Related papers: Analytical Framework for the Approximate Master Eq…
In the study of dynamics on networks, moment closure is a commonly used method to obtain low-dimensional evolution equations amenable to analysis. The variables in the evolution equations are mean counts of subgraph states and are referred…
We develop the method of stochastic modified equations (SME), in which stochastic gradient algorithms are approximated in the weak sense by continuous-time stochastic differential equations. We exploit the continuous formulation together…
This work introduces a new general approach for the numerical analysis of stable equilibria to second order mean field games systems in cases where the uniqueness of solutions may fail. For the sake of simplicity, we focus on a simple…
In this paper we extend the work of Smith and Papamichail (1999) and present fast approximate Bayesian algorithms for learning in complex scenarios where at any time frame, the relationships between explanatory state space variables can be…
Adaptive voter models (AVMs) are simple mechanistic systems that model the emergence of mesoscopic structure from local networked processes driven by conflict and homophily. AVMs display rich behavior, including a phase transition from a…
In recent years, many design automation methods have been developed to routinely create approximate implementations of circuits and programs that show excellent trade-offs between the quality of output and required resources. This paper…
The framework outlined in [arXiv:2010.13024] provides an approximation algorithm for computing Nash equilibria of normal form games. Since NASH is a well-known PPAD-complete problem, this framework has potential applications to other $PPAD$…
In real-world scenarios, although data entities may possess inherent relationships, the specific graph illustrating their connections might not be directly accessible. Latent graph inference addresses this issue by enabling Graph Neural…
We introduce methods for deriving analytic solutions from differential-algebraic systems of equations (DAEs), as well as methods for deriving governing equations for analytic characterization which is currently limited to very small systems…
The analysis on stability and bifurcations in the macroscopic dynamics exhibited by the system of two coupled large populations comprised of $N$ stochastic excitable units each is performed by studying an approximate system, obtained by…
Mean field games (MFGs) offer a powerful framework for modeling large-scale multi-agent systems. This paper addresses MFGs formulated in continuous time with discrete state spaces, where agents' dynamics are governed by continuous-time…
We consider classical spin systems evolving in continuous time with interactions given by a locally tree-like graph. Several approximate analysis methods have earlier been reported based on the idea of Belief Propagation / cavity method. We…
This paper presents extensions of finite-time stability results to some prototypical adaptive control and estimation frameworks. First, we present a novel scheme of online parameter estimation that guarantees convergence of the estimation…
Approximate message passing (AMP) type algorithms have been widely used in the signal reconstruction of certain large random linear systems. A key feature of the AMP-type algorithms is that their dynamics can be correctly described by state…
Evolutionary game theory is a framework to formalize the evolution of collectives ("populations") of competing agents that are playing a game and, after every round, update their strategies to maximize individual payoffs. There are two…
We introduce auxiliary quantum master equation - dual fermion approach (QME-DF) and argue that it presents a convenient way to describe steady-states of correlated impurity systems. The combined scheme yields an expansion around a reference…
Approximate Message Passing (AMP) has been shown to be a superior method for inference problems, such as the recovery of signals from sets of noisy, lower-dimensionality measurements, both in terms of reconstruction accuracy and in…
We introduce a theoretical approach for designing generalizations of the approximate message passing (AMP) algorithm for compressed sensing which are valid for large observation matrices that are drawn from an invariant random matrix…
We present a novel approach for designing complex approximate arithmetic circuits that trade correctness for power consumption and play important role in many energy-aware applications. Our approach integrates in a unique way formal methods…
Given a locally consistent set of reduced density matrices, we construct approximate density matrices which are globally consistent with the local density matrices we started from when the trial density matrix has a tree structure. We…