Haplotype inferring via galled-tree networks using a hypergraph covering problem for special genotype matrices

Since exact determination of haplotype blocks is usually not possible, it is desirable to develop a haplotyping method which can account for recombinations. A natural candidate for such a method is haplotyping via phylogenetic networks or their simplified version: galled-tree networks. In earlier work we characterized the existence of the galled-tree networks. Building on this, we reduce the problem of haplotype inferring via galled-tree networks to a hypergraph covering problem for genotype matrices satisfying a combinatorial condition. Our experiments on actual data show that this condition is almost always satisfied when the percentage of minor alleles for each SNP reaches at least 30%.     

Closure for the property of having a hamiltonian prism

We prove that a graph G of order n has a hamiltonian prism if and only if the graph Cl_4n/3–4/3(G) has a hamiltonian prism where Cl_4n/3–4/3(G) is the graph obtained from G by sequential adding edges between non‐adjacent vertices whose degree sum is at least 4n/3–4/3. We show that this cannot be improved to less than 4n/3–5. © 2006 Wiley Periodicals, Inc. J Graph Theory 54: 209–220, 2007     

The fourth power of the Fermat quotient

Let p be an odd prime and qp(a)=(ap−1−1)/p be the Fermat quotient with base a, p?a. The main purpose of this paper is to investigate the fourth power problem of qp(2) and deduce an explicit formula represented by a linear combination of Mirimanoff polynomial values.     

Calcium and strontium thio­sulfate,CaS2O3·6H2O and SrS2O3·5H2O

In contrast to former morphological studies, the results presented here show that calcium(II) thio­sulfate hexahydrate, CaS₂O₃·6H₂O, crystallizes centrosymmetrically in the pinacoidal class (point group ). The structure is characterized by chains, parallel to [100], of alternating S₂O₃ and Ca(H₂O)₆O₂ groups sharing common O atoms. The composition of each chain link is [Ca(H₂O)₆(S₂O₃)]. The geometry is analysed and compared in detail with the structural features of monoclinic strontium(II) thio­sulfate pentahydrate, SrS₂O₃·5H₂O, which forms layers, parallel to (100), of alternating S₂O₃ and Sr(H₂O)₄O₅ groups connected via common O atoms and O–O edges. Each layer contains [Sr(H₂O)₃O(S₂O₃)]_∞ as the unique repeat unit.     

Three novel non‐centrosymmetric compounds of glycine: glycine lithium sulfate,glycine nickel dichloride dihydrate and glycine zinc sulfate trihydrate

The crystal structures of three compounds of glycine and inorganic materials are presented and discussed. The ortho­rhombic structure of glycinesulfatodilithium(I), [Li₂(SO₄)(C₂H₅NO₂)]_n, consists of corrugated sheets of [LiO₄] and [SO₄] tetrahedra. The glycine mol­ecules are located between these sheets. The main features of the monoclinic structure of di­aqua­di­chloro­glycinenickel(II), [NiCl₂(C₂H₅NO₂)(H₂O)₂]_n, are helical chains of [NiO₄Cl₂] octahedra connected by glycine mol­ecules. The orthorhombic structure of tri­aqua­glycinesulfatozinc(II), [Zn(SO₄)(C₂H₅NO₂)(H₂O)₃]_n, is made up of [O₃SOZnO₅] clusters. These clusters are linked by glycine mol­ecules into zigzag chains. All three compounds are examples of non‐centrosymmetric glycine compounds.     

Logarithmic Finite-Size Correction in Non-neutral Two-Component Plasma on Sphere

We consider a general two-component plasma of classical pointlike charges \(+e\) (e is say the elementary charge) and \(-Z e\) (valency \(Z=1,2,\ldots \)), living on the surface of a sphere of radius R. The system is in thermal equilibrium at the inverse temperature \(\beta \), in the stability region against collapse of oppositely charged particle pairs \(\beta e^2 < 2/Z\). We study the effect of the system excess charge Qe on the finite-size expansion of the (dimensionless) grand potential \(\beta \varOmega \). By combining the stereographic projection of the sphere onto an infinite plane, the linear response theory and the planar results for the second moments of the species density correlation functions we show that for any \(\beta e^2 < 2/Z\) the large-R expansion of the grand potential is of the form \(\beta \varOmega \sim A_V R^2 + \left[ \chi /6 - \beta (Qe)^2/2\right] \ln R\), where \(A_V\) is the non-universal coefficient of the volume (bulk) part and the Euler number of the sphere \(\chi =2\). The same formula, containing also a non-universal surface term proportional to R, was obtained previously for the disc domain (\(\chi =1\)), in the case of the symmetric \((Z=1)\) two-component plasma at the collapse point \(\beta e^2=2\) and the jellium model \((Z\rightarrow 0)\) of identical e-charges in a fixed neutralizing background charge density at any coupling \(\beta e^2\) being an even integer. Our result thus indicates that the prefactor to the logarithmic finite-size expansion does not depend on the composition of the Coulomb fluid and its non-universal part \(-\beta (Qe)^2/2\) is independent of the geometry of the confining domain.     

Finite-Size Effects in Non-neutral Two-Dimensional Coulomb Fluids

Thermodynamic potential of a neutral two-dimensional (2D) Coulomb fluid, confined to a large domain with a smooth boundary, exhibits at any (inverse) temperature \(\beta \) a logarithmic finite-size correction term whose universal prefactor depends only on the Euler number of the domain and the conformal anomaly number \(c=-1\). A minimal free boson conformal field theory, which is equivalent to the 2D symmetric two-component plasma of elementary \(\pm e\) charges at coupling constant \(\Gamma =\beta e^2\), was studied in the past. It was shown that creating a non-neutrality by spreading out a charge Qe at infinity modifies the anomaly number to \(c(Q,\Gamma ) = - 1 + 3\Gamma Q^2\). Here, we study the effect of non-neutrality on the finite-size expansion of the free energy for another Coulomb fluid, namely the 2D one-component plasma (jellium) composed of identical pointlike e-charges in a homogeneous background surface charge density. For the disk geometry of the confining domain we find that the non-neutrality induces the same change of the anomaly number in the finite-size expansion. We derive this result first at the free-fermion coupling \(\Gamma \equiv \beta e^2=2\) and then, by using a mapping of the 2D one-component plasma onto an anticommuting field theory formulated on a chain, for an arbitrary even coupling constant.     

Observation of stimulated Raman scattering in polar tetragonal crystals of barium antimony tartrate trihydrate,Ba[Sb2((+)C4H2O6)2]·3H2O

The non‐centrosymmetric polar tetragonal (P 4₁) barium antimony tartrate trihydrate, Ba[Sb₂((+)C₄H₂O₆)₂]·3H₂O, was found to be an attractive novel semi‐organic crystal manifesting numerous χ ⁽²⁾‐ and χ ⁽³⁾‐nonlinear optical interactions. In particular, with picosecond single‐ and dual‐wavelength pumping SHG and THG via cascaded parametric four‐wave processes were observed. High‐order Stokes and anti‐Stokes lasing related to two SRS‐promoting vibration modes of the crystal, with ω_SRS1 ≈ 575 cm^?1 and ω_SRS2 ≈ 2940 cm^?1, takes place. Basing on a spontaneous Raman investigation an assignment of the two SRS‐active vibration modes is discussed.

     

A novel analytical model and energy analysis of thermal stresses in two-phase composites

This paper deals with analytical modelling of thermal stresses in a multi-particle-matrix system with isotropic spherical particles. These particles are periodically distributed in an isotropic infinite matrix. This model system which is characterized by microstructural parameters (particle volume fraction, particle radius) is applicable to two-phase composites of a precipitate-matrix type with isotropic phases. The thermal stresses originate during a cooling process due to a difference in thermal expansion coefficients. The analytical modelling which is based on fundamental equations of solid continuum mechanics represents a combination of different mathematical procedures applied to equilibrium and compatibility equations. This novel analytical model is compared with that which is based on mathematical procedures applied to the equilibrium equations only. The energy analysis of both analytical models which is applied to the SiC-Al₂O₃ composite is presented.