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.

IMPROVED POSTFILTERING TECHNIQUE FOR BLOCK QUANTISATION OF SPEECH.

A modified comb filtering technique is proposed which can be used to reduce framing noise generated when speech signals are transform-coded or vector-quantized. Application of this filter to 9. 6 kbit/s speech in a vector transform coder has been found to improve the perceptual quality of the coded speech.

Systolic array system for vector quantization using transformed sub-band coding.

The use of bit-level systolic arrays in the design of a vector quantized transformed subband coding system for speech signals is described. It is shown how the major components of this system can be decomposed into a small number of highly regular building blocks that interface directly to one another. These include circuits for the computation of the discrete cosine transform, the inverse discrete cosine transform, and vector quantization codebook search.

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.

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.

Advancing impact prediction and hypothesis testing in invasion ecology using a comparative functional response approach

Invasion ecology urgently requires predictive methodologies that can forecast the ecological impacts of existing, emerging and potential invasive species. We argue that many ecologically damaging invaders are characterised by their more efficient use of resources. Consequently, comparison of the classical ‘functional response’ (relationship between resource use and availability) between invasive and trophically analogous native species may allow prediction of invader ecological impact. We review the utility of species trait comparisons and the history and context of the use of functional responses in invasion ecology, then present our framework for the use of comparative functional responses. We show that functional response analyses, by describing the resource use of species over a range of resource availabilities, avoids many pitfalls of ‘snapshot’ assessments of resource use. Our framework demonstrates how comparisons of invader and native functional responses, within and between Type II and III functional responses, allow testing of the likely population-level outcomes of invasions for affected species. Furthermore, we describe how recent studies support the predictive capacity of this method; for example, the invasive ‘bloody red shrimp’ Hemimysis anomala shows higher Type II functional responses than native mysids and this corroborates, and could have predicted, actual invader impacts in the field. The comparative functional response method can also be used to examine differences in the impact of two or more invaders, two or more populations of the same invader, and the abiotic (e.g. temperature) and biotic (e.g. parasitism) context-dependencies of invader impacts. Our framework may also address the previous lack of rigour in testing major hypotheses in invasion ecology, such as the ‘enemy release’ and ‘biotic resistance’ hypotheses, as our approach explicitly considers demographic consequences for impacted resources, such as native and invasive prey species. We also identify potential challenges in the application of comparative functional responses in invasion ecology. These include incorporation of numerical responses, multiple predator effects and trait-mediated indirect interactions, replacement versus non-replacement study designs and the inclusion of functional responses in risk assessment frameworks. In future, the generation of sufficient case studies for a meta-analysis could test the overall hypothesis that comparative functional responses can indeed predict invasive species impacts.

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.

Existing and emerging high impact invasive species are characterized by higher functional responses than natives

Predicting ecological impacts of invasive species and identifying potentially damaging future invaders are research priorities. Since damage by invaders is characterized by their depletion of resources, comparisons of the ‘functional response’ (FR; resource uptake rate as a function of resource density) of invaders and natives might predict invader impact. We tested this by comparing FRs of the ecologically damaging ‘world's worst’ invasive fish, the largemouth bass (Micropterus salmoides), with a native equivalent, the Cape kurper (Sandelia capensis), and an emerging invader, the sharptooth catfish (Clarias gariepinus), with the native river goby (Glossogobius callidus), in South Africa, a global invasion hotspot. Using tadpoles (Hyperolius marmoratus) as prey, we found that the invaders consumed significantly more than natives. Attack rates at low prey densities within invader/native comparisons reflected similarities in predatory strategies; however, both invasive species displayed significantly higher Type II FRs than the native comparators. This was driven by significantly lower prey handling times by invaders, resulting in significantly higher maximum feeding rates. The higher FRs of these invaders are thus congruent with, and can predict, their impacts on native communities. Comparative FRs may be a rapid and reliable method for predicting ecological impacts of emerging and future invasive species.

Reconstructing the quantum state of oscillator networks with a single qubit

We introduce a scheme to reconstruct arbitrary states of networks composed of quantum oscillators-e. g., the motionalstate of trapped ions or the radiation state of coupled cavities. The scheme involves minimal resources and minimal access, in the sense that it (i) requires only the interaction between a one-qubit probe and a single node of the network; (ii) provides the Weyl characteristic function of the network directly from the data, avoiding any tomographic transformation; (iii) involves the tuning of only one coupling parameter. In addition, we show that a number of quantum properties can be extracted without full reconstruction of the state. The scheme can be used for probing quantum simulations of anharmonic many-body systems and quantum computations with continuous variables. Experimental implementation with trapped ions is also discussed and shown to be within reach of current technology.

Tackling Invasive Alien Species in Europe: the Top 20 Issues

Globally, Invasive Alien Species (IAS) are considered to be one of the major threats to native biodiversity, with the World Conservation Union (IUCN) citing their impacts as ?immense, insidious, and usually irreversible?. It is estimated that 11% of the c. 12,000 alien species in Europe are invasive, causing environmental, economic and social damage; and it is reasonable to expect that the rate of biological invasions into Europe will increase in the coming years. In order to assess the current position regarding IAS in Europe and to determine the issues that were deemed to be most important or critical regarding these damaging species, the international Freshwater Invasives - Networking for Strategy (FINS) conference was convened in Ireland in April 2013. Delegates from throughout Europe and invited speakers from around the world were brought together for the conference. These comprised academics, applied scientists, policy makers, politicians, practitioners and representative stakeholder groups. A horizon scanning and issue prioritization approach was used by in excess of 100 expert delegates in a workshop setting to elucidate the Top 20 IAS issues in Europe. These issues do not focus solely on freshwater habitats and taxa but relate also to marine and terrestrial situations. The Top 20 issues that resulted represent a tool for IAS management and should also be used to support policy makers as they prepare European IAS legislation.

Habitat simplification increases the impact of a freshwater invasive fish

Biodiversity continues to decline at a range of spatial scales and there is an urgent requirement to understand how multiple drivers interact in causing such declines. Further, we require methodologies that can facilitate predictions of the effects of such drivers in the future. Habitat degradation and biological invasions are two of the most important threats to biodiversity and here we investigate their combined effects, both in terms of understanding and predicting impacts on native species. The predatory largemouth bass Micropterus salmoides is one of the World’s Worst Invaders, causing declines in native prey species, and its introduction often coincides with habitat simplification. We investigated the predatory functional response, as a measure of ecological impact, of juvenile largemouth bass in artificial vegetation over a range of habitat complexities (high, intermediate, low and zero). Prey, the female guppy Poecilia reticulata, were representative of native fish. As habitats became less complex, significantly more prey were consumed, since, even although attack rates declined, reduced handling times resulted in higher maximum feeding rates by bass. At all levels of habitat complexity, bass exhibited potentially population destabilising Type II functional responses, with no emergence of more stabilising Type III functional responses as often occurs in predator-prey relationships in complex habitats. Thus, habitat degradation and simplification potentially exacerbate the impact of this invasive species, but even highly complex habitats may ultimately not protect native species. The utilisation of functional responses under varying environmental contexts provides a method for the understanding and prediction of invasive species impacts.

Theory of phonon dissipation in the conduction of stressed Au nanowires

Recent experiments on Au break junctions [Phys. Rev. Lett. 88 (2002) 216803] have characterized the nonlinear conductance of stretched short Au nanowires. They reveal in the voltage range 10-20 meV the signatures of dissipation effects, likely due to phonons in the nanowire, reducing the conductance below the quantized value of 2e(2)/h. We present here a theory, based on a model tight-binding Hamiltonian and on non-equilibrium Green's function techniques, which accounts for the main features of the experiment. The theory helps in revealing details of the experiment which need to be addressed with a more realistic, less idealized, theoretical framework. (C) 2004 Elsevier B.V. All rights reserved.

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.