相关论文: From Combinatorics to Partial Differential Equatio…

The collinear factorization theorem, combined with finite-order calculations in perturbative QCD, provides a powerful framework to obtain predictions for many collider observables. However, for observables which involve multiple energy…

It is well known that one can map certain properties of random matrices, fermionic gases, and zeros of the Riemann zeta function to a unique point process on the real line. Here we analytically provide exact generalizations of such a point…

These lectures give an introduction to the methods of conformal field theory as applied to deriving certain results in two-dimensional critical percolation: namely the probability that there exists at least one cluster connecting two…

The paper investigates the problem of performing correlation analysis when the number of observations is very large. In such a case, it is often necessary to combine the random observations to achieve dimensionality reduction of the…

In a general class of one dimensional random differential equation the convergence of the distribution function of the solution to stationary state distribution is studied. In particular it is proved the boundedness respectively the…

We consider a multidimensional search problem that is motivated by questions in contextual decision-making, such as dynamic pricing and personalized medicine. Nature selects a state from a $d$-dimensional unit ball and then generates a…

The phenomenon of solidification of a substance from its liquid phase is of the greatest practical and theoretical importance, and atomistic simulations can provide precious information towards its understanding and control. Unfortunately,…

Statistical moments of particle multiplicities in heavy-ion collision experiments are an important probe in the exploration of the phase diagram of strongly interacting matter and, particularly, in the search for the QCD critical end point.…

One of the outstanding challenges of cross-identification is multiplicity: detections in crowded regions of the sky are often linked to more than one candidate associations of similar likelihoods. We map the resulting maximum likelihood…

In this letter we show how to perform a systematic perturbative approach for the mode-coupling theory. The results coincide with those obtained via the replica approach. The upper critical dimension turns out to be always 8 and the…

Point cloud analysis (such as 3D segmentation and detection) is a challenging task, because of not only the irregular geometries of many millions of unordered points, but also the great variations caused by depth, viewpoint, occlusion, etc.…

Many real objects are modeled as discrete sets of points, such as corners or other salient features. For our main applications in chemistry, points represent atomic centers in a molecule or a solid material. We study the problem of…

As 3D point cloud analysis has received increasing attention, the insufficient scale of point cloud datasets and the weak generalization ability of networks become prominent. In this paper, we propose a simple and effective augmentation…

In this paper, we present a local information theoretic approach to explicitly learn probabilistic clustering of a discrete random variable. Our formulation yields a convex maximization problem for which it is NP-hard to find the global…

Markov Decision Processes (Mdps) form a versatile framework used to model a wide range of optimization problems. The Mdp model consists of sets of states, actions, time steps, rewards, and probability transitions. When in a given state and…

It is proposed that the $O(n)$ spin and geometrical percolation models can help to study the QCD phase diagram due to the universality properties of the phase transition. In this paper, correlations and fluctuations of various sizes of…

The proper handling of 3D orientations is a central element in many optimization problems in engineering. Unfortunately many researchers and engineers struggle with the formulation of such problems and often fall back to suboptimal…

A wide variety of methods have been used to compute percolation thresholds. In lattice percolation, the most powerful of these methods consists of microcanonical simulations using the union-find algorithm to efficiently determine the…

Determinant maximization provides an elegant generalization of problems in many areas, including convex geometry, statistics, machine learning, fair allocation of goods, and network design. In an instance of the determinant maximization…

We have numerically studied the trapping problem in a two-dimensional lattice where particles are continuously generated. We have introduced interaction between particles and directionality of their movement. This model presents a critical…