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Continuous integration of renewable energy sources into power networks is causing a paradigm shift in energy generation and distribution with regards to trading and control; the intermittent nature of renewable sources affects pricing of…

We review Boltzmann machines and energy-based models. A Boltzmann machine defines a probability distribution over binary-valued patterns. One can learn parameters of a Boltzmann machine via gradient based approaches in a way that log…

In this paper, we present an algorithm which lies in the domain of task allocation for a set of static autonomous radars with rotating antennas. It allows a set of radars to allocate in a fully decentralized way a set of active tracking…

The Boltzmann distribution is one of the key equations of thermal physics and is widely used in machine learning as well. Here I derive a Boltzmann distribution in a simple pedagogical example using only tools from a first-year probability…

This study shows that the generalized Boltzmann distribution is the only distribution mathematically consistent with thermodynamics when the system is described by an ensemble of a certain mathematical form. This mathematical form is very…

Traditional regulatory methods for spectrum licensing have been recently identified as one of the causes for the under-utilization of the valuable radio spectrum. Governmental agencies such as the Federal Communications Commission (FCC) are…

We define a message-passing algorithm for computing magnetizations in Restricted Boltzmann machines, which are Ising models on bipartite graphs introduced as neural network models for probability distributions over spin configurations. To…

The generation of equilibrium samples of molecular systems has been a long-standing problem in statistical physics. Boltzmann Generators are a generative machine learning method that addresses this issue by learning a transformation via a…

For a plasma with fixed total energy, number of particles, and momentum, the distribution function that maximizes entropy is a Boltzmann distribution. If, in addition, the rearrangement of charge is constrained, as happens on ion-ion…

We provide a theoretical framework to examine how carbon pricing policies influence inflation and to estimate the policy-driven impact on goods prices from achieving net-zero emissions. Firms control emissions by adjusting production,…

We propose a general stochastic framework for modelling repeated auctions in the Real Time Bidding (RTB) ecosystem using point processes. The flexibility of the framework allows a variety of auction scenarios including configuration of…

Managing and unlocking the flexibility hidden in electric vehicles (EVs) has emerged as a critical yet challenging task towards low-carbon power and energy systems. This paper focuses on the online bidding and dispatch strategies for an EV…

We construct a theoretical model for equilibrium distribution of workers across sectors with different labor productivity, assuming that a sector can accommodate a limited number of workers which depends only on its productivity. A general…

The international trade is one of the classic areas of study in economics. Nowadays, given the availability of data, the tools used for the analysis can be complemented and enriched with new methodologies and techniques that go beyond the…

Achieving net-zero carbon emissions requires a transformation of energy systems, industrial processes, and consumption patterns. In particular, a transition towards that goal involves a gradual reduction of excess carbon emissions that are…

The implementation of electricity markets based on locational marginal pricing in a multi-settlement process has allowed wholesale competition, with pricing mechanisms that incentivize the optimal allocation of generation, transmission, and…

Coin selection refers to the problem of choosing a set of tokens to fund a transaction in token-based payment systems such as, e.g., cryptocurrencies or central bank digital currencies (CBDCs). In this paper, we propose the Boltzmann Draw…

We study the problem of designing a two-sided market (double auction) to maximize the gains from trade (social welfare) under the constraints of (dominant-strategy) incentive compatibility and budget-balance. Our goal is to do so for an…

A universal and rigorous ensemble framework for nonequilibrium system remains lacking. Here, we provide a concise framework for the generalized ensemble theory of nonequilibrium discrete systems using matrix-based approach. By introducing…

The deployment of distributed energy resources, combined with a more proactive demand side, is inducing a new paradigm in power system operation and electricity markets. Within a consumer-centric market framework, peer-to-peer approaches…