Hybrid consumption paths in the attribute space: A model and application with scanner data

This paper presents and estimates a dynamic choice model in the attribute space considering rational consumers. In light of the evidence of several state-dependence patterns, the standard attribute-based model is extended by considering a general utility function where pure inertia and pure variety-seeking behaviors can be explained in the model as particular linear cases. The dynamics of the model are fully characterized by standard dynamic programming techniques. The model presents a stationary consumption pattern that can be inertial, where the consumer only buys one product, or a variety-seeking one, where the consumer shifts among varied products.We run some simulations to analyze the consumption paths out of the steady state. Underthe hybrid utility assumption, the consumer behaves inertially among the unfamiliar brandsfor several periods, eventually switching to a variety-seeking behavior when the stationary levels are approached. An empirical analysis is run using scanner databases for three different product categories: fabric softener, saltine cracker, and catsup. Non-linear specifications provide the best fit of the data, as hybrid functional forms are found in all the product categories for most attributes and segments. These results reveal the statistical superiority of the non-linear structure and confirm the gradual trend to seek variety as the level of familiarity with the purchased items increases.

Space Competition and Time Delays in Human Range Expansions. Application to the Neolithic Transition

Space competition effects are well-known in many microbiological and ecological systems. Here we analyze such an effectin human populations. The Neolithic transition (change from foraging to farming) was mainly the outcome of a demographic process that spread gradually throughout Europe from the Near East. In Northern Europe, archaeological data show a slowdown on the Neolithic rate of spread that can be related to a high indigenous (Mesolithic) population density hindering the advance as a result of the space competition between the two populations. We measure this slowdown from a database of 902 Early Neolithic sites and develop a time-delayed reaction-diffusion model with space competition between Neolithic and Mesolithic populations, to predict the observed speeds. The comparison of the predicted speed with the observations and with a previous non-delayed model show that both effects, the time delay effect due to the generation lag and the space competition between populations, are crucial in order to understand the observations

Meta-structure correlation in protein space unveils different selection rules for folded and intrinsically disordered proteins

The number of existing protein sequences spans a very small fraction of sequence space. Natural proteins have overcome a strong negative selective pressure to avoid the formation of insoluble aggregates. Stably folded globular proteins and intrinsically disordered proteins (IDP) use alternative solutions to the aggregation problem. While in globular proteins folding minimizes the access to aggregation prone regions IDPs on average display large exposed contact areas. Here, we introduce the concept of average meta-structure correlation map to analyze sequence space. Using this novel conceptual view we show that representative ensembles of folded and ID proteins show distinct characteristics and responds differently to sequence randomization. By studying the way evolutionary constraints act on IDPs to disable a negative function (aggregation) we might gain insight into the mechanisms by which function - enabling information is encoded in IDPs.

Characterizing major avalanche episodes in space and time in the twentieth and early twentyfirst centuries in the Catalan Pyrenees

With the aim of better understanding avalanche risk in the Catalan Pyrenees, the present work focuses on the analysis of major (or destructive) avalanches. For such purpose major avalanche cartography was made by an exhaustive photointerpretation of several flights, winter and summer field surveys and inquiries to local population. Major avalanche events were used to quantify the magnitude of the episodes during which they occurred, and a Major Avalanche Activity Magnitude Index (MAAMI) was developed. This index is based on the number of major avalanches registered and its estimated frequency in a given time period, hence it quantifies the magnitude of a major avalanche episode or winter. Furthermore, it permits a comparison of the magnitude between major avalanche episodes in a given mountain range, or between mountain ranges, and for a long enough period, it should allow analysis of temporal trends. Major episodes from winter 1995/96 to 2013/14 were reconstructed. Their magnitude, frequency and extent were also assessed. During the last 19 winters, the episodes of January 22-23 and February 6-8 in 1996 were those with highest MAAMI values,followed by January 30-31, 2003, January 29, 2006, and January 24-25, 2014. To analyze the whole twentieth century, a simplified MAAMI was defined in order to attain the same purpose with a less complete dataset. With less accuracy, the same parameters were obtained at winter time resolution throughout the twentieth century. Again, 1995/96 winter had the highest MAAMI value followed by 1971/72, 1974/75 and 1937/38 winter seasons. The analysis of the spatial extent of the different episodes allowed refining the demarcation of nivological regions, and improving our knowledge about the atmospheric patterns that cause major episodes and their climatic interpretation. In some cases, the importance of considering a major avalanche episode as the result of a previous preparatory period, followed by a triggering one was revealed.

Contractions in the 2-wasserstein lenght space and thermalization of granular media

An algebraic decay rate is derived which bounds the time required for velocities to equilibrate in a spatially homogeneous flow-through model representing the continuum limit of a gas of particles interacting through slightly inelastic collisions. This rate is obtained by reformulating the dynamical problem as the gradient flow of a convex energy on an infinite-dimensional manifold. An abstract theory is developed for gradient flows in length spaces, which shows how degenerate convexity (or even non-convexity) | if uniformly controlled | will quantify contractivity (limit expansivity) of the flow.

Contractive metrics for a Boltzmann equation for granular gases: diffusive equilibriaThe Patterson-Sullivan embedding and minimal volume entropy for outer space

We quantify the long-time behavior of a system of (partially) inelastic particles in a stochastic thermostat by means of the contractivity of a suitable metric in the set of probability measures. Existence, uniqueness, boundedness of moments and regularity of a steady state are derived from this basic property. The solutions of the kinetic model are proved to converge exponentially as t→ ∞ to this diffusive equilibrium in this distance metrizing the weak convergence of measures. Then, we prove a uniform bound in time on Sobolev norms of the solution, provided the initial data has a finite norm in the corresponding Sobolev space. These results are then combined, using interpolation inequalities, to obtain exponential convergence to the diffusive equilibrium in the strong L¹-norm, as well as various Sobolev norms.

The Patterson-Sullivan embedding and minimal volume entropy for outer space

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

Metrics on diagram groups and uniform embeddings in a Hilbert space

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

An ordinal shapley value for economic environments

We propose a new solution concept to address the problem of sharing a surplus among the agents generating it. The sharing problem is formulated in the preferences-endowments space. The solution is defined in a recursive manner incorporating notions of consistency and fairness and relying on properties satisfied by the Shapley value for Transferable Utility (TU) games. We show a solution exists, and refer to it as an Ordinal Shapley value (OSV). The OSV associates with each problem an allocation as well as a matrix of concessions ``measuring'' the gains each agent foregoes in favor of the other agents. We analyze the structure of the concessions, and show they are unique and symmetric. Next we characterize the OSV using the notion of coalitional dividends, and furthermore show it is monotone in an agent's initial endowments and satisfies anonymity. Finally, similarly to the weighted Shapley value for TU games, we construct a weighted OSV as well.

Infinite time aggregation for the critical Patlak-Keller-Segel model in R2

We analyze the two-dimensional parabolic-elliptic Patlak-Keller-Segel model in the whole Euclidean space R2. Under the hypotheses of integrable initial data with finite second moment and entropy, we first show local in time existence for any mass of "free-energy solutions", namely weak solutions with some free energy estimates. We also prove that the solution exists as long as the entropy is controlled from above. The main result of the paper is to show the global existence of free-energy solutions with initial data as before for the critical mass 8 Π/Χ. Actually, we prove that solutions blow-up as a delta dirac at the center of mass when t→∞ keeping constant their second moment at any time. Furthermore, all moments larger than 2 blow-up as t→∞ if initially bounded.

Data size sufficiency analyses of haplotype inference algortihms

We present experimental and theoretical analyses of data requirements for haplotype inference algorithms. Our experiments include a broad range of problem sizes under two standard models of tree distribution and were designed to yield statistically robust results despite the size of the sample space. Our results validate Gusfield's conjecture that a population size of n log n is required to give (with high probability) sufficient information to deduce the n haplotypes and their complete evolutionary history. The experimental results inspired our experimental finding with theoretical bounds on the population size. We also analyze the population size required to deduce some fixed fraction of the evolutionary history of a set of n haplotypes and establish linear bounds on the required sample size. These linear bounds are also shown theoretically.

Label Space Reduction in All-Optical Label Switchiing Networks

Report for the scientific sojourn at the Department of Information Technology (INTEC) at the Ghent University, Belgium, from january to june 2007. All-Optical Label Swapping (AOLS) forms a key technology towards the implementation of All-Optical Packet Switching nodes (AOPS) for the future optical Internet. The capital expenditures of the deployment of AOLS increases with the size of the label spaces (i.e. the number of used labels), since a special optical device is needed for each recognized label on every node. Label space sizes are affected by the wayin which demands are routed. For instance, while shortest-path routing leads to the usage of fewer labels but high link utilization, minimum interference routing leads to the opposite. This project studies and proposes All-Optical Label Stacking (AOLStack), which is an extension of the AOLS architecture. AOLStack aims at reducing label spaces while easing the compromise with link utilization. In this project, an Integer Lineal Program is proposed with the objective of analyzing the softening of the aforementioned trade-off due to AOLStack. Furthermore, a heuristic aiming at finding good solutions in polynomial-time is proposed as well. Simulation results show that AOLStack either a) reduces the label spaces with a low increase in the link utilization or, similarly, b) uses better the residual bandwidth to decrease the number of labels even more.

Agglomeration and inequality across space: what can we learn from the European experience?

The purpose of this contribution is to draw a picture of the (uneven) distribution of economic activities across the states of the European Union (EU) and the consequences entailed by it. We will briefly summarize the most salient and recent contributions. Then, in the light of the economic geography theory, we will discuss the economic and social advantages and disadvantages associated with a core- periphery structure. In this sense, particular attention will be addressed to the EU financial system of Structural Funds and the effects they produced. Finally, we will formulate some suggestions, relying on the EU experience, that could be of interest to the current Brazilian regional policy.