Finite dimensional semigroup quadratic algebras with the minimal number of relations

A quadratic semigroup algebra is an algebra over a field given by the generators x_1, . . . , x_n and a finite set of quadratic relations each of which either has the shape x_j x_k = 0 or the shape x_j x_k = x_l x_m . We prove that a quadratic semigroup algebra given by n generators and d=(n^2+n)/4 relations is always infinite dimensional. This strengthens the Golod–Shafarevich estimate for the above class of algebras. Our main result however is that for every n, there is a finite dimensional quadratic semigroup algebra with n generators and d_n relations, where d_n is the first integer greater than (n^2+n)/4 . That is, the above Golod–Shafarevich-type estimate for semigroup algebras is sharp.

Hypercyclic tuples of operators on $C^n$ and $R^n$

A tuple $(T_1,\dots,T_n)$ of continuous linear operators on a topological vector space $X$ is called hypercyclic if there is $x\in X$ such that the the orbit of $x$ under the action of the semigroup generated by $T_1,\dots,T_n$ is dense in $X$. This concept was introduced by N.~Feldman, who have raised 7 questions on hypercyclic tuples. We answer those 4 of them, which can be dealt with on the level of operators on finite dimensional spaces. In
particular, we prove that the minimal cardinality of a hypercyclic tuple of operators on $\C^n$ (respectively, on $\R^n$) is $n+1$ (respectively, $\frac n2+\frac{5+(-1)^n}{4}$), that there are non-diagonalizable tuples of operators on $\R^2$ which possess an orbit being neither dense nor nowhere dense and construct a hypercyclic 6-tuple of operators on $\C^3$ such that every operator commuting with each member of the tuple is non-cyclic.

On Quillen's calculation of graded K-theory

We adapt Quillen’s calculation of graded K-groups of Z-graded rings with support in N to graded K-theory, allowing gradings in a product Z×G with G an arbitrary group. This in turn allows us to use induction and calculate graded K-theory of Z -multigraded rings.

STO and GTO field-induced polarization functions for H to Kr

Field-induced polarization (FIP) functions were proposed over two decades ago to improve the accuracy of calculated response properties, and the FIP functions in GTO form for H and C to F were tested on small molecules, with encouraging results. The concept of FIP,is now extended to all atoms up to Kr. New simplifying approximations for the description of asymptotic highest occupied atomic orbitals. (HOAOs) are introduced in this study. They provide the basis for STO and GTO exponents of a complete set of FIP functions from H to Kr, which are both listed for the convenience of the users. Tests on the polarizabilities of a series of atoms and molecules demonstrate that addition of the FIP basis functions to a series' of standard basis sets drastically improves the performance of all these basis sets compared to converged results. Moreover, the byproduct of this study (approximate asymptotic HOAOs) provides information for the construction of accurate basis sets for long-range ground state properties. (C) 2003 Wiley Periodicals, Inc.

Deployment on GPUs of an application in computational atomic physics

This paper describes the deployment on GPUs of PROP, a program of the 2DRMP suite which models electron collisions with H-like atoms and ions. Because performance on GPUs is better in single precision than in double precision, the numerical stability of the PROP program in single precision has been studied. The numerical quality of PROP results computed in single precision and their impact on the next program of the 2DRMP suite has been analyzed. Successive versions of the PROP program on GPUs have been developed in order to improve its performance. Particular attention has been paid to the optimization of data transfers and of linear algebra operations. Performance obtained on several architectures (including NVIDIA Fermi) are presented.

Testing metabolic scaling theory using intraspecific allometries in Antarctic microarthropods

Quantitative scaling relationships among body mass, temperature and metabolic rate of organisms are still controversial, while resolution may be further complicated through the use of different and possibly inappropriate approaches to statistical analysis. We propose the application of a modelling strategy based on the theoretical approach of Akaike's information criteria and non-linear model fitting (nlm). Accordingly, we collated and modelled available data at intraspecific level on the individual standard metabolic rate of Antarctic microarthropods as a function of body mass (M), temperature (T), species identity (S) and high rank taxa to which species belong (G) and tested predictions from metabolic scaling theory (mass-metabolism allometric exponent b = 0.75, activation energy range 0.2-1.2 eV). We also performed allometric analysis based on logarithmic transformations (lm). Conclusions from lm and nlm approaches were different. Best-supported models from lm incorporated T, M and S. The estimates of the allometric scaling exponent linking body mass and metabolic rate resulted in a value of 0.696 +/- 0.105 (mean +/- 95% CI). In contrast, the four best-supported nlm models suggested that both the scaling exponent and activation energy significantly vary across the high rank taxa (Collembola, Cryptostigmata, Mesostigmata and Prostigmata) to which species belong, with mean values of b ranging from about 0.6 to 0.8. We therefore reached two conclusions: 1, published analyses of arthropod metabolism based on logarithmic data may be biased by data transformation; 2, non-linear models applied to Antarctic microarthropod metabolic rate suggest that intraspecific scaling of standard metabolic rate in Antarctic microarthropods is highly variable and can be characterised by scaling exponents that greatly vary within taxa, which may have biased previous interspecific comparisons that neglected intraspecific variability.

Global quantum correlations in finite-size spin chains

We perform an extensive study of the properties of global quantum correlations in finite-size one-dimensional quantum spin models at finite temperature. By adopting a recently proposed measure for global quantum correlations (Rulli and Sarandy 2011 Phys. Rev. A 84 042109), called global discord, we show that critical points can be neatly detected even for many-body systems that are not in their ground state. We consider the transverse Ising model, the cluster-Ising model where three-body couplings compete with an Ising-like interaction, and the nearest-neighbor XX Hamiltonian in transverse magnetic field. These models embody our canonical examples showing the sensitivity of global quantum discord close to criticality. For the Ising model, we find a universal scaling of global discord with the critical exponents pertaining to the Ising universality class.

Scaling of the entanglement spectrum near quantum phase transitions

The entanglement spectrum describing quantum correlations in many-body systems has been recently recognized as a key tool to characterize different quantum phases, including topological ones. Here we derive its analytically scaling properties in the vicinity of some integrable quantum phase transitions and extend our studies also to nonintegrable quantum phase transitions in one-dimensional spin models numerically. Our analysis shows that, in all studied cases, the scaling of the difference between the two largest nondegenerate Schmidt eigenvalues yields with good accuracy critical points and mass scaling exponents.

Why Northern Ireland’s Institutions Need Stability

Northern Ireland’s consociational institutions were reviewed by a committee of its Assembly in 2012–13. The arguments of both critics and exponents of the arrangements are of general interest to scholars of comparative politics, powersharing and constitutional design. The authors of this article review the debates and evidence on the d’Hondt rule of executive formation, political designation, the likely impact of changing district magnitudes for assembly elections, and existing patterns of opposition and accountability. They evaluate the scholarly, political and legal literature before commending the merits of maintaining the existing system, including the rules under which the system might be modified in future.

Economies of scaling: More evidence that allometry of metabolism is linked to activity, metabolic rate and habitat

Organismal metabolic rates influence many ecological processes, and the mass-specific metabolic rate of organisms decreases with increasing body mass according to a power law. The exponent in this equation is commonly thought to be the three-quarter-power of body mass, determined by fundamental physical laws that extend across taxa. However, recent work has cast doubt as to the universality of this relationship, the value of 0.75 being an interspecies 'average' of scaling exponents that vary naturally between certain boundaries. There is growing evidence that metabolic scaling varies significantly between even closely related species, and that different values can be associated with lifestyle, activity and metabolic rates. Here we show that the value of the metabolic scaling exponent varies within a group of marine ectotherms, chitons (Mollusca: Polyplacophora: Mopaliidae), and that differences in the scaling relationship may be linked to species-specific adaptations to different but overlapping microhabitats. Oxygen consumption rates of six closely related, co-occurring chiton species from the eastern Pacific (Vancouver Island, British Columbia) were examined under controlled experimental conditions. Results show that the scaling exponent varies between species (between 0.64 and 0.91). Different activity levels, metabolic rates and lifestyle may explain this variation. The interspecific scaling exponent in these data is not significantly different from the archetypal 0.75 value, even though five out of six species-specific values are significantly different from that value. Our data suggest that studies using commonly accepted values such as 0.75 derived from theoretical models to extrapolate metabolic data of species to population or community levels should consider the likely variation in exponents that exists in the real world, or seek to encompass such error in their models. This study, as in numerous previous ones, demonstrates that scaling exponents show large, naturally occurring variation, and provides more evidence against the existence of a universal scaling law. © 2012 Elsevier B.V.

K-Theory of Azumaya Algebras over Schemes

Let X be a connected, noetherian scheme and A{script} be a sheaf of Azumaya algebras on X, which is a locally free O{script}-module of rank a. We show that the kernel and cokernel of K(X) ? K(A{script}) are torsion groups with exponent a for some m and any i = 0, when X is regular or X is of dimension d with an ample sheaf (in this case m = d + 1). As a consequence, K(X, Z/m) ? K(A{script}, Z/m), for any m relatively prime to a. © 2013 Copyright Taylor and Francis Group, LLC.

Finite domination and Novikov rings: Laurent polynomial rings in two variables

Let C be a bounded cochain complex of finitely generatedfree modules over the Laurent polynomial ring L = R[x, x−1, y, y−1].The complex C is called R-finitely dominated if it is homotopy equivalentover R to a bounded complex of finitely generated projective Rmodules.Our main result characterises R-finitely dominated complexesin terms of Novikov cohomology: C is R-finitely dominated if andonly if eight complexes derived from C are acyclic; these complexes areC ⊗L R[[x, y]][(xy)−1] and C ⊗L R[x, x−1][[y]][y−1], and their variants obtainedby swapping x and y, and replacing either indeterminate by its inverse.

Rational equivariant rigidity

We prove that if G is S1 or a profinite group, then all of the homotopical information of the category of rational G-spectra is captured by the triangulated structure of the rational G-equivariant stable homotopy category.

That is, for G profinite or S1, the rational G-equivariant stable homotopy category is rigid. For the case of profinite groups this rigidity comes from an intrinsic formality statement, so we carefully relate the notion of intrinsic formality of a differential graded algebra to rigidity.

Full characterization of the quantum linear-zigzag transition in atomic chains

A string of repulsively interacting particles exhibits a phase transition to a zigzag structure, by reducing the transverse trap potential or the interparticle distance. Based on the emergent symmetry Z2 it has been argued that this instability is a quantum phase transition, which can be mapped to an Ising model in transverse field. An extensive Density Matrix Renormalization Group analysis is performed, resulting in an high-precision evaluation of the critical exponents and of the central charge of the system, confirming that the quantum linear-zigzag transition belongs to the critical Ising model universality class. Quantum corrections to the classical phase diagram are computed, and the range of experimental parameters where quantum effects play a role is provided. These results show that structural instabilities of one-dimensional interacting atomic arrays can simulate quantum critical phenomena typical of ferromagnetic systems.