A dual algorithm for the minimum covering weighted ball problem in {\mathbb{R}^n}

The nonlinear convex programming problem of finding the minimum covering weighted ball of a given finite set of points in ${\mathbb{R}^n}$ is solved by generating a finite sequence of subsets of the points and by finding the minimum covering weighted ball of each subset in the sequence until all points are covered. Each subset has at most n + 1 points and is affinely independent. The radii of the covering weighted balls are strictly increasing. The minimum covering weighted ball of each subset is found by using a directional search along either a ray or a circular arc, starting at the solution to the previous subset. The step size is computed explicitly at each iteration.     

Electrosprayed Shrimp and Mushroom Nanochitins on Cellulose Tissue for Skin Contact Application

Cosmetics has recently focused on biobased skin-compatible materials. Materials from natural sources can be used to produce more sustainable skin contact products with enhanced bioactivity. Surface functionalization using natural-based nano/microparticles is thus a subject of study, aimed at better understanding the skin compatibility of many biopolymers also deriving from biowaste. This research investigated electrospray as a method for surface modification of cellulose tissues with chitin nanofibrils (CNs) using two different sources—namely, vegetable (i.e., from fungi), and animal (from crustaceans)—and different solvent systems to obtain a biobased and skin-compatible product. The surface of cellulose tissues was uniformly decorated with electrosprayed CNs. Biological analysis revealed that all treated samples were suitable for skin applications since human dermal keratinocytes (i.e., HaCaT cells) successfully adhered to the processed tissues and were viable after being in contact with released substances in culture media. These results indicate that the use of solvents did not affect the final cytocompatibility due to their effective evaporation during the electrospray process. Such treatments did not also affect the characteristics of cellulose; in addition, they showed promising anti-inflammatory and indirect antimicrobial activity toward dermal keratinocytes in vitro. Specifically, cellulosic substrates decorated with nanochitins from shrimp showed strong immunomodulatory activity by first upregulating then downregulating the pro-inflammatory cytokines, whereas nanochitins from mushrooms displayed an overall anti-inflammatory activity via a slight decrement of the pro-inflammatory cytokines and increment of the anti-inflammatory marker. Electrospray could represent a green method for surface modification of sustainable and biofunctional skincare products.     

Homogenization of spatially dispersive metamaterial arrays in terms of generalized electric and magnetic polarizations

An anisotropic homogenization theory for spatially dispersive periodic arrays is developed, based on the microscopic Maxwell equations, that yields causal, macroscopic permittivities, and inverse permeabilities for the fundamental Floquet modes of the arrays. (Macroscopic magnetoelectric coefficients are not required.) Reality conditions, reciprocity relations, passivity conditions, and causality relations are derived for these spatially dispersive macroscopic constitutive parameters. A significant feature of the formulation is that the macroscopic permittivities and permeabilities reduce to their anisotropic-continuum definitions in terms of ordinary macroscopic averages at the low spatial and temporal frequencies. In addition, diamagnetic metamaterial arrays require no special considerations or modifications to accommodate their unusual characteristics. A numerical example of a 2D array comprised of circular–cylinder inclusions is given that confirms the theoretical results for the computed electric and magnetic or diamagnetic macroscopic polarizations.     

The Beneficial Role of Random Strategies in Social and Financial Systems

In this paper we focus on the beneficial role of random strategies in social sciences by means of simple mathematical and computational models. We briefly review recent results obtained by two of us in previous contributions for the case of the Peter principle and the efficiency of a Parliament. Then, we develop a new application of random strategies to the case of financial trading and discuss in detail our findings about forecasts of markets dynamics.     

Invertible symmetric 3 × 3 binary matrices and GQ(2, 4)

We reveal an intriguing connection between the set of 27 (disregarding the identity) invertible symmetric 3?×?3 matrices over GF(2) and the points of the generalized quadrangle GQ(2,?4). The 15 matrices with eigenvalue one correspond to a copy of the subquadrangle GQ(2,?2), whereas the 12 matrices without eigenvalues have their geometric counterpart in the associated double-six. The fine details of this correspondence, including the precise algebraic meaning/analogue of collinearity, are furnished by employing the representation of GQ(2,?4) as a quadric in PG(5,?2) of projective index one. An interesting physics application of our findings is also mentioned.     

Study of Dependence for Some Stochastic Processes

Abstract

This article is concerned with studying the following problem: Consider a multivariate stochastic process whose law is characterized in terms of some infinitesimal characteristics, such as the infinitesimal generator in case of finite Markov chains. Under what conditions imposed on these infinitesimal characteristics of this multivariate process, the univariate components of the process agree in law with given univariate stochastic processes. Thus, in a sense, we study a stochastic processe' counterpart of the stochastic dependence problem, which in case of real valued random variables is solved in terms of Sklar's theorem.     

Effects of Co-Solvent Nature and Acid Concentration in the Size and Morphology of Wrinkled Mesoporous Silica Nanoparticles for Drug Delivery Applications

Hierarchically porous materials, such as wrinkled mesoporous silica (WMS), have gained interest in the last couple of decades, because of their wide range of applications in fields such as nanomedicine, energy, and catalysis. The mechanism of formation of these nanostructures is not fully understood, despite various groups reporting very comprehensive studies. Furthermore, achieving particle diameters of 100 nm or less has proven difficult. In this study, the effects on particle size, pore size, and particle morphology of several co-solvents were evaluated. Additionally, varying concentrations of acid during synthesis affected the particle sizes, yielding particles smaller than 100 nm. The morphology and physical properties of the nanoparticles were characterized by X-ray diffraction (XRD), Fourier transform infrared spectroscopy (FTIR), scanning electron microscopy (SEM), and dynamic light scattering (DLS). Homogeneous and spherical WMS, with the desired radial wrinkle morphology and particle sizes smaller than 100 nm, were obtained. The effect of the nature of the co-solvents and the concentration of acid are explained within the frame of previously reported mechanisms of formation, to further elucidate this intricate process.     

Exact and heuristic approaches for the index tracking problem with UCITS constraints

Index tracking aims at determining an optimal portfolio that replicates the performance of an index or benchmark by investing in a smaller number of constituents or assets. The tracking portfolio should be cheap to maintain and update, i.e., invest in a smaller number of constituents than the index, have low turnover and low transaction costs, and should avoid large positions in few assets, as required by the European Union Directive UCITS (Undertaking for Collective Investments in Transferable Securities) rules. The UCITS rules make the problem hard to be satisfactorily modeled and solved to optimality: no exact methods but only heuristics have been proposed so far. The aim of this paper is twofold. First, we present the first Mixed Integer Quadratic Programming (MIQP) formulation for the constrained index tracking problem with the UCITS rules compliance. This allows us to obtain exact solutions for small- and medium-size problems based on real-world datasets. Second, we compare these solutions with the ones provided by the state-of-art heuristic Differential Evolution and Combinatorial Search for Index Tracking (DECS-IT), obtaining information about the heuristic performance and its reliability for the solution of large-size problems that cannot be solved with the exact approach. Empirical results show that DECS-IT is indeed appropriate to tackle the index tracking problem in such cases. Furthermore, we propose a method that combines the good characteristics of the exact and of the heuristic approaches.     

A Novel Prospective Study Assessing the Combination of Photodynamic Therapy and Proton Radiation Therapy: Safety and Outcomes When Treating Malignant Pleural Mesothelioma

Malignant pleural mesothelioma remains difficult to treat, with high failure rates despite optimal therapy. We present a novel prospective trial combining proton therapy (PT) and photodynamic therapy (PDT) and the largest‐ever mesothelioma PT experience (n = 10). PDT photosensitizers included porfimer sodium (2 mg·kg^?1; 24 h drug‐light interval) or 2‐[1‐hexyloxyethyl]‐2‐devinyl pyropheophorbide‐a (HPPH) (4 mg·m^?2;48 h) with wavelengths of 630 nm to 60J·cm^?2 and 665 nm to 15‐45J·cm^?2, respectively. With a median age of 69 years, patients were predominantly male (90%) with epithelioid histology (100%) and stage III‐IV disease (100%). PT was delivered to a median of 55.0 CGE/1.8‐2.0 CGE (range 50–75 CGE) adjuvantly (n = 8) or as salvage therapy (n = 2) following extended pleurectomy/decortication (ePD)/PDT. Two‐year local control was 90%, with distant and regional failure rates of 50% and 30%, respectively. All patients received chemotherapy, and four received immunotherapy. Surgical complications included atrial fibrillation (n = 3), pneumonia (n = 2), and deep vein thrombosis (n = 2). Median survival from PT completion was 19.5 months (30.3 months from diagnosis), and 1‐ and 2‐year survival rates were 58% and 29%. No patient experienced CTCAEv4 grade ≥2 acute or late toxicity. Our prolonged survival in very advanced‐stage patients compares favorably to survival for PT without PDT and photon therapy with PDT, suggesting possible spatial or systemic cooperativity and immune effect.