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We propose a new framework that unifies different fairness measures into a general, parameterized class of convex fairness measures suitable for optimization contexts. First, we propose a new class of order-based fairness measures, discuss…
We make use of the previously developed formalism for a monomer ensemble and include angular dependence of the segments of the polymer chains thus described. In particular we show how to deal with stiffness when the polymer chain is…
For linear multivariate purely second order highla degenerated parabolic equations with univariate convex data, monotonicity of the coefficent matrices implies monotonicity of the related value functions under usual regularity and growth…
In structured system theory, a pattern matrix is a matrix with entries either fixed to zero or free to take arbitrary numbers. The (generic) rank of a pattern matrix is the rank of almost all its realizations. The resilience of various…
We study the notion of structured realizability for linear systems defined over graphs. A stabilizable and detectable realization is structured if the state-space matrices inherit the sparsity pattern of the adjacency matrix of the…
A method is suggested for treating those complicated physical problems for which exact solutions are not known but a few approximation terms of a calculational algorithm can be derived. The method permits one to answer the following rather…
Matrix regression plays an important role in modern data analysis due to its ability to handle complex relationships involving both matrix and vector variables. We propose a class of regularized regression models capable of predicting both…
In many matching markets--such as athlete recruitment or academic admissions--participants on one side are evaluated by attribute vectors known to the other side, which in turn applies individual \emph{salience vectors} to assign relative…
The goal of the present paper is to derive some conditions on saturation of (strong) subadditivity inequality for the stochastic matrices. The notion of relative entropy of stochastic matrices is introduced by mimicking quantum relative…
We introduce a novel kind of robustness in linear programming. A solution x* is called robust optimal if for all realizations of objective functions coefficients and constraint matrix entries from given interval domains there are…
The generic linear evolution of the density matrix of a system with a finite-dimensional state space is by stochastic maps which take a density matrix linearly into the set of density matrices. These dynamical stochastic maps form a linear…
We study the robustness of system estimation to parametric perturbations in system dynamics and initial conditions. We define the problem of sensitivity-based parametric uncertainty quantification in dynamical system estimation. The main…
Conventional approaches to grasp planning require perfect knowledge of an object's pose and geometry. Uncertainties in these quantities induce uncertainties in the quality of planned grasps, which can lead to failure. Classically, grasp…
We revisit a model of semiflexible Gaussian chains proposed by Winkler \textit{et al}, solve the dynamics of the discrete description of the model and derive exact algebraic expressions for some of the most relevant dynamical observables,…
This paper draws distinctions among various concepts related to tipping points, robustness, path dependence, and other properties of system dynamics. For each concept a formal definition is provided that utilizes Markov model…
We consider a class of matrices with a specific structure that arises, among other examples, in dynamic models for biological regulation of enzyme synthesis (Tyson and Othmer, 1978). We first show that a stability condition given in (Tyson…
The notion of a (metric) modular on an arbitrary set and the corresponding modular space, more general than a metric space, were introduced and studied recently by the author [V. V. Chistyakov, Metric modulars and their application, Dokl.…
The coordination modelling language Paradigm addresses collaboration between components in terms of dynamic constraints. Within a Paradigm model, component dynamics are consistently specified at a detailed and a global level of abstraction.…
Continuum parallel robots (CPR) combine rigid actuation mechanisms with multiple elastic rods in a closed-loop topology, making forward statics challenging when rigid--continuum junctions are enforced by explicit kinematic constraints. Such…
New lattice model for the gradient elasticity is suggested. This lattice model gives a microstructural basis for second-order strain-gradient elasticity of continuum that is described by the linear elastic constitutive relation with the…