Related papers: A SAT Encoding to Compute Aperiodic Tiling Rhythmi…
This note describes a SAT encoding for the $n$-fractions puzzle which is problem 041 of the CSPLib. Using a SAT solver we obtain a solution for two of the six remaining open instances of this problem.
We present determinant formulae for the number of tilings of various domains in relation with Alternating Sign Matrix and Fully Packed Loop enumeration.
This is a report on our ongoing research on a combinatorial approach to knot recognition, using coloring of knots by certain algebraic objects called quandles. The aim of the paper is to summarize the mathematical theory of knot coloring in…
In the domain of Music Information Retrieval (MIR), Automatic Music Transcription (AMT) emerges as a central challenge, aiming to convert audio signals into symbolic notations like musical notes or sheet music. This systematic review…
The control synthesis of a dynamic system subject to a signal temporal logic (STL) specification is commonly formulated as a mixed-integer linear/convex programming (MILP/MICP) problem. Solving such a problem is computationally expensive…
We briefly review the standard methods used to construct quasiperiodic tilings, such as the projection, the inflation, and the grid method. A number of sample Mathematica programs, implementing the different approaches for one- and…
Estimating the performance difficulty of a musical score is crucial in music education for adequately designing the learning curriculum of the students. Although the Music Information Retrieval community has recently shown interest in this…
Finding exact circuit size is a notorious optimization problem in practice. Whereas modern computers and algorithmic techniques allow to find a circuit of size seven in blink of an eye, it may take more than a week to search for a circuit…
Determining the satisfiability of Boolean constraint-satisfaction problems with different types of constraints, that is hybrid constraints, is a well-studied problem with important applications. We study here a new application of hybrid…
Analytical solutions to acoustic scattering problems involving nonspherical shapes, such as spheroids and disks, have long been known and have many applications. However, these solutions require special functions that are not easily…
The generalized list $T$-coloring is a common generalization of many graph coloring models, including classical coloring, $L(p,q)$-labeling, channel assignment and $T$-coloring. Every vertex from the input graph has a list of permitted…
The digitization of vocal music scores presents unique challenges that go beyond traditional Optical Music Recognition (OMR) and Optical Character Recognition (OCR), as it necessitates preserving the critical alignment between music…
We study space--time isogeometric discretizations of the linear acoustic wave equation that use splines of arbitrary degree p, both in space and time. We propose a space--time variational formulation that is obtained by adding a…
Clique-width is a graph invariant that has been widely studied in combinatorics and computer science. However, computing the clique-width of a graph is an intricate problem, the exact clique-width is not known even for very small graphs. We…
Periodic orbit quantization requires an analytic continuation of non-convergent semiclassical trace formulae. We propose a method for semiclassical quantization based upon the Pade approximant to the periodic orbit sums. The Pade…
We investigate time encoding as an alternative method to classical sampling, and address the problem of reconstructing classes of non-bandlimited signals from time-based samples. We consider a sampling mechanism based on first filtering the…
The Collatz problem is related to the fixed point problem, and is widely used in mathematics. It has attracted a wide range of math enthusiasts, but is still difficult to solve. So, this article aimed to study the extension of the Collatz…
We consider the harmonic balance method for finding approximate periodic solutions of the Lorenz system. When developing software that implements the described method, the math package Maxima was chosen. The drawbacks of symbolic…
MIDI-sheet music alignment is the task of finding correspondences between a MIDI representation of a piece and its corresponding sheet music images. Rather than using optical music recognition to bridge the gap between sheet music and MIDI,…
We approach the task of computing a carefully synchronizing word of minimum length for a given partial deterministic automaton, encoding the problem as an instance of SAT and invoking a SAT solver. Our experimental results demonstrate that…