The conjugacy problem for two-by-two matrices over polynomial rings

We give an effective solution of the conjugacy problem for two-by-two matrices over the polynomial ring in one variable over a finite field.

Performance Analysis of Randomized Distributed Space-Time Codes over Composite Gamma/Lognormal Fading Channels

This work investigates the end-to-end performance of randomized distributed space-time codes with complex Gaussian distribution, when employed in a wireless relay network. The relaying nodes are assumed to adopt a decode-and-forward strategy and transmissions are affected by small and large scale fading phenomena. Extremely tight, analytical approximations of the end-to-end symbol error probability and of the end-to-end outage probability are derived and successfully validated through Monte-Carlo simulation. For the high signal-to-noise ratio regime, a simple, closed-form expression for the symbol error probability is further provided.

Finite domination and Novikov rings. Iterative approach

Suppose C is a bounded chain complex of finitely generated free modules over the Laurent polynomial ring L = R[x,x -1]. Then C is R-finitely dominated, i.e. homotopy equivalent over R to a bounded chain complex of finitely generated projective R-modules if and only if the two chain complexes C ? L R((x)) and C ? L R((x -1)) are acyclic, as has been proved by Ranicki (A. Ranicki, Finite domination and Novikov rings, Topology 34(3) (1995), 619–632). Here R((x)) = R[[x]][x -1] and R((x -1)) = R[[x -1]][x] are rings of the formal Laurent series, also known as Novikov rings. In this paper, we prove a generalisation of this criterion which allows us to detect finite domination of bounded below chain complexes of projective modules over Laurent rings in several indeterminates.

Data Mapping for Unreliable Memories

Future digital signal processing (DSP) systems must provide robustness on algorithm and application level to the presence of reliability issues that come along with corresponding implementations in modern semiconductor process technologies. In this paper, we address this issue by investigating the impact of unreliable memories on general DSP systems. In particular, we propose a novel framework to characterize the effects of unreliable memories, which enables us to devise novel methods to mitigate the associated performance loss. We propose to deploy specifically designed data representations, which have the capability of substantially improving the system reliability compared to that realized by conventional data representations used in digital integrated circuits, such as 2's-complement or sign-magnitude number formats. To demonstrate the efficacy of the proposed framework, we analyze the impact of unreliable memories on coded communication systems, and we show that the deployment of optimized data representations substantially improves the error-rate performance of such systems.

Triangular Objects and Systematic K-Theory

We investigate modules over “systematic” rings. Such rings are “almost graded” and have appeared under various names in the literature; they are special cases of the G-systems of Grzeszczuk. We analyse their K-theory in the presence of conditions on the support, and explain how this generalises and unifies calculations of graded and filtered K-theory scattered in the literature. Our treatment makes systematic use of the formalism of idempotent completion and a theory of triangular objects in additive categories, leading to elementary and transparent proofs throughout.

Finite domination and Novikov homology over strongly Z-graded rings

Let L be a unital Z-graded ring, and let C be a bounded chain complex of finitely generated L-modules. We give a homological characterisation of when C is homotopy equivalent to a bounded complex of finitely generated projective L0-modules, generalising known results for twisted Laurent polynomial rings. The crucial hypothesis is that L is a strongly graded ring. 

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.

Finite domination and Novikov rings. Laurent polynomial rings in several variables

We present a homological characterisation of those chain complexes of modules over a Laurent polynomial ring in several indeterminates which are finitely dominated over the ground ring (that is, are a retract up to homotopy of a bounded complex of finitely generated free modules). The main tools, which we develop in the paper, are a non-standard totalisation construction for multi-complexes based on truncated products, and a high-dimensional mapping torus construction employing a theory of cubical diagrams that commute up to specified coherent homotopies.

Finite Element Simulations of stretch-blow moulding with experimental validation over a broad process window

Injection stretch blow moulding is a well-established method of forming thin-walled containers and has been extensively researched for numerous years. This paper is concerned with validating the finite element analysis of the free-stretch-blow process in an effort to progress the development of injection stretch blow moulding of poly(ethylene terephthalate). Extensive data was obtained experimentally over a wide process window accounting for material temperature and air flow rate, while capturing cavity pressure, stretch-rod reaction force and preform surface strain. This data was then used to assess the accuracy of the correlating FE simulation constructed using ABAQUS/Explicit solver and an appropriate viscoelastic material subroutine. Results reveal that the simulation is able to give good quantitative correlation for conditions where the deformation was predominantly equal biaxial whilst qualitative correlation was achievable when the mode of deformation was predominantly sequential biaxial. Overall the simulation was able to pick up the general trends of how the pressure, reaction force, strain rate and strain vary with the variation in preform temperature and air flow rate. The knowledge gained from these analyses provides insight into the mechanisms of bottle formation, subsequently improving the blow moulding simulation and allowing for reduction in future development costs.

In vitro release of nonoxynol-9 from silicone matrix intravaginal rings

The controlled-release characteristics of matrix silicone intravaginal rings loaded with between 100 and 971 mg of nonoxynol-9 have been investigated with a view to developing a ring that may offer a new female-controlled method for the prevention of transmission of sexually transmitted diseases, particularly HIV. Intravaginal rings containing 253, 487 and 971 mg of nonoxynol-9 provided a daily release of 2 mg or more over the 8-day release period, the minimal amount of nonoxynol-9 considered to provide an effective vaginal concentration for the prevention of HIV. Furthermore, the maximum daily release of N9 was about 6 mg, an amount significantly smaller than that observed for other nonoxynol-9 products whose large daily doses may in fact increase the occurrence of HIV by causing epithelial damage to the vaginal tissue. The release mechanism of the liquid nonoxynol-9 from the intravaginal rings has also been investigated and compared to models describing the release of solid drugs from the rings. It has been demonstrated through release studies and surface microscopy that a drug depletion zone is not established in such liquid-loaded intravaginal ring systems, with implications for the release kinetics. (C) 2003 Elsevier B.V. All rights reserved.

Dimension theory and nonstable K1 of quadratic modules

Employing Bak’s dimension theory, we investigate the nonstable quadratic K-group K1,2n(A, ) = G2n(A, )/E2n(A, ), n 3, where G2n(A, ) denotes the general quadratic group of rank n over a form ring (A, ) and E2n(A, ) its elementary subgroup. Considering form rings as a category with dimension in the sense of Bak, we obtain a dimension filtration G2n(A, ) G2n0(A, ) G2n1(A, ) E2n(A, ) of the general quadratic group G2n(A, ) such that G2n(A, )/G2n0(A, ) is Abelian, G2n0(A, ) G2n1(A, ) is a descending central series, and G2nd(A)(A, ) = E2n(A, ) whenever d(A) = (Bass–Serre dimension of A) is finite. In particular K1,2n(A, ) is solvable when d(A) <.

Numerical ‘health check’ for scientific codes: the CADNA approach

Scientific computation has unavoidable approximations built into its very fabric. One important source of error that is difficult to detect and control is round-off error propagation which originates from the use of finite precision arithmetic. We propose that there is a need to perform regular numerical `health checks' on scientific codes in order to detect the cancerous effect of round-off error propagation. This is particularly important in scientific codes that are built on legacy software. We advocate the use of the CADNA library as a suitable numerical screening tool. We present a case study to illustrate the practical use of CADNA in scientific codes that are of interest to the Computer Physics Communications readership. In doing so we hope to stimulate a greater awareness of round-off error propagation and present a practical means by which it can be analyzed and managed.

Safety and Pharmacokinetics of Dapivirine Delivery From Matrix and Reservoir Intravaginal Rings to HIV-Negative Women

Vaginal microbicides for the prevention of HIV transmission may be an important option for protecting women from infection. Incorporation of dapivirine, a lead candidate nonnucleoside reverse transcriptase inhibitor, into intravaginal rings (IVRs) for sustained mucosal delivery may increase microbicide product adherence and efficacy compared with conventional vaginal formulations. Twentyfour
healthy HIV-negative women 18–35 years of age were randomly assigned (1:1:1) to dapivirine matrix IVR, dapivirine reservoir IVR, or placebo IVR. Dapivirine concentrations were measured in plasma
and vaginal fluid samples collected at sequential time points over the 33-day study period (28 days of IVR use, 5 days of follow-up). Safety was assessed by pelvic/colposcopic examinations, clinical laboratory tests, and adverse events. Both IVR types were safe and well tolerated with similar adverse events observed in the placebo and dapivirine groups. Dapivirine from both IVR types was successfully distributed throughout the lower genital tract at concentrations over 4 logs greater than the EC50 against wild-type HIV-1 (LAI) in MT4 cells. Maximum concentration (Cmax) and area under the concentration–time curve (AUC) values were significantly higher with the matrix than reservoir IVR. Mean plasma concentrations of dapivirine were ,2 ng/mL. These findings suggest that IVR delivery of microbicides is a viable option meriting further study.