Related papers: Play time with determinants
We study games with finitely many participants, each having finitely many choices. We consider the following categories of participants: (I) populations: sets of nonatomic agents, (II) atomic splittable players, (III) atomic non splittable…
According to the dominant view, time in perceptual decision making is used for integrating new sensory evidence. Based on a probabilistic framework, we investigated the alternative hypothesis that time is used for gradually refining an…
We derive identities for the determinants of matrices whose entries are (rising) powers of (products of) polynomials that satisfy a recurrence relation. In particular, these results cover the cases for Fibonacci polynomials, Lucas…
The estimation of causal effects using quasiexperiments often relies on the use of unusual or serendipitous sources of exogenous variation. When the goal is estimating the same causal effects across many different settings, the same unusual…
By embedding uncertainty into time, we obtain a conjoint axiomatic characterization of both Exponential Discounting and Subjective Expected Utility that accommodates arbitrary state and outcome spaces. In doing so, we provide a novel and…
We prove two determinacy and decidability results about two-players stochastic reachability games with partial observation on both sides and finitely many states, signals and actions.
We study well-constrained bilinear algebraic systems in order to formulate their discriminant. We derive a new determinantal formula for the discriminant of a multilinear system that appears in the study of Nash equilibria of multiplayer…
This paper surveys main and recent studies on temporal logics in a broad sense by presenting various logic systems, dealing with various time structures, and discussing important features, such as decidability (or undecidability) results,…
We give new definitions for the determinant over commutative ring $K$, noncommutative ring $\mathbf{K}$, noncommutative ring $\mathcal{K}$ with associative powers, over noncommutative nonassociative ring $\mathfrak{K}$, and study their…
Determinantal point processes have arisen in diverse settings in recent years and have been investigated intensively. We study basic combinatorial and probabilistic aspects in the discrete case. Our main results concern relationships with…
An expository introduction to bidding chess and other bidding games. To appear in Mathematical Intelligencer.
Eliciting informative prior distributions for Bayesian inference can often be complex and challenging. While popular methods rely on asking experts probability based questions to quantify uncertainty, these methods are not without their…
The instrumental variable method is widely used in the health and social sciences for identification and estimation of causal effects in the presence of potentially unmeasured confounding. In order to improve efficiency, multiple…
We attempt to make superdeterminism more intuitive, notably by simulating a deterministic model system, a billiard game. In this system an initial 'bang' correlates all events, just as in the superdeterministic universe. We introduce the…
Preference elicitation plays a central role in interactive recommender systems. Most preference elicitation approaches use either item queries that ask users to select preferred items from a slate, or attribute queries that ask them to…
We introduce deterministic concurrent systems as a subclass of concurrent systems. Deterministic concurrent system are "locally commutative" concurrent systems. We prove that irreducible and deterministic concurrent systems have a unique…
To be usable in practice, interactive theorem provers need to provide convenient and efficient means of writing expressions, definitions, and proofs. This involves inferring information that is often left implicit in an ordinary…
We consider the set of $n\times n$ matrices with rational entries having numerator and denominator of size at most $H$ and obtain upper and lower bounds on the number of such matrices of a given rank and then apply them to count such…
We investigate the expressive power of a Turing-complete logic based on game-theoretic semantics. By defining suitable fragments and variants of the logic, we obtain a range of natural characterizations for some fundamental families of…
This dissertation introduces executable refinement types, which refine structural types by semi-decidable predicates, and establishes their metatheory and accompanying implementation techniques. These results are useful for undecidable type…