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We show how the tangent functor extends from ordinary smooth maps to "microformal morphisms" (also called "thick morphisms") of supermanifolds. Microformal morphisms generalize ordinary maps and correspond to formal canonical relations…
This work adresses the question of density of piecewise constant (resp. rigid) functions in the space of vector valued functions with bounded variation (resp. deformation) with respect to the strict convergence. Such an approximation…
We investigate the properties of lax comma categories over a base category $X$, focusing on topologicity, extensivity, cartesian closedness, and descent. We establish that the forgetful functor from $\mathsf{Cat}//X$ to $\mathsf{Cat}$ is…
Disentanglement is a highly desirable property of representation due to its similarity with human's understanding and reasoning. This improves interpretability, enables the performance of down-stream tasks, and enables controllable…
Language models are increasingly being used in important decision pipelines, so ensuring the correctness of their outputs is crucial. Recent work has proposed evaluating the "factuality" of claims decomposed from a language model generation…
The study of equality types is central to homotopy type theory. Characterizing these types is often tricky, and various strategies, such as the encode-decode method, have been developed. We prove a theorem about equality types of…
In the present paper, we establish the uniqueness of tangent maps for general weakly holomorphic and locally approximable maps from an arbitrary almost complex manifold into projective algebraic varieties. As a byproduct of the approach and…
Shape-constrained functional data encompass a wide array of application fields, such as activity profiling, growth curves, healthcare and mortality. Most existing methods for general functional data analysis often ignore that such data are…
Since their introduction in the shape analysis community, functional maps have met with considerable success due to their ability to compactly represent dense correspondences between deformable shapes, with applications ranging from shape…
Stable derivators provide an enhancement of triangulated categories as is indicated by the existence of canonical triangulations. In this paper we show that exact morphisms of stable derivators induce exact functors of canonical…
Shape constraints (such as non-negativity, monotonicity, convexity) play a central role in a large number of applications, as they usually improve performance for small sample size and help interpretability. However enforcing these shape…
One fundamental consequence of a scheme $X$ being proper is that the functor classifying maps from $X$ to any other suitably nice scheme or algebraic stack is representable by an algebraic stack. This result has been generalized by…
Functions that are piecewise defined are a common sight in mathematics while convexity is a property especially desired in optimization. Suppose now a piecewise-defined function is convex on each of its defining components - when can we…
The scaling properties of one-dimensional deconstructed surfaces are studied by numerical simulations of a disaggregation model. The model presented here for the disaggregation process takes into account the possibility of having quenched…
Using hyperbolic localization, we identify the nearby cycles along the Vinberg degeneration with the composition of Radon and Harish-Chandra functors, both considered for the category of character sheaves. This provides a new, simple proof…
We distinguish between faint, weak, strong and strict localizations of categories at morphism families and show that this framework captures the different types of derived functors that are considered in the literature. More precisely, we…
Violation of a noncontextuality inequality or the phenomenon referred to `quantum contextuality' is a fundamental feature of quantum theory. In this article, we derive a novel family of noncontextuality inequalities along with their…
We characterize the class of homotopy pull-back squares by means of elementary closure properties. The so called Puppe theorem which identifies the homotopy fiber of certain maps constructed as homotopy colimits is a straightforward…
Many models of quintessence predict a time variation of the fundamental constants as well as a composition-dependent gravity like long-range force mediated by the cosmon. We present bounds for the cosmon coupling to matter and radiation…
In this paper, we propose a method for image-set classification based on convex cone models, focusing on the effectiveness of convolutional neural network (CNN) features as inputs. CNN features have non-negative values when using the…