The Supercore for Normal Form Games

We study the supercore of a system derived from a normal form game. For the case of a finite game with pure strategies, we define a sequence of games and show that the supercore of that system coincides with the set of Nash equilibrium strategy profiles of the last game in the sequence. This result is illustrated with the characterization of the supercore for the n-person prisoners’ dilemma. With regard to the mixed extension of a normal form game, we show that the set of Nash equilibrium profiles coincides with the supercore for games with a finite number of Nash equilibria. For games with an infinite number of Nash equilibria this need not be no longer the case. Yet, it is not difficult to find a binary relation which guarantees the coincidence of these two sets.

Invariant-free deduction systems for temporal logic

In this thesis we propose a new approach to deduction methods for temporal logic. Our proposal is based on an inductive definition of eventualities that is different from the usual one. On the basis of this non-customary inductive definition for eventualities, we first provide dual systems of tableaux and sequents for Propositional Linear-time Temporal Logic (PLTL). Then, we adapt the deductive approach introduced by means of these dual tableau and sequent systems to the resolution framework and we present a clausal temporal resolution method for PLTL. Finally, we make use of this new clausal temporal resolution method for establishing logical foundations for declarative temporal logic programming languages. The key element in the deduction systems for temporal logic is to deal with eventualities and hidden invariants that may prevent the fulfillment of eventualities. Different ways of addressing this issue can be found in the works on deduction systems for temporal logic. Traditional tableau systems for temporal logic generate an auxiliary graph in a first pass.Then, in a second pass, unsatisfiable nodes are pruned. In particular, the second pass must check whether the eventualities are fulfilled. The one-pass tableau calculus introduced by S. Schwendimann requires an additional handling of information in order to detect cyclic branches that contain unfulfilled eventualities. Regarding traditional sequent calculi for temporal logic, the issue of eventualities and hidden invariants is tackled by making use of a kind of inference rules (mainly, invariant-based rules or infinitary rules) that complicates their automation. A remarkable consequence of using either a two-pass approach based on auxiliary graphs or aone-pass approach that requires an additional handling of information in the tableau framework, and either invariant-based rules or infinitary rules in the sequent framework, is that temporal logic fails to carry out the classical correspondence between tableaux and sequents. In this thesis, we first provide a one-pass tableau method TTM that instead of a graph obtains a cyclic tree to decide whether a set of PLTL-formulas is satisfiable. In TTM tableaux are classical-like. For unsatisfiable sets of formulas, TTM produces tableaux whose leaves contain a formula and its negation. In the case of satisfiable sets of formulas, TTM builds tableaux where each fully expanded open branch characterizes a collection of models for the set of formulas in the root. The tableau method TTM is complete and yields a decision procedure for PLTL. This tableau method is directly associated to a one-sided sequent calculus called TTC. Since TTM is free from all the structural rules that hinder the mechanization of deduction, e.g. weakening and contraction, then the resulting sequent calculus TTC is also free from this kind of structural rules. In particular, TTC is free of any kind of cut, including invariant-based cut. From the deduction system TTC, we obtain a two-sided sequent calculus GTC that preserves all these good freeness properties and is finitary, sound and complete for PLTL. Therefore, we show that the classical correspondence between tableaux and sequent calculi can be extended to temporal logic. The most fruitful approach in the literature on resolution methods for temporal logic, which was started with the seminal paper of M. Fisher, deals with PLTL and requires to generate invariants for performing resolution on eventualities. In this thesis, we present a new approach to resolution for PLTL. The main novelty of our approach is that we do not generate invariants for performing resolution on eventualities. Our method is based on the dual methods of tableaux and sequents for PLTL mentioned above. Our resolution method involves translation into a clausal normal form that is a direct extension of classical CNF. We first show that any PLTL-formula can be transformed into this clausal normal form. Then, we present our temporal resolution method, called TRS-resolution, that extends classical propositional resolution. Finally, we prove that TRS-resolution is sound and complete. In fact, it finishes for any input formula deciding its satisfiability, hence it gives rise to a new decision procedure for PLTL. In the field of temporal logic programming, the declarative proposals that provide a completeness result do not allow eventualities, whereas the proposals that follow the imperative future approach either restrict the use of eventualities or deal with them by calculating an upper bound based on the small model property for PLTL. In the latter, when the length of a derivation reaches the upper bound, the derivation is given up and backtracking is used to try another possible derivation. In this thesis we present a declarative propositional temporal logic programming language, called TeDiLog, that is a combination of the temporal and disjunctive paradigms in Logic Programming. We establish the logical foundations of our proposal by formally defining operational and logical semantics for TeDiLog and by proving their equivalence. Since TeDiLog is, syntactically, a sublanguage of PLTL, the logical semantics of TeDiLog is supported by PLTL logical consequence. The operational semantics of TeDiLog is based on TRS-resolution. TeDiLog allows both eventualities and always-formulas to occur in clause heads and also in clause bodies. To the best of our knowledge, TeDiLog is the first declarative temporal logic programming language that achieves this high degree of expressiveness. Since the tableau method presented in this thesis is able to detect that the fulfillment of an eventuality is prevented by a hidden invariant without checking for it by means of an extra process, since our finitary sequent calculi do not include invariant-based rules and since our resolution method dispenses with invariant generation, we say that our deduction methods are invariant-free.

A High Degree of LINE-1 Hypomethylation Is a Unique Feature of Early-Onset Colorectal Cancer

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A novel form of human disease with a protease-sensitive prion protein and heterozygosity methionine/valine at codon 129: Case report

Background: Sporadic Creutzfeldt-Jakob disease (sCJD) is a rare neurodegenerative disorder in humans included in the group of Transmissible Spongiform Encephalopathies or prion diseases. The vast majority of sCJD cases are molecularly classified according to the abnormal prion protein (PrPSc) conformations along with polymorphism of codon 129 of the PRNP gene. Recently, a novel human disease, termed "protease-sensitive prionopathy", has been described. This disease shows a distinct clinical and neuropathological phenotype and it is associated to an abnormal prion protein more sensitive to protease digestion. Case presentation: We report the case of a 75-year-old-man who developed a clinical course and presented pathologic lesions compatible with sporadic Creutzfeldt-Jakob disease, and biochemical findings reminiscent of "protease-sensitive prionopathy". Neuropathological examinations revealed spongiform change mainly affecting the cerebral cortex, putamen/globus pallidus and thalamus, accompanied by mild astrocytosis and microgliosis, with slight involvement of the cerebellum. Confluent vacuoles were absent. Diffuse synaptic PrP deposits in these regions were largely removed following proteinase treatment. PrP deposition, as revealed with 3F4 and 1E4 antibodies, was markedly sensitive to pre-treatment with proteinase K. Molecular analysis of PrPSc showed an abnormal prion protein more sensitive to proteinase K digestion, with a five-band pattern of 28, 24, 21, 19, and 16 kDa, and three aglycosylated isoforms of 19, 16 and 6 kDa. This PrPSc was estimated to be 80% susceptible to digestion while the pathogenic prion protein associated with classical forms of sporadic Creutzfeldt-Jakob disease were only 2% (type VV2) and 23% (type MM1) susceptible. No mutations in the PRNP gene were found and genotype for codon 129 was heterozygous methionine/valine. Conclusions: A novel form of human disease with abnormal prion protein sensitive to protease and MV at codon 129 was described. Although clinical signs were compatible with sporadic Creutzfeldt-Jakob disease, the molecular subtype with the abnormal prion protein isoforms showing enhanced protease sensitivity was reminiscent of the "protease-sensitive prionopathy". It remains to be established whether the differences found between the latter and this case are due to the polymorphism at codon 129. Different degrees of proteinase K susceptibility were easily determined with the chemical polymer detection system which could help to detect proteinase-susceptible pathologic prion protein in diseases other than the classical ones.

Leukemia-Associated Mutations in Nucleophosmin Alter Recognition by CRM1: Molecular Basis of Aberrant Transport

Nucleophosmin (NPM) is a nucleocytoplasmic shuttling protein, normally enriched in nucleoli, that performs several activities related to cell growth. NPM mutations are characteristic of a subtype of acute myeloid leukemia (AML), where mutant NPM seems to play an oncogenic role. AML-associated NPM mutants exhibit altered subcellular traffic, being aberrantly located in the cytoplasm of leukoblasts. Exacerbated export of AML variants of NPM is mediated by the nuclear export receptor CRM1, and due, in part, to a mutationally acquired novel nuclear export signal (NES). To gain insight on the molecular basis of NPM transport in physiological and pathological conditions, we have evaluated the export efficiency of NPM in cells, and present new data indicating that, in normal conditions, wild type NPM is weakly exported by CRM1. On the other hand, we have found that AML-associated NPM mutants efficiently form complexes with CRM1HA (a mutant CRM1 with higher affinity for NESs), and we have quantitatively analyzed CRM1HA interaction with the NES motifs of these mutants, using fluorescence anisotropy and isothermal titration calorimetry. We have observed that the affinity of CRM1HA for these NESs is similar, which may help to explain the transport properties of the mutants. We also describe NPM recognition by the import machinery. Our combined cellular and biophysical studies shed further light on the determinants of NPM traffic, and how it is dramatically altered by AML-related mutations.

A Novel Micro- and Nano-Scale Positioning Sensor Based on Radio Frequency Resonant Cavities

In many micro- and nano-scale technological applications high sensitivity displacement sensors are needed, especially in ultraprecision metrology and manufacturing. In this work a new way of sensing displacement based on radio frequency resonant cavities is presented and experimentally demonstrated using a first laboratory prototype. The principle of operation of the new transducer is summarized and tested. Furthermore, an electronic interface that can be used together with the displacement transducer is designed and proved. It has been experimentally demonstrated that very high and linear sensitivity characteristic curves, in the range of some kHz/nm; are easily obtainable using this kind of transducer when it is combined with a laboratory network analyzer. In order to replace a network analyzer and provide a more affordable, self-contained, compact solution, an electronic interface has been designed, preserving as much as possible the excellent performance of the transducer, and turning it into a true standalone positioning sensor. The results obtained using the transducer together with a first prototype of the electronic interface built with cheap discrete elements show that positioning accuracies in the micrometer range are obtainable using this cost-effective solution. Better accuracies would also be attainable but using more involved and costly electronics interfaces.

Microwave Resonant and Zero-Field Absorption Study of Doped Magnetite Prepared by a Co-Precipitation Method

Fe3O4 and ZnxFe3-xO4 pure and doped magnetite magnetic nanoparticles (NPs) were prepared in aqueous solution (Series A) or in a water-ethyl alcohol mixture (Series B) by the co-precipitation method. Only one ferromagnetic resonance line was observed in all cases under consideration indicating that the materials are magnetically uniform. The shortfall in the resonance fields from 3.27 kOe (for the frequency of 9.5 GHz) expected for spheres can be understood taking into account the dipolar forces, magnetoelasticity, or magnetocrystalline anisotropy. All samples show non-zero low field absorption. For Series A samples the grain size decreases with an increase of the Zn content. In this case zero field absorption does not correlate with the changes of the grain size. For Series B samples the grain size and zero field absorption behavior correlate with each other. The highest zero-field absorption corresponded to 0.2 zinc concentration in both A and B series. High zero-field absorption of Fe3O4 ferrite magnetic NPs can be interesting for biomedical applications.

Beyond Q-Resolution and Prenex Form: a Proof System for Quantified Constraint Satisfaction

We consider the quanti fied constraint satisfaction problem (QCSP) which is to decide, given a structure and a first-order sentence (not assumed here to be in prenex form) built from conjunction and quanti fication, whether or not the sentence is true on the structure. We present a proof system for certifying the falsity of QCSP instances and develop its basic theory; for instance, we provide an algorithmic interpretation of its behavior. Our proof system places the established Q-resolution proof system in a broader context, and also allows us to derive QCSP tractability results.