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Archive 2009

December 9, 2009: Frank Redig (Universiteit Leiden) Duality and hidden symmetries in interacting particle systems We consider a model of heat conduction, the so-called Brownian momentum process. We show that this model is dual to a particle system which is a natural analogue of the symmetric exclusion process, with attractive instead of repulsive interaction. We further show that this model is self-dual, and give some applications of these duality relations. We also show in a general context how to obtain duality functions from symmetries of the generator. The talk is based on joint work with C. Giardina, J. Kurchan and K. Vafayi. December 2, 2009: Shota Gugushvili (Eurandom / TU Eindhoven) Nonparametric inference for discretely sampled Levy processes Given a sample from a discretely observed L'evy process $X=(X_t)_{tgeq 0}$ of the finite jump activity, we study the problem of nonparametric estimation of the L'evy density $ho$ corresponding to the process $X.$ We propose an estimator of $ho$ that is based on a suitable inversion of the L'evy-Khintchine formula and a plug-in device. Our main result deals with an upper bound on the mean square error of the estimator of $ho$ at a fixed point $x.$ We also show that the estimator attains the minimax convergence rate over a suitable class of L'evy densities. November 25, 2009: Roberto Fernandez (Universiteit Utrecht) Loss of gibbssiannes in un-quenching evolutions If an Ising ferrmognet at low temperature is subjected to a high-temperature spin-flip dynamics, the evolved measure may cease to be Gibbsian after a finite time. In this talk I will discuss such phenomenon. The talk will include a survey of the notion of Gibbs and non-Gibbsian measures and a discussion of what is known an expected regarding the dynamical loss of Gibsianness. November 11, 2009: Rik Lopuhaa (TU Delft) Central limit theorem and influence function for the MCD estimators at general multivariate distributions The minimum covariance determinant (MCD) estimators of multivariate location and scatter are robust alternatives to the ordinary sample mean and sample covariance matrix. Nowadays they are used to determine robust Mahalanobis distances in a reweighting procedure, and used as robust plug-ins in all sorts of multivariate statistical techniques which need a location and/or covariance estimate, such as principal component analysis, factor analysis, discriminant analysis and linear multivariate regression. For this reason, the distributional and the robustness properties of the MCD estimators are essential for conducting inference and perform robust estimation in several statistical models. Butler, Davies and Jhun (1993) show asymptotic normality only for the MCD location estimator, whereas the MCD covariance estimator is only shown to be consistent. Croux and Haesbroeck (1999) give the expression for the influence function of the MCD covariance functional and use this to compute limiting variances of the MCD covariance estimator. However, the expression is obtained under the assumption of existence, continuity and differentiability of the MCD-functionals at perturbed distributions, which is not proven. Moreover, the computation of the limiting variances relies on the von Mises expansion of the estimator, which has not been established. In this presentation we define the MCD functional by means of trimming functions which are in a wide class of measurable functions. The class is very flexible and allows a uniform treatment at general probability measures, including empirical measures and perturbed measures. We prove existence of the MCD functional for any multivariate distribution P and provide a separating ellipsoid property for the functional. Furthermore, we prove continuity of the functional, which also yields strong consistency of the MCD estimators. Finally, we derive an asymptotic expansion of the functional, from which we rigorously derive the influence function, and establish a central limit theorem for both MCD-estimators. All results are obtained under very mild conditions on P and essentially all conditions are automatically satisfied for distributions with a density. For distributions with an elliptically contoured density that is unimodal we do not need any extra condition and one may recover the results in Butler, Davies and Jhun (1993) and Croux October 28, 2009: Nelly Litvak (Universiteit Twente) The power law behaviour of the PageRank distribution. The PageRank algorithm is designed by Google to rank Web pages according to their importance. According to this algorithm, the importance scores of pages depend on the quantity and the quality of incoming links. We study and explain the properties of PageRank scores in complex information networks characterized by power laws. It is a well-known fact that in the Web, the distribution of the PageRank and In-degree follows a power law distribution with the same exponent. We explain this similarity by presenting a PageRank distribution as a solution of a stochastic equation. Using this model, we apply analytical methods to derive the asymptotic behavior of the PageRank distribution. The obtained results are in good agreement with experimental data. Next, we suggest to measure the dependencies between power law parameters using the notion of angular measure developed within extreme value theory. This technique reveals that the WWW, the Wikipedia and the Growing Network graphs have a completely different dependence structure. In our stochastic model, we can also derive the angular measure analytically, which allows to quantify the proportion of pages that receive a high ranking due to a large in-degree. This is a joint work with Yana Volkovich, Debora Donato, Werner Scheinhardt and Bert Zwart. October 21, 2009: Judith Timmer (Universiteit Twente) Cooperation in Tandem Lines We consider a number of servers in a tandem line. The servers may improve the efficiency of the system by redistributing their service capacities. This improvement is due to the reduction in the steady-state mean total number of customers in the tandem line. We investigate how the cost of the system after redistribution should be divided among the servers. For this we use tools from cooperative game theory. October 14, 2009: Noel van Erp & Pieter van Gelder (TU Delft ) Finding Proper Non-informative Priors for Regression Coefficients It is a known fact that in problems of Bayesian model selection improper priors may lead to biased conclusions. In this presentation we first give a short introduction to the procedure of Bayesian model selection. We then demonstrate for a simple model selection problem, involving two regression models, how improper uniform priors for the regression coefficients will exclude automatically the model with the most regression coefficients. Having established the problematic nature of improper priors for this particular case we proceed to derive a parsimoneous proper uniform prior for univariate regression models, firstly, and then generalize this result to multivariate regression models, secondly. October 7, 2009: Sasha Gnedin (Universiteit Utrecht) Quasi-exchangeability and generalizations of de Finetti's theorem A random sequence is quasi-exchangeable if its distribution is quasi-invariant under permutations. We discuss generalizations of de Finetti's theorem for this setting, and make connections to a boundary problem for lattice random walks. Major attention is given to the q-exchangeability, for which it is shown that all ergodic sequences are obtainable from a single measure on the space of infinite permutations. September 30, 2009: Charles Berger (Nederlands Forensisch Instituut) Modern forensic methodology In this talk we will introduce the modern forensic methodology, where the aim is to find objective evidence using the likelihood ratio as a measure for the strength of that evidence given a set of hypotheses. We will illustrate this approach with some example projects, such as the inference of identity of source for varied traces such as ballpoint ink, speech, paper structure and fingermarks. September 23, 2009: Dierk Schleicher (Jacobs-Universitaet Bremen) Dynamics of transcendental entire functions and a dimension paradox. September 16, 2009: Paul Vitanyi (CWI) om 4 uur Similarity by Compression We survey a new area of parameter-free similarity distance measures useful in data-mining, pattern recognition, learning and automatic semantics extraction. Given a family of distances on a set of objects, a distance is universal up to a certain precision for that family if it minorizes every distance in the family between every two objects in the set, up to the stated precision (we do not require the universal distance to be an element of the family). We consider similarity distances for two types of objects: literal objects that as such contain all of their meaning, like genomes or books, and names for objects. The latter may have literal embodyments like the first type, but may also be abstract like ``red'' or ``christianity.'' For the first type we consider a family of computable distance measures corresponding to parameters expressing similarity according to particular features between pairs of literal objects. For the second type we consider similarity distances generated by web users corresponding to particular semantic relations between the (names for) the designated objects. For both families we give universal similarity distance measures, incorporating all particular distance measures in the family. In the first case the universal distance is based on compression and in the second case it is based on Google page counts related to search terms. In both cases experiments on a massive scale give evidence of the viability of the approaches September 9, 2009: Anne Fey (TU Delft) A splitting headache. We consider the following game. Start with a pile of mass n at the origin of the rectangular grid, and mass h<1 at every other site. Mass may be moved by `splitting piles', that is, one may take all the mass from one site, and divide it evenly among the neighbors. There are restrictions though: One may only split piles of mass at least 1, and one may not stop before all the piles have mass less than 1. We call T the set of sites where at least one split was performed. Will the mass spread over the whole grid, or will T be finite? In the first case, how does it spread? In the last case, what is the size and shape of T, depending on h and n? How many splits are needed? Do any of these answers depend on the order of splitting? This game is related to the abelian sandpile growth model, for which a number of limiting shape results are known. The splitting game however is more difficult to analyse because it is not abelian. Nevertheless, we found several limiting shape results for the splitting game, some of which have no counterpart in the abelian sandpile growth model. August 17, 2009: Schmuel Gal (University of Haifa) Coordinated Linear Search June 17, 2009: Ian Melbourne (University of Surrey) Statistical properties of Lorentz gases June 10, 2009: Henk Bruin (TU Delft and University of Surrey) Li-Yorke chaos and Cantor attractors for interval maps. Whereas most unimodal interval maps are either chaotic in any mathematical sense of the word, or have periodic attractors attracting almost every point, there are unimodal maps with more interesting attractors. Such attractors are Cantor sets, and the dynamics on them is less chaotic: e.g. entropy and Lyapunov exponents are 0.In this talk, I want to explain that regarding the existence of Li-Yorke pairs (i.e., points x,y such that 0 = liminf |f^n(x)-f^n(y)| limsup |f^n(x)-f^n(y)| ), these attractors can still be quite interesting.(This work is joint with Victor Lopez-Jimenez, Murcia) June 3, 2009: Guus Balkema (UvA en ETH) ZAAL F (different location!) Level sets and dependence The behaviour of multivariate extremes is determined by the tail behaviour of the marginals and by the (asymptotic) dependence structure of the distribution. Multivariate dfs tell us little about the distribution of the probability mass and the structure of large sample clouds. In this talk we focus on densities, which are assumed to be continuous and unimodal, and to have level sets which are of the same shape asymptotically. This gives a good impression of what sample clouds from the distribution look like. I will discuss recent work with Natalia Lysenko and Paul Embrechts (both ETH, Zurich) on the relation between the shape of level sets and asymptotic dependency. May 27, 2009: Bert van Es (UvA) Two dimensional uniform kernel deconvolution In a general deconvolution model we have a sample of n independent X i which are equal to the sum of independent and unknown Y i and Z i . So X i =Y i +Z i . We assume that the Z i have a known distribution. The aim is to estimate the probability density f of the Y i from this sample of X i . Since the density of the observed X i is equal to the convolution of the densities of the Y i and Z i one can derive a density estimator of f by Fourier inversion and kernel estimation of the density of the observations. This approach has proven to be useful in many deconvolution models, i.e. different known distributions of the Z i . However, it fails in the model where the known density of the Z i is uniform. This model is usually called uniform deconvolution. We will present an alternative method based on kernel density estimation and a different, non Fourier, type of inversion of the convolution operator in this model. Following earlier work for the one dimensional model, cf Van Es 2002, we will use the same approach in the two dimensional model where the X i , Y i and Z i are two dimensional random vectors and where the distribution of the Z i is uniform on the unit square. We will derive expansions for the bias and variance and present some simulated examples. Reference [1] B. van Es. (2002) Combining kernel estimators in the uniform deconvolution model , ArXiv:math.PR/0211079. May 20, 2009: Ruud van Ommen (TU Delft) Monitoring of complex chemical systems - a chemical engineer's view on applying non-linear signal analysis In the chemical process industry, various pieces of equipment show complex behaviour. A good example is a fluidized bed: a vessel filled with powder, through which a gas is blown upward at such a velocity that the particles (the grains of the powder) become fluidized (i.e., they are 'floating' on the gas stream). These particles are constantly colliding with each other and with the vessel wall, and form density patterns on a scale much larger than the particle diameter. In various industrial operations (e.g, burning biomass for "green electricity" or production of polymers) the particle can become sticky and form large lumps of materials. This can eventually lead to an unscheduled shut-down of the bed. Currently, the process industry measures typically just average properties such a pressure or temperature. These measurements often do not give an early warning for the operational problem. We propose to base the analysis on dynamic signal (typically pressure measurements at ~ 200 Hz) to obtain more information from the system. We reconstruct an 'attractor' in the state space, a technique borrowed from chaos analysis. By following this attractor in time, it can be observed if this attractor - and thus the monitored system - is changing, which is an indication of particles start to stick together. The above described technique of 'attractor comparison' is very sensitive, but we would like to improve the selectivity of the monitoring: unimportant events in the system should not be detected. To this end, we recently developed a screening methodology to find the most selective combination of filtering method and analysis method. Some practical results from this methodology will be shown. May 13, 2009: Michael Schroeder (VU Amsterdam en Universität Mannheim) A perspective on the integral of geometric Brownian motion, with applications to finance The talk will concentrate on exponential functionals of Brownian motion, with the values of Asian options in the BS model as typical examples from finance. We survey how their structure theory emerges by way of establishing interconnections between stochastics and complex analysis on the upper half plane, taking work of Yor's and Dufresne's as starting points. Explicit valuation of Asian options furnishes the points of reference for measuring the progress here; we demonstrate how this is given expression to by at least 2 "arbitrary precision" methods whose potential we illustrate by way of numerical examples." April 22, 2009: Nelly Litvak (UT) The power law behaviour of the PageRank distribution. The PageRank algorithm is designed by Google to rank Web pages according to their importance. According to this algorithm, the importance scores of pages depend on the quantity and the quality of incoming links. We study and explain the properties of PageRank scores in complex information networks characterized by power laws. It is a well-known fact that in the Web, the distribution of the PageRank and In-degree follows a power law distribution with the same exponent. We explain this similarity by presenting a PageRank distribution as a solution of a stochastic equation. Using this model, we apply analytical methods to derive the asymptotic behavior of the PageRank distribution. The obtained results are in good agreement with experimental data. Next, we suggest to measure the dependencies between power law parameters using the notion of angular measure developed within extreme value theory. This technique reveals that the WWW, the Wikipedia and the Growing Network graphs have a completely different dependence structure. In our stochastic model, we can also derive the angular measure analytically, which allows to quantify the proportion of pages that receive a high ranking due to a large in-degree. This is a joint work with Yana Volkovich, Debora Donato, Werner Scheinhardt and Bert Zwart. April 15, 2009: Eric Cator (TU Delft) Hammersley process with random weights: stationary measures and Busemann functions (joint work with Leandro Pimentel) In this talk I will discuss the Hammersley process with random weights, both as a longest path percolation and as an interacting fluid process. We will show how we can use the Busemann function, as defined in geometry for metric spaces, to find mixing stationary measures for the Hammersley process. This gives us insight in the Busemann function for the classical Hammersley process, and a new description of the multi-class process. If time permits, we will discuss how these methods could be used to prove the cube-root behavior of the Hammersley process with random weights. April 1, 2009: Christophe Croux (K.U.Leuven) Classification Efficiencies for Robust Discriminant Analysis Linear discriminant analysis is typically carried out using Fisher's method. This method relies on the sample averages and covariance matrices computed from the different groups constituting the training sample. Since sample averages and covariance matrices are not robust, it has been proposed to use robust estimators of location and covariance instead, yielding a robust version of Fisher's method. In this paper relative classification efficiencies of the robust procedures with respect to the classical method are computed. Second order influence functions appear to be useful for computing these classification efficiencies. It turns out that, when using an appropriate robust estimator, the loss in classification efficiency at the normal model remains limited. March 11, 2009: Ronald Geskus (Academisch Medisch Centrum) Three Equivalent Forms of the Cause-Specific Cumulative Incidence Estimator and the Fine and Gray Model The standard estimator for the cause specific cumulative incidence in a competing risks setting with left truncated and/or right censored data can be written in two alternative forms. One is as an inverse probability weighted estimator and another as a product-limit estimator. The product-limit estimator is based on a simple estimator of the subdistribution hazard, i.e. the hazard that corresponds to the cause specific cumulative incidence curve. As a consequence, estimation of the cause-specific cumulative incidence and regression on the subdistribution hazard can be performed using standard software for survival analysis if the software allows for inclusion of time dependent weights. March 4, 2009: Bas Kleijn (UvA) Differentiability and the semiparametric Bernstein-Von Mises theorem The Bernstein-Von Mises theorem provides a detailed relation between frequentist and Bayesian statistical methods in smooth, parametric models. It states that the posterior distribution converges to a normal distibution centred on the maximum-likelihood estimator with covariance proportional to the Fisher information. In this talk we consider conditions under which the analogous assertion holds for the marginal posterior of a parameter of interest in smooth semiparametric estimation problems. Central is a no-bias condition, requiring that the nuisance posterior converges at a rate fast enough to suppress the bias. (Joint work with P. Bickel.) February 25, 2009: Kees Oosterlee (TU Delft / CWI) On Efficient Methods for Pricing Options with and Without Early Exercise In this presentation we will discuss option pricing techniques in the context of numerical integration. Based on a Fourier-cosine expansion of the density function we can efficiently obtain European option prices and corresponding hedge parameters. Moreover a whole vector of strike prices can be valued in one computation. This technique can speed up calibration to plain vanilla options substantially. This pricing method, called the COS method, is generalized to pricing Bermudan and barrier options. We explain this and present a calibration study based on CDS spreads (if time permits). February 18, 2009: Mark Veraar (TU Delft) Probability and moment estimates for centered random variables In this talk we discuss some sharp inequalities for centered random variables and their applications. In particular we give sharp lower bounds for P(X>0) in terms of moment estimates on X. Here X is a nonzero centered random variable. February 11, 2009: Ionica Smeets (UL) The LLL-algorithm: how it originated and how we can use it as a multidimensional continued fraction algorithm Hendrik Lenstra, Arjen Lenstra and László Lovász published their famous LLL-algorithm for basis reduction in 1982. In 2007 the 25th birthday of this algorithm was celebrated in Caen, France with a three- day conference. Lenstra, Lenstra, Lovász and close bystander Peter van Emde Boas started the conference by telling how the algorithm emerged from misunderstandings, errors and coincidences. Ionica Smeets wrote down these memories for an upcoming book from Springer about the LLL- algorithm. The first part of her talk will be this nice historic story. In the second part she will talk about her own research on continued fractions and explain how you can iterate the LLL-algorithm to find a series of multidimensional continued fractions. February 4, 2009: Gerard Hooghiemstra (TU Delft) First passage percolation on random graphs with finite mean degrees joint work with: Shankar Bhamidi and Remco van der Hofstad This talk is about first passage percolation on the configuration model. Assuming that each edge of the graph has an independent exponentially distributed edge weight, we derive distributional asymptotics for the minimum weight between two randomly chosen vertices in the network, as well as for the number of edges on the least weight path.

Archive 2019

December 16, 2019 : Franco Flandoli (University of Pisa) When: Monday, December 16, 16:00 Where: TU Delft, Faculty EWI, Mekelweg 4, EWI-Lecture hall F Brownian particles with local interaction: attempts and open problems on the PDE macroscopic limit Opposite to the theory of interacting particle systems on Z^d where the macroscopic behavior is usually well understood, the case of Brownian particles moving in R^d and subject to local interaction is less complete. We have been motivated to investigate this direction by the problem of modeling cell adhesion in biology; an overview of models proposed in the literature on this topic will be given but it is clear that the interaction is usually mean field or intermediate between mean field and local, like in the works of Karl Oelschleger. The case of true local interaction has been studied by Varadhan and few other authors and the results are fragmentary and less explicit from the quantitative viewpoint. We have devised heuristic computation and numerical test which produce some agreement and some discrepancy or open cases, and also in the case of agreement a rigorous proof is missing. The purpose of the talk is to illustrate this topic and the relative conjectures. December 02, 2019 : Thomas Nagler (Leiden University/TU Munich) When: Monday, December 02, 16:00 Where:TU Delft, Faculty EWI, Mekelweg 4, EWI-Lecture hall F Vine copula regression Vine copulas are graphical models for the dependence in a random vector. In regression problems, we are interested in some aspects of the distribution of a response variable conditional on a set of predictors, e.g., conditional means, probabilities, or quantiles. Vine copulas can be used to model the dependence between response and predictors. There are two main questions: how can we tailor the vine structure to the regression problem? And how to extract the regression function from the joint dependence model? In this talk, I review several variants that were developed in recent years and discuss open problems. November 25, 2019 : Extreme TiDE seminar [link: http://evt-seminar.nl/ ] When: Monday November 25, 15:00 - 17:00 Where: TU Delft, Faculty EWI, Mekelweg 4, EWI-Lecture hall F). November 18, 2019 : Michele Salvi ( École Polytechnique ) When: Monday, November 18, 16:00 Where: TU Delft, Faculty EWI, Mekelweg 4, EWI-Lecture hall F Scale-free percolation in continuous space Random graphs are a fundamental tool for the analysis of large real-world networks (such as social networks, communication networks, inter-banking systems and so on) which are not directly treatable, often because of their size. The scale-free percolation random graph features three properties that are never present at once in classical models, but that are relevant for applications: (1) Scale-free: the degree of the nodes follows a power law; (2) Small-world: two nodes are typically at a very small graph distance; (3) Positive clustering coefficient: two nodes with a common neighbour have a good chance to be linked. We study a continuous version of scale-free percolation and try to infer why it is a suitable model for the cattle trading network in France. Our final goal is to understand how an epidemic would spread on this kind of structures. October 28, 2019 : Barbara Franci (TU Delft) When: Monday, October 28, 16:00 Where:TU Delft, Faculty EWI, Mekelweg 4, EWI-Lecture room D@ta Stochastic Nash Equilibrium problems Nash equilibrium problems have been widely studied and number of results are present concerning algorithms and methodologies to find an equilibrium. On the other hand, the analysis of the stochastic case is not fully developed yet. Several problems of interest cannot be modelled without uncertainty as, for instance, transportation systems, electricity markets or gas markets. One possible motivation for this lack of results is the presence of the expected value cost functions that can be hard to compute. The aim of this talk is therefore to describe the stochastic Nash equilibrium problem and a possible approach to find equilibria. October 14, 2019 : Maite Wilke Berenguer (University of Bochum) When: Monday, October 14, 16:00 Where: TU Delft, Faculty EWI, Mekelweg 4, EWI-Lecture hall F The seed bank coalescent with spontaneous and simultaneous switching Population Genetics is an area of probability theory where mathematical structures arises from biological problems. Such is the case for the geometric seed bank model we introduced to describe a population with an active and a dormant form (picture plants with seeds). It models spontaneous switching, where individuals become active/dormant at a constant rate independently of each other as well as simultaneous switching, i.e. a correlation in their behaviour where positive fractions of the population become active/dorman simultaneously. Its scaling limits going backwards and forwards in time respectively are the seed bank coalescent and the seed bank diffusion (with spontaneous and simultaneous switching) and retain the moment duality. We will compare the effect of both spontaneous and simultaneous switching through the property of "coming down from infinity" (or not) of the coalescent structures. September 23, 2019 : Philipp Sibbertsen (University of Hannover) When: Monday, September 23, 16:00 Where: TU Delft, Faculty EWI, Mekelweg 4, EWI-Lecture hall F Robust Multivariate Local Whittle Estimation and Spurious Fractional Cointegration This paper derives a multivariate local Whittle estimator for the memory parameter of a possibly long memory process and the fractional cointegration vector robust to low frequency contaminations. This estimator as many other local Whittle based procedures requires a priori knowledge of the cointegration rank. It is shown that low frequency contaminations bias inference on the cointegration rank. We, therefore, also provide a robust estimator of the cointegration rank. Both estimators are obtained by trimming the periodogram. As all of our procedures are periodogram based we further derive some insights in the behaviour of the periodogram of a process under very general types of low frequency contaminations which may be of some interest on its own. An extensive Monte Carlo exercise shows the usefulness of our estimators in small samples. Our procedures are applied to realized betas of two American energy companies discovering that the series are fractionally cointegrated. As the series exhibit low frequency contaminations, standard procedures were unable to detect this relation. September 20, 2019: Debleena Thacker, Uppsala University When: Friday, September 20, 11:00 Where: TU Delft, Building 28, van Mourik Broekmanweg 6, Hilbert room, west second floor. Embedding balanced infinite color urn models into trees. Based on joint works with Antar Bandyopadhyay and Svante Janson. In this work the authors introduce the embedding into random recursive trees to study classical and generalized balanced urn models with non-negative balanced replacement matrices, for both finite and infinitely many colors. We provide a coupling of the balanced urn model with branching Markov chain on a random recursive tree, and use the properties of the later to deduce results for the former. We use this embedding to calculate the covariance between the proportions of any two colors when the replacement matrix is irreducible, aperiodic, positive recurrent and uniformly ergodic. This proves the strong law of large numbers for the proportion of colors. This method is especially useful for infinitely many colors, since the use of operator theory leads to technical difficulties for infinitely many colors. September 19, 2019 : Bernardo N.B. de Lima (extra talk at the Optimization seminar) When: Thursday, September 19, 16:00 Where: TU Delft, Faculty EWI, Mekelweg 4, Room Chip The Constrained-degree percolation model In the Constrained-degree percolation model on a graph (V,E) there are a sequence, (Ue)e∈E, of i.i.d. random variables with distribution U[0,1] and a positive integer k. Each bond e tries to open at time Ue, it succeeds if both its end-vertices would have degrees at most k−1. We prove a phase transition theorem for this model on the square lattice L2, as well on the d-ary regular tree. We also prove that on the square lattice the infinite cluster is unique in the supercritical phase. Joint work with R. Sanchis, D. dos Santos, V. Sidoravicius and R. Teodoro. September 9, 2019: Mini-workshop " Critical behaviour of spin systems: phase transition, metastability and ergodicity " When: September 9, 10:00 Where: Please mind the new location! TU Delft Building 26; Van der Burghweg 1 A0.360 Program : 10.00 – 10.45 Pierre-Yves Louis, U Poitiers 11.00 – 11.45 Christof Kϋlske, U Bochum 12.00 – 13.30 Lunch break 13.30 – 14.15 Aernout van Enter, U Groningen 14.30 –15.15 Bruno Kimura, TU Delft 15.30 –16.00 Coffee break 16.00 –16.45 Evgeny Verbitskiy, U Leiden Titles and abstracts: Pierre-Yves Louis Systems of reinforced processes through mean-field interaction Abstract: Reinforced processes are used to study urns (Polya, Friedman rules), stochastic algorithms and in many applications... We consider systems of stochastic processes where the interaction holds through the reinforcement. Each component (urn) is updated in a parallel way at discrete time steps. We consider a mean field type interaction. We will present a class of such systems introduced these last years. Issues we will address are : long time behaviour, existence of an a.s. limit shared by the whole system (synchronization), nature of this limit : random or deterministic. Fluctuations are studied through central limit theorems. This talk is based on joint works with I. Crimaldi, P. Dai Pra, I. Minelli ( hal-01277974 , hal-01287461) and M. Mirebrahimi ⟨hal-01856584v2⟩ . Christof Kϋlske Metastates and measurable extremal decomposition in random spin systems Metastates are measures on the infinite-volume states of a random spin system (introduced by Newman and Stein) which depend measurably on the realization of the random environment. They are useful in the presence of phase transitions to describe the large-volume asymptotics, also when chaotic volume-dependence may occur. We show that, for any metastate (possibly supported on non-extremal states) there is an associated decomposition metastate which has the same barycenter, and which is fully supported on the extremal states. (Joint with Codina Cotar and Benedikt Jahnel, ECP Volume 23 (2018), paper no. 95) Aernout van Enter Dyson models with random boundary conditions I discuss the behaviour of Dyson (long-range Ising) models with random boundary conditions. At low temperature, there is chaotic size-dependence, non-convergence of the Gibbs measure. The metastate , the distributional limit, is shown to be dispersed, and qualitatively a difference is shown to occur between decay power faster than 3/2 where the metastate is concentrated on mixed states and decay power slower than 3/2 when the metastate is concentrated on extremal Gibbs measures Bruno Kimura Nucleation for 1D long range Ising models The rigorous study of metastability in the setting of stochastic dynamics is a relatively recent topic. One of the most interesting problems that have been investigated is the study of the dependence on the dynamics of metastable behavior and nucleation toward the stable phase . Such class of problems appears in the literature considering several dynamic regimes, however, in most of them the microscopic interactions are assumed to be of shot range. Therefore, the following questions naturally arise: Does indeed a long range interaction change substantially the nucleation process? Are we able to define in this framework a critical configuration triggering the crossover towards the stable phase? In this talk I will show that under very general assumptions, the 1D long range Ising mode with a weak uniform field (without loss can be assumed to be positive) evolving according to the Metropolis dynamics, the state -1 is a metastable configuration that nucleates toward the stable phase +1 . It is possible to determine the tunneling time and the critical configurations that triggers the nucleation. Some model-dependent examples and generalizations are also discussed. Evgeny Verbitskiy On the relation between one-sided and two-sided Gibbs measure We will discuss the relation between Gibbs measures on the lattices Z_+ and Z. Joint work with S. Berghout, A. van Enter, and R. Fernandez. June 3, 2019: Alberto Chiarini (ETH Zürich) When: Monday, June 3rd, 16:00 Where: TU Delft, Faculty EWI, Mekelweg 4, EWI-Lecture hall F Entropic repulsion for the occupation-time field of random interlacements by disconnection. The model of random interlacements was introduced in 2007 by A.-S. Sznitman, motivated by questions about the disconnection of discrete cylinders or tori by the trace of simple random walk. Since then, it has gained popularity among probabilists due to its percolative properties and also because of its connections to the free field. Random interlacements on transient graphs can be constructed as a Poisson point process of doubly infinite trajectories. After reviewing this model, we will focus on the rare event that these trajectories disconnect a macroscopic body from infinity, in the strongly percolative regime. We will ask the following question: What is the most efficient way for random interlacements to enforce such disconnection? In other words, how do the trajectories of random interlacements look like conditionally on disconnection? This talk is based on joint work with M. Nitzschner. May 20, 2019: Nestor Parolya (TU Delft) When: Monday, May 20th, 16:00 Where: TU Delft, Faculty EWI, Mekelweg 4, EWI-Lecture hall F Large dimensional random matrices and their applications The random matrix theory (RMT) is originated from the multivariate statistics, nuclear physics and quantum mechanics under the strong impetus of Dyson, Gaudin, Mehta, Wigner, Wishart and others in the 1960's and 1970's. In particular, in 1967 two Ukrainian mathematicians Marchenko and Pastur derive the celebrated equation for the limiting spectral measure for the large dimensional sample covariance matrix. RMT has emerged as an extremely powerful tool for a variety of applications, especially in statistical signal processing, wireless communications, statistical finance and econometrics. Estimation of covariance/precision matrices is particularly important in portfolio allocation and risk assessment in finance, classification and large scale hypothesis testing in statistics or forecasting of time series in macroeconomics. In this talk we will give a short introduction to the theory of large random matrices and discuss our recent results on applications in high-dimensional statistics and finance. April 15, 2019 : Richard Kraaij (TU Delft) When: Monday, April 15th Where: TU Delft, Faculty 3mE, Mekelweg 2, 3mE-CZ F (Simon Stevin) How close is the critical Kac-Ising of ferromagnetism to solutions of the Allen-Cahn equation? The Kac-Ising model for ferromagnetism is used in statistical physics to study phase transitions in lattice systems. If we study the dynamic Kac-Ising model close to its critical temperature, it is known that field of local magnetizations converges to a solution of the Allen-Cahn equation as lattice spacing is sent to 0. The Allen-Cahn equation is a PDE that is used for the study of phase-separation phenomena. I will present work in progress in which I use the probabilistic technique of large deviations to study how close the dynamic Kac-Ising model is to the solution of the Allen-Cahn equation. April 1, 2019 : Timothy Budd (Radboud University) When: Monday, April 1st Where: TU Delft, EWI-Lecture hall F Geometry of random planar maps with high degrees For many types of random planar maps, i.e. planar graphs embedded in the sphere, it is known that their geometry possesses a scaling limit described by a universal random continuous metric space known as the Brownian sphere. One way to escape this universality class is to consider random planar maps that harbor vertices of very high degree. In this talk I will describe a peeling exploration that allows us to study distances in such maps. Based on the results we conjecture the existence of a new one-parameter family of random continuous metric spaces, referred to tentatively as the stable spheres. March 11, 2019 : Botond Szabó (Leiden Univeristy) When: Monday, March 11 Where: EWI-Lecture hall F Bayesian nonparametric approach to log-concave density estimation In the beginning of the talk I will give a (somewhat) lengthier introduction to Bayesian nonparametric methods and their theoretical analysis. Then I will focus on estimating log-concave densities, which is a canonical problem in the area of shape-constrained nonparametric inference. I will present a Bayesian nonparametric approach to this problem based on an exponentiated Dirichlet process mixture prior and show that the corresponding posterior distribution converges to the log-concave truth at the (near-) minimax rate in Hellinger distance. I demonstrate the applicability of the proposed method for estimating the underlying log-concave density and its mode in a simulation study and compare our Bayesian method with the classical MLE. Finally, I will briefly talk about potential application in cluster analysis. It is a joint work with Ester Mariucci and Kolyan Ray. February 25, 2019 : Ayan Bhattacharya (CWI Amsterdam) When: Monday, February 25 Where: EWI-Lecture hall F Large deviation for extremes of branching random walk with regularly varying tails. We consider discrete time branching random walk on real line where the displacements have regularly varying tail. Using the one large jump asymptotics, we derive large deviation for the extremal processes associated to the suitably scaled positions of particles in the nth generation where the genealogical tree satisfies Kesten-Stigum condition. The large deviation limiting measure in this case is identified in terms of the cluster Poisson point process obtained in the underlying weak limit of the point processes. As a consequence of this, we derive large deviation for the rightmost particle in the nth generation giving the heavy-tailed analogue of recent work by Gantert and Höfelsauer(2018). Reference: Large deviation for extremes of branching random walk with regularly varying displacements ( https://arxiv.org/abs/1802.05938v1 ). February 11, 2019 : Jaron Sanders (TU Delft) When: Monday, February 11 Where: EWI-Lecture hall F Clustering in Block Markov Chains In this talk, I will discuss our recent paper that considers cluster detection in Block Markov Chains (BMCs). These Markov chains are characterized by a block structure in their transition matrix. More precisely, the n possible states are divided into a finite number of K groups or clusters, such that states in the same cluster exhibit the same transition rates to other states. One observes a trajectory of the Markov chain, and the objective is to recover, from this observation only, the (initially unknown) clusters. In this paper we devise a clustering procedure that accurately, efficiently, and provably detects the clusters. We first derive a fundamental information-theoretical lower bound on the detection error rate satisfied under any clustering algorithm. This bound identifies the parameters of the BMC, and trajectory lengths, for which it is possible to accurately detect the clusters. We next develop two clustering algorithms that can together accurately recover the cluster structure from the shortest possible trajectories, whenever the parameters allow detection. These algorithms thus reach the fundamental detectability limit, and are optimal in that sense. This is joint work with Alexandre Proutière and Se-Young Yun. January 28, 2019 : Pasquale Cirillo (Tu Delft) When: Monday, January 28th Where: TU Delft, EWI-Lecture hall F The arithmetic of finance Take finance, remove the trendy words, remove the acronyms and the obscure jargon, admit you will not be rich, but be happy because you will not lose money either. What do you get? Interestingly you discover that all those changes of measure, those coherent risk measures, even the pay-off of a European option, not to mention utility theory in its many declinations, are nothing but the result of sums and products. So, let’s come back to basics. January 14, 2019 : Lixue Pang (TU Delft) When: Monday, January 14th Where: TU Delft, EWI-Lecture hall F Bayesian estimation of a decreasing density Consider the problem of estimating a decreasing density function, with special interest in zero. It is well known that the maximum likelihood estimator is inconsistent at zero. This has led several authors to propose alternative estimators which are consistent. As any decreasing density can be represented as a scale mixture of uniform densities, a Bayesian estimator is obtained by endowing the mixture distribution with the Dirichlet process prior. Assuming this prior, we derive contraction rates of the posterior density at zero. Several choices of base measure are numerically evaluated and compared. In a simulation various frequentist methods and a Bayesian estimator are compared. Finally, the Bayesian procedure is applied to current durations data.

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TU Delft jointly wins XPRIZE Rainforest drone competition in Brazil

TU Delft jointly wins in the XPRIZE Rainforest competition in the Amazon, Brazil Imagine using rapid and autonomous robot technology for research into the green and humid lungs of our planet; our global rainforests. Drones that autonomously deploy eDNA samplers and canopy rafts uncover the rich biodiversity of these complex ecosystems while revealing the effects of human activity on nature and climate change. On November 15, 2024, after five years of intensive research and competition, the ETHBiodivX team, which included TU Delft Aerospace researchers Salua Hamaza and Georg Strunck, achieved an outstanding milestone: winning the XPRIZE Rainforest Bonus Prize for outstanding effort in co-developing inclusive technology for nature conservation. The goal: create automated technology and methods to gain near real-time insights about biodiversity – providing necessary data that can inform conservation action and policy, support sustainable bioeconomies, and empower Indigenous Peoples and local communities who are the primary protectors and knowledge holders of the planet’s tropical rainforests. The ETHBiodivX team, made of experts in Robotics, eDNA, and Data Insights, is tackling the massive challenge of automating and streamlining the way we monitor ecosystems. Leading the Robotics division, a collaboration between TU Delft’s Prof. Salua Hamaza, ETH Zurich’s Prof. Stefano Mintchev and Aarhus University’s Profs. Claus Melvad and Toke Thomas Høye, is developing cutting-edge robotic solutions to gather ecology and biology data autonomously. “We faced the immense challenge of deploying robots in the wild -- and not just any outdoor environment but one of the most demanding and uncharted: the wet rainforests. This required extraordinary efforts to ensure robustness and reliability, pushing the boundaries of what the hardware could achieve for autonomous data collection of images, sounds, and eDNA, in the Amazon” says prof. Hamaza. “Ultimately, this technology will be available to Indigenous communities as a tool to better understand the forest's ongoing changes in biodiversity, which provide essential resources as food and shelter to the locals.” . . . .

Students Amos Yusuf, Mick Dam & Bas Brouwer winners of Mekel Prize 2024

Master students Amos Yusuf, from the ME faculty (Mick Dam, from the EEMCS faculty and graduate Bas Brouwer have won the Mekel Prize 2024 for the best extra scientific activity at TU Delft: the development of an initiative that brings master students into the classroom teaching sciences to the younger generations. The prize was ceremonially awarded by prof Tim van den Hagen on 13 November after the Van Hasselt Lecture at the Prinsenhof, Delft. They received a statue of Professor Jan Mekel and 1.500,- to spend on their project. Insights into climate change are being openly doubted. Funding for important educational efforts and research are being withdrawn. Short clips – so called “reels” – on Youtube and TikTok threaten to simplify complex political and social problems. AI fakes befuddle what is true and what is not. The voices of science that contribute to those discussion with modesty, careful argument and scepticism, are drowned in noise. This poses a threat for universities like TU Delft, who strive to increase student numbers, who benefit from diverse student populations and aim to pass on their knowledge and scientific virtues to the next generation. It is, therefore, alarming that student enrolments to Bachelor and Master Programs at TU Delft have declined in the past year. Students in front of the class The project is aimed to make the sciences more appealing to the next generation. They have identified the problem that students tend miss out on the opportunity of entering a higher education trajectory in the Beta sciences – because they have a wrong picture of such education. In their mind, they depict it as boring and dry. In his pilot lecture at the Stanislas VMBO in Delft, Amos Yusuf has successfully challenged this image. He shared his enthusiasm for the field of robotics and presented himself as a positive role model to the pupils. And in return the excitement of the high school students is palpable in the videos and pictures from the day. The spark of science fills their eyes. Bas Brouwer Mick Dam are the founders of NUVO – the platform that facilitates the engagement of Master Students in high school education in Delft Their efforts offer TU Delft Master Students a valuable learning moment: By sharing insights from their fields with pupils at high school in an educational setting, our students can find identify their own misunderstandings of their subject, learn to speak in front of non-scientific audiences and peak into education as a work field they themselves might not have considered. An extraordinary commitment According to the Mekel jury, the project scored well on all the criteria (risk mitigation, inclusiveness, transparency and societal relevance). However, it was the extraordinary commitment of Amos who was fully immersed during his Master Project and the efforts of Brouwer and Dam that brought together teaching and research which is integral to academic culture that made the project stand out. About the Mekel Prize The Mekel Prize will be awarded to the most socially responsible research project or extra-scientific activity (e.g. founding of an NGO or organization, an initiative or realization of an event or other impactful project) by an employee or group of employees of TU Delft – projects that showcase in an outstanding fashion that they have been committed from the beginning to relevant moral and societal values and have been aware of and tried to mitigate as much as possible in innovative ways the risks involved in their research. The award recognizes such efforts and wants to encourage the responsible development of science and technology at TU Delft in the future. For furthermore information About the project: https://www.de-nuvo.nl/video-robotica-pilot/ About the Mekel Prize: https://www.tudelft.nl/en/tpm/our-faculty/departments/values-technology-and-innovation/sections/ethics-philosophy-of-technology/mekel-prize

New catheter technology promises safer and more efficient treatment of blood vessels

Each year, more than 200 million catheters are used worldwide to treat vascular diseases, including heart disease and artery stenosis. When navigating into blood vessels, friction between the catheter and the vessel wall can cause major complications. With a new innovative catheter technology, Mostafa Atalla and colleagues can change the friction from having grip to completely slippery with the flick of a switch. Their design improves the safety and efficiency of endovascular procedures. The findings have been published in IEEE. Catheter with variable friction The prototype of the new catheter features advanced friction control modules to precisely control the friction between the catheter and the vessel wall. The friction is modulated via ultrasonic vibrations, which overpressure the thin fluid layer. This innovative variable friction technology makes it possible to switch between low friction for smooth navigation through the vessel and high friction for optimal stability during the procedure. In a proof-of-concept, Atalla and his team show that the prototype significantly reduces friction, averaging 60% on rigid surfaces and 11% on soft surfaces. Experiments on animal aortic tissue confirm the promising results of this technology and its potential for medical applications. Fully assembled catheters The researchers tested the prototype during friction experiments on different tissue types. They are also investigating how the technology can be applied to other procedures, such as bowel interventions. More information Publicatie DOI : 10.1109/TMRB.2024.3464672 Toward Variable-Friction Catheters Using Ultrasonic Lubrication | IEEE Journals & Magazine | IEEE Xplore Mostafa Atalla: m.a.a.atalla@tudelft.nl Aimee Sakes: a.sakes@tudelft.nl Michaël Wiertlewski: m.wiertlewski@tudelft.nl Would you like to know more and/or attend a demonstration of the prototype please contact me: Fien Bosman, press officer Health TU Delft: f.j.bosman@tudelft.nl/ 0624953733