Improved bounds for Hadwiger's covering problem via thin-shell estimates

A central problem in discrete geometry, known as Hadwiger's covering problem, asks what the smallest natural number $N\left(n\right)$ is such that every convex body in ${\mathbb R}^{n}$ can be covered by a union of the interiors of at most $N\left(n\right)$ of its translates. Despite continuous efforts, the best general upper bound known for this number remains as it was more than sixty years ago, of the order of ${2n \choose n}n\ln n$. In this note, we improve this bound by a sub-exponential factor. That is, we prove a bound of the order of ${2n \choose n}e^{-c\sqrt{n}}$ for some universal constant $c>0$. Our approach combines ideas from previous work by Artstein-Avidan and the second named author with tools from Asymptotic Geometric Analysis. One of the key steps is proving a new lower bound for the maximum volume of the intersection of a convex body $K$ with a translate of $-K$; in fact, we get the same lower bound for the volume of the intersection of $K$ and $-K$ when they both have barycenter at the origin. To do so, we make use of measure concentration, and in particular of thin-shell estimates for isotropic log-concave measures. Using the same ideas, we establish an exponentially better bound for $N\left(n\right)$ when restricting our attention to convex bodies that are $\psi_{2}$. By a slightly different approach, an exponential improvement is established also for classes of convex bodies with positive modulus of convexity

Extremal spacings between eigenphases of random unitary matrices and their tensor products

Extremal spacings between eigenvalues of random unitary matrices of size N pertaining to circular ensembles are investigated. Explicit probability distributions for the minimal spacing for various ensembles are derived for N = 4. We study ensembles of tensor product of k random unitary matrices of size n which describe independent evolution of a composite quantum system consisting of k subsystems. In the asymptotic case, as the total dimension N = n^k becomes large, the nearest neighbor distribution P(s) becomes Poissonian, but statistics of extreme spacings P(s_min) and P(s_max) reveal certain deviations from the Poissonian behavior

FOXA1 repression is associated with loss of BRCA1 and increased promoter methylation and chromatin silencing in breast cancer

FOXA1 expression correlates with the breast cancer luminal subtype and patient survival. RNA and protein analysis of a panel of breast cancer cell lines revealed that BRCA1 deficiency is associated with the downregulation of FOXA1 expression. Knockdown of BRCA1 resulted in the downregulation of FOXA1 expression and enhancement of FOXA1 promoter methylation in MCF-7 breast cancer cells, whereas the reconstitution of BRCA1 in Brca1-deficent mouse mammary epithelial cells (MMECs) promoted Foxa1 expression and methylation. These data suggest that BRCA1 suppresses FOXA1 hypermethylation and silencing. Consistently, the treatment of MMECs with the DNA methylation inhibitor 5-aza-2'-deoxycitydine induced Foxa1 mRNA expression. Furthermore, treatment with GSK126, an inhibitor of EZH2 methyltransferase activity, induced FOXA1 expression in BRCA1-deficient but not in BRCA1-reconstituted MMECs. Likewise, the depletion of EZH2 by small interfering RNA enhanced FOXA1 mRNA expression. Chromatin immunoprecipitation (ChIP) analysis demonstrated that BRCA1, EZH2, DNA methyltransferases (DNMT)1/3a/3b and H3K27me3 are recruited to the endogenous FOXA1 promoter, further supporting the hypothesis that these proteins interact to modulate FOXA1 methylation and repression. Further co-immunoprecipitation and ChIP analysis showed that both BRCA1 and DNMT3b form complexes with EZH2 but not with each other, consistent with the notion that BRCA1 binds to EZH2 and negatively regulates its methyltransferase activity. We also found that EZH2 promotes and BRCA1 impairs the deposit of the gene silencing histone mark H3K27me3 on the FOXA1 promoter. These associations were validated in a familial breast cancer patient cohort. Integrated analysis of the global gene methylation and expression profiles of a set of 33 familial breast tumours revealed that FOXA1 promoter methylation is inversely correlated with the transcriptional expression of FOXA1 and that BRCA1 mutation breast cancer is significantly associated with FOXA1 methylation and downregulation of FOXA1 expression, providing physiological evidence to our findings that FOXA1 expression is regulated by methylation and chromatin silencing and that BRCA1 maintains FOXA1 expression through suppressing FOXA1 gene methylation in breast cancer.Oncogene advance online publication, 22 December 2014; doi:10.1038/onc.2014.421.published_or_final_versio

Trolley-bus transportation versus the cultural landscape of Tychy

W artykule przedstawiono zarys rozwoju komunikacji trolejbusowej w Tychach oraz wybrane elementy krajobrazu kulturowego tego miasta roztaczające się wzdłuż tras linii trolejbusowych. Przebieg tras trolejbusowych daje możliwość poznania jedynego w swoim rodzaju miasta zaplanowanego i konsekwentnie realizowanego jako miasto o dominującej funkcji mieszkaniowej. W zagospodarowaniu przestrzeni Tychów odzwierciedlają się wszystkie tendencje urbanistyczno-architektoniczne realizowane w Polsce po II wojnie światowej, od socrealizmu charakterystycznego dla lat 50. XX w., poprzez wielokondygnacyjne bloki z „wielkiej płyty” do deweloperskich osiedli jedno- i wielorodzinnych XXI w. Podróż trolejbusem umożliwia poznanie różnorodnych architektonicznie i funkcjonalnie osiedli tworzących niepowtarzalny krajobraz miasta zaplanowanego jako „ sypialnia” dla Górnośląskiego Okręgu Przemysłowego.The article presents an outline of trolley-bus transportation in Tychy, as well as selected elements of the cultural landscape of the city extending along trolley-bus lines. The trolley-bus routes provide the possibility to get to know a city unique in its kind - designed and consistently developed as a city with a dominating residential function. The space development of Tychy reflects all urban and architectural tendencies realized in Poland after World War II, from socialist realism characteristic of the 1950s, through prefab high-rises, to developed single- and multi-family apartment complexes. Travelling by trolley-bus allows one to familiarize themselves with the architecturally and functionally diverse housing complexes that create the unique landscape of the city designed to be a sleeper city for the Upper-Silesian Industrial Region

Sharp Rosenthal-type inequalities for mixtures and log-concave variables

Funder: Trinity College, CambridgeWe obtain Rosenthal‐type inequalities with sharp constants for moments of sums of independent random variables which are mixtures of a fixed distribution. We also identify extremizers in log‐concave settings when the moments of summands are individually constrained

The influence of zinc on properties of common cements

W pracy omówiono wyniki badań dotyczących wpływu cynku na właściwości cementów. Celem artykułu było wyjaśnienie niektórych ważnych problemów związanych ze zwiększonym dodatkiem cynku, a także różnic wynikających z dodawania związków cynku bezpośrednio do cementu oraz do zestawu surowcowego do produkcji klinkieru portlandzkiego. Omówiono także wpływ cynkano-glinianów wapnia, które powstają w klinkierze ze zwiększoną zawartością cynku w składzie surowcowym, na właściwości cementów. Przedstawiono również opis ostatnich badań dotyczących granicznej zawartości cynku (dodawanego wraz z surowcami), po przekroczeniu której następuje gwałtowne pogorszenie właściwości cementu.In the paper the results of recent studies of the zinc influence on cement properties are presented. The aim of this work was clarification of some important issues associated with higher zinc content, and also the explanation of the differences, which result from the way of zinc introduction i.e. addition of zinc compounds directly to cement and to the raw mix to Portland clinker production. The influence of zinc phases, which form in clinker with higher zinc content in raw mix, on cement properties was also discussed. Description of recent studies concerning the limit zinc content (added with raw materials), which exceeding causes rapid deterioration of cement properties

Molding properties of blast furnace slag cements with addition of granular blast furnace slag with different glassy phase content

W artykule przedstawiono wyniki badań właściwości cementów żużlowych wykonanych z granulowanego żużla wielkopiecowego o różnej zawartości fazy szklistej. Program badań obejmował próbki żużla o wyraźnie zróżnicowanej zawartości fazy szklistej od 58 do 99% masy. Przygotowano cementy CEM II/A-S, CEM II/B-S i hutniczy CEM III/A, zawierające odpowiednio 15, 30 i 60% masy żużla. Badano podstawowe właściwości cementów, będące przedmiotem wymagań i oceny zgodności norm PN-EN 197-1 i PN-EN 15167-1. Na podstawie uzyskanych wyników badań potwierdzono, że największy wpływ na aktywność hydrauliczną żużla ma zawartość fazy szklistej. Drugim ważnym parametrem oceny aktywności żużla jest jego współczynnik aktywności (CaO + MgO/SiO2). Przy tej samej zawartości fazy szklistej, im większy współczynnik aktywności, tym żużel wykazuje większą aktywność hydrauliczną. Wyniki badań cementów żużlowych potwierdzają te zależności. Spośród badanego żużla krajowego i zagranicznego, największe wskaźniki aktywności hydraulicznej wykazał żużel z Huty Katowice i Huty Sendzimira, zawierający odpowiednio 99 i 88% fazy szklistej; miały one zdecydowanie lepsze właściwości w porównaniu do żużla sprowadzanego w ostatnich latach w dużych ilościach z importu.Test results of properties of slag cements made of granulated blast furnace slag of different glassy phase content are presented in the paper. Research covered samples of blast furnace slags of significantly diverse glassy phase content, from 58% up to 99% by mass. Cements CEM II/A-S, CEM II/B-S and CEM III/A containing 15%, 30% and 60% of slag respectively have been prepared. Basic properties of cements, being a subject of requirements and conformity assessment of standard PN-EN 197-1 and PN-EN 15167-1, have been tested. On the basis of obtained test results it has been confirmed that the glassy phase content has the highest impact on the hydraulic activity of blast furnace slag. The oxides ratio (CaO + MgO/SiO2) of blast furnace slag is the second important parameter of its evaluation. With the same glassy phase content the higher is the oxides ratio the higher hydraulic activity of blast furnace slag is indicated. Test results of slag cements confirm these relationships. Among examined of domestic and foreign blast furnace slags the highest hydraulic activity indexes have been indicated by slags from Huta Katowice and Huta Sendzimir containing 99% and 98% of glassy phase respectively; they have had definitely better properties comparing to foreign blast furnace slags imported in high amounts during recent years

The Effect of Extrusion in the Complex Strain State on the Microstructure and Mechanical Properties of MgAlZn Magnesium Alloys

The paper presents the results of tests concerning the effect of the extrusion process in the complex strain state on the microstructure and properties of one of magnesium alloy with aluminium, zinc and manganese, designated AZ61. Due to its specific gravity, it is increasingly being used in the automotive and aerospace industries to reduce the weight of structural elements. As a result of plastic deformation processes, rods with a diameter of 8, 6 and 4 mm were obtained from AZ61 magnesium alloy. The microstructure analysis was performed using light and electron microscopy (STEM) techniques in the initial state and afterplastic deformation. Microstructure studies were supplemented with a quantitative analysis using the Metilo program. A number of stereological parameters were determined: average diameter of grain, shape factor. A static tensile test was carried out at 250ºC and 300ºC, at deformation rates of 0.01, 0.001 and 0.0001 m·s-1. Better plastic properties after deformation using KoBo methodwere obtained than with conventional extrusion

The Influence of Deformation Method on the Microstructure and Properties of Magnesium Alloy WE43

The article presents tests results of the influence of deformation methods on the microstructure and properties of alloy WE43. There were direct extrusion tests and extrusion with KoBo method performed. An assessment of the influence of the methods of deformation on the microstructure and the mechanical properties of the achieved rods from alloy WE43 was conducted. There was an analysis of microstructure carried out with the use of light and scanning microscopy techniques in the initial state and after plastic deformation. Static tensile test was conducted in temperature of 350°C at a speed of 0.0001 m·s-1 and microhardness measurements were performed of HV0.2. On the basis of the achieved mechanical tests results it was stated that in the temperature of 350°C for samples deformed with the use of KoBo method there was an effect of superplastic flow found. The value of elongation achieved was 250% which was 3 times higher than in case of classic extrusion (80%)