Related papers: Coherent systems of finite support iterations
We study triples of coisotropic or isotropic subspaces in symplectic vector spaces; in particular, we classify indecomposable structures of this kind. The classification depends on the ground field, which we only assume to be perfect and…
We show that the order dimension of the weak order on a Coxeter group of type A, B or D is equal to the rank of the Coxeter group, and give bounds on the order dimensions for the other finite types. This result arises from a unified…
We present a version with non-definable forcing notions of Shelah's theory of iterated forcing along a template. Our main result, as an application, is that, if $\kappa$ is a measurable cardinal and $\theta<\kappa<\mu<\lambda$ are…
We review aspects of superconformal indices in three dimension. Three dimensional superconformal indices can be exactly computed by using localization method including monopole contribution, and can be applied to provide evidences for…
In our previous papers, together with J. Paseka we introduced so-called sectionally pseudocomplemented lattices and posets and illuminated their role in algebraic constructions. We believe that - similar to relatively pseudocomplemented…
We present a new third-order, semi-discrete, central method for approximating solutions to multi-dimensional systems of hyperbolic conservation laws, convection-diffusion equations, and related problems. Our method is a high-order extension…
Complex systems may morph between structures with different dimensionality and degrees of freedom. As a tool for their modelling, nonlinear embeddings are introduced that encompass objects with different dimensionality as a continuous…
We study the sets of planes in an even dimensional real vector space $V$ which are simultaneously stabilised by a pair of complex structures on $V$. We completely describe these sets of planes for pairs of orthogonal complex structures.…
We consider here 6-regular plane graphs whose faces have size 1, 2 or 3. In Section 2 a practical enumeration method is given that allowed us to enumerate them up to 53 vertices. Subsequently, in Section 3 we enumerate all possible symmetry…
In this review article, we discuss connections between the physics of disordered systems, phase transitions in inference problems, and computational hardness. We introduce two models representing the behavior of glassy systems, the spiked…
Persistent homology is a popular and useful tool for analysing finite metric spaces, revealing features that can be used to distinguish sets of unlabeled points and as input into machine learning pipelines. The famous stability theorem of…
The purpose of this paper is to study stable representations of partially ordered sets (posets) and compare it to the well known theory for quivers. In particular, we prove that every indecomposable representation of a poset of finite type…
Learning about the three-dimensional world from two-dimensional images is a fundamental problem in computer vision. An ideal neural network architecture for such tasks would leverage the fact that objects can be rotated and translated in…
Shelah shows that certain revised countable support (RCS) iterations do not add reals. His motivation is to establish the independence (relative to large cardinals) of Avraham's problem on the existence of uncountable non-constuctible…
While persistent homology has taken strides towards becoming a wide-spread tool for data analysis, multidimensional persistence has proven more difficult to apply. One reason is the serious drawback of no longer having a concise and…
We compute the Betti numbers and describe the cohomology algebras of the ordered and unordered configuration spaces of three points in complex projective spaces, including the infinite dimensional case. We also compute these invariants for…
In this article, we continue the investigation of hep-th 1611.02179 regarding iterative properties of dual conformal integrals in higher dimensions. In d=4, iterative properties of four and five point dual conformal integrals manifest…
We investigate the presence of defects in systems described by real scalar field in (D,1) spacetime dimensions. We show that when the potential assumes specific form, there are models which support stable global defects for D arbitrary. We…
We describe the notion of stability of coherent systems as a framework to deal with redundancy. We define stable coherent systems and show how this notion can help the design of reliable systems. We demonstrate that the reliability of…
This paper is about metric data structures in high-dimensional or non-Euclidean space that permit cached sufficient statistics accelerations of learning algorithms. It has recently been shown that for less than about 10 dimensions,…