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.

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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

We provide an empirical analysis of the network structure of the Austrian interbank market based on Austrian Central Bank (OeNB) data. The interbank market is interpreted as a network where banks are nodes and the claims and liabilities between banks define the links. This allows us to apply methods from general network theory. We find that the degree distributions of the interbank network follow power laws. Given this result we discuss how the network structure affects the stability of the banking system with respect to the elimination of a node in the network, i.e. the default of a single bank. Further, the interbank liability network shows a community structure that exactly mirrors the regional and sectoral organization of the current Austrian banking system. The banking network has the typical structural features found in numerous other complex real-world networks: a low clustering coefficient and a short average path length. These empirical findings are in marked contrast to the network structures th...

Network topology of the interbank market

Motivated by the hope that the thermodynamical framework might be extended to strongly interacting statistical systems —complex systems in particular— a number of generalized entropies has been proposed in the past. So far the understanding of their fundamental origin has remained unclear. Here we address this question from first principles. We start by observing that many statistical systems fulfill a set of three general conditions (Shannon-Khinchin axioms, K1–K3). A fourth condition (separability) holds for non-interacting, uncorrelated or Markovian systems only (Shannon-Khinchin axiom, K4). If all four axioms hold the Shannon theorem provides a unique entropy, , i.e. Boltzmann-Gibbs entropy. Here we ask about the consequences of violating the 4th axiom while assuming the first three to hold. By a simple scaling argument we prove that under these conditions each statistical system is characterized by a unique pair of scaling exponents (c, d) in the large size limit. These exponents define equivalence classes for all interacting and non-interacting systems and parametrize a unique entropy, , where Γ(a,b) is the incomplete Gamma function. It covers all systems respecting K1–K3. A series of known entropies can be classified in terms of these equivalence classes. Corresponding distribution functions are special forms of Lambert- exponentials containing —as special cases— Boltzmann, stretched exponential and Tsallis distributions (power laws) —all widely abundant in Nature. In the derivation we assume , with g some function, however more general entropic forms can be classified along the same lines. This is to our knowledge the first ab initio justification for generalized entropies. We discuss a physical example displaying two sets of scaling exponents depending on the external parameters.

https://iopscience.iop.org/article/10.1209/0295-5075/93/20006/pdf

A comprehensive classification of complex statistical systems and an axiomatic derivation of their entropy and distribution functions

To characterize strongly interacting statistical systems within a thermodynamical framework - complex systems in particular - it might be necessary to introduce generalized entropies, $S_g$. A series of such entropies have been proposed in the past, mainly to accommodate important empirical distribution functions to a maximum ignorance principle. Until now the understanding of the fundamental origin of these entropies and its deeper relations to complex systems is limited. Here we explore this questions from first principles. We start by observing that the 4th Khinchin axiom (separability axiom) is violated by strongly interacting systems in general and ask about the consequences of violating the 4th axiom while assuming the first three Khinchin axioms (K1-K3) to hold and $S_g=\sum_ig(p_i)$. We prove by simple scaling arguments that under these requirements {\em each} statistical system is uniquely characterized by a distinct pair of scaling exponents $(c,d)$ in the large size limit. The exponents define equivalence classes for all interacting and non interacting systems. This allows to derive a unique entropy, $S_{c,d}\propto \sum_i \Gamma(d+1, 1- c \ln p_i)$, which covers all entropies which respect K1-K3 and can be written as $S_g=\sum_ig(p_i)$. Known entropies can now be classified within these equivalence classes. The corresponding distribution functions are special forms of Lambert-$W$ exponentials containing as special cases Boltzmann, stretched exponential and Tsallis distributions (power-laws) -- all widely abundant in nature. This is, to our knowledge, the first {\em ab initio} justification for the existence of generalized entropies. Even though here we assume $S_g=\sum_ig(p_i)$, we show that more general entropic forms can be classified along the same lines.

A comprehensive classification of complex statistical systems and an ab-initio derivation of their entropy and distribution functions

We provide an empirical analysis of the network structure of the Austrian interbank market based on a unique data set of the Oesterreichische Nationalbank (OeNB). The analysis relies on the idea that an interbank market can be interpreted as a network where the banks form the nodes and the claims and liabilities between them define the edges of the network. This approach allows us to apply results from general network theory, which is widely applied in other scientific disciplines — mainly in physics. Specifically, we use different measures from this network theory to investigate the empirical network structure of the Austrian banking system. We focus on the question of how this structure affects the stability of the network (the banking system) with respect to the elimination of a node in the network (the default of a single bank). Regarding the network structure, we find that there are very few banks with many interbank linkages whereas there are many with only a few links. This feature of networks has been repeatedly found to be conducive to the robustness of the network against the random breakdown of links (the default of single institutions due to external shocks). In addition, the interbank network shows a community structure that exactly mirrors the regional and sectoral organization of the current Austrian banking system. Moreover, the banking network has typical structural features found in numerous other complex real world networks: a low clustering coefficient and a relatively short average shortest path length. These empirical findings are in marked contrast to network structures that have been assumed in the theoretical economic and econo-physics literature.

An Empirical Analysis of the Network Structure of the Austrian Interbank Market 1

We study a dataset containing all financial transactions between the accounts of practically all major financial players within Austria over one year. We empirically analyze transaction networks of money (in and out) flows and report the characteristic network parameters. We observe a significant dependence of network topology on the time scales of observation, and remarkably low correlation between node degrees and transaction volume. We further use transaction timeseries of the financial agents to compute covariance matrices and their eigenvalue spectra. Eigenvectors corresponding to eigenvalues deviating from the Marcenko-Pastur law are analyzed in detail. The potential for practical use as an automated detection mechanism for abnormal behavior of financial players is discussed. The opinion expressed in this paper is that of the authors and does not necessarily reflect the opinion of the OeNB or the ESCB.

Stefan Thurner

Papers

Network topology of the interbank market

A comprehensive classification of complex statistical systems and an axiomatic derivation of their entropy and distribution functions

A comprehensive classification of complex statistical systems and an ab-initio derivation of their entropy and distribution functions

An Empirical Analysis of the Network Structure of the Austrian Interbank Market 1

Network and eigenvalue analysis of financial transaction networks