Closable multipliers

Let $(X,\mu)$ and $(Y,\nu)$ be standard measure spaces. A function $\nph\in L^\infty(X\times Y,\mu\times\nu)$ is called a (measurable) Schur multiplier if the map $S_\nph$, defined on the space of Hilbert-Schmidt operators from $L_2(X,\mu)$ to $L_2(Y,\nu)$ by multiplying their integral kernels by $\nph$, is bound-ed in the operator norm. The paper studies measurable functions $\nph$ for which $S_\nph$ is closable in the norm topology or in the weak* topology. We obtain a characterisation of w*-closable multipliers and relate the question about norm closability to the theory of operator synthesis. We also study multipliers of two special types: if $\nph$ is of Toeplitz type, that is, if $\nph(x,y)=f(x-y)$, $x,y\in G$, where $G$ is a locally compact abelian group, then the closability of $\nph$ is related to the local inclusion of $f$ in the Fourier algebra $A(G)$ of $G$. If $\nph$ is a divided difference, that is, a function of the form $(f(x)-f(y))/(x-y)$, then its closability is related to the ``operator smoothness'' of the function $f$. A number of examples of non closable, norm closable and w*-closable multipliers are presented.

A hypercyclic finite rank perturbation of a unitary operator

A unitary operator V and a rank 2 operator R acting on a Hilbert space H are constructed such that V + R is hypercyclic. This answers affirmatively a question of Salas whether a finite rank perturbation of a hyponormal operator can be supercyclic.

Faithful test of nonlocal realism with entangled coherent states

We investigate the violation of Leggett's inequality for nonlocal realism using entangled coherent states and various types of local measurements. We prove mathematically the relation between the violation of the Clauser-Horne-Shimony-Holt form of Bell's inequality and Leggett's one when tested by the same resources. For Leggett inequalities, we generalize the nonlocal realistic bound to systems in Hilbert spaces larger than bidimensional ones and introduce an optimization technique that allows one to achieve larger degrees of violation by adjusting the local measurement settings. Our work describes the steps that should be performed to produce a self-consistent generalization of Leggett's original arguments to continuous-variable states.

In-situ strength assessment of concrete - The European Concrete Frame Building Project (Reprinted from Non-Destructive Testing Civil Engineering, April, pg 583-592, 2000)

A full-scale seven-storey in-situ advanced reinforced concrete building frame was constructed in the Building Research Establishment's Cardington laboratory encompassing a range of different concrete mixes and construction techniques. This provided an opportunity to use in-situ non-destructive test methods, namely Lok and CAPO tests, on a systematic basis during the construction of the building. They were used in conjunction with both standard and temperature-matched cube specimens to assess their practicality and their individual capabilities under field conditions. Results have been analysed and presented to enable comparisons of the performance of the individual test methods employed.

The use of recycled demolition aggregate in precast concrete products – Phase III: Concrete pavement flags

A study undertaken at the University of Liverpool has investigated the potential for using construction and demolition waste (C&DW) derived aggregate in the manufacture of a range of precast concrete products, i.e. building and paving blocks and pavement flags. Phase III, which is reported here, investigated
concrete pavement flags. This was subsequent to studies on building and paving blocks. Recycled demolition aggregate can be used to replace newly quarried limestone aggregate, usually used in coarse (6 mm) and fine (4 mm-to-dust) gradings. The first objective was, as was the case with concrete building
and paving blocks, to replicate the process used by industry in fabricating concrete pavement flags in the laboratory. The ‘‘wet’’ casting technique used by industry for making concrete flags requires a very workable mix so that the concrete flows into the mould before it is compressed. Compression squeezes out water from the top as well as the bottom of the mould. This industrial casting procedure was successfully replicated in the laboratory by using an appropriately modified cube crushing machine and a special mould typical of what is used by industry. The mould could be filled outside of the cube crushing machine and then rolled onto a steel frame and into the machine for it to be compressed. The texture and mechanical properties of the laboratory concrete flags were found to be similar to the factory ones. The experimental work involved two main series of tests, i.e. concrete flags made with concrete- and
masonry-derived aggregate. Investigation of flexural strength was required for concrete paving flags. This is different from building blocks and paving blocks which required compressive and tensile splitting strength respectively. Upper levels of replacement with recycled demolition aggregate were determined
that produced similar flexural strength to paving flags made with newly quarried aggregates, without requiring an increase in the cement content. With up to 60% of the coarse or 40% of the fine fractions replaced with concrete-derived aggregates, the target mean flexural strength of 5.0 N/mm2 was still
achieved at the age of 28 days. There was similar detrimental effect by incorporating the fine masonry-derived aggregate. A replacement level of 70% for coarse was found to be satisfactory and also conservative. However, the fine fraction replacement could only be up to 30% and even reduced to 15% when used for mixes where 60% of the coarse fraction was also masonry-derived aggregate.

Disjoint mixing operators

Chan and Shapiro showed that each (non-trivial) translation operator acting on the Fréchet space of entire functions endowed with the topology of locally uniform convergence supports a universal function of exponential type zero. We show the existence of d-universal functions of exponential type zero for arbitrary finite tuples of pairwise distinct translation operators. We also show that every separable infinite-dimensional Fréchet space supports an arbitrarily large finite and commuting disjoint mixing collection of operators. When this space is a Banach space, it supports an arbitrarily large finite disjoint mixing collection of C0-semigroups. We also provide an easy proof of the result of Salas that every infinite-dimensional Banach space supports arbitrarily large tuples of dual d-hypercyclic operators, and construct an example of a mixing Hilbert space operator T so that (T,T2) is not d-mixing.

Diastereoselective 1,3-dipolar cycloaddition of pyrylium ylides with chiral enamides

Chiral enamides5f-i were found to react with pyrylium ylides to give cycloadducts 6d-i in good yields with an excellent level of stereoselectivity. The chiral auxiliary was successfully removed on hydrogenolysis of compound 6f in continuous flow (H-Cube) resulting in the first asymmetric synthesis of complex amine 8.

Almost all quantum states have nonclassical correlations

Quantum discord quantifies nonclassical correlations in a quantum system including those not captured by entanglement. Thus, only states with zero discord exhibit strictly classical correlations. We prove that these states are negligible in the whole Hilbert space: typically a state picked out at random has positive discord and, given a state with zero discord, a generic arbitrarily small perturbation drives it to a positive-discord state. These results hold for any Hilbert-space dimension and have direct implications for quantum computation and for the foundations of the theory of open systems. In addition, we provide a simple necessary criterion for zero quantum discord. Finally, we show that, for almost all positive-discord states, an arbitrary Markovian evolution cannot lead to a sudden, permanent vanishing of discord.

Local temperature in quantum thermal states

We consider blocks of quantum spins in a chain at thermal equilibrium, focusing on their properties from a thermodynamical perspective. In a classical system the temperature behaves as an intensive magnitude, above a certain block size, regardless of the actual value of the temperature itself. However, a deviation from this behavior is expected in quantum systems. In particular, we see that under some conditions the description of the blocks as thermal states with the same global temperature as the whole chain fails. We analyze this issue by employing the quantum fidelity as a figure of merit, singling out in detail the departure from the classical behavior. As it may be expected, we see that quantum features are more prominent at low temperatures and are affected by the presence of zero-temperature quantum phase transitions. Interestingly, we show that the blocks can be considered indeed as thermal states with a high fidelity, provided an effective local temperature is properly identified. Such a result may originate from typical properties of reduced subsystems of energy-constrained Hilbert spaces. Finally, the relation between local and global temperatures is analyzed as a function of the size of the blocks and the system parameters.

Liouville-space R-matrix-Floquet description of atomic radiative processes involving autoionizing states in the presence of intense electromagnetic fields

A reduced-density-operator description is developed for coherent optical phenomena in many-electron atomic systems, utilizing a Liouville-space, multiple-mode Floquet–Fourier representation. The Liouville-space formulation provides a natural generalization of the ordinary Hilbert-space (Hamiltonian) R-matrix-Floquet method, which has been developed for multi-photon transitions and laser-assisted electron–atom collision processes. In these applications, the R-matrix-Floquet method has been demonstrated to be capable of providing an accurate representation of the complex, multi-level structure of many-electron atomic systems in bound, continuum, and autoionizing states. The ordinary Hilbert-space (Hamiltonian) formulation of the R-matrix-Floquet method has been implemented in highly developed computer programs, which can provide a non-perturbative treatment of the interaction of a classical, multiple-mode electromagnetic field with a quantum system. This quantum system may correspond to a many-electron, bound atomic system and a single continuum electron. However, including pseudo-states in the expansion of the many-electron atomic wave function can provide a representation of multiple continuum electrons. The 'dressed' many-electron atomic states thereby obtained can be used in a realistic non-perturbative evaluation of the transition probabilities for an extensive class of atomic collision and radiation processes in the presence of intense electromagnetic fields. In order to incorporate environmental relaxation and decoherence phenomena, we propose to utilize the ordinary Hilbert-space (Hamiltonian) R-matrix-Floquet method as a starting-point for a Liouville-space (reduced-density-operator) formulation. To illustrate how the Liouville-space R-matrix-Floquet formulation can be implemented for coherent atomic radiative processes, we discuss applications to electromagnetically induced transparency, as well as to related pump–probe optical phenomena, and also to the unified description of radiative and dielectronic recombination in electron–ion beam interactions and high-temperature plasmas.

Corrosion resistant fibre reinforced polymer (FRP) reinforcement for bridge deck slabs

This paper discusses the beneficial influence of compressive membrane action in fibre reinforced polymer (FRP)reinforced in-plane restrained slabs in bridge deck slabs and the improved service performance when archingaction occurs. Bridge deck slabs that are exposed to extreme environmental conditions can experience severecorrosion damage. Expansive corrosion in steel reinforcement significantly reduces the design life and durabilityof concrete structures; for example, on one short section of the M1 in Northern Ireland, nearly £1 million was spent last year on the maintenance and repair of bridges due to corrosion. Corrosion-resistant compositereinforcement such as basalt fibre reinforced polymer (BFRP) and glass fibre reinforced polymer (GFRP) provides adurable alternative to reinforcing steel. In this research, two BFRP reinforced slabs and two GFRP reinforced slabswere constructed using high-strength concrete with a target cube compressive strength of 65 N/mm2. The slabsrepresented typical full-scale dimensions of a real bridge deck slab 475 mm wide by 1425 mm long and 150 mmdeep. The service and ultimate behaviour of the slabs are discussed and the results are compared with the relevantdesign guidelines.

Classifying pedestrian movement behaviour from GPS trajectories using visualization and clustering

The quantity and quality of spatial data are increasing rapidly. This is particularly evident in the case of movement data. Devices capable of accurately recording the position of moving entities have become ubiquitous and created an abundance of movement data. Valuable knowledge concerning processes occurring in the physical world can be extracted from these large movement data sets. Geovisual analytics offers powerful techniques to achieve this. This article describes a new geovisual analytics tool specifically designed for movement data. The tool features the classic space-time cube augmented with a novel clustering approach to identify common behaviour. These techniques were used to analyse pedestrian movement in a city environment which revealed the effectiveness of the tool for identifying spatiotemporal patterns. © 2014 Taylor & Francis.

Interpreting pedestrian behaviour by visualising and clustering movement data

Recent technological advances have increased the quantity of movement data being recorded. While valuable knowledge can be gained by analysing such data, its sheer volume creates challenges. Geovisual analytics, which helps the human cognition process by using tools to reason about data, offers powerful techniques to resolve these challenges. This paper introduces such a geovisual analytics environment for exploring movement trajectories, which provides visualisation interfaces, based on the classic space-time cube. Additionally, a new approach, using the mathematical description of motion within a space-time cube, is used to determine the similarity of trajectories and forms the basis for clustering them. These techniques were used to analyse pedestrian movement. The results reveal interesting and useful spatiotemporal patterns and clusters of pedestrians exhibiting similar behaviour.

Learning from time series:Supervised Aggregative Feature Extraction

Many modeling problems require to estimate a scalar output from one or more time series. Such problems are usually tackled by extracting a fixed number of features from the time series (like their statistical moments), with a consequent loss in information that leads to suboptimal predictive models. Moreover, feature extraction techniques usually make assumptions that are not met by real world settings (e.g. uniformly sampled time series of constant length), and fail to deliver a thorough methodology to deal with noisy data. In this paper a methodology based on functional learning is proposed to overcome the aforementioned problems; the proposed Supervised Aggregative Feature Extraction (SAFE) approach allows to derive continuous, smooth estimates of time series data (yielding aggregate local information), while simultaneously estimating a continuous shape function yielding optimal predictions. The SAFE paradigm enjoys several properties like closed form solution, incorporation of first and second order derivative information into the regressor matrix, interpretability of the generated functional predictor and the possibility to exploit Reproducing Kernel Hilbert Spaces setting to yield nonlinear predictive models. Simulation studies are provided to highlight the strengths of the new methodology w.r.t. standard unsupervised feature selection approaches. © 2012 IEEE.

Optimizing geometric accuracy of four dimensional CT scans acquired using the wall and couch mounted Varian Real-Time Position Management camera systems

Objective:

The aim of this study was to identify sources of anatomical misrepresentation due to the location of camera mounting, tumour motion velocity and image processing artefacts in order to optimise the 4DCT scan protocol and improve geometrical-temporal accuracy.

A phantom with an imaging insert was driven with a sinusoidal superior-inferior motion of varying amplitude and period for 4DCT scanning. The length of a high density cube within the insert was measured using treatment planning software to determine the accuracy of its spatial representation. Scan parameters were varied including the tube rotation period and the cine time between reconstructed images. A CT image quality phantom was used to measure various image quality signatures under the scan parameters tested.

No significant difference in spatial accuracy was found for 4DCT scans carried out using the wall mounted or couch mounted camera for sinusoidal target motion. Greater spatial accuracy was found for 4DCT scans carried out using a tube rotation speed of 0.5s rather than 1.0s. The reduction in image quality when using a faster rotation speed was not enough to require an increase in patient dose.

4DCT accuracy may be increased by optimising scan parameters, including choosing faster tube rotation speeds. Peak misidentification in the recorded breathing trace leads to spatial artefacts and this risk can be reduced by using a couch mounted infrared camera.

This study explicitly shows that 4DCT scan accuracy is improved by scanning with a faster CT tube rotation speed.