Loop spaces, and coherence for monoidal and braided monoidal bicategories

We prove a coherence theorem for braided monoidal bicategories and relate it to the coherence theorem for monoidal bicategories. We show how coherence for these structures can be interpreted topologically using up-to-homotopy operad actions and the algebraic classification of surface braids.     

The coarse Baum–Connes conjecture via coarse geometry

The C₀ coarse structure on a metric space is a refinement of the bounded structure and is closely related to the topology of the space. In this paper we will prove the C₀ version of the coarse Baum–Connes conjecture and show that K_*(C^*X₀) is a topological invariant for a broad class of metric spaces. Using this result we construct a ‘geometric’ obstruction group to the coarse Baum–Connes conjecture for the bounded coarse structure. We then show under the assumption of finite asymptotic dimension that the obstructions vanish, and hence we obtain a new proof of the coarse Baum–Connes conjecture in this context.     

Modeling Transverse Dispersion and Variable Density Flow in Porous Media

A two-dimensional numerical model is used to study the nonlinear behavior of density gradients on transverse dispersion. Numerical simulations are conducted using d ³ f, a computer code for simulation of density-dependent flow in porous media. Considering a density-stratified horizontal flow in a heterogeneous porous media, a series of simulations is carried out to examine the effect of the density gradient on macro-scale transverse dispersivity. Changing salt concentration significantly affects fluid properties. This physical behavior of the fluid involves a non-linearity in modeling the interaction between salt and fresh water. It is concluded that the large-scale transport properties for high density flow deviate significantly from the tracer case due to the spatial variation of permeability, described by statistical parameters, at the local-scale. Indeed, the presence of vertical flow velocities induced by permeability variations is responsible for the reduction of the mixing zone width in the steady state in the case of a high density gradient. Uncertainties in the model simulations are studied in terms of discretization errors, boundary conditions, and convergence of ensemble averaging. With respect to the results, the gravity number appears to be the controlling parameter for dispersive flux. In addition, the applicability and limitations of the nonlinear model of Hassanizadeh (1990) and Hassanizadeh and Leijnse (1995) (Adv Water Resour 18(4):203–215, 1995) in heterogeneous porous media are investigated. We found that the main cause of the nonlinear behavior of dispersion, which is the interaction between density contrast and vertical velocity, needs to be explicitly accounted for in a macro-scale model.     

Sensitivity to point-spread function parameters in medical ultrasound image deconvolution

Clinical ultrasound images are often perceived as difficult to interpret due to image blurring and speckle inherent in the ultrasound imaging. But the image quality can be improved by deconvolution using an estimate of the point-spread function. However, it is difficult to obtain a sufficiently accurate estimate of the point-spread function in vivo because of the unknown properties of the soft tissue in clinical applications. Local variations in the speed of sound and attenuation change the pulse and beam shape. These in turn affect the point-spread function. The purpose and novelty of this paper is therefore to explore the sensitivity of a state-of-the-art deconvolution algorithm to uncertainty in the point-spread function. The point-spread function in our restoration algorithm is made shift invariant in the lateral dimension but shift dependent in the axial direction, and is modelled to match a 128-element 1D linear array often found in clinical use. We present simulated and in vitro sensitivity analyses of two-dimensional deconvolution while varying six parameters on which the point-spread function depends. Uncertainty in the ultrasound machine is analysed by varying the axial depths of lateral and elevational foci alongside height and width of transducer elements. Sensitivity to tissue influence is investigated by varying the speed of sound and frequency-dependent attenuation of the electro-mechanical impulse response. The results are analysed both quantitatively and in terms of the perceived image quality. First, the assessment of deconvolution using the logarithmic image amplitude is found to be a better indicator of the perceived improvement in the restoration. Secondly, the two most critical parameters for two-dimensional deconvolution are discovered to be the lateral focus and the speed of sound, because the success of deconvolution is perceived primarily in terms of deblurring. We also observed similar patterns for the simulation and in vitro experiment. Finally, we show that it is possible to restore in vivo ultrasound images using an assumed point-spread function and hence conclude that an exact point-spread function is not necessary for enhancing ultrasound image quality by deconvolution.     

Semi‐analytical method for departure point determination

A new method for departure point determination on Cartesian grids, the semi‐analytical upwind path line tracing (SUT) method, is presented and compared to two typical departure point determination methods used in semi‐Lagrangian advection schemes, the Euler method and the four‐step Runge–Kutta method. Rigorous comparisons of the three methods were conducted for a severely curving hypothetical flow field and for advective transport in the rotation of a Gaussian concentration hill. The SUT method was shown to have equivalent accuracy to the Runge–Kutta method but with significantly improved computational efficiency. Depending on the case being simulated, the SUT method provides either far greater or equivalent computational efficiency and more certain accuracy than the Euler method. Copyright © 2004 John Wiley & Sons, Ltd.     

Quantum Bayesian computation

Quantum Bayesian computation is an emerging field that levers the computational gains available from quantum computers. They promise to provide an exponential speed-up in Bayesian computation. Our article adds to the literature in three ways. First, we describe how quantum von Neumann measurement provides quantum versions of popular machine learning algorithms such as Markov chain Monte Carlo and deep learning that are fundamental to Bayesian learning. Second, we describe quantum data encoding methods needed to implement quantum machine learning including the counterparts to traditional feature extraction and kernel embeddings methods. Third, we show how quantum algorithms naturally calculate Bayesian quantities of interest such as posterior distributions and marginal likelihoods. Our goal then is to show how quantum algorithms solve statistical machine learning problems. On the theoretical side, we provide quantum versions of high dimensional regression, Gaussian processes and stochastic gradient descent. On the empirical side, we apply a quantum FFT algorithm to Chicago house price data. Finally, we conclude with directions for future research.     

Categories of models of R-mingle

We give a new Esakia-style duality for the category of Sugihara monoids based on the Davey-Werner natural duality for lattices with involution, and use this duality to greatly simplify a construction due to Galatos-Raftery of Sugihara monoids from certain enrichments of their negative cones. Our method of obtaining this simplification is to transport the functors of the Galatos-Raftery construction across our duality, obtaining a vastly more transparent presentation on duals. Because our duality extends Dunn's relational semantics for the logic R-mingle to a categorical equivalence, this also explains the Dunn semantics and its relationship with the more usual Routley-Meyer semantics for relevant logics.     

A multianalytical approach to investigate stone biodeterioration at a UNESCO world heritage site: the volcanic rock-hewn churches of Lalibela, Northern Ethiopia

A multianalytical approach combining Optical Microscopy (OM), Backscattered Variable Pressure Scanning Electron Microscopy + Energy Dispersive X-ray Spectroscopy (VP-BSEM + EDS), Powder X-ray Diffractometry (PXRD), Raman Spectroscopy, and Microbiological techniques has been applied to characterize decay products and processes occurring at the surface of two rock-hewn churches (Bete Gyorgis and Bete Amanuel) at the UNESCO’s World Heritage site of Lalibela, Northern Ethiopia. The two churches were carved into volcanic scoria deposits of basaltic composition. In their geological history, the Lalibela volcanic rocks underwent late to post-magmatic hydrothermal alteration together with partial laterization and are therefore characterized by a decay-prone highly vesicular microtexture with late stage to post-magmatic precipitation of secondary mineral phases (calcite–zeolite–smectite). The main objective of the study was to gain a better insight into the weathering products and mechanisms affecting the surface of the stone monuments and to assess the relative contribution of natural “geological” weathering processes versus biological/salt attack in stone decay at this unique heritage site. Results indicate that while the main cause of bulk rock deterioration and structural failure could be related to the stone inherited “geological” features, biological attack by micro- (bacteria) and/or macro- (lichens) organisms is currently responsible for severe stone surface physical and chemical weathering leading to significant weakening of the stone texture and to material loss at the surface of the churches walls. A prompt and careful removal of the biological patinas with the correct biocidal treatment is therefore recommended.     

Protonolysis of the Hg-C bond of chloromethylmercury and dimethylmercury. A DFT and QTAIM study

Possible mechanisms for degrading chloromethylmercury (CH(3)HgCl) and dimethylmercury [(CH3)2Hg] involving thiol and ammonium residues were investigated by DFT and atoms-in-molecules (QTAIM) calculations. Using H2S and HS- as models for thiol and thiolate groups RSH and RS-, respectively, we obtained transition states and energy barriers for possible decomposition routes to Hg(SH)2 based on a model proposed by Moore and Pitts (Moore, M. J.; Distefano, M. D.; Zydowsky, L. D.; Cummings, R. T.; Walsh, C. T. Acc. Chem. Res. 1990, 23, 301. Pitts, K. E.; Summers, A. O. Biochemistry 2002, 41, 10287). Demethylation was found to be a multistep process that involved initial substitution of Cl- by RS-. We found that successive coordination of Hg with thiolates leads to increased negative charge on the methyl group and facilitates the protonolysis of the Hg-C bond by H-SH. This was also found to be the case for (CH3)2Hg. We found that NH4(+) readily protonolyzes the Hg-C bond of these thiolate complexes, suggesting that ammonium residues of protonated amino acids might also act as effective proton donors.