Split Applied Mathematics Day 2018

Split Applied Mathematics Day 2018 (SAMD2018) is a one-day meeting focused on presenting new ideas and recent developments in the field of applied mathematics and fostering collaborations between researchers.

Date: Friday, June 15, 2018
Time: 9 a.m. - 5:30 p.m.
Location: Room B3-17, University of Split, Faculty of Science, Ruđera Boškovića 33, 21000 Split, Croatia.

Students are especially encouraged to attend!

Registration

While SAMD2018 is a free and open event, registration is required. Please register here. Last day to register is Monday, June 4, 2018.

Speakers

• Anita Carević
• Andrijana Ćurković
• Vesna Gotovac
• Nevena Jakovčević Stor
• Saša Krešić Jurić
• Lana Periša
• Ivan Slapničar
• Damir Vukičević

Organizers

• Faculty of Electrical Engineering, Mechanical Engineering and Naval Architecture, Ivan Slapničar (email)
• Faculty of Science, Nikola Koceić Bilan (email)
• Split Mathematical Society, Borka Jadrijević (email)

Schedule

9:00 - 9:45 Jesse Barlow, Penn State (abstract)
9:45 - 10:30 Eric Goles, UAI (abstract)
10:30 - 11:00 Coffee break, Room B3-35 11:00 - 11:45 Krešimir Veselić, FernUniversität
11:45 - 12:30 Daniel Kressner, EPFL (abstract)
12:30 - 14:00 Lunch break 14:00 - 14:20 Anita Carević, FESB (abstract)
14:20 - 14:40 Andrijana Ćurković, PMF (abstract)
14:40 - 15:00 Vesna Gotovac, PMF (abstract)
15:00 - 15:20 Nevena Jakovčević Stor, FESB (abstract)
15:20 - 16:00 Coffee break, Room B3-35 16:00 - 16:20 Saša Krešić Jurić, PMF (abstract)
16:20 - 16:40 Lana Periša, FESB (abstract)
16:40 - 17:00 Ivan Slapničar, FESB (abstract)
17:00 - 17:20 Damir Vukičević, PMF (abstract)

Venue Map

University of Split, Faculty of Science
Ruđera Boškovića 33, 21000 Split, Croatia

Keynote speakers

Jesse Barlow

Jesse Barlow is Professor at the Department of Computer Science and Engineering, the Pennsylvania State University, USA. His research interests are numerical mathematics, numerical linear algebra and algorithms for image processing. Professor Barlow holds Ph.D. in Computer Science from the Northwestern University.

He was awarded second prize at the Leslie Fox Prize in 1986 and second place at the SIAG Linear Algebra Prize in 1991.

http://www.cse.psu.edu/~b58/

Eric Goles Chacc

Dr. Eric Goles is Professor at the Engineering Faculty of the Adolfo Ibanez University, Santiago, Chile. He was member of the French CNRS, first director of the Center for Mathematical Modeling (University of Chile), creator and director of the Institute for Complex System (Valparaiso-Chile), and creator and current scientific director of the PhD program in Complex System. He was also the head of the Chilean Agency for Science and Technology (2000-2006).

Dr. Goles is interested in Theoretical Computer Science, Discrete Mathematics, Complex Systems and Automata Networks. He has about 200 publications and several books.

Dr. Goles is a member of the Chilean Academy of Sciences since 1990 and the corresponding member of the Croatian Academy of Sciences and Arts since 2006.

Krešimir Veselić

Krešimir Veselić is Professor emeritus of Mathematics at the FernUniversität in Hagen, German. He obtained his Ph.D. in Mathematics from the University of Zagreb. His research interests are accuracy of eigenvalue and singular value computations, optimization of vibrating systems and matrix and operator methods in classical and quantum mechanics. He published over 100 scientific papers and supervised 19 doctoral thesis.

Professor Veselić was an Alexander-von-Humboldt fellow in 1972. He received SIAG Linear Algebra Prize in 2009.

He is a corresponding member of the Croatian Academy of Sciences and Arts since 1997.

https://www.fernuni-hagen.de/MATHPHYS/veselic/

Daniel Kressner

Daniel Kressner is Professor of Numerical Analysis and High Performance Computing at the École polytechnique fédérale de Lausanne. He obtained Ph.D in Mathematics in 2004 at the TU Berlin. After postdoctoral positions in Umea and Zagreb, he was Assistant Professor at the ETH Zurich from 2007 until 2011.

His main area of research is the numerical linear algebra including wide range of applications, in particular low-rank matrices and tensor approximation techniques.

He won the John Todd Oberwolfach Foundation Award in 2011 and the SIAM Outstanding Paper Prize in 2013.

https://people.epfl.ch/daniel.kressner

A class of modified Gram-Schmidt algorithms and their analysis

Jesse L. Barlow, Computer Science and Engineering, The Pennsylvania State University

We develop a block modified Gram-Schmidt (BMGS) algorithm to factor a full column rank matrix $X \in \mathbf{R}^{m\times n}$, $m \geq n$, into $Q \in \mathbf{R}^{m\times n}$ and upper triangular $R \in \mathbf{R}^{m\times n}$ such that $$X = QR \label{eq:QRfact}$$ and, in exact arithmetic, $Q$ is left orthogonal, i.e, $Q^T Q=I_n$. The BLAS-3 algorithm builds upon block Householder representation of Schreiber and Van Loan [R. Schreiber and C.F. Van Loan, A storage-efficient WY representation for products of Householder transformations, SIAM J. Sci. Stat. Computing,10:53--57,1989] and an observation by Charles Sheffield analyzed by Paige [C.C. Paige, A useful form of unitary matrix from any sequence of unit 2-norm $n$-vectors, SIAM J. Matrix Anal. Appl., 31(2):565--583, 2009] about the relationship between modified Gram-Schmidt and Householder QR factorization. Using the Sheffield framework, we show that the BMGS has a similar relationship to Householder QR factorization and thus has similar error analysis properties to modified Gram-Schmidt.

Dynamics and Complexity of Majority Automata: application to some discrete social models

A Majority Automata consists of applying over the vertices of a undirected graph (with states 0’s and 1’s) an operator that chooses the most represented state among the neighbors of a vertex. This rule is applied in parallel over all the nodes of the graph. When the graph is a regular lattice (in one or more dimensions) it is called the Majority Cellular Automata.

In this seminar we will study the computational complexity of the following prediction problem: PRED: Given an initial configuration and a specific site initially at state a ( 0 or 1), is there a time step T≥1 such that this site changes state?

The complexity of PRED is characterized by the possibility to find an algorithm that give the answer faster than the running of the automata simulation in a serial computer. More precisely, if we are able to determine an algorithm running in a parallel computer in polylog time (class NC). Otherwise, the problem may be P-Complete ( one of the most dificult in class P of Polynomial problems) or … worse.

We will applied this kind of results to the discrete Schelling’s segregation model. Also we will present the Sakoda’s Social Discret model.

Bivariate matrix functions: Algorithms and Applications

Daniel Kressner, EPF Lausanne

Bivariate matrix functions provide a unified framework for various tasks in numerical linear algebra, including the solution of linear matrix equations and the computation of Frechet derivative. In this talk, we discuss a novel variants of Krylov subspace methods for approximating such bivariate matrix functions and analyze their convergence. We then focus on the particular case of Frechet derivatives and its application to the solution of inverse problems and graph learning.

Solving the inverse scattering problem in ultrasound tomography using regularized total least squares

Anita Carević, FESB

In recent years there have been significant improvements in the use of ultrasound tomography (UT) for the detection of breast cancer. However, ill-posed inverse problem in numerical algorithms utilized for UT is still an issue. To overcome this, we are solving the inverse problem with two forms of the regularized total least squares (RTLS) method. In order to reconstruct the ultrasound image from the synthetic data, we used the distorted Born iterative (DBI) method, which convergence is ensured using aforementioned RTLS, resulting in a high quality image reconstruction.

This is a joint work with Jesse Barlow, Ivan Slapničar and Mohamed Almekkawy.

Interaction of a thin fluid layer with an elastic plate

Andrijana Ćurković, PMF

The interaction of an incompressible fluid occupying thin two-dimensional channel with an elastic plate located on the upper part of the fluid domain boundary is considered. The flow is modeled by non-steady Stokes equations and it is governed by a time-dependent pressure drop and an external force. The problem is studied in the limit when the thickness of the channel tends to zero. A sixth order parabolic equation is obtained for the effective plate displacement. We state and prove results on existence, uniqueness and regularity of the solution of the effective problem.

This is joint work with Eduard Marušić-Paloka.

Similarity measures of random sets based on N-distances and their applications to two-realisation problem

Vesna Gotovac, PMF

In recent years random sets were recognised as a valuable tool in modelling different processes from fields like biology, biomedicine or material sciences. These random sets could be of very ragged shaped and therefore difficult to compare or describe using simple models.

In this talk, we focus on statistical testing of similarity of random sets in a nonparametric way.

We propose two different approaches for assessing the similarity between random sets based on two realisations. In the first approach, we compare their inner structure with the aim to capture the repulsion or clustering tendencies of the set components. The second approach takes into account the general position and the shape of the set components. We define similarity measures as the p-values of tests of equality in distribution based on N-distances.

Both approaches are justified by a simulation study and applied to real data.

Hamiltonian Integrable Systems and Geometric Numerical Integration

Saša Krešić Jurić, PMF

Accurate computation of roots of real polynomials with real simple roots

Nevena Jakovcević Stor, FESB

As showed in (Fiedler, 1990), any polynomial can be expressed as a characteristic polynomial of a complex symmetric arrowhead matrix. This expression is not unique. If the polynomial is real with only real distinct roots, the matrix can be chosen real. By using the algorithm for computing eigenvalues of the real symmetric arrowhead matrices we derive a new algorithm for computation of roots of such polynomials in $\mathcal{O}(n^2)$ operations. The algorithm computes each root to almost full accuracy. In some cases, the algorithm invokes extended precision routines, but only in the non-iterative part. The algorithm compares favorably to other method for polynomial root-finding, like MPSolve or Newton’s method. This is joint work with Ivan Slapničar.

Multidimensional arrays with Julia

Lana Periša, FESB

Writing algorithms with multidimensional arrays (i.e. tensors) can be tedious and frustrating. Starting with release 0.4, Julia makes it easy to write elegant and efficient multidimensional algorithms. The new capabilites rest on two foundations: a new type of iterator and sophisticated array indexing mechanism. This simplifes the notation and can significantly speed up tensor operations such as creating block diagonal tensors and Kronecker products of tensors, which is particularly useful when dealing with compressed schemes of tensors, such as Tucker format.

Fast Optimal Damping

Ivan Slapničar, FESB

We formulate the eigenvalue problem underlying the mathematical model of a linear vibrational system as an eigenvalue problem of a diagonal-plus-rank-one matrix $A$. The eigenvector matrix of $A$ has Cauchy-like structure. We compute the trace of the solution of the Lyapunov equation $AX+XA^*=-GG^*$ using fast computations with Cauchy-like and Toeplitz-like matrices. Here $G$ is a low-rank matrix which depends on the damped eigenfrequencies. This is joint work with Nevena Jakovčević Stor.

MMR vaccination rates predicted by combining epidemic spread models, game theory, wisdom of crowds, Fibonacci trading, and Google search statistics

Damir Vukičević, PMF

Bauch and Earn proposed analysis of vaccination by combining SIR epidemic spread model and game theory. This model will be amended here. Mentioned model is amended by adding assumptions of wisdom of crowd (different irrational behaviors of individuals cancel each one out when averaged). Hence, all the irrationality comes from only one systematic error - assumption that parents can detect weather MMR vaccination contributed to their children autistic disorder. This assumption is used to extrapolate vaccination rate during vaccination scare. Analogy between vaccination rates and movements of stock prices is explored by applying Fibonacci trading. Connection of vaccination-rates and number of results of Google search engine is analyzed. Developed model corresponds well to England’s vaccination rates during vaccination scare caused by infamous Wakefield paper.