412 research outputs found
On the expected number of equilibria in a multi-player multi-strategy evolutionary game
In this paper, we analyze the mean number of internal equilibria in
a general -player -strategy evolutionary game where the agents' payoffs
are normally distributed. First, we give a computationally implementable
formula for the general case. Next we characterize the asymptotic behavior of
, estimating its lower and upper bounds as increases. Two important
consequences are obtained from this analysis. On the one hand, we show that in
both cases the probability of seeing the maximal possible number of equilibria
tends to zero when or respectively goes to infinity. On the other hand,
we demonstrate that the expected number of stable equilibria is bounded within
a certain interval. Finally, for larger and , numerical results are
provided and discussed.Comment: 26 pages, 1 figure, 1 table. revised versio
Quantum-based Distributed Algorithms for Edge Node Placement and Workload Allocation
Edge computing is a promising technology that offers a superior user
experience and enables various innovative Internet of Things applications. In
this paper, we present a mixed-integer linear programming (MILP) model for
optimal edge server placement and workload allocation, which is known to be
NP-hard. To this end, we explore the possibility of addressing this
computationally challenging problem using quantum computing. However, existing
quantum solvers are limited to solving unconstrained binary programming
problems. To overcome this obstacle, we propose a hybrid quantum-classical
solution that decomposes the original problem into a quadratic unconstrained
binary optimization (QUBO) problem and a linear program (LP) subproblem. The
QUBO problem can be solved by a quantum solver, while the LP subproblem can be
solved using traditional LP solvers. Our numerical experiments demonstrate the
practicality of leveraging quantum supremacy to solve complex optimization
problems in edge computing
Weighted bounds for multilinear operators with non-smooth kernels
Let be a multilinear integral operator which is bounded on certain
products of Lebesgue spaces on . We assume that its associated
kernel satisfies some mild regularity condition which is weaker than the usual
H\"older continuity of those in the class of multilinear Calder\'on-Zygmund
singular integral operators. In this paper, given a suitable multiple weight
, we obtain the bound for the weighted norm of multilinear operators
in terms of . As applications, we exploit this result to obtain
the weighted bounds for certain singular integral operators such as linear and
multilinear Fourier multipliers and the Riesz transforms associated to
Schr\"odinger operators on . Our results are new even in the
linear case
Analysis of the expected density of internal equilibria in random evolutionary multi-player multi-strategy games
In this paper, we study the distribution and behaviour of internal equilibria in a d-player n-strategy random evolutionary game where the game payoff matrix is generated from normal distributions. The study of this paper reveals and exploits interesting connections between evolutionary game theory and random polynomial theory. The main contributions of the paper are some qualitative and quantitative results on the expected density, fn,dfn,d, and the expected number, E(n, d), of (stable) internal equilibria. Firstly, we show that in multi-player two-strategy games, they behave asymptotically as √d−1 as d is sufficiently large. Secondly, we prove that they are monotone functions of d. We also make a conjecture for games with more than two strategies. Thirdly, we provide numerical simulations for our analytical results and to support the conjecture. As consequences of our analysis, some qualitative and quantitative results on the distribution of zeros of a random Bernstein polynomial are also obtained
A closed-form solution for free vibration of multiple cracked Timoshenko beam and application
A closed-form solution for free vibration is constructed and used for obtaining explicit frequency equation and mode shapes of  Timoshenko beams with arbitrary number of cracks. The cracks are represented by the rotational springs of stiffness calculated from the crack depth.  Using the obtained frequency equation, the sensitivity of natural frequencies to crack of the beams is examined in comparison with the  Euler-Bernoulli beams. Numerical results demonstrate that the Timoshenko beam theory is efficiently applicable not only for short or fat beams but also for the long or slender ones. Nevertheless, both the theories are equivalent in sensitivity analysis of fundamental frequency to cracks and they get to be different for higher frequencies
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