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Let $\overline{p}_o(n)$ denote the number of overpartitions of $n$ into odd parts. The partition function $\overline{p}_o(n)$ has been the subject of many recent studies where many explicit Ramanujan-like congruences were discovered. In…
Inverse boundary value problems for the radiative transport equation play important roles in optics-based medical imaging techniques such as diffuse optical tomography (DOT) and fluorescence optical tomography (FOT). Despite the rapid…
In this paper we relate the partition function to the max-statistics of random variables. In particular, we provide a novel framework for approximating and bounding the partition function using MAP inference on randomly perturbed models. As…
Quantum imaging has a potential of enhancing precision of the object reconstruction by using quantum correlations of the imaging field. This is especially important for imaging requiring low-intensity fields up to the level of few-photons.…
In this paper we introduce a family of rational approximations of the reciprocal of a $\phi$-function involved in the explicit solutions of certain linear differential equations, as well as in integration schemes evolving on manifolds. The…
The number of ordered factorizations and the number of recursive divisors are two related arithmetic functions that are recursively defined. But it is hard to construct explicit representations of these functions. Taking advantage of their…
In this paper, we study functional approximations where we choose the so-called radial basis function method and more specifically, quasi-interpolation. From the various available approaches to the latter, we form new quasi-Lagrange…
We present a generic partition refinement algorithm that quotients coalgebraic systems by behavioural equivalence, an important task in system analysis and verification. Coalgebraic generality allows us to cover not only classical…
An algorithm for irreducible decomposition of representations of finite groups over fields of characteristic zero is described. The algorithm uses the fact that the decomposition induces a partition of the invariant inner product into a…
Probabilistic graphical models have emerged as a powerful modeling tool for several real-world scenarios where one needs to reason under uncertainty. A graphical model's partition function is a central quantity of interest, and its…
A recursion operator is an integro-differential operator which maps a generalized symmetry of a nonlinear PDE to a new symmetry. Therefore, the existence of a recursion operator guarantees that the PDE has infinitely many higher-order…
Closed orbit theory is generalized to the semiclassical calculation of cross-correlated recurrence functions for atoms in external fields. The cross-correlation functions are inverted by a high resolution spectral analyzer to obtain the…
Cooperative optimization is a new way for finding global optima of complicated functions of many variables. It has some important properties not possessed by any conventional optimization methods. It has been successfully applied in solving…
The input of almost every machine learning algorithm targeting the properties of matter at the atomic scale involves a transformation of the list of Cartesian atomic coordinates into a more symmetric representation. Many of the most popular…
We present a method for evaluating the partition function in a varying external field. Specifically, we look at the case of a non-interacting, charged, massive scalar field at finite temperature with an associated chemical potential in the…
In this paper, we identify partial correlation information structures that allow for simpler reformulations in evaluating the maximum expected value of mixed integer linear programs with random objective coefficients. To this end, assuming…
We develop a calculus that gives an elementary approach to enumerate partition-like objects using an infinite upper-triangular number-theoretic matrix. We call this matrix the Partition-Frequency Enumeration (PFE) matrix. This matrix…
We give a characterizations of Ramsey ultrafilters on $\mathscr P(\omega)$ in terms of functions $f:\omega^n\to\omega$ and their ultrafilter extensions. To do this, we prove that for any partition $\mathcal P$ of $[\omega]^n$ there is a…
The construction of good effective models is an essential part of understanding and simulating complex systems in many areas of science. It is a particular challenge for correlated many body quantum systems displaying emergent physics. We…
In this article, we define and study a geometry and an order on the set of partitions of an even number of objects. One of the definitions involves the partition algebra, a structure of algebra on the set of such partitions depending on an…