A survey on discriminatory processor sharing

The Discriminatory Processor Sharing (DPS) model is a multi-class generalization of the egalitarian Processor Sharing model. In the DPS model all jobs present in the system are served simultaneously at rates controlled by a vector of weights {g_k > 0; k = 1,..., K }. If there are N_k jobs of class k present in the system, k = 1,..., K, each class-k job is served at rate . The present article provides an overview of the analytical results for the DPS model. In particular, we focus on response times and numbers of jobs in the system. This work is part of a French-Dutch Van Gogh research project funded by NWO (The Netherlands Organization for Scientific Research) and EGIDE under grant VGP 61-520. We also acknowledge the support of EuroNGI Network of Excellence. This work was done while U. Ayesta was an ERCIM Postdoc fellow at CWI.     

Dithiaporphyrin derivatives as photosensitizers in membranes and cells

We synthesized a series of analogues of 5,20-diphenyl-10,15-bis(4-carboxylatomethoxy)phenyl-21,23-dithiaporphyrin (I) as potential photosensitizers for photodynamic therapy (PDT). The photosensitizers differ in the length of the side chains that bind the carboxyl to the phenol at positions 10 and 15 of the thiaporphyrin. The spectroscopic, photophysical, and biophysical properties of these photosensitizers are reported. The structural changes have almost no effect on the excitation/emission spectra with respect to I's spectra or on singlet oxygen generation in MeOH. All of the photosensitizers have a very high, close to 1.00, singlet oxygen quantum yield in MeOH. On the contrary, singlet oxygen generation in liposomes was considerably affected by the structural change in the photosensitizers. The photosensitizers possessing short side chains (one and three carbons) showed high quantum yields of around 0.7, whereas the photosensitizers possessing longer side chains showed smaller quantum yield, down to 0.14 for compound X (possessing side-chain length of 10 carbons), all at 1 microM. Moreover a self-quenching process of singlet oxygen was observed, and the quantum yield decreased as the photosensitizer's concentration increased. We measured the binding constant of I to liposomes and found Kb = 23.3 +/- 1.6 (mg/mL)-1. All the other photosensitizers with longer side chains exhibited very slow binding to liposomes, which prevented us from assessing their Kb's. We carried out fluorescence resonance energy transfer (FRET) measurements to determine the relative depth in which each photosensitizer is intercalated in the liposome bilayer. We found that the longer the side chain the deeper the photosensitizer core is embedded in the bilayer. This finding suggests that the photosensitizers are bound to the bilayer with their acid ends close to the aqueous medium interface and their core inside the bilayer. We performed PDT with the dithiaporphyrins on U937 cells and R3230AC cells. We found that the dark toxicity of the photosensitizers with the longer side chain (X, VI, V) is significantly higher than the dark toxicity of sensitizers with shorter side chains (I, III, IV). Phototoxicity measurements showed the opposite direction; the photosensitizers with shorter side chains were found to be more phototoxic than those with longer side chains. These differences are attributed to the relationship between diffusion and endocytosis in each photosensitizer, which determines the location of the photosensitizer in the cell and hence its phototoxicity.     

Spectroscopy, binding to liposomes and production of singlet oxygen by porphyrazines with modularly variable water solubility

Three novel classes of porphyrazine-like structures were synthesized to form modular structures in which lipophilicity and water solubility can be tuned. Subtle modification of solubility is an important criterion in selecting a compound for biological photosensitization. The general structure takes the form H2[pz(AnB4-n)], where the core is a porphyrazine (pz) group, A is a pyrrole ring with two sulfide linkages (SR moieties) and B is a pyrrole fused with a 4,7-bis(isopropyloxy)benzo group, with n=4, 3 and 2. These molecules possess their longest wavelength absorption band between 700 and 810 nm, hence laser beams of higher tissue penetration depth could be used to illuminate them in photodynamic therapy (PDT). Armed with absorption bands in the far-red and near-infrared (near-IR), and a capability to tune the solubility, these molecules could make for better sensitizers because of optimized uptake by lipidic membranes and better optical properties. We tested several derivatives of the A4, A3B and A2B2 structures for their singlet oxygen quantum yields in methanol and in liposomes, using 9,10-dimethyl anthracene (DMA) as a singlet oxygen target. Singlet oxygen quantum yields in liposomes ranged from 0.01 to 0.44, with the A2B2 group showing the most promise. In the binding assay to find the equilibrium binding constant, Kb, we detected fluorescence changes due to a change in environment. Peripheral long-chain moieties (the R group in the SR moieties) dominate lipid binding. These moieties range in the hydrophobicity that they induce from C8H17 and benzene, which rendered the molecule totally insoluble in water, to polyethylene glycol (PEG) and carboxylate groups, which imparted water solubility. Each molecule had between 4 and 8 such identical chains. Chains bearing an ether or ester link resulted in measurable equilibrium constants, with a higher Kb for ether substituents. Results for Kb ranged from 0.23 to 26.52 (mg mL(-1))(-1). A delicate balance exists between water solubility and good partitioning to membranes. In general, a higher oxygen-to-carbon ratio in the chains improves binding. Fewer chains and a centrally coordinated zinc ion further improve binding and singlet oxygen production.     

Urchin-like α-MnO<Subscript>2</Subscript> formed by nanoneedles for high-performance lithium batteries

MnO₂ nanoneedles (NNs) were synthesized by sol-gel assisted by a redox reaction between ascorbic acid and KMnO₄. X-ray powder diffraction (XRD), thermogravimetric analysis (TGA), Raman, far-infrared spectroscopy, and magnetic measurements confirm the tunnel structure of the tetragonal α-MnO₂ phase. The MnO₂ NNs prepared by sol-gel at moderate temperature (T ≈ 350 °C) aggregate with an urchin-like morphology observed by scanning electron (SEM) and high-resolution transmission electron (TEM) microscopy. Electrochemical investigations show an outstanding initial specific capacity ca. 230 mAh g^?1 and 45 % capacity retention at 100th cycle was obtained for these MnO₂ nanoneedles.     

Vibrational energy relaxation rates of H2 and D2 in liquid argon via the linearized semiclassical method

The vibrational energy relaxation (VER) rates for H2 and D2 in liquid argon (T=152 K, rho=1.45x1022 cm-3) are calculated using the linearized semiclassical (LSC) method (J. Phys. Chem. 2003, 107, 9059, 9070). The calculation is based on Fermi's golden rule. The VER rate constant is expressed in terms of the quantum-mechanical force-force correlation function, which is then estimated using the LSC method. A local harmonic approximation (LHA) is employed in order to compute the multidimensional Wigner integrals underlying the LSC approximation. The H2-Ar and D2-Ar interactions are described by the three-body potential of Bissonette et al. (J. Phys. Chem. A 1996, 105, 2639). The LHA-LSC-based VER rate constants for both D2 and H2 are found to be about 2-3 orders of magnitude slower than those obtained experimentally. However, their ratio agrees quantitatively with the corresponding experimental result. In contrast, the classical VER rate constants are found to be 8-9 orders of magnitude slower than those obtained experimentally, and their ratio is found to be qualitatively different from the corresponding experimental result.     

Flocking With Short-Range Interactions

Journal of Statistical Physics - We study the large-time behavior of continuum alignment dynamics based on Cucker–Smale (CS)-type interactions which involve short-range kernels, that is,...     

$$(O( V \oplus F), O( V))$$ is a Gelfand pair for any quadratic space V over a local field F

Let V be a quadratic space with a form q over an arbitrary local field F of characteristic different from 2. Let with the form Q extending q with Q(e) = 1. Consider the standard embedding and the two-sided action of on . In this note we show that any -invariant distribution on is invariant with respect to transposition. This result was earlier proven in a bit different form in van Dijk (Math Z 193:581–593, 1986) for , in Aparicio and van Dijk (Complex generalized Gelfand pairs. Tambov University, 2006) for and in Bosman and van Dijk (Geometriae Dedicata 50:261–282, 1994) for p-adic fields. Here we give a different proof. Using results from Aizenbud et al. (arXiv:0709.1273 (math.RT), submitted), we show that this result on invariant distributions implies that the pair (O(V), O(W)) is a Gelfand pair. In the archimedean setting this means that for any irreducible admissible smooth Fréchet representation (π, E) of we have A stronger result for p-adic fields is obtained in Aizenbud et al. (arXiv:0709.4215 (math.RT), submitted).     

Stability of an encapsulated bubble shell

The stability of an encapsulated bubble filled with gas is studied where gas is allowed to diffuse out of the bubble. A mechanistic model that takes into account shell stiffness and surface tension is considered. A critical shell radius for loss of mechanical stability is derived based on a technique adapted for small radius, where surface tension effects become substantial. A new parameter is defined that determines the relative importance of surface tension forces and shell stiffness for shell stability. The developed technique allows to predict, for a given bubble population and gas saturation level of the surrounding liquid, a range of bubble sizes which may collapse in time. Surface tension effects are dominant in determining the critical radius but have a negligible effect on the minimal radius for collapse. The influence of the surface tension on the stability of the shell is illustrated for Optison, a typical ultrasound contrast agent.