Join sizes, urn models and normal limiting distributions

AbstractWe study some parameters of relational databases (sizes of relations obtained by a join) that can be described by generating functions on three variables, of the kind ϕ(x, y, z)d. We modelize these parameters by suitable urn models and give conditions under which they asymptotically follow a gaussian distribution

Spatial competition and price formation

We look at price formation in a retail setting, that is, companies set prices, and consumers either accept prices or go someplace else. In contrast to most other models in this context, we use a two-dimensional spatial structure for information transmission, that is, consumers can only learn from nearest neighbors. Many aspects of this can be understood in terms of generalized evolutionary dynamics. In consequence, we first look at spatial competition and cluster formation without price. This leads to establishement size distributions, which we compare to reality. After some theoretical considerations, which at least heuristically explain our simulation results, we finally return to price formation, where we demonstrate that our simple model with nearly no organized planning or rationality on the part of any of the agents indeed leads to an economically plausible price.Comment: Minor change

On the occurrences of motifs in recursive trees, with applications to random structures

In this dissertation we study three problems related to motifs and recursive trees. In the first problem we consider a collection of uncorrelated motifs and their occurrences on the fringe of random recursive trees. We compute the exact mean and variance of the multivariate random vector of the counts of occurrences of the motifs. We further use the Cramér-Wold device and the contraction method to show an asymptotic convergence in distribution to a multivariate normal random variable with this mean and variance. ^ The second problem we study is that of the probability that a collection of motifs (of the same size) do not occur on the fringe of recursive trees. Here we use analytic and complex-valued methods to characterize this asymptotic probability. The asymptotics are complemented with human assisted Maple computation. We are able to completely characterize the asymptotic probability for two families of growing motifs. ^ In the third problem we introduce a new tree model where at each time step a new block (motif) is joined to the tree. This is one of the earlier investigations in the random tree literature where such a model is studied, i.e., in which trees grow from building blocks which are themselves trees. We consider the building blocks to be of the same size and characterize the number of leaves, the depth of insertion, the total path length and the height of such trees. The tools used in this analysis include stochastic recurrences, Pólya urn theory, moment generating functions and martingales

ISIPTA'07: Proceedings of the Fifth International Symposium on Imprecise Probability: Theories and Applications

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The NASA-AMES Research Center Stratospheric Aerosol Model. 1. Physical Processes and Computational Analogs

A time-dependent one-dimensional model of the stratospheric sulfate aerosol layer is presented. In constructing the model, a wide range of basic physical and chemical processes are incorporated in order to avoid predetermining or biasing the model predictions. The simulation, which extends from the surface to an altitude of 58 km, includes the troposphere as a source of gases and condensation nuclei and as a sink for aerosol droplets. The size distribution of aerosol particles is resolved into 25 categories with particle radii increasing geometrically from 0.01 to 2.56 microns such that particle volume doubles between categories

Combinatorial Complexity and Compositional Drift in Protein Interaction Networks

The assembly of molecular machines and transient signaling complexes does not typically occur under circumstances in which the appropriate proteins are isolated from all others present in the cell. Rather, assembly must proceed in the context of large-scale protein-protein interaction (PPI) networks that are characterized both by conflict and combinatorial complexity. Conflict refers to the fact that protein interfaces can often bind many different partners in a mutually exclusive way, while combinatorial complexity refers to the explosion in the number of distinct complexes that can be formed by a network of binding possibilities. Using computational models, we explore the consequences of these characteristics for the global dynamics of a PPI network based on highly curated yeast two-hybrid data. The limited molecular context represented in this data-type translates formally into an assumption of independent binding sites for each protein. The challenge of avoiding the explicit enumeration of the astronomically many possibilities for complex formation is met by a rule-based approach to kinetic modeling. Despite imposing global biophysical constraints, we find that initially identical simulations rapidly diverge in the space of molecular possibilities, eventually sampling disjoint sets of large complexes. We refer to this phenomenon as “compositional drift”. Since interaction data in PPI networks lack detailed information about geometric and biological constraints, our study does not represent a quantitative description of cellular dynamics. Rather, our work brings to light a fundamental problem (the control of compositional drift) that must be solved by mechanisms of assembly in the context of large networks. In cases where drift is not (or cannot be) completely controlled by the cell, this phenomenon could constitute a novel source of phenotypic heterogeneity in cell populations

Nonlinear lift and pressure distribution of slender conical bodies with strakes at low speeds

Nonlinear lift and pressure distribution of slender conical bodies with strakes at low spee