arXiv subjects

Ilias Kotsireas

Publications and source records attributed to Ilias Kotsireas.

23 records · Page 2Linked to original sources

arXiv2018

Enumeration of Complex Golay Pairs via Programmatic SAT

We provide a complete enumeration of all complex Golay pairs of length up to 25, verifying that complex Golay pairs do not exist in lengths 23 and 25 but do exist in length 24. This independently verifies work done by F. Fiedler in 2013 that confirms the 2002 conjecture of Craigen, Holzmann, and Kharaghani that complex Golay pairs of length 23 don't exist. Our enumeration method relies on the recently proposed SAT+CAS paradigm of combining computer algebra systems with SAT solvers to take advantage of the advances made in the fields of symbolic computation and satisfiability checking. The enumeration proceeds in two stages: First, we use a fine-tuned computer program and functionality from computer algebra systems to construct a list containing all sequences which could appear as the first sequence in a complex Golay pair (up to equivalence). Second, we use a programmatic SAT solver to construct all sequences (if any) that pair off with the sequences constructed in the first stage to form a complex Golay pair.

cs.LO↗

arXiv2017

A feasibility approach for constructing combinatorial designs of circulant type

In this work, we propose an optimization approach for constructing various classes of circulant combinatorial designs that can be defined in terms of autocorrelations. The problem is formulated as a so-called feasibility problem having three sets, to which the Douglas-Rachford projection algorithm is applied. The approach is illustrated on three different classes of circulant combinatorial designs: circulant weighing matrices, D-optimal matrices, and Hadamard matrices with two circulant cores. Furthermore, we explicitly construct two new circulant weighing matrices, a $CW(126,64)$ and a $CW(198,100)$, whose existence was previously marked as unresolved in the most recent version of Strassler's table.

math.CO↗

arXiv2017

Low Auto-correlation Binary Sequences explored using Warning Propagation

The search of binary sequences with low auto-correlations (LABS) is a discrete combinatorial optimization problem contained in the NP-hard computational complexity class. We study this problem using Warning Propagation (WP) , a message passing algorithm, and compare the performance of the algorithm in the original problem and in two different disordered versions. We show that in all the cases Warning Propagation converges to low energy minima of the solution space. Our results highlight the importance of the local structure of the interaction graph of the variables for the convergence time of the algorithm and for the quality of the solutions obtained by WP. While in general the algorithm does not provide the optimal solutions in large systems it does provide, in polynomial time, solutions that are energetically similar to the optimal ones. Moreover, we designed hybrid models that interpolate between the standard LABS problem and the disordered versions of it, and exploit them to improved the convergence time of WP and the quality of the solutions.

cond-mat.dis-nn↗

arXiv2015

Quantum and Post-Newtonian Effects in the Anomalistic Period and the Mean Motion of Celestial Bodies

We study the motion of a secondary celestial body under the influence of the corrected gravitational force of a primary. We study the effect of quantum and relativistic corrections to the gravitational potential of a primary body acting on the orbiting body. More specifically, two equations are derived to approximate the perigee/perihelion/periastron time rate of change and its total variation over one revolution (i.e., the difference between the anomalistic period and the Keplerian period) under the influence of the quantum as well as post- Newtonian accelerations. Numerical results have been obtained for the artificial Earth satellite Molnya, Mercury, and, finally, the for the HW Vir c, planetary companion.

physics.gen-ph↗

arXiv2015

Charm bracelets and their application to the construction of periodic Golay pairs

A $k$-ary charm bracelet is an equivalence class of length $n$ strings with the action on the indices by the additive group of the ring of integers modulo $n$ extended by the group of units. By applying an $O(n^3)$ amortized time algorithm to generate charm bracelet representatives with a specified content, we construct 29 new periodic Golay pairs of length $68$.

math.CO↗