8 citations · 28 across the 15 of their papers we have counts for
17 papers
Hyperbolic embeddings for graph compression
Dorota Celinska-Kopczynska, Eryk Kopczynski
Network theoreticians hypothesize that the structure of real-world networks has a geometric origin. Especially, hyperbolic geometry was proven insightful in representing and modeli…
Numerical Aspects of Hyperbolic Geometry
Dorota Celinska-Kopczynska, Eryk Kopczynski
Hyperbolic geometry has recently found applications in social networks, machine learning and computational biology. With the increasing popularity, questions about the best represe…
Coordination Sequences of Periodic Structures are Rational via Automata Theory
Eryk Kopczynski
We prove the conjecture of Grosse-Kunstleve et al. that coordination sequences of periodic structures in n-dimensional Euclidean space are rational. This has been recently proven b…
Simulating, Visualizing and Playing with de Sitter and anti de Sitter spacetime
Eryk Kopczynski
In this paper we discuss computer simulations of de Sitter and anti de Sitter spacetimes, which are maximally symmetric, relativistic analogs of non-Euclidean geometries. We presen…
Non-Euclidean Self-Organizing Maps
Dorota Celińska-Kopczyńska, Eryk Kopczyński
Self-Organizing Maps (SOMs, Kohonen networks) belong to neural network models of the unsupervised class. In this paper, we present the generalized setup for non-Euclidean SOMs. Mos…
Axiomatizing rectangular grids with no extra non-unary relations
Eryk Kopczynski
We construct a formula which axiomatizes non-narrow rectangular grids without using any binary relations other than the grid neighborship relations. As a corollary, we prove th…
Logical properties of random graphs from small addable classes
Anuj Dawar, Eryk Kopczyński
We establish zero-one laws and convergence laws for monadic second-order logic (MSO) (and, a fortiori, first-order logic) on a number of interesting graph classes. In particular, w…
A note on first-order spectra with binary relations
Eryk Kopczynski, Tony Tan
The spectrum of a first-order sentence is the set of the cardinalities of its finite models. In this paper, we consider the spectra of sentences over binary relations that use at l…
Bounded degree and planar spectra
Anuj Dawar, Eryk Kopczyński
The finite spectrum of a first-order sentence is the set of positive integers that are the sizes of its models. The class of finite spectra is known to be the same as the complexit…
Invisible pushdown languages
Eryk Kopczynski
Context free languages allow one to express data with hierarchical structure, at the cost of losing some of the useful properties of languages recognized by finite automata on word…
Non-dominating sequences of vectors using only resets and increments
Wojciech Czerwinski, Tomasz Gogacz, Eryk Kopczynski
We consider a variant of Dickson lemma, where each entry of a vector can be reseted or incremented by 1 in respect to the previous one. We give an example of non dominating sequenc…
Complexity of Problems of Commutative Grammars
Eryk Kopczynski
We consider commutative regular and context-free grammars, or, in other words, Parikh images of regular and context-free languages. By using linear algebra and a branching analog o…
On the variable hierarchy of first-order spectra
Eryk Kopczynski, Tony Tan
The spectrum of a first-order logic sentence is the set of natural numbers that are cardinalities of its finite models. In this paper we study the hierarchy of first-order spectra…
Regular graphs and the spectra of two-variable logic with counting
Eryk Kopczynski, Tony Tan
The {\em spectrum} of a first-order logic sentence is the set of natural numbers that are cardinalities of its finite models. In this paper we show that when restricted to using on…
Definability of linear equation systems over groups and rings
Anuj Dawar, Eryk Kopczynski, Bjarki Holm +2
Motivated by the quest for a logic for PTIME and recent insights that the descriptive complexity of problems from linear algebra is a crucial aspect of this problem, we study the s…
Complexity of Problems for Commutative Grammars
Eryk Kopczyński
We consider Parikh images of languages accepted by non-deterministic finite automata and context-free grammars; in other words, we treat the languages in a commutative way --- we d…
Acute triangulations of polyhedra and R^n
Eryk Kopczyński, Igor Pak, Piotr Przytycki
We study the problem of acute triangulations of convex polyhedra and the space R^n. Here an acute triangulation is a triangulation into simplices whose dihedral angles are acute. W…