Stochastic flows of mappings

In this paper,the stochastic flow of mappings generated by a Feller convolution semigroup on a compact metric space is studied.This kind of flow is the generalization of superprocesses of stochastic flows and stochastic diffeomorphism induced by the strong solutions of stochastic differential equations.     

A Banking Platform to Leverage Data Driven Marketing with Machine Learning

Payment data is one of the most valuable assets that retail banks can leverage as the major competitive advantage with respect to new entrants such as Fintech companies or giant internet companies. In marketing, the value behind data relates to the power of encoding customer preferences: the better you know your customer, the better your marketing strategy. In this paper, we present a B2B2C lead generation application based on payment transaction data within the online banking system. In this approach, the bank is an intermediary between its private customers and merchants. The bank uses its competence in Machine Learning driven marketing to build a lead generation application that helps merchants run data driven campaigns through the banking channels to reach retail customers. The bank’s retail customers trade the utility hidden in its payment transaction data for special offers and discounts offered by merchants. During the entire process banks protects the privacy of the retail customer.     

A realistic coronary artery phantom for particle image velocimetry

Myocardial infarction results from the rupture of an atherosclerotic plaque, which occurs in response to both mechanical stress and inflammatory processes. In order experimentally observe flow into atherosclerotic coronary artery morphologies, a novel technique for molding realistic compliant phantom featuring injection-molded inclusions and multiple layers has been developed. This transparent phantom allows for particle image velocimetry (PIV) flow analysis and can supply experimental data to validate computational fluid dynamics algorithms and hypothesis.     

Q parameter estimation using numerical simulations for linear and nonlinear transmission systems

We compare the Q parameter obtained from scalar, semi-analytical and full vector models for realistic transmission systems. One set of systems is operated in the linear regime, while another is using solitons at high peak power. We report in detail on the different results obtained for the same system using different models. Polarisation mode dispersion is also taken into account and a novel method to average Q parameters over several independent simulation runs is described.     

Mathematical modelling and numerical simulation of the morphological development of neurons

Background

The morphological development of neurons is a very complex process involving both genetic and environmental components. Mathematical modelling and numerical simulation are valuable tools in helping us unravel particular aspects of how individual neurons grow their characteristic morphologies and eventually form appropriate networks with each other.

Methods

A variety of mathematical models that consider (1) neurite initiation (2) neurite elongation (3) axon pathfinding, and (4) neurite branching and dendritic shape formation are reviewed. The different mathematical techniques employed are also described.

Results

Some comparison of modelling results with experimental data is made. A critique of different modelling techniques is given, leading to a proposal for a unified modelling environment for models of neuronal development.

Conclusion

A unified mathematical and numerical simulation framework should lead to an expansion of work on models of neuronal development, as has occurred with compartmental models of neuronal electrical activity.

     

Fluctuations for the Ginzburg-Landau $${\nabla \phi}$$ Interface Model on a Bounded Domain

We study the massless field on \({D_n = D \cap \tfrac{1}{n} \mathbf{Z}^2}\), where \({D \subseteq \mathbf{R}^2}\) is a bounded domain with smooth boundary, with Hamiltonian \({\mathcal {H}(h) = \sum_{x \sim y} \mathcal {V}(h(x) - h(y))}\). The interaction \({\mathcal {V}}\) is assumed to be symmetric and uniformly convex. This is a general model for a (2 + 1)-dimensional effective interface where h represents the height. We take our boundary conditions to be a continuous perturbation of a macroscopic tilt: h(x) = n x · u + f(x) for \({x \in \partial D_n,\,u \in \mathbf{R}^2}\), and f : R ² → R continuous. We prove that the fluctuations of linear functionals of h(x) about the tilt converge in the limit to a Gaussian free field on D, the standard Gaussian with respect to the weighted Dirichlet inner product \({(f,g)_\nabla^\beta = \int_D \sum_i \beta_i \partial_i f_i \partial_i g_i}\) for some explicit β = β(u). In a subsequent article, we will employ the tools developed here to resolve a conjecture of Sheffield that the zero contour lines of h are asymptotically described by SLE(4), a conformally invariant random curve.     

A New Derivation of the Quantum Navier–Stokes Equations in the Wigner–Fokker–Planck Approach

A quantum Navier–Stokes system for the particle, momentum, and energy densities is formally derived from the Wigner–Fokker–Planck equation using a moment method. The viscosity term depends on the particle density with a shear viscosity coefficient which equals the quantum diffusion coefficient of the Fokker–Planck collision operator. The main idea of the derivation is the use of a so-called osmotic momentum operator, which is the sum of the phase-space momentum and the gradient operator. In this way, a Chapman–Enskog expansion of the Wigner function, which typically leads to viscous approximations, is avoided. Moreover, we show that the osmotic momentum emerges from local gauge theory.     

One-pot synthesis of uniform hollow cuprous oxide spheres fabricated by single-crystalline particles via a simple solvothermal route

Uniform Cu₂O hollow spheres fabricated by single-crystalline particles (smaller than 20 nm) are facile synthesized in ethylene glycol (EG) solution by a simple solvothermal route without using pre-fabricated templates and reductive agents. EG in this protocol is not only used as a solvent, complexing agent, and reducing agent, but also served as a structure-directing agent for the formation of hollow structure. By control of reaction conditions, such as reaction time, temperature, and the anions, the morphology and structure of the hollow spheres can be tuned. A coordination adsorption and oriented attachment and Ostwald ripening mechanism is proposed for explaining the formation process of hollow Cu₂O spheres in EG solution; and importantly, the hollow Cu₂O spheres exhibit an excellent property for the electro-catalytic oxidization of ascorbic acid in acetic acid buffer solution. Moreover, the hollow spherical Cu₂O particles could be potentially applied in catalysis, sensor, and as model for fundamental research.     

Leading-order actions of Goldstino fields

This paper starts with a self-contained discussion of the so-called Akulov–Volkov action S_AV\mathcal{S}_{\mathrm{AV}}, which is traditionally taken to be the leading-order action of the Goldstino field. Explicit expressions for S_AV\mathcal{S}_{\mathrm{AV}} and its chiral version S_AV^ch\mathcal{S}_{\mathrm{AV}}^{\mathrm{ch}} are presented. We then turn to the issue on how these actions are related to the leading-order action S_NL\mathcal{S}_{\mathrm{NL}} proposed in the newly proposed constrained superfield formalism. We show that S_NL\mathcal{S}_{\mathrm{NL}} may yield S_AV/S_AV^ch\mathcal{S}_{\mathrm {AV}}/\mathcal{S}_{\mathrm{AV}}^{\mathrm{ch}} or a totally different action S_KS\mathcal{S}_{\mathrm{KS}}, depending on how the auxiliary field in the former is integrated out. However, S_KS\mathcal{S}_{\mathrm{KS}} and S_AV/S_AV^ch\mathcal{S}_{\mathrm {AV}}/\mathcal{S}_{\mathrm{AV}}^{\mathrm{ch}} always yield the same S-matrix elements, as one would have expected from general considerations in quantum field theory.