Geometric computing \/ Geometric modeling<\/h3>\n\n\n\n![\"\"](\"http:\/\/erga.di.uoa.gr\/wp-content\/uploads\/2021\/07\/Sextic1.jpg\")
<\/figure><\/div>\n\n\n\n- Sampling and volume estimation of (non)linear (non)convex regions (volesti<\/a>\u00a0software) by poly-time methods. Applications include scoring financial portfolios (our paper<\/a>), and forecasting market crises via copulas.<\/li>
- There are various useful representations of geometric objects, most notably implicit, parametric, and point clouds. We develop efficient ways for switching between representations while exploiting properties such as sparseness. <\/li>
- Voronoi diagrams of complex objects and the corresponding algebraic operations for constructing them. Large datasets, nonlinear objects and applications (paper for ellipses<\/a>).<\/li><\/ul>\n\n\n\n
Machine Learning<\/h3>\n\n\n\n![\"\"](\"http:\/\/erga.di.uoa.gr\/wp-content\/uploads\/2021\/07\/windspeed2019RNN.png\")
<\/figure><\/div>\n\n\n\n- Approximate Nearest Neighbors (ANN) and randomized projections (following our\u00a0first paper<\/a>): Queries lying in a subspace (bio data); ANN on complex 1D objects, e.g. time series, exploit time parameter (vs. Frechet distance as in our\u00a0paper<\/a>); experimental validation of the Dolphinn approach; farthest directional neighbor.<\/li>
- Clustering of complex objects (representation via Neural Networks), IQ-Means algorithm.<\/li>
- Deep geometric learning for 3d shapes (representation, mining, classification, segmentation).<\/li><\/ul>\n\n\n\n
Algebraic algorithms \/ polynomials<\/h3>\n\n\n\n![\"\"](\"http:\/\/erga.di.uoa.gr\/wp-content\/uploads\/2021\/07\/detSylvMatrix.png\")
<\/figure><\/div>\n\n\n\n- Discrete geometry for capturing and exploiting algebraic properties. Mixed volume and root bounds via the Permanent.<\/li>
- Approximate Mixed volume via the volume approximation methods (telescoping method on mixed cells or fraction of “mixed” sample); sample of mixed cells for MV estimation and sample of root homotopies.<\/li>
- Polynomial system solving by linear algebra. Sparse resultants and Macaulay formulae. Structured systems such as multi-homogeneous systems.<\/li><\/ul>\n\n\n\n
Bioinformatics<\/h3>\n\n\n\n![\"\"](\"http:\/\/erga.di.uoa.gr\/wp-content\/uploads\/2021\/07\/ribosome.jpg\")
<\/figure><\/div>\n\n\n\n- Molecular 3d structure, folding. Cryo-EM. Geometric, statistical (sampling).<\/li>
- Docking, Rotamers and Geometric Learning.<\/li>
- Rigidity theory (counting rigid graphs), and Distance geometry on NMR data for ab initio structure prediction (in Greek<\/a>).<\/li><\/ul>\n\n\n\n
Robotics<\/h3>\n\n\n\n![\"\"](\"http:\/\/erga.di.uoa.gr\/wp-content\/uploads\/2021\/07\/hexaCMWcol.jpg\")
<\/figure><\/div>\n\n\n\n- Parallel and wire robots, kinematics, calibration, collision avoidance. Applications to molecular kinematics\u00a0<\/li>
- Distance geometry and pose counting. Over-constrained algebraic systems and applications in calibration.<\/li><\/ul>\n","protected":false},"excerpt":{"rendered":"
Research Topics For immediate openings look under News: an 8.5-month Marie-Curie fellowship is currently available in Geometric Learning, for students…<\/span> Read more \"Open Positions\"<\/span><\/a><\/span><\/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\/402"}],"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=402"}],"version-history":[{"count":7,"href":"https:\/\/erga.di.uoa.gr\/index.php\/wp-json\/wp\/v2\/pages\/402\/revisions"}],"predecessor-version":[{"id":796,"href":"https:\/\/erga.di.uoa.gr\/index.php\/wp-json\/wp\/v2\/pages\/402\/revisions\/796"}],"wp:attachment":[{"href":"https:\/\/erga.di.uoa.gr\/index.php\/wp-json\/wp\/v2\/media?parent=402"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}
<\/figure><\/div>\n\n\n\n- Sampling and volume estimation of (non)linear (non)convex regions (volesti<\/a>\u00a0software) by poly-time methods. Applications include scoring financial portfolios (our paper<\/a>), and forecasting market crises via copulas.<\/li>
- There are various useful representations of geometric objects, most notably implicit, parametric, and point clouds. We develop efficient ways for switching between representations while exploiting properties such as sparseness. <\/li>
- Voronoi diagrams of complex objects and the corresponding algebraic operations for constructing them. Large datasets, nonlinear objects and applications (paper for ellipses<\/a>).<\/li><\/ul>\n\n\n\n
Machine Learning<\/h3>\n\n\n\n
<\/figure><\/div>\n\n\n\n- Approximate Nearest Neighbors (ANN) and randomized projections (following our\u00a0first paper<\/a>): Queries lying in a subspace (bio data); ANN on complex 1D objects, e.g. time series, exploit time parameter (vs. Frechet distance as in our\u00a0paper<\/a>); experimental validation of the Dolphinn approach; farthest directional neighbor.<\/li>
- Clustering of complex objects (representation via Neural Networks), IQ-Means algorithm.<\/li>
- Deep geometric learning for 3d shapes (representation, mining, classification, segmentation).<\/li><\/ul>\n\n\n\n
Algebraic algorithms \/ polynomials<\/h3>\n\n\n\n
<\/figure><\/div>\n\n\n\n- Discrete geometry for capturing and exploiting algebraic properties. Mixed volume and root bounds via the Permanent.<\/li>
- Approximate Mixed volume via the volume approximation methods (telescoping method on mixed cells or fraction of “mixed” sample); sample of mixed cells for MV estimation and sample of root homotopies.<\/li>
- Polynomial system solving by linear algebra. Sparse resultants and Macaulay formulae. Structured systems such as multi-homogeneous systems.<\/li><\/ul>\n\n\n\n
Bioinformatics<\/h3>\n\n\n\n
<\/figure><\/div>\n\n\n\n- Molecular 3d structure, folding. Cryo-EM. Geometric, statistical (sampling).<\/li>
- Docking, Rotamers and Geometric Learning.<\/li>
- Rigidity theory (counting rigid graphs), and Distance geometry on NMR data for ab initio structure prediction (in Greek<\/a>).<\/li><\/ul>\n\n\n\n
Robotics<\/h3>\n\n\n\n
<\/figure><\/div>\n\n\n\n- Parallel and wire robots, kinematics, calibration, collision avoidance. Applications to molecular kinematics\u00a0<\/li>
- Distance geometry and pose counting. Over-constrained algebraic systems and applications in calibration.<\/li><\/ul>\n","protected":false},"excerpt":{"rendered":"
Research Topics For immediate openings look under News: an 8.5-month Marie-Curie fellowship is currently available in Geometric Learning, for students…<\/span> Read more \"Open Positions\"<\/span><\/a><\/span><\/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\/402"}],"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=402"}],"version-history":[{"count":7,"href":"https:\/\/erga.di.uoa.gr\/index.php\/wp-json\/wp\/v2\/pages\/402\/revisions"}],"predecessor-version":[{"id":796,"href":"https:\/\/erga.di.uoa.gr\/index.php\/wp-json\/wp\/v2\/pages\/402\/revisions\/796"}],"wp:attachment":[{"href":"https:\/\/erga.di.uoa.gr\/index.php\/wp-json\/wp\/v2\/media?parent=402"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}