Optimal control of Markovian jump processes with partial information and applications to a parallel queueing model

We consider a stochastic control problem over an infinite horizon where the state process is influenced by an unobservable environment process. In particular, the Hidden-Markov-model and the Bayesian model are included. This model under partial information is transformed into an equivalent one with complete information by using the well-known filter technique. In particular, the optimal controls and the value functions of the original and the transformed problem are the same. An explicit representation of the filter process which is a piecewise-deterministic process, is also given. Then we propose two solution techniques for the transformed model. First, a generalized verification technique (with a generalized Hamilton–Jacobi–Bellman equation) is formulated where the strict differentiability of the value function is weaken to local Lipschitz continuity. Second, we present a discrete-time Markovian decision model by which we are able to compute an optimal control of our given problem. In this context we are also able to state a general existence result for optimal controls. The power of both solution techniques is finally demonstrated for a parallel queueing model with unknown service rates. In particular, the filter process is discussed in detail, the value function is explicitly computed and the optimal control is completely characterized in the symmetric case.     

Heuristics and lower bounds for minimizing fuel consumption in hybrid-electrical vehicles

In hybrid electric vehicles, the electrical powertrain system has multiple energy sources that it can gather power from to satisfy the propulsion power requested by the vehicle at each instant. This paper focusses on the minimization of the fuel consumption of such a vehicle, taking advantage of the different energy sources. Based on global optimization approaches, the proposed heuristics find solutions that best split the power requested between the multi-electrical sources available. A lower bounding procedure is introduced to validate the quality of the solutions. Computational results show a significant improvement over previous results from the literature in both the computing time and the quality of the solutions.     

Analysis,modeling and solution of the concrete delivery problem

This paper describes a specific local search approach to solve a problem arising in logistics which we prove to be NP-hard. The problem is a complex scheduling or vehicle routing problem where we have to schedule the tours of concrete mixer vehicles over a working day from concrete-producing depots to concrete-demanding customers and vice versa. We give a general mixed integer programming model which is too hard to solve for state of the art mixed integer programming optimizers in the case of the usually huge problem instances coming from practice. Therefore we present a certain local search approach to be able to handle huge practical problem instances.     

Low rank matrix recovery from rank one measurements

We study the recovery of Hermitian low rank matrices $X\in {\mathbb{C}}^{n\times n}$ from undersampled measurements via nuclear norm minimization. We consider the particular scenario where the measurements are Frobenius inner products with random rank-one matrices of the form $a_j{a}_j^{?}$ for some measurement vectors $a_1,\dots ,a_m$, i.e., the measurements are given by $b_j=\mathrm{tr}(X{a}_j{a}_j^{?})$. The case where the matrix $X=x{x}^{?}$ to be recovered is of rank one reduces to the problem of phaseless estimation (from measurements $b_j=|〈x,a_j〉{|}^2$) via the PhaseLift approach, which has been introduced recently. We derive bounds for the number m of measurements that guarantee successful uniform recovery of Hermitian rank r matrices, either for the vectors $a_j$, $j=1,\dots ,m$, being chosen independently at random according to a standard Gaussian distribution, or $a_j$ being sampled independently from an (approximate) complex projective t-design with $t=4$. In the Gaussian case, we require $m\ge Crn$ measurements, while in the case of 4-designs we need $m\ge \mathit{Cr}n\log ?(n)$. Our results are uniform in the sense that one random choice of the measurement vectors $a_j$ guarantees recovery of all rank r-matrices simultaneously with high probability. Moreover, we prove robustness of recovery under perturbation of the measurements by noise. The result for approximate 4-designs generalizes and improves a recent bound on phase retrieval due to Gross, Krahmer and Kueng. In addition, it has applications in quantum state tomography. Our proofs employ the so-called bowling scheme which is based on recent ideas by Mendelson and Koltchinskii.     

Reply to the ‘Comment on “Uncommon structural and bonding properties in Ag16B4O10” by A. Lobato,Miguel Á. Salvadó, and J. Manuel Recio,Chem. Sci., 2021, 12, DOI: 10.1039/D1SC02152D

Where are the excess electrons in Ag₁₆B₄O₁₀?

Ag₁₆B₄O₁₀ features an exotic scheme of chemical bonding and extends the growing family of subvalent silver oxides. These findings constitute a new general and intrinsic facet of the chemistry of silver, which has not been fully understood, yet, and definitely deserves to be analysed from different perspectives. Against this background, we distinctly appreciate the efforts made by A. Lobato, Miguel Á. Salvadó, and J. Manuel Recio (LSR) in studying these phenomena at the example of the title compound.¹ While the computational results presented in the Comment article well comply with those published in our original paper,² the interpretations follow different routes. Whereas LSR focus on the analogy of pattern of the Electron Localization Function (ELF) in position space in the title compound with those found in elemental silver, we interpreted the electronic structure of Ag₁₆B₄O₁₀, both in position and reciprocal space, also considering the interactions between cationic and anionic partial structures.     

Speciation of antimony(III) and antimony(V) in cell extracts by anion chromatography/inductively coupled plasma mass spectrometry

An analytical method for the separation and quantification of Sb(III) and Sb(V) using anion chromatography with ICP-MS is presented. The optimum conditions for the separation of the antimony species were established with 15 mmol/L nitric acid at pH 6 as eluent system on a PRP-X100 column. The retention times for antimony(V) and antimony(III) were 85 s and 300 s with detection limits of 0.06 microg/L and 0.29 microg/L, respectively. The proposed method was applied to cell extracts of Leishmania donovani, which were incubated with antimony(III) and antimony(V). Some metabolism seemed to occur within the cells.     

Speciation of antimony(III) and antimony(V) in cell extracts by anion chromatography/ inductively coupled plasma mass spectrometry

An analytical method for the separation and quantification of Sb(III) and Sb(V) using anion chromatography with ICP-MS is presented. The optimum conditions for the separation of the antimony species were established with 15 mmol/L nitric acid at pH 6 as eluent system on a PRP-X100 column. The retention times for antimony(V) and antimony(III) were 85 s and 300 s with detection limits of 0.06 μg/L and 0.29 μg/L, respectively. The proposed method was applied to cell extracts of Leishmania donovani, which were incubated with antimony(III) and antimony(V). Some metabolism seemed to occur within the cells.     

Trans-cis isomerization is responsible for the red-shifted fluorescence in variants of the red fluorescent protein eqFP611

An important class of red fluorescent proteins (RFPs) feature a 2-iminomethyl-5-(4-hydroxybenzylidene)imidazolinone chromophore. Among these proteins, eqFP611 has the chromophore in a coplanar trans orientation, whereas the cis isomer is preferred by other RFPs such as DsRed and its variants. In the photoactivatable protein asFP595, the chromophore can even be switched from the nonfluorescent trans to the fluorescent cis state by light. By using X-ray crystallography, we have determined the structure of dimeric eqFP611 at high resolution (up to 1.1 A). In the far-red emitting eqFP611 variant d2RFP630, which carries an additional Asn143Ser mutation, the chromophore resides predominantly (approximately 80%) in the cis isomeric state, and in RFP639, which has Asn143Ser and Ser158Cys mutations, the chromophore is found completely in the cis form. The pronounced red shift of excitation and emission maxima of RFP639 can thus unambiguously be assigned to trans-cis isomerization of the chromophore. Among RFPs, eqFP611 is thus unique because its chromophore is highly fluorescent in both the cis and trans isomeric forms.     

Reactivity of 2,2′‐Bis(2N‐(1,1′,3,3′‐tetramethyl‐guanidino))diphenylene‐amine with CuI and [Cu(MeCN)4][PF6]: Benzimidazole Formation vs. Cu Oxidation

The reaction of 2,2′‐Bis(2N‐(1,1′,3,3′‐tetramethyl‐guanidino))diphenylene‐amine (TMG₂PA) ( 1 ) with CuI in MeCN results in the formation of [Cu^II(TMG₂PA^amid)I] ( 2 ) indicatingthat Cu^I is the target of an oxidative attack of the N‐H proton of the ligand which itself is converted to molecular hydrogen. In contrast, if [Cu(MeCN)₄][PF₆] is used as the Cu^I source, [Cu^I₂(TMGbenz)₂][PF₆]₂ ( 3 ) is obtained instead. The use of the non‐coordinating counterion [PF₆]^– apparently prevents Cu^I from oxidation but induces itself a cyclisation reaction within the ligand which results in the formation of a benzimidazole‐guanidine ligand.     

Multidentate surface ligand exchange for the immobilization of CdSe/ZnS quantum dots and surface quantum dot-oligonucleotide conjugates

A method for synthesizing multidentate thiol ligands on fused silica surfaces (e.g., optical fibers) was developed for the immobilization of CdSe/ZnS quantum dots (QDs) capped with hydrophilic or hydrophobic ligands. This work was motivated by the poor stability of QDs immobilized via monodentate thiol ligands and the need for stable immobilization strategies in the development of sensor technologies based on QDs. Multi-dentate immobilization was able to withstand washing protocols, and surface ligand exchange occurred via self-assembly through the zinc-metal affinity interaction. Atomic force and scanning electron microscopy images suggested that the QDs were immobilized at high density, approximately 2-4 x 10 (13) cm (-2). It was possible to immobilize one, two, or three colors of QD. Upon immobilization, 1-2 nm bathochromic shifts in the PL spectra were observed. This was attributed to both ligand exchange and the change in local environment. The change in environment was accompanied by a decrease in PL lifetime. Self-assembly of immobilized QD-oligonucleotide and QD-avidin conjugates was also demonstrated. These conjugates were able to hybridize with complementary oligonucleotide and bind biotin, respectively. This versatile immobilization chemistry is an important step in the development of surface-based QD nanosensors. Such technology requires QDs to be immobilized such that they remain accessible to target molecules in solution.