The complexity of random ordered structures

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

Optimal monitoring to implement clean technologies when pollution is random

We analyze a model where firms chose a production technology which, together with some random event, determines the final emission level. We consider the coexistence of two alternative technologies: a "clean" technology, and a "dirty" technology. The environmental regulation is based on taxes over reported emissions, and on penalties over unreported emissions. We show that the optimal inspection policy is a cut-off strategy, for several scenarios concerning the observability of the adoption of the clean technology and the cost of adopting it. We also show that the optimal inspection policy induces the firm to adopt the clean technology if the adoption cost is not too high, but the cost levels for which the firm adopts it depend on the scenario.

Random graphs on surfaces

Counting labelled planar graphs, and typical properties of random labelled planar graphs, have received much attention recently. We start the process here of extending these investigations to graphs embeddable on any fixed surface S. In particular we show that the labelled graphs embeddable on S have the same growth constant as for planar graphs, and the same holds for unlabelled graphs. Also, if we pick a graph uniformly at random from the graphs embeddable on S which have vertex set {1, . . . , n}, then with probability tending to 1 as n → ∞, this random graph either is connected or consists of one giant component together with a few nodes in small planar components.

A class of stochastic games with infinitely many interacting agents related to Glauber dynamics on random graphs

We introduce and study a class of infinite-horizon nonzero-sum non-cooperative stochastic games with infinitely many interacting agents using ideas of statistical mechanics. First we show, in the general case of asymmetric interactions, the existence of a strategy that allows any player to eliminate losses after a finite random time. In the special case of symmetric interactions, we also prove that, as time goes to infinity, the game converges to a Nash equilibrium. Moreover, assuming that all agents adopt the same strategy, using arguments related to those leading to perfect simulation algorithms, spatial mixing and ergodicity are proved. In turn, ergodicity allows us to prove “fixation”, i.e. that players will adopt a constant strategy after a finite time. The resulting dynamics is related to zerotemperature Glauber dynamics on random graphs of possibly infinite volume.

Towards an emotion-driven interactive music system: ridging the gaps between affect, physiology and sound generation

Report for the scientific sojourn at the Stanford University from January until June 2007. Music is well known for affecting human emotional states, yet the relationship between specific musical parameters and emotional responses is still not clear. With the advent of new human-computer interaction (HCI) technologies, it is now possible to derive emotion-related information from physiological data and use it as an input to interactive music systems. Providing such implicit musical HCI will be highly relevant for a number of applications including music therapy, diagnosis, nteractive gaming, and physiologically-based musical instruments. A key question in such physiology-based compositions is how sound synthesis parameters can be mapped to emotional states of valence and arousal. We used both verbal and heart rate responses to evaluate the affective power of five musical parameters. Our results show that a significant correlation exists between heart rate and the subjective evaluation of well-defined musical parameters. Brightness and loudness showed to be arousing parameters on subjective scale while harmonicity and even partial attenuation factor resulted in heart rate changes typically associated to valence. This demonstrates that a rational approach to designing emotion-driven music systems for our public installations and music therapy applications is possible.

Spectral analysis of random sparse matrices

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Propagation connectivity of random hypergraphs

We study the concept of propagation connectivity on random 3-uniform hypergraphs. This concept is inspired by a simple linear time algorithm for solving instances of certain constraint satisfaction problems. We derive upper and lower bounds for the propagation connectivity threshold, and point out some algorithmic implications.

Pseudomarkets with priorities in large random assignment economies

I study large random assignment economies with a continuum of agents and a finite number of object types. I consider the existence of weak priorities discriminating among agents with respect to their rights concerning the final assignment. The respect for priorities ex ante (ex-ante stability) usually precludes ex-ante envy-freeness. Therefore I define a new concept of fairness, called no unjustified lower chances: priorities with respect to one object type cannot justify different achievable chances regarding another object type. This concept, which applies to the assignment mechanism rather than to the assignment itself, implies ex-ante envy-freeness among agents of the same priority type. I propose a variation of Hylland and Zeckhauser' (1979) pseudomarket that meets ex-ante stability, no unjustified lower chances and ex-ante efficiency among agents of the same priority type. Assuming enough richness in preferences and priorities, the converse is also true: any random assignment with these properties could be achieved through an equilibrium in a pseudomarket with priorities. If priorities are acyclical (the ordering of agents is the same for each object type), this pseudomarket achieves ex-ante efficient random assignments.

Music identification

L'evolució ens els últims decennis de les possibilitats relacionades amb les tecnologies de la informació han provocat l'aparició de diferents camps, entre ells l'anomenat “recuperació de música basant-se en el contingut”, que tracta de calcular la similitud entre diferents sons. En aquest projecte hem fet una recerca sobre els diferents mètodes que existeixen avui en dia, i posteriorment n'hem comparat tres, un basat en característiques del so, un basat en la transformada discreta del cosinus, i un que combina els dos anteriors. Els resultats han mostrat, que el basat en la transformada de Fourier és el més fiable.

Growth in a Cross-Section of Cities: Location, Increasing Returns or Random Growth?

This article analyzes empirically the main existing theories on income and population city growth: increasing returns to scale, locational fundamentals and random growth. To do this we implement a threshold nonlinearity test that extends standard linear growth regression models to a dataset on urban, climatological and macroeconomic variables on 1,175 U.S. cities. Our analysis reveals the existence of increasing returns when per-capita income levels are beyond $19; 264. Despite this, income growth is mostly explained by social and locational fundamentals. Population growth also exhibits two distinct equilibria determined by a threshold value of 116,300 inhabitants beyond which city population grows at a higher rate. Income and population growth do not go hand in hand, implying an optimal level of population beyond which income growth stagnates or deteriorates

On the writer identification in old handwritten music scores

Report for the scientific sojourn at the University of Bern, Swiss, from Mars until June 2008. Writer identification consists in determining the writer of a piece of handwriting from a set of writers. Even though an important amount of compositions contains handwritten text in the music scores, the aim of the work is to use only music notation to determine the author. It’s been developed two approaches for writer identification in old handwritten music scores. The methods proposed extract features from every music line, and also features from a texture image of music symbols. First of all, the music sheet is first preprocessed for obtaining a binarized music score without the staff lines. The classification is performed using a k-NN classifier based on Euclidean distance. The proposed method has been tested on a database of old music scores from the 17th to 19th centuries, achieving encouraging identification rates.

Hierarchical conditional random fields for parts based models matching

A parts based model is a parametrization of an object class using a collection of landmarks following the object structure. The matching of parts based models is one of the problems where pairwise Conditional Random Fields have been successfully applied. The main reason of their effectiveness is tractable inference and learning due to the simplicity of involved graphs, usually trees. However, these models do not consider possible patterns of statistics among sets of landmarks, and thus they sufffer from using too myopic information. To overcome this limitation, we propoese a novel structure based on a hierarchical Conditional Random Fields, which we explain in the first part of this memory. We build a hierarchy of combinations of landmarks, where matching is performed taking into account the whole hierarchy. To preserve tractable inference we effectively sample the label set. We test our method on facial feature selection and human pose estimation on two challenging datasets: Buffy and MultiPIE. In the second part of this memory, we present a novel approach to multiple kernel combination that relies on stacked classification. This method can be used to evaluate the landmarks of the parts-based model approach. Our method is based on combining responses of a set of independent classifiers for each individual kernel. Unlike earlier approaches that linearly combine kernel responses, our approach uses them as inputs to another set of classifiers. We will show that we outperform state-of-the-art methods on most of the standard benchmark datasets.

Predicting random level and seasonality of hotel prices. A structural equation growth curve approach

This article examines the effect on price of different characteristics of holiday hotels in the sun-and-beach segment, under the hedonic function perspective. Monthly prices of the majority of hotels in the Spanish continental Mediterranean coast are gathered from May to October 1999 from the tour operator catalogues. Hedonic functions are specified as random-effect models and parametrized as structural equation models with two latent variables, a random peak season price and a random width of seasonal fluctuations. Characteristics of the hotel and the region where they are located are used as predictors of both latent variables. Besides hotel category, region, distance to the beach, availability of parking place and room equipment have an effect on peak price and also on seasonality. 3- star hotels have the highest seasonality and hotels located in the southern regions the lowest, which could be explained by a warmer climate in autumn

Medical image registration based on random line sampling

One of the key aspects in 3D-image registration is the computation of the joint intensity histogram. We propose a new approach to compute this histogram using uniformly distributed random lines to sample stochastically the overlapping volume between two 3D-images. The intensity values are captured from the lines at evenly spaced positions, taking an initial random offset different for each line. This method provides us with an accurate, robust and fast mutual information-based registration. The interpolation effects are drastically reduced, due to the stochastic nature of the line generation, and the alignment process is also accelerated. The results obtained show a better performance of the introduced method than the classic computation of the joint histogram

Error and complexity of random walk Monte Carlo radiosity

The author studies the error and complexity of the discrete random walk Monte Carlo technique for radiosity, using both the shooting and gathering methods. The author shows that the shooting method exhibits a lower complexity than the gathering one, and under some constraints, it has a linear complexity. This is an improvement over a previous result that pointed to an O(n log n) complexity. The author gives and compares three unbiased estimators for each method, and obtains closed forms and bounds for their variances. The author also bounds the expected value of the mean square error (MSE). Some of the results obtained are also shown