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Using the Robertson projection operator formalism, we derive generalized Bloch equations which describe the dynamics of a biased two-level tunneling system strongly driven by an external field and weakly coupled to a super-Ohmic heat bath.…

Condensed Matter · Physics 2008-12-18 Peter Neu , Jochen Rau

A collection of $n$ random events is said to be $(n - 1)$-wise independent if any $n - 1$ events among them are mutually independent. We characterise all probability measures with respect to which $n$ random events are $(n - 1)$-wise…

Probability · Mathematics 2022-11-04 Karthik Natarajan , Arjun Kodagehalli Ramachandra , Colin Tan

In counting experiments, one can set an upper limit on the rate of a Poisson process based on a count of the number of events observed due to the process. In some experiments, one makes several counts of the number of events, using…

Data Analysis, Statistics and Probability · Physics 2014-11-20 Patrick J. Sutton

We consider linear programming (LP) problems in infinite dimensional spaces that are in general computationally intractable. Under suitable assumptions, we develop an approximation bridge from the infinite-dimensional LP to tractable finite…

Optimization and Control · Mathematics 2017-02-22 Peyman Mohajerin Esfahani , Tobias Sutter , Daniel Kuhn , John Lygeros

We study the Borel complexity of sets of normal numbers in several numeration systems. Taking a dynamical point of view, we offer a unified treatment for continued fraction expansions and base $r$ expansions, and their various…

Dynamical Systems · Mathematics 2020-01-17 Dylan Airey , Steve Jackson , Dominik Kwietniak , Bill Mance

We study the problem of probabilistic deduction with conditional constraints over basic events. We show that globally complete probabilistic deduction with conditional constraints over basic events is NP-hard. We then concentrate on the…

Artificial Intelligence · Computer Science 2011-05-30 T. Lukasiewicz

In decision-making problems under uncertainty, probabilistic constraints are a valuable tool to express safety of decisions. They result from taking the probability measure of a given set of random inequalities depending on the decision…

Optimization and Control · Mathematics 2021-02-09 Yassine Laguel , Wim van Ackooij , Jérôme Malick , Guilherme Ramalho

This paper presents a deterministic algorithmic approach of exploring the solution space of the Subset Sum Problem. The algorithm presented is input-robust and structurally adaptive. Exploration is guided and narrows into areas in the…

Computational Complexity · Computer Science 2025-06-19 Thami Nkosi

We extend Fano's inequality, which controls the average probability of events in terms of the average of some $f$--divergences, to work with arbitrary events (not necessarily forming a partition) and even with arbitrary $[0,1]$--valued…

Statistics Theory · Mathematics 2019-06-12 Sebastien Gerchinovitz , Pierre Ménard , Gilles Stoltz

We consider the problem of determining feasible systems from a finite set of simulated alternatives with respect to probability constraints, where the observations from stochastic simulations are Bernoulli distributed. Most statistically…

Optimization and Control · Mathematics 2026-05-27 Taehoon Kim , Sigrun Andradottir , Seong-Hee Kim , Yuwei Zhou

We describe an abstract control-theoretic framework in which the validity of the dynamic programming principle can be established in continuous time by a verification of a small number of structural properties. As an application we treat…

Optimization and Control · Mathematics 2014-03-18 Gordan Zitkovic

We enable aProbLog---a probabilistic logical programming approach---to reason in presence of uncertain probabilities represented as Beta-distributed random variables. We achieve the same performance of state-of-the-art algorithms for highly…

Artificial Intelligence · Computer Science 2018-11-16 Federico Cerutti , Lance Kaplan , Angelika Kimmig , Murat Sensoy

In real-life temporal scenarios, uncertainty and preferences are often essential and coexisting aspects. We present a formalism where quantitative temporal constraints with both preferences and uncertainty can be defined. We show how three…

Artificial Intelligence · Computer Science 2021-04-12 F. Rossi , K. B. Venable , N. Yorke-Smith

We give the proof of a tight lower bound on the probability that a binomial random variable exceeds its expected value. The inequality plays an important role in a variety of contexts, including the analysis of relative deviation bounds in…

Machine Learning · Computer Science 2013-11-12 Spencer Greenberg , Mehryar Mohri

While useful probability bounds for $n$ pairwise independent Bernoulli random variables adding up to at least an integer $k$ have been proposed in the literature, none of these bounds are tight in general. In this paper, we provide several…

Optimization and Control · Mathematics 2022-11-24 Arjun Ramachandra , Karthik Natarajan

This paper deals with (finite or infinite) sequences of arbitrary independent events in some probability space. We find sharp lower bounds for the probability of a union of such events when the sum of their probabilities is given. The…

Probability · Mathematics 2016-09-29 Jürgen Grahl , Shahar Nevo

In this paper, we develop efficient randomized algorithms for estimating probabilistic robustness margin and constructing robustness degradation curve for uncertain dynamic systems. One remarkable feature of these algorithms is their…

Optimization and Control · Mathematics 2008-05-13 Xinjia Chen , Kemin Zhou , Jorge L. Aravena

We derive new upper and lower bounds for probabilities that $r$ or at least $r$ from $n$ events occur. These bounds can turn to equalities. The method is discussed as well. It works for measurable space and measures with sign, too. We also…

Probability · Mathematics 2020-08-12 Andrei N. Frolov

In this paper, starting from a generalized coherent (i.e. avoiding uniform loss) intervalvalued probability assessment on a finite family of conditional events, we construct conditional probabilities with quasi additive classes of…

Artificial Intelligence · Computer Science 2012-10-19 Giuseppe Sanfilippo

Mixture distributions provide a versatile and widely used framework for modeling random phenomena, and are particularly well-suited to the analysis of geoscientific processes and their attendant risks to society. For continuous mixtures of…

Machine Learning · Statistics 2025-06-18 Michael R. Powers , Jiaxin Xu