Related papers: Characterizing Van Kampen Squares via Descent Data
Carpet-type structures constitute an ideal laboratory to study and analyze the robustness of the interference process that underlies this phenomenon against the harmful effects of decoherence. Here, without losing any generality, for…
Smoothness has long been the dominant form of parsimony in functional data analysis, to the point of occasionally being conflated with the very notion of functional data. However, many core inferential tasks depend on the inverse…
Disentangled representations seek to recover latent factors of variation underlying observed data, yet their identifiability is still not fully understood. We introduce a unified framework in which disentanglement is achieved through…
We propose Automatic Feature Explanation using Contrasting Concepts (FALCON), an interpretability framework to explain features of image representations. For a target feature, FALCON captions its highly activating cropped images using a…
A category is adhesive if it has all pullbacks, all pushouts along monomorphisms, and all exactness conditions between pullbacks and pushouts along monomorphisms which hold in a topos. This condition can be modified by considering only…
A relatively new topic in computability theory is the study of notions of computation that are robust against mistakes on some kind of small set. However, despite the recent popularity of this topic relatively foundational questions about…
The asymptotic strong-coupling behavior as well as the exact critical exponents from scalar field theory even in the simplest case of $1+1$ dimensions have not been obtained yet. Hagen Kleinert has linked both critical exponents and strong…
This paper is the second in a series exploring the properties of a functor which assigns a homotopy double groupoid with connections to a Hausdorff space. We show that this functor satisfies a version of the van Kampen theorem, and so is a…
Let $\mathbb{A}$ be a $2$-category with suitable opcomma objects and pushouts. We give a direct proof that, provided that the codensity monad of a morphism $p$ exists and is preserved by a suitable morphism, the factorization given by the…
In this paper, we interpret disentanglement as the discovery of local charts of the data manifold and trace how this definition naturally leads to an equivalent condition for disentanglement: commutativity between factors of variation. We…
We provide and discuss complex analytic methods for overcoming the formal character of formal deformation quantization. This is a necessity for returning to physically meaningful statements, and accounts for the fact that the formal…
Decoupling inequalities disentangle complex dependence structures of random objects so that they can be analyzed by means of standard tools from the theory of independent random variables. We study decoupling inequalities for vector-valued…
The Seifert-van Kampen theorem computes the fundamental group of a space from the fundamental groups of its constituents. We develop a modular SVK framework within the setting of computational paths - an approach to equality where witnesses…
This work is a part of my upcoming thesis [7]. We establish an equiconsistency between (1) weak indestructibility for all $\kappa +2$-degrees of strength for cardinals $\kappa $ in the presence of a proper class of strong cardinals, and (2)…
We develop the theory of n-stacks (or more generally Segal n-stacks which are $\infty$-stacks such that the morphisms are invertible above degree n). This is done by systematically using the theory of closed model categories (cmc). Our main…
Many studies have been carried out in order to increase the search efficiency of constraint satisfaction problems; among them, some make use of structural properties of the constraint network; others take into account semantic properties of…
Let u be a local homomorphism of noetherian local rings forming part of a commutative square vf=gu. We give some conditions on the square which imply that u is formally smooth. This result encapsulates a variety of (apparently unrelated)…
In this article we discuss an exactly solvable, one-dimensional, periodic toy charge density wave model introduced in [D.C. Kaspar, M. Mungan, EPL {\bf 103}, 46002 (2013)]. In particular, driving the system with a uniform force, we show…
A folklore result in category theory is that a (weakly) Cartesian closed category with finite co-products is distributive. Usually, the proof of this small result is carried on using the fact that the exponential functor is right adjoint to…
We define a notion of stable and measurable map between cones endowed with measurability tests and show that it forms a cpo-enriched cartesian closed category. This category gives a denotational model of an extension of PCF supporting the…