Transient Analysis for State-Dependent Queues with Catastrophes

Abstract

Queueing systems with catastrophes and state-dependent arrival and service rates are considered. For two types of queueing systems namely, queues with discouraged arrivals and infinite server queue, explicit expressions for the transient probabilities of system size are obtained by using continued fractions technique. Some system performance measures and steady-state probabilities are studied. The effect of system parameters on system size probabilities are also illustrated numerically. It is observed that the steady-state probabilities differ when catastrophes are present, while they are identical in the absence of catastrophes.     

Sequence‐Defined Introduction of Hydrophobic Motifs and Effects in Lectin Binding of Precision Glycomacromolecules

This study investigates the influence of an increasingly hydrophobic backbone of multivalent glycomimetics based on sequence‐defined oligo(amidoamines) on their resulting affinity toward bacterial lectins. Glycomacromolecules are obtained by stepwise assembly of tailor‐made building blocks on solid support, using both hydrophobic aliphatic and aromatic building blocks to enable a gradual change in hydrophobicity of the backbone. Their binding behavior toward model lectin Concanavalin A (ConA) is evaluated using isothermal titration calorimetry (ITC) and surface plasmon resonance (SPR) showing higher affinities for glycomacromolecules with higher content of hydrophobic and aromatic moieties in the backbone. Finally, glycomacromolecules are tested in a bacterial adhesion inhibition study against Escherichia coli where more hydrophobic backbones yield higher inhibitory potentials most likely due to additional secondary interactions with hydrophobic regions of the protein receptor as well as a change in conformation exposing carbohydrate ligands for increased binding. Overall, the results highlight the influence and thereby importance of the polymer backbone itself on the resulting properties of polymeric biomimetics.     

Synthesis of 7a-substituted Hajos-Wiechert ketone analogues

A general and efficient route to 2-substituted 1,3-cyclopentadiones 3 has been developed. This operationally simple, two-step procedure is amenable to multigram scale preparations of these useful synthetic intermediates. These compounds are then transformed to previously unknown, higher analogues of the Hajos-Parrish-Eder-Sauer-Wiechert ketone (enone 1, R = Me) following an enantioselective Robinson annulation.     

Fiber Integrated Metal-Organic Frameworks as Functional Components in Smart Textiles

Owing to high modularity and synthetic tunability, metal–organic frameworks (MOFs) on textiles are poised to contribute to the development of state-of-the-art wearable systems with multifunctional performance. While these composite materials have demonstrated promising functions in sensing, filtration, detoxification, and biomedicine, their applicability in multifunctional systems is only beginning to materialize. This review highlights the multifunctionality and versatility of MOF-integrated textile systems. It summarizes the operational goals of MOF@textile composites, encompassing sensing, filtration, detoxification, drug delivery, UV protection, and photocatalysis. Building upon these recent advances, this review concludes with an outlook on emerging opportunities for the diverse applications of MOF@textile systems in the realm of smart wearables.     

Physical insights from a penetration depth model of optically pumped NMR

A model of optically pumped NMR (OPNMR) behavior in GaAs that connects the photon energy dependence of the OPNMR signal intensity for (69)Ga with different polarizations of light has been developed. Inputs to this model include experimental conditions--external magnetic field (B(0)), temperature (T), and optical pumping parameters (tau(L), laser helicity)--as well as parameters that arise from sample-specific characteristics--electron spin lifetime (T(1e)), electron lifetime (tau(e)), electron-nuclear correlation time (tau(c)), and sample thickness (z). These various inputs affect the profile of the OPNMR signal intensity as a function of photon energy (E) in a predictable manner. Therefore, the profile can serve as a composite fingerprint by which individual parameters can be inferred when not known. Characteristics of the profile include the photon energy for maximum OPNMR signal intensity and the intensity ratio between sigma(+) and sigma(-) light.     

Optically pumped nuclear magnetic resonance of semiconductors

Optically pumped NMR (OPNMR) of direct gap and indirect gap semiconductors has been an area of active research interest, motivated by both basic science and technological perspectives. Proposals to enhance and to spatially localize nuclear polarization have stimulated interest in this area. Recent progress in OPNMR has focused on exploring the experimental parameter space in order to elucidate details of the underlying photophysics of optical pumping phenomena. The focus of this review is on recent studies of bulk samples of GaAs and InP, namely, the photon energy dependence, the magnetic field dependence, and the phase dependence of OPNMR resonances. Models for the development of nuclear polarization are discussed.     

Perfect state transfer in Laplacian quantum walk

For a graph G and a related symmetric matrix M, the continuous-time quantum walk on G relative to M is defined as the unitary matrix \(U(t) = \exp (-itM)\), where t varies over the reals. Perfect state transfer occurs between vertices u and v at time \(\tau \) if the (u, v)-entry of \(U(\tau )\) has unit magnitude. This paper studies quantum walks relative to graph Laplacians. Some main observations include the following closure properties for perfect state transfer. If an n-vertex graph has perfect state transfer at time \(\tau \) relative to the Laplacian, then so does its complement if \(n\tau \in 2\pi {\mathbb {Z}}\). As a corollary, the join of \(\overline{K}_{2}\) with any m-vertex graph has perfect state transfer relative to the Laplacian if and only if \(m \equiv 2\pmod {4}\). This was previously known for the join of \(\overline{K}_{2}\) with a clique (Bose et al. in Int J Quant Inf 7:713–723, 2009). If a graph G has perfect state transfer at time \(\tau \) relative to the normalized Laplacian, then so does the weak product \(G \times H\) if for any normalized Laplacian eigenvalues \(\lambda \) of G and \(\mu \) of H, we have \(\mu (\lambda -1)\tau \in 2\pi {\mathbb {Z}}\). As a corollary, a weak product of \(P_{3}\) with an even clique or an odd cube has perfect state transfer relative to the normalized Laplacian. It was known earlier that a weak product of a circulant with odd integer eigenvalues and an even cube or a Cartesian power of \(P_{3}\) has perfect state transfer relative to the adjacency matrix. As for negative results, no path with four vertices or more has antipodal perfect state transfer relative to the normalized Laplacian. This almost matches the state of affairs under the adjacency matrix (Godsil in Discret Math 312(1):129–147, 2011).     

A liquid chromatographic/tandem mass spectroscopic method for quantification of the cyclic peptide melanotan-II. Plasma and brain tissue concentrations following administration in mice

Melanotan-II (MT-II), a synthetic analogue of the natural melanocortin peptide, alpha-melanocyte-stimulating hormone (alpha-MSH), is well known for the anorexic effects it elicits in rodents. These effects are, at least partly, associated with agonistic action on the centrally located melanocortin receptors, MC3R and MC4R. Whether MT-II exerts this effect via brain penetration still remains unclear. In order to address this question we administered MT-II in rodents at efficacious doses and then employed a sensitive methodology for the determination of MT-II in plasma and brain samples. MT-II was extracted from mouse plasma and brain tissue by acetonitrile precipitation followed by liquid chromatography/tandem mass spectrometry (LC/MS/MS) analysis. The described assay improved significantly previously reported MT-II levels of quantification in rat plasma and brain. The lower limits of quantification (LLOQs) of 0.5 ng/mL and 2.5 ng/g were obtained in 50 microL plasma and 100 microL brain homogenate, respectively. The calibration curve was linear over the concentration range of 0.5-500 ng/mL for plasma and 2.5-250 ng/g for brain tissue. The method was successfully applied in measuring levels of MT-II in plasma and brain tissue following intraperitoneal (ip) administration of 1 mg/kg of peptide in mice. Following administration of MT-II, clearance from plasma was rapid. The sensitivity of the assay allowed the determination of low concentrations of MT-II (11.4 +/- 5.5 ng/g) in brain homogenate at 30 min after dosing. However, the brain concentrations when compared with the high plasma levels of MT-II at the same time point confirmed the low penetrability of the peptide in mouse brain.