A Uniform Method for Proving Lower Bounds of the Computational Complexity of Logical Theories

https://deepblue.lib.umich.edu/bitstream/2027.42/154178/1/39015100081655.pd

A deductive system for existential least fixpoint logic

Existential least fixpoint logic (ELFP) is a logic with a least fixpoint operator but only existential quantification. It arises in many areas of computer science including logic programming, database theory, program verification, complexity theory, and recursion theory on abstract structures. A sequent calculus (Gentzen-style deductive system) for this logic is presented and proved to be complete. Basic model theoretic facts about ELFP are derived from the completeness theorem and the construction used in its proof. The relationship of these model theoretic facts to logic programming and database queries is explored

Stratified least fixpoint logic

Stratified least fixpoint logic or SLFP characterizes the expressibility of stratified logic programs and in a different formulation has been used as a logic of imperative programs. These two formulations of SLFP are proved to be equivalent and a complete sequent calculus for SLFP is presented. It is argued that SLFP is the most appropriate assertion language for program verification. In particular, it is shown that traditional approaches using first-order logic as an assertion language only restrict to interpretations where first-order logic has the same expressibility as SLFP

Nonconvergence, Undecidability, and Intractability in Asymptotic Problems

https://deepblue.lib.umich.edu/bitstream/2027.42/154144/1/39015099114582.pd

Average Case Analysis of Gosper’s Algorithm for aClass of Urn Model Inputs

In this paper we perform an asymptotic average case analysis of some of the most important steps of Gosper’s algorithm for indefinite summation of hypergeometric terms. The space of input functions of the algorithm is described in terms of urn models, and the analysis is performed by using specialized probabilistic transform techniques. We analyze two different types of urn model classes: one in which the input functions are assumed to be rational, and another for which a certain function of two inputs is assumed to be rational. The first set of results shows that the asymptotic complexity of the algorithm is the same within each of the two classes. The second set of results indicates that the complexity of the algorithm scales differently for the two classes of models: one can observe the logarithmic versus square root type of difference that is also present in other combinatorial models.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/41350/1/453_2005_Article_1173.pd

Expected deadlock time in a multiprocessing system

Projet ICSLAWe consider multiprocessing systems where processes make independent, Poisson distributed resource requests with mean arrival time 1. We assume that resources are not released. It is shown that the expected deadlock time is never less than 1, no matter how many processes and resources are in the system. Also, the expected number of processes blocked by deadlock time is one half more than half the number of initially active processes. We obtain expressions for system statistics such as expected deadlock time, expected total processing time, and system efficiency in terms of Abel sums. We derive asymptotic expressions for these statictics in the case of systems with many processes and the case of systems with a fixed number of processes. In the latter, generalizations of the Ramanujan Q-function arise. We use singularity analysis to obtain asymptotics of coefficients of generalized Q-functions

DoD-GEIS Rift Valley Fever Monitoring and Prediction System as a Tool for Defense and US Diplomacy

Over the last 10 years the Armed Forces Health Surveillance Center's Global Emerging Infections Surveillance and Response System (GEIS) partnering with NASA'S Goddard Space Flight Center and USDA's USDA-Center for Medical, Agricultural & Veterinary Entomology established and have operated the Rift Valley fever Monitoring and Prediction System to monitor, predict and assess the risk of Rift Valley fever outbreaks and other vector-borne diseases over Africa and the Middle East. This system is built on legacy DoD basic research conducted by Walter Reed Army Institute of Research overseas laboratory (US Army Medical Research Unit-Kenya) and the operational satellite environmental monitoring by NASA GSFC. Over the last 10 years of operation the system has predicted outbreaks of Rift Valley fever in the Horn of Africa, Sudan, South Africa and Mauritania. The ability to predict an outbreak several months before it occurs provides early warning to protect deployed forces, enhance public health in concerned countries and is a valuable tool use.d by the State Department in US Diplomacy. At the international level the system has been used by the Food and Agricultural Organization (FAD) and the World Health Organization (WHO) to support their monitoring, surveillance and response programs in the livestock sector and human health. This project is a successful testament of leveraging resources of different federal agencies to achieve objectives of force health protection, health and diplomacy

The largest set partitioned by a subfamily of a cover

Define [lambda](n) to be the largest integer such that for each set A of size n and cover J of A, there exist B [subset of or equal to] A and G [subset of or equal to] J such that |B| = [lambda](n) and the restriction of G to B is a partition of B. It is shown that when n [ges] 3. The lower bound is proved by a probabilistic method. A related probabilistic algorithm for finding large sets partitioned by a subfamily of a cover is presented.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/28503/1/0000300.pd

Telomere dysfunction accurately predicts clinical outcome in chronic lymphocytic leukaemia, even in patients with early stage disease

© 2014 John Wiley & Sons Ltd. Defining the prognosis of individual cancer sufferers remains a significant clinical challenge. Here we assessed the ability of high-resolution single telomere length analysis (STELA), combined with an experimentally derived definition of telomere dysfunction, to predict the clinical outcome of patients with chronic lymphocytic leukaemia (CLL). We defined the upper telomere length threshold at which telomere fusions occur and then used the mean of the telomere 'fusogenic' range as a prognostic tool. Patients with telomeres within the fusogenic range had a significantly shorter overall survival (P  <  0·0001; Hazard ratio [HR] = 13·2, 95% confidence interval [CI]  = 11·6-106·4) and this was preserved in early-stage disease patients (P  <  0·0001, HR=19·3, 95% CI = 17·8-802·5). Indeed, our assay allowed the accurate stratification of Binet stage A patients into those with indolent disease (91% survival at 10 years) and those with poor prognosis (13% survival at 10 years). Furthermore, patients with telomeres above the fusogenic mean showed superior prognosis regardless of their IGHV mutation status or cytogenetic risk group. In keeping with this finding, telomere dysfunction was the dominant variable in multivariate analysis. Taken together, this study provides compelling evidence for the use of high-resolution telomere length analysis coupled with a definition of telomere dysfunction in the prognostic assessment of CLL