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This paper is a contribution to the theoretical foundations of strategies. We first present a general definition of abstract strategies which is extensional in the sense that a strategy is defined explicitly as a set of derivations of an…

The behavior of certain weighted Hardy-type operators on rearrangement-invariant function spaces is thoroughly studied with emphasis being put on the optimality of the obtained results. First, the optimal rearrangement-invariant function…

We present a spectral analysis for matrix scaling and operator scaling. We prove that if the input matrix or operator has a spectral gap, then a natural gradient flow has linear convergence. This implies that a simple gradient descent…

Syntactic dependency parsing is an important task in natural language processing. Unsupervised dependency parsing aims to learn a dependency parser from sentences that have no annotation of their correct parse trees. Despite its difficulty,…

Assessing variability according to distinct factors in data is a fundamental technique of statistics. The method commonly regarded to as analysis of variance (ANOVA) is, however, typically confined to the case where all levels of a factor…

This paper considers the problem of learning, from samples, the dependency structure of a system of linear stochastic differential equations, when some of the variables are latent. In particular, we observe the time evolution of some…

We discuss Bayesian model uncertainty analysis and forecasting in sequential dynamic modeling of multivariate time series. The perspective is that of a decision-maker with a specific forecasting objective that guides thinking about relevant…

This paper continues the study of [11, 13] for stationary solutions of stochastic linear retarded functional differential equations with the emphasis on delays which appear in those terms including spatial partial derivatives. As a…

Recurrence equations have played a central role in static cost analysis, where they can be viewed as abstractions of programs and used to infer resource usage information without actually running the programs with concrete data. Such…

Timed systems, such as timed automata, are usually analyzed using their operational semantics on timed words. The classical region abstraction for timed automata reduces them to (untimed) finite state automata with the same time-abstract…

In many stochastic models, the observables of interest are naturally encoded in double transforms (e.g., Laplace transforms) that couple spatial and temporal variables. Notably, the double transform often provides the only analytically…

Various linearizations have been proposed to cast syntactic dependency parsing as sequence labeling. However, these approaches do not support more complex graph-based representations, such as semantic dependencies or enhanced universal…

Adaptive robust optimization (ARO) extends static robust optimization by allowing decisions to depend on the realized uncertainty - weakly dominating static solutions within the modeled uncertainty set. However, ARO makes previous…

This paper derives for non-linear, time-varying and feedback linearizable systems simple controller designs to achieve specified state-and timedependent complex convergence rates. This approach can be regarded as a general gain-scheduling…

This paper presents a mathematics-informed approach to neural operator design, building upon the theoretical framework established in our prior work. By integrating rigorous mathematical analysis with practical design strategies, we aim to…

Strictness analysis is critical to efficient implementation of languages with non-strict evaluation, mitigating much of the performance overhead of laziness. However, reasoning about strictness at the source level can be challenging and…

This thesis develops exact analytical tools to study strongly correlated stochastic systems, with a focus on extreme value statistics, gap statistics, and full counting statistics in multi-particle processes. A central contribution is the…

Humans are often incapable of precisely identifying and implementing the desired control strategy in controlling unstable dynamical systems. That is, the operator of a dynamical system treats the current control effort as acceptable even if…

Replacing operators with continuous operator-valued functions, we prove time-dependent versions of well-known results on compressions and diagonals of bounded operators. The setting of smooth functions is also addressed. Our results have no…

The execution behavior of a program often depends on external resources, such as program inputs or file contents, and so cannot be run in isolation. Nevertheless, software developers benefit from fast iteration loops where automated tools…