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The purpose of this paper is to investigate fixed point arithmetic
in ring-based Somewhat Homomorphic Encryption (SHE) schemes.
We provide three main contributions: Firstly, we investigate the repre...
On the Complexity of 2D Discrete Fixed Point Problem
Complexity 2D Discrete Fixed Point Problem
2012/12/3
While the 3-dimensional analogue of Sperner’s problem in the plane was known to be complete in class PPAD, the complexity of 2D-SPERNER itself is not known to be PPAD-complete or not. In this paper, w...
Quantum Separation of Local Search and Fixed Point Computation
Quantum query complexity Fixed-point computation Local search Sperner’s lemma Quantum adversary method
2012/12/4
We give a lower bound of (n(d−1)/2) on the quantum query complexity for finding a fixed point of a discrete Brouwer function over grid [n]d. Our lower
bound is nearly tight, as Grover Search c...
Quadratic BSDEs with Jumps and Related Non-linear Expectations: a Fixed-point Approach
BSDEs quadratic growth jumps non-linear Doob-Meyer decomposition dy-namical risk measures inf-convolution.
2012/9/17
We prove the existence of bounded solutions of quadratic backward SDEs with jumps, using a direct fixed point approach as in Tevzadze [35]. Under an additional standard assumption, we prove a uniquene...
A Brouwer fixed point theorem for graph endomorphisms
Graph theory graph endormorphisms Lefschetz number Euler characteristic Brouwer fixed point Dynamical zeta function
2012/6/21
We prove a Lefschetz formula for general simple graphs which equates the Lefschetz number L(T) of an endomorphism T with the sum of the degrees i(x) of simplices in G which are fixed by T. The degree ...
Symplectic 4-manifolds with fixed point free circle actions
Symplectic 4-manifolds point free circle actions Geometric Topology
2012/6/19
We show that recent results of Friedl-Vidussi and Chen imply that a symplectic manifold admits a fixed point free circle action if and only if it admits a symplectic circle action and we give a comple...
Modified van der Pauw method based on formulas solvable by the Banach fixed point method
van der Pauw method sheet resistance Banach fixed point method cross ratio
2012/4/19
We propose a modification of the standard van der Pauw method for determining the resistivity and Hall coefficient of flat thin samples of arbitrary shape. Considering a different choice of resistance...
Distributional fixed point equations for island nucleation in one dimension: a retrospective approach for capture zone scaling
Gap size distribution capture zone distribution
2012/2/27
The distribution of the capture zones of point islands nucleated in one dimension are considered using a retrospective view, providing an alternative perspective on why scaling occurs in this continuo...
Existence of a Lorenz renormalization fixed point of an arbitrary critical order
Lorenz renormalization fixed point arbitrary critical order Dynamical Systems
2011/9/19
Abstract: We present a proof of the existence of a renormalization fixed point for Lorenz maps of the simplest non-unimodal combinatorial type ({0,1},{1,0,0}), and with a critical point of arbitrary o...
Rare event simulation for processes generated via stochastic fixed point equations
Monte Carlo methods importance sampling perpetuities
2011/7/19
In a number of applications, particularly in financial and actuarial mathematics, it is of interest to characterize the tail distribution of a random variable V satisfying the distributional equation ...
Rare event simulation for processes generated via stochastic fixed point equations
Monte Carlo methods importance sampling perpetuities large deviations nonlinear renewal theory Harris recurrent Markov chains
2011/9/13
Abstract: In a number of applications, particularly in financial and actuarial mathematics, it is of interest to characterize the tail distribution of a random variable V satisfying the distributional...
Finite-dimensional vertex algebra modules over fixed point commutative subalgebras
vertex algebra Galois extension commutative algebra
2011/1/18
Let A be a connected commutative C-algebra with derivation D,G a finite linear automorphism group of A which preserves D, and R = AG the fixed point subalgebra of A under the action of G. We show that...
Andr´es Navas asked us if there is a fixed point theorem for all isometries of L1 that preserve a given bounded set. Unlike many known cases where a geometric argument applies, there is a fundam...
Fixed-Point Approaches to Computing Bertrand-Nash Equilibrium Prices Under Mixed Logit Demand: A Technical Framework for Analysis and Efficient Computational Methods
Mixed Logit Demand Technical Framework Analysis Efficient Computational Methods
2011/2/28
Bertrand competiton has been a prominent paradigm for the empirical study of differentiated
product markets for at least twenty years. Firms engaged in Bertrand competition maximize profits by choosi...
The aim of this paper is to obtain fixed point theorems for hybrid pairs of single valued and multivalued mappings satisfying a contractive condition of integral type in general settings. Several well...