Schwartz - Zippelov teorem i neke njegove primjene

U ovom radu izložen je rezultat poznat pod nazivom Schwartz - Zippelova lema ili Schwartz - Zippelov teorem. Tema rada pripada pretežno algebri, ali ima značajne primjene u drugim matematičkim područjima kao što je na primjer teorija algoritama, te kombinatorika. Rad se sastoji od tri poglavlja. U uvodu je ukratko opisana tema i cilj rada. Prvo poglavlje sadrži kratku povijest nastanka teorema, različite oblike rezultata pojedinih autora, te kratki opis pojmova korištenih u samom radu. Drugo poglavlje sastoji se od iskaza i dokaza Schwartz - Zippelovog teorema, a u trećem poglavlju izložene su neke primjene tog teorema na probleme koji se mogu svesti na testiranje jednakosti polinoma. Takvi su, primjerice, problem postojanja savršenog sparivanja u grafu i ispitivanje svojstva asocijativnosti u grupoidu. Uz svaku primjenu navedeni su i prikladni primjeri.In this diploma thesis we present the result usually called the Schwartz-Zippel lemma or the Schwartz-Zippel theorem. The nature of this theorem is basically algebraic, but it has significant applications in other areas of mathematics, such as the theory of algorithms and combinatorial theory. The thesis consists of three chapters. The main theme and objective are briefly described in the introduction. The first chapter contains a short history of the theorem’s origins, various forms of the main results by different authors and some comments of basic concepts related to this topic. The statement and a proof of the Schwartz-Zippel theorem are given in the second chapter, together with the general outline of its applications. The third and final chapter consists of some applications to problems which can be reduced to polynomial identity testing, including the existence of a perfect matching in a graph and testing of the associativity property in a groupoi

Conformational polymorphic changes in the crystal structure of the chiral antiparasitic drug praziquantel and interactions with calcium carbonate

Praziquantel is an antiparasitic drug used for decades. Currently, the praziquantel commercial preparation is a racemic mixture, in which only the levo-enantiomer possesses anthelmintic activity. The knowledge of its properties in the solid state and other chemical-physical properties is necessary for improving its efficacy and applications. Drug solid dispersions were prepared with calcium carbonate at 1:5 drug to excipient weight ratio by solvent evaporation method. Then, the modification of the crystal structure of the racemic polymorph of praziquantel in presence of calcium carbonate has been studied by means of several analytical techniques (DSC,TGA, XRD, SEM, FTIR, Raman spectroscopy and chiral liquid chromatography). This study has been completed with atomistic calculations based on empirical interatomic force fields and quantum mechanics methods applied to the crystal structure of praziquantel and of intermolecular interactions. The results evidenced that calcium carbonate provoked a conformational change in the praziquantel molecule yielding the formation of different polymorphs of praziquantel crystal. These alterations were not observed replacing calcium carbonate with colloidal silica as excipient in the solid dispersion

Cytotoxic Acetogenins from the Roots of Annona purpurea

Annona purpurea, known in Mexico as "cabeza de negro" or "ilama", belongs to the Annonaceae family. Its roots are employed in folk medicine in several regions of Mexico. Taking that information into account, a chemical and biological analysis of the components present in the roots of this species was proposed. Our results demonstrated that the dichloromethane (DCM) extract was exclusively constituted by a mixture of five new acetogenins named annopurpuricins A-E (1-5). These compounds have an aliphatic chain of 37 carbons with a terminal \u3b1,\u3b2 unsaturated \u3b3-lactone. Compounds 1 and 2 belong to the adjacent bis-THF (tetrahydrofuran) \u3b1-monohydroxylated type, while compounds 3 and 4 belong to the adjacent bis-THF \u3b1,\u3b1'-dihydroxylated type; only compound 5 possesses a bis-epoxide system. Complete structure analysis was carried out by spectroscopy and chemical methods. All compounds were evaluated for their antiproliferative activity on three human tumor cell lines (MSTO-211H, HeLa and HepG2). Compounds 1-4 inhibited significantly the growth of HeLa and HepG2 cells, showing GI50 values in the low/subnanomolar range, while 5 was completely ineffective under the tested conditions. The investigation of the mechanism of action responsible for cytotoxicity revealed for the most interesting compound 1 the ability to block the complex I activity on isolated rat liver mitochondria (RLM)

Mass calibration of distant SPT galaxy clusters through expanded weak-lensing follow-up observations with HST, VLT, & Gemini-South

Expanding from previous work, we present weak-lensing (WL) measurements for a total sample of 30 distant (zmedian = 0.93) massive galaxy clusters from the South Pole Telescope Sunyaev-Zel'dovich (SPT-SZ) Survey, measuring galaxy shapes in Hubble Space Telescope (HST) Advanced Camera for Surveys images. We remove cluster members and preferentially select z 73 1.4 background galaxies via V - I colour, employing deep photometry from VLT/FORS2 and Gemini-South/GMOS. We apply revised calibrations for the WL shape measurements and the source redshift distribution to estimate the cluster masses. In combination with earlier Magellan/Megacam results for lower-redshifts clusters, we infer refined constraints on the scaling relation between the SZ detection significance and the cluster mass, in particular regarding its redshift evolution. The mass scale inferred from the WL data is lower by a factor $0.76^{+0.10}_{-0.14}$ (at our pivot redshift z = 0.6) compared to what would be needed to reconcile a flat Planck \u3bd\u39bCDM cosmology (in which the sum of the neutrino masses is a free parameter) with the observed SPT-SZ cluster counts. In order to sensitively test the level of (dis-)agreement between SPT clusters and Planck, further expanded WL follow-up samples are needed

Stable expression and characterization of a fungal pectinase and bacterial peroxidase genes in tobacco chloroplast

Background: The high capacity of chloroplast genome response to integrate and express transgenes at high levels makes this technology a good option to produce proteins of interest. This report presents the stable expression of Pectin lyase (PelA gene) and the first stable expression of manganese peroxidase (MnP-2 gene) from the chloroplast genome. Results: pES4 and pES5 vectors were derived from pPV111A plasmid and contain the PelA and MnP-2 synthetic genes, respectively. Both genes are flanked by a synthetic rrn16S promoter and the 3\u2032UTR from rbcL gene. Efficient gene integration into both inverted repeats of the intergenic region between rrn16S and 3\u2032rps\u203212 was confirmed by Southern blot. Stable processing and expression of the RNA were confirmed by Northern blot analysis. Enzymatic activity was evaluated to detect expression and functionality of both enzymes. In general, mature plants showed more activity than young transplastomic plants. Compared to wild type plants, transplastomic events expressing pectin lyase exhibited enzymatic activity above 58.5% of total soluble protein at neutral pH and 60\ub0C. In contrast, MnP-2 showed high activity at pH 6 with optimum temperature at 65\ub0C. Neither transplastomic plant exhibited an abnormal phenotype. Conclusion: This study demonstrated that hydrolytic genes PelA and MnP-2 could be integrated and expressed correctly from the chloroplast genome of tobacco plants. A whole plant, having ~470 g of biomass could feasibly yield 66,676.25 units of pectin or 21,715.46 units of manganese peroxidase. Also, this study provides new information about methods and strategies for the expression of enzymes with industrial value

Corrigendum: Analysis of the common genetic component of large-vessel vasculitides through a meta-Immunochip strategy.

Giant cell arteritis (GCA) and Takayasu's arteritis (TAK) are major forms of large-vessel vasculitis (LVV) that share clinical features. To evaluate their genetic similarities, we analysed Immunochip genotyping data from 1,434 LVV patients and 3,814 unaffected controls. Genetic pleiotropy was also estimated. The HLA region harboured the main disease-specific associations. GCA was mostly associated with class II genes (HLA-DRB1/HLA-DQA1) whereas TAK was mostly associated with class I genes (HLA-B/MICA). Both the statistical significance and effect size of the HLA signals were considerably reduced in the cross-disease meta-analysis in comparison with the analysis of GCA and TAK separately. Consequently, no significant genetic correlation between these two diseases was observed when HLA variants were tested. Outside the HLA region, only one polymorphism located nearby the IL12B gene surpassed the study-wide significance threshold in the meta-analysis of the discovery datasets (rs755374, P\u2009=\u20097.54E-07; ORGCA\u2009=\u20091.19, ORTAK\u2009=\u20091.50). This marker was confirmed as novel GCA risk factor using four additional cohorts (PGCA\u2009=\u20095.52E-04, ORGCA\u2009=\u20091.16). Taken together, our results provide evidence of strong genetic differences between GCA and TAK in the HLA. Outside this region, common susceptibility factors were suggested, especially within the IL12B locus

Characterization and comparability of biosimilars: A filgrastim case of study and regulatory perspectives for Latin America

Background: Developing countries have an estimate of ten times more approved biosimilars than developed countries. This disparity demands the need of an objective regulation that incorporates health policies according to the technological and economical capabilities of each country. One of the challenges lies on the establishment of comparability principles based on a physicochemical and biological characterization that should determine the extent of additional non-clinical and clinical studies. This is particularly relevant for licensed biosimilars in developing countries, which have an extensive clinical experience since their approval as generics, in some cases more than a decade. To exemplify the current status of biosimilars in Mexico, a characterization exercise was conducted on licensed filgrastim biosimilars using pharmacopeial and extended characterization methodologies. Results: Most of the evaluated products complied with the pharmacopeial criteria and showed comparability in their Critical Quality Attributes (CQAs) towards the reference product. These results were expected in accordance with their equivalent performance during their licensing as generics. Accordingly, a rational approval and registration renewal scheme for biosimilars is proposed, that considers the proper identification of CQAs and its thoroughly evaluation using selected techniques. Conclusions: This approach provides support to diminish uncertainty of exhibiting different pharmacological profiles and narrows or even avoids the necessity of comparative clinical studies. Ultimately, this proposal is intended to improve the accessibility to high quality biosimilars in Latin America and other developing countries

Two-pion Bose-Einstein correlations in central Pb-Pb collisions at sNN\sqrt{s_{\rm NN}} = 2.76 TeV

The first measurement of two-pion Bose-Einstein correlations in central Pb-Pb collisions at $\sqrt{s_{\rm NN}} = 2.76$ TeV at the Large Hadron Collider is presented. We observe a growing trend with energy now not only for the longitudinal and the outward but also for the sideward pion source radius. The pion homogeneity volume and the decoupling time are significantly larger than those measured at RHIC.Comment: 17 pages, 5 captioned figures, 1 table, authors from page 12, published version, figures at http://aliceinfo.cern.ch/ArtSubmission/node/388

Suppression of charged particle production at large transverse momentum in central Pb-Pb collisions at sNN=2.76\sqrt{s_{\rm NN}} = 2.76 TeV

Inclusive transverse momentum spectra of primary charged particles in Pb-Pb collisions at $\sqrt{s_{_{\rm NN}}}$ = 2.76 TeV have been measured by the ALICE Collaboration at the LHC. The data are presented for central and peripheral collisions, corresponding to 0-5% and 70-80% of the hadronic Pb-Pb cross section. The measured charged particle spectra in $|\eta|<0.8$ and $0.3 < p_T < 20$ GeV/$c$ are compared to the expectation in pp collisions at the same $\sqrt{s_{\rm NN}}$, scaled by the number of underlying nucleon-nucleon collisions. The comparison is expressed in terms of the nuclear modification factor $R_{\rm AA}$. The result indicates only weak medium effects ($R_{\rm AA} \approx$ 0.7) in peripheral collisions. In central collisions, $R_{\rm AA}$ reaches a minimum of about 0.14 at $p_{\rm T}=6$-7GeV/$c$ and increases significantly at larger $p_{\rm T}$. The measured suppression of high-$p_{\rm T}$ particles is stronger than that observed at lower collision energies, indicating that a very dense medium is formed in central Pb-Pb collisions at the LHC.Comment: 15 pages, 5 captioned figures, 3 tables, authors from page 10, published version, figures at http://aliceinfo.cern.ch/ArtSubmission/node/98

Strange particle production in proton-proton collisions at s=0.9\sqrt{s}=0.9 TeV with ALICE at the LHC

The production of mesons containing strange quarks (K$^0_s$, $\phi$) and both singly and doubly strange baryons ($\Lambda$, Anti-$\Lambda$, and $\Xi$+Anti-$\Xi$) are measured at central rapidity in pp collisions at $\sqrt{s}$ = 0.9 TeV with the ALICE experiment at the LHC. The results are obtained from the analysis of about 250 k minimum bias events recorded in 2009. Measurements of yields (dN/dy) and transverse momentum spectra at central rapidities for inelastic pp collisions are presented. For mesons, we report yields () of 0.184 $\pm$ 0.002 stat. $\pm$ 0.006 syst. for K$^0_s$ and 0.021 $\pm$ 0.004 stat. $\pm$ 0.003 syst. for $\phi$. For baryons, we find = 0.048 $\pm$ 0.001 stat. $\pm$ 0.004 syst. for $\Lambda$, 0.047 $\pm$ 0.002 stat. $\pm$ 0.005 syst. for Anti-$\Lambda$ and 0.0101 $\pm$ 0.0020 stat. $\pm$ 0.0009 syst. for $\Xi$+Anti-$\Xi$. The results are also compared with predictions for identified particle spectra from QCD-inspired models and provide a baseline for comparisons with both future pp measurements at higher energies and heavy-ion collisions.Comment: 33 pages, 21 captioned figures, 10 tables, authors from page 28, published version, figures at http://aliceinfo.cern.ch/ArtSubmission/node/387