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The roulette wheel selection is a critical process in heuristic algorithms, enabling the probabilistic choice of items based on assigned fitness values. It selects an item with a probability proportional to its fitness value. This technique…
Boltzmann sampling is commonly used to uniformly sample objects of a particular size from large combinatorial sets. For this technique to be effective, one needs to prove that (1) the sampling procedure is efficient and (2) objects of the…
Many cryptocurrency brokers nowadays offer a variety of derivative assets that allow traders to perform hedging or speculation. This paper proposes an effective algorithm based on neural networks to take advantage of these investment…
Cryptocurrencies come with a variety of tokenomic policies as well as aspirations of desirable monetary characteristics that have been described by proponents as 'sound money' or even 'ultra sound money.' These propositions are typically…
The Coupon Collector Problem (CCP) is a well-known combinatorial problem that seeks to estimate the number of random draws required to complete a collection of $n$ distinct coupon types. Various generalizations of this problem have been…
The Boltzmann model for the random generation of "decomposable" combinatorial structures is a set of techniques that allows for efficient random sampling algorithms for a large class of families of discrete objects. The usual requirement of…
In this article, we study a notion of the extraction rate of Turing functionals that translate between notions of randomness with respect to different underlying probability measures. We analyze several classes of extraction procedures: a…
Though voting-based consensus algorithms in Blockchain outperform proof-based ones in energy- and transaction-efficiency, they are prone to incur wrong elections and bribery elections. The former originates from the uncertainties of…
In this paper, we consider a novel two-dimensional randomized Kaczmarz method and its improved version with simple random sampling, which chooses two active rows with probability proportional to the square of their cross-product-like…
We present the Boltzmann classifier, a novel distance based probabilistic classification algorithm inspired by the Boltzmann distribution. Unlike traditional classifiers that produce hard decisions or uncalibrated probabilities, the…
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…
The Kaczmarz method is an iterative algorithm for solving systems of linear equalities and inequalities, that iteratively projects onto these constraints. Recently, Strohmer and Vershynin [J. Fourier Anal. Appl., 15(2):262-278, 2009] gave a…
Common models for random graphs, such as Erd\H{o}s-R\'{e}nyi and Kronecker graphs, correspond to generating random adjacency matrices where each entry is non-zero based on a large matrix of probabilities. Generating an instance of a random…
Self-interested behavior in sharing economies often leads to inefficient aggregate outcomes compared to a centrally coordinated allocation, ultimately harming users. Yet, centralized coordination removes individual decision power. This…
Many-body dynamical models in which Boltzmann statistics can be derived directly from the underlying dynamical laws without invoking the fundamental postulates of statistical mechanics are scarce. Interestingly, one such model is found in…
The change-making problem consists of representing a certain amount of money with the least possible number of coins, from a given, pre-established set of denominations. The greedy algorithm works by choosing the coins of largest possible…
Normalizing flows are a popular class of models for approximating probability distributions. However, their invertible nature limits their ability to model target distributions whose support have a complex topological structure, such as…
Randomisation is a critical tool in designing distributed systems. The common coin primitive, enabling the system members to agree on an unpredictable random number, has proven to be particularly useful. We observe, however, that it is…
With the technology development, the need of analyze and extraction of useful information is increasing. Bayesian networks contain knowledge from data and experts that could be used for decision making processes But they are not easily…
Most online lotteries today fail to ensure the verifiability of the random process and rely on a trusted third party. This issue has received little attention since the emergence of distributed protocols like Bitcoin that demonstrated the…