A ferromagnet with a glass transition

We introduce a finite-connectivity ferromagnetic model with a three-spin interaction which has a crystalline (ferromagnetic) phase as well as a glass phase. The model is not frustrated, it has a ferromagnetic equilibrium phase at low temperature which is not reached dynamically in a quench from the high-temperature phase. Instead it shows a glass transition which can be studied in detail by a one step replica-symmetry broken calculation. This spin model exhibits the main properties of the structural glass transition at a solvable mean-field level.Comment: 7 pages, 2 figures, uses epl.cls (included

Almost clean rings and arithmetical rings

It is shown that a commutative B\'ezout ring $R$ with compact minimal prime spectrum is an elementary divisor ring if and only if so is $R/L$ for each minimal prime ideal $L$. This result is obtained by using the quotient space $\mathrm{pSpec} R$ of the prime spectrum of the ring $R$ modulo the equivalence generated by the inclusion. When every prime ideal contains only one minimal prime, for instance if $R$ is arithmetical, $\mathrm{pSpec} R$ is Hausdorff and there is a bijection between this quotient space and the minimal prime spectrum $\mathrm{Min} R$, which is a homeomorphism if and only if $\mathrm{Min} R$ is compact. If $x$ is a closed point of $\mathrm{pSpec} R$, there is a pure ideal $A(x)$ such that $x=V(A(x))$. If $R$ is almost clean, i.e. each element is the sum of a regular element with an idempotent, it is shown that $\mathrm{pSpec} R$ is totally disconnected and, $\forall x\in\mathrm{pSpec} R$, $R/A(x)$ is almost clean; the converse holds if every principal ideal is finitely presented. Some questions posed by Facchini and Faith at the second International Fez Conference on Commutative Ring Theory in 1995, are also investigated. If $R$ is a commutative ring for which the ring $Q(R/A)$ of quotients of $R/A$ is an IF-ring for each proper ideal $A$, it is proved that $R_P$ is a strongly discrete valuation ring for each maximal ideal $P$ and $R/A$ is semicoherent for each proper ideal $A$

КВАЗИПЕРИОДИЧЕСКИЕ АЛГЕБРЫ, ИНВАРИАНТНЫЕ ОТНОСИТЕЛЬНО ЛИНЕЙНОГО ОТОБРАЖЕНИЯ

In this paper we consider the following problem. Let A0 be some quasi-periodic subalgebra of the algebra of almost periodic functions on Rm and a : Rm → Rm, a(x) = Mx, is a linear map defined by a square matrix of size m. There exists the smallest closed subalgebra A+, containing A0 and invariant under α, and there exists the smallest closed subalgebra A, containing A0, invariant under α and α–1. We obtain conditions on the linear map α when these subalgebras are quasi-periodic.В работе рассмотрена следующая задача. Пусть A0 есть некоторая квазипериодическая подалгебра в алгебре почти периодических функций на Rm и a : Rm → Rm, α(x) = Mx, – линейное отображение, задаваемое квадратной матрицей размера m.  Существует наименьшая замкнутая подалгебра A+ , содержащая A0 и инвариантная относительно α, и существует наименьшая замкнутая подалгебра A, содержащая A0, инвариантная относительно α и α–1. В работе получены условия на линейное отображение α, при которых эти подалгебры являются квазипериодическими

Toward an Unsteady Aerodynamic ROM for Multiple Mach Regimes

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/97065/1/AIAA2012-1708.pd

On the chromatic number of random geometric graphs

Given independent random points X_1,...,X_n\in\eR^d with common probability distribution $\nu$, and a positive distance $r=r(n)>0$, we construct a random geometric graph $G_n$ with vertex set $\{1,...,n\}$ where distinct $i$ and $j$ are adjacent when \norm{X_i-X_j}\leq r. Here \norm{.} may be any norm on \eR^d, and $\nu$ may be any probability distribution on \eR^d with a bounded density function. We consider the chromatic number $\chi(G_n)$ of $G_n$ and its relation to the clique number $\omega(G_n)$ as $n \to \infty$. Both McDiarmid and Penrose considered the range of $r$ when $r \ll (\frac{\ln n}{n})^{1/d}$ and the range when $r \gg (\frac{\ln n}{n})^{1/d}$, and their results showed a dramatic difference between these two cases. Here we sharpen and extend the earlier results, and in particular we consider the `phase change' range when $r \sim (\frac{t\ln n}{n})^{1/d}$ with $t>0$ a fixed constant. Both McDiarmid and Penrose asked for the behaviour of the chromatic number in this range. We determine constants $c(t)$ such that $\frac{\chi(G_n)}{nr^d}\to c(t)$ almost surely. Further, we find a "sharp threshold" (except for less interesting choices of the norm when the unit ball tiles $d$-space): there is a constant $t_0>0$ such that if $t \leq t_0$ then $\frac{\chi(G_n)}{\omega(G_n)}$ tends to 1 almost surely, but if $t > t_0$ then $\frac{\chi(G_n)}{\omega(G_n)}$ tends to a limit $>1$ almost surely.Comment: 56 pages, to appear in Combinatorica. Some typos correcte

Surface free energy of polyurethane coatings with improved hydrophobicity

The polarity of polyurethane coats was studied on the basis of the goniometric method for determination of wetting angle values, on the basis of calculated surface free energy (SFE) values by the van Oss–Good and Owens–Wendt methods, and on the basis of polarity measurements with the use of the 1H NMR spectra. Test polyurethanes were synthesised in the reaction of methylene diphenyl 4,4′-diisocyanate (MDI) or 3-izocyanatomethyl –3,5,5- trimethylcyclohexyl isocyanate (IPDI) and polyoxyethylene glycols or polyesters poly(ε-caprolactone) diols and poly(ethyleneadipate) diol with different molecular weights, and some diols as chain extenders, in dioxane. The type of raw material was found to significantly affect the phase structure of the obtained polyurethane elastomers and to control physical interactions within those structures, thus influencing the SFE values. Fundamental reduction in the SFE value of a coating below 28 mJ/m2 was achieved by the use of 2,2,3,3-tetrafluoro-1,4-butanediol as the urethane prepolymer chain extender

Statistical method on nonrandom clustering with application to somatic mutations in cancer

<p>Abstract</p> <p>Background</p> <p>Human cancer is caused by the accumulation of tumor-specific mutations in oncogenes and tumor suppressors that confer a selective growth advantage to cells. As a consequence of genomic instability and high levels of proliferation, many passenger mutations that do not contribute to the cancer phenotype arise alongside mutations that drive oncogenesis. While several approaches have been developed to separate driver mutations from passengers, few approaches can specifically identify activating driver mutations in oncogenes, which are more amenable for pharmacological intervention.</p> <p>Results</p> <p>We propose a new statistical method for detecting activating mutations in cancer by identifying nonrandom clusters of amino acid mutations in protein sequences. A probability model is derived using order statistics assuming that the location of amino acid mutations on a protein follows a uniform distribution. Our statistical measure is the differences between pair-wise order statistics, which is equivalent to the size of an amino acid mutation cluster, and the probabilities are derived from exact and approximate distributions of the statistical measure. Using data in the Catalog of Somatic Mutations in Cancer (COSMIC) database, we have demonstrated that our method detects well-known clusters of activating mutations in KRAS, BRAF, PI3K, and <it>β</it>-catenin. The method can also identify new cancer targets as well as gain-of-function mutations in tumor suppressors.</p> <p>Conclusions</p> <p>Our proposed method is useful to discover activating driver mutations in cancer by identifying nonrandom clusters of somatic amino acid mutations in protein sequences.</p

A Latent Variable Partial Least Squares Path Modeling Approach to Regional Association and Polygenic Effect with Applications to a Human Obesity Study

Genetic association studies are now routinely used to identify single nucleotide polymorphisms (SNPs) linked with human diseases or traits through single SNP-single trait tests. Here we introduced partial least squares path modeling (PLSPM) for association between single or multiple SNPs and a latent trait that can involve single or multiple correlated measurement(s). Furthermore, the framework naturally provides estimators of polygenic effect by appropriately weighting trait-attributing alleles. We conducted computer simulations to assess the performance via multiple SNPs and human obesity-related traits as measured by body mass index (BMI), waist and hip circumferences. Our results showed that the associate statistics had type I error rates close to nominal level and were powerful for a range of effect and sample sizes. When applied to 12 candidate regions in data (N = 2,417) from the European Prospective Investigation of Cancer (EPIC)-Norfolk study, a region in FTO was found to have stronger association (rs7204609∼rs9939881 at the first intron P = 4.29×10−7) than single SNP analysis (all with P>10−4) and a latent quantitative phenotype was obtained using a subset sample of EPIC-Norfolk (N = 12,559). We believe our method is appropriate for assessment of regional association and polygenic effect on a single or multiple traits