the performance of the algorithm in two applications. A pedestrian flow is considered and the transportation of goods on a conveyor belt is optimized. The numerical results underline the feasibility of the proposed algorithm.

Author(s):  
Dmitry V. Bugai ◽  

The task of the paper is to determine what is the philosophical meaning of Plato’s Philebus. To define the meaning is to show which way of understanding Phile­bus is the most fruitful, most fully grasping and revealing what forms the sub­stantive core of Plato’s text. It’s no secret that the meaning of Philebus is not at all self-evident. From our point of view, the main subject of the dialogue lies not in the plane of ontology, but in ethics, and what is taken for ontological aspects in Philebus is much more related to the logical and methodological conditions for solving the main ethical problem. Therefore, in this article an attempt was made to show that the key themes of Philebus(the problem of the one-many, the relationship of the four kinds of beings, the theory of false pleasures) are inter­nally related. The question of the relationship between the one and the many is raised in connection with the clarification of the question of the logical status of pleasure. Division into four kinds (limit, unlimited, mixture, reason) is the ful­fillment of the methodological requirement for the necessity of division. The ana­lysis of pleasures following this methodological introduction examines pleasure in an entirely new light, in the light of truth/falsity.


2020 ◽  
pp. 309-342
Author(s):  
Helen Moore

Taking its cue from the Victorian periodical debates characterizing realism as a crocodile and romance as a monster or ‘catawampus’, this chapter examines the role played by Amadis in early discussions of what the novel was, or should be; how it had developed; and where its future direction lay. For literary historians, Amadis constituted a bridge between the newly constructed ‘medieval’ and the emergent ‘modern’. Philosopher-theorists (Bakhtin) and novelists (Nabokov) alike continued to be fascinated by the relationship of Amadis to Don Quixote and its implications for theories of the novel. Novelists themselves (Bulwer Lytton, Ouida, and Thackeray) enlisted Amadis in their critique of modern masculinity. The final iteration of Amadis in English takes the form of chivalric compilations and abridgements for children; this concluding transformation proves to be emblematic of the many varieties of cultural work into which romance can be enlisted.


1998 ◽  
Vol 35 (3) ◽  
pp. 633-641 ◽  
Author(s):  
Yoshiaki Itoh ◽  
Colin Mallows ◽  
Larry Shepp

We introduce a new class of interacting particle systems on a graph G. Suppose initially there are Ni(0) particles at each vertex i of G, and that the particles interact to form a Markov chain: at each instant two particles are chosen at random, and if these are at adjacent vertices of G, one particle jumps to the other particle's vertex, each with probability 1/2. The process N enters a death state after a finite time when all the particles are in some independent subset of the vertices of G, i.e. a set of vertices with no edges between any two of them. The problem is to find the distribution of the death state, ηi = Ni(∞), as a function of Ni(0).We are able to obtain, for some special graphs, the limiting distribution of Ni if the total number of particles N → ∞ in such a way that the fraction, Ni(0)/S = ξi, at each vertex is held fixed as N → ∞. In particular we can obtain the limit law for the graph S2, the two-leaf star which has three vertices and two edges.


1999 ◽  
Vol 31 (3) ◽  
pp. 819-838 ◽  
Author(s):  
D. Crişan ◽  
P. Del Moral ◽  
T. J. Lyons

In this paper we consider the continuous-time filtering problem and we estimate the order of convergence of an interacting particle system scheme presented by the authors in previous works. We will discuss how the discrete time approximating model of the Kushner-Stratonovitch equation and the genetic type interacting particle system approximation combine. We present quenched error bounds as well as mean order convergence results.


Author(s):  
Zoe Avstreih

This chapter explores the possibility of a relationship between spiritual practices and some of the many facets of wellbeing. It considers the distinction between religion and spirituality with reference to the literature. It discusses Authentic Movement, an inner-directed movement process rooted in the intersection of dance/movement therapy and Jungian depth psychology, and the concept of embodied spirituality in which the relationship between the mover and the witness is explored. In particular, it explores the relationship of this practice to health and the increased sense of wellbeing that stems from a direct experience of the sacred, which supports a deepening sense of connection to one’s true self.


2000 ◽  
Vol 37 (01) ◽  
pp. 118-125
Author(s):  
Raúl Gouet ◽  
F. Javier López ◽  
Gerardo Sanz

The estimation of critical values is one of the most interesting problems in the study of interacting particle systems. The bounds obtained analytically are not usually very tight and, therefore, computer simulation has been proved to be very useful in the estimation of these values. In this paper we present a new method for the estimation of critical values in any interacting particle system with an absorbing state. The method, based on the asymptotic behaviour of the absorption time of the process, is very easy to implement and provides good estimates. It can also be applied to processes different from particle systems.


Author(s):  
Jianhai Bao ◽  
Christoph Reisinger ◽  
Panpan Ren ◽  
Wolfgang Stockinger

In this paper, we derive fully implementable first-order time-stepping schemes for McKean–Vlasov stochastic differential equations, allowing for a drift term with super-linear growth in the state component. We propose Milstein schemes for a time-discretized interacting particle system associated with the McKean–Vlasov equation and prove strong convergence of order 1 and moment stability, taming the drift if only a one-sided Lipschitz condition holds. To derive our main results on strong convergence rates, we make use of calculus on the space of probability measures with finite second-order moments. In addition, numerical examples are presented which support our theoretical findings.


2012 ◽  
Vol 14 (3) ◽  
pp. 253-262 ◽  

Rett syndrome (RTT, MIM#312750) is a neurodevelopmental disorder that is classified as an autism spectrum disorder. Clinically, RTT is characterized by psychomotor regression with loss of volitional hand use and spoken language, the development of repetitive hand stereotypies, and gait impairment. The majority of people with RTT have mutations in Methyl-CpG-binding Protein 2 (MECP2), a transcriptional regulator. Interestingly, alterations in the function of the protein product produced by MECP2, MeCP2, have been identified in a number of other clinical conditions. The many clinical features found in RTT and the various clinical problems that result from alteration in MeCP2 function have led to the belief that understanding RTT will provide insight into a number of other neurological disorders. Excitingly, RTT is reversible in a mouse model, providing inspiration and hope that such a goal may be achieved for RTT and potentially for many neurodevelopmental disorders.


2010 ◽  
Vol 28 (2) ◽  
pp. 200-217
Author(s):  
Rachel Duerden

Mark Morris's L'Allegro, Il Penseroso ed Il Moderato (1988), embodies ideas about how to live a good life. L'Allegro is unusual in that it is a full evening-length work, yet has no through-narrative; it has characters and action, but these change in each of the many individual sections. However, together these embody a dialogue – really a three (or four or even five)-way discussion between poet, composer and choreographer about the best way to live. The relationship between dance, music and text, and the implied conversation across the centuries between Milton, Handel, Jennens and Morris, offer insights into the way such layering of creativity can illuminate our engagement with art. As in so much of Mark Morris's work, the relationship of choreography and music is of paramount importance, and this will form the main focus of the discussion here. Handel's secular oratorio of 1740 is itself a setting of John Milton's companion poems, L'Allegro and Il Penseroso (1631), which explicitly explore through debate the relative merits of different approaches to life. Handel's musical setting includes an additional ‘voice’ in the debate: Il Moderato, words by Handel's librettist Charles Jennens, offering a ‘middle way’, or ‘18th century balance’, as John Eliot Gardiner has it (1980:16). 1 For the purposes of this essay I focus chiefly on the dialogue between dance and music as manifest in a few ‘moments’, with reference also at times to the poetry and its rhythms. In this, I am guided by theories of art as embodiment as expounded by Paul Crowther. When we engage with art, we do so in the fullest sense of perceptual, that is, with our whole, embodied selves. Art, as the embodiment of ideas, does not teach us anything specific about the artist or his/her world, but it does reveal something of the world-view of the artist as an embodied being. There is thus the potential for empathy, and imaginative engagement; we are not passive consumers but active reciprocal participants. Through close reading of a few short examples drawn from the work, I employ structural analysis to examine music-dance relationships, referring also from time to time to the poetry, which itself reflects key characteristics of both choreography and music. These examples show how dance, music and poetry manifest characteristics that are suggestive of similar perspectives on life, both individually and in relationship with one another. John Creaser, writing of Milton's poems, observes that they embody a sophisticated and resilient playfulness conveyed through verbal nuance and rhythmic buoyancy, a revelation of temperament and sensibility rather than an exploration of ideals. (Creaser 2001:377)


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