Related papers: Measuring the interactions among variables of func…
We introduce a class of cooperative games induced by weighted directed graphs. Specifically, the coalitional value combines an internal interaction term given by the induced subgraph game with an external component based on minimal incoming…
Quantifying the similarity between two mathematical structures or datasets constitutes a particularly interesting and useful operation in several theoretical and applied problems. Aimed at this specific objective, the Jaccard index has been…
Quantifying animal interactions is crucial for understanding various ecological processes, including social community structures, predator-prey dynamics, spreading of pathogens and information. Despite the ubiquity of interaction processes…
When it comes to the mathematical modelling of social interaction patterns, a number of different models have emerged and been studied over the last decade, in which individuals randomly interact on the basis of an underlying graph…
Analyzing the relationships among the parameters for quantifying the quality of research published in journals is a challenging task. In this paper, we analyze the relationships between impact factor, h-index, and g-index of a journal. To…
The influence of a variable is an important concept in the analysis of Boolean functions. The more general notion of influence of a set of variables on a Boolean function has four separate definitions in the literature. In the present work,…
In the seminal work [9], several macroscopic market observables have been introduced, in an attempt to find characteristics capturing the diversity of a financial market. Despite the crucial importance of such observables for investment…
Inequality measures are quantitative measures that take values in the unit interval, with a zero value characterizing perfect equality. Although originally proposed to measure economic inequalities, they can be applied to several other…
A multidimensional generalization of the Bernstein class of functions and the properties of functions of the introduced class are examined. In particular, a new proof of the integral representation of Bernstein functions of many variables…
We study high-dimensional sparse estimation under three natural constraints: communication constraints, local privacy constraints, and linear measurements (compressive sensing). Without sparsity assumptions, it has been established that…
Given a system where the real-valued states of the agents are aggregated by a function to a real-valued state of the entire system, we are interested in the influence or importance of the different agents for that function. This generalizes…
An important consideration for variable selection in interaction models is to design an appropriate penalty that respects hierarchy of the importance of the variables. A common theme is to include an interaction term only after the…
Integral properties of multifunctions determined by vector valued functions are presented. Such multifunctions quite often serve as examples and counterexamples. In particular it can be observed that the properties of being integrable in…
Factorization Machine (FM) is a widely used supervised learning approach by effectively modeling of feature interactions. Despite the successful application of FM and its many deep learning variants, treating every feature interaction…
Multiplex graphs, characterised by their layered structure, exhibit informative interdependencies within layers that are crucial for understanding complex network dynamics. Quantifying the interaction and shared information among these…
A new scheme for the computation of dispersive interactions from first principles is presented. This cost-effective approach relies on a Wannier function representation compatible with density function theory descriptions. This is an…
Accurate interaction potentials between microscopic components such as colloidal particles or cells are crucial to understanding a range of processes, including colloidal crystallization, bacterial colony formation, and cancer metastasis.…
Related to an idea of Lewin, a mathematical model for behavioral changes under the influence of a social field is developed. The social field reflects public opinion, social norms and trends. It is not only given by external factors (the…
When data on treatment assignment, outcomes, and covariates from a randomized trial are available, a question of interest is to what extent covariates can be used to optimize treatment decisions. Statistical hypothesis testing of…
A new indicator, a real valued $s$-index, is suggested to characterize a quality and impact of the scientific research output. It is expected to be at least as useful as the notorious $h$-index, at the same time avoiding some its obvious…