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A central challenge in the study of complex systems is the quantification of emergence -- understood as the ability of the system to exhibit collective behaviours that cannot be traced down to the individual components. While recent work…
The expectation-maximization (EM) algorithm introduced by Dempster et al in 1977 is a very general method to solve maximum likelihood estimation problems. In this informal report, we review the theory behind EM as well as a number of EM…
We introduce a novel algorithm for the task of coherently controlling a quantum mechanical system to implement any chosen unitary dynamics. It performs faster than existing state of the art methods by one to three orders of magnitude…
While load balancing in distributed-memory computing has been well-studied, we present an innovative approach to this problem: a unified, reduced-order model that combines three key components to describe "work" in a distributed system:…
Both the backpropagation algorithm in machine learning and the maximum principle in optimal control theory are posed as a two-point boundary problem, resulting in a "forward-backward" lock. We derive a reformulation of the maximum principle…
We investigate the existence of solutions of reversible and irreversible port-Hamiltonian systems. To this end, we utilize the associated exergy, a function that is composed of the system's Hamiltonian and entropy, to prove global existence…
Power systems modeling and planning has long leveraged mathematical programming for its ability to provide optimality and feasibility guarantees. One feature that has been recognized in the optimization literature since the 1970s is the…
This article proposes the Ecological Cycle Optimizer (ECO), a novel metaheuristic algorithm inspired by energy flow and material cycling in ecosystems. ECO draws an analogy between the dynamic process of solving optimization problems and…
Rigidity regulates the integrity and function of many physical and biological systems. This is the first of two papers on the origin of rigidity, wherein we propose that "energetic rigidity," in which all non-trivial deformations raise the…
Optimal control and sequential decision making are widely used in many complex tasks. Optimal control over a sequence of natural images is a first step towards understanding the role of vision in control. Here, we formalize this problem as…
This paper presents a framework to tackle constrained combinatorial optimization problems using deep Reinforcement Learning (RL). To this end, we extend the Neural Combinatorial Optimization (NCO) theory in order to deal with constraints in…
The main purpose of this paper is to study the NP-complete subset-sum problem, not in the usual context of time-complexity-based classification of the algorithms (exponential/polynomial), but through a new kind of algorithmic classification…
The kinematics and dynamics of deterministic physical systems have been a foundation of our understanding of the world since Galileo and Newton. For real systems, however, uncertainty is largely present via external forces such as friction…
A system of renewal equations on a graph provides a framework to describe the exploitation of a biological resource. In this context, we formulate an optimal control problem, prove the existence of an optimal control and ensure that the…
Whether a population of decision-making individuals will reach a state of satisfactory decisions is a fundamental problem in studying collective behaviors. In the framework of evolutionary game theory and by means of potential functions,…
Nature is known to be the best optimizer. Natural processes most often than not reach an optimal equilibrium. Scientists have always strived to understand and model such processes.Thus, many algorithms exist today that are inspired by…
Although energy system optimisation based on linear optimisation is often used for influential energy outlooks and studies for political decision-makers, the underlying background still needs to be described in the scientific literature in…
We initiate the systematic study of the energy complexity of algorithms (in addition to time and space complexity) based on Landauer's Principle in physics, which gives a lower bound on the amount of energy a system must dissipate if it…
Recent results by Harrow et. al. and by Ta-Shma, suggest that quantum computers may have an exponential advantage in solving a wealth of linear algebraic problems, over classical algorithms. Building on the quantum intuition of these…
Finding a large set of optima in a multimodal optimization landscape is a challenging task. Classical population-based evolutionary algorithms typically converge only to a single solution. While this can be counteracted by applying niching…