Convex Hull of Planar H-Polyhedra

Suppose are planar (convex) H-polyhedra, that is, $A_i \in \mathbb{R}^{n_i \times 2}$ and $\vec{c}_i \in \mathbb{R}^{n_i}$. Let $P_i = \{\vec{x} \in \mathbb{R}^2 \mid A_i\vec{x} \leq \vec{c}_i \}$ and $n = n_1 + n_2$. We present an $O(n \log n)$ algorithm for calculating an H-polyhedron with the smallest $P = \{\vec{x} \in \mathbb{R}^2 \mid A\vec{x} \leq \vec{c} \}$ such that $P_1 \cup P_2 \subseteq P$

Automatic Abstraction for Congruences

One approach to verifying bit-twiddling algorithms is to derive invariants between the bits that constitute the variables of a program. Such invariants can often be described with systems of congruences where in each equation $\vec{c} \cdot \vec{x} = d \mod m$, (unknown variable m)$is a power of two,$\vec{c}$is a vector of integer coefficients, and$\vec{x}$ is a vector of propositional variables (bits). Because of the low-level nature of these invariants and the large number of bits that are involved, it is important that the transfer functions can be derived automatically. We address this problem, showing how an analysis for bit-level congruence relationships can be decoupled into two parts: (1) a SAT-based abstraction (compilation) step which can be automated, and (2) an interpretation step that requires no SAT-solving. We exploit triangular matrix forms to derive transfer functions efficiently, even in the presence of large numbers of bits. Finally we propose program transformations that improve the analysis results

Cognitive and neural signatures of the APOE E4 allele in mid-aged adults

The apolipoprotein E (APOE) e4 allele is strongly associated with increased risk of cognitive impairments in older adulthood. There is also a possible link to enhanced cognitive performance in younger adults, and the APOE e4 allele may constitute an example of antagonistic pleiotropy. The aim of this work was to investigate the cognitive and neural (functional) effects of the APOE e4 allele during mid-age (45-55 years), where a transition toward cognitive deficit might be expected. APOE e4 carriers (e4+) were compared with non-e4 carriers (e4-) on tasks of sustained and covert attention and prospective memory, and functional magnetic resonance imaging data acquired. Performance by e4+ was equivalent or better than e4- on all 3 tasks, although performance benefits were less pronounced than in youth. Neurally, e4+ showed less task-related recruitment of extrastriate and parietal areas. This became more evident when neural activation data were compared with that of young adults acquired in a parallel study. As expected, mid-age participants showed more diffuse neural activation. Notable was the fact that e4+ showed a relative inability to recruit parietal regions as they aged. This was coupled with a tendency to show greater recruitment of frontal regions, and underactivation of extrastriate visual regions. Thus, mid-age e4+ show a pattern of neural recruitment usually seen later in life, possibly reflecting the source of an accelerated aging profile that describes the e4 genotype

Mid age APOE ε4 carriers show memory-related functional differences and disrupted structure-function relationships in hippocampal regions

Carriers of the APOE e4 allele are at higher risk of age-related cognitive decline and Alzheimer's disease (AD). The underlying neural mechanisms are uncertain, but genotype differences in medial temporal lobe (MTL) functional activity and structure at mid-age might contribute. We tested 16 non-e4 and 16 e4 carriers (aged 45-55) on a subsequent memory task in conjunction with MRI to assess how hippocampal volume (from T1 structural) and microstructure (neurite orientation-dispersion, from NODDI) differs by genotype and in relation to memory encoding. No previous study has investigated APOE effects on hippocampal microstructure using NODDI. Recall performance did not differ by genotype. A genotype by condition interaction in left parahippocampus indicated that in e4 carriers activity did not differentiate subsequently remembered from forgotten words. Hippocampal volumes and microstructure also did not differ by genotype but hippocampal volumes correlated positively with recognition performance in non-e4 carriers only. Similarly, greater hippocampal neurite orientation-dispersion was linked to better recall but only in non-e4s. Thus, we suggest that mid-age e4 carriers show a breakdown of normal MTL activation and structure-performance relationships. This could reflect an inability to utilise compensatory mechanisms, and contribute to higher risk of cognitive decline and AD in later life

Warp propagation in astrophysical discs

Astrophysical discs are often warped, that is, their orbital planes change with radius. This occurs whenever there is a non-axisymmetric force acting on the disc, for example the Lense-Thirring precession induced by a misaligned spinning black hole, or the gravitational pull of a misaligned companion. Such misalignments appear to be generic in astrophysics. The wide range of systems that can harbour warped discs - protostars, X-ray binaries, tidal disruption events, quasars and others - allows for a rich variety in the disc's response. Here we review the basic physics of warped discs and its implications.Comment: To be published in Astrophysical Black Holes by Haardt et al., Lecture Notes in Physics, Springer 2015. 19 pages, 2 figure

Median-based generation of synthetic speech durations using a non-parametric approach

This paper proposes a new approach to duration modelling for statistical parametric speech synthesis in which a recurrent statistical model is trained to output a phone transition probability at each timestep (acoustic frame). Unlike conventional approaches to duration modelling -- which assume that duration distributions have a particular form (e.g., a Gaussian) and use the mean of that distribution for synthesis -- our approach can in principle model any distribution supported on the non-negative integers. Generation from this model can be performed in many ways; here we consider output generation based on the median predicted duration. The median is more typical (more probable) than the conventional mean duration, is robust to training-data irregularities, and enables incremental generation. Furthermore, a frame-level approach to duration prediction is consistent with a longer-term goal of modelling durations and acoustic features together. Results indicate that the proposed method is competitive with baseline approaches in approximating the median duration of held-out natural speech.Comment: 7 pages, 1 figure -- Accepted for presentation at IEEE Workshop on Spoken Language Technology (SLT 2016

Improving Dispersion of Recycled Discontinuous Carbon Fibres to Increase Fibre Throughput in the HiPerDiF Process

In order to increase the material throughput of aligned discontinuous fibre composites using technologies such as HiPerDiF, stability of the carbon fibres in an aqueous solution needs to be achieved. Subsequently, a range of surfactants, typically employed to disperse carbon-based materials, have been assessed to determine the most appropriate for use in this regard. The optimum stability of the discontinuous fibres was observed when using the anionic surfactant, sodium dodecylbenzene sulphonate, which was superior to a range of other non-ionic and anionic surfactants, and single-fibre fragmentation demonstrated that the employment of sodium dodecylbenzene sulphonate did not affect the interfacial adhesion between fibres. Rheometry was used to complement the study, to understand the potential mechanisms of the improved stability of discontinuous fibres in aqueous suspension, and it led to the understanding that the increased viscosity was a significant factor. For the shear rates employed, fibre deformation was neither expected nor observed

Multiplicativity of completely bounded p-norms implies a new additivity result

We prove additivity of the minimal conditional entropy associated with a quantum channel Phi, represented by a completely positive (CP), trace-preserving map, when the infimum of S(gamma_{12}) - S(gamma_1) is restricted to states of the form gamma_{12} = (I \ot Phi)(| psi >< psi |). We show that this follows from multiplicativity of the completely bounded norm of Phi considered as a map from L_1 -> L_p for L_p spaces defined by the Schatten p-norm on matrices; we also give an independent proof based on entropy inequalities. Several related multiplicativity results are discussed and proved. In particular, we show that both the usual L_1 -> L_p norm of a CP map and the corresponding completely bounded norm are achieved for positive semi-definite matrices. Physical interpretations are considered, and a new proof of strong subadditivity is presented.Comment: Final version for Commun. Math. Physics. Section 5.2 of previous version deleted in view of the results in quant-ph/0601071 Other changes mino

Inflation dynamics and the output-inflation trade-off: international panel data evidence

We explore the impact of inflation and its variability on the output-inflation trade-off using a unified single-step approach in a panel data context. A limitation of earlier empirical approaches is that they focus on either cross-country or country-by-country time-series analyses. This paper employs a dynamic heterogeneous panel data specification and uses an all-encompassing estimation framework that accounts for parameter heterogeneity, cross-sectional dependence, dynamics, and non-stationarity. Our sample covers 60 countries from 1970 to 2010. While inflation variability reduces the trade-off for specific periods and country groups, an unambiguous and more pronounced negative relation emerges between the inflation rate and the responsiveness of real output to nominal shocks. The findings are in line with the New Keynesian view of a negative association between the rate of inflation and the output-inflation trade-off, as well as with the observed flattening of the Phillips curve over the past decades