Gonc̆arov polynomials and parking functions

AbstractLet u be a sequence of non-decreasing positive integers. A u-parking function of length n is a sequence (x1,x2,…,xn) whose order statistics (the sequence (x(1),x(2),…,x(n)) obtained by rearranging the original sequence in non-decreasing order) satisfy x(i)⩽ui. The Gonc̆arov polynomials gn(x;a0,a1,…,an−1) are polynomials defined by the biorthogonality relation:ε(ai)Dign(x;a0,a1,…,an−1)=n!δin,where ε(a) is evaluation at a and D is the differentiation operator. In this paper we show that Gonc̆arov polynomials form a natural basis of polynomials for working with u-parking functions. For example, the number of u-parking functions of length n is (−1)ngn(0;u1,u2,…,un). Various properties of Gonc̆arov polynomials are discussed. In particular, Gonc̆arov polynomials satisfy a linear recursion obtained by expanding xn as a linear combination of Gonc̆arov polynomials, which leads to a decomposition of an arbitrary sequence of positive integers into two subsequences: a “maximum” u-parking function and a subsequence consisting of terms of higher values. Many counting results for parking functions can be derived from this decomposition. We give, as examples, formulas for sum enumerators, and a linear recursion and Appell relation for factorial moments of sums of u-parking functions

Parent Actions, Dualities and New Weyl-invariant Actions of Bosonic p-branes

By using the systematic approach of parent action method, we derive one Weyl-noninvariant and two Weyl-invariant actions of bosonic $p$-branes ($p\geq 2$) starting from the Nambu-Goto action, and establish the duality symmetries in this set of four actions. Moreover, we discover a new bosonic $p$-brane action (including the string theory) and deduce two corresponding Weyl-invariant formulations by proposing a new special parent action. We find that the same duality symmetries as those mentioned above exist in this new set of actions. The new $p$-brane actions are also briefly analyzed.Comment: 19 pages, 14 figures. The first section is modified slightly, and references are adde

Predictive biometrics: A review and analysis of predicting personal characteristics from biometric data

Interest in the exploitation of soft biometrics information has continued to develop over the last decade or so. In comparison with traditional biometrics, which focuses principally on person identification, the idea of soft biometrics processing is to study the utilisation of more general information regarding a system user, which is not necessarily unique. There are increasing indications that this type of data will have great value in providing complementary information for user authentication. However, the authors have also seen a growing interest in broadening the predictive capabilities of biometric data, encompassing both easily definable characteristics such as subject age and, most recently, `higher level' characteristics such as emotional or mental states. This study will present a selective review of the predictive capabilities, in the widest sense, of biometric data processing, providing an analysis of the key issues still adequately to be addressed if this concept of predictive biometrics is to be fully exploited in the future

Calcium-Mediated Protein Folding and Stabilisation of Salmonella Biofilm-Associated Protein a

Biofilm-associated proteins (BAPs) are important for early biofilm formation (adhesion) by bacteria and are also found in mature biofilms. BapA from Salmonella is a ~386 kDa surface protein, comprised of 27 tandem repeats predicted to be bacterial Ig-like (BIg) domains. Such tandem repeats are conserved for BAPs across different bacterial species, but the function of these domains is not completely understood. In this work, we report the first study of the mechanical stability of the BapA protein. Using magnetic tweezers, we show that the folding of BapA BIg domains requires calcium- binding and the folded domains have differential mechanical stabilities. Importantly, we identify that >100 nM concentration of calcium is needed for folding of the BIg domains, and the stability of the folded BIg domains is regulated by calcium over a wide concentration range from sub-micromolar (?M) to millimolar (mM). Only at mM calcium concentrations, as found in the extracellular environment, do the BIg domains have the saturated mechanical stability. BapA has been suggested to be involved in Salmonella invasion, and it is likely a crucial mechanical component of biofilms. Therefore, our results provide new insights into the potential roles of BapA as a structural maintenance component of Salmonella biofilm and also Salmonella invasion

Stochastic association of neighboring replicons creates replication factories in budding yeast

Peer reviewedPublisher PD

The geology of Tianshui‐Qin'an area of the western Loess Plateau and the chemical characteristics of its Neolithic pottery

The difference in the chemical compositions between Neolithic pottery from the eastern and western ends of the northern Chinese Loess Plateau has been known for some time and a number of possible explanations have been proposed. However, a full understanding of the difference is yet to be achieved. Based on recent geological studies of the Tianshui-Qin’an area on the western Loess Plateau, the present study establishes a logical connection between the chemical characteristics of Neolithic pottery from the western Loess Plateau and the primary sediments available in the area. Moreover, this study reveals that the chemical compositions of clay used for fine wares and coarse wares at Dadiwan also bear some clear differences. Based on these findings, the paper discusses possible clay selection methods by potters in the Neolithic western Loess Plateau to make their different wares based on the locales where suitable raw materials are available. The paper demonstrates that the raw materials available for pottery making on the eastern and western Loess Plateau differ significantly and this explains the marked difference in ceramic composition between the two locations

van der Waals coefficients for positronium-atom interactions

The van der Waals coefficients for positronium interactions with a number of rare gases (He, Ne, Ar, Kr, and Xe) and alkali-metal atoms (Li, Na, K, and Rb) are estimated using a variety of ab initio and semiempirical methods. Dispersion coefficients are also presented for atomic hydrogen and a number of rare-gas and alkali-metal atoms for validation purposes

Modelling spectral and timing properties of accreting black holes: the hybrid hot flow paradigm

The general picture that emerged by the end of 1990s from a large set of optical and X-ray, spectral and timing data was that the X-rays are produced in the innermost hot part of the accretion flow, while the optical/infrared (OIR) emission is mainly produced by the irradiated outer thin accretion disc. Recent multiwavelength observations of Galactic black hole transients show that the situation is not so simple. Fast variability in the OIR band, OIR excesses above the thermal emission and a complicated interplay between the X-ray and the OIR light curves imply that the OIR emitting region is much more compact. One of the popular hypotheses is that the jet contributes to the OIR emission and even is responsible for the bulk of the X-rays. However, this scenario is largely ad hoc and is in contradiction with many previously established facts. Alternatively, the hot accretion flow, known to be consistent with the X-ray spectral and timing data, is also a viable candidate to produce the OIR radiation. The hot-flow scenario naturally explains the power-law like OIR spectra, fast OIR variability and its complex relation to the X-rays if the hot flow contains non-thermal electrons (even in energetically negligible quantities), which are required by the presence of the MeV tail in Cyg X-1. The presence of non-thermal electrons also lowers the equilibrium electron temperature in the hot flow model to <100 keV, making it more consistent with observations. Here we argue that any viable model should simultaneously explain a large set of spectral and timing data and show that the hybrid (thermal/non-thermal) hot flow model satisfies most of the constraints.Comment: 26 pages, 13 figures. To be published in the Space Science Reviews and as hard cover in the Space Sciences Series of ISSI - The Physics of Accretion on to Black Holes (Springer Publisher

Physical Property Characterization of Bulk MgB2 Superconductor

We report synthesis, structure/micro-structure, resistivity under magnetic field [R(T)H], Raman spectra, thermoelectric power S(T), thermal conductivity K(T), and magnetization of ambient pressure argon annealed polycrystalline bulk samples of MgB2, processed under identical conditions. The compound crystallizes in hexagonal structure with space group P6/mmm. Transmission electron microscopy (TEM) reveals electron micrographs showing various types of defect features along with the presence of 3-4nm thick amorphous layers forming the grain boundaries of otherwise crystalline MgB2. Raman spectra of the compound at room temperature exhibited characteristic phonon peak at 600 cm-1. Superconductivity is observed at 37.2K by magnetic susceptibility C(T), resistivity R(T), thermoelectric power S(T), and thermal conductivity K(T) measurements. The power law fitting of R(T) give rise to Debye temperature at 1400K which is found consistent with the theoretical fitting of S(T), exhibiting ThetaD of 1410K and carrier density of 3.81x 1028/m3. Thermal conductivity K(T) shows a jump at 38K, i.e., at Tc, which was missing in some earlier reports. Critical current density (Jc) of up to 105 A/cm2 in 1-2T (Tesla) fields at temperatures (T) of up to 10K is seen from magnetization measurements. The irreversibility field, defined as the field related to merging of M(H) loops is found to be 78, 68 and 42 kOe at 4, 10 and 20K respectively. The superconducting performance parameters viz. irreversibility field (Hirr) and critical current density Jc(H) of the studied MgB2 are improved profoundly with addition of nano-SiC and nano-Diamond. The physical property parameters measured for polycrystalline MgB2 are compared with earlier reports and a consolidated insight of various physical properties is presented.Comment: 41 pages TEXT+Fig

Search for direct production of charginos and neutralinos in events with three leptons and missing transverse momentum in √s = 7 TeV pp collisions with the ATLAS detector

A search for the direct production of charginos and neutralinos in final states with three electrons or muons and missing transverse momentum is presented. The analysis is based on 4.7 fb−1 of proton–proton collision data delivered by the Large Hadron Collider and recorded with the ATLAS detector. Observations are consistent with Standard Model expectations in three signal regions that are either depleted or enriched in Z-boson decays. Upper limits at 95% confidence level are set in R-parity conserving phenomenological minimal supersymmetric models and in simplified models, significantly extending previous results