Some Remarks about the Complexity of Epidemics Management

Recent outbreaks of Ebola, H1N1 and other infectious diseases have shown that the assumptions underlying the established theory of epidemics management are too idealistic. For an improvement of procedures and organizations involved in fighting epidemics, extended models of epidemics management are required. The necessary extensions consist in a representation of the management loop and the potential frictions influencing the loop. The effects of the non-deterministic frictions can be taken into account by including the measures of robustness and risk in the assessment of management options. Thus, besides of the increased structural complexity resulting from the model extensions, the computational complexity of the task of epidemics management - interpreted as an optimization problem - is increased as well. This is a serious obstacle for analyzing the model and may require an additional pre-processing enabling a simplification of the analysis process. The paper closes with an outlook discussing some forthcoming problems

Every countable model of set theory embeds into its own constructible universe

The main theorem of this article is that every countable model of set theory M, including every well-founded model, is isomorphic to a submodel of its own constructible universe. In other words, there is an embedding $j:M\to L^M$ that is elementary for quantifier-free assertions. The proof uses universal digraph combinatorics, including an acyclic version of the countable random digraph, which I call the countable random Q-graded digraph, and higher analogues arising as uncountable Fraisse limits, leading to the hypnagogic digraph, a set-homogeneous, class-universal, surreal-numbers-graded acyclic class digraph, closely connected with the surreal numbers. The proof shows that $L^M$ contains a submodel that is a universal acyclic digraph of rank $Ord^M$. The method of proof also establishes that the countable models of set theory are linearly pre-ordered by embeddability: for any two countable models of set theory, one of them is isomorphic to a submodel of the other. Indeed, they are pre-well-ordered by embedability in order-type exactly $\omega_1+1$. Specifically, the countable well-founded models are ordered by embeddability in accordance with the heights of their ordinals; every shorter model embeds into every taller model; every model of set theory $M$ is universal for all countable well-founded binary relations of rank at most $Ord^M$; and every ill-founded model of set theory is universal for all countable acyclic binary relations. Finally, strengthening a classical theorem of Ressayre, the same proof method shows that if $M$ is any nonstandard model of PA, then every countable model of set theory---in particular, every model of ZFC---is isomorphic to a submodel of the hereditarily finite sets $HF^M$ of $M$. Indeed, $HF^M$ is universal for all countable acyclic binary relations.Comment: 25 pages, 2 figures. Questions and commentary can be made at http://jdh.hamkins.org/every-model-embeds-into-own-constructible-universe. (v2 adds a reference and makes minor corrections) (v3 includes further changes, and removes the previous theorem 15, which was incorrect.

Structural Properties of Gibbsian Point Processes in Abstract Spaces

In the language of random counting measures, many structural properties of the Poisson process can be studied in arbitrary measurable spaces. We provide a similarly general treatise of Gibbs processes. With the GNZ equations as a definition of these objects, Gibbs processes can be introduced in abstract spaces without any topological structure. In this general setting, partition functions, Janossy densities, and correlation functions are studied. While the definition covers finite and infinite Gibbs processes alike, the finite case allows, even in abstract spaces, for an equivalent and more explicit characterization via a familiar series expansion. Recent generalizations of factorial measures to arbitrary measurable spaces, where counting measures cannot be written as sums of Dirac measures, likewise allow to generalize the concept of Hamiltonians. The DLR equations, which completely characterize a Gibbs process, as well as basic results for the local convergence topology, are also formulated in full generality. We prove a new theorem on the extraction of locally convergent subsequences from a sequence of point processes and use this statement to provide existence results for Gibbs processes in general spaces with potentially infinite range of interaction. These results are used to guarantee the existence of Gibbs processes with cluster-dependent interactions and to prove a recent conjecture concerning the existence of Gibbsian particle processes

Affordable Housing: Of Inefficiency, Market Distortion, and Government Failure

In this essay, I examine the types of costs that are imposed on society as a whole due to the absence of a sufficient number of decent housing units that are affordable to the low-income population. These costs present themselves in relation to health care, education, employment, productivity, homelessness, and incarceration. Some of the costs are direct expenditures while others are the result of lost opportunities. My hypothesis is that these costs are significant and offer, at the very least, a substantial offset to the cost of creating and subsidizing the operation of the necessary number of affordable housing units that are currently missing. I suggest a series of reasons why, in the face of this potentially inefficient outcome, the market/society does not produce the required units. The essay is conceptual in nature, not empirical. I recognize the issues associated with the quantification of often opaque costs and with their causal relationship to the lack of affordable housing. It is clear, however, that the costs are sizable and the correlations are strong and therefore, I believe, the hypothesis requires empirical study

Throughput and Yield Improvement for a Continuous Discrete-Product Manufacturing System

A seam-welded steel pipe manufacturing process has mainly four distinct major design and/or operational problems dealing with buffer inventory, cutting tools, pipe sizing and inspection-rework facility. The general objective of this research is to optimally solve these four important problems to improve the throughput and yield of the system at a minimum cost. The first problem of this research finds the optimal buffer capacity of steel strip coils to minimize the maintenance and downtime related costs. The total cost function for this coil feeding system is formulated as a constrained non-linear programming (NLP) problem which is solved with a search algorithm. The second problem aims at finding the optimal tool magazine reload timing, magazine size and the order quantity for the cutting tools. This tool magazine system is formulated as a mixed-integer NLP problem which is solved for minimizing the total cost. The third problem deals with different type of manufacturing defects. The profit function of this problem forms a binary integer NLP problem which involves multiple integrals with several exponential and discrete functions. An exhaustive search method is employed to find the optimum strategy for dealing with the defects and pipe sizing. The fourth problem pertains to the number of servers and floor space allocations for the off-line inspection-rework facility. The total cost function forms an integer NLP structure, which is minimized with a customized search algorithm. In order to judge the impact of the above-mentioned problems, an overall equipment effectiveness (OEE) measure, coined as monetary loss based regression (MLBR) method, is also developed as the fifth problem to assess the performance of the entire manufacturing system. Finally, a numerical simulation of the entire process is conducted to illustrate the applications of the optimum parameters setting and to evaluate the overall effectiveness of the simulated system. The successful improvement of the simulated system supports this research to be implemented in a real manufacturing setup. Different pathways shown here for improving the throughput and yield of industrial systems reflect not only to the improvement of methodologies and techniques but also to the advancement of new technology and national economy