Related papers: Tredoku Patterns
These are the notes for my 2017 Takagi lectures on DT counts of curves in algebraic threefolds. We discuss the fundamentals of the subject, its origins, open questions, and certain recent advances.
Modeling the complex interactions between users and items as well as amongst items themselves is at the core of designing successful recommender systems. One classical setting is predicting users' personalized sequential behavior (or…
The site percolation problem is studied on d-dimensional generalisations of the Kagome' lattice. These lattices are isotropic and have the same coordination number q as the hyper-cubic lattices in d dimensions, namely q=2d. The site…
Many innovations are inspired by past ideas in a non-trivial way. Tracing these origins and identifying scientific branches is crucial for research inspirations. In this paper, we use citation relations to identify the descendant chart,…
In this paper, we introduce the notion of a $(a,b)$-rectangle pattern on permutations that not only generalizes the notion of successive elements (bonds) in permutations, but is also related to mesh patterns introduced recently by…
Localized patterns are coherent structures embedded in a quiescent state and occur in both discrete and continuous media across a wide range of applications. While it is well-understood how domain covering patterns (for example stripes and…
Morley's Theorem about angle trisectors can be viewed as the statement that a certain diagram `exists', meaning that triangles of prescribed shapes meet in a prescribed pattern. This diagram is the case n=3 of a class of diagrams we call…
On folio 855 recto of the Codex Atlanticus, Leonardo da Vinci drew three 'easily movable' bridges, but one of them is enigmatic: all 'replicas' in Leonardo museums and exhibitions come as a surprise, to say the least, to any engineer or…
On the occasion of the 60th birthday of Professor Keiji Kikkawa, Kikkawa-type physics performed at Ochanomizu was personally reviewed, and the generation of the metric is discussed with the condensation of the string fields.
This paper is based on my talks (`Skein modules with a cubic skein relation: properties and speculations' and `Symplectic structure on colorings, Lagrangian tangles and its applications') given in Kyoto (RIMS), September 11 and September 18…
We discuss here the history of the rhombocuboctahedron and pseudorombocuboctahedron and describe the structure of their paper models. It turns out that one of them serves as an excellent basis for creating a Jack-o'-lantern. The note is…
Traceroute is widely used: from the diagnosis of network problems to the assemblage of internet maps. Unfortu- nately, there are a number of problems with traceroute methodology, which lead to the inference of erroneous routes. This paper…
We study the propagation in three dimensions of internal waves using ray tracing methods and traditional dynamical systems theory. The wave propagation on a cone that generalizes the Saint Andrew's cross justifies the introduction of an…
In a recent paper A.Beardon and I.Short proposed to use chains of tangent horocycles as an extended tool describing continued fractions. We review the origin of such construction from the Moebius transformations point of view. Related…
These are course notes I wrote for my Fall 2013 graduate topics course on geometric structures, taught at ICERM. The notes rework many of proofs in William P. Thurston's beautiful but hard-to-understand paper, "Shapes of Polyhedra". A…
Nakano's "later" modality, inspired by G\"{o}del-L\"{o}b provability logic, has been applied in type systems and program logics to capture guarded recursion. Birkedal et al modelled this modality via the internal logic of the topos of…
The type of a complex projective plane curve has been recently introduced by T. Abe, P. Pokora and the first author. In the same paper they have studied the type two curves. In this paper we study plane curves of type three, with special…
Trajectory Prediction of dynamic objects is a widely studied topic in the field of artificial intelligence. Thanks to a large number of applications like predicting abnormal events, navigation system for the blind, etc. there have been many…
This article is about my memories from the discovery that the Veneziano model describes in fact interacting strings. I came to the understanding of that the dual or Veneziano model is really a model of strings independently of L. Susskind…
We introduce and study a family of axioms that closely follows the pattern of parametrized diamonds, studied by Moore, Hru\v{s}\'ak, and D\v{z}amonja in [13]. However, our approach appeals to model theoretic / forcing theoretic notions,…