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

VALES VI: ISM enrichment in star-forming galaxies up to z∼\sim0.2 using 12^{12}CO(1-0), 13^{13}CO(1-0) and C18^{18}O(1-0) line luminosity ratios

We present Atacama Large Millimeter/sub-millimeter Array (ALMA) observations towards 27 low-redshift ($0.02< z<0.2$) star-forming galaxies taken from the Valpara\'iso ALMA/APEX Line Emission Survey (VALES). We perform stacking analyses of the $^{12}$CO($1-0$), $^{13}$CO($1-0$) and C$^{18}$O($1-0$) emission lines to explore the $L'$ ($^{12}$CO($1-0$))/$L'$($^{13}$CO($1-0$))) (hereafter $L'$($^{12}$CO)/$L'$($^{13}$CO)) and $L'$($^{13}$CO($1-0$))/$L'$(C$^{18}$O($1-0$)) (hereafter $L'$($^{13}$CO)/$L'$(C$^{18}$O) line luminosity ratio dependence as a function of different global galaxy parameters related to the star formation activity. The sample has far-IR luminosities $10^{10.1-11.9}$L$_{\odot}$ and stellar masses of $10^{9.8-10.9}$M$_{\odot}$ corresponding to typical star-forming and starburst galaxies at these redshifts. On average we find a $L'$($^{12}$CO)/$L'$($^{13}$CO) line luminosity ratio value of 16.1$\pm$2.5. Galaxies with evidences of possible merging activity tend to show higher $L'$($^{12}$CO)/$L'$($^{13}$CO) ratios by a factor of two, while variations of this order are also found in galaxy samples with higher star formation rates or star formation efficiencies. We also find an average $L'$($^{13}$CO)/$L'$(C$^{18}$O) line luminosity ratio of 2.5$\pm$0.6, which is in good agreement with those previously reported for starburst galaxies. We find that galaxy samples with high $L_{\text{IR}}$, SFR and SFE show low $L'$($^{13}$CO)/$L'$(C$^{18}$O) line luminosity ratios with high $L'$($^{12}$CO)/$L'$($^{13}$CO) line luminosity ratios, suggesting that these trends are produced by selective enrichment of massive stars in young starbursts.Comment: 16 pages, 10 figures to be published in MNRA

Synthesis of Densely Packaged, Ultrasmall Pt02Clusters within a Thioether-Functionalized MOF: Catalytic Activity in Industrial Reactions at Low Temperature

The gram\u2010scale synthesis, stabilization, and characterization of well\u2010defined ultrasmall subnanometric catalytic clusters on solids is a challenge. The chemical synthesis and X\u2010ray snapshots of Pt02 clusters, homogenously distributed and densely packaged within the channels of a metal\u2013organic framework, is presented. This hybrid material catalyzes efficiently, and even more importantly from an economic and environmental viewpoint, at low temperature (25 to 140\u2009\ub0C), energetically costly industrial reactions in the gas phase such as HCN production, CO2 methanation, and alkene hydrogenations. These results open the way for the design of precisely defined catalytically active ultrasmall metal clusters in solids for technically easier, cheaper, and dramatically less\u2010dangerous industrial reactions

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

Stormwater Analysis and Water Quality Assessment of Urban Areas

4400011482, PIT WO 14Salt is widely used for road deicing purpose in winter, and salt application could raise stream chloride level and leads to deterioration of water quality. This study represents the first steps toward developing a comprehensive understanding of how the streams chloride levels are impacted by the salt operation. Toward this goal, this study developed a procedure for the flow path modeling of urban watersheds and applied it to two sites in Pittsburgh, PA, which are potentially susceptible to road salt application by PennDOT. The procedure was used in identifying areas contributing flows to PennDOT right-of-way, and vice versa. This study further took stream water quality samples during non-winter months for establishing baselines and during the winters of 2017 and 2018. Results show that over the non-winter months, the baseline stream chloride concentration has already exceeded criteria continuous concentration most of the time, but lies below the criteria maximum concentration of the environmental regulation. Test results on winter samples show that stream chloride concentration has risen following salt application after snow events, and has exceeded the criteria maximum concentration. The study also shows how surface model of different detail levels would affect the identified contributing areas related to target watersheds, and the importance of properly incorporating roadway features such as curves and bridges

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

The bacterial community structure in an alkaline saline soil spiked with anthracene

Background: The application of polycyclic aromatic hydrocarbons (PAHs) will affect the bacterial community structure as some groups will be favoured and others not. An alkaline saline soil with electrolytic conductivity (EC) 56 dS m-1 was spiked with anthracene and acetone while their effect on bacterial community structure was investigated. Results: The percentages of Acidobacteria and Actinobacteria decreased over time, while the percentage of Proteobacteria, mostly Xanthomonadales, increased. The percentage of the phylotypes belonging to the Nocardioides , Rhodococcus and Streptomyces , known degraders of PAHs, was larger in the anthracene-amended soil than in the acetone-amended and unamended soil at day 14. The phylotypes belonging to the genera Sphingomonas , also a known degrader of PAHs, however, was lower. Weighted and unweighted PCoA with UniFrac indicated that phylotypes were similar in the different treatments at day 0, but changed at day 1. After 14 days, phylotypes in the unamended and acetone-amended soil were similar, but different from those in the anthracene-spiked soil. Conclusions: It was found that incubating the soil and contaminating it with anthracene changed the bacterial community structure, but spiking the soil with acetone had little or no effect on the bacterial community structure compared to the unamended soil

Comparison of proteomic responses as global approach to antibiotic mechanism of action elucidation

This is an open-access article distributed under the terms of the Creative Commons Attribution 4.0 International license. New antibiotics are urgently needed to address the mounting resistance challenge. In early drug discovery, one of the bottlenecks is the elucidation of targets and mechanisms. To accelerate antibiotic research, we provide a proteomic approach for the rapid classification of compounds into those with precedented and unprecedented modes of action. We established a proteomic response library of Bacillus subtilis covering 91 antibiotics and comparator compounds, and a mathematical approach was developed to aid data analysis. Comparison of proteomic responses (CoPR) allows the rapid identification of antibiotics with dual mechanisms of action as shown for atypical tetracyclines. It also aids in generating hypotheses on mechanisms of action as presented for salvarsan (arsphenamine) and the antirheumatic agent auranofin, which is under consideration for repurposing. Proteomic profiling also provides insights into the impact of antibiotics on bacterial physiology through analysis of marker proteins indicative of the impairment of cellular processes and structures. As demonstrated for trans-translation, a promising target not yet exploited clinically, proteomic profiling supports chemical biology approaches to investigating bacterial physiology

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

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