BIOE 402. Medical Technology Assessment. 2 or 3 hours. Bioentrepreneur course. Assessment of medical technology in the context of commercialization. Objectives, competition, market share, funding, pricing, manufacturing, growth, and intellectual property; many issues unique to biomedical products. Course Information: 2 undergraduate hours. 3 graduate hours. Prerequisite(s): Junior standing or above and consent of the instructor.

“Bioinformatics” 특집을 내면서

Statistical physics has proven to be a fruitful framework to describe phenomena outside the realm of traditional physics. Recent years have witnessed an attempt by physicists to study collective phenomena emerging from the interactions of individuals as elementary units in social structures. A wide list of topics are reviewed ranging from opinion and cultural and language dynamics to crowd behavior, hierarchy formation, human dynamics, and social spreading. The connections between these problems and other, more traditional, topics of statistical physics are highlighted. Comparison of model results with empirical data from social systems are also emphasized.

Statistical physics of social dynamics

The structure and dynamics of multilayer networks

Many ``real-world'' networks are clearly defined while most ``social'' networks are to some extent subjective. Indeed, the accuracy of empirically-determined social networks is a question of some concern because individuals may have distinct perceptions of what constitutes a social link. One unambiguous type of connection is sexual contact. Here we analyze data on the sexual behavior of a random sample of individuals, and find that the cumulative distributions of the number of sexual partners during the twelve months prior to the survey decays as a power law with similar exponents $\alpha \approx 2.4$ for females and males. The scale-free nature of the web of human sexual contacts suggests that strategic interventions aimed at preventing the spread of sexually-transmitted diseases may be the most efficient approach.

The Web of Human Sexual Contacts

In the run-up to the recent financial crisis, an increasingly elaborate set of financial instruments emerged, intended to optimize returns to individual institutions with seemingly minimal risk. Essentially no attention was given to their possible effects on the stability of the system as a whole. Drawing analogies with the dynamics of ecological food webs and with networks within which infectious diseases spread, we explore the interplay between complexity and stability in deliberately simplified models of financial networks. We suggest some policy lessons that can be drawn from such models, with the explicit aim of minimizing systemic risk.

/pdf/systemic-risk-in-banking-ecosystems-3qxa8ahram.pdf

Systemic risk in banking ecosystems

Path-dependent stochastic processes are often non-ergodic and observables can no longer be computed within the ensemble picture. The resulting mathematical difficulties pose severe limits to the analytical understanding of path-dependent processes. Their statistics is typically non-multinomial in the sense that the multiplicities of the occurrence of states is not a multinomial factor. The maximum entropy principle is tightly related to multinomial processes, non-interacting systems, and to the ensemble picture; It loses its meaning for path-dependent processes. Here we show that an equivalent to the ensemble picture exists for path-dependent processes, such that the non-multinomial statistics of the underlying dynamical process, by construction, is captured correctly in a functional that plays the role of a relative entropy. We demonstrate this for self-reinforcing Polya urn processes, which explicitly generalise multinomial statistics. We demonstrate the adequacy of this constructive approach towards non-multinomial pendants of entropy by computing frequency and rank distributions of Polya urn processes. We show how microscopic update rules of a path-dependent process allow us to explicitly construct a non-multinomial entropy functional, that, when maximized, predicts the time-dependent distribution function.

Analytical computation of frequency distributions of path-dependent processes by means of a non-multinomial maximum entropy approach

In the world of generalized entropies---which, for example, play a role in physical systems with sub- and super-exponential phasespace growth per degree of freedom---there are two ways for implementing constraints in the maximum entropy principle: linear- and escort constraints. Both appear naturally in different contexts. Linear constraints appear e.g. in physical systems, when additional information about the system is available through higher moments. Escort distributions appear naturally in the context of multifractals and information geometry. It was shown recently that there exists a fundamental duality that relates both approaches on the basis of the corresponding deformed logarithms (deformed-log duality). Here we show that there exists another duality that arises in the context of information geometry, relating the Fisher information of $\phi$-deformed exponential families that correspond to linear constraints (as studied by J. Naudts), with those that are based on escort constraints (as studied by S.-I. Amari). We explicitly demonstrate this information geometric duality for the case of $(c,d)$-entropy that covers all situations that are compatible with the first three Shannon-Khinchin axioms, and that include Shannon, Tsallis, Anteneodo-Plastino entropy, and many more as special cases. Finally, we discuss the relation between the deformed-log duality and the information geometric duality, and mention that the escort distributions arising in the two dualities are generally different and only coincide for the case of the Tsallis deformation.

Information geometric duality of $\phi$-deformed exponential families

We show that within classical statistical mechanics, without taking the thermodynamic limit, the most general Boltzmann factor for the canonical ensemble is a q-exponential function. The only assumption here is that microcanonical distributions have to be separated from the total system energy, which is the prerequisite for any sensible measurement. We derive that all separable distributions are parametrized by a mathematical separation constant Q, which can be related to the non-extensivity q-parameter in Tsallis distributions. We further demonstrate that nature fixes the separation constant Q to 1 for large dimensionality of Gibbs Γ -phase space. Our results will be relevant for systems with a low-dimensional Γ -space, for example nanosystems, comprised of a small number of particles, or for systems with a dimensionally collapsed phase space, which might be the case for a large class of complex systems.

http://www.sigmaphi.polito.it/2005/Proceedings/Physica%20A/Hanel/thurner5.pdf

On the derivation of power-law distributions within classical statistical mechanics far from the thermodynamic limit

Evolution is a process in which some variations that emerge within a population (of, e.g., biological species or industrial goods) get selected, survive, and proliferate, whereas others vanish. Survival probability, proliferation, or production rates are associated with the “fitness” of a particular variation. We argue that the notion of fitness is an a posteriori concept in the sense that one can assign higher fitness to species or goods that survive but one can generally not derive or predict fitness per se. Whereas proliferation rates can be measured, fitness landscapes, that is, the inter-dependence of proliferation rates, cannot. For this reason we think that in a physical theory of evolution such notions should be avoided. Here we review a recent quantitative formulation of evolutionary dynamics that provides a framework for the co-evolution of species and their fitness landscapes (Thurner et al., 2010, Physica A 389, 747; Thurner et al., 2010, New J. Phys. 12, 075029; Klimek et al., 2009, Phys. Rev. E 82, 011901 (2010). The corresponding model leads to a generic evolutionary dynamics characterized by phases of relative stability in terms of diversity, followed by phases of massive restructuring. These dynamical modes can be interpreted as punctuated equilibria in biology, or Schumpeterian business cycles (Schumpeter, 1939, Business Cycles, McGraw-Hill, London) in economics. We show that phase transitions that separate phases of high and low diversity can be approximated surprisingly well by mean-field methods. We demonstrate that the mathematical framework is suited to understand systemic properties of evolutionary systems, such as their proneness to collapse, or their potential for diversification. The framework suggests that evolutionary processes are naturally linked to self-organized criticality and to properties of production matrices, such as their eigenvalue spectra. Even though the model is phrased in general terms it is also practical in the sense that it’s predictions can be used to understand a series of experimental data ranging from the fossil record to macroeconomic indices.

A Simple General Model of Evolutionary Dynamics

A dynamical price formation model for financial assets is presented. It aims to capture the essence of speculative trading where mispricings of assets are used to make profits. It is shown that together with the incorporation of the concept of risk aversion of agents the model is able to reproduce several key characteristics of financial price series. The approach is contrasted to the conventional view of price formation in financial economics.

Stefan Thurner

Papers

Analytical computation of frequency distributions of path-dependent processes by means of a non-multinomial maximum entropy approach

Information geometric duality of $\phi$-deformed exponential families

On the derivation of power-law distributions within classical statistical mechanics far from the thermodynamic limit

A Simple General Model of Evolutionary Dynamics

A Dynamical Thermostat Approach To Financial Asset Price Dynamics