{"id":41,"date":"2021-07-18T12:17:32","date_gmt":"2021-07-18T09:17:32","guid":{"rendered":"http:\/\/erga.di.uoa.gr\/?page_id=41"},"modified":"2022-09-03T13:38:27","modified_gmt":"2022-09-03T10:38:27","slug":"research","status":"publish","type":"page","link":"https:\/\/erga.di.uoa.gr\/index.php\/research\/","title":{"rendered":"Research"},"content":{"rendered":"\n<h2>Algebraic algorithms and computing<\/h2>\n\n\n\n<div class=\"wp-block-columns\">\n<div class=\"wp-block-column\" style=\"flex-basis:66.66%\">\n<ul><li><strong>Polynomial system solving<\/strong>, sparse\/toric elimination theory, structured matrices. Resultants reduce system solving to linear algebra.&nbsp;Newton polytopes provide the bridge between algebra and combinatorial geometry.&nbsp;Optimal sparse resultant matrices for&nbsp;multihomogeneous polynomial systems&nbsp;(<a rel=\"noreferrer noopener\" href=\"http:\/\/www.sciencedirect.com\/science\/article\/pii\/S0747717111002021?np=y\" target=\"_blank\">article<\/a>), and MAPLE software&nbsp;<a rel=\"noreferrer noopener\" href=\"http:\/\/www-sop.inria.fr\/galaad\/amantzaf\/soft.html\" target=\"_blank\">MHRES<\/a>.&nbsp;Macaulay-type formulae for sparse resultants of generalized unmixed systems&nbsp;(<a rel=\"noreferrer noopener\" href=\"http:\/\/erga.di.uoa.gr\/wp-content\/uploads\/2021\/07\/EmKo10.pdf\" target=\"_blank\">article<\/a>). More&nbsp;<a rel=\"noreferrer noopener\" href=\"http:\/\/cgi.di.uoa.gr\/~emiris\/soft_alg.html\" target=\"_blank\">Algebraic software<\/a>.<\/li><\/ul>\n<\/div>\n\n\n\n<div class=\"wp-block-column\" style=\"flex-basis:33.33%\">\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-full is-resized\"><img loading=\"lazy\" src=\"http:\/\/erga.di.uoa.gr\/wp-content\/uploads\/2021\/07\/p.sdiv_.jpg\" alt=\"\" class=\"wp-image-97\" width=\"215\" height=\"167\" srcset=\"https:\/\/erga.di.uoa.gr\/wp-content\/uploads\/2021\/07\/p.sdiv_.jpg 576w, https:\/\/erga.di.uoa.gr\/wp-content\/uploads\/2021\/07\/p.sdiv_-300x235.jpg 300w\" sizes=\"(max-width: 215px) 100vw, 215px\" \/><\/figure><\/div>\n<\/div>\n<\/div>\n\n\n\n<div style=\"height:10px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<div class=\"wp-block-columns\">\n<div class=\"wp-block-column\">\n<ul><li><strong>Real solving<\/strong>, Real algebraic numbers. Solvers based on Continued Fractions and Sturm sequences. Software tools in C++ (<a rel=\"noreferrer noopener\" href=\"http:\/\/www.mathemagix.org\/www\/main\/index.en.html\" target=\"_blank\">Mathemagix<\/a>): module Realroot, interval-Newton method, solvers for polynomial systems (subdivision methods). MAPLE software&nbsp;<a href=\"http:\/\/erga.di.uoa.gr\/SLV\/SLV_index.html\" target=\"_blank\" rel=\"noreferrer noopener\">SLV<\/a>&nbsp;for real algebraic numbers,&nbsp;real solving of equations and bivariate systems.&nbsp;<a href=\"http:\/\/erga.di.uoa.gr\/zaf\/unibench\/index.html\" target=\"_blank\" rel=\"noreferrer noopener\">Benchmarking<\/a>&nbsp;of black-box univariate real solvers.<\/li><\/ul>\n<\/div>\n\n\n\n<div class=\"wp-block-column\">\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-full is-resized\"><img loading=\"lazy\" src=\"http:\/\/erga.di.uoa.gr\/wp-content\/uploads\/2021\/07\/algEq.jpg\" alt=\"\" class=\"wp-image-55\" width=\"507\" height=\"58\" srcset=\"https:\/\/erga.di.uoa.gr\/wp-content\/uploads\/2021\/07\/algEq.jpg 833w, https:\/\/erga.di.uoa.gr\/wp-content\/uploads\/2021\/07\/algEq-300x35.jpg 300w, https:\/\/erga.di.uoa.gr\/wp-content\/uploads\/2021\/07\/algEq-768x89.jpg 768w\" sizes=\"(max-width: 507px) 100vw, 507px\" \/><\/figure><\/div>\n<\/div>\n<\/div>\n\n\n\n<hr class=\"wp-block-separator is-style-wide\"\/>\n\n\n\n<h2>Geometric computing, and Optimization<\/h2>\n\n\n\n<div class=\"wp-block-columns\">\n<div class=\"wp-block-column\" style=\"flex-basis:66.66%\">\n<ul><li><strong>Geometric Modeling and Nonlinear Computational geometry<\/strong>. Exact and approximate implicitization of parametric hypersurfaces by interpolation using matrix operations, and sparse elimination for exploiting structure (<a href=\"http:\/\/www.sciencedirect.com\/science\/article\/pii\/S1524070315000260\">article<\/a>). Extensions to space curves and objects defined by point clouds (<a rel=\"noreferrer noopener\" href=\"http:\/\/ergawiki.di.uoa.gr\/index.php\/Implicitization\" target=\"_blank\">Wiki page<\/a>).&nbsp;Voronoi diagrams of circles and ellipses (<a rel=\"noreferrer noopener\" href=\"http:\/\/www.ima.umn.edu\/nuggets\/voronoi.html\" target=\"_blank\">IMA nugget<\/a>), arrangements of curved objects (<a rel=\"noreferrer noopener\" href=\"http:\/\/erga.di.uoa.gr\/wp-content\/uploads\/2021\/07\/conic.slides.pdf\" target=\"_blank\">talk<\/a>) on&nbsp;<a rel=\"noreferrer noopener\" href=\"http:\/\/www.cgal.org\" target=\"_blank\">CGAL<\/a>. Python projects and CGAL-Python bindings, including visibility tools:&nbsp;<a rel=\"noreferrer noopener\" href=\"http:\/\/cgi.di.uoa.gr\/%7Ecompgeom\/pycgalvisual\/index.shtml\" target=\"_blank\">webpage<\/a>.&nbsp;Pictured is a teapot modeled using sparse and Bezout resultants (courtesy F. Groh).<\/li><\/ul>\n<\/div>\n\n\n\n<div class=\"wp-block-column\" style=\"flex-basis:33.33%\">\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-full is-resized\"><img loading=\"lazy\" src=\"http:\/\/erga.di.uoa.gr\/wp-content\/uploads\/2021\/07\/teapotGroh-SpRes-Bezout-2020.png\" alt=\"\" class=\"wp-image-76\" width=\"210\" height=\"139\" srcset=\"https:\/\/erga.di.uoa.gr\/wp-content\/uploads\/2021\/07\/teapotGroh-SpRes-Bezout-2020.png 709w, https:\/\/erga.di.uoa.gr\/wp-content\/uploads\/2021\/07\/teapotGroh-SpRes-Bezout-2020-300x200.png 300w\" sizes=\"(max-width: 210px) 100vw, 210px\" \/><\/figure><\/div>\n<\/div>\n<\/div>\n\n\n\n<div style=\"height:10px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<div class=\"wp-block-columns\">\n<div class=\"wp-block-column\" style=\"flex-basis:66.66%\">\n<ul><li><strong>Convex geometry<\/strong>&nbsp;in general dimension. Random walks for sampling convex regions, and for poly-time approximation of polytope volume (<a rel=\"noreferrer noopener\" href=\"https:\/\/github.com\/TolisChal\/volume_approximation\/tree\/R_volesti\" target=\"_blank\">C++ and R software<\/a>). Convex hull and symbolic perturbation, mixed volume (<a rel=\"noreferrer noopener\" href=\"http:\/\/cgi.di.uoa.gr\/~emiris\/soft_geo.html\" target=\"_blank\">software<\/a>). Regular fine mixed subdivisions of Minkowski sums, regular triangulations, secondary polytopes, resultant polytopes (<a rel=\"noreferrer noopener\" href=\"http:\/\/cgi.di.uoa.gr\/~emiris\/soft_geo.html\" target=\"_blank\">software<\/a>). Minkowski decomposition (<a rel=\"noreferrer noopener\" href=\"http:\/\/cgi.di.uoa.gr\/~amantzaf\/geo\" target=\"_blank\">webpage<\/a>): optimal algorithms with a fixed-size summand, approximation of general (NP-hard) problem. Polytopal computations: normals, faces, ridges, extreme or interior points&nbsp;(module Polytopix in&nbsp;<a rel=\"noreferrer noopener\" href=\"http:\/\/www.mathemagix.org\/www\/main\/index.en.html\" target=\"_blank\">Mathemagix<\/a>).<\/li><\/ul>\n\n\n\n<p><\/p>\n<\/div>\n\n\n\n<div class=\"wp-block-column\" style=\"flex-basis:33.33%\">\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-full is-resized\"><img loading=\"lazy\" src=\"http:\/\/erga.di.uoa.gr\/wp-content\/uploads\/2021\/07\/volume_sketch.jpg\" alt=\"\" class=\"wp-image-77\" width=\"177\" height=\"177\" srcset=\"https:\/\/erga.di.uoa.gr\/wp-content\/uploads\/2021\/07\/volume_sketch.jpg 200w, https:\/\/erga.di.uoa.gr\/wp-content\/uploads\/2021\/07\/volume_sketch-150x150.jpg 150w\" sizes=\"(max-width: 177px) 100vw, 177px\" \/><\/figure><\/div>\n<\/div>\n<\/div>\n\n\n\n<div style=\"height:10px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<div class=\"wp-block-columns\">\n<div class=\"wp-block-column\" style=\"flex-basis:66.66%\">\n<ul><li><strong>Optimization<\/strong>. Geometric optimization and clustering. Combinatorial optimization, capacitated vehicle routing with time windows, matching, bin packing (an example of computed routes in the Figure). Mathematical modeling. Use of Google&#8217;s OR-Tools. Collaboration with&nbsp;<a rel=\"noreferrer noopener\" href=\"https:\/\/www.emdot.gr\/\" target=\"_blank\">EmDoT<\/a>.<\/li><\/ul>\n<\/div>\n\n\n\n<div class=\"wp-block-column\" style=\"flex-basis:33.33%\">\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-full is-resized\"><img loading=\"lazy\" src=\"http:\/\/erga.di.uoa.gr\/wp-content\/uploads\/2021\/07\/routeExample.png\" alt=\"\" class=\"wp-image-72\" width=\"180\" height=\"184\" srcset=\"https:\/\/erga.di.uoa.gr\/wp-content\/uploads\/2021\/07\/routeExample.png 398w, https:\/\/erga.di.uoa.gr\/wp-content\/uploads\/2021\/07\/routeExample-293x300.png 293w\" sizes=\"(max-width: 180px) 100vw, 180px\" \/><\/figure><\/div>\n<\/div>\n<\/div>\n\n\n\n<div style=\"height:10px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<hr class=\"wp-block-separator is-style-wide\"\/>\n\n\n\n<h2>Data science and Machine Learning<\/h2>\n\n\n\n<div class=\"wp-block-columns\">\n<div class=\"wp-block-column\" style=\"flex-basis:66.66%\">\n<ul><li><strong>Geometric search in high dimensions<\/strong>. kd-GeRaf: Generalized Randomized kd-trees for fast approximate nearest-neighbors of points, in very high dimensions (competitive in dimension of up to 10,000):&nbsp;<a href=\"http:\/\/bioerga.di.uoa.gr:8080\" target=\"_blank\" rel=\"noreferrer noopener\">Web tool<\/a>,&nbsp;<a href=\"https:\/\/github.com\/gsamaras\/kd_GeRaF\" target=\"_blank\" rel=\"noreferrer noopener\">Software<\/a>,&nbsp;<a href=\"https:\/\/gsamaras.wordpress.com\/projects\/#geraf\" target=\"_blank\" rel=\"noreferrer noopener\">further info<\/a>. Dimensionality reduction by a weak version of the JL lemma, and record complexity bounds for ANN (<a href=\"http:\/\/dx.doi.org\/10.4230\/LIPIcs.SOCG.2015.436\" target=\"_blank\" rel=\"noreferrer noopener\">SoCG 2015<\/a>). Software in C++ and&nbsp;<a href=\"https:\/\/github.com\/ipsarros\/DolphinnPy\" target=\"_blank\" rel=\"noreferrer noopener\">Python<\/a>. Fast, high-dimensional, approximate nets (<a href=\"https:\/\/arxiv.org\/abs\/1607.04755\" target=\"_blank\" rel=\"noreferrer noopener\">SODA 2017<\/a>). Practical applications to data mining of 3D shapes by various encodings, including geometric learning.<\/li><\/ul>\n<\/div>\n\n\n\n<div class=\"wp-block-column\" style=\"flex-basis:33.33%\">\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-full is-resized\"><img loading=\"lazy\" src=\"http:\/\/erga.di.uoa.gr\/wp-content\/uploads\/2021\/07\/182px-Data3classes.png\" alt=\"\" class=\"wp-image-53\" width=\"200\" height=\"132\"\/><\/figure><\/div>\n<\/div>\n<\/div>\n\n\n\n<div style=\"height:10px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<div class=\"wp-block-columns\">\n<div class=\"wp-block-column\" style=\"flex-basis:66.66%\">\n<ul><li><strong>Clustering algorithms<\/strong>. IQ-means: Clustering for big data: we improve k-means by reverse assignment, combined with ideas from product quantization (image), to cluster 100 Mil SIFT images in 1hr (<a href=\"https:\/\/github.com\/iavr\/iqm\" target=\"_blank\" rel=\"noreferrer noopener\">Software tool IQ-means<\/a>,&nbsp;<a href=\"http:\/\/www.cv-foundation.org\/openaccess\/content_iccv_2015\/html\/Avrithis_Web-Scale_Image_Clustering_ICCV_2015_paper.html\" target=\"_blank\" rel=\"noreferrer noopener\">paper at ICCV 2015<\/a>). Applications to 3D objects such as molecular structures and mechanical parts.<\/li><\/ul>\n<\/div>\n\n\n\n<div class=\"wp-block-column\" style=\"flex-basis:33.33%\">\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-full is-resized\"><img loading=\"lazy\" src=\"http:\/\/erga.di.uoa.gr\/wp-content\/uploads\/2021\/07\/iqm.jpg\" alt=\"\" class=\"wp-image-65\" width=\"134\" height=\"132\"\/><\/figure><\/div>\n<\/div>\n<\/div>\n\n\n\n<div style=\"height:10px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<div class=\"wp-block-columns\">\n<div class=\"wp-block-column\" style=\"flex-basis:66.66%\">\n<ul><li><strong>Wind and wind-energy forecasting<\/strong>. We employ Scientific computing for processing open meteorological data (GFS) in creating WRF grid models for large geographic domains (within Greece), then develop original Machine Learning architectures for long-term (48h) prediction of wind speed as well as wind energy. Recurrent Neural Networks (also for&nbsp;<a rel=\"noreferrer noopener\" href=\"https:\/\/www.researchgate.net\/publication\/339242465_Neural_Networks_for_Cryptocurrency_Evaluation_and_Price_Fluctuation_Forecasting\" target=\"_blank\">cryptocurrency evaluation<\/a>) capture time dependencies, Convolutional Neural Networks capture geographic structure (grid). Deep learning, transfer learning, ensembles.<\/li><\/ul>\n<\/div>\n\n\n\n<div class=\"wp-block-column\" style=\"flex-basis:33.33%\">\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-full is-resized\"><img loading=\"lazy\" src=\"http:\/\/erga.di.uoa.gr\/wp-content\/uploads\/2021\/07\/4a7e905f3343b6be37a597cba8b31821.jpg\" alt=\"\" class=\"wp-image-172\" width=\"186\" height=\"186\" srcset=\"https:\/\/erga.di.uoa.gr\/wp-content\/uploads\/2021\/07\/4a7e905f3343b6be37a597cba8b31821.jpg 300w, https:\/\/erga.di.uoa.gr\/wp-content\/uploads\/2021\/07\/4a7e905f3343b6be37a597cba8b31821-150x150.jpg 150w\" sizes=\"(max-width: 186px) 100vw, 186px\" \/><\/figure><\/div>\n<\/div>\n<\/div>\n\n\n\n<hr class=\"wp-block-separator is-style-wide\"\/>\n\n\n\n<h2><a href=\"https:\/\/bioerga.di.uoa.gr\">Structural bioinformatics<\/a>&nbsp;and Robotics<\/h2>\n\n\n\n<p>For our research in bioinformatics please also visit our&nbsp;<a href=\"http:\/\/bioerga.di.uoa.gr\" target=\"_blank\" rel=\"noreferrer noopener\">dedicated webpage<\/a>.<\/p>\n\n\n\n<div class=\"wp-block-columns\">\n<div class=\"wp-block-column\" style=\"flex-basis:66.66%\">\n<ul><li><strong>Structure of Transmembrane proteins<\/strong>. Geometric modelling of \u03b2-barrels and detection of the transmembrane region of a \u03b2-barrel transmembrane protein. Given a PDB file, the transmembrane region is detected by profiling the external residues of the \u03b2-barrel along its axis in terms of hydrophobicity and existence of aromatic and charged residues. Our geometric modeling of the barrel relies on combining nonlinear least square minimization and a genetic algorithm.&nbsp;<a href=\"http:\/\/147.102.20.141\/TbB_Tool.php\" target=\"_blank\" rel=\"noreferrer noopener\">TbB-Tool<\/a>&nbsp;is the software tool.&nbsp;<a href=\"http:\/\/www.ncbi.nlm.nih.gov\/pubmed\/17097352\" target=\"_blank\" rel=\"noreferrer noopener\">Paper<\/a>.<\/li><\/ul>\n<\/div>\n\n\n\n<div class=\"wp-block-column\" style=\"flex-basis:33.33%\">\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-full is-resized\"><img loading=\"lazy\" src=\"http:\/\/erga.di.uoa.gr\/wp-content\/uploads\/2021\/07\/maltoporin_a_trimeric.jpg\" alt=\"\" class=\"wp-image-68\" width=\"221\" height=\"168\"\/><\/figure><\/div>\n<\/div>\n<\/div>\n\n\n\n<div style=\"height:10px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<div class=\"wp-block-columns\">\n<div class=\"wp-block-column\" style=\"flex-basis:66.66%\">\n<ul><li><strong>Molecular conformations<\/strong>&nbsp;in Structural bioinformatics. Enumeration of all possible conformations of (small) molecules\/proteins under geometric constrains; C-Space (<a rel=\"noreferrer noopener\" href=\"http:\/\/erga.di.uoa.gr\/cspace.html\" target=\"_blank\">interactive example<\/a>).&nbsp;<a rel=\"noreferrer noopener\" href=\"http:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/qua.20703\/abstract;jsessionid=4AB5B834FDCCC09FF5104DB4E2DDCAAF.f04t02\" target=\"_blank\">Paper<\/a>&nbsp;by Emiris, Fritzilas, Manocha. Sampling of rotamers, and clustering to deduce structural determinants. Graph embedding in Euclidean spaces, rigidity theory, enumerative problems of embeddings, <a href=\"https:\/\/www.youtube.com\/watch?v=ZTR8txn2wBU\" data-type=\"URL\" data-id=\"https:\/\/www.youtube.com\/watch?v=ZTR8txn2wBU\" target=\"_blank\" rel=\"noreferrer noopener\">distance geometry<\/a> to compute conformations from NMR data.<\/li><\/ul>\n\n\n\n<p><\/p>\n<\/div>\n\n\n\n<div class=\"wp-block-column\" style=\"flex-basis:33.33%\">\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-full is-resized\"><img loading=\"lazy\" src=\"http:\/\/erga.di.uoa.gr\/wp-content\/uploads\/2021\/07\/sols3.jpg\" alt=\"\" class=\"wp-image-74\" width=\"262\" height=\"163\" srcset=\"https:\/\/erga.di.uoa.gr\/wp-content\/uploads\/2021\/07\/sols3.jpg 575w, https:\/\/erga.di.uoa.gr\/wp-content\/uploads\/2021\/07\/sols3-300x187.jpg 300w\" sizes=\"(max-width: 262px) 100vw, 262px\" \/><\/figure><\/div>\n<\/div>\n<\/div>\n\n\n\n<div style=\"height:10px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<div class=\"wp-block-columns\">\n<div class=\"wp-block-column\" style=\"flex-basis:66.66%\">\n<ul><li><strong>Lakes<\/strong>&nbsp;is a&nbsp;<a href=\"http:\/\/erga.di.uoa.gr\/wp-content\/uploads\/2021\/07\/Lakes.zip\" target=\"_blank\" rel=\"noreferrer noopener\">software tool<\/a>&nbsp;for the prediction of protein binding sites. It analyzes the solvent and its contacts with proteins&nbsp;and defines clusters of water molecules, which mark potentially exposed interaction and binding sites of the protein. Contact:&nbsp;<a href=\"http:\/\/www.eie.gr\/nhrf\/institutes\/iopc\/cvs\/cv-Thanassis-Tartas-en.pdf\" target=\"_blank\" rel=\"noreferrer noopener\">Dr Thanassis Tartas<\/a>. Figure: black is the protein, colored are the oxygen atoms of clusters, red being the largest cluster.<\/li><\/ul>\n<\/div>\n\n\n\n<div class=\"wp-block-column\" style=\"flex-basis:33.33%\">\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-full is-resized\"><img loading=\"lazy\" src=\"http:\/\/erga.di.uoa.gr\/wp-content\/uploads\/2021\/07\/lakes.png\" alt=\"\" class=\"wp-image-67\" width=\"209\" height=\"120\" srcset=\"https:\/\/erga.di.uoa.gr\/wp-content\/uploads\/2021\/07\/lakes.png 407w, https:\/\/erga.di.uoa.gr\/wp-content\/uploads\/2021\/07\/lakes-300x174.png 300w\" sizes=\"(max-width: 209px) 100vw, 209px\" \/><\/figure><\/div>\n<\/div>\n<\/div>\n\n\n\n<div style=\"height:10px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<div class=\"wp-block-columns\">\n<div class=\"wp-block-column\" style=\"flex-basis:66.66%\">\n<ul><li><strong>Robot kinematics<\/strong>. Robust calibration of parallel robots (by applying elimination techniques), forward kinematics of Stewart\/Gough platforms,&nbsp;and design of robotic platforms for medical applications such as physiotherapy.<\/li><\/ul>\n<\/div>\n\n\n\n<div class=\"wp-block-column\" style=\"flex-basis:33.33%\">\n<div class=\"wp-block-image\"><figure class=\"aligncenter size-full is-resized\"><img loading=\"lazy\" src=\"http:\/\/erga.di.uoa.gr\/wp-content\/uploads\/2021\/07\/stewart.png\" alt=\"\" class=\"wp-image-75\" width=\"136\" height=\"166\" srcset=\"https:\/\/erga.di.uoa.gr\/wp-content\/uploads\/2021\/07\/stewart.png 365w, https:\/\/erga.di.uoa.gr\/wp-content\/uploads\/2021\/07\/stewart-247x300.png 247w\" sizes=\"(max-width: 136px) 100vw, 136px\" \/><\/figure><\/div>\n<\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>Algebraic algorithms and computing Polynomial system solving, sparse\/toric elimination theory, structured matrices. Resultants reduce system solving to linear algebra.&nbsp;Newton polytopes<span class=\"more-dots\">&#8230;<\/span> <span class=\"more-tag\"><a class=\"more-link\" href=\"https:\/\/erga.di.uoa.gr\/index.php\/research\/\">Read more<span class=\"screen-reader-text\"> \"Research\"<\/span><\/a><\/span><!-- .more-tag --><\/p>\n","protected":false},"author":1,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":[],"_links":{"self":[{"href":"https:\/\/erga.di.uoa.gr\/index.php\/wp-json\/wp\/v2\/pages\/41"}],"collection":[{"href":"https:\/\/erga.di.uoa.gr\/index.php\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/erga.di.uoa.gr\/index.php\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/erga.di.uoa.gr\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/erga.di.uoa.gr\/index.php\/wp-json\/wp\/v2\/comments?post=41"}],"version-history":[{"count":47,"href":"https:\/\/erga.di.uoa.gr\/index.php\/wp-json\/wp\/v2\/pages\/41\/revisions"}],"predecessor-version":[{"id":632,"href":"https:\/\/erga.di.uoa.gr\/index.php\/wp-json\/wp\/v2\/pages\/41\/revisions\/632"}],"wp:attachment":[{"href":"https:\/\/erga.di.uoa.gr\/index.php\/wp-json\/wp\/v2\/media?parent=41"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}