Monadické NP množiny

Generalised spectra, id est classes finitely axiomatisable in existential second-order logic restricted to finite structures, are known by Fagin's theorem to coincide with members of the complexity class NP. Thereby, the problem of NP being closed under complementation reduces to the problem whether every class of finite struc- tures complementary to a generalised spectrum is, too, a generalised spectrum. Provided P ̸= NP, a proof thereof could then possibly be based on finding a par- ticular generalised spectrum (thereby an NP class) whose complement, while in coNP would not be in NP. Pursuits of such a proof, too, however, have been to no avail. A partial resolution of this problem (itself a special case to so called Asser's problem) is Fagin-Hájek theorem, claiming that a subclass of NP, the class of so called monadic NP sets is not closed under complementation. Reproduc- ing Fagin's original proof of the theorem is the aim of this thesis, along with introducing the reader to all preliminary apparatus needed for the proof. 1Jako zobecněná spektra se označují třídy konečně axiomatisovatelné v existenční druhořádové logice s relací platnosti omezenou na konečné struktury. Jest známým faktem, že korrespondují dle Faginovy věty s prvky složitostní třídy NP. Prob- lém uzavřenosti NP na komplementaci se tedy redukuje na problém uzavřenosti zobecněných spekter na komplementaci. Důkaz P ̸= NP, za předpokladu, že ono tvrzení skutečně platí, by tak mohl spočívat v nalezení konkretního zobecněného spektra (a tedy třídy v NP), jehož doplněk, jsa arci v coNP, by nebyl prvkem NP. Hledání takového důkazu ovšem též nepřineslo úspěch. Částečné rozřešení tohoto problému (an sám je toliko speciálním příkladem obecnějšího tak zvaného prob- lému Asserova) přinesla Fagin-Hájkova věta, tvrdící, že jistá podtřída NP, třída tak zvaných monadických NP množin vskutku netvoří třídu uzavřenou na kom- plementaci. Reprodukce Faginova původního důkazu této věty, spolu s uvedením veškerého potřebného apparátu, je cílem této práce. 1Katedra logikyDepartment of LogicFaculty of ArtsFilozofická fakult

Primary mediastinal synovial sarcoma: a case report and review of the literature

Primary mediastinal synovial sarcoma is a rare malignancy with only a few cases reported so far. A 56-year-old woman was admitted to our hospital for an investigation of a nodule in the left middle lung on chest radiography. Computed tomography revealed a mediastinal mass first described as a solitary fibrous tumor. The diagnosis of synovial sarcoma was established by computed tomography-guided percutaneous needle biopsy. Work up showed no metastasis to distant organs or contralateral pleural cavity. The mass was surgically resected; pathological and immunohistochemical analyses confirmed the diagnosis of a monophasic spindle cell synovial sarcoma probably originating from phrenic nerve. The patient received adjuvant chemotherapy and radiation and is free of recurrence after a follow up of 16 months

Search for supersymmetry with a dominant R-parity violating LQDbar couplings in e+e- collisions at centre-of-mass energies of 130GeV to 172 GeV

A search for pair-production of supersymmetric particles under the assumption that R-parity is violated via a dominant LQDbar coupling has been performed using the data collected by ALEPH at centre-of-mass energies of 130-172 GeV. The observed candidate events in the data are in agreement with the Standard Model expectation. This result is translated into lower limits on the masses of charginos, neutralinos, sleptons, sneutrinos and squarks. For instance, for m_0=500 GeV/c^2 and tan(beta)=sqrt(2) charginos with masses smaller than 81 GeV/c^2 and neutralinos with masses smaller than 29 GeV/c^2 are excluded at the 95% confidence level for any generation structure of the LQDbar coupling.Comment: 32 pages, 30 figure

Search for the glueball candidates f0(1500) and fJ(1710) in gamma gamma collisions

Data taken with the ALEPH detector at LEP1 have been used to search for gamma gamma production of the glueball candidates f0(1500) and fJ(1710) via their decay to pi+pi-. No signal is observed and upper limits to the product of gamma gamma width and pi+pi- branching ratio of the f0(1500) and the fJ(1710) have been measured to be Gamma_(gamma gamma -> f0(1500)). BR(f0(1500)->pi+pi-) < 0.31 keV and Gamma_(gamma gamma -> fJ(1710)). BR(fJ(1710)->pi+pi-) < 0.55 keV at 95% confidence level.Comment: 10 pages, 3 figure

Search for CP Violation in the Decay Z -> b (b bar) g

About three million hadronic decays of the Z collected by ALEPH in the years 1991-1994 are used to search for anomalous CP violation beyond the Standard Model in the decay Z -> b \bar{b} g. The study is performed by analyzing angular correlations between the two quarks and the gluon in three-jet events and by measuring the differential two-jet rate. No signal of CP violation is found. For the combinations of anomalous CP violating couplings, ${\hat{h}}_b = {\hat{h}}_{Ab}g_{Vb}-{\hat{h}}_{Vb}g_{Ab}$ and $h^{\ast}_b = \sqrt{\hat{h}_{Vb}^{2}+\hat{h}_{Ab}^{2}}$, limits of \hat{h}_b < 0.59$and$h^{\ast}_{b} < 3.02$ are given at 95\% CL.Comment: 8 pages, 1 postscript figure, uses here.sty, epsfig.st

Comprehensive genomic profiles of small cell lung cancer

We have sequenced the genomes of 110 small cell lung cancers (SCLC), one of the deadliest human cancers. In nearly all the tumours analysed we found bi-allelic inactivation of TP53 and RB1, sometimes by complex genomic rearrangements. Two tumours with wild-type RB1 had evidence of chromothripsis leading to overexpression of cyclin D1 (encoded by the CCND1 gene), revealing an alternative mechanism of Rb1 deregulation. Thus, loss of the tumour suppressors TP53 and RB1 is obligatory in SCLC. We discovered somatic genomic rearrangements of TP73 that create an oncogenic version of this gene, TP73Dex2/3. In rare cases, SCLC tumours exhibited kinase gene mutations, providing a possible therapeutic opportunity for individual patients. Finally, we observed inactivating mutations in NOTCH family genes in 25% of human SCLC. Accordingly, activation of Notch signalling in a pre-clinical SCLC mouse model strikingly reduced the number of tumours and extended the survival of the mutant mice. Furthermore, neuroendocrine gene expression was abrogated by Notch activity in SCLC cells. This first comprehensive study of somatic genome alterations in SCLC uncovers several key biological processes and identifies candidate therapeutic targets in this highly lethal form of cancer