ALCYON lab

ALgorithms for
Combinatorics,
geometrY,
Optimization and
Number theory
Home Members Projects Publications

In ALCYON (Algorithms for Combinatorics, Geometry, Optimization and Number Theory) we work on Symbolic Computation. Both on the mathematics to improve algorithms and on the efficient (high performance) implementations of algorithms in order to push mathematics further. Symbolic Computation lies in the intersection of mathematics and computer science. This means that it is both 100% mathematics and 100% computer science.
If you want to join us, fill in this form.

News

CASC 2020 - Computer Algebra in Scientific Computing
This year CASC will take place in Linz, Austria. See you there!

ALCYON lab Opening!
The ALCYON lab will open on 24 January 2020 at 12:00. You are cordially invited to join us.

See you there!

NEMO kick off
The kick off meeting for the NEMO project will take place on 23-24 January 2020. See you there!

Events

Machine Learning and Computer Algebra 18 July 2020 Greece
Polytopes - Algebra - Computation 18 July 2020 Greece
NEMO kick-off 23 January 2020 GTU

Members

Zafeirakis Zafeirakopoulos Faculty Gebze TU
Elias Tsigaridas Associate Faculty Inria/IMJ-PRG
Mohan Ravichandran Associate Faculty Bogazici University
Tulay Ayyildiz Akoglu Associate Faculty Karadeniz TU
Gizem Süngü PhD Student Gebze TU
Başak Karakaş MSc Student Gebze TU
Meryem Özkan MSc Student Gebze TU
Umutcan Önal MSc Student Gebze TU
Nurgül Kangal Undergraduate Student MSGSU
Alumni
Büşra Sert MSc Student MSGSU
Nurdan Ünlü MSc Student MSGSU

Projects

Ongoing
2019 Jun-
2021 Jun
Gröbner Bases, Resultants and Polyhedral Geometry - GRAPE Bilateral Project with France - TUBITAK 2509 ~50k euro
2017 Oct-
2020 Oct
Heterogeneous Algorithms for Combinatorics, Geometry, Optimization and Number Theory - HALCYON TUBITAK 3501 ~80k euro
2018 Oct-
2020 Feb
Algebraic Motion Planning Reasearch Council of Gebze Technical University ~3k euro
Concluded
2017 Mar-
2019 Jul
A system for efficient representation of mathematical data and benchmarking of mathematical software and algorithms TUBITAK 3001 ~17k euro
2016 Aug-
2017 Feb
Parallel Computation of Discrete and Continuous Volume Reasearch Council of Gebze Technical University ~3k euro

Seminar

2019

Publications

Conference Papers
2009 Michael Hemmer, Elias P. Tsigaridas, Zafeirakis Zafeirakopoulos, Ioannis Z. Emiris, Menelaos I. Karavelas, Bernard Mourrain - "Experimental evaluation and cross-benchmarking of univariate real solvers" - Symbolic Numeric Computation - SNC 2009.
2017 Vissarion Fisikopoulos, Zafeirakis Zafeirakopoulos - "Experimental Study of the Ehrhart Interpolation Polytope" - Mathematical Aspects of Computer and Information Sciences - MACIS 2017.
2015 Ioannis Z. Emiris, Christos Konaxis, Zafeirakis Zafeirakopoulos - "Minkowski Decomposition and Geometric Predicates in Sparse Implicitization" - 40th International Symposium on Symbolic and Algebraic Computation - ISSAC.
2017 Ioannis Z. Emiris, Anna Karasoulou, Eleni Tzanaki, Zafeirakis Zafeirakopoulos - "On the space of Minkowski summands of a convex polytope" - EuroCG '16.
2013 Christos Koukouvinos, Dimitris E. Simos, Zafeirakis Zafeirakopoulos - "A Gröbner Bases Method for Complementary Sequences" - Proceedings of Applications of Computer Algebra ACA 2013.
Journal Papers
2014 Matthias Beck, Benjamin Braun, Matthias Köppe, Carla D. Savage, Zafeirakis Zafeirakopoulos - "s-Lecture hall partitions, self-reciprocal polynomials, and Gorenstein cones" - The Ramanujan Journal.
2016 Matthias Beck, Benjamin Braun, Matthias Köppe, Carla D. Savage, Zafeirakis Zafeirakopoulos - "Generating Functions and Triangulations for Lecture Hall Cones" - SIAM Journal on Discrete Mathematics.
2017 Felix Breuer, Zafeirakis Zafeirakopoulos - "Polyhedral Omega: a New Algorithm for Solving Linear Diophantine Systems" - Annals of Combinatorics.
2014 Angelos Mantzaflaris, Hamid Rahkooy, Zafeirakis Zafeirakopoulos - "Efficient computation of dual space and directional multiplicity of an isolated point" - Computer Aided Geometric Design.
2014 Christos Koukouvinos, Veronika Pillwein, Dimitris E. Simos, Zafeirakis Zafeirakopoulos - "On the average complexity for the verification of compatible sequences" - Information Processing Letters.
Talks (Invited & Symposia w/o Proceedings)
Theses
2012 Zafeirakis Zafeirakopoulos - "Linear Diophantine Systems: Partition Analysis and Polyhedral Geometry" - Research Institute for Symbolic Computation / DK-compmath.
2008 Zafeirakis Zafeirakopoulos - "Study and Benchmarks for Real Root Isolation methods" - Departments of Informatics and Telecommunication.

Final Year Projects (Bitirme)

Machine Learning for Polynomials

Use machine learning for predicting statistics or properties of polynomials. The main goal is to find appropriate encodings of polynomials and answer questions such as the number of real roots, the distance of the closest real roots, the existence of double roots etc.

You have to try and compare different architectures and design an interface that will be easy to use for the predictions you cover.


A software citation system

Design a system that parses code in Python and C/C++ in order to create a list of citations. Functions in libraries will be decorated by something like: @citation{KnuthTAOCP} Then your system will compile a list of all citations used by an input program (based on which functions are called).

You need basic understanding of compilation, programming in C/C++ and Python. For the citations we will use the standard bibtex format.