# Archive 2015

**December 15, 2015: ****Huijuan Wang**** ****(TU Delft)**

When: Tuesday December 15th, 12:45

Where: TU Delft, Faculty EWI, Mekelweg 4, Snijderszaal (LB 01.010).

*Viral Spreading on Networks*

Viral spreading on networks has been widely used to model the diffusion of information, the propagation of computer worms and infectious diseases, the cascade of failures across infrastructures, and the spread of social opinions etc. In this talk, I will introduce our recent research lines related to viral spreading models on Networks. We will start with the definition, methods, results and applications of one of the most studied viral spreading models, the Susceptible-Infected-Susceptible SIS model. Afterwards, we will introduce our recent work in e.g. SIS model on interconnected, multi-layer networks, heterogenous SIS model and epidemic mitigation via awareness propagation in communications network. The talk will end with future challenges.

December 1, 2015: Karma Dajani **(Utrecht University)**

When: Tuesday December 1st, 12:45

Where: TU Delft, Faculty EWI, Mekelweg 4, Snijderszaal (LB 01.010).

*Random expansions, infinite Bernoulli convolutions, and Local di**mensions.*

For a certain class of algebraic bases β > 1, we consider the associated random β-transformation equipped with the unique measure ν_{β} of maximal entropy. Under a suitable metric, we study the local dimension of ν_{β}. As a consequence, we are able to find the local dimension of the associated infinite Bernoulli convolution which can be seen as a marginal measure of ν_{β}.

November 17, 2015: Teddy Seidenfeld **(Carnegie Mellon University)**

When: Tuesday November 17th, 12:45

Where: TU Delft, Faculty EWI, Mekelweg 4, v/d Poelzaal (LB 01.220).

*Non-conglomerability for countably additive measures that are not κ-additive*

Let κ be an uncountable cardinal. Using the theory of conditional probability associated with de Finetti (1974) and Dubins (1975), subject to several structural assumptions for creating sufficiently many measurable sets, and assuming that κ is not a weakly inaccessible cardinal, we show that each probability that is not κ-additive has conditional probabilities that fail to be conglomerable in a partition of cardinality no greater than κ. This generalizes our (1984) result, where we established that each finite but not countably additive probability has conditional probabilities that fail to be conglomerable in some countable partition. Joint with M.J.Schervish, and J.B.Kadane

**November 3, 2015: Timon Idema (TU Delft) **

When: Tuesday November 3rd, 12:45

Where: TU Delft, Faculty EWI, Mekelweg 4, v/d Poelzaal (LB 01.220).

*The maths of membranes - how differential geometry can be useful for biology*

Membranes are ubiquitous in the cell. They form not only the plasma membrane that separates the interior of a cell from its exterior, they are also the boundaries of the various organelles (cellular `organs’) present in eukaryotic cells. Moreover, rather than being passive packaging material, membranes are highly active parts of the living cell, functioning both as reaction platforms and dynamic components that change their shape to suit the cell’s needs. To achieve these goals, membranes interact strongly with two other cellular components: proteins, including molecular motors, and the cytoskeleton.

To describe the membrane mathematically and study its shapes, we use tools from differential geometry. Membranes themselves usually prefer to minimize their curvature. In contrast, proteins typically impose a finite curvature on the membrane, and can interact with each other through the deformations they cause. We study these membrane-mediated interactions on flat and curved membranes, and find that overall membrane curvature has a major effect on the equilibrium protein distributions. Using those same proteins, we can build complicated networks of membrane tubes and sheets. Moreover, by coupling to active components like molecular motors or a growing and shrinking cytoskeleton, we can make the membrane dynamical, adapting its shape in response to a varying environment. These membrane dynamics are the basis of many biological functions, and by studying them we can eventually understand not only what a cell does, but also how it manages to do just that.

**October 27, 2015:**** Jeffrey Shallit**** ****(University of Waterloo)**

When: Tuesday October 27th, 12:45

Where: TU Delft, Faculty EWI, Mekelweg 4, Snijderszaal (LB 01.010).

*New and Old Results on Continued Fractions*

In this talk I will give a survey of what is known about "unusual" continued fractions for real numbers, focusing in particular on recent results (with Badziahin) about the number s = [1,2,1,4,1,2,1,8,....].

**October 20, 2015: Gioia Carinci ****(TU Delft)**

When: Tuesday October 20th, 12:45

Where: TU Delft, Faculty EWI, Mekelweg 4, Snijderszaal (LB 01.010).

*From the quantum Lie algebra U _{q}(sl_{2}) to the *ASEP

*(q, j)*

Stochastic duality is a key tool that allows to study an interacting particle system in terms of a finite number of dual particles. In many cases duality can be traced back to the underlying algebraic structure of the system. In this talk I will present a new constructive algebraic approach to self-duality based on the link with representation theory of Lie algebras. In particular I will show how the general scheme has been implemented in the case of the *U _{q}(sl_{2})* Lie algebra, to construct a new self-dual process, the ASEP(q, j), that is an extension of the standard Asymmetric Exclusion Process to a situation where sites can accommodate more than one (namely 2j) particles per site. The process is constructed from a (2j + 1)-dimensional representation of a quantum Hamiltonian with

*U*invariance by applying a suitable ground-state transformation.

_{q}(sl_{2})

**October 13, 2015: Cees de Valk ****(Tilburg University)**

When: Tuesday October 13th, 12:45

Where: TU Delft, Faculty EWI, Mekelweg 4, v/d Poelzaal (LB 01.220).

*A large-deviations approach to estimation of probabilities of extreme events*

This presentation discusses modelling of the tail of a multivariate distribution function by means of a tail large deviation principle (LDP) and its application to the estimation of very small probabilities of multivariate extreme events. A tail LDP provides asymptotic bounds for normalised logarithms of probabilities of extreme events. This differs from classical extreme value theory, which concerns limits of suitably normalised probabilities. Connections are made with the univariate log-GW tail limit recently proposed within the context of high quantile estimation, and with residual tail dependence/hidden regular variation. Based on the tail LDP, a simple consistent estimator for very small probabilities of extreme events is formulated. Examples are shown to demonstrate how the estimator works, and to illustrate the difference between the classical approach and the large deviations approach.

**October 6, 2015: Richard Kraaij ****(TU Delft)**

When: Tuesday October 6th, 12:45

Where: TU Delft, Faculty EWI, Mekelweg 4, v/d Poelzaal (LB 01.220).

*Large deviations for trajectories of interacting jump processes*

We will consider large deviations of the trajectory of the empirical mean of n weakly interacting Markov jump processes. Using the functional approach to large deviations introduced by Feng and Kurtz[2006], we prove the large deviation principle under some monotonicity conditions on the jump rates of these processes. A notable feature of the result is that the large deviation principle holds also in cases that the functional approach to the law of large numbers for the trajectories fails. The main example in the talk will be Glauber dynamics for the mean-field Ising model, that models the behaviour of the empirical magnetisation of n interacting spins when heated or cooled down.

**September 29, 2015: Bo Zhou ****(Tilburg University)**

When: Tuesday September 29th, 12:45

Where: TU Delft, Faculty EWI, Mekelweg 4, Snijderszaal (LB 01.010).

*Semiparametrically Optimal Hybrid Rank Tests for Unit Roots*

We propose a new class of unit root tests that exploits invariance properties in the Locally Asymptotically Brownian Functional limiting experiment of the unit root model. These invariance structures naturally suggest tests based on the ranks of the increments of the observations, their mean, and an assumed reference density for the innovations. The tests are semiparametric in the sense that the reference density need not equal the true innovation density. For correctly specified reference density, the asymptotic power curve of our test is point-optimal and nearly efficient (in the sense of Elliott, Rothenberg, and Stock (1996)). When using a Gaussian reference density, our test performs as well as commonly used tests under true Gaussian innovations and better under other distributions, e.g., fat-tailed or skewed. Monte Carlo evidence shows that our test also behaves well in small samples

**September 22, 2015: ****Shota Gugushvili**** (University of Leiden)**

When: Tuesday September 22nd, 12:45

Where: TU Delft, Faculty EWI, Mekelweg 4, Snijderszaal (LB 01.010).

*A non-parametric Bayesian approach to decompounding from high frequency data*

Given a sample from a discretely observed compound Poisson process, we consider non-parametric estimation of the density $f_0$ of its jump sizes, as well as of its intensity $\lambda_0.$ We take a Bayesian approach to the problem and specify the prior on $f_0$ as the Dirichlet location mixture of normal densities. An independent prior for $\lambda_0$ is assumed to be compactly supported and possess a positive density with respect to the Lebesgue measure. We show that under suitable assumptions the posterior contracts around the pair $(\lambda_0,f_0)$ at essentially (up to a logarithmic factor) the $\sqrt{n\Delta}$-rate, where $n$ is the number of observations and $\Delta$ is the mesh size at which the process is sampled. The emphasis is on high frequency data, $\Delta\to 0$, but the obtained results are also valid for fixed $\Delta$. In either case we assume that $n\Delta\rightarrow\infty$. Our main result implies existence of Bayesian point estimates converging (in the frequentist sense, in probability) to $(\lambda_0,f_0)$ at the same rate.

Joint work with Frank van der Meulen and Peter Spreij.

**September 15, 2015: ****Moritz Schauer (University of Amsterdam)**

When: Tuesday September 15th, 12:45

Where: TU Delft, Faculty EWI, Mekelweg 4, Snijderszaal (LB 01.010).

*Central limit theorems for diffusions on the circle*

Building up upon Feller's classical analysis of diffusion processes on the line, a diffusion on the circle is represented by a rescaled and time-changed Brownian motion. This Brownian motion with constant drift is characterized by having the same probability as the diffusion to complete a clockwise turn before a counterclockwise turn. Bolthausen proved a uniform central limit theorem for the local time of Brownian motion on the circle with a rescaled Brownian bridge as limiting process. Using the representation we generalize Bolthausen's result to general diffusions on the circle.

**June 4, 2015: Giulio Bottazzi ****(****Sant'Anna School of Advanced Studies****)**

When: Thursday June 4th, 15.00

Where: TU Delft, Faculty EWI, Mekelweg 4, Snijderzaal (LB 01.010).

*On the bosonic nature of business opportunities*

Among the most robust empirical regularities observed in economics is the peculiar shape of the growth rate distribution of firms. This distribution displays indeed a shape which is remarkably similar to a symmetric, or double, Exponential, irrespective of the economic sector, the year or even the size proxy considered to measure it. I will show that this regularity is in fact the signature of a specific competition dynamics which drives the allocation of business opportunities across competitors. The probabilistic laws regulating this assignment are similar to those that have been postulated many years ago for a large class of sub-nuclear particles. These laws are responsible for the formation of clusters of growth events which can explain the high variability observed in the dynamics of the firm.

**June 4, 2015: Manfred Madritsch ****(****Université de Lorraine)**

When: Thursday June 4th, 16.00

Where: TU Delft, Faculty EWI, Mekelweg 4, Snijderzaal (LB 01.010).

*Van der Corput sets*

A set H of positive integers is a van der Corput set if the sequence {u_{n}} of real numbers is uniformly distributed (mod 1) whenever the differenced sequence {u_{n+h}-u_{n}} is uniformly distributed (mod 1) for all h∈H.

We start the talk with a historical background together with some properties and examples of van der Corput sets. Then we present connections of these sets with intersective sets, recurrent sets and Heilbronn sets. Finally extensions of these questions to sets in Z^{d} together with recent examples are considered.

**May 28, 2015: Fred Vermolen ****(****TU Delft****)**

When: Thursday May 28th, 16.00

Where: TU Delft, Faculty EWI, Mekelweg 4, v/d Poelzaal (LB 01.220).

*A tour over the world of semi-stochastic cell-based modeling for wound healing and tumor initiation*

We consider mathematical modelling approaches for the simulation of processes like wound healing, wound contraction and tumor initiation. The approaches are based on the solution of partial differential equations by Fundamental Solutions and Finite-Element method and on stochastic principles for cell migration, division and death.

The treatment will be rather informal where emphasis is on methodology and possible outcomes of model simulations.

**May 21, 2015: Pasquale Cirillo ****(****TU Delft****) **

When: Thursday May 21st, 16.00

Where: TU Delft, Faculty EWI, Mekelweg 4, v/d Poelzaal (LB 01.220).

*On the risk of violent conflicts and the "long peace" that will kill us*

Violence is much more severe than it seems from conventional analyses, and the prevailing "long peace" theory, which claims that we are living in a world more peaceful than before.

Using extreme value theory, we look at the various statistical pictures of violent conflicts, with focus on those with more than 50k victims (in equivalent ratio of today’s population).

Contrary to current discussions, we show that the risk of violent conflicts has not been decreasing, but it is rather underestimated, given the extreme fat-tailedness of the phenomenon, and that armed conflicts follow a homogenous Poisson process, thus contrasting the common idea of a time trend in the number of conflicts.

In the talk we also discuss the problem of inaccuracies in the historical assessment of the number of casualties in conflicts, and we propose a simple but effective solution based on resampling.

Our analyses are based on a new data set collecting all main armed conflicts of humanity, in the last 2014 years.

This is a joint work with Nassim Nicholas Taleb (NYU Poly).

**May 14, 2015: No seminar - Holiday**

**May 7, 2015: Cor Kraaikamp ****(****TU Delft)**

When: Thursday May 7th, 16.00

Where: TU Delft, Faculty EWI, Mekelweg 4, Vassiliadeszaal (HB 10.230).

*Continued fractions and other number theoretic transformations*

Since Gauss wrote in 1800 in his mathematical diary that he found the invariant measure of the regular continued fraction map, there has been a surprisingly strong relation between number theoretic transformations (such as the Gauss-map), dynamical systems and ergodic theory. In this introductory talk I will outline some of the history and the contributions by Paul Levy, Khintchine, Doeblin, Renyi, but also will mention (and in a few cases prove) some recent results.

**April 30, 2015: Elena Pulvirenti (Leiden University)**

When: Thursday April 30th, 16.00

Where: TU Delft, Faculty EWI, Mekelweg 4, v/d Poelzaal (LB 01.220).

*Metastability for the Widom-Rowlinson model*

In this paper we study the Widom-Rowlinson model on a finite two-dimensional box subject to a stochastic dynamics in which particles are randomly created and annihilated inside the box according to an infinite reservoir with a given chemical potential. The particles are viewed as points carrying disks and the energy of a particle configuration is equal to minus the volume of the total overlap of the disks. Consequently, the interaction between the particles is attractive. We are interested in the metastable behaviour of the system at low temperature when the chemical potential is supercritical. In particular, we start with the empty box and are interested in the first time when the box is fully covered by disks. In order to achieve the transition from empty to full, the system needs to create a sufficiently large droplet, called critical droplet, which triggers the crossover. We compute the distribution of the crossover time, identify the size and the shape of the critical droplet, and investigate how the system behaves on its way from empty to full.

This is a joint work in progress with F. den Hollander, S. Jansen, R. Kotecky.

**April 23, 2015: Armelle Guillou (Université de Strasbourg)**

When: Thursday April 23rd, 16.00

Where: TU Delft, Faculty EWI, Mekelweg 4, v/d Poelzaal (LB 01.220).

*A local moment type estimator for the extreme value index and extreme quantile in regression with random covariates*

This talk deals with the nonparametric estimation of some conditional extreme parameters (index or quantile) of a response in presence of random covariates. In particular, it is assumed that the conditional response distribution belongs to the max-domain of attraction of the extreme value distribution. The moment estimators originally proposed by Dekkers, Einmahl & de Haan (1989) are adjusted to the local estimation context. The asymptotic properties of our estimators are investigated under some mild conditions on the response distribution, the density function of the covariates, the kernel function and for appropriately chosen sequences of bandwidth and threshold parameters. The finite sample performance of the proposed estimators is evaluated by means of an extensive simulation study where a comparison with alternatives from the recent literature is provided. We also illustrate the practical applicability of the estimators on the world catalogue of earthquake magnitudes.

This is a joint work with Yuri Goegebeur and Michael Osmann.

**April 16, 2015: Karen Aardal (TU Delft)**

When: Thursday April 16th, 15.45 (Different time!)

Where: TU Delft, Faculty EWI, Mekelweg 4, v/d Poelzaal (LB 01.220).

*Using optimization to plan ambulance services*

Ambulance services are concerned with providing adequate care to emergency patients. When a call arrives at the dispatch center, an ambulance is assigned to the call. The probability of survival of a patient that is involved in an accident is highly dependent on the time it takes before an ambulance arrives at the scene. Consequently, it is of great importance that EMS vehicles respond as quickly as possible to the calls.

In this talk we describe optimization models and algorithms related to finding the optimal location of ambulance stations.

The talk is based on joint work with Pieter van den Berg and Rutger Kerkkamp.

**April 9, 2015: Júlia Komjáthy (TU Eindhoven)**

When: Thursday April 9th, 16.00

Where: TU Delft, Faculty EWI, Mekelweg 4, Vassiliadeszaal (HB 10.230).

*Degree distribution of shortest path trees and bias in network sampling algorithms *

In this talk, we investigate the degree distribution of shortest path trees of various weighted network models. The aim of many empirical studies is to determine the degree distribution of a network with unknown structure by using trace-route sampling. We derive the limiting degree distribution of the shortest path tree from a single source on various random network models with edge weights: the configuration model and r-regular graphs with i.i.d. power law degrees and i.i.d. edge weights, the complete graph with edge weights that are powers of i.i.d. exponential random variables. We use these results to shed light on an empirically observed bias in network sampling methods.

**April 2, 2015: Christof Külske (Bochum University)**

When: Thursday April 2nd, 16.00

Where: TU Delft, Faculty EWI, Mekelweg 4, Vassiliadeszaal (HB 10.230).

*Extremality and non-extremality of Gibbs measures for the Potts model on trees*

Statistical mechanics models on trees often show rich behavior with multiple transition values which do not occur on the lattice or in mean field.

An example is the free boundary condition Gibbs-state of the ferromagnetic Ising model: It undergoes a transition from extremal to non-extremal at a temperature which is strictly lower than the phase transition temperature, which was proved by Bleher and Ioffe.

We discuss the situation for the Potts model, and our results on the existence or non-existence of such transitions for all of its translation-invariant phases.

This is a joint work with Utkir Rozikov.

**March 26, 2015: No Seminar**

**March 19, 2015: Arnoud den Boer (Twente University)**

When: Thursday March 19th, 16.00

Where: TU Delft, Faculty EWI, Mekelweg 4, v/d Poelzaal (LB 01.220).

*Online learning in stochastic optimization problems*

Online learning refers to optimization problems where the objective function is unknown to the decision maker, but is gradually learned from accumulating data. This type of problems has many applications in e.g. dynamic pricing, online advertisement, and recommendation systems. A decision policy that is frequently used in practice is to use, at each decision moment, the decision that seems optimal given the available data. Perhaps surprisingly, this simple policy may lead to detrimental results. In this talk I will explain some of the intuition behind this phenomenon, discuss alternative policies and characterize their performance, and point to challenging open problems.

**March 12, 2015: Cristian Spitoni (Utrecht University)**

When: Thursday March 12th, 16.00

Where: TU Delft, Faculty EWI, Mekelweg 4, Vassiliadeszaal (HB 10.230).

*Sum of exit times in series of metastable states*

Metastable states are very common in nature and are typical of systems close to a first order phase transition. Classical examples are the supersaturated vapor and the magnetic hysteresis. In this talk we study the metastability properties of stochastic systems with multiple metastable states. In the presence of such deep wells, we prove an addition formula for the exit times from the metastable states in the case they form a series. With this expression we mean that the structure of the energy landscape is such that the system has two non–degenerate metastable states and the system, started at the one with highest energy, must necessarily pass through the second one before relaxing to the stable state. Furthermore, we show the application of the addition theorem in case of the Blume–Capel model with zero chemical potential, and in case of the reversible Probabilistic Cellular Automata without self–interaction.

This is a joint work with E.N.M. Cirillo (Rome University, Italy) and F.R. Nardi (TU Eindhoven).

**February 26, 2015: Cor Kraaikamp ****(****TU Delft) ****- POSTPONED**

When: Thursday February 26th, 16.00

Where: TU Delft, Faculty EWI, Mekelweg 4, v/d Poelzaal (LB 01.220).

*Continued fractions and other number theoretic transformations*

Since Gauss wrote in 1800 in his mathematical diary that he found the invariant measure of the regular continued fraction map, there has been a surprisingly strong relation between number theoretic transformations (such as the Gauss-map), dynamical systems and ergodic theory. In this introductory talk I will outline some of the history and the contributions by Paul Levy, Khintchine, Doeblin, Renyi, but also will mention (and in a few cases prove) some recent results.

**February 19, 2015: Marc Hallin ****(****Université Libre de Bruxelles & Princeton University)**

When: Thursday February 19th, 16.00

Where: TU Delft, Faculty EWI, Mekelweg 4, v/d Poelzaal (LB 01.220).

*Dynamic Factor Models and Volatilities: Recovering the Market Volatility Shocks*

Decomposing volatilities into a common market-driven component and an idiosyncratic item-specific one is an important issue in financial econometrics. This, however, as any study involving market-related features, requires the statistical analysis of large panels of time series, hence faces the usual challenges associated with high-dimensional data. Factor model methods in such a context are an ideal tool, but they do not readily apply to the analysis of volatilities. Focusing on the reconstruction of the unobserved market shocks and the way they are loaded by the various items (stocks) in the panel, we propose an entirely nonparametric and model-free two-step general dynamic factor approach to the problem, which avoids the usual curse of dimensionality. Applied to the S&P100 asset return dataset, the method provides evidence that a non-negligible proportion of the market-driven volatility of returns originates in the volatilities of level-idiosyncratic components.

Joint work with Matteo Barigozzi (LSE).

**February 12, 2015: Tom Lidbetter ****(****London School of Economics****)**

When: Thursday February 12th, 16.00

Where: TU Delft, Faculty EWI, Mekelweg 4, Vassiliadeszaal (HB 10.230).

*Optimal search for a small (or well hidden) object*

A Searcher seeks to find a stationary Hider located at some point H (not necessarily a node) on a given network Q. The Searcher can move along the network from a given starting point at unit speed, but to actually find the Hider she must pass it while moving at a fixed slower speed (which may depend on the arc). In this ‘bimodal search game’, the payoff is the first time the Searcher passes the Hider while moving at her slow speed. This game models the search for a small or well hidden object (e.g., a contact lens, improvised explosive device, predator search for camouflaged prey). We define a Bimodal Chinese Postman tour as a tour of minimum time t which traverses every point of every arc at least once in the slow mode. For trees and weakly Eulerian networks (networks containing a number of disjoint Eulerian cycles connected in a tree-like fashion) the value of the bimodal search game is t/2. For trees, the optimal Hider strategy has full support on the network.

This differs from traditional search games, where it is optimal for him to hide only at leaf nodes. We then consider the notion of a lucky Searcher who can also detect the Hider with a positive probability q even when passing him at her fast speed. This paper has particular importance for demining problems.

**February 5, 2015: Cars Hommes ****(****University of Amsterdam****)**

When: Thursday February 5th, 16.00

Where: TU Delft, Faculty EWI, Mekelweg 4, v/d Poelzaal (LB 01.220).

*Identifying booms and busts in house prices under heterogeneous expectations*

We introduce heterogeneous expectations in a standard housing market model linking housing rental levels to fundamental buying prices. Using quarterly data we estimate the model parameters for eight different countries, US, UK, NL, JP, CH, ES, SE and BE. We find that the data support heterogeneity in expectations, with temporary endogenous switching between fundamental mean-reverting and trend-following chartists beliefs based on their relative performance. For all countries we identify temporary house price bubbles, amplified by trend extrapolation, and crashes reinforced by fundamentalists. The qualitative predictions of such non-linear models are very different from standard linear benchmarks, with important policy implications. The fundamental price becomes unstable, e.g. when the interest rate is set too low or mortgage tax deductions too high, giving rise to multiple non-fundamental equilibria and/or global instability.

Joint work with Wilko Bolt, Maria Demertzis, Cees Diks and Marco van der Leij.

**January 22, 2015: Fred Vermolen ****(****TU Delft****) - POSTPONED**

When: Thursday January 22nd, 16.00

Where: TU Delft, Faculty EWI, Mekelweg 4, v/d Poelzaal (LB 01.220).

*A tour over the world of semi-stochastic cell-based modeling for wound healing and tumor initiation*

We consider mathematical modelling approaches for the simulation of processes like wound healing, wound contraction and tumor initiation. The approaches are based on the solution of partial differential equations by Fundamental Solutions and Finite-Element method and on stochastic principles for cell migration, division and death.

The treatment will be rather informal where emphasis is on methodology and possible outcomes of model simulations.