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Tree models are very widely used in practice of machine learning and data mining. In this paper, we study the problem of model integrity authentication in tree models. In general, the task of model integrity authentication is the design \&…
Proving Koszulness of a properad can be very hard, but sometimes one can look at its Koszul complex to look for obstructions for Koszulness. In this paper, we present a method and tools to prove non-Koszulness of many properads in a family…
We give a constructive proof of Carpenter's Theorem due to Kadison. Unlike the original proof our approach also yields the real case of this theorem.
This paper explains a flaw in the published proof of the Scalable Commutativity Rule (SCR), presents a revised and formally verified proof of the SCR in the Coq proof assistant, and discusses the insights and open questions raised from our…
We investigate the mathematical structure of the world sheet in two-dimensional conformal field theories.
This is a summary of the proof of BAB conjecture. All material are taken from the two BAB paper in the reference. The aim of this summary is to help reader to understand the more technical side of the proof of BAB.
We demonstrate the versatility of the tangle-tree duality theorem for abstract separation systems by using it to prove tree-of-tangles theorems. This approach allows us to strengthen some of the existing tree-of-tangles theorems by bounding…
Given a category with a bifunctor and natural isomorphisms for associativity, commutativity and left and right identity we do not assume that extra constraining diagrams hold. We introduce groupoids of coupling trees to describe a version…
Staircase tableaux are combinatorial objects which appear as key tools in the study of the PASEP physical model. The aim of this work is to show how the discovery of a tree structure in staircase tableaux is a significant feature to derive…
Many concurrent and distributed systems are safety-critical and therefore have to provide a high degree of assurance. Important properties of such systems are frequently proved on the specification level, but implementations typically…
In this paper we prove a strong nonstructure theorem for kappa (T)-saturated models of a stable theory T with dop.
This very short correction notes a gap in an argument of an earlier paper, and also provides a theorem of similar flavor to the main result of that paper.
In this paper we formulate and prove a general theorem of stability of exactness properties under the pro-completion, which unifies several such theorems in the literature and gives many more. The theorem depends on a formal approach to…
A method is presented for using the consistent part of inconsistent axiomatic systems.
This contains Part I of the book: Congruence lattices of finite lattices, which covers about 80 years of research and more than 250 papers.
In this work a new empirical tolerance factor for compounds with pyrochlore structure is proposed. This suggested tolerance factor is based on experimental structural data and on the tolerance factors currently proposed. However, since it…
In this note on coarse geometry we revisit coarse homotopy. We prove that coarse homotopy indeed is an equivalence relation, and this in the most general context of abstract coarse structures. We introduce (in a geometric way) coarse…
I explain the motivation for investigating the high energy limit of QCD and give a brief presentation of recent progress in the understanding of unitarity corrections in this kinematic regime. Special emphasis is given to the conformal…
We give criteria for a first-order theory to be NCTP or NBTP using tree-indiscernibility. As an application, we show that Mekler's construction preserves NCTP and NBTP.
Recent work of Garvan, Sellers, Smoot, and others has made connections between infinite families of congruences for various partition functions. Here, we apply this approach to families of congruences for PED and POD partitions and find…