2,938 research outputs found
Spontaneous Breaking of Scale Invariance in a d=3 U(N) Model with Chern-Simons Gauge Field
We study spontaneous breaking of scale invariance in the large N limit of
three dimensional Chern-Simons theories coupled to a scalar field
in the fundamental representation. When a
self interaction term is added to the action we find a massive phase at a
certain critical value for a combination of the and 't Hooft's
couplings. This model attracted recent attention since at
finite it contains a singlet sector which is conjectured to be dual to
Vasiliev's higher spin gravity on . Our paper concentrates on the
massive phase of the 3d boundary theory. We discuss the advantage of
introducing masses in the boundary theory through spontaneous breaking of scale
invariance.Comment: 23 pages, 8 figures. several lines changed in the introduction. typos
correcte
A Hydraulic Approach to Equilibria of Resource Selection Games
Drawing intuition from a (physical) hydraulic system, we present a novel
framework, constructively showing the existence of a strong Nash equilibrium in
resource selection games (i.e., asymmetric singleton congestion games) with
nonatomic players, the coincidence of strong equilibria and Nash equilibria in
such games, and the uniqueness of the cost of each given resource across all
Nash equilibria. Our proofs allow for explicit calculation of Nash equilibrium
and for explicit and direct calculation of the resulting (unique) costs of
resources, and do not hinge on any fixed-point theorem, on the Minimax theorem
or any equivalent result, on linear programming, or on the existence of a
potential (though our analysis does provide powerful insights into the
potential, via a natural concrete physical interpretation). A generalization of
resource selection games, called resource selection games with I.D.-dependent
weighting, is defined, and the results are extended to this family, showing the
existence of strong equilibria, and showing that while resource costs are no
longer unique across Nash equilibria in games of this family, they are
nonetheless unique across all strong Nash equilibria, drawing a novel
fundamental connection between group deviation and I.D.-congestion. A natural
application of the resulting machinery to a large class of
constraint-satisfaction problems is also described.Comment: Hebrew University of Jerusalem Center for the Study of Rationality
discussion paper 67
Stable subnorms revisited
Let A be a finite-dimensional, power-associative algebra over a field F, either R or C, and let S, a subset of A, be closed under scalar multiplication. A real-valued function f defined on S, shall be called a subnorm if f(a) > 0 for all 0 not equal a is an element of S, and f(alpha a) = |alpha| f(a) for all a is an element of S and alpha is an element of F. If in addition, S is closed under raising to powers, then a subnorm f shall be called stable if there exists a constant sigma > 0 so that f(a(m)) less than or equal to sigma f(a)(m) for all a is an element of S and m = 1, 2, 3....
The purpose of this paper is to provide an updated account of our study of stable subnorms on subsets of finite-dimensional, power-associative algebras over F. Our goal is to review and extend several of our results in two previous papers, dealing mostly with continuous subnorms on closed sets
Valuation and hedging of the ruin-contingent life annuity (RCLA)
This paper analyzes a novel type of mortality contingent-claim called a
ruin-contingent life annuity (RCLA). This product fuses together a
path-dependent equity put option with a "personal longevity" call option. The
annuitant's (i.e. long position) payoff from a generic RCLA is \$1 of income
per year for life, akin to a defined benefit pension, but deferred until a
pre-specified financial diffusion process hits zero. We derive the PDE and
relevant boundary conditions satisfied by the RCLA value (i.e. the hedging
cost) assuming a complete market where No Arbitrage is possible. We then
describe some efficient numerical techniques and provide estimates of a typical
RCLA under a variety of realistic parameters.
The motivation for studying the RCLA on a stand-alone basis is two-fold.
First, it is implicitly embedded in approximately \$1 trillion worth of U.S.
variable annuity (VA) policies; which have recently attracted scrutiny from
financial analysts and regulators. Second, the U.S. administration - both
Treasury and Department of Labor - have been encouraging Defined Contribution
(401k) plans to offer stand-alone longevity insurance to participants, and we
believe the RCLA would be an ideal and cost effective candidate for that job
A Simple Cellular Automation that Solves the Density and Ordering Problems
Cellular automata (CA) are discrete, dynamical systems that perform computations
in a distributed fashion on a spatially extended grid. The dynamical behavior
of a CA may give rise to emergent computation, referring to the appearance of
global information processing capabilities that are not explicitly represented in the
system's elementary components nor in their local interconnections.1 As such, CAs
o?er an austere yet versatile model for studying natural phenomena, as well as a
powerful paradigm for attaining ?ne-grained, massively parallel computation.
An example of such emergent computation is to use a CA to determine the
global density of bits in an initial state con?guration. This problem, known as
density classi?cation, has been studied quite intensively over the past few years. In
this short communication we describe two previous versions of the problem along with their CA solutions, and then go on to show that there exists yet a third version
| which admits a simple solution
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