Personalized PageRank with Node-dependent Restart

Personalized PageRank is an algorithm to classify the improtance of web pages on a user-dependent basis. We introduce two generalizations of Personalized PageRank with node-dependent restart. The first generalization is based on the proportion of visits to nodes before the restart, whereas the second generalization is based on the probability of visited node just before the restart. In the original case of constant restart probability, the two measures coincide. We discuss interesting particular cases of restart probabilities and restart distributions. We show that the both generalizations of Personalized PageRank have an elegant expression connecting the so-called direct and reverse Personalized PageRanks that yield a symmetry property of these Personalized PageRanks

Numerical analysis of a dual-phase-lag model involving two temperatures

In this paper, we numerically analyse a phase-lag model with two temperatures which arises in the heat conduction theory. The model is written as a linear partial differential equation of third order in time. The variational formulation, written in terms of the thermal acceleration, leads to a linear variational equation, for which we recall an existence and uniqueness result and an energy decay property. Then, using the finite element method to approximate the spatial variable and the implicit Euler scheme to discretize the time derivatives, fully discrete approximations are introduced. A discrete stability property is proved, and a priori error estimates are obtained, from which the linear convergence of the approximation is derived. Finally, some one-dimensional numerical simulations are described to demonstrate the accuracy of the approximation and the behaviour of the solution.Peer ReviewedPostprint (author's final draft

Stress distribution during cold compression of a quartz aggregate using synchrotron X-ray diffraction: Observed yielding, damage, and grain crushing

We report new experimental results that quantify the stress distribution within a quartz aggregate during pore collapse and grain crushing. The samples were probed with synchrotron X-ray diffraction as they were compressed in a multianvil deformation apparatus at room temperature from low pressure (tens of megapascal) to pressures of a few gigapascal. In such a material, stress is likely to concentrate at grain-to-grain contacts and vanish where grains are bounded by open porosity. Therefore, internal stress is likely to vary significantly from point to point in such an aggregate, and hence, it is important to understand both the heterogeneity and anisotropy of such variation with respect to the externally applied stress. In our quartz aggregate (grain size of ~4 μm), the measured diffraction peaks broaden asymmetrically at low pressure (tens of megapascal), suggesting that open pores are still a dominant characteristic of grain boundaries. In contrast, a reference sample of novaculite (a highly dense quartz polycrystal, grain size of ~6–9 μm) showed virtually no peak broadening with increasing pressure. In the quartz aggregate, we observed significant deviation in the pressure-volume curves in the range of P = 400–600 MPa. We suggest that this marks the onset of grain crushing (generally denoted as P* in the rock mechanic literature), which is commonly reported to occur in sandstones at pressures of this order, in general agreement with a Hertzian analysis of fracturing at grain contacts

Space-by-time manifold representation of dynamic facial expressions for emotion categorization

Visual categorization is the brain computation that reduces high-dimensional information in the visual environment into a smaller set of meaningful categories. An important problem in visual neuroscience is to identify the visual information that the brain must represent and then use to categorize visual inputs. Here we introduce a new mathematical formalism—termed space-by-time manifold decomposition—that describes this information as a low-dimensional manifold separable in space and time. We use this decomposition to characterize the representations used by observers to categorize the six classic facial expressions of emotion (happy, surprise, fear, disgust, anger, and sad). By means of a Generative Face Grammar, we presented random dynamic facial movements on each experimental trial and used subjective human perception to identify the facial movements that correlate with each emotion category. When the random movements projected onto the categorization manifold region corresponding to one of the emotion categories, observers categorized the stimulus accordingly; otherwise they selected “other.” Using this information, we determined both the Action Unit and temporal components whose linear combinations lead to reliable categorization of each emotion. In a validation experiment, we confirmed the psychological validity of the resulting space-by-time manifold representation. Finally, we demonstrated the importance of temporal sequencing for accurate emotion categorization and identified the temporal dynamics of Action Unit components that cause typical confusions between specific emotions (e.g., fear and surprise) as well as those resolving these confusions

Graphene films printable on flexible substrates for sensor applications

Fifteen-layered graphene films have been successfully deposited onto flexible substrates using a commercial ink consisting of graphene particles dispersed in an acrylic polymer binder. A value of 74.9 × 105cm−2 was obtained for the density of defects, primarily located at the flake edges, from the ratio of the D and G Raman peaks located at 1345cm1 and 1575cm1 respectively. 0.5μm thick drop-cast films on interdigitated silver electrodes exhibited Ohmic conduction with a small activation energy of 12meV over the temperature range from 260K to 330K . The photo-thermoelectric effect is believed to be responsible for photoconduction through graphene films under illumination intensity of 10mWm-2 at 270 nm, corresponding to the UV absorption peak. The photo-transient decay at the bias of 1V involves two relaxation processes when the illumination is switched off and values of 8.9 × 103 and 4.3 × 104 are found for the relaxation time constant using the Kohlrauch stretched exponential function analysis.Dr. Indrani Banerjee is grateful to Commonwealth Association, UK for funding the present research work under the fellowship placement scheme (Grant reference INCF-2014-66). The studentship of Ms Faris is partially sponsored by the Air Force Office of Scientific Research, Air Force Material Command, USAF, under Grant No. FA9550-15-1-0123. We are also thankful to Miss V. M. Torrejon of Brunel University for support in computer graphics

Experimental demonstration of a hyper-entangled ten-qubit Schr\"odinger cat state

Coherent manipulation of an increasing number of qubits for the generation of entangled states has been an important goal and benchmark in the emerging field of quantum information science. The multiparticle entangled states serve as physical resources for measurement-based quantum computing and high-precision quantum metrology. However, their experimental preparation has proved extremely challenging. To date, entangled states up to six, eight atoms, or six photonic qubits have been demonstrated. Here, by exploiting both the photons' polarization and momentum degrees of freedom, we report the creation of hyper-entangled six-, eight-, and ten-qubit Schr\"odinger cat states. We characterize the cat states by evaluating their fidelities and detecting the presence of genuine multi-partite entanglement. Small modifications of the experimental setup will allow the generation of various graph states up to ten qubits. Our method provides a shortcut to expand the effective Hilbert space, opening up interesting applications such as quantum-enhanced super-resolving phase measurement, graph-state generation for anyonic simulation and topological error correction, and novel tests of nonlocality with hyper-entanglement.Comment: 11 pages, 5 figures, comments welcom

Experimental demonstration of a BDCZ quantum repeater node

Quantum communication is a method that offers efficient and secure ways for the exchange of information in a network. Large-scale quantum communication (of the order of 100 km) has been achieved; however, serious problems occur beyond this distance scale, mainly due to inevitable photon loss in the transmission channel. Quantum communication eventually fails when the probability of a dark count in the photon detectors becomes comparable to the probability that a photon is correctly detected. To overcome this problem, Briegel, D\"{u}r, Cirac and Zoller (BDCZ) introduced the concept of quantum repeaters, combining entanglement swapping and quantum memory to efficiently extend the achievable distances. Although entanglement swapping has been experimentally demonstrated, the implementation of BDCZ quantum repeaters has proved challenging owing to the difficulty of integrating a quantum memory. Here we realize entanglement swapping with storage and retrieval of light, a building block of the BDCZ quantum repeater. We follow a scheme that incorporates the strategy of BDCZ with atomic quantum memories. Two atomic ensembles, each originally entangled with a single emitted photon, are projected into an entangled state by performing a joint Bell state measurement on the two single photons after they have passed through a 300-m fibre-based communication channel. The entanglement is stored in the atomic ensembles and later verified by converting the atomic excitations into photons. Our method is intrinsically phase insensitive and establishes the essential element needed to realize quantum repeaters with stationary atomic qubits as quantum memories and flying photonic qubits as quantum messengers.Comment: 5 pages, 4 figure

Positive approximations of the inverse of fractional powers of SPD M-matrices

This study is motivated by the recent development in the fractional calculus and its applications. During last few years, several different techniques are proposed to localize the nonlocal fractional diffusion operator. They are based on transformation of the original problem to a local elliptic or pseudoparabolic problem, or to an integral representation of the solution, thus increasing the dimension of the computational domain. More recently, an alternative approach aimed at reducing the computational complexity was developed. The linear algebraic system $\cal A^\alpha \bf u=\bf f$, $0< \alpha <1$ is considered, where $\cal A$ is a properly normalized (scalded) symmetric and positive definite matrix obtained from finite element or finite difference approximation of second order elliptic problems in $\Omega\subset\mathbb{R}^d$, $d=1,2,3$. The method is based on best uniform rational approximations (BURA) of the function $t^{\beta-\alpha}$ for $0 < t \le 1$ and natural $\beta$. The maximum principles are among the major qualitative properties of linear elliptic operators/PDEs. In many studies and applications, it is important that such properties are preserved by the selected numerical solution method. In this paper we present and analyze the properties of positive approximations of $\cal A^{-\alpha}$ obtained by the BURA technique. Sufficient conditions for positiveness are proven, complemented by sharp error estimates. The theoretical results are supported by representative numerical tests

A study into the behaviour of the formation level of an excavation under different unloading patterns in soft deposits

The construction of basements in urban areas is often associated with the possible damage to existing structures and services. The varying construction processes inevitably lead to different stress unloading patterns and therefore the dissipation of these excess pore-water pressures may lead to non-standard deformation profiles. The three main types of basement construction processes are layered excavation (LE), basin excavation (BE) and island excavation (IE). The effect of the various unloading patterns has been investigated by a three dimensional (3D) effective stress analysis method using the developed computer program 3DBCPE4.0. An excavation of length 50 m, width 50 m and depth 9 m in a certain homogenous and isotropic saturated soft soil was modelled. This included a diaphragm wall of 800-mm thickness embedded 18 m deep into the soft soil. The different excavation deformation profiles under different excavation patterns were related to the different unloading process, the exposure time of excavation face and the dissipation of negative excess pore-water pressures. The most favourable process for controlling the horizontal deformation of a retaining wall or the heave deformation of the formation level is suggested. The ground water potentials within the formation level are also presented