Related papers: A Collective, Probabilistic Approach to Schema Map…

This paper extends the algorithm schemes proposed in \cite{Nesterov2007a} and \cite{Nesterov2007b} to the minimization of the sum of a composite objective function and a convex function. Two proximal point-type schemes are provided and…

We introduce dependent adders. A dependent adder $A$ has for every $x \in A$ a way of adding together $x$ many elements of $A$. We provide examples from many disparate branches of mathematics. Examples include the field with one element…

We present a technique for constructing suitable posterior probability distributions in situations for which the sampling distribution of the data is not known. This is very useful for modern scientific data analysis in the era of "big…

We perform certain alternating binomial summations with parameters that occur in the analysis of algorithms. A combination of integral and special function and special number representations is used. The results are sufficiently general to…

Conditional preference statements have been used to compactly represent preferences over combinatorial domains. They are at the core of CP-nets and their generalizations, and lexicographic preference trees. Several works have addressed the…

We discuss a structural approach to subset-sum problems in additive combinatorics. The core of this approach are Freiman-type structural theorems, many of which will be presented through the paper. These results have applications in various…

The aim of these notes is to provide a reasonably short and "hands-on" introduction to the differential calculus on associative algebras over a field of characteristic zero. Following a suggestion of Ginzburg's we call the resulting theory…

Probabilistic graphical models (PGMs) are tools for solving complex probabilistic relationships. However, suboptimal PGM structures are primarily used in practice. This dissertation presents three contributions to the PGM literature. The…

We correct some oversights in the paper "A spectral sequence for stratified spaces and configuration spaces of points" by the second named author. In particular we explain that an additional hypothesis should be added to Theorem 4.15 in…

We show, that the Complex Step approximation to the Fr\'echet derivative of real matrix functions is applicable to the matrix sign, square root and polar mapping using iterative schemes. While this property was already discovered for the…

In this paper, we obtain some new results on closed subschemes. Specially, we define natural addition and multiplication on the closed subschemes of a scheme. It is shown that "the multiplication" precisely coincides with the well known…

In the first part of this note, we review results concerning analytic characterization of convexity for planar sets. The second part is devoted to results valid for arbitrary $m \ge 2$.

The paper develops the method for construction of families of particular solutions to some classes of nonlinear Partial Differential Equations (PDE). Method is based on the specific link between algebraic matrix equations and PDE.…

We give a characterization of subsets of effect algebras, that can be embedded into a range of an observable. To give this characterization, we introduce a new notion of {\em compatibility support mappings.}

Many problems in the geophysical sciences demand the ability to calibrate the parameters and predict the time evolution of complex dynamical models using sequentially-collected data. Here we introduce a general methodology for the joint…

This paper addresses the mapping problem. Using a conjugate prior form, we derive the exact theoretical batch multi-object posterior density of the map given a set of measurements. The landmarks in the map are modeled as extended objects,…

Generalized Additive Models (GAMs) are commonly considered *interpretable* within the ML community, as their structure makes the relationship between inputs and outputs relatively understandable. Therefore, it may seem natural to…

We introduce an alternative to the method of matched asymptotic expansions. In the "traditional" implementation, approximate solutions, valid in different (but overlapping) regions are matched by using "intermediate" variables. Here we…

Multicriteria decision analysis aims at supporting a person facing a decision problem involving conflicting criteria. We consider an additive utility model which provides robust conclusions based on preferences elicited from the decision…

Learning the parameters of graphical models using the maximum likelihood estimation is generally hard which requires an approximation. Maximum composite likelihood estimations are statistical approximations of the maximum likelihood…