Random many-particle systems: applications from biology, and propagation of chaos in abstract models

The paper discusses a family of Markov processes that represent many particle systems, and their limiting behaviour when the number of particles go to infinity. The first part concerns model of biological systems: a model for sympatric speciation, i.e. the process in which a genetically homogeneous population is split in two or more different species sharing the same habitat, and models for swarming animals. The second part of the paper deals with abstract many particle systems, and methods for rigorously deriving mean field models.Comment: These are notes from a series of lectures given at the 5$^{th}$ Summer School on Methods and Models of Kinetic Theory, Porto Ercole, 2010. They are submitted for publication in "Rivista di Matematica della Universit\`a di Parma

Regularity theory for the spatially homogeneous Boltzmann equation with cut-off

We develop the regularity theory of the spatially homogeneous Boltzmann equation with cut-off and hard potentials (for instance, hard spheres), by (i) revisiting the Lp-theory to obtain constructive bounds, (ii) establishing propagation of smoothness and singularities, (iii) obtaining estimates about the decay of the sin- gularities of the initial datum. Our proofs are based on a detailed study of the "regularity of the gain operator". An application to the long-time behavior is presented.Comment: 47 page

Chaotic distributions for relativistic particles

We study a modified Kac model where the classical kinetic energy is replaced by an arbitrary energy function $\phi(v)$, $v \in \mathbb{R}$. The aim of this paper is to show that the uniform density with respect to the microcanonical measure is $Ce^{-z_0\phi(v)}$-chaotic, $C,z_0 \in \mathbb{R}_+$. The kinetic energy for relativistic particles is a special case. A generalization to the case $v\in \mathbb{R}^d$ which involves conservation momentum is also formally discussed

Variations Among Regions and Hospitals in Managing Chronic Illness: How Much Care Is Enough? Seventeenth Annual Herbert Lourie Memorial Lecture on Health Policy.

Classic epidemiology looks at what happens to people who live in a defined region over time. For example, birth rate, the number of births that occur among populations over a year, is a common statistics that we're all familiar with. Since the early 1990s we have conducted research at Dartmouth Medical School to convert that classic epidemiologic perspective into looking at what is happening in terms of the health care system itself. We ask how much care people are getting in different regions of the country. We want to know the patterns of that care. And we want to get into the causes of so-called unwarranted variation, that is, differences that cannot be explained on the basis of patient illness, the dictates of scientific medicine, or the preferences of patients. Those three key words--illness, preference, and science--ultimately don't explain very much of the variation we see. We began the Dartmouth Atlas Project in 1993 as a study of health care markets in the United States, measuring variations in health care resources and their utilization among geographic areas. In recent years, we have expanded our research agenda to include the resources and utilization among patients at specific hospitals. We use very large claims databases from the Medicare program and other sources to define where people go for medical care, what kind of care they receive, and whether increasing investments in health care resources and their use result in better health outcomes.nursing home, Medicare, Medicaid, long-term care, elderly, social welfare.

Problemistic Search and International Entrepreneurship

This paper explains the internationalization process of small firms using the theory of performance relative to aspiration levels. The study complements prior theory by explaining why and how small firms are triggered to engage in internationalization despite not reaching maturity in their home market. We outline a model where firms’ internationalization is triggered by problemistic search, following periods of below-aspiration performance. The model is tested on 860 Swedish firms followed during an economic downturn. Results indicate that internationalization activities follow a boundedly rational process characterized by search behavior which is triggered by performance feedback. The study complements prior theories of internationalization and offers a first empirical demonstration of the viability of aspiration-level performance theory in international entrepreneurship research.Entrepreneurship; International Entry; Behavioral Theory of the Firm

How do entrepreneurs in clusters contribute to economic growth?

This paper investigates the long-term survival and performance of new entrepreneurial firms, comparing firms located within regional clusters with those located outside of clusters.We use matched employee-employer databases to investigate all Swedish firms started in the telecom and consumer electronic s, financial services, information technology, medical equipment, and pharmaceuticals and biotech sectors (N = 4,397). We follow these firms from 1993 to 2002 and measure their contribution to local economic vitality in term of job creation, payment of taxes, and payment of salaries to employees. Controlling for factors such as firm size, age, and absorptive innovative capabilities, we find strong empirical evidence that being located within a cluster has positive effects on the survival of new firms. We also find that clustered firm creates more jobs, higher tax payments, and higher wages to employees. The effects are consistent across alternative measures of agglomeration and different regional levels. Thid study contributes to the literatures on entrepreneurship and economic geography. By measuring the economic contributions of clustered and non-clustered firms, the empirical evidence also provides support for basing economic policies on clusters.Clusters; Entrepreneurship; Economic Development

Adaptive and Recursive Time Relaxed Monte Carlo methods for rarefied gas dynamics

Recently a new class of Monte Carlo methods, called Time Relaxed Monte Carlo (TRMC), designed for the simulation of the Boltzmann equation close to fluid regimes have been introduced. A generalized Wild sum expansion of the solution is at the basis of the simulation schemes. After a splitting of the equation the time discretization of the collision step is obtained from the Wild sum expansion of the solution by replacing high order terms in the expansion with the equilibrium Maxwellian distribution; in this way speed up of the methods close to fluid regimes is obtained by efficiently thermalizing particles close to the equilibrium state. In this work we present an improvement of such methods which allows to obtain an effective uniform accuracy in time without any restriction on the time step and subsequent increase of the computational cost. The main ingredient of the new algorithms is recursivity. Several techniques can be used to truncate the recursive trees generated by the schemes without deteriorating the accuracy of the numerical solution. Techniques based on adaptive strategies are presented. Numerical results emphasize the gain of efficiency of the present simulation schemes with respect to standard DSMC methods

Emergence of Firms: A Sociogeographic Demand Side Perspective

This paper presents an analysis of regional start-up rates in the knowledge intensive services and high-tech industries. To supplement prevailing frameworks focusing mainly on supply-side economic factors, we integrate insights from economic geography and population ecology to the entrepreneurship literature as to present a theoretical framework that captures both supply-and demand-side factors, with a specific emphasis on the demand side. Using a rich multi-level data material on all knowledge intensive start-ups across the 286 Swedish municipalities between 1994 and 2002, the empirical analysis focuses on how characteristics of the economic milieu of regions influence firm births. We find that economically affluent regions dominate entrepreneurial activity in terms of firm births, yet a number of much smaller rural region revealed high levels of start ups. Both economic and sociological variables such as knowledge spillovers from universities and firm R&D, and the political regulatory regime within the municipality, exhibit strong influences on firm births. These patterns points to strong support for the notion that ‘the geographic connection’ is important for analyzing entrepreneurial processes.Firm birth; Geography; Entrepreneurship

Global CO_2 fluxes inferred from surface air-sample measurements and from TCCON retrievals of the CO_2 total column

We present the first estimate of the global distribution of CO_2 surface fluxes from 14 stations of the Total Carbon Column Observing Network (TCCON). The evaluation of this inversion is based on 1) comparison with the fluxes from a classical inversion of surface air-sample-measurements, and 2) comparison of CO_2 mixing ratios calculated from the inverted fluxes with independent aircraft measurements made during the two years analyzed here, 2009 and 2010. The former test shows similar seasonal cycles in the northern hemisphere and consistent regional carbon budgets between inversions from the two datasets, even though the TCCON inversion appears to be less precise than the classical inversion. The latter test confirms that the TCCON inversion has improved the quality (i.e., reduced the uncertainty) of the surface fluxes compared to the assumed or prior fluxes. The consistency between the surface-air-sample-based and the TCCON-based inversions despite remaining flaws in transport models opens the possibility of increased accuracy and robustness of flux inversions based on the combination of both data sources and confirms the usefulness of space-borne monitoring of the CO_2 column