Past events 2011

Abstract: Taylor's "universal" power law is an empirical law for the relationship between the mean and variance of population abundance, which over time has been observed for a wide range of different species and ecosystems. Ever since it was proposed 50 years ago, the power law has given rise to discussions, because it seemed to lack a satisfactory theoretical explanation, in spite of its frequent observation in many different ecological, genomic, social science and epidemiological settings. We investigate a possible theoretical explanation for Taylor's power law based on the Tweedie distribution, which is an exponential dispersion model characterized by scale invariance; representing a statistical equilibrium that a system subject to random perturbations will approach over time. By exploring a new self-similarity hypothesis we derive the spatial correlation structure of the population, from which parameters may be estimated by means of estimating functions. These results enable us to investigate the mechanisms that control the spatial structure of the population, including the effects of environmental factors and interaction between species.

In this talk I will talk about Alan Turing and his groundbreaking ideas in mathematics, logic and what has since become a science in its own right now known as computer science. Along the way I will also provide some insight into the life of Turing - and into his tragic, early death. In this way I hope to help us all better understand one of the most important figures in 20th century science.

Informationsmøde for studerende om ph.d. uddannelse

Jesper Møller, som er leder for forskerskolens program "Mathematics & Physics" afholder  et møde for interesserede studerende , hvor han fortæller om om Ph.D.-uddannelse (forudsætninger, finansiering, fremtidsperspektiver etc.). Det er også hensigten, at mødet skal give de studerende et realistisk billede af det faglige niveau for et Ph.D.-studium og hvilke emner, vi hér kan vejlede i.

Informationsudvalget

The course will be given by Daniel Simpson, Norwegian University of Science and Technology.

Participation in the course is free but does require registration.

Further information about registration, course content etc. can be found on the following web page.

http://people.math.aau.dk/~kkb/INLAcourse/

The course is co-organised and sponsored by Centre for Stochastic Geometry and Advanced Bioimaging (www.csgb.dk).

It sounds like a fairy tale: Within a few years Sergey Brin and Lawrence Page, the founders of GOOGLE, became some of the richest men in this world. Their secret is an algorithm by which the “importance” of web pages is calculated. This „Page-Rank-Algorithmus“ has a mathematical background that will be explained in this lecture.

Strictly speaking it is „only“ necessary to solve a system of linear equations similar to such systems that one treats in school. But the number of unknown parameters is gigantic, and it is necessary to use methods from probability theory to overcome this difficulty.

• Om formiddagen er emnet grafteori.
  Der er mange anvendelser, som vil være relevante for såvel AT(studieområdet i htx, hhx) som SRP, SRO og de tilsvarende opgaver på hhx og htx.

• Midt på dagen holder Ehrhard Behrends foredrag (Se ovenfor).
  Dette indslag bliver på engelsk.  Behrends er formand for den europæiske matematiske forenings komite for "Raising Public Awareness".
  
  

• Dagens sidste emne er Knudeteori med anvendelser.
  Igen er der mange muligheder - især med forbindelser til kemi og biologi.

 Cognitive Radio is one of the candidate technology stream that could help in this process. The term cognition (from latin cognoscere, "to know", "to conceptualize" or "to recognize") refers to a faculty for the processing of information, applying knowledge, and changing preferences. Cognitive Radio is then a paradigm for wireless communication in which either a network or a wireless node changes its transmission or reception parameters to communicate efficiently by avoiding interference with licensed or unlicensed users. Cognitive Radio was thought of as an ideal goal towards which a radio system should evolve: a fully reconfigurable wireless black-box that automatically changes its communication variables in response to network and user demands.

In one hand the smart  adaptability of Cognitive Radio opens a number of possibilities, but on the other hand it also open a number of issues: How do cognitive radios adapt to each other? If each cognitive radio is making autonomous decisions, what is the outcome of such decisions? The application of game theory in cognitive radio is emerging as a fundamental theoretical background to answer such questions.

 In the talk, we will provide an introduction to the world of cognitive radio, by first presenting a general overview on the technology and the related issues and theoretical fields. Afterwards, we will focus on a specific problem and a specific solution: how to solve the spectrum allocation problem with game theoretic tools. In particular, we will present non-cooperative game theoretic models including potential games, supermodular games and submodular games. Specially within the field of submodular games we will discuss open issues which could be of interest of research for mathematicians.

Host: Horia Cornean

In the case the antennas on the TX and RX sides form an array and we increase the number of antennas equally on both sides, maintaining fixed the distances inside the arrays, under some conditions on the transfer matrix, we proved [1] that the capacity increases sublinearly with the number of antennas. This result is different of those obtained considering probabilistic models which give a linear behavior.

In the case we increase similarly the number of  TX and RX antennas, in fixed volumes, we prove [3] that the capacity grows less rapidly than any positive power of the number of  antennas.

These two results use the description of the transfer matrix in terms of  three angular functions:

two of them are related to the antennas diagrams while the third , called the spread function , is related to the scattering properties of the environment. This description has been justified mathematically [2] starting from the global Maxwell equations.

We will discuss some open problems which might be solved using these deterministic models.

For instance,  in a given environment,  we would like to study capacity changes with  rotations of the arrays, or  capacity variation when the environment is enriched ( furniture in indoor or new buildings in outdoor).

It will also be nice to get, in the case of small number of antennas, simple formulas for the capacity in terms of  some antennas parameters and  crude probabilistic description of the environment .

[1] F.Bentosela, E. Soccorsi. Sub-linear capacity scaling for multi-path channel models, Math. Methods Appl. Sci. 33 no. 9 (2010), 1164—1180
[2] F.Bentosela, H. Cornean, B.Fleury, N. Marchetti. On the tranfer matrix of a MIMO system, Math. Methods Appl. Sci  (2011)(wileyonlinelibrary.com) DOI: 10.1002/mma.1415
[3] F.Bentosela, H. Cornean, N. Marchetti. Capacity dependence of a  MIMO system on the number of antennas (to be submitted)

Host: Horia Cornean

Abstract: Network coding is a fairly new topic in the area of communication. The gain of using network coding is for instance in a setting where multiple receivers all demands the same information from a source. In network coding, network nodes are allowed to "mix" incoming information. When this "mixing" is done randomly we call it random network coding.

The natural question to ask is: How often does the information get through? We dive into and compare algebraic and combinatorial methods to lower bound the probability that "the information gets through".

When information travels (through computer networks, from a CD to your loudspeakers, etc.), errors might occur. Error-correcting codes is on devising ways to "safety wrap" the information such that when information on a wire is infected by errors, we are still able to recover the information that was originally sent. We introduce a new class of such codes, show that they are a generalisation of several well-known codes, introduce two list-decoding algorithms (recovering the sent information), and show how they perform. For one of the decoding algorithms we utilise new knowledge regarding how many zeros a multivariate polynomial has.

Everybody is welcome!

Abstract: I will discuss a generalization of the Shannon Sampling Theorem that allows for reconstruction of signals in arbitrary bases (and frames).

Not only can one reconstruct in arbitrary bases, but this can also be done in a completely stable way. When extra information is available, such as sparsity or compressibility of the signal in a particular basis, one may reduce the number of samples dramatically. This is done via Compressed Sensing techniques, however, the usual finite-dimensional framework is not sufficient. To overcome this obstacle I'll introduce the concept of Infinite-Dimensional Compressed Sensing.

Excitons (one electron and one hole) have proven to dominate the absorption spectrum in semiconducting nanostructures, and one may therefore expect that the charged excitons (trions) and exciton couples (biexcitons) also may be of importance. In this talk we study trions and biexcitons in low-dimensional semiconductors with focus on carbon nanotubes (CNTs). In the description of these three and four particle complexes two continuum models are used: a model with cylinder geometry and a fractional dimensional model, in which one interpolates the Laplacian and integration measure between 1, 2 and 3 dimensions. With regards to the first model two studies are made: First we find a solution to  an effective Hamiltonian and then we extent this approach to support the full cylindrical geometry. Next we investigate the line shape of the trion absorption peak in CNTs using a method developed by Stébé et al. With regards to the fractional dimensional approach we first apply the model to estimate the binding energy of trions in CNTs using a basis expansion. We then estimate the binding energy of trions in GaAs quantum wells and CNTs using variational quantum Monte Carlo. The results are compared with experimentally observed binding energies. To this end we discuss the difficulties of applying the VQMC approach to the fractional dimensional model. Finally, we apply the model to estimate biexciton binding energies in CNTs. We conclude on the applicability of this model and briefly discuss further perspectives of this work.

Målgruppen er medarbejdere, der tidligere har brugt Maple eller kun bruger Maple sporadisk. Har man specifikke ønsker til indhold, kan man skrive til Preben Alsholm, som vil tage hensyn hertil ved planlægningen.

Indledning om basal brug af Maple. 30-45 minutter.
Øvelser 2 timer
Afsluttende kommentarer

Friday, June 17, at 13.00 in NOVI Auditorium, Niels Jernes Vej 10
DOCTORAL DEFENSE

Jon Johnsen, Department of Mathematical Sciences, Aalborg University, will give a talk and defend his Doctoral Thesis

On the Theory of Type 1,1-Operators

The abstract can be found here.

After the defense there will be a reception in the NOVI canteen - everybody is welcome.

Matthias Westrich, TU Braunschweig and IMF Aarhus: Characterisation of the quasi-stationary state of an impurity driven by monochromatic light

We study rigorously a pumping scheme of a solid state laser model starting from a microscopical model, which is composed of an impurity in a crystal interacting with a monochromatic external light source. The crystal-impurity interaction is assumed to be translation analytic and the external light source is of moderate strength in a specific sense. We prove for the effective dynamics the existence of and relaxation to a quasi-stationary state, which is a stationary state up to small Rabi oscillations due to the external light source. Moreover, we characterise the state in terms of “generalised Einstein relations

of spontaneous/stimulated emission/absorption, which are conceptually related to the phenomenological relations derived by Einstein in 1916.

Our approach is based on a spectral analysis of the evolution semigroup pertaining to the non-autonomous Cauchy problem.

Host: Horia Cornean

Abstract:
Alpha diversity is commonly defined as total number species in an area. Understanding mechanisms of such diversity has invaluable insight on biodiversity conservation. As evidences accumulated, we have already known that alpha diversity of a given community (the given community means that we know total species number and global species abundance distribution of a community at first) is totally determined by spatial distributions of species within the community. Therefore, studies on spatial pattern of species could help us to comprehend the alpha diversity and other relative theories. In the talk I will give a brief introduction on what kinds of spatial data we have collected for answering this question; and then I will present how to find main spatial constructing processes of alpha diversity based on those data. I will also show how to evaluate the relative importance of the main processes found in above on forming spatial structure of species. Finally, I will touch several open questions for discussing.

Host: Rasmus Waagepetersen

We consider the discrete time unitary dynamics given by a quantum walk on the d-dimensional lattice performed by a quantum particle with internal degree of freedom, called coin state, according to the following iterated rule: a unitary update of the coin state takes place, followed by a shift on the lattice, conditioned on the coin state of the particle. We study the large time behavior of the quantum mechanical probability distribution of the position observable on the lattice when the sequence of unitary updates is given by an i.i.d.

sequence of random matrices. In particular, when averaged over the randomness, this distribution is shown to display a drift proportional to the time and its centered counterpart is shown to display a diffusive behavior. A moderate deviation principle is also proven to hold.

Host: Horia Cornean

Abstract: In the film which is alluded to (with a twist) in the title above, Q says:

"If it hadn't been for Q Branch, you'd have been dead long ago"

- to which Bond has no answer.

Vi har reduceret antallet af bøger, som ellers tidligere blev brugt i Matematik 1 på DTU, fra 7 til 0. Til gengæld tilbydes de 724 førsteårs-studerende en hel del (andre) lærings-gadgets, som i passende udvalg vil blive både motiveret og aktiveret i løbet af foredraget.

Jakob Gulddahl Rasmussen, medlem af Studienævnet, et informationsmøde for jer vedrørende bestemmelser i bekendtgørelser og studieordninger, der har indflydelse på valg af tilvalgsfag/suppleringsfag og kandidatstudium.