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We propose a novel ECGAN for the challenging semantic image synthesis task. Although considerable improvement has been achieved, the quality of synthesized images is far from satisfactory due to three largely unresolved challenges. 1) The…
Inequalities for norms of different versions of the geometric mean of two positive definite matrices are presented.
The linearizability of differential equations was first considered by Lie for scalar second order semi-linear ordinary differential equations. Since then there has been considerable work done on the algebraic classification of linearizable…
The notion of "super convex spaces" generalizes the idea of convex spaces by replacing finite affine sums with countable affine sums. Using this notion permits a very elegant approach for analysis of the Giry monad on standard measurable…
Many deep generative models are defined as a push-forward of a Gaussian measure by a continuous generator, such as Generative Adversarial Networks (GANs) or Variational Auto-Encoders (VAEs). This work explores the latent space of such deep…
In this paper, we study metric completions of triangulated categories in a representation-theoretic context. We provide a concrete description of completions of bounded derived categories of hereditary finite dimensional algebras of finite…
In this article, we analyze three classes of time-reversal of a Markov process with Gaussian noise on a manifold. We first unveil a commutativity constraint for the most general of these time-reversals to be well defined. Then we give a…
We define a regularized size-shape distortion (quality) measure for curved high-order elements on a Riemannian space. To this end, we measure the deviation of a given element, straight-sided or curved, from the stretching, alignment, and…
A geometric graph is a combinatorial graph, endowed with a geometry that is inherited from its embedding in a Euclidean space. Formulation of a meaningful measure of (dis-)similarity in both the combinatorial and geometric structures of two…
Noticing that all of the 19th, 20th and 21st centuries treatments of trigonometry surveyed in this article are conceptually or logically defective, it is required to seek a conceptually sound and logically correct foundations of the…
Generalized equations are problems emerging in contexts of modern variational analysis as an adequate formalism to treat such issues as constraint systems, optimality and equilibrium conditions, variational inequalities, differential…
The convex and metric structures underlying probabilistic physical theories are generally described in terms of base normed vector spaces. According to a recent proposal, the purely geometrical features of these spaces are appropriately…
An inductive mean is a mean defined as a limit of a convergence sequence of other means. Historically, this notion of inductive means obtained as limits of sequences was pioneered independently by Lagrange and Gauss for defining the…
Uniform measures have played a fundamental role in geometric measure theory since they naturally appear as tangent objects. For instance, they were essential in the groundbreaking work of Preiss on the rectifiability of Radon measures.…
For a large class of statistical systems a geometric mean value of the observables is constrained. These observables are characterized by a power-law statistical distribution.
A natural way of handling imbalanced data is to attempt to equalise the class frequencies and train the classifier of choice on balanced data. For two-class imbalanced problems, the classification success is typically measured by the…
In recent years, in an effort to promote fairness in the election process, a wide variety of techniques and metrics have been proposed to determine whether a map is a partisan gerrymander. The most accessible measures, requiring easily…
Three-way dissimilarities are a generalization of (two-way) dissimilarities which can be used to indicate the lack of homogeneity or resemblance between any three objects. Such maps have applications in cluster analysis, and have been used…
In the approximate integration some inequalities between the quadratures and the integrals approximated by them are called \emph{extremalities}. On the other hand, the set of all quadratures is convex. We are trying to find possible…
We propose an improved estimator for the multi-task averaging problem, whose goal is the joint estimation of the means of multiple distributions using separate, independent data sets. The naive approach is to take the empirical mean of each…