Related papers: Graphical C(3)-T(6) implies CAT(0)
We examine subgroups of locally compact groups that are continuous homomorphic images of connected Lie groups and we give a criterion for being such an image. We also provide a new characterisation of Lie groups and a characterisation of…
In this article we introduce the {\it cylindrical construction} for graphs and investigate its basic properties. We state a main result claiming a weak tensor-like duality for this construction. Details of our motivations and applications…
Let B be a unital C*-algebra, let A be a unital subalgebra, and let E be a conditional expectation from B to A with index-finite type and a quasi-basis of n elements. Then the topological stable rank satisfies \tsr (B) \leq \tsr (A) + n -…
We study expressive power of continuous logic in classes of (locally compact) groups. We also describe locally compact groups which are separably categorical structures.
We construct non-minimal GUT local models in the F-theory configuration. The gauge group on the bulk G_S is one rank higher than the GUT gauge group. The line bundles on the curves are non-trivial to break G_S down to the GUT gauge groups.…
Classification is an important goal in many branches of mathematics. The idea is to describe the members of some class of mathematical objects, up to isomorphism or other important equivalence in terms of relatively simple invariants. Where…
We prove a reduction theorem for capacity of positive maps of finite dimensional C*-algebras, thus reducing the computation of capacity to the case when the image of a nonscalar projection is never a projection.
The Gauss decompositions of the quantum groups, related to classical Lie groups and supergroups are considered by the elementary algebraic and $R$-matrix methods. The commutation relations between new basis generators (which are introduced…
The use of graphics processing units for scientific computations is an emerging strategy that can significantly speed up various different algorithms. In this review, we discuss advances made in the field of computational physics, focusing…
We construct CAT(0) groups containing subgroups whose Dehn functions are given by $x^s$, for a dense set of numbers $s \in [2, \infty)$. This significantly expands the known geometric behavior of subgroups of CAT(0) groups.
Canonical quantization may be approached from several different starting points. The usual approaches involve promotion of c-numbers to q-numbers, or path integral constructs, each of which generally succeeds only in Cartesian coordinates.…
Graph Contrastive Learning (GCL) has emerged as a powerful paradigm for training Graph Neural Networks (GNNs) in the absence of task-specific labels. However, its scalability on large-scale graphs is hindered by the intensive message…
We construct the universal realized limit sketch associated to a given limit sketch. The construction uses factorization systems to organize the classical argument of [2], yielding a streamlined and conceptually unified formulation of the…
The fractional versions of graph theoretic-invariants multiply the range of applications in scheduling, assignment and operational research problems. In this paper, we introduce the fractional version of local metric dimension of graphs.…
In this paper, we apply the machinery developed in arXiv:2401.06641(2) to study the behavior of computable categoricity relativized to non-c.e. degrees. In particular, we show that we can build a computable structure which is not computably…
We consider methods for obtaining local lower bounds on characteristics of quantum (correspondingly, classical) systems, i.e. lower bounds valid in the trace norm $\epsilon$-neighborhood of a given state (correspondingly, probability…
In this paper, we present a characterization of metric projection in CAT(0) spaces by using the concept of quasilinearization. Furthermore, some basic properties of matric projection are investigated.
It is well known that every word hyperbolic group has a well-defined visual boundary. An example of C. Croke and B. Kleiner shows that the same cannot be said for CAT(0) groups. All boundaries of a CAT(0) group are, however, shape…
We give an elementary criterion on a group G for the map from Aut(G) to Out(G) to split virtually. This criterion applies to many residually finite CAT(0) groups and hyperbolic groups, and in particular to all finitely generated Coxeter…
Complex classical Cayley-Klein categories ${\bf A({\bj})}$, ${\bf B({\bj})}$, ${\bf C({\bj})}$ and ${\bf D({\bj})}$ are constructed by the method of categorical extension of the complex classical Cayley-Klein groups $SL(2n;{\bj};{\Bbb C}),…