Self-similar stable processes arising from high-density limits of occupation times of particle systems

We extend results on time-rescaled occupation time fluctuation limits of the $(d,\alpha, \beta)$-branching particle system $(0<\alpha \leq 2, 0<\beta \leq 1)$ with Poisson initial condition. The earlier results in the homogeneous case (i.e., with Lebesgue initial intensity measure) were obtained for dimensions $d>\alpha / \beta$ only, since the particle system becomes locally extinct if $d\le \alpha / \beta$. In this paper we show that by introducing high density of the initial Poisson configuration, limits are obtained for all dimensions, and they coincide with the previous ones if $d>\alpha/\beta$. We also give high-density limits for the systems with finite intensity measures (without high density no limits exist in this case due to extinction); the results are different and harder to obtain due to the non-invariance of the measure for the particle motion. In both cases, i.e., Lebesgue and finite intensity measures, for low dimensions ($d<\alpha(1+\beta)/\beta$ and $d<\alpha(2+\beta)/(1+\beta)$, respectively) the limits are determined by non-L\'evy self-similar stable processes. For the corresponding high dimensions the limits are qualitatively different: ${\cal S}'(R^d)$-valued L\'evy processes in the Lebesgue case, stable processes constant in time on $(0,\infty)$ in the finite measure case. For high dimensions, the laws of all limit processes are expressed in terms of Riesz potentials. If $\beta=1$, the limits are Gaussian. Limits are also given for particle systems without branching, which yields in particular weighted fractional Brownian motions in low dimensions. The results are obtained in the setup of weak convergence of S'(R^d)$-valued processes.Comment: 28 page

Conversion Rate Optimization through Evolutionary Computation

Conversion optimization means designing a web interface so that as many users as possible take a desired action on it, such as register or purchase. Such design is usually done by hand, testing one change at a time through A/B testing, or a limited number of combinations through multivariate testing, making it possible to evaluate only a small fraction of designs in a vast design space. This paper describes Sentient Ascend, an automatic conversion optimization system that uses evolutionary optimization to create effective web interface designs. Ascend makes it possible to discover and utilize interactions between the design elements that are difficult to identify otherwise. Moreover, evaluation of design candidates is done in parallel online, i.e. with a large number of real users interacting with the system. A case study on an existing media site shows that significant improvements (i.e. over 43%) are possible beyond human design. Ascend can therefore be seen as an approach to massively multivariate conversion optimization, based on a massively parallel interactive evolution

Communities That Care: A Guide for Developing Services for Children

Hogg Foundation for Mental Healt

Fluctuation limits of strongly degenerate branching systems

Functional limit theorems for scaled fluctuations of occupation time processes of a sequence of critical branching particle systems in $\R^d$ with anisotropic space motions and strongly degenerated splitting abilities are proved in the cases of critical and intermediate dimensions. The results show that the limit processes are constant measure-valued Wienner processes with degenerated temporal and simple spatial structures.Comment: 15 page

Adaptive Simulation of the Heston Model

Recent years have seen an increased level of interest in pricing equity options under a stochastic volatility model such as the Heston model. Often, simulating a Heston model is difficult, as a standard finite difference scheme may lead to significant bias in the simulation result. Reducing the bias to an acceptable level is not only challenging but computationally demanding. In this paper we address this issue by providing an alternative simulation strategy -- one that systematically decreases the bias in the simulation. Additionally, our methodology is adaptive and achieves the reduction in bias with "near" minimum computational effort. We illustrate this feature with a numerical example.Comment: 23 pages, 4 Postscript figure

A Future View of Mental Health

Hogg Foundation for Mental Healt

Supplementary oxygen for nonhypoxemic patients: O2 much of a good thing?

Supplementary oxygen is routinely administered to patients, even those with adequate oxygen saturations, in the belief that it increases oxygen delivery. But oxygen delivery depends not just on arterial oxygen content but also on perfusion. It is not widely recognized that hyperoxia causes vasoconstriction, either directly or through hyperoxia-induced hypocapnia. If perfusion decreases more than arterial oxygen content increases during hyperoxia, then regional oxygen delivery decreases. This mechanism, and not (just) that attributed to reactive oxygen species, is likely to contribute to the worse outcomes in patients given high-concentration oxygen in the treatment of myocardial infarction, in postcardiac arrest, in stroke, in neonatal resuscitation and in the critically ill. The mechanism may also contribute to the increased risk of mortality in acute exacerbations of chronic obstructive pulmonary disease, in which worsening respiratory failure plays a predominant role. To avoid these effects, hyperoxia and hypocapnia should be avoided, with oxygen administered only to patients with evidence of hypoxemia and at a dose that relieves hypoxemia without causing hyperoxia

Domain and Specification Models for Software Engineering

This paper discusses our approach to representing application domain knowledge for specific software engineering tasks. Application domain knowledge is embodied in a domain model. Domain models are used to assist in the creation of specification models. Although many different specification models can be created from any particular domain model, each specification model is consistent and correct with respect to the domain model. One aspect of the system-hierarchical organization is described in detail

Reuse: A knowledge-based approach

This paper describes our research in automating the reuse process through the use of application domain models. Application domain models are explicit formal representations of the application knowledge necessary to understand, specify, and generate application programs. Furthermore, they provide a unified repository for the operational structure, rules, policies, and constraints of a specific application area. In our approach, domain models are expressed in terms of a transaction-based meta-modeling language. This paper has described in detail the creation and maintenance of hierarchical structures. These structures are created through a process that includes reverse engineering of data models with supplementary enhancement from application experts. Source code is also reverse engineered but is not a major source of domain model instantiation at this time. In the second phase of the software synthesis process, program specifications are interactively synthesized from an instantiated domain model. These specifications are currently integrated into a manual programming process but will eventually be used to derive executable code with mechanically assisted transformations. This research is performed within the context of programming-in-the-large types of systems. Although our goals are ambitious, we are implementing the synthesis system in an incremental manner through which we can realize tangible results. The client/server architecture is capable of supporting 16 simultaneous X/Motif users and tens of thousands of attributes and classes. Domain models have been partially synthesized from five different application areas. As additional domain models are synthesized and additional knowledge is gathered, we will inevitably add to and modify our representation. However, our current experience indicates that it will scale and expand to meet our modeling needs