相关论文: A deterministic pseudorandom perturbation scheme f…
In this paper we present methods for the synthesis of polynomial invariants for probabilistic transition systems. Our approach is based on martingale theory. We construct invariants in the form of polynomials over program variables, which…
Orthogonal polynomial approximations form the foundation to a set of well-established methods for uncertainty quantification known as polynomial chaos. These approximations deliver models for emulating physical systems in a variety of…
Central issues of the Dirac constraint formalism are discussed in relation to the algorithmic methods of commutative algebra based on the Groebner basis techniques. For a wide class of finite dimensional polynomial degenerate Lagrangian…
Computing Delaunay triangulations in $\mathbb{R}^d$ involves evaluating the so-called in\_sphere predicate that determines if a point $x$ lies inside, on or outside the sphere circumscribing $d+1$ points $p_0,\ldots ,p_d$. This predicate…
We present a new approach for performing predicate abstraction based on symbolic decision procedures. Intuitively, a symbolic decision procedure for a theory takes a set of predicates in the theory and symbolically executes a decision…
We consider the semiring of abstract finite dynamical systems up to isomorphism, with the operations of alternative and synchronous execution. We continue searching for efficient algorithms for solving polynomial equations of the form $P(X)…
Saliency methods can make deep neural network predictions more interpretable by identifying a set of critical features in an input sample, such as pixels that contribute most strongly to a prediction made by an image classifier.…
A generalized method is proposed to compose new orbits from a given chaotic map. The method provides an approach to examine discrete-time chaotic maps in a "deep-zoom" manner by using $k$-digits to the right from the decimal separator of a…
Influence diagrams provide a compact graphical representation of decision problems. Several algorithms for the quick computation of their associated expected utilities are available in the literature. However, often they rely on a full…
We present dPASP, a novel declarative probabilistic logic programming framework for differentiable neuro-symbolic reasoning. The framework allows for the specification of discrete probabilistic models with neural predicates, logic…
A pseudorandom code is a keyed error-correction scheme with the property that any polynomial number of encodings appear random to any computationally bounded adversary. We show that the pseudorandomness of any code tolerating a constant…
In this paper, we propose a general framework to design {efficient} polynomial time approximation schemes (EPTAS) for fundamental stochastic combinatorial optimization problems. Given an error parameter $\epsilon>0$, such algorithmic…
In a seminal paper (Weitz, 2006), Weitz gave a deterministic fully polynomial approximation scheme for count- ing exponentially weighted independent sets (equivalently, approximating the partition function of the hard-core model from…
The choice of the parameter value for regularized inverse problems is critical to the results and remains a topic of interest. This article explores a criterion for selecting a good parameter value by maximizing the probability of the data,…
Subdivision schemes are iterative methods for the design of smooth curves and surfaces. Any linear subdivision scheme can be identified by a sequence of Laurent polynomials, also called subdivision symbols, which describe the linear rules…
We investigate the use of invariant polynomials in the construction of data-driven interatomic potentials for material systems. The "atomic body-ordered permutation-invariant polynomials" (aPIPs) comprise a systematic basis and are…
Nonlinear dynamical systems with continuous variables can be used for solving combinatorial optimization problems with discrete variables. Numerical simulations of them are also useful as heuristic algorithms with a desirable property,…
Quantum pseudorandomness, also known as unitary designs, comprise a powerful resource for quantum computation and quantum engineering. While it is known in theory that pseudorandom unitary operators can be constructed efficiently, realizing…
We investigate algorithms with predictions in computational geometry, specifically focusing on the basic problem of computing 2D Delaunay triangulations. Given a set $P$ of $n$ points in the plane and a triangulation $G$ that serves as a…
We study the arithmetic circuit complexity of some well-known family of polynomials through the lens of parameterized complexity. Our main focus is on the construction of explicit algebraic branching programs (ABP) for determinant and…