Related papers: Pair functions computed recursively in ordered and…
A functional theory based on single-particle occupation numbers is developed for pairing. This functional, that generalizes the BCS approach, directly incorporates corrections due to particle number conservation. The functional is…
Calculating interactions or correlations between pairs of particles is typically the most time-consuming task in particle simulation or correlation analysis. Straightforward implementations using a double loop over particle pairs have…
A sound and complete algorithm for nominal unification of higher-order expressions with a recursive let is described, and shown to run in non-deterministic polynomial time. We also explore specializations like nominal letrec-matching for…
For a classical system of noninteracting particles we establish recursive integral equations for the density of states on the microcanonical ensemble. The recursion can be either on the number of particles or on the dimension of the system.…
Quantifying the complexity of systems consisting of many interacting parts has been an important challenge in the field of complex systems in both abstract and applied contexts. One approach, the complexity profile, is a measure of the…
We consider a system of particles which interact through a jump process. The jump intensities are functions of the proximity rank of the particles, a type of interaction referred to as topological in the literature. Such interactions have…
A statistical inference method is developed and tested for pairwise interacting systems whose degrees of freedom are continuous angular variables, such as planar spins in magnetic systems or wave phases in optics and acoustics. We…
The exact interaction energy of a many-electron system is determined by the electron pair density, which is not well-approximated in standard Kohn-Sham density functional models. Here we study the (complicated but well-defined) exact…
In the rapidly emerging field of nanotechnology, as well as in biology where chemical reaction phenomena take place in systems with characteristic length scales ranging from micrometer to the nanometer range, understanding of chemical…
We study the correlations of pairs of complex logarithms of $\mathbb Z$-lattice points in the complex line at various scalings, proving the existence of pair correlation functions. We prove that at the linear scaling, the pair correlations…
Recursive partitioning is the core of several statistical methods including CART, random forest, and boosted trees. Despite the popularity of tree based methods, to date, there did not exist methods for combining multiple trees into a…
This paper examines the problem of ranking a collection of objects using pairwise comparisons (rankings of two objects). In general, the ranking of $n$ objects can be identified by standard sorting methods using $n log_2 n$ pairwise…
We study the effect of coherent propagation of two interacting particles in an effective 2-3-d disordered potential. Our numerical data demonstrate that in dimension $d > 2$, interaction can lead to two--particles delocalization below…
A standard approach to approximate inference in state-space models isto apply a particle filter, e.g., the Condensation Algorithm.However, the performance of particle filters often varies significantlydue to their stochastic nature.We…
Reconstructing the structural connectivity between interacting units from observed activity is a challenge across many different disciplines. The fundamental first step is to establish whether or to what extent the interactions between the…
We develop a pairing-field formalism for ab initio studies of non-relativistic two-component fermions on a $(d\!+\!1)$-dimensional spacetime lattice. More specifically, we focus on theories where the interaction between the two components…
We study the noise correlations of one-dimensional binary Bose mixtures, as a probe of their quantum phases. In previous work, we found a rich structure of many-body phases in such mixtures, such as paired and counterflow superfluidity.…
We review the recent approach to the construction of (3+1)-dimensional integrable dispersionless partial differential systems based on their contact Lax pairs and the related $R$-matrix theory for the Lie algebra of functions with respect…
Motivated by a general principle governing regulation mechanisms in biological cells, we investigate a general interaction scheme between different populations of particles and specific particles, referred to as agents. Assuming that each…
Let $\mathcal{L}_n$ denote the set of all paths from $[0,0]$ to $[n, n]$ which consist of either unit north steps $N$ or unit east steps $E$ or, equivalently, the set of all words $L \in \{E,N\}^*$ with $n$ $E$'s and $n$ $N$'s. Given $L \in…