A New Framework for Decomposing Multivariate Information

What are the distinct ways in which a set of predictor variables can provide information about a target variable? When does a variable provide unique information, when do variables share redundant information, and when do variables combine synergistically to provide complementary information? The redundancy lattice from the partial information decomposition of Williams and Beer provided a promising glimpse at the answer to these questions. However, this structure was constructed using a much-criticised measure of redundant information, and despite sustained research, no completely satisfactory replacement measure has been proposed. This thesis presents a new framework for information decomposition that is based upon the decomposition of pointwise mutual information rather than mutual information. The framework is derived in two separate ways. The first of these derivations is based upon a modified version of the original axiomatic approach taken by Williams and Beer. However, to overcome the difficulty associated with signed pointwise mutual information, the decomposition is applied separately to the unsigned entropic components of pointwise mutual information which are referred to as the specificity and ambiguity. This yields a separate redundancy lattice for each component. Based upon an operational interpretation of redundancy, measures of redundant specificity and redundant ambiguity are defined which enables one to evaluate the partial information atoms separately for each lattice. These separate atoms can then be recombined to yield the sought-after multivariate information decomposition. This framework is applied to canonical examples from the literature and the results and various properties of the decomposition are discussed. In particular, the pointwise decomposition using specificity and ambiguity is shown to satisfy a chain rule over target variables, which provides new insights into the so-called two-bit-copy example. The second approach begins by considering the distinct ways in which two marginal observers can share their information with the non-observing individual third party. Several novel measures of information content are introduced, namely the union, intersection and unique information contents. Next, the algebraic structure of these new measures of shared marginal information is explored, and it is shown that the structure of shared marginal information is that of a distributive lattice. Furthermore, by using the fundamental theorem of distributive lattices, it is shown that these new measures are isomorphic to a ring of sets. Finally, by combining this structure together with the semi-lattice of joint information, the redundancy lattice form partial information decomposition is found to be embedded within this larger algebraic structure. However, since this structure considers information contents, it is actually equivalent to the specificity lattice from the first derivation of pointwise partial information decomposition. The thesis then closes with a discussion about whether or not one should combine the information contents from the specificity and ambiguity lattices

Managed Care’s Crimea: Medical Necessity, Therapeutic Benefit, and the Goals of Administrative Process in Health Insurance

En brotyp som är vanlig bland brokonstruktioner är plattrambron. Denna brotyp byggs både med slak- och spännarmering. Det är dock vanligare att bygga med slakarmering än spännarmering, vilket övervägs särskilt då spännvidderna är ungefär 25- 30 meter eller mer. Inledningsvis har en noggrann litteraturstudie genomförts tillsammans med en intervju av en kunnig brokonstruktör för att säkerställa en interaktion mellan teori och aktuell praxis. Detta arbete har haft ett huvudmål, vilket är att ur ett struktur- och kostnadsperspektiv jämföra och utvärdera hur behovet av slakarmering varierar i en plattrambros farbana då spännvidder varieras och betongtvärsnitt ändras. Arbetet har utförts med hjälp av finita elementprogrammet ”Brigade Standard”, vilket erbjuder en tre-dimensionell strukturanalys. Fyra olika tvärsnitt för spännvidder mellan 10-20 meter analyseras. Dimensioner på brodelar bestäms med hjälp av tumregler samt generella råd från intervjuperson; höjd i fält enligt L/20, L/25, L/30 samt L/35, där L är spännvidden. Resultatet visar främst att för ökade spännvidder mot 20 meter ökar lasteffekten på grund av egentyngd drastiskt och då särskilt det tvärsnitt som är störst, det vill säga L/20. Vidare visas även att slankare tvärsnitt resulterar i aningen högre armeringsmängd. Dock påverkas betongkostnaden i större utsträckning av slankare tvärsnitt och särskilt större spännvidder. Även om större spännvidd och slankare tvärsnitt föranleder ett större armeringsbehov, fås en lägre totalkostnad. Det bör noteras att priset på betong och stål är starkt beroende av konjunktur och tillgång till material. Denna studie kan bli ännu intressantare då priset varierar kraftigt för stål och föranleder att betongpriset blir mindre dominerande än vad det är idag. Huvudprodukten från detta arbete är att med hjälp av tabeller och nya priser kunna beräkna en preliminär totalkostnad för plattrambrons farbana för olika spännvidder och hur olika tvärsnittsalternativ påverkar denna kostnad

Managed Care’s Crimea: Medical Necessity, Therapeutic Benefit, and the Goals of Administrative Process in Health Insurance

This Essay explores the concept of medical necessity as it has evolved in the judicial and administrative oversight of managed care. The goals of the Essay are to illustrate the range of plausible rationales for establishing administrative procedures to govern medical necessity disputes, and to demonstrate the difficulty of incorporating into those procedures the most important professional and social responsibilities of managed care in today’s health care system. Part I of the Essay explains the ideological and practical significance of medical necessity as managed care has evolved. Part II examines medical necessity as a legal problem, and questions whether current independent review programs match social needs. Part III offers an alternative perspective on oversight of decisionmaking in managed care that emphasizes therapeutic effect rather than contractual enforcement. Part IV describes improvements in both independent review and overall medical necessity policy that would better serve therapeutic objectives. Among other things, the Essay suggests that independent review procedures should be different for insured individuals who are severely or chronically ill than for those who are only occasional users of health care services

Universality classes in nonequilibrium lattice systems

This work is designed to overview our present knowledge about universality classes occurring in nonequilibrium systems defined on regular lattices. In the first section I summarize the most important critical exponents, relations and the field theoretical formalism used in the text. In the second section I briefly address the question of scaling behavior at first order phase transitions. In section three I review dynamical extensions of basic static classes, show the effect of mixing dynamics and the percolation behavior. The main body of this work is given in section four where genuine, dynamical universality classes specific to nonequilibrium systems are introduced. In section five I continue overviewing such nonequilibrium classes but in coupled, multi-component systems. Most of the known nonequilibrium transition classes are explored in low dimensions between active and absorbing states of reaction-diffusion type of systems. However by mapping they can be related to universal behavior of interface growth models, which I overview in section six. Finally in section seven I summarize families of absorbing state system classes, mean-field classes and give an outlook for further directions of research.Comment: Updated comprehensive review, 62 pages (two column), 29 figs included. Scheduled for publication in Reviews of Modern Physics in April 200

Universality classes in nonequilibrium lattice systems

This work is designed to overview our present knowledge about universality classes occurring in nonequilibrium systems defined on regular lattices. In the first section I summarize the most important critical exponents, relations and the field theoretical formalism used in the text. In the second section I briefly address the question of scaling behavior at first order phase transitions. In section three I review dynamical extensions of basic static classes, show the effect of mixing dynamics and the percolation behavior. The main body of this work is given in section four where genuine, dynamical universality classes specific to nonequilibrium systems are introduced. In section five I continue overviewing such nonequilibrium classes but in coupled, multi-component systems. Most of the known nonequilibrium transition classes are explored in low dimensions between active and absorbing states of reaction-diffusion type of systems. However by mapping they can be related to universal behavior of interface growth models, which I overview in section six. Finally in section seven I summarize families of absorbing state system classes, mean-field classes and give an outlook for further directions of research.Comment: Updated comprehensive review, 62 pages (two column), 29 figs included. Scheduled for publication in Reviews of Modern Physics in April 200