Superquantiles at Work: Machine Learning Applications and Efficient Subgradient Computation

Set-Valued and Variational Analysis - R. Tyrell Rockafellar and his collaborators introduced, in a series of works, new regression modeling methods based on the notion of superquantile (or...     

An Infinite Antichain of Planar Tanglegrams

Contrary to the expectation arising from the tanglegram Kuratowski theorem of Czabarka et al. (SIAM J. Discrete Math. 31(3), 1732–1750, 2017), we construct an infinite antichain of planar tanglegrams with respect to the induced subtanglegram partial order. R.E. Tarjan, R. Laver, D.A. Spielman and M. Bóna, and possibly others, showed that the partially ordered set of finite permutations ordered by deletion of entries contains an infinite antichain, i.e., there exists an infinite collection of permutations, such that none of them contains another as a pattern. Our construction adds a twist to the construction of Spielman and Bóna (Electr. J. Comb. 7, N2, 2000).

     

On-line Method for Montelukast Determination in Bile Salt Medium with Multivariate Optimization and Fluorescent Detection

Journal of Analytical Chemistry - The present development involved a flow injection strategy using a mini-column of multiwalled carbon nanotubes and fluorescent detection (λex of 283 nm,...     

Electroosmosis modulated peristaltic biorheological flow through an asymmetric microchannel: mathematical model

A theoretical study is presented of peristaltic hydrodynamics of an aqueous electrolytic non-Newtonian Jeffrey bio-rheological fluid through an asymmetric microchannel under an applied axial electric field. An analytical approach is adopted to obtain the closed form solution for velocity, volumetric flow, pressure difference and stream function. The analysis is also restricted under the low Reynolds number assumption (Stokes flow) and lubrication theory approximations (large wavelength). Small ionic Peclét number and Debye–Hückel linearization (i.e. wall zeta potential ≤ 25 mV) are also considered to simplify the Nernst–Planck and Poisson–Boltzmann equations. Streamline plots are also presented for the different electro-osmotic parameter, varying magnitudes of the electric field (both aiding and opposing cases) and for different values of the ratio of relaxation to retardation time parameter. Comparisons are also included between the Newtonian and general non-Newtonian Jeffrey fluid cases. The results presented here may be of fundamental interest towards designing lab-on-a-chip devices for flow mixing, cell manipulation, micro-scale pumps etc. Trapping is shown to be more sensitive to an electric field (aiding, opposing and neutral) rather than the electro-osmotic parameter and viscoelastic relaxation to retardation ratio parameter. The results may also help towards the design of organ-on-a-chip like devices for better drug design.     

Inference for a change-point problem under a generalised Ornstein–Uhlenbeck setting

Determining accurately when regime and structural changes occur in various time-series data is critical in many social and natural sciences. We develop and show further the equivalence of two consistent estimation techniques in locating the change point under the framework of a generalised version of the one-dimensional Ornstein–Uhlenbeck process. Our methods are based on the least sum of squared error and the maximum log-likelihood approaches. The case where both the existence and the location of the change point are unknown is investigated and an informational methodology is employed to address these issues. Numerical illustrations are presented to assess the methods’ performance.     

Two-Photon Absorption Enhancement by the Inclusion of a Tropone Ring in Distorted Nanographene Ribbons

A new family of distorted ribbon-shaped nanographenes was designed, synthesized, and their optical and electrochemical properties were evaluated, pointing out an unprecedented correlation between their structural characteristics and the two-photon absorption (TPA) responses and electrochemical band gaps. Three nanographene ribbons have been prepared: a seven-membered-ring-containing nanographene presenting a tropone moiety at the edge, its full-carbon analogue, and a purely hexagonal one. We have found that the TPA cross-sections and the electrochemical band gaps of the seven-membered-ring-containing compounds are higher and lower, respectively, than those of the fully hexagonal polycyclic aromatic hydrocarbon (PAH). Interestingly, the inclusion of additional curvature has a positive effect in terms of non-linear optical properties of those ribbons.     

Thermodynamical consistency of the dual-phase-lag heat conduction equation

Dual-phase-lag equation for heat conduction is analyzed from the point of view of non-equilibrium thermodynamics. Its first-order Taylor series expansion is consistent with the second law as long as the two relaxation times are not negative.     

Local linear convergence analysis of Primal–Dual splitting methods

In this paper, we study the local linear convergence properties of a versatile class of Primal–Dual splitting methods for minimizing composite non-smooth convex optimization problems. Under the assumption that the non-smooth components of the problem are partly smooth relative to smooth manifolds, we present a unified local convergence analysis framework for these methods. More precisely, in our framework, we first show that (i) the sequences generated by Primal–Dual splitting methods identify a pair of primal and dual smooth manifolds in a finite number of iterations, and then (ii) enter a local linear convergence regime, which is characterized based on the structure of the underlying active smooth manifolds. We also show how our results for Primal–Dual splitting can be specialized to cover existing ones on Forward–Backward splitting and Douglas–Rachford splitting/ADMM (alternating direction methods of multipliers). Moreover, based on these obtained local convergence analysis result, several practical acceleration techniques are discussed. To exemplify the usefulness of the obtained result, we consider several concrete numerical experiments arising from fields including signal/image processing, inverse problems and machine learning. The demonstration not only verifies the local linear convergence behaviour of Primal–Dual splitting methods, but also the insights on how to accelerate them in practice.