Maximum Principles of Markov Regime-Switching Forward–Backward Stochastic Differential Equations with Jumps and Partial Information

This paper presents three versions of maximum principle for a stochastic optimal control problem of Markov regime-switching forward–backward stochastic differential equations with jumps. First, a general sufficient maximum principle for optimal control for a system, driven by a Markov regime-switching forward–backward jump–diffusion model, is developed. In the regime-switching case, it might happen that the associated Hamiltonian is not concave and hence the classical maximum principle cannot be applied. Hence, an equivalent type maximum principle is introduced and proved. In view of solving an optimal control problem when the Hamiltonian is not concave, we use a third approach based on Malliavin calculus to derive a general stochastic maximum principle. This approach also enables us to derive an explicit solution of a control problem when the concavity assumption is not satisfied. In addition, the framework we propose allows us to apply our results to solve a recursive utility maximization problem.     

Autoregressive functions estimation in nonlinear bifurcating autoregressive models

Bifurcating autoregressive processes, which can be seen as an adaptation of autoregressive processes for a binary tree structure, have been extensively studied during the last decade in a parametric context. In this work we do not specify any a priori form for the two autoregressive functions and we use nonparametric techniques. We investigate both nonasymptotic and asymptotic behaviour of the Nadaraya–Watson type estimators of the autoregressive functions. We build our estimators observing the process on a finite subtree denoted by \(\mathbb {T}_n\), up to the depth n. Estimators achieve the classical rate \(|\mathbb {T}_n|^{-\beta /(2\beta +1)}\) in quadratic loss over Hölder classes of smoothness. We prove almost sure convergence, asymptotic normality giving the bias expression when choosing the optimal bandwidth. Finally, we address the question of asymmetry: we develop an asymptotic test for the equality of the two autoregressive functions which we implement both on simulated and real data.     

In Vitro Antiplasmodial and Cytotoxic Activities of Compounds from the Roots of Eriosema montanum Baker f. (Fabaceae)

Malaria remains one of the leading causes of death in sub-Saharan Africa, ranked in the top three infectious diseases in the world. Plants of the Eriosema genus have been reported to be used for the treatment of this disease, but scientific evidence is still missing for some of them. In the present study, the in vitro antiplasmodial activity of the crude extract and compounds from Eriosema montanum Baker f. roots were tested against the 3D7 strain of Plasmodium falciparum and revealed using the SYBR Green, a DNA intercalating compound. The cytotoxicity effect of the compounds on a human cancer cell line (THP-1) was assessed to determine their selectivity index. It was found that the crude extract of the plant displayed a significant antiplasmodial activity with an IC₅₀ (µg/mL) = 17.68 ± 4.030 and a cytotoxic activity with a CC₅₀ (µg/mL) = 101.5 ± 12.6, corresponding to a selective antiplasmodial activity of 5.7. Bioactivity-guided isolation of the major compounds of the roots’ crude extract afforded seven compounds, including genistein, genistin and eucomic acid. Under our experimental conditions, using Artemisinin as a positive control, eucomic acid showed the best inhibitory activity against the P. falciparum 3D7, a well-known chloroquine-sensitive strain. The present results provide a referential basis to support the traditional use of Eriosema species in the treatment of malaria.     

Characterization of Functional Groups in Estuarine Dissolved Organic Matter by DNP-enhanced 15N and 13C Solid-State NMR

Estuaries are key ecosystems with unique biodiversity and are of high economic importance. Along the estuaries, variations in environmental parameters, such as salinity and light penetration, can modify the characteristics of dissolved organic matter (DOM). Nevertheless, there is still limited information about the atomic-level transformations of DOM in this ecosystem. Solid-state NMR spectroscopy provides unique insights into the nature of functional groups in DOM. A major limitation of this technique is its lack of sensivity, which results in experimental time of tens of hours for the acquisition of ¹³C NMR spectra and generally precludes the observation of ¹⁵N nuclei for DOM. We show here how the sensitivity of solid-state NMR experiments on DOM of Seine estuary can be enhanced using dynamic nuclear polarization (DNP) under magic-angle spinning. This technique allows the acquisition of ¹³C NMR spectra of these samples in few minutes, instead of hours for conventional solid-state NMR. Both conventional and DNP-enhanced ¹³C NMR spectra indicate that the ¹³C local environments in DOM are not strongly modified along the Seine estuary. Furthermore, the sensitivity gain provided by the DNP allows the detection of ¹⁵N NMR signal of DOM, in spite of the low nitrogen content. These spectra reveal that the majority of nitrogen is in the amide form in these DOM samples and show an increased disorder around these amide groups near the mouth of the Seine.     

Zn-Induced Interactions Between SARS-CoV-2 orf7a and BST2/Tetherin

We present in this work a first X-ray Absorption Spectroscopy study of the interactions of Zn with human BST2/tetherin and SARS-CoV-2 orf7a proteins as well as with some of their complexes. The analysis of the XANES region of the measured spectra shows that Zn binds to BST2, as well as to orf7a, thus resulting in the formation of BST2-orf7a complexes. This structural information confirms the the conjecture, recently put forward by some of the present Authors, according to which the accessory orf7a (and possibly also orf8) viral protein are capable of interfering with the BST2 antiviral activity. Our explanation for this behavior is that, when BST2 gets in contact with Zn bound to the orf7a Cys₁₅ ligand, it has the ability of displacing the metal owing to the creation of a new disulfide bridge across the two proteins. The formation of this BST2-orf7a complex destabilizes BST2 dimerization, thus impairing the antiviral activity of the latter.     

Naphthalene Exchange in [Re(η6-napht)2]+ with Pharmaceuticals Leads to Highly Functionalized Sandwich Complexes [M(η6-pharm)2]+ (M=Re/99mTc)

Bis-arene sandwich complexes are generally prepared by the Fischer-Hafner reaction, which conditions are incompatible with most O- and N- functional groups. We report a new way for the synthesis of sandwich type complexes [Re(η⁶-arene)₂]⁺ and [Re(η⁶-arene)(η⁶-benzene)]⁺ from [Re(η⁶-napht)₂]⁺ and [Re(η⁶-napht)(η⁶-benzene)]⁺, with functionalized arenes and pharmaceuticals. N-methylpyrrolidine (NMP) facilitates the substitution of naphthalene with the incoming arene. A series of fully characterized rhenium sandwich complexes with simple arenes, such as aniline, as well as with active compounds like lidocaine and melatonin are presented. With these rhenium compounds in hand, the radioactive sandwich complexes [^99mTc(η⁶-pharm)₂]⁺ (pharm=pharmaceutical) can be unambiguously confirmed. The direct labelling of pharmaceuticals with ^99mTc through η⁶-coordination to phenyl rings and the confirmation of the structures with the rhenium homologues opens a path into molecular theranostics.     

Influence of Differential Diffusion on Super-Equilibrium Temperature in Turbulent Non-Premixed Hydrogen/Air Flames

In this paper we wish to investigate the occurrence of super-equilibrium temperature values, observed in many experimental configurations. We would like to understand the origin of this phenomenon. Previous authors have already shown that differential diffusion can lead to considerable changes in the temperature field and we would like to build on top of this observation. We investigate numerically super-equilibrium combustion by considering both laminar counter-flow and turbulent diluted hydrogen/air diffusion flames. These turbulent flames are computed using direct numerical simulations (DNS). A detailed reaction mechanism is employed and the transport properties are modeled using multicomponent diffusion velocities, including the Soret effect. Analyzing these results we introduce three complementary parameters (dilution-free mixture fraction, dilution excess and local enthalpy) to describe the local combustion conditions. Introducing a measure of dilution separately from the mixture fraction is necessary for a proper analysis. Using this set of parameters it becomes possible to explain super-equilibrium temperature levels as a consequence of differential diffusion.