Design of electron band pass filters for electrically biased finite superlattices

We design optimal band pass filters for electrons in semiconductor heterostructures, under a uniform applied electric field. The inner cells are chosen to provide a desired transmission window. The outer cells are then designed to transform purely incoming or outgoing waves into Bloch states of the inner cells. The transfer matrix is interpreted as a conformal mapping in the complex plane, which allows us to write constraints on the outer cell parameters, from which physically useful values can be obtained.

Phase-only filters codified with Burckhardt's method

We show that Burckhardt's method is available to codify phase-only filters with amplitude-only variations. Correlation experimental results are given.

Full complex Fresnel holograms displayed on liquid cristal displays

We propose a method to display full complex Fresnel holograms by adding the information displayed on two analogue ferroelectric liquid crystal spatial light modulators. One of them works in real-only configuration and the other in imaginary-only mode. The Fresnel holograms are computed by backpropagating an object at a selected distance with the Fresnel transform. Then, displaying the real and imaginary parts on each panel, the object is reconstructed at that distance from the modulators by simple propagation of light. We present simulation results taking into account the specifications of the modulators as well as optical results. We have also studied the quality of reconstructions using only real, imaginary, amplitude or phase information. Although the real and imaginary reconstructions look acceptable for certain distances, full complex reconstruction is always better and is required when arbitrary distances are used.

Identifying the preferred subset of enzymatic profiles in nonlinear kinetic metabolic models via multiobjective global optimization and pareto filters

Optimization models in metabolic engineering and systems biology focus typically on optimizing a unique criterion, usually the synthesis rate of a metabolite of interest or the rate of growth. Connectivity and non-linear regulatory effects, however, make it necessary to consider multiple objectives in order to identify useful strategies that balance out different metabolic issues. This is a fundamental aspect, as optimization of maximum yield in a given condition may involve unrealistic values in other key processes. Due to the difficulties associated with detailed non-linear models, analysis using stoichiometric descriptions and linear optimization methods have become rather popular in systems biology. However, despite being useful, these approaches fail in capturing the intrinsic nonlinear nature of the underlying metabolic systems and the regulatory signals involved. Targeting more complex biological systems requires the application of global optimization methods to non-linear representations. In this work we address the multi-objective global optimization of metabolic networks that are described by a special class of models based on the power-law formalism: the generalized mass action (GMA) representation. Our goal is to develop global optimization methods capable of efficiently dealing with several biological criteria simultaneously. In order to overcome the numerical difficulties of dealing with multiple criteria in the optimization, we propose a heuristic approach based on the epsilon constraint method that reduces the computational burden of generating a set of Pareto optimal alternatives, each achieving a unique combination of objectives values. To facilitate the post-optimal analysis of these solutions and narrow down their number prior to being tested in the laboratory, we explore the use of Pareto filters that identify the preferred subset of enzymatic profiles. We demonstrate the usefulness of our approach by means of a case study that optimizes the ethanol production in the fermentation of Saccharomyces cerevisiae.

Efficiency and environmental regulation: a 'complex situation'

Production of desirable outputs is often accompanied by undesirable by products that have damaging effects on the environment, and whose disposal is frequently regulated by public authorities. In this paper, we compute directional technology distance functions under particular assumptions concerning disposability of bads in order to test for the existence of what we call ‘complex situations’, where the biggest producer is not the greatest polluter. Furthermore, we show that how in such situations, environmental regulation could achieve an effective reduction in the aggregate level of bad outputs without reducing the production of good outputs. Finally, we illustrate our methodology with an empirical application to a sample of Spanish tile ceramic producers.

Empiricism in ecological economics: a perspective from complex systems theory

Economies are open complex adaptive systems far from thermodynamic equilibrium, and neo-classical environmental economics seems not to be the best way to describe the behaviour of such systems. Standard econometric analysis (i.e. time series) takes a deterministic and predictive approach, which encourages the search for predictive policy to ‘correct’ environmental problems. Rather, it seems that, because of the characteristics of economic systems, an ex-post analysis is more appropriate, which describes the emergence of such systems’ properties, and which sees policy as a social steering mechanism. With this background, some of the recent empirical work published in the field of ecological economics that follows the approach defended here is presented. Finally, the conclusion is reached that a predictive use of econometrics (i.e. time series analysis) in ecological economics should be limited to cases in which uncertainty decreases, which is not the normal situation when analysing the evolution of economic systems. However, that does not mean we should not use empirical analysis. On the contrary, this is to be encouraged, but from a structural and ex-post point of view.

Accuracy vs. simplicity: a complex trade-off

Inductive learning aims at finding general rules that hold true in a database. Targeted learning seeks rules for the predictions of the value of a variable based on the values of others, as in the case of linear or non-parametric regression analysis. Non-targeted learning finds regularities without a specific prediction goal. We model the product of non-targeted learning as rules that state that a certain phenomenon never happens, or that certain conditions necessitate another. For all types of rules, there is a trade-off between the rule's accuracy and its simplicity. Thus rule selection can be viewed as a choice problem, among pairs of degree of accuracy and degree of complexity. However, one cannot in general tell what is the feasible set in the accuracy-complexity space. Formally, we show that finding out whether a point belongs to this set is computationally hard. In particular, in the context of linear regression, finding a small set of variables that obtain a certain value of R2 is computationally hard. Computational complexity may explain why a person is not always aware of rules that, if asked, she would find valid. This, in turn, may explain why one can change other people's minds (opinions, beliefs) without providing new information.

Periodic orbits in complex Abel equation

"Vegeu el resum a l'inici del document del fitxer adjunt."

Propietats d'absorció bifotònica del tetrafenilporficè i el seu complex de palladi: potencials sensibilitzadors per a Teràpia Fotodinàmica bifotònica.

Estudi elaborat a partir d’una estada a la Universitat de Aarhus, Dinamarca, durant juliol 2006. En el present treball s’investiguen, per primer cop, les propietats de absorció bifotòniques del fotosensibilitzador 2,7,12,17-tetrafenilporficè (TPPo) i del seu complex de pal•ladi (II) (PdTPPo). Ambos compostos han rebut molta atenció com a possibles otosensibilitzadors per a Teràpia Fotodinàmica (TFD). S’utilitza la detecció de la fosforescència de l’oxigen singlet, centrada a 1270 nm i produïda per l’absorció de dos fotons, per quantificar la magnitud de la secció d’absorció bifotònica, "delta", dels porficèns estudiats. Els experiments se han dut a terme en el marge espectral 750-850 nm i a l’infraroig proper a 1100nm. Aquestes longituds d’ona corresponen a les zones d’absorció bifotònica en les bandes de Soret i Q. Les propietats bifotòniques obtingudes es comparen i contrasten amb les dades conegudes de la tetrafenilporfirina (TPP), isòmer estructural del tetrafenilporficè però amb més gran simetria, i es troba que en la banda de Soret (que coincideix amb la regió de la pell més transparent) els valors de delta per el TPPo i PdTPPo son aproximadament 2000 GM en el màxim, pràcticament cent vegades més grans que per la TPP. A més a més, aquestos valors son dos ordres de magnitud més grans que els obtinguts a l’irradiar a 1100 nm (bandes Q). Aquestes observacions es poden explicar mitjançant la amplificació per ressonància deguda a la presència de transicions monofotòniques ressonants en la regió de les bandes Q. Els elevats valors de "delta" obtinguts per els tetrafenilporficèns estudiats junt a les principals característiques que aquestos presenten (elevat rendiment de formació d’oxigen singlet, estabilitat química i fotoquímica, absència de citotoxicitat,...) qualifiquen al TPPo y PdTPPo com a possibles fotosensibilitzadors per a Teràpia Fotodinàmica Bifotònica.

Construcció i explotació d’un complex de turisme rural a la població d’Àreu (Pirineu de Lleida)

Aquest treball de fi de carrera pretén desenvolupar el pla de negoci per a la construcció i l’explotació d’un complex de turisme rural al Pallars Sobirà. El projecte compren l’enderroc de les construccions preexistents, construcció i posterior explotació d’apartaments d’ús turístic i una cafeteria a la població d’ Àreu. Dins el pla de negoci s’hi contemplen els plans comercial, financer, l’anàlisi del mercat i l’entorn i una acurada definició del servei que s’oferirà. Amb el treball es vol, doncs, aportar idees pràctiques i útils per a la consecució dels objectius plantejats en el projecte familiar.

Modelling of bird distribution under complex mediterranean landscape dynamics: open habitat birds and fire (MEDFIRE)

Report for the scientific sojourn at the Simon Fraser University, Canada, from July to September 2007. General context: landscape change during the last years is having significant impacts on biodiversity in many Mediterranean areas. Land abandonment, urbanisation and specially fire are profoundly transforming large areas in the Western Mediterranean basin and we know little on how these changes influence species distribution and in particular how these species will respond to further change in a context of global change including climate. General objectives: integrate landscape and population dynamics models in a platform allowing capturing species distribution responses to landscape changes and assessing impact on species distribution of different scenarios of further change. Specific objective 1: develop a landscape dynamic model capturing fire and forest succession dynamics in Catalonia and linked to a stochastic landscape occupancy (SLOM) (or spatially explicit population, SEPM) model for the Ortolan bunting, a species strongly linked to fire related habitat in the region. Predictions from the occupancy or spatially explicit population Ortolan bunting model (SEPM) should be evaluated using data from the DINDIS database. This database tracks bird colonisation of recently burnt big areas (&50 ha). Through a number of different SEPM scenarios with different values for a number of parameter, we should be able to assess different hypothesis in factors driving bird colonisation in new burnt patches. These factors to be mainly, landscape context (i.e. difficulty to reach the patch, and potential presence of coloniser sources), dispersal constraints, type of regenerating vegetation after fire, and species characteristics (niche breadth, etc).

Solid-phase synthesis and NMR studies of modified oligonucleotides forming triplex helix and of oligonucleopeptides mimicking the topoisomerase I-DNA covalent complex

Report for the scientific sojourn carried out at the Institut de Biologia Molecular de Barcelona of the CSIC –state agency – from april until september 2007. Topoisomerase I is an essential nuclear enzyme that modulates the topological status of DNA, facilitating DNA helix unwinding during replication and transcription. We have prepared the oligonucleotide-peptide conjugate Ac-NLeu-Asn-Tyr(p-3’TTCAGAAGC5’)-LeuC-CONH-(CH2)6-OH as model compound for NMR studies of the Topoisomerase I- DNA complex. Special attention was made on the synthetic aspects for the preparation of this challenging compound especially solid supports and protecting groups. The desired peptide was obtained although we did not achieve the amount of the conjugate needed for NMR studies. Most probably the low yield is due to the intrinsic sensitive to hydrolysis of the phosphate bond between oligonucleotide and tyrosine. We have started the synthesis and the structural characterization of oligonucleotides carrying intercalating compounds. At the present state we have obtained model duplex and quadruplex sequences modified with acridine and NMR studies are underway. In addition to this project we have successfully resolved the structure of a fusion peptide derived from hepatitis C virus envelope synthesized by the group of Dr. Haro and we have synthesized and started the characterization of a modified G-quadruplex.

Point-occurrence self-similarity in crackling-noise systems and in other complex systems

It has been recently found that a number of systems displaying crackling noise also show a remarkable behavior regarding the temporal occurrence of successive events versus their size: a scaling law for the probability distributions of waiting times as a function of a minimum size is fulfilled, signaling the existence on those systems of self-similarity in time-size. This property is also present in some non-crackling systems. Here, the uncommon character of the scaling law is illustrated with simple marked renewal processes, built by definition with no correlations. Whereas processes with a finite mean waiting time do not fulfill a scaling law in general and tend towards a Poisson process in the limit of very high sizes, processes without a finite mean tend to another class of distributions, characterized by double power-law waiting-time densities. This is somehow reminiscent of the generalized central limit theorem. A model with short-range correlations is not able to escape from the attraction of those limit distributions. A discussion on open problems in the modeling of these properties is provided.

Bergman-type singular operators and the characterization of Carleson measures for Besov-Sobolev spaces on the complex ball

"Vegeu el resum a l'inici del document del fitxer adjunt."

La programació al servei de la matemàtica

Treball de recerca realitzat per un alumne d'ensenyament secundari i guardonat amb un Premi CIRIT per fomentar l'esperit cientí­fic del Jovent l'any 2009. La programació al servei de la matemàtica és un programa informàtic fet amb Excel i Visual Basic. Resol equacions de primer grau, equacions de segon grau, sistemes d'equacions lineals de dues equacions i dues incògnites, sistemes d'equacions lineals compatibles determinats de tres equacions i tres incògnites i troba zeros de funcions amb el teorema de Bolzano. En cadascun dels casos, representa les solucions gràficament. Per a això, en el treball s'ha hagut de treballar, en matemàtiques, amb equacions, nombres complexos, la regla de Cramer per a la resolució de sistemes, i buscar la manera de programar un mètode iteratiu pel teorema de Bolzano. En la part gràfica, s'ha resolt com fer taules de valors amb dues i tres variables i treballar amb rectes i plans. Per la part informàtica, s'ha emprat un llenguatge nou per l'alumne i, sobretot, ha calgut saber decidir on posar una determinada instrucció, ja que el fet de variar-ne la posició una sola lí­nea ho pot canviar tot. A més d'això, s'han resolt altres problemes de programació i també s'ha realitzat el disseny de pantalles.