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We extend recent computer-assisted design and analysis techniques for first-order optimization over structured functions--known as performance estimation--to apply to structured sets. We prove "interpolation theorems" for smooth and…
For a high temperature non-Abelian plasma, we reformulate the hard thermal loop approximation as an effective classical thermal field theory for the soft modes. The effective theory is written in local Hamiltonian form, and the thermal…
Numerically obtaining the inverse of a function is a common task for many scientific problems, often solved using a Newton iteration method. Here we describe an alternative scheme, based on switching variables followed by spline…
In this paper, we simulate sample paths of a class of symmetric $\alpha$-stable processes using their series expression. We will develop a result in the approximation of shot-noise series. And finally, we will get a convergence rate for the…
We consider efficient estimation of flexible transformation models with interval-censored data. To reduce the dimension of semi-parametric models, the unknown monotone transformation function is approximated via monotone splines. A…
Satisfiability Modulo the Theory of Nonlinear Real Arithmetic, SMT(NRA) for short, concerns the satisfiability of polynomial formulas, which are quantifier-free Boolean combinations of polynomial equations and inequalities with integer…
Profile likelihood confidence intervals are a robust alternative to Wald's method if the asymptotic properties of the maximum likelihood estimator are not met. However, the constrained optimization problem defining profile likelihood…
A general conversion strategy by involving a shifted parameter $\theta$ is proposed to construct high-order accuracy difference formulas for fractional calculus operators. By converting the second-order backward difference formula with such…
Conformal prediction is a framework for providing prediction intervals with distribution-free validity, guaranteeing predictive coverage for data drawn from any distribution. Its two main variants are full conformal prediction and split…
This study considers quadrature-based algorithms to compute $A^\alpha \boldsymbol{b}$, the action of a real power of a Hermitian positive-definite matrix $A$ on a vector $ \boldsymbol{b}$. In these algorithms, the computation of an integral…
Turning pass-through network architectures into iterative ones, which use their own output as input, is a well-known approach for boosting performance. In this paper, we argue that such architectures offer an additional benefit: The…
t-SNE and hierarchical clustering are popular methods of exploratory data analysis, particularly in biology. Building on recent advances in speeding up t-SNE and obtaining finer-grained structure, we combine the two to create tree-SNE, a…
In this work we present a new simple but efficient scheme - Subsquares approach - for development of algorithms for enclosing the solution set of overdetermined interval linear systems. We are going to show two algorithms based on this…
The accelerated failure time (AFT) model is widely used to analyze relationships between variables in the presence of censored observations. However, this model relies on some assumptions such as the error distribution, which can lead to…
Iterative Refinement (IR) is a classical computing technique for obtaining highly precise solutions to linear systems of equations, as well as linear optimization problems. In this paper, motivated by the limited precision of quantum…
Alternating automata have been widely used to model and verify systems that handle data from finite domains, such as communication protocols or hardware. The main advantage of the alternating model of computation is that complementation is…
In this paper we study the asymptotic theory for samples problem based on the functional empirical process (fep), this new method is called general samples problem. We suggest this method to develop the full theory of estimation of means,…
Hermite polynomials and functions have extensive applications in scientific and engineering problems. Although it is recognized that employing the scaled Hermite functions rather than the standard ones can remarkably enhance the…
We take our first step toward getting finite results from the alpha'-corrected D=4 N=4 SYM theory with emphasis on the field theory techniques. Starting with the classical action of N=4 SYM with the leading alpha'-corrections, we examine…
What is called "numerical reproducibility" is the problem of getting the same result when the scientific computation is run several times, either on the same machine or on different machines, with different types and numbers of processing…