Related papers: A Bifurcation Lemma for Invariant Subspaces
Consider a Bayesian inference problem where a variable of interest does not take values in a Euclidean space. These "non-standard" data structures are in reality fairly common. They are frequently used in problems involving latent discrete…
We extend bifurcation results of nonlinear eigenvalue problems from real Banach spaces to any neighbourhood of a given point. For points of odd multiplicity on these restricted domains, we establish that the component of solutions through…
Axiomatization and expressibility problems for Milner's process semantics (1984) of regular expressions modulo bisimilarity have turned out to be difficult for the full class of expressions with deadlock 0 and empty step~1. We report on a…
Convergence properties of binary stationary subdivision schemes for curves have been analyzed using the techniques of z-transforms and eigenanalysis. Eigenanalysis provides a way to determine derivative continuity at specific points based…
Blind Source Separation (BSS) is an active domain of Classical Information Processing. The development of Quantum Information Processing has made possible the appearance of Blind Quantum Source Separation (BQSS). This article discusses some…
Recent work on bilingual lexicon induction (BLI) has frequently depended either on aligned bilingual lexicons or on distribution matching, often with an assumption about the isometry of the two spaces. We propose a technique to…
Although Breadth-First Search (BFS) has several advantages over Depth-First Search (DFS) its prohibitive space requirements have meant that algorithm designers often pass it over in favor of DFS. To address this shortcoming, we introduce a…
We study a simplified model of the representation of colors in the primate primary cortical visual area V1. The model is described by an initial value problem related to a Hammerstein equation. The solutions to this problem represent the…
A vertex of a plane digraph is bimodal if all its incoming edges (and hence all its outgoing edges) are consecutive in the cyclic order around it. A plane digraph is bimodal if all its vertices are bimodal. Bimodality is at the heart of…
The Poisson bipolar model considers user-base station pairs distributed at random on a flat domain, similar to matchsticks scattered onto a table. Though this is a simple and tractable setting in which to study dense networks, it doesn't…
We generalize two classical homotopy theory results, the Blakers-Massey Theorem and Quillen's Theorem B, to G-equivariant cubical diagrams of spaces, for a discrete group G. We show that the equivariant Freudenthal suspension Theorem for…
The two-level normal hierarchical model (NHM) has played a critical role in the theory of small area estimation (SAE), one of the growing areas in statistics with numerous applications in different disciplines. In this paper, we address…
The Bethe-Salpeter equation (BSE) for bound states in scalar theories is reformulated and solved in terms of a generalized spectral representation directly in Minkowski space. This differs from the conventional approach, where the BSE is…
In a data stream environment, classification models must handle concept drift efficiently and effectively. Ensemble methods are widely used for this purpose; however, the ones available in the literature either use a large data chunk to…
In this work, we advocate for the importance of singular learning theory (SLT) as it pertains to the theory and practice of variational inference in Bayesian neural networks (BNNs). To begin, using SLT, we lay to rest some of the confusion…
Phenotypic variability in a population of cells can work as the bet-hedging of the cells under an unpredictably changing environment, the typical example of which is the bacterial persistence. To understand the strategy to control such…
We consider the bifurcation problem u'' + \lambda u = N(u) with two point boundary conditions where N(u) is a general nonlinear term which may also depend on the eigenvalue \lambda. A new derivation of a variational principle for the lowest…
Empirical Bayes (EB) improves the accuracy of simultaneous inference "by learning from the experience of others" (Efron, 2012). Classical EB theory focuses on latent variables that are iid draws from a fitted prior (Efron, 2019). Modern…
Bifurcation with symmetry is considered in the case of an isotropy subgroup with a two-dimensional fixed point subspace and non-zero quadratic terms. In general, there are one or three branches of solutions, and five qualitatively different…
Progress in the behavioral analysis of software product lines at the family level benefits from further development of the underlying semantical theory. Here, we propose a behavioral equivalence for feature transition systems (FTS)…