Related papers: Exclusion statistics: A resolution of the problem …
Quantum state exclusion is the task of determining which states from a given set a system was not prepared in. We provide a complete solution to optimal quantum state exclusion for arbitrary sets of pure states generated by finite groups,…
In many classification settings, the class of primary interest is underrepresented, leading to imbalanced data problems that arise in applications such as rare disease detection and fraud identification. In these contexts, identifying a…
We present a novel approach to Bayesian inference and general Bayesian computation that is defined through a sequential decision loop. Our method defines a recursive partitioning of the sample space. It neither relies on gradients nor…
For fixed weights w_1,...,w_n, and for d>0, we let B denote a collection of d*n balls, with d balls of weight w_i for each i=1,...,n. We consider the problem of assigning the balls to n bins with capacities C_1,...,C_n, in such a way that…
We investigate the issue of parameter estimation with nonuniform negative sampling for imbalanced data. We first prove that, with imbalanced data, the available information about unknown parameters is only tied to the relatively small…
For nearly any challenging scientific problem evaluation of the likelihood is problematic if not impossible. Approximate Bayesian computation (ABC) allows us to employ the whole Bayesian formalism to problems where we can use simulations…
We consider the following problem in which a given number of items has to be chosen from a predefined set. Each item is described by a vector of attributes and for each attribute there is a desired distribution that the selected set should…
Problems of the numerical solution of the Cauchy problem for a first-order differential-operator equation are discussed. A fundamental feature of the problem under study is that the equation includes a fractional power of the self-adjoint…
We propose a novel method for selective classification (SC), a problem which allows a classifier to abstain from predicting some instances, thus trading off accuracy against coverage (the fraction of instances predicted). In contrast to…
Colloidal clusters consist of small numbers of colloidal particles bound by weak, short-range attractions. The equilibrium probability of observing a cluster in a particular geometry is well-described by a statistical mechanical model…
We propose an entanglement concentration scheme which uses only the effects of quantum statistics of indistinguishable particles. This establishes the fact that useful quantum information processing can be accomplished by quantum statistics…
We analyze an optimal stopping problem with a series of inequality-type and equality-type expectation constraints in a general non-Markovian framework. We show that the optimal stopping problem with expectation constraints (OSEC) in an…
As a solvable and broadly applicable model system, the totally asymmetric exclusion process enjoys iconic status in the theory of non-equilibrium phase transitions. Here, we focus on the time dependence of the total number of particles on a…
The problem of estimating the proportion of satisfiable instances of a given CSP (constraint satisfaction problem) can be tackled through weighting. It consists in putting onto each solution a non-negative real value based on its…
The main goal of the paper is to define and use a condition sufficient to choose a unique solution to conservation law systems with a singular measure in initial data. Different approximations can lead to solutions with different…
Numerical codes based on a direct implementation of the standard ADM formulation of Einstein's equations have generally failed to provide long-term stable and convergent evolutions of black hole spacetimes when excision is used to remove…
We consider the integrable family of symmetric boundary-driven interacting particle systems that arise from the non-compact XXX Heisenberg model in one dimension with open boundaries. In contrast to the well-known symmetric exclusion…
In Phys. Rev. Lett. 67, 937 (1991) [1], Haldane introduced the fruitful concept of fractional exclusion statistics (FES). One of the most influential papers in which the thermodynamics of FES systems was deduced is Y.-S. Wu, Phys. Rev.…
We develop an operator-theoretical method for the analysis on well posedness of partial differential equations that can be modeled in the form \begin{equation*} \left\{ \begin{array}{rll} \Delta^{\alpha} u(n) &= Au(n+2) + f(n,u(n)), \quad n…
We study an inverse problem for the fractional wave equation with a potential by the measurement taking on arbitrary subsets of the exterior in the space-time domain. We are interested in the issues of uniqueness and stability estimate in…