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The problem of mismatched guesswork considers the additional cost incurred by using a guessing function which is optimal for a distribution $q$ when the random variable to be guessed is actually distributed according to a different…
Ladder tournaments are widely used to rank individuals in real-world organizations and games. Their mathematical properties however are still poorly understood. We formalize the ranking rule generated by a ladder tournament, and we show…
Geometrical distance is an important constraining factor underpinning the emergence of social and economic interactions of complex systems. Yet, agent-based studies supported by granular analysis of distances are limited. Here, we develop a…
The law of total probability may be deployed in binary classification exercises to estimate the unconditional class probabilities if the class proportions in the training set are not representative of the population class proportions. We…
Various aspects of recent sociophysics research are shortly reviewed: Schelling model as an example for lack of interdisciplinary cooperation, opinion dynamics, combat, and citation statistics as an example for strong interdisciplinarity.
The label ranking problem is a supervised learning scenario in which the learner predicts a total order of the class labels for a given input instance. Recently, research has increasingly focused on the partial label ranking problem, a…
Accurate modeling of opinion dynamics has the potential to help us understand polarization and what makes effective political discourse possible or impossible. Here, we use physics-based methods to model the evolution of political opinions…
In recent years, model collapse has become a critical issue in language model training, making it essential to understand the underlying mechanisms driving this phenomenon. In this paper, we investigate recursive parametric model training…
Using theory and experiments, this paper shows that the difficulty of making tradeoffs offers a parsimonious explanation for a wide range of behavioral phenomena. We develop a model of imprecise comparisons applicable to multiattribute,…
We show that the rare events present in dissipated work that enters Jarzynski equality, when mapped appropriately to the phenomenon of large deviations found in a biased coin toss, are enough to yield a quantitative work probability…
The matching problem and the distribution law of Galton boards with interactions are studied in this paper. The general matching problem appeals at many scenarios, such as the reaction rate of molecules and the hailing rate of ride-hailing…
The conventional economic approaches explore very little about the dynamics of the economic systems. Since such systems consist of a large number of agents interacting nonlinearly they exhibit the properties of a complex system. Therefore…
We study the role of correlation in matching markets, where multiple decision-makers simultaneously face selection problems from the same pool of candidates. We propose a model in which a candidate's priority scores across different…
We study a stochastic model of collective motion in which individuals update their orientation through pairwise aligning or anti-aligning copying interactions. We analyze both annealed dynamics, where interaction types are chosen…
Spin models of markets inspired by physics models of magnetism, as the Ising model, allow for the study of the collective dynamics of interacting agents in a market. The number of possible states has been mostly limited to two (buy or sell)…
Statistical thermodynamics delivers the probability distribution of the equilibrium state of matter through the constrained maximization of a special functional, entropy. Its elegance and enormous success have led to numerous attempts to…
I review few conceptual steps in analytic description of topological interactions, which constitute the basis of a new interdisciplinary branch in mathematical physics, "Statistical Topology", emerged at the edge of topology and statistical…
We investigate the general problem of how to model the kinematics of stock prices without considering the dynamical causes of motion. We propose a stochastic process with long-range correlated absolute returns. We find that the model is…
We consider a random matrix model with both pairwise and non-pairwise contracted indices. The partition function of the matrix model is similar to that appearing in some replicated systems with random tensor couplings, such as the p-spin…
Multivariate Distributions are needed to capture the correlation structure of complex systems. In previous works, we developed a Random Matrix Model for such correlated multivariate joint probability density functions that accounts for the…