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In this article, we propose a Lyapunov stability approach to analyze the convergence of the density operator of a quantum system. In analog to the classical probability measure for Markovian processes, we show that the set of invariant…
We introduce a dual-threshold probabilistic knowing value logic for uncertain multi-agent settings. The framework captures within a single formalism both probabilistic-threshold attitudes toward propositions and high-confidence attitudes…
Diagonalization in the spirit of Cantor's diagonal arguments is a widely used tool in theoretical computer sciences to obtain structural results about computational problems and complexity classes by indirect proofs. The Uniform…
We introduce $\textit{Backward Conformal Prediction}$, a method that guarantees conformal coverage while providing flexible control over the size of prediction sets. Unlike standard conformal prediction, which fixes the coverage level and…
We introduce relativistic multi-party biased die rolling protocols, generalizing coin flipping to $M \geq 2$ parties and to $N \geq 2$ outcomes for any chosen outcome biases, and show them unconditionally secure. Our results prove that the…
Variational regularization of ill-posed inverse problems is based on minimizing the sum of a data fidelity term and a regularization term. The balance between them is tuned using a positive regularization parameter, whose automatic choice…
While decomposition of one-parameter persistence modules behaves nicely, as demonstrated by the algebraic stability theorem, decomposition of multiparameter modules is known to be unstable in a certain precise sense. Until now, it has not…
This work studies the threats of adversarial attack on multivariate probabilistic forecasting models and viable defense mechanisms. Our studies discover a new attack pattern that negatively impact the forecasting of a target time series via…
The solution of parameter-dependent linear systems, by classical methods, leads to an arithmetic effort that grows exponentially in the number of parameters. This renders the multigrid method, which has a well understood convergence theory,…
The minimax robust hypothesis testing problem for the case where the nominal probability distributions are subject to both modeling errors and outliers is studied in twofold. First, a robust hypothesis testing scheme based on a relative…
Low-rank matrix recovery problems arise naturally as mathematical formulations of various inverse problems, such as matrix completion, blind deconvolution, and phase retrieval. Over the last two decades, a number of works have rigorously…
As predictive models are increasingly being deployed in high-stakes decision making (e.g., loan approvals), there has been growing interest in post hoc techniques which provide recourse to affected individuals. These techniques generate…
If mutually mistrustful parties A and B control two or more appropriately located sites, special relativity can be used to guarantee that a pair of messages exchanged by A and B are independent. In earlier work, we used this fact to define…
We propose a conservative algorithm to test the geometrical validity of simplicial (triangles, tetrahedra), tensor product (quadrilaterals, hexahedra), and mixed (prisms) elements of arbitrary polynomial order as they deform over a…
Probabilistic separation logic offers an approach to reasoning about imperative probabilistic programs in which a separating conjunction is used as a mechanism for expressing independence properties. Crucial to the effectiveness of the…
Recent work has shown that state-of-the-art classifiers are quite brittle, in the sense that a small adversarial change of an originally with high confidence correctly classified input leads to a wrong classification again with high…
Wyner's soft-covering lemma is a valuable tool for achievability proofs of information theoretic security, resolvability, channel synthesis, and source coding. The result herein sharpens the claim of soft-covering by moving away from an…
In this paper we introduce a new technique, based on dual quaternions, for the analysis of closed linkages with revolute joints: the theory of bonds. The bond structure comprises a lot of information on closed revolute chains with a…
We consider a two-component mixture model with one known component. We develop methods for estimating the mixing proportion and the unknown distribution nonparametrically, given i.i.d.~data from the mixture model, using ideas from shape…
We prove that a topological homeomorphism conjugating two generic 1-parameter unfoldings of 1-variable complex analytic resonant diffeomorphisms is holomorphic or anti-holomorphic by restriction to the unperturbed parameter. We provide…