### Department of Mathematics and Systems Analysis

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* Dates within the next 7 days are marked by a star.

Miska Rissanen**Estimates for the spherical maximal function (diploma thesis talk)***** Today * ** Tuesday 22 January 2019, 14:15, M3 (M234)

Seminar on analysis and geometry

Julian Weigt**Almost-Orthogonality of Restricted Haar Functions***** ** Wednesday 23 January 2019, 12:15, M3 (M234)

Seminar on analysis and geometry

Dr. Tomasz Szemberg**Linear systems with assigned base loci***** ** Wednesday 23 January 2019, 14:00, M2 (M233)

I will report on special linear systems on complex projective spaces. Even though
the topic is classical and studied for more than 100 years, many important questions are not answered in a satisfactory way.

Algebra Seminar

Dr. Justyna Szpond**Fermat-type configurations in projective spaces***** ** Wednesday 23 January 2019, 15:00, M2 (M233)

A Fermat arrangement of lines in the complex projective plane is given by linear
factors of the polynomial $(x^n-y^n)(y^n-z^n)(z^n-x^n)$ for some $n\geq 3$.
Singular points of these arrangements have appeared recently in commutative algebra, more precisely in the containment problem between symbolic and ordinary powers of homogeneous polynomials and in algebraic geometry in the theory of linear systems and unexpected hypersurfaces. I will explain these two appearances and present considerable generalizations which led to substantial, new results in both fields.

Jaakko Lehtinen**Simulation + machine learning = interpretable, less data hungry AI?**

Tuesday 29 January 2019, 15:00, A2

How do we make computers perceive the everyday world and deeply understand it just by looking at it? How do we build virtual agents and real robots that build on this perception and are able to move and interact with the world, including us humans, in a natural manner? In this talk, Ill talk about the currently accelerating congruence of physically-based simulation and machine learning in solving very hard problems in artificial intelligence. Ill argue that the classic approach of merely learning from human-labeled examples is doomed there is simply no way for us to cover all the variability in the real world with annotated examples and that making use of interpretable models (simulators!) in the learning process is the way forward. Ill give examples of my own work, as well as that of my close colleagues and collaborators, and other highlights from around the world.

Department Colloquium

Kristian Moring**TBA**

Wednesday 30 January 2019, 12:15, M3 (M234)

Seminar on analysis and geometry

Vincenzo Vespri (University of Firenze)**Some regularity problems concerning anisotropic operators**

Wednesday 06 February 2019, 12:15, M3 (M234)

Seminar on analysis and geometry

Emma-Karoliina Kurki**TBA**

Wednesday 13 February 2019, 12:15, M3 (M234)

Seminar on analysis and geometry

Leah Schätzler (University of Erlangen)**Existence of variational solutions for doubly nonlinear equations of porous medium type**

Wednesday 27 February 2019, 12:15, M3 (M234)

Seminar on analysis and geometry

Cintia Pacchiano**TBA**

Wednesday 06 March 2019, 12:15, M3 (M234)

Seminar on analysis and geometry

Olli Saari (University of Bonn)**TBA**

Wednesday 13 March 2019, 12:15, M3 (M234)

Seminar on analysis and geometry

Anastasia Molchanova (Sobolev Institute of Mathematics, Novosibirsk)**TBA**

Wednesday 16 January 2019, 12:15, M3 (M234)

Seminar on analysis and geometry

Christian Webb (Aalto University)**When is a random variable close to being normally distributed?**

Wednesday 19 December 2018, 16:15, U3

Further information

Stochastic Sauna 2018

Alexandre Proutiere (KTH, Stockholm)**Clustering in Block Markov Chains**

Wednesday 19 December 2018, 15:15, U3

Further information

Stochastic Sauna 2018

Stefan Geiss (University of Jyväskylä)**Approximation of stochastic integrals, Riemann-Liouville operators, and bounded mean oscillation**

Wednesday 19 December 2018, 14:00, U3

Further information

Stochastic Sauna 2018

Mari Myllymäki (Natural Resources Institute Finland (Luke))**Global envelopes for testing with functional test statistics and functional data analysis**

Wednesday 19 December 2018, 13:00, U3

Further information

Stochastic Sauna 2018

Ioan Manolescu (Université de Fribourg)**Uniform Lipschitz functions on the triangular lattice have logarithmic variations**

Wednesday 19 December 2018, 11:00, U3

Further information

Stochastic Sauna 2018

Luis Alvarez Esteban (University of Turku)**A Class of Solvable Stationary Singular Stochastic Control Problems of Linear Diffusions**

Wednesday 19 December 2018, 10:00, U3

Further information

Stochastic Sauna 2018

Joonas Laihanen**A distribution-based subpopulation framework for statistic estimation**

Tuesday 18 December 2018, 15:15, M2 (M233)

MS-E1609 - Seminar on stochastics and statistics

Istvan Prause**Arctic curves beyond the arctic circle**

Monday 17 December 2018, 15:00, M3 (M234)

The dimer model studies random configurations of perfect matchings (dimer covers) of bipartite planar graphs. Through an associated height function such a configuration is encoded in a random surface. These random surfaces (with a fixed boundary) exhibit limit shape formation: a deterministic limit surface emerges in the macroscopic limit. The imposed boundary condition can have dramatic effect: in certain regions the dimers line up in an ordered fashion (form a frozen facet) and do not look random at all. A prime example of this phenomenon is the arctic circle of domino tilings of the Aztec diamond from 1995.
We now have, mostly due to Kenyon et al., a general theory which describes these phenomena in unprecedented detail. The limit shape is described by a convex but singular and degenerate variational problem with a gradient constraint. These features are responsible for facet formation and the appearance of arctic curves. In the talk, I will use the lozenge tiling model (dimer model on the hexagonal lattice) to showcase these issues and address how one can analyse the variational problem.

Aalto Stochastics and Statistics seminar / Ilmonen, Kytölä, Leskelä

Johan Salmelin (Aalto)**Energy disaggregation of electric heating appliances (MSc thesis talk)**

Friday 14 December 2018, 11:15, M3 (M234)

Antti Pöllänen (Aalto)**Optimization of dense Wi-Fi networks via Markov chain models**

Monday 10 December 2018, 15:15, M3 (M234)

MSc thesis presentation.

Michele Miranda (University of Ferrara)**Properties of convex sets in Wiener spaces**

Wednesday 05 December 2018, 12:00, M3 (M234)

We show some recent results on convex sets in Wiener spaces. We characterize the essential and reduced bound- ary of open convex sets and investigate integration by parts formulae. Of particular interest is the investigation of trace theorems for functions of bounded variation on boundaries of subsets in Wiener spaces.

Seminar on analysis and geometry

Eveliina Peltola (University of Geneva)**Crossing Probabilities of Multiple Ising Interfaces**

Monday 03 December 2018, 15:15, M3 (M234)

Crossing Probabilities of Multiple Ising Interfaces
The planar Ising model is one of the most studied lattice models in statistical physics. Exhibiting a continuous phase transition, it enjoys conformal invariance in the scaling limit, as has been verified recently in celebrated works initiated by S. Smirnov. In this talk, I discuss crossing probabilities of multiple interfaces in the critical Ising model with alternating boundary conditions. In the scaling limit, they are conformally invariant expressions given by so-called pure partition functions of multiple SLE(kappa) with kappa=3.
I also describe analogous results for critical percolation and the Gaussian free field.
Joint work with Hao Wu (Yau Mathematical Sciences Center, Tsinghua University)

Aalto stochastics and statistics seminar / Ilmonen, Kytölä, Leskelä

Razane Tajeddine**Private Information Retrieval from Coded Storage**

Wednesday 28 November 2018, 13:30, Tuuma

Mid-term PhD talk.

Mid-term PhD talk

Matthias Grezet**Application of Matroid Theory to Distributed Data Storage Systems**

Wednesday 28 November 2018, 13:00, Tuuma

Mid-term PhD talk.

Mid-term PhD talk

Taoufiq Damir**Well-rounded lattices in wireless communications**

Wednesday 28 November 2018, 12:30, Tuuma

Mid-term PhD talk.

Mid-term PhD talk

Carlos Mudarra (Complutense University of Madrid)**$C^1$ and $C^{1, \omega}$ Whitney's theorems for convex functions**

Wednesday 28 November 2018, 12:15, M3 (M234)

Seminar on analysis and geometry

Prof Tuomo Kuusi (University of Helsinki)**Quantitative Stochastic Homogenization and Large-Scale Regularity**

Tuesday 27 November 2018, 15:15, E

One of the principal difficulties in stochastic homogenization is transferring quantitative ergodic information from the coefficients to the solutions, since the latter are nonlocal functions of the former. In our recent book, jointly with S. Armstrong and J.-C. Mourrat, we have addressed this problem from a new perspective. Essentially, we use recently developed regularity theory for stochastic homogenization to accelerate the weak convergence of the energy density, flux and gradient of the solutions as we pass to larger and larger length scales, until it saturates at the CLT scaling. I will discuss our approach and give, at the same time, an informal introduction to our book.

Department Colloquium

Negin Karimi**Generalized regenerating codes and security of distributed storage system**

Wednesday 21 November 2018, 15:15, M3 (M234)

Traditional regenerating codes are efficient tools to optimize both storage and repair bandwidth in storing data across a distributed storage system, particularly in comparison to erasure codes and data replication. In traditional regenerating codes, the collection of any k nodes can reconstruct the information file and is called the reconstruction set, N_R. Also, a failed node can be regenerated from any d surviving nodes. These collections of d nodes are called the regeneration sets, N_H. The number of reconstruction sets and the number of regeneration sets satisfies N_R= C_n^k and N _H=C_{n-1}^d, where C_n^k denotes "n choose k". In generalized regenerating codes, we will have, 1 \le N_R \le C^k_n and 1 \le N_H \le C_{n-1}^d. In this talk, I address the problem of secure generalized regenerating codes and present a coding scheme by focusing on the features of the generalized regenerating codes that protect data in the distributed storage system in presence of an active omniscient adversary.

ANTA seminar

Aleksis Koski (University of Jyväskylä)**Sobolev homeomorphic extensions**

Wednesday 21 November 2018, 12:15, M3 (M234)

In the mathematical theory of nonlinear elasticity one typically represents elastic bodies as domains in Euclidean space, and the main object of study are deformations (mappings) between two such bodies. The class of acceptable deformations one considers usually consists of Sobolev homeomorphisms between the respective domains, for example, with some given boundary values. It is hence a fundamental question in this theory to ask whether a given boundary map admits a homeomorphic extension in the Sobolev class or not. We share some recent developments on this subject, including sharp existence results and counterexamples.

Seminar on Analysis and Geometry

Title. Firstname Lastname (Home organisation)**TBA**

Wednesday 14 November 2018, 15:29, M3 (M234)

Karl Brustad (NTNU, Trondheim)**The dominative p-Laplacian and sublinear elliptic operators**

Wednesday 14 November 2018, 12:15, M3 (M234)

Seminar on analysis and geometry

Olga Kuznetsova**MSc thesis presentation: Private information retrieval with arbitrary collusion patterns**

Wednesday 07 November 2018, 15:15, M3 (M234)

In coded Private Information Retrieval (PIR), a user wants to download a file from a coded database without revealing the identity of the file. We consider the setting where certain subsets of servers collude to deduce the requested file. These subsets form an abstract simplicial complex called the collusion pattern. In this talk we will discuss the combinatorics of the general star product scheme for PIR under the assumption that the database is encoded using a repetition code.
Advisor Ragnar Freij-Hollanti, supervisor Camilla Hollanti.

ANTA Seminar

Vito Buffa (University of Ferrara)**New insights into BV Functions and Integration by Parts Formulæ in Metric Measure Spaces**

Wednesday 07 November 2018, 12:15, M3 (M234)

The starting point of our discussion is a notion of BV functions tailored for RCD(K,\infty) metric measure spaces, which makes use of suitable vector fields.
This definition motivates both the study of integration by parts formulæ in terms of essentially bounded divergence-measure vector fields in diverse metric settings, and an investigation of the issue of traces of BV functions
in the context of a doubling metric measure space supporting a Poincaré inequality.
Based on joint works with G. E. Comi (Scuola Normale Superiore, Pisa) and M. Miranda Jr (University of Ferrara).

Seminar on analysis and geometry

Vitaly Skachek (University of Tartu)**[NOTE the unusual time and place!] Batch and PIR Codes and Their Connections to Locally Repairable Codes**

Monday 05 November 2018, 14:15, M205

In this survey talk, we discuss two related families of codes: batch codes and codes for private information retrieval. These two families can be viewed as natural generalizations of locally repairable codes, which were extensively studied in the context of coding for fault tolerance in distributed data storage systems. Bounds on the parameters of the codes, as well as basic constructions, are presented. Connections between different code families are discussed.

ANTA Seminar

Mateo Rendon**An algebraic and combinatorial perspective on rank-one tensor completion**

Thursday 01 November 2018, 15:15, M2 (M233)

Master's thesis presentation

Ratan Kumar Giri (National Institute of Technology Rourkela)**Singular Nonlocal Problem Involving Measure Data**

Wednesday 31 October 2018, 12:15, M3 (M234)

Seminar on analysis and geometry

Prof Chris Brzuska (Aalto University)**Proof Theory for Cryptography**

Tuesday 30 October 2018, 15:15, E

Most of our cryptography is not perfectly unbreakable. Given enough time, one could, theoretically, perform an exhaustive search over the key space and e.g., decrypt messages intended for another receiver. Modern cryptography, thus, relies on computationally hard problems that (are conjectured to) require an exorbitant amount of computation to solve. Complex systems such as TLS, the backbone of secure communication on the internet, rely on quite a number of such hard problems, and the protocol itself has a specification of over 100 pages. The relation between the protocol security (in a model) and the underlying assumptions needs to be established via a rigorous reduction proof. Due to the complexity of the protocols, the reduction proofs for modern protocols escape what a human can grasp. Therefore, in recent years, the proofs have been partially delegated to computers which, to be fair, also struggle with the tremendous complexity. We propose a new level of abstraction that allows to recover human understanding of security reductions for complex protocols and show how to apply it to the new TLS 1.3 standard (ongoing work).
Joint work with Ben Dowling, Antoine Délignat-Lavaud, Cédric Fournet, Konrad Kohbrok & Markulf Kohlweiss

Department Colloquium

Prof. Luka Grubisic, University of Zagreb**Analysis of an eigenvalue problem on a metric graph**

Friday 26 October 2018, 14:15, M2 (M233)

We analyze a second order constrained eigenvalue problem on a metric graph. The underlying vector valued differential operator originates in the vibration analysis in the modelling of endovasular stents. We also study the dynamical problem for such a configuration and show that standard DAE integrators can solve the problem well. This is a joint work with V. Mehrmann and J. Tambaca.

Razane Tajeddine and Lukas Holzbaur**On private keyword and stream search**

Wednesday 24 October 2018, 15:15, M3 (M234)

In the first part of the talk, we discuss private keyword search (PKS). Some work has been done to ensure privacy for the user when searching for keywords from a distributed storage system.
In the second part of the talk, we discuss the concept of private search on streaming data (PSS), and its connection to PIR and PKS on the example of a scheme given by Ostrovsky et al. The problem of private search on streaming data (PSS) has been considered under various cryptographic assumptions, e.g. by means of homomorphic cryptosystems and public-key program obfuscation.

ANTA seminar

Hans Tylli (University of Helsinki)**Structural rigidity of generalised Volterra operators on Hardy spaces**

Wednesday 24 October 2018, 12:15, M3 (M234)

will describe generalised analytic Volterra operators T_g on the Hardy spaces H^p
over the unit disk D for 1 \le p < \infty, where
T_gf(z) = \int_0^z f(w)g'(w) dw,
for z in D and f in H^p. Above the analytic map g from BMOA is the symbol of T_g.
The systematic study of this class of operators was initiated by Aleman, Cima and
Siskakis around 1995. Earlier certain T_g were used by Pommerenke (1977)
and the class contains e.g. a version of the classical Cesaro averaging operator,
which is obtained with g(z) = - \log(1-z).
I will focus attention on recent work on the structural rigidity of the class of
non-compact operators T_g on H^p for p different from 2.
The main result says that if T_g defines an isomorphism from M to T_g(M)
for the infinite-dimensional closed subspace M of H^p,
then M contains a subspace linearly isomorphic to the sequence space \ell^p.
In particular, this implies that the non-compact Volterra operators T_g have a
quite restricted range of linear qualitative behaviour compared to that of
arbitrary bounded operators on H^p (for p different from 2).
This is joint work with Santeri Miihkinen (Åbo), Pekka Nieminen (Turku) and
Eero Saksman (Helsinki).

Seminar on Analysis and Geometry

Vasiliki Evdoridou (The Open University, UK)**Singularities of inner functions and entire maps of finite order**

Wednesday 17 October 2018, 12:15, M3 (M234)

Let f be a transcendental entire function of finite order and U an unbounded, invariant Fatou component of f. We can associate an inner function, g say, to the restriction of f to U. We will show that for two classes of entire functions whose set of singular values is bounded, the number of singularities of g on the unit circle is at most twice the order of f. This is joint work with N. Fagella, X. Jarque and D. Sixsmith.

Seminar on analysis and geometry

Arttu Karppinen (University of Turku)**Higher integrability of the gradient of a minimizer with generalized Orlicz growth**

Wednesday 10 October 2018, 12:15, M3 (M234)

In this talk we prove global higher integrability of a minimizer of an obstacle problem with generalized Orlicz growth conditions. This recovers the similiar results of the special cases such as polynomial, variable exponent and double phase growth.

Seminar on Analysis and Geometry

Augusto Gerolin (University of Jyväskylä)**Kantorovich Duality in Optimal Transport Theory with repulsive costs**

Wednesday 03 October 2018, 12:15, M3 (M234)

Seminar on Analysis and Geometry

Juha-Pekka Puska**Optimizing heating patterns in thermal tomography**

Thursday 27 September 2018, 14:15, M2 (M233)

Christoph Scheven (University of Duisburg-Essen)**The obstacle problem for the porous medium equation: Existence and regularity results**

Wednesday 26 September 2018, 12:15, M3 (M234)

In the talk we will present some results on existence and regularity of solutions to the obstacle problem associated to the porous medium equation. In particular, we will report on recent results concerning the higher integrability of the spatial gradient of solutions.

Seminar on analysis and geometry

Prof Matthieu Jonckheere (University of Buenos Aires)**Distance learning using Euclidean percolation: Following Fermat's principle**

Tuesday 25 September 2018, 15:15, E

In unsupervised statistical learning tasks such as clustering, recommendation, or dimension reduction, a notion of distance or similarity between points is crucial but usually not directly available as an input. We discuss recent techniques to infer a metric from observed data. Then we propose a new density-based estimator for weighted geodesic distances that takes into account the underlying density of the data, and that is suitable for nonuniform data lying on a manifold of lower dimension than the ambient space. The consistency of the estimator is proven using tools from first passage percolation. After discussing its properties and implementation, we evaluate its performance for clustering tasks.

Department Colloquium

Verena Bögelein (University of Salzburg)**Higher integrability for doubly nonlinear evolution equations**

Wednesday 19 September 2018, 12:15, M3 (M234)

In this talk we establish the higher integrability of the spatial gradient of weak solutions to doubly nonlinear evolution equations.

Seminar on analysis and geometry

Jens Zumbrägel (Universität Passau)**Indiscrete Logarithms?**

Thursday 13 September 2018, 15:15, M2 (M233)

The modern public-key cryptography, as originated from the seminal work
by Diffie and Hellman, is since connected with the difficulty of the
discrete logarithm problem. However, for finite fields of small
characteristic, this problem turns out to be not as intractable as
thought for a long time. In fact, some striking observations have
recently led to considerable record computations and severe consequences
for the security of certain cryptosystems. This talk aims to illustrate
the main mathematical ideas behind these rather new developments.

ANTA seminar

Prof. Stefano Giani (Durham)**High-Order/hp-Adaptive Multilevel Discontinuous Galerkin Methods**

Tuesday 04 September 2018, 14:00, M2 (M233)

After a brief introduction on discontinuous Galerkin (DG) methods I describe the DG composite finite element (DGCFE) method, a DG multilevel method with hp-adaptivity. The main advantage of this multilevel method is that the number of degrees of freedom of the finite element space is independent of the presence of complicated or tiny features in the domain. In other words, even on a very complicated domain, an approximation of the solution can be computed with only a fistful of degrees of freedom. Unlikely other multilevel methods, this method does not perturb the problem, in the sense that the problem solved on the coarse mesh is always a discretization of the DG weak form of the problem, no matter how coarse the mesh is.
The hp-adaptivity algorithm for the DGCFE method is completely automatic and capable of exploiting both local polynomial-degree-variation (p-refinement) and local mesh subdivision (h-refinement), thereby offering greater flexibility and efficiency than numerical techniques which only incorporate h-refinement or p-refinement alone.
Two types of error estimators are used to drive the adaptivity: an explicit one and an implicit one based on a duality argument. In the latter case, the element residuals of the computed numerical solution are multiplied by local weights involving the solution of a certain dual or adjoint problem.
The performance of the hp-refinement algorithm is demonstrated through a series of numerical experiments.
DGCFE can also be used to solve problems on polygonal meshes. This will be shown for elliptic eigenvalue problems.

Veli Kangas**Informaatioteoreettinen tarkastelu neuroverkoista**

Thursday 30 August 2018, 15:15, M3 (M234)

kandiseminaari

Joona Savela**On Feature Extraction of Multispectral Mobile Laser Scanner Data**

Thursday 30 August 2018, 14:15, M3 (M234)

kandiseminaari

Jaakko Visti**Group theory in image classification**

Thursday 30 August 2018, 13:15, M3 (M234)

kandiseminaari

Mikko Karjalainen (Imaqen Ltd)**Time-series registration of thermal breast images**

Thursday 30 August 2018, 13:15, M2 (M233)

Master's thesis presentation

Jaakko Visti**Group theory in image classification**

Thursday 30 August 2018, 13:15, M3 (M234)

BSc presentation. Advised by Laia Amoros.

Marco Fiorucci (Ca' Foscari U, Venice)**Graph Summarization Using Regular Partitions**

Thursday 30 August 2018, 11:15, M3 (M234)

The world we live in is becoming more and more interconnected and huge amounts of data are produced and stored every day by different interrelated entities. This high-throughput generation calls for the development of efficient algorithms to understand and process large and noisy network data. To address this challenging task, we develop a principled approach to summarize (compress) large graphs based on regular partitions, the existence of which was first established in a celebrated result proved by Endre Szemerédi in the mid-1970. A regular partition is defined as a partition of the vertex set into a bounded number of random-like bipartite graphs, called regular pairs. In particular, a regular pair is a highly uniform bipartite graph in which the density of any reasonably sized subgraphs is about the same as the overall density of the bipartite graph.
In this talk, I will provide an overview of the regularity lemma and will discuss its potential usefulness in real-world applications.

Aalto Stochastics & Statistics Seminar

Onni Pohjavirta**Multi-p methods for the p-version of finite element method**

Thursday 30 August 2018, 11:15, M2 (M233)

kandiseminaari

Tuukka Piipponen**Reitin estimointi Kalman-suotimen avulla**

Thursday 30 August 2018, 10:15, M2 (M233)

kandiseminaari

Tero Hyytiäinen**Kneser graphs that are Folkman**

Tuesday 28 August 2018, 14:15, M3 (M234)

kandiseminaari

Teemu Mäki**Betti Diagrams of Perfect Graphs**

Tuesday 28 August 2018, 13:15, M3 (M234)

kandiseminaari

Essi Rantanen**Quasi-Monte Carlo**

Tuesday 28 August 2018, 12:15, M3 (M234)

kandiseminaari

Jaakko Lehtonen**Diskreetti momenttiongelma stokastisen lohkomallin estimoinnissa**

Thursday 23 August 2018, 15:15, M3 (M234)

kandiseminaari

Kari Väisänen**Fatoun lause harmonisille funktioille ylemmässä puoliavaruudessa**

Thursday 23 August 2018, 14:15, M3 (M234)

kandiseminaari

Mikko Kaivola**Assessing the covariates of property and violent crime in Helsinki using spatial controls**

Thursday 23 August 2018, 13:15, M3 (M234)

kandiseminaari

Kévin Selänne**Funktionaalisen datan ryhmäkeskiarvojen yhtäläisyyden testaaminen bootstrapilla**

Thursday 23 August 2018, 11:15, M3 (M234)

kandiseminaari

Jaakko Pere**Asymptotic properties of the Hill estimator**

Thursday 23 August 2018, 10:15, M3 (M234)

kandiseminaari

Katri Ailus**On modeling train energy consumption (Master's thesis presentation)**

Wednesday 22 August 2018, 15:15, M3 (M234)

Aalto Stochastics and Statistics Seminar

Tuomas Lebedeff**Minimipinnat**

Tuesday 21 August 2018, 11:15, M3 (M234)

kandiseminaari

Joel Himanen**Toiminnalisen neurokuvantamisen data-analyysi: konvolutiivinen lähestymistapa MEG:n design-matriisiin**

Tuesday 21 August 2018, 10:15, M3 (M234)

kandiseminaari

Elmer Bergman**Tikhonov regularization and a polynomial surrogate**

Tuesday 21 August 2018, 09:30, M3 (M234)

kandiseminaari

Topi Kuutela (Aalto University)**Beamforming in frequency division duplex cellular networks **

Friday 17 August 2018, 11:15, M2 (M233)

Sung Chul Park (EPFL)**Local correlations in the critical and near-critical planar Ising model**

Wednesday 15 August 2018, 14:15, M3 (M234)

The scaling limit of the 2D critical Ising model is expected to exhibit conformal invariance, which has been proved in the case of spin (Chelkak, Hongler and Izyurov 2015) and energy (local 2-point) correlations (Hongler and Smirnov 2013). We extend these results by giving a conformally covariant description for the local n-point correlations in the scaling limit. Then we will go on to discuss preliminary results and ongoing work in the near-critical (scaling towards criticality) setting and their significance from the viewpoint of Conformal Field Theory. Based on joint work with R. Gheissari (first part) and C. Hongler.

Stochastics seminar / Ilmonen, Kytölä, Leskelä

Patrik Muhojoki **Power Decoding of Reed-Solomon Codes**

Wednesday 15 August 2018, 13:15, M3 (M234)

BSc presentation. Advised by Oliver Gnilke and Razane Tajeddine.

Patrik Muhojoki **Power Decoding of Reed-Solomon Codes**

Wednesday 15 August 2018, 13:15, M3 (M234)

kandiseminaari

Rustam Latypov **Vastusverkon käänteisongelma**

Wednesday 15 August 2018, 11:15, M3 (M234)

kandiseminaari

Valtteri Helaakoski **Cohenin luokan aikataajuusjakaumat**

Wednesday 15 August 2018, 10:15, M3 (M234)

kandiseminaari

Kalle Kytölä [Math physics afternoon]**Probabilistic lattice models and conformal field theory**

Wednesday 08 August 2018, 16:30, M3 (M234)

A major conjecture in two-dimensional statistical mechanics is that scaling limits of lattice models are described by conformally invariant quantum field theories. The main ingredient of conformal field theories is a Virasoro algebra representation on local fields. In two lattice models, the critical Ising model and the discrete Gaussian free field, we find this exact structure even before passing to the scaling limit.
The result is joint work with Clément Hongler (EPFL) and Fredrik Viklund (KTH).

Mathematical physics afternoon organized by Karrila & Kytölä

Christian Webb [Math physics afternoon]**On the eigenvalues of a random Hermitian matrix**

Wednesday 08 August 2018, 16:00, M3 (M234)

I will discuss some recent work concerning rigidity of eigenvalues of a random Hermitian matrix: that is, how much can the eigenvalues of a large random Hermitian matrix fluctuate around certain deterministic quantities.

Mathematical physics afternoon organized by Karrila & Kytölä

David Radnell [Math physics afternoon]**Moduli spaces in conformal field theory**

Wednesday 08 August 2018, 15:30, M3 (M234)

One of the standard axiomatic approaches to conformal field theory involves infinite-dimensional moduli spaces of Riemann surfaces. The rigorous definition and study of these moduli spaces requires complex analysis and geometry, quasiconformal Teichmueller theory, functional analysis etc. I will outline the connection between these topics and state some recent results.

Mathematical physics afternoon organized by Karrila & Kytölä

Alex Karrila [Math physics afternoon]**On the weak convergence of multiple plane curves**

Wednesday 08 August 2018, 14:30, M3 (M234)

In statistical mechanics, one often studies a random model on a fine-mesh lattice approximating a continuum domain. One descriptive feature of such models are interface curves, such as boundaries of magnetization clusters in a ferromagnetism model. Consider a situation where boundary conditions, for instance alternating +/- magnetizations on the boundary of the ferromagnet, force the existence of multiple macroscopic chordal interfaces. We derive criteria, valid for various random models, that guarantee the existence of a weak limit of such chordal interfaces as the lattice mesh turns finer.

Mathematical physics afternoon organized by Karrila & Kytölä

Armando Gutierrez [Math physics afternoon]**On the metric compactification of Banach spaces**

Wednesday 08 August 2018, 14:00, M3 (M234)

I will explain a method that has recently appeared in metric geometry and has shown to be an effective technique to compactify metric spaces. Afterwards, I will present a complete description of the metric compactification of the classical Banach spaces Lp in finite and infinite dimensions.

Mathematical physics afternoon organized by Karrila & Kytölä

Antti Suominen [Math physics afternoon]**Spin correlation functions of the 2D Ising model [MSc talk]**

Wednesday 08 August 2018, 13:15, M3 (M234)

I will discuss how discrete complex analysis and orthogonal polynomials can be used to study the spin correlation functions of the two dimensional Ising model.

Mathematical physics afternoon organized by Karrila & Kytölä

Osama Abuzaid [Math physics afternoon]**Infinite self avoiding half space random walks [MSc talk]**

Wednesday 08 August 2018, 12:30, M3 (M234)

A self avoiding walk (SAW) is an injective walk in a lattice embedded in an Euclidean space. A random SAW of length n is a uniformly distributed random variable on all self avoiding walks of length n starting from origin. In this talk, we are mainly interested in random SAWs in a d-dimensional qubic lattice which are restricted to the upper half plane. These are called self avoiding half space random walks (SAHSW). I will present necessary tools to show the existence of an infinite random SAHSW which is defined as the limit of random SAHSWs of length n, as n tends to infinity.

Mathematical physics afternoon organized by Karrila & Kytölä

Pihla Karanko **MSc thesis presentation: Protocol verification in Tamarin in an access sharing application**

Wednesday 25 July 2018, 15:15, M3 (M234)

I study the use of formal methods in protocol verification, in particular Tamarin language. Tamarin (https://tamarin-prover.github.io) is an automated symbolic verification tool for security protocols. It allows you to specify a protocol and its security properties using so called facts, rewrite rules and lemmas. You can then use it to check the validity of the security properties.
In the talk I explain the theory and syntax of Tamarin and show how to use it to specify and validate a part of an access protocol. I work for a company called Bitwards that provides access sharing software for electronic locks and the protocol I am going to present is part of their access sharing system that we want to formally validate.
MSc thesis presentation. Thesis work is carried out at Bitwards. Advisor Chris Brzuska, supervisor Camilla Hollanti.

ANTA seminar

**Kanditöiden aihe-esittelyt, sessio 2**

Tuesday 19 June 2018, 14:30, M3 (M234)

**Kanditöiden aihe-esittelyt, sessio 1**

Tuesday 19 June 2018, 13:00, M3 (M234)

Leo Tuhkanen**Differentiaaliyhtälöiden visualisointi verkko-opetuksessa**

Monday 11 June 2018, 10:15, M2 (M233)

Diplomityöesitelmä

Joonas Laukka (kandiesitelmä)**Satunnaiskävelyt ja niiden kasvattamat puut**

Friday 08 June 2018, 14:00, M3 (M234)

**Departmental meeting**

Tuesday 29 May 2018, 14:15, Coffee room

Lauri Nyman (kandiesitelmä)**Binääristen luokitteluongelmien ratkaisu hypoteesitestauksen menetelmin**

Monday 28 May 2018, 11:15, M3 (M234)

Timo Takala (kandiesitelmä)**Elliptisen osittaisdifferentiaaliyhtälön heikko ratkaisu**

Monday 28 May 2018, 10:15, M3 (M234)

Summer School at Åbo Akademi on**Number Theory and Coding Theory: Contemporary Applications in Security"**

Monday 28 May 2018, 09:00, Turku

Ferenc Szöllösi (Aalto - Department of Communications and Networking )**Constructions of maximum few-distance sets**

Wednesday 23 May 2018, 15:15, M2 (M233)

Abstract: A finite set of distinct vectors X in the d-dimensional Euclidean space is called an s-distance set, if the set of mutual distances between distinct elements of X has cardinality exactly s. In this talk I will present a computer-aided approach for construction and classification of s-distances for small parameter values. In particular, I will discuss the largest 3-distance set in dimension 4.

ANTA seminar

Vedran Krčadinac (University of Zagreb)**Extensions of quasi-symmetric designs**

Wednesday 16 May 2018, 15:15, M2 (M233)

Let $D$ be a t-(v,k,\lambda) design. If there is a
(t+1)-(v+1,k+1,\lambda) design E such that the derived design
with respect to some point is D, then E is called an extension
of D and D is called extendable. In 1973, P. Cameron classified
the extendable symmetric designs. In this talk we shall look at
extensions of quasi-symmetric designs. Although no parametric
classification is in sight, there is a known infinite family and
several sporadic examples. There are also numerous parameter sets
for which extensions seem feasible, but it is not known whether the
designs and their extensions exist.

ANTA seminar

Lauri Oksanen (University College London)**Teaching Demonstration**

Wednesday 16 May 2018, 09:30, M2 (M233)

Least squares problem/Numerical linear algebra

Vanni Noferini (University of Essex)**Teaching Demonstration**

Wednesday 16 May 2018, 09:00, M2 (M233)

Least squares problem/Numerical linear algebra

Jilu Wang (Florida State University)**Teaching Demonstration**

Tuesday 15 May 2018, 09:30, M1 (M232)

Least squares problem/Numerical linear algebra

Prof. Clément Hongler **Statistical Field Theory and the Ising Model**

Tuesday 24 April 2018, 15:15, D

The developments of statistical mechanics and of quantum field theory are among the major achievements of 20th century's science. In the second half of the century, these two subjects started to converge, resulting in some of the most remarkable successes of mathematical physics. At the heart of this convergence lies the conjecture that critical lattice models are connected, in the continuous limit, to conformally symmetric field theories. This conjecture has led to much insight into the nature of phase transitions and to beautiful formulae describing lattice models, which have remained unproven for decades.
In this talk, I will focus on the planar Ising model, perhaps the most studied lattice model, whose investigation has initiated much of the research in statistical mechanics. I will explain how, in the last ten years, we have developed tools to understand mathematically the emerging conformal symmetry of the model, and the connections with quantum field theory. This has led one to the proof of celebrated conjectures for the Ising correlations and for the description of the emerging random geometry. I will then explain how these tools have then yielded a rigorous formulation of the field theory describing this model, allowing one to make mathematical sense of the seminal ideas at the root of the subject of conformal field theory.

Colloquim

Changsun Choi (Helsinki)**On the Lebesgue space of vector measures**

Friday 20 April 2018, 15:15, Kumpula Exactum C124

The Bochner integral, the integral of vector valued functions with respect to a measure, is well known. What if we integrate scalar functions with respect to a vector measure? In this talk we consider the Lebesgue space L^1(G) of scalar functions which are integrable with respect to a vector measure G in the sense of D. R. Lewis. First, we investigate simpler conditions on a scalarly integrable function f that guarantee f in L^1(G) Next, when a new vector measure F is obtained via the integral F(E)=/int_E f dG, we show that certain properties of the vector measure G are inherited to F; for instance, relative compactness or convexity of the range of vector measures. Along the presentation some of basic properties of vector measures will be explained.

Harmonic analysis and PDE seminar

Matias Vestberg (Aalto)**Local Boundedness of Shallow Water**

Friday 20 April 2018, 14:15, Kumpula Exactum C124

We show that weak solutions of the Diffusive Shallow Water Equation are locally bounded, and obtain an explicit estimate for the essential supremum. Also continuity w.r.t. time is considered. Joint work with Thomas Singer.

Harmonic analysis and PDE seminar

Gleb Pogudin (Courant Institute, New York University)**Teaching demonstration **

Friday 13 April 2018, 15:30, M1 (M232)

Katharina Jochemko (KTH)**Teaching demonstration**

Friday 13 April 2018, 13:30, M1 (M232)

Gleb Pogudin**Elimination for differential and difference equations**

Friday 13 April 2018, 11:15, M1 (M232)

Katharina Jochemko **Positivity and unimodality questions in geometric combinatorics**

Friday 13 April 2018, 09:00, M1 (M232)

Liam Solus**Geometry, Combinatorics, and the Shape of a Distribution**

Thursday 12 April 2018, 15:15, M1 (M232)

Mateusz Michalek**Algebraic Phylogenetics**

Thursday 12 April 2018, 13:00, M240

Liam Solus (KTH)**Teaching demonstration **

Thursday 12 April 2018, 09:35, M1 (M232)

Mateusz Michalek (Max Planck Institute, Leipzig)**Teaching demonstration **

Thursday 12 April 2018, 09:00, M1 (M232)

Amal Attouchi (University of Jyväskylä)**Qualitative properties of viscosity solutions of a degenerate or singular parabolic equation in non-divergence form.**

Wednesday 11 April 2018, 12:15, M3 (M234)

Seminar on analysis and geometry

Emma-Karoliina Kurki**Homogenisation of the Stokes equations in a perforated domain by the energy decomposition method (Master thesis talk)**

Thursday 29 March 2018, 13:15, M237

Augusto Gerolin (University of Jyväskylä)**Optimal Transport meets Density Functional Theory **

Wednesday 28 March 2018, 12:15, M3 (M234)

Seminar on analysis and geometry

**STACK-koulutus / STACK-training**

Wednesday 28 March 2018, 10:15, Y342a

Koulutustilaisuus automaattisesti tarkastettavien STACK-tehtävien laadinnasta Aalto-yliopiston matematiikan laitoksen henkilökunnalle. Tilaisuudessa tutustutaan tehtävien laadinnan perusteisiin kuten käytettyyn syntaksiin, notaatioihin jne.
--
A training session on the creation of STACK exercises for Aalto University Math Department staff. During the session we will cover the basics, i.e. how exercises are created, the used syntax, notation, etc.

Prof. Heikki Haario (Lappeenranta University of Technology)**Statistical invariance in chaos and random patterns**

Tuesday 27 March 2018, 15:15, D

We apply a recent statistical algorithm, originally developed for
parameter estimation of chaotic dynamical systems, to identify
model parameters of reaction-diffusion systems by ensembles of
Turing patterns created by unknown random initial values. The
method is tested using the Fitzhugh-Nagumo model, a classical
model of excitable media. It is shown that the approach is able to
detect small but systematic structural changes of patterns, practically
impossible to distinguish by naked eye.

Colloquim

Study Group**Moduli of families of curves**

Tuesday 27 March 2018, 12:15, M2 (M233)

Ekaterina Kruglov**Pointwise Convergence of Jacobi Polynomials**

Monday 26 March 2018, 13:00, M2 (M233)

Diplomityöesitelmä / Hakula

Antti Vähäkangas (Jyväskylä)**Self-improvement results for two-measure Poincaré inequalities**

Friday 23 March 2018, 15:15, M3 (M234)

Harmonic analysis and PDE seminar

Henri Martikainen (Helsinki)**Boundedness properties of bilinear bi-parameter singular integrals**

Friday 23 March 2018, 14:15, M3 (M234)

Harmonic analysis and PDE seminar

Professor Hans-Georg Weigand (University of Würzburg)**Gottfried Wilhelm Leibniz (1646-1716) and the Invention of Calculus**

Thursday 22 March 2018, 13:15, U149 U6

Rasila/A!OLE

Sylvester Eriksson-Bique (UCLA)**A New proof of Keith-Zhong self improvement**

Wednesday 21 March 2018, 12:15, M3 (M234)

I will discuss how some curve based ideas lead to a fairly
simple proof of Keith-Zhong self improvement with also simple bounds for
the quantity of self improvement. Additionally I will discuss briefly
some ways these ideas work in other contexts.

Seminar on analysis and geometry

**Teaching meeting**

Tuesday 20 March 2018, 14:15, Coffee room

Study Group**Moduli of families of curves**

Tuesday 20 March 2018, 12:15, M2 (M233)

Ari-Pekka Perkkiö (LMU Munich)**Optional projection in duality**

Monday 19 March 2018, 15:15, M203

In this talks we characterize topological duals of Frechet spaces of stochastic processes. This is done by analyzing the optional projection on spaces of cadlag processes whose pathwise supremum norm belongs to a given Frechet space of random variables. We employ functional analytic arguments that unify various results in the duality theory of stochastic processes and also yields new ones of both practical and theoretical interest. In particular, we find an explicit characterization of dual of the Banach space of adapted cadlag processes of class (D). When specialized to regular processes, we obtain a simple proof of a result of Bismut on projections of continuous processes.

Aalto Stochastics & Statistics Seminar

Ilmari Kangasniemi (University of Helsinki)**A sharp uniformly quasiregular Bonk-Heinonen theorem**

Wednesday 14 March 2018, 12:15, M3 (M234)

Bonk and Heinonen have proved that if a closed connected oriented Riemannian n-manifold M receives a non-constant K-quasiregular map from R^n, there exists a bound C(n,K) on the dimension of the cohomology ring of M. It is conjectured that the sharp bound is actually 2^n, with the maximal example given by the n-torus. In this talk, a sharp counterpart of the theorem is presented for uniformly quasiregular maps. Furthermore, the proof of this counterpart theorem also yields a result on the Julia sets of uniformly quasiregular maps, which raises a question about an even stronger limitation. The talk is a continuation of my last talk in Fall 2017, but can be followed without having heard the previous one.

Seminar on analysis and geometry

Study Group**Moduli of families of curves**

Tuesday 13 March 2018, 12:15, M2 (M233)

Laura Jakobsson**The Category of Cellular Resolutions**

Saturday 10 March 2018, 12:15, Y229c

Workshop on Algebraic Combinatorics

Riikka Kangaslampi**Discrete Ricci curvatures**

Saturday 10 March 2018, 11:15, Y229c

We discuss discrete Ricci curvatures on graphs. We define Ollivier-Ricci curvature notion, give motivation to the definition and present a few examples. We also briefly mention the idea behind Bakry-Emery curvature notion. Then we present a few recent results on Ollivier-Ricci and Bakry-Emery curvatures, like classification results for non-negatively curved graphs and based on them, the non-existence of non-positively curved expanders.
Joint work with D.Cushing, N.Peyerimhoff, S.Liu, V.Lipiäinen, Y.Lin, L.Lu, G.W.Stagg and S.-T.Yau.

Workshop on Algebraic Combinatorics

Patrik Noren**Discrete Morse theory and tropical convexity**

Saturday 10 March 2018, 10:15, Y229c

Tropical convexity has recently been used to prove results in commutative algebra. In particular it has been used to construct cellular resolutions of large classes of monomial ideals. In some important cases the classes of ideals have restrictions that are in some sense unnatural and it has been conjectured that the construction work in a larger setting where tropical methods will not work. We give two examples where discrete Morse theory can be used to prove the more general case.

Workshop on Algebraic Combinatorics

Milo Orlich**Algebraic invariants of Booth-Lueker graphs and their edge ideals**

Friday 09 March 2018, 15:15, Y229c

To understand modules over polynomial rings, we can study some of their homological invariants: the Betti numbers and the more recently introduced Boij-Söderberg coefficients. Whereas there are algorithms to compute these invariants, there are no general formulas for them. We will see that there are such formulas for the Booth-Lueker ideal associated to a graph.

Workshop on Algebraic Combinatorics

Alexander Engström**Transfer-Matrix Methods meet Ehrhart Theory**

Friday 09 March 2018, 14:15, Y229c

Workshop on Algebraic Combinatorics

Emanuele Ventura**Tight tensors**

Friday 09 March 2018, 13:15, Y229c

To study the complexity of the matrix multiplication tensor,
Strassen introduced a class of tensors that vastly generalize it, the tight tensors.
Tight tensors are essentially tensors with a good positive dimensional symmetry group.
In this talk, I will present some examples of tight tensors along with some of their combinatorial
and geometric properties. This is joint work with A. Conner, JM Landsberg, and Y. Wang.

Workshop on Algebraic Combinatorics

Sebastian Schwarzacher (University of Bonn)**Parabolic non-linear Calderon Zygmund covering and the porous medium equation**

Wednesday 07 March 2018, 12:15, M3 (M234)

The talk is about some recent results in collaboration with U. Gianazza from Pavia. We introduce a technique that implies that the gradient of solutions to degenerate and singular parabolic equations of porous medium-type satisfy higher integrability properties. The core is to modify the by-now classical Gehring lemma by introducing an intrinsic Calderon-Zygmund covering argument.

Seminar on analysis and geometry

**Departmental meeting**

Tuesday 06 March 2018, 14:15, Coffee room

Study Group**Moduli of families of curves**

Tuesday 06 March 2018, 12:15, M2 (M233)

Lassi Helanti (Diploma thesis talk)**Schauder estimates**

Friday 02 March 2018, 14:15, M3 (M234)

Pekka Alestalo (Aalto University)**Extension of bilipschitz maps: A survey**

Wednesday 28 February 2018, 12:15, M3 (M234)

Seminar on analysis and geometry

Acadamy Research Fellow Kaisa Matomäki (University of Turku)**Correlations of arithmetic functions**

Tuesday 27 February 2018, 15:15, D

Important arithmetic functions include the von Mangoldt function $\Lambda(n)$ which is essentially a weighted characteristic function of the primes, and the Liouville function $\lambda(n)$ which is $-1$ or $+1$ depending on whether $n$ has an odd or even number of prime factors. Mean values of these functions have been known for more than a century and in both cases the asymptotic evaluation of the mean value is equivalent to the prime number theorem which says that the number of primes up to $x$ is $x/\log x$.
Much more difficult question is whether there is correlation between consecutive values of $\lambda(n)$ or between $\Lambda(n)$ and $\Lambda(n+2)$. Such questions are closely related to the notoriously difficult twin prime conjecture which claims that there are infinitely many primes $p$ such that $p+2$ is also prime. Though the twin prime conjecture is still a distant goal, there has been some recent progress on this sort of correlations which I will discuss.

Colloquim

Nick Lindemulder (TU Delft)**A randomized difference norm for vector-valued Bessel potential spaces**

Friday 23 February 2018, 15:15, Kumpula Exactum C124

In this talk we discuss a randomized difference norm characterization for Bessel potential spaces in the UMD Banach space-valued setting. The main ingredients are R-boundedness results for Fourier multiplier operators, which are of independent interest. As an application we characterize the pointwise multiplier property of the indicator function of the half-space on these spaces. All results are proved in the setting of weighted spaces

Harmonic analysis and PDE seminar

Pekka Lehtelä (Aalto)**Obstacle problem for the porous medium equation**

Friday 23 February 2018, 14:15, Kumpula Exactum C124

Harmonic analysis and PDE seminar

Jung-Tae Park (Seoul National University)**Global gradient estimates for measure data problems in nonsmooth domains**

Wednesday 21 February 2018, 12:15, M3 (M234)

Seminar on analysis and geometry

Stavros Evdoridis, Antti Rasila**Conformal geometry study group (first meeting)**

Tuesday 20 February 2018, 12:15, Y225a (Riihi)

Further information

The goal of the meeting is to study the book Moduli of Families of Curves for Conformal and Quasiconformal Mappings, by Alexander Vasil'ev. Everybody interested in geometric complex analysis is welcome.

Conformal geometry study group

Marzieh Arabi Kakavand**Cyclic Subspace Codes**

Wednesday 14 February 2018, 15:15, M205

Subspaces codes are of great interest due to their applications to multiple sender-receiver schemes. As in classical algebraic coding theory, one of the most important research area in random network coding is the existence and construction of subspace codes and cyclic subspace codes with good parameters.
Recently Etzion et al. have presented a method for constructing cyclic subspace codes, which includes some special kind of linearized polynomials, namely subspaces polynomials and also Frobenius mappings. This new approach, especially the representation of some families of subspace codes via polynomials, is a very interesting contribution to this area of research. Some of the research on cyclic subspace codes, it becomes relevant the following conjecture.
Conjecture: For every positive integers n, k such that k < n/2, there exists a subspace cyclic code of size (q^n-1)/(q-1) in G_q(n,k) and minimum distance 2k-2.
For a fixed natural number k<= n let G_q(n,k) denote the set of all subspaces of F_q^n of dimension k and we call it the k-Grassmannian.
I will talk about the efforts that were done for solving this Conjecture.

ANTA seminar

Tuomas Orponen (University of Helsinki)**On uniformly rectifiable surfaces in the Heisenberg group**

Wednesday 14 February 2018, 12:15, M3 (M234)

Abstract: A closed set in a metric space X satisfies Condition B, if for all x in S and r > 0, there exist two balls, which are contained in B(x,r), have radii comparable to r, and are contained in two distinct components of X \ S. In R^n, an (n - 1)-regular set satisfying Condition B is known to contain big pieces of Lipschitz graphs, by a result of G. David. I discuss joint work with K. Fässler and S. Rigot, where we prove an analogue of the result for 3-regular sets in the first Heisenberg group.

Seminar on analysis and geometry

Stanislav Nagy (Charles University)**Unified approach to the theory of functional data depth**

Wednesday 07 February 2018, 17:00, M3 (M234)

Depth has become a quite popular concept in functional data analysis. In the talk we discuss its general framework. We show that most known functional depths can be classified into few groups, within which they share similar theoretical properties. We focus on uniform consistency results for the sample versions of these functionals, and demonstrate that some well-known approaches to depth assessment are hardly theoretically adequate.

Workshop on statistical depths and functional data analysis

Joni Virta (Aalto SCI)**Independent component analysis of multivariate functional data**

Wednesday 07 February 2018, 16:15, M3 (M234)

We extend a classic method of independent component analysis, the fourth order blind identification (FOBI), to vector-valued functional data. The use of multivariate instead of univariate functions allows for natural definitions for both the marginals of a random function and their mutual independence. Our model assumes that the observed functions are mixtures of latent independent functions residing in suitable Hilbert spaces, mixed with a bounded linear operator from the product space to itself. To enable the inversion of the covariance operator we make the assumption that the dependency between the mixed component functions lies in a finite-dimensional subspace. In this subspace we define fourth cross-cumulant operators and use them to construct a novel Fisher consistent method for solving the independent component problem for vector-valued functions. Finally, both simulations and an application to hand gesture data set are used to demonstrate the advantages of the proposed method over its closest competitors.

Workshop on statistical depths and functional data analysis

Sami Helander (Aalto SCI)**On typicality of functional observations**

Wednesday 07 February 2018, 15:00, M3 (M234)

Most of the functional depth approaches presented in the literature are solely interested in the -pointwise- centrality of the observations as a measure of (global) centrality. As a result, they are missing some important features inherent to functional data such as variation in shape, roughness or range. Thus, due to the richness of functional data, we opt to talk about typicality rather than centrality of an observation. We discuss assessing typicality of functional observations. Moreover, we provide a new concept of depth for functional data. It is based on a new multivariate Pareto depth applied after mapping the functional observations to a vector of statistics of interest. These quantities allow incorporating the inherent features of the distribution, such as shape or roughness. In particular, in contrast to most existing functional depths, the method is not limited to centrality only. Properties of the new depth are explored and the benefits of a flexible choice of features are illustrated.

Workshop on statistical depths and functional data analysis

Germain Van Bever (Université libre de Bruxelles)**Halfspace depths for scatter, concentration and shape matrices**

Wednesday 07 February 2018, 14:15, M3 (M234)

We propose halfspace depth concepts for scatter, concentration and shape matrices. For scatter matrices, our concept extends the one from Chen, Gao and Ren (2015) to the non-centered case, and is in the same spirit as the one in Zhang (2002). Rather than focusing, as in these earlier works, on deepest scatter matrices, we thoroughly investigate the properties of the proposed depth and of the corresponding depth regions. We do so under minimal assumptions and, in particular, we do not restrict to elliptical distributions nor to absolutely continuous distributions. Interestingly, fully understanding scatter halfspace depth requires considering different geometries/topologies on the space of scatter matrices. We also discuss, in the spirit of Zuo and Serfling (2000), the structural properties a scatter depth should satisfy, and investigate whether or not these are met by the proposed depth. As mentioned above, companion concepts of depth for concentration matrices and shape matrices are also proposed and studied.

Workshop on statistical depths and functional data analysis

Ratan Kumar Giri (National Institute of Technology Rourkela, India)**Reduced limit corresponding to the second order semilinear elliptic PDEs with measure data**

Wednesday 07 February 2018, 12:15, M3 (M234)

Seminar on analysis and geometry

**Teaching meeting**

Tuesday 06 February 2018, 14:15, Coffee room

Pekka Pankka (University of Helsinki )**Deformation of cubical Alexander maps**

Wednesday 31 January 2018, 12:15, M3 (M234)

I will discuss parts of a recent work with Jang-Mei Wu related to extension theory of spatial quasiregular mappings. The talk is mostly on the topological/combinatorial aspects of the extension theory and I will focus on a certain class PL branched covers, called cubical Alexander maps, and their branched cover homotopy theory following Rickman's ideas. As a particular result I will discuss a version of the Hopf theorem in this category: Two cubical and cubically shellable Alexander maps of an n-sphere are branched cover homotopic if and if they have the same degree.

Seminar on Analysis and Geometry

Prof. Petteri Kaski (Aalto Univeristy)**Proofs and computation**

Tuesday 30 January 2018, 15:15, D

A highly desirable property for a mathematical proof is that its correctness is easier to verify than it is to prepare the proof from scratch. One possibility to quantify such "ease of verification" is to view the tasks of preparing and verifying a proof from a computational perspective and in terms of the computational resources employed for a task. Indeed, such proof-system-based characterizations are in many ways fundamental to our current understanding of computational complexity and complexity classes such as P, NP, and beyond. This talk explores classical and recent work on proof systems for computational problems, including some of our own recent work involving proof systems that tolerate adversarial errors during proof preparation.

Colloquim

Teemu Murtola (University of Tampere, Faculty of Medicine and Life Sciences)**Benefits of cholesterol-lowering statins in prostate cancer**

Tuesday 30 January 2018, 10:00, M3 (M234)

Many commonly used drugs target intracellular signaling pathways
that have importance in carcinogenesis and progression of cancer. One
example is the mevalonate pathway which is targeted by
cholesterol-lowering statin drugs. Examining possible anticancer
effects of drug groups established for other indications requires
comprehensive multidisciplinary approach including epidemiological
studies to explore associations with cancer risk and prognosis,
experimental laboratory studies to elucidate possible anticancer
mechanisms and ultimately clinical trials to test for clinical
benefit. This lecture describes such project testing statins' effects
against prostate cancer.

Aalto Stochastics and Statistics Seminar

Jari Miettinen (Aalto ELEC)**Independent component analysis for graph data using graph-autocorrelation matrices**

Monday 29 January 2018, 15:15, M3 (M234)

The first independent component analysis estimators were designed for i.i.d. data, and they assume that at most one of the independent components has Gaussian density. Afterwards, methods have been developed for data with dependencies between the observations, including for example time series and spatial data. Those methods utilize solely or partially the structure of the data. For the most general case, graph data, Blochl et al. introduced an ICA estimator called GraDe (graph decorrelation) which uses approximate joint diagonalization of graph-autocorrelation matrices. GraDe contains the best-known time series and spatial methods as special cases. The structure of the graph is given in an adjacency matrix which is to be known or estimated prior to performing the ICA task. As one example in our paper on the effects of adjacency matrix estimation errors in graph signal processing, we study how the GraDe method is affected by misspecification of the adjacency matrix, using both theoretical and simulation results.

Aalto Stochastics and Statistics Seminar

Stefan Sturm (Universität Salzburg)**Regularity of weak solutions and supersolutions to the porous medium equation**

Friday 26 January 2018, 15:15, M3 (M234)

Harmonic analysis and PDE seminar

Paolo Marcellini (Università di Firenze)**Elliptic and parabolic equations under general and p,q growth conditions**

Friday 26 January 2018, 14:15, M3 (M234)

Harmonic analysis and PDE seminar

Jouni Parkkonen (University of Jyväskylä)**Equidistribution and counting in negatively curved spaces**

Wednesday 24 January 2018, 12:15, M3 (M234)

Seminar on analysis and geometry

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