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.     

14-Noreudesmanes and a phenylpropane heterodimer from sea buckthorn berry inhibit Herpes simplex type 2 virus replication

Two new 14-noreudesmane sesquiterpenes, one new phenylpropane heterodimer, caulilexin C, and uvaol were isolated from the 70% MeOH extract of the fruit peel of Elaeagnus rhamnoides. The structures of the compounds were elucidated by HRESIMS and advanced NMR methods. The absolute configuration of (R)-6,9-dihydroxy-1-oxo-14-noreudesm-5,7,9-triene was determined by the TDDFT-ECD method. The new compounds, together with structurally similar naphthalenes (musizin, musizin-8-O-glucoside, torachrysone-8-O-glucoside) and 1,4-naphthoquinone (2-methylstipandrone), isolated previously from Rumex aquaticus, were investigated for their antiviral activity against Herpes simplex virus type 2 (HSV-2) using two different methods. Applying the traditional virus yield reduction test, (R)-6,9-dihydroxy-1-oxo-14-noreudesm-5,7,9-triene, 1-[3-methoxy-4-(2-methoxy-4-(1E)-propenyl-phenoxy)-phenyl]-propane-1,2-diol, and musizin caused a 2.00 log₁₀, 3.49 log₁₀, and 2.33 log₁₀ reduction of HSV-2 yield, respectively, at a concentration of 12.5?μM. 2-Hydroxy-1-methoxy-6,9-dioxo-14-noreudesm-1,3,5(10),7-tetraene exhibited an antiviral effect at concentration of 50?μM only. Similar results were obtained when the qPCR method was used to test the antiviral activity of the compounds.     

Individual‐Molecule Perspective Analysis of Chemical Reaction Networks: The Case of a Light‐Driven Supramolecular Pump

The first study in which stochastic simulations of a two‐component molecular machine are performed in the mass‐action regime is presented. This system is an autonomous molecular pump consisting of a photoactive axle that creates a directed flow of rings through it by exploiting light energy away from equilibrium. The investigation demonstrates that the pump can operate in two regimes, both experimentally accessible, in which light‐driven steps can be rate‐determining or not. The number of photons exploited by an individual molecular pump, as well as the precision of cycling and the overall efficiency, critically rely on the operating regime of the machine. This approach provides useful information not only to guide the chemical design of a self‐assembling molecular device with desired features, but also to elucidate the effect of the environment on its performance, thus facilitating its experimental investigation.     

Long‐Term Photostability in Terephthalate Metal–Organic Frameworks

Prolonged (weeks) UV/Vis irradiation under Ar of UiO‐66(Zr), UiO66 Zr‐NO₂, MIL101 Fe, MIL125 Ti‐NH₂, MIL101 Cr and MIL101 Cr(Pt) shows that these MOFs undergo photodecarboxylation of benzenedicarboxylate (BDC) linker in a significant percentage depending on the structure and composition of the material. Routine characterization techniques such as XRD, UV/Vis spectroscopy and TGA fail to detect changes in the material, although porosity and surface area change upon irradiation of powders. In contrast to BCD‐containing MOFs, zeolitic imidazolate ZIF‐8 does not evolve CO₂ or any other gas upon irradiation.     

Application of affinity capillary electrophoresis for charge heterogeneity profiling of biopharmaceuticals

Charge heterogeneity profiling is important for the quality control (QC) of biopharmaceuticals. Because of the increasing complexity of these therapeutic entities [1], the development of alternative analytical techniques is needed. In this work, flow‐through partial‐filling affinity capillary electrophoresis (FTPFACE) has been established as a method for the analysis of a mixture of two similar monoclonal antibodies (mAbs). The addition of a specific ligand results in the complexation of one mAb in the co‐formulation, thus changing its migration time in the electric field. This allows the characterization of the charged variants of the non‐shifted mAb without interferences. Adsorption of proteins to the inner capillary wall has been circumvented by rinsing with guanidine hydrochloride before each injection. The presented FTPFACE approach requires only very small amounts of ligands and provides complete comparability with a standard CZE of a single mAb.     

Self-Assembly and Fluorescence of Tetracationic Liquid Crystalline Tetraphenylethene

A series of tetraguanidinium tetraphenylethene (TPE) arylsulfonates with different chain lengths was prepared via ionic self-assembly of tetraguanidinium TPE chloride and the respective methyl arylsulfonates. Liquid crystalline properties were studied by differential scanning calorimetry, polarizing optical microscopy and X-ray diffraction. Tetraguanidinium TPE arylsulfonates with chain lengths of C₈–C₁₂ displayed hexagonal columnar mesophases over a broad temperature range, while derivatives with longer chains showed oblique columnar phases. In solution all compounds displayed aggregation-induced emission behaviour. Temperature-dependent luminescence spectra of the bulk phase of the tetraguanidinium TPE arylsulfonate with C₁₄ side chains revealed a strong luminescence both in the solid state and the oblique columnar mesophase. The emission behaviour was rationalized by a unique combination of restriction of intramolecular rotation of the TPE core, Coulomb interaction between the guanidinium cations and π–π interactions of the anionic arylsulfonate moieties.