On lattices from combinatorial game theory modularity and a representation theorem: finite case

We show that a self-generated set of combinatorial games, S. may not be hereditarily closed but, strong self-generation and hereditary closure are equivalent in the universe of short games. In [13], the question "Is there a set which will give a non-distributive but modular lattice?" appears. A useful necessary condition for the existence of a finite non-distributive modular L(S) is proved. We show the existence of S such that L(S) is modular and not distributive, exhibiting the first known example. More, we prove a Representation Theorem with Games that allows the generation of all finite lattices in game context. Finally, a computational tool for drawing lattices of games is presented. (C) 2014 Elsevier B.V. All rights reserved.

Long-Term Recurrence of Nonmelanoma Skin Cancer after Topical Methylaminolevulinate Photodynamic Therapy in a Dermato-Oncology Department

BACKGROUND: Most available studies on the efficacy of topical photodynamic therapy focus on short-to medium-term results. Long-term data are scarce. OBJECTIVE: To evaluate the long-term efficacy of photodynamic therapy with topical methylaminolevulinate to treat Bowen's disease and basal cell carcinoma in the clinical practice setting of a dermato-oncology department. METHODS: The study included patients diagnosed with Bowen's disease or basal cell carcinoma, and who received photodynamic therapy from 2004 to 2008. Treatment protocol and clinical follow-up were standardized. The primary endpoint was clinically observed recurrence in a previous photodynamic therapy-treated area. Descriptive and survival analyses were performed. RESULTS: A total of 31 Bowen's disease lesions and 44 superficial basal cell carcinoma were treated, with a median follow-up of 43.5 months. Recurrence was observed in 14 Bowen's disease lesions (53.8%) and in 11 superficial basal cell carcinoma (33.3%). Significantly higher estimates for recurrence rates were found in patients with Bowen's disease (p=0.0036) or those aged under 58 years (p=0.039). The risk of recurrence was higher in patients with Bowen's disease than in those with superficial basal cell carcinoma and younger patients. CONCLUSIONS: Recurrence should be considered when choosing to treat non-melanoma skin cancer with photodynamic therapy. Younger age and Bowen's disease were independent predictors for long-term recurrence, suggesting the need to establish an extended period of follow-up for this subset of patients.

Abortion trends 1990-1999 in a Swiss region and determinants of abortion recurrence.

OBJECTIVE: To assess age- and nationality-specific trends in abortion rates over the last decade, and to describe women's characteristics, identifying risk factors for repeated abortion. METHODS: From 1990-1999, the Health Department of Canton Vaud (Switzerland) received 13'857 abortion requests from residents aged 14-49. Population data were obtained to compute rates. RESULTS: Both the number of abortions (1400 annually) as well as their rate (8.9 per thousand women [95% confidence interval (CI) 7.3-10.5]) were stable over the decade in question. The rate of abortion for foreign women, especially from ex-Yugoslavia and Africa, was twice that for Swiss women. Half of the requests came from single women, 43% had a low education level, and half were childless. The main reason for requesting termination of pregnancy was psychosocial (93%). The mean gestational age was 7.7 weeks (SD +/- 2.3), but 96% of requests were submitted before 12 weeks. Sixty-three percent of women reported that they had used no contraception, 36% the condom and 17% the pill. Among requests, the adjusted risk of repeated abortion (22% of abortion candidates) was greater among divorced/separated/widowed women (odds ratio [OR] 1.9 [95% CI 1.5-2.4]), unemployed women (OR 1.8 [95% CI 1.5-2.1]), and those who had not attended university (OR 1.6 [95% CI 1.1-2.2]). CONCLUSIONS: Although Swiss law only permitted abortion under strict conditions, this procedure was widely available in Vaud, which nevertheless has one of the lowest rates worldwide. Efforts must be intensified to ensure universal access to family planning services, especially for foreign women and adolescents. Professionals should also target "repeaters" to provide personalised counselling.

Predicting recurrence after unprovoked venous thromboembolism: prospective validation of the updated Vienna Prediction Model.

The updated Vienna Prediction Model for estimating recurrence risk after an unprovoked venous thromboembolism (VTE) has been developed to identify individuals at low risk for VTE recurrence in whom anticoagulation (AC) therapy may be stopped after 3 months. We externally validated the accuracy of the model to predict recurrent VTE in a prospective multicenter cohort of 156 patients aged ≥65 years with acute symptomatic unprovoked VTE who had received 3 to 12 months of AC. Patients with a predicted 12-month risk within the lowest quartile based on the updated Vienna Prediction Model were classified as low risk. The risk of recurrent VTE did not differ between low- vs higher-risk patients at 12 months (13% vs 10%; P = .77) and 24 months (15% vs 17%; P = 1.0). The area under the receiver operating characteristic curve for predicting VTE recurrence was 0.39 (95% confidence interval [CI], 0.25-0.52) at 12 months and 0.43 (95% CI, 0.31-0.54) at 24 months. In conclusion, in elderly patients with unprovoked VTE who have stopped AC, the updated Vienna Prediction Model does not discriminate between patients who develop recurrent VTE and those who do not. This study was registered at www.clinicaltrials.gov as #NCT00973596.

Association between smoking and recurrence of venous thromboembolism and bleeding in elderly patients with past acute venous thromboembolism.

BACKGROUND: While the association between smoking and arterial cardiovascular events has been well established, the association between smoking and venous thromboembolism (VTE) remains controversial. OBJECTIVES: To assess the association between smoking and the risk of recurrent VTE and bleeding in patients who have experienced acute VTE. PATIENTS/METHODS: This study is part of a prospective Swiss multicenter cohort that included patients aged ≥65years with acute VTE. Three groups were defined according to smoking status: never, former and current smokers. The primary outcome was the time to a first symptomatic, objectively confirmed VTE recurrence. Secondary outcomes were the time to a first major and clinically relevant non-major bleeding. Associations between smoking status and outcomes were analysed using proportional hazard models for the subdistribution of a competing risk of death. RESULTS: Among 988 analysed patients, 509 (52%) had never smoked, 403 (41%) were former smokers, and 76 (8%) current smokers. After a median follow-up of 29.6months, we observed a VTE recurrence rate of 4.9 (95% confidence interval [CI] 3.7-6.4) per 100 patient-years for never smokers, 6.6 (95% CI 5.1-8.6) for former smokers, and 5.2 (95% CI 2.6-10.5) for current smokers. Compared to never smokers, we found no association between current smoking and VTE recurrence (adjusted sub-hazard ratio [SHR] 1.05, 95% CI 0.49-2.28), major bleeding (adjusted SHR 0.59, 95% CI 0.25-1.39), and clinically relevant non-major bleeding (adjusted SHR 1.21, 95% CI 0.73-2.02). CONCLUSIONS: In this multicentre prospective cohort study, we found no association between smoking status and VTE recurrence or bleeding in elderly patients with VTE.

Nietzsche's eternal recurrence of the same : the effect of logic abridgement, contradictions and inconsistencies

I will argue that the doctrine of eternal recurrence of the same no better interprets cosmology than pink elephants interpret zoology. I will also argue that the eternal-reiurn-of-the-same doctrine as what Magnus calls "existential imperative" is without possibility of application and thus futile. To facilitate those arguments, the validity of the doctrine of the eternal recurrence of the same will be tested under distinct rubrics. Although each rubric will stand alone, one per chapter, as an evaluation of some specific aspect of eternal recurrence, the rubric sequence has been selected to accommodate the identification of what I shall be calling logic abridgments. The conclusions to be extracted from each rubric are grouped under the heading CONCLUSION and appear immediately following rubric ten. Then, or if, at the end of a rubric a reader is inclined to wonder which rubric or topic is next, and why, the answer can be found at the top of the following page. The question is usually answered in the very first sentence, but always answered in the first paragraph. The first rubric has been placed in order by chronological entitlement in that it deals with the evolution of the idea of eternal recurrence from the time of the ancient Greeks to Nietzsche's August, 1881 inspiration. This much-recommended technique is also known as starting at the beginning. Rubric 1 also deals with 20th. Century philosophers' assessments of the relationship between Nietzsche and ancient Greek thought. The only experience of E-R, Zarathustra's mountain vision, is second only because it sets the scene alluded to in following rubrics. The third rubric explores .ii?.ih T jc,i -I'w Nietzsche's evaluation of rationality so that his thought processes will be understood appropriately. The actual mechanism of E-R is tested in rubric four...The scientific proof Nietzsche assembled in support of E-R is assessed by contemporary philosophers in rubric five. E-R's function as an ethical imperative is debated in rubrics six and seven.. .The extent to which E-R fulfills its purpose in overcoming nihilism is measured against the comfort assured by major world religions in rubric eight. Whether E-R also serves as a redemption for revenge is questioned in rubric nine. Rubric ten assures that E-R refers to return of the identically same and not merely the similar. In addition to assemblage and evaluation of all ten rubrics, at the end of each rubric a brief recapitulation of its principal points concludes the chapter. In this essay I will assess the theoretical conditions under which the doctrine cannot be applicable and will show what contradictions and inconsistencies follow if the doctrine is taken to be operable. Harold Alderman in his book Nietzsche's Gift wrote, the "doctrine of eternal recurrence gives us a problem not in Platonic cosmology, but in Socratic selfreflection." ^ I will illustrate that the recurrence doctrine's cosmogony is unworkable and that if it were workable, it would negate self-reflection on the grounds that selfreflection cannot find its cause in eternal recurrence of the same. Thus, when the cosmology is shown to be impossible, any expected ensuing results or benefits will be rendered also impossible. The so-called "heaviest burden" will be exposed as complex, engrossing "what if speculations deserving no linkings to reality. To identify ^Alderman p. 84 abridgments of logic, contradictions and inconsistencies in Nietzsche's doctrine of eternal recurrence of the same, I. will examine the subject under the following schedule. In Chapter 1 the ancient origins of recurrence theories will be introduced. ..This chapter is intended to establish the boundaries within which the subsequent chapters, except Chapter 10, will be confined. Chapter 2, Zarathustra's vision of E-R, assesses the sections of Thus Spoke Zarathustra in which the phenomenon of recurrence of the same is reported. ..Nihilism as a psychological difficulty is introduced in this rubric, but that subject will be studied in detail in Chapter 8. In Chapter 2 the symbols of eternal recurrence of the same will be considered. Whether the recurrence image should be of a closed ring or as a coil will be of significance in many sections of my essay. I will argue that neither symbolic configuration can accommodate Nietzsche's supposed intention. Chapter 3 defends the description of E-R given by Zarathustra. Chapter 4, the cosmological mechanics of E-R, speculates on the seriousness with which Nietzsche might have intended the doctrine of eternal recurrence to be taken. My essay reports, and then assesses, the argument of those who suppose the doctrine to have been merely exploratory musings by Nietzsche on cosmological hypotheses...The cosmogony of E-R is examined. In Chapter 5, cosmological proofs tested, the proofs for Nietzsche's doctrine of return of the same are evaluated. This chapter features the position taken by Martin ' Heidegger. My essay suggests that while Heidegger's argument that recurrence of the same is a genuine cosmic agenda is admirable, it is not at all persuasive. Chapter 6, E-R is an ethical imperative, is in essence the reporting of a debate between two scholars regarding the possibility of an imperative in the doctrine of recurrence. Their debate polarizes the arguments I intend to develop. Chapter 7, does E-R of the same preclude alteration of attitudes, is a continuation of the debate presented in Chapter 6 with the focus shifted to the psychological from the cosmological aspects of eternal recurrence of the same. Chapter 8, Can E-R Overcome Nihilism?, is divided into two parts. In the first, nihilism as it applies to Nietzsche's theory is discussed. ..In part 2, the broader consequences, sources and definitions of nihilism are outlined. My essay argues that Nietzsche's doctrine is more nihilistic than are the world's major religions. Chapter 9, Is E-R a redemption for revenge?, examines the suggestion extracted from Thus Spoke Zarathustra that the doctrine of eternal recurrence is intended, among other purposes, as a redemption for mankind from the destructiveness of revenge. Chapter 10, E-R of the similar refuted, analyses a position that an element of chance can influence the doctrine of recurrence. This view appears to allow, not for recurrence of the same, but recurrence of the similar. A summary will recount briefly the various significant logic abridgments, contradictions, and inconsistencies associated with Nietzsche's doctrine of eternal recurrence of the same. In the 'conclusion' section of my essay my own opinions and observations will be assembled from the body of the essay.

The relationship between body mass index and breast cancer recurrence/progression and breast cancer-specific death

The aim of this study was to describe the nonlinear association between body mass index (BMI) and breast cancer outcomes and to determine whether BMI improves prediction of outcomes. A cohort of906 breast cancer patients diagnosed at Henry Ford Health System, Detroit (1985-1990) were studied. The median follow-up was 10 years. Multivariate logistic regression was used to model breast cancer recurrence/progression and breast cancer-specific death. Restricted cubic splines were used to model nonlinear effects. Receiver operator characteristic areas under the curves (ROC AUC) were used to evaluate prediction. BMI was nonlinearly associated with recurrence/progression and death (p= 0.0230 and 0.0101). Probability of outcomes increased with increase or decrease ofBMI away from 25. BMI splines were suggestive of improved prediction of death. The ROC AUCs for nested models with and without BMI were 0.8424 and 0.8331 (p= 0.08). I f causally associated, modifying patients BMI towards 25 may improve outcomes.

The von Neumann Minimax Theorem and its relatives and a study of externality in on-line auctions

This work consists of a theoretical part and an experimental one. The first part provides a simple treatment of the celebrated von Neumann minimax theorem as formulated by Nikaid6 and Sion. It also discusses its relationships with fundamental theorems of convex analysis. The second part is about externality in sponsored search auctions. It shows that in these auctions, advertisers have externality effects on each other which influence their bidding behavior. It proposes Hal R.Varian model and shows how adding externality to this model will affect its properties. In order to have a better understanding of the interaction among advertisers in on-line auctions, it studies the structure of the Google advertisements networ.k and shows that it is a small-world scale-free network.

An Interactive Theorem Prover for First-Order Dynamic Logic

Dynamic logic is an extension of modal logic originally intended for reasoning about computer programs. The method of proving correctness of properties of a computer program using the well-known Hoare Logic can be implemented by utilizing the robustness of dynamic logic. For a very broad range of languages and applications in program veri cation, a theorem prover named KIV (Karlsruhe Interactive Veri er) Theorem Prover has already been developed. But a high degree of automation and its complexity make it di cult to use it for educational purposes. My research work is motivated towards the design and implementation of a similar interactive theorem prover with educational use as its main design criteria. As the key purpose of this system is to serve as an educational tool, it is a self-explanatory system that explains every step of creating a derivation, i.e., proving a theorem. This deductive system is implemented in the platform-independent programming language Java. In addition, a very popular combination of a lexical analyzer generator, JFlex, and the parser generator BYacc/J for parsing formulas and programs has been used.

A Representation Theorem for Domains with Discrete and Continuous Variables.

This paper proves a new representation theorem for domains with both discrete and continuous variables. The result generalizes Debreu's well-known representation theorem on connected domains. A strengthening of the standard continuity axiom is used in order to guarantee the existence of a representation. A generalization of the main theorem and an application of the more general result are also presented.

Arrow's Theorem in Spatial Environments

In spatial environments, we consider social welfare functions satisfying Arrow's requirements. i.e., weak Pareto and independence of irrelevant alternatives. When the policy space os a one-dimensional continuum, such a welfare function is determined by a collection of 2n strictly quasi-concave preferences and a tie-breaking rule. As a corrollary, we obtain that when the number of voters is odd, simple majority voting is transitive if and only if each voter's preference is strictly quasi-concave. When the policy space is multi-dimensional, we establish Arrow's impossibility theorem. Among others, we show that weak Pareto, independence of irrelevant alternatives, and non-dictatorship are inconsistent if the set of alternatives has a non-empty interior and it is compact and convex.

Harsanyi’s Social Aggregation Theorem : A Multi-Profile Approach with Variable-Population Extensions

This paper provides new versions of Harsanyi’s social aggregation theorem that are formulated in terms of prospects rather than lotteries. Strengthening an earlier result, fixed-population ex-ante utilitarianism is characterized in a multi-profile setting with fixed probabilities. In addition, we extend the social aggregation theorem to social-evaluation problems under uncertainty with a variable population and generalize our approach to uncertain alternatives, which consist of compound vectors of probability distributions and prospects.

A Generalization of a Theorem of Boyd and Lawton

Ce mémoire s’applique à étudier d’abord, dans la première partie, la mesure de Mahler des polynômes à une seule variable. Il commence en donnant des définitions et quelques résultats pertinents pour le calcul de telle hauteur. Il aborde aussi le sujet de la question de Lehmer, la conjecture la plus célèbre dans le domaine, donne quelques exemples et résultats ayant pour but de résoudre la question. Ensuite, il y a l’extension de la mesure de Mahler sur les polynômes à plusieurs variables, une démarche semblable au premier cas de la mesure de Mahler, et le sujet des points limites avec quelques exemples. Dans la seconde partie, on commence par donner des définitions concernant un ordre supérieur de la mesure de Mahler, et des généralisations en passant des polynômes simples aux polynômes à plusieurs variables. La question de Lehmer existe aussi dans le domaine de la mesure de Mahler supérieure, mais avec des réponses totalement différentes. À la fin, on arrive à notre objectif, qui sera la démonstration de la généralisation d’un théorème de Boyd-Lawton, ce dernier met en évidence une relation entre la mesure de Mahler des polynômes à plusieurs variables avec la limite de la mesure de Mahler des polynômes à une seule variable. Ce résultat a des conséquences en termes de la conjecture de Lehmer et sert à clarifier la relation entre les valeurs de la mesure de Mahler des polynômes à une variable et celles des polynômes à plusieurs variables, qui, en effet, sont très différentes en nature.

Studies on Thermodynamics and No-hair Theorem in Black hole Spacetime

Department of Physics, Cochin University of Science and Technology