Related papers: The Rosenberg-Strong Pairing Function

In this work we develop an algebraic theory of linear recurrence equations and systems with constant coefficients and reflection. We obtain explicit solutions and the Green's functions associated to different problems under general linear…

We study Schroder paths drawn in a (m,n) rectangle, for any positive integers m and n. We get explicit enumeration formulas, closely linked to those for the corresponding (m,n)-Dyck paths. Moreover we study a Schroder version of…

Random Forests have been one of the most popular bagging methods in the past few decades, especially due to their success at handling tabular datasets. They have been extensively studied and compared to boosting models, like XGBoost, which…

We study the enumeration problem for different kind of tree parking functions introduced recently, called tree parking functions, tree parking distributions, prime tree parking functions, and prime tree parking distributions, for rooted…

Generative models offer a direct way of modeling complex data. Energy-based models attempt to encode the statistical correlations observed in the data at the level of the Boltzmann weight associated with an energy function in the form of a…

We study the statistical capacity of the classical binary perceptrons with general thresholds $\kappa$. After recognizing the connection between the capacity and the bilinearly indexed (bli) random processes, we utilize a recent progress in…

Any function can be constructed using a hierarchy of simpler functions through compositions. Such a hierarchy can be characterized by a binary rooted tree. Each node of this tree is associated with a function which takes as inputs two…

We investigate adjoint and Frobenius pairs between categories of comodules over rather general corings. We particularize to the case of the adjoint pair of functors associated to a morphism of corings over different base rings, which leads…

We introduce a notion of Poincar\'e duality for pairs of $\infty$-categories, extending Poincar\'e-Lefschetz duality for pairs of spaces. This categorical extension yields an efficient book-keeping device that affords, among other things, a…

Our results can be viewed as applications of algebraic combinatorics in random matrix theory. These applications are motivated by the predictive power of random matrix theory for the statistical behavior of the celebrated Riemann…

Semiclassical expansion of the Wigner function for spin-1/2 fermions having an effective spacetime-dependent mass is used to analyze spin-polarization effects. The existing framework is reformulated to obtain a differential equation…

Nuclear pairing is studied both in atomic nuclei and in neutron-star crusts in the unified framework of the energy-density functional theory using generalized Skyrme functionals complemented with a local pairing functional obtained from…

We review some applications of self-consistent Green's function theory to studies of one- and two-nucleon structure in finite nuclei. Large-scale microscopic calculations that employ realistic nuclear forces are now possible. Effects of…

The Legendre type relation for the counting function of ordinary twin primes is reworked in terms of the inverse of the Riemann zeta function. Its analysis sheds light on the distribution of the zeros of the Riemann zeta function in the…

We prove that the error in the prime number theorem can be quantitatively improved beyond the Riemann Hypothesis bound by using versions of Montgomery's conjecture for the pair correlation of zeros of the Riemann zeta-function which are…

Full strong-branching is a well-known variable selection rule that is known experimentally to produce significantly smaller branch-and-bound trees in comparison to all other known variable selection rules. In this paper, we attempt an…

Isotopic pairs and their representations are considered in a general framework of the vector superalgebra. Numerous examples of finite-dimensional and infinite-dimensional isotopic pairs are discussed. Several types of their representations…

Scalar-tensor theories are the best motivated alternatives to general relativity and provide a mathematically consistent framework to test the various observable predictions. They can involve three functions of the scalar field: (i) a…

Knoblauch (2014) and Knoblauch (2015) investigate the relative size of the collection of binary relations with desirable features as compared to the set of all binary relations using symmetric difference metric (Cantor) topology and…

In this work we use the number classification in families of the form 6n+1, and 6n+5 with n integer (Such families contain all odd prime numbers greater than 3 and other compound numbers related with primes). We will use this kind of…