Search results for " Bounds"
showing 10 items of 291 documents
On the propagation of a perturbation in an anharmonic system
2007
We give a not trivial upper bound on the velocity of disturbances in an infinitely extended anharmonic system at thermal equilibrium. The proof is achieved by combining a control on the non equilibrium dynamics with an explicit use of the state invariance with respect to the time evolution.
AIs for Dominion Using Monte-Carlo Tree Search
2015
Dominion is a complex game, with hidden information and stochastic elements. This makes creating any artificial intelligence AI challenging. To this date, there is little work in the literature on AI for Dominion, and existing solutions rely upon carefully tuned finite-state solutions. This paper presents two novel AIs for Dominion based on Monte-Carlo Tree Search MCTS methods. This is achieved by employing Upper Confidence Bounds UCB and Upper Confidence Bounds applied to Trees UCT. The proposed solutions are notably better than existing work. The strongest proposal is able to win 67% of games played against a known, good finite-state solution, even when the finite-state solution has the u…
Warrant Exercise and Bond Conversion in Large Trader Economies
2006
It is well known that the sequential (premature) exercise of American-type warrants may be advantageous for large warrantholders, even in the absence of regular dividends, because using exercise proceeds to repurchase stock or to expand the firm's scale increases the riskiness of an equity share. We present an upper bound on this advantage and show that this advantage is negligible for a realistic parameter setting. This result, however, does not justify in general the simplifying restriction that warrants or convertible securities are valued as if exercised as a block. It turns out that the option to exercise only a fraction of the outstanding convertibles at the maturity date (partial exe…
Sobolev and bounded variation functions on metric measure spaces
2014
International audience
Finite index subgroups of mapping class groups
2011
Let g ≥ 3 and n ≥ 0, and let Mg,n be the mapping class group of a surface of genus g with n boundary components. We prove that Mg,n contains a unique subgroup of index 2g−1(2g − 1) up to conjugation, a unique subgroup of index 2g−1(2g + 1) up to conjugation, and the other proper subgroups ofMg,n are of index greater than 2g−1(2g+1). In particular, the minimum index for a proper subgroup of Mg,n is 2g−1(2g − 1). AMS Subject Classification. Primary: 57M99. Secondary: 20G40, 20E28. 0 Introduction and statement of results The interaction between mapping class groups and finite groups has long been a topic of interest. The famous Hurwitz bound of 1893 showed that the mapping class group of a clo…
Discrete and differential homotopy in circular restricted three-body control
2010
The planar circular restricted three-body problem is considered. The control enters linearly in the equation of motion to model the thrust of the third body. The minimum time optimal control problem has two scalar parameters: The ratio of the primaries masses which embeds the two-body problem into the three-body one, and the upper bound on the control norm. Regular extremals of the maximum principle are computed by shooting thanks to continuations with respect to both parameters. Discrete and di erential homotopy are compared in connection with second order sucient conditions in optimal control. Homotopy with respect to control bound gives evidence of various topological structures of extr…
Fractal Weyl law for open quantum chaotic maps
2014
We study the semiclassical quantization of Poincar\'e maps arising in scattering problems with fractal hyperbolic trapped sets. The main application is the proof of a fractal Weyl upper bound for the number of resonances/scattering poles in small domains near the real axis. This result encompasses the case of several convex (hard) obstacles satisfying a no-eclipse condition.
Reliable numerical solution of a class of nonlinear elliptic problems generated by the Poisson-Boltzmann equation
2020
We consider a class of nonlinear elliptic problems associated with models in biophysics, which are described by the Poisson-Boltzmann equation (PBE). We prove mathematical correctness of the problem, study a suitable class of approximations, and deduce guaranteed and fully computable bounds of approximation errors. The latter goal is achieved by means of the approach suggested in [S. Repin, A posteriori error estimation for variational problems with uniformly convex functionals. Math. Comp., 69:481-500, 2000] for convex variational problems. Moreover, we establish the error identity, which defines the error measure natural for the considered class of problems and show that it yields computa…
On the performance of hybrid-ARQ with code combining over double rayleigh fading channels
2011
In this paper, we study the performance of hybrid automatic repeat request (HARQ) with code combining (CC) over double Rayleigh channels. This channel can be utilized to model the fading envelope of vehicle-to-vehicle (V2V) channels. We derive analytical solutions for the characteristic quantities of double Rayleigh channels, such as the outage probability, the ergodic capacity, and the bit error probability (BEP). Moreover, we study the performance of HARQ with CC. Our analysis focuses on information theoretic aspects of HARQ with CC. closed-form analytical approximations are derived for the e-outage capacity, the average number of transmissions, and the average transmission rate of HARQ w…
Computable majorants of the limit load in Hencky’s plasticity problems
2018
Abstract We propose a new method for analyzing the limit (safe) load of elastoplastic media governed by the Hencky plasticity law and deduce fully computable bounds of this load. The main idea of the method is based on a combination of kinematic approach and new estimates of the distance to the set of divergence free fields. We show that two sided bounds of the limit load are sharp and the computational efficiency of the method is confirmed by numerical experiments.