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Interatomic potentials are essential to go beyond ab initio size limitations, but simulation results depend sensitively on potential parameters. Forward propagation of parameter variation is key for uncertainty quantification, whilst…
Best possible bounds are obtained for the concentration function of an additive arithmetic function on sequences of shifted primes.
We study the optimal contract problem in the \emph{combinatorial actions} framework of D\"utting et al.~[FOCS'21], where a principal delegates a project to an agent who chooses a subset of hidden, costly actions, and the resulting reward is…
In computing, as in many aspects of life, changes incur cost. Many optimization problems are formulated as a one-time instance starting from scratch. However, a common case that arises is when we already have a set of prior assignments, and…
We extend the varying coefficient functional linear model to the nonlinear model and propose a varying coefficient functional additive model. The proposed method can represent the relationship between functional predictors and a scalar…
Hadronic tau decay data is used to study the reliability of various finite energy sum rules (FESR's). For intermediate scales (of order 2-3 GeV^2), those FESR's with weights s^k are found to have significant errors, whereas those with…
All scientific interpretations of statistical outputs depend on background (auxiliary) assumptions that are rarely delineated or explicitly interrogated. These include not only the usual modeling assumptions, but also deeper assumptions…
We discuss the approach to estimate aggregation and adaptive estimation based upon (nearly optimal) testing of convex hypotheses. We show that in the situation where the observations stem from {\em simple observation schemes} and where set…
In many areas of engineering and sciences, decision rules and control strategies are usually designed based on nominal values of relevant system parameters. To ensure that a control strategy or decision rule will work properly when the…
We generalise and improve some recent bounds for additive energies of modular roots. Our arguments use a variety of techniques, including those from additive combinatorics, algebraic number theory and the geometry of numbers. We give…
We prove that the set of large values of the trigonometric polynomial over a subset of density of the primes has some additive structure, similarly to what happens for subsets of densities in $\mathbb{Z}/{N}\mathbb{Z}$ but in a weaker form.…
We consider the convex quadratic optimization problem with indicator variables and arbitrary constraints on the indicators. We show that a convex hull description of the associated mixed-integer set in an extended space with a quadratic…
We prove new results on additive properties of finite sets $A$ with small multiplicative doubling $|AA|\leq M|A|$ in the category of real/complex sets as well as multiplicative subgroups in the prime residue field. The improvements are…
We present a versatile inequality of uncertainty relations which are useful when one approximates an observable and/or estimates a physical parameter based on the measurement of another observable. It is shown that the optimal choice for…
The problem of detecting new signals in the presence of an unknown background is ubiquitous in scientific discoveries and is especially prominent in the physical sciences. Most solutions proposed thus far to address the problem focus on…
This paper studies hypothesis testing and parameter estimation in the context of the divide and conquer algorithm. In a unified likelihood based framework, we propose new test statistics and point estimators obtained by aggregating various…
Large graphs abound in machine learning, data mining, and several related areas. A useful step towards analyzing such graphs is that of obtaining certain summary statistics - e.g., or the expected length of a shortest path between two…
Following a growing number of studies that, over the past 15 years, have established entropy inequalities via ideas and tools from additive combinatorics, in this work we obtain a number of new bounds for the differential entropy of sums,…
Algorithmic predictions are emerging as a promising solution concept for efficiently allocating societal resources. Fueling their use is an underlying assumption that such systems are necessary to identify individuals for interventions. We…
Optimization of complex functions, such as the output of computer simulators, is a difficult task that has received much attention in the literature. A less studied problem is that of optimization under unknown constraints, i.e., when the…