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Stability and causality are studied for linear perturbations about equilibrium in Carter's multifluid theory. Our stability analysis is grounded on the requirement that the entropy of the multifluid, plus that of the environment, must be…
Necessary and sufficient conditions for the internal stability of formations whose dynamics are obtained is determined by linear differential equations.
Linear systems governed by continuous-time difference equations cover a wide class of linear systems. From the Lyapunov-Krasovskii approach, we investigate stability for such a class of systems. Sufficient conditions, and in some particular…
This technical report replies to the comments of [2] in detail, and corrects a possible mis-interpretation of [1] in terms of the conventional robust stability concept. After defining the robust stability and quadratic stability concepts,…
We investigate stability of linear delay differential systems. Stability criteria of the systems are derived based on integrals of the fundamental matrix. They are necessary and sufficient conditions for delay-dependent stability of the…
In this work, we have exclusively employed the linear stability analysis at ultra-high boost on two well-known stable-causal theories - second-order MIS and first-order BDNK, to identify the region of parameter space over which they are…
This paper proposes a novel method for determining the number of factors in linear factor models under stability considerations. An instability measure is proposed based on the principal angle between the estimated loading spaces obtained…
We discuss recent work for causal inference and predictive robustness in a unifying way. The key idea relies on a notion of probabilistic invariance or stability: it opens up new insights for formulating causality as a certain risk…
This contribution presents two exponential stability criteria for linear systems with multiple pointwise and distributed delays. These results (necessary and sufficient conditions) are given in terms of the delay Lyapunov matrix and the…
Background: Symbolic models, particularly decision trees, are widely used in software engineering for explainable analytics in defect prediction, configuration tuning, and software quality assessment. Most of these models rely on…
Many methods of estimating causal models do not provide estimates of confidence in the resulting model. In this work, a metric is proposed for validating the output of a causal model fit; the robustness of the model structure with resampled…
Preserving stability is a central problem in data-driven model order reduction of dynamical systems. For linear systems whose dynamics depend on geometric or physical parameters, multivariate rational approximation algorithms such as the…
Classical sufficient conditions for ensuring the robust stability of a dynamical system in feedback with a nonlinearity include passivity, small gain, circle, and conicity theorems. We present a generalized version of these results for…
A brief overview of some open questions in general relativity with important consequences for causality theory is presented, aiming to a better understanding of the causal structure of the spacetime. Special attention is accorded to the…
A criterion on the asymptotic stability of fractional-order systems with incomensurate orders is proposed in this paper. Existing methods always assume order parameters be rational numbers or the ratios of any two orders be rational…
A nonlinear stochastic differential equation with the order of nonlinearity higher than one, with several discrete and distributed delays and time varying coefficients is considered. It is shown that the sufficient conditions for…
We investigate the causality and stability of relativistic dissipative fluid dynamics in the absence of conserved charges. We perform a linear stability analysis in the rest frame of the fluid and find that the equations of relativistic…
We extend the definition of $n$-dimensional difference equations to complex order $\alpha\in \mathbb{C} $. We investigate the stability of linear systems defined by an $n$-dimensional matrix $A$ and derive conditions for the stability of…
A typical problem in causal modeling is the instability of model structure learning, i.e., small changes in finite data can result in completely different optimal models. The present work introduces a novel causal modeling algorithm for…
A necessary and sufficient condition for linear stability of inviscid parallel shear flow is formulated by developing a novel variational principle, where the velocity profile is assumed to be monotonic and analytic. It is shown that…