The age of the arrival process in the G/M/1 and M/G/1 queues

This paper shows that in the G/M/1 queueing model, conditioning on a busy server, the age of the inter-arrival time and the number of customers in the queue are independent. The same is the case when the age is replaced by the residual inter-arrival time or by its total value. Explicit expressions for the conditional density functions, as well as some stochastic orders, in all three cases are given. Moreover, we show that this independence property, which we prove by elementary arguments, also leads to an alternative proof for the fact that given a busy server, the number of customers in the queue follows a geometric distribution. We conclude with a derivation for the Laplace Stieltjes Transform (LST) of the age of the inter-arrival time in the M/G/1 queue.     

Rings and boxes in dissipative environments

We study a particle on a ring in presence of a dissipative Caldeira-Leggett environment and derive its response to a dc field. We find, through a 2-loop renormalization group analysis, that a large dissipation parameter η flows to a fixed point η(R)=η(c)=?/2π. We also reexamine the mapping of this problem to that of the Coulomb box and show that the relaxation resistance, of recent interest, is quantized for large η. For finite η>η(c) we find that a certain average of the relaxation resistance is quantized. We propose a box experiment to measure a quantized noise.     

Large-mode-area fused-fiber combiners, with nearly lowest-mode brightness conservation

We show the feasibility of producing a low-mode all-fiber combiner fabricated from a large core and extremely small NA fibers. Although these fibers support multiple modes, the combiner that we produce can be operated nearly at the single mode regime while preserving the brightness of the combined beam almost perfectly with respect to the inputs. The M-square parameter of the combined beam was 2.3 and the power transfer efficiency was close to 100%. Such an all-fiber beam combining device is a rugged solution for high-brightness, high-efficiency beam delivery.     

Real-time quantification of protein expression and translocation at individual cell resolution using imaging-dish-based live cell array

Cell populations represent intrinsically heterogeneous systems with a high level of spatiotemporal complexity. Monitoring and understanding cell-to-cell diversity is essential for the research and application of intra- and interpopulation variations. Optical analysis of live cells is challenging since both adherent and nonadherent cells change their spatial location. However, most currently available single-cell techniques do not facilitate treatment and monitoring of the same live cells over time throughout multistep experiments. An imaging-dish-based live cell array (ID-LCA) has been developed and produced for cell handling, culturing, and imaging of numerous live cells. The dish is composed of an array of pico scale cavities—pico wells (PWs) embossed on its glass bottom. Cells are seeded, cultured, treated, and spatiotemporally measured on the ID-LCA, while each cell or small group of cells are locally constrained in the PWs. Finally, predefined cells can be retrieved for further evaluation. Various types of ID-LCAs were used in this proof-of-principle work, to demonstrate on-ID-LCA transfection of fluorescently tagged chimeric proteins, as well as the detection and kinetic analysis of their induced translocation. High variability was evident within cell populations with regard to protein expression levels as well as the extent and dynamics of protein redistribution. The association of these parameters with cell morphology and functional parameters was examined. Both the new methodology and the device facilitate research of the translocation process at individual cell resolution within large populations and thus, can potentially be used in high-throughput fashion. Graphical Abstract

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Tight upper bounds on the number of invariant components on translation surfaces

An abelian differential on a surface defines a flat metric and a vector field on the complement of a finite set of points. The vertical flow that can be defined on the surface has two kinds of invariant closed sets (i.e. invariant components) — periodic components and minimal components. We give upper bounds on the number of minimal components, on the number of periodic components and on the total number of invariant components in every stratum of abelian differentials. We also show that these bounds are tight in every stratum.     

Interactions of glucose and polyacrylamide in solutions and gels

The swelling of polyacrylamide (PAAm) gels increased with rising glucose concentrations, and so did the osmotic pressure of the soluble polymer and its intrinsic viscosity. A Flory–Huggins‐based model for the osmotic pressure of a nonionic hydrophilic polymer in a ternary solution consisting of a main solvent, a polymer, and a nondissociating low‐molecular‐weight cosolute was developed and examined. The model‐calculated values were in reasonably good agreement with experimental results for the water–PAAm–glucose system studied when PAAm–water and glucose–water interaction coefficients from the binary systems were used, and only the PAAm–glucose interaction coefficient was adjusted. Its negative value suggested a favorable interaction of glucose and PAAm, supporting the notion of glucose being a good cosolvent for PAAm. Isothermal titration microcalorimetry results showed no evidence for the binding of glucose to PAAm, but an exothermic interaction was indicated between glucose and PAAm. Microcalorimetrically determined enthalpic contributions to the Flory–Huggins interaction coefficients showed enthalpically favorable binary interactions, particularly the enthalpic component of the PAAm–glucose interaction coefficient (χ_H23), which was slightly negative. The enthalpically favorable interaction between glucose and PAAm may explain the increased osmotic pressure of PAAm in glucose solutions. © 2003 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 41: 3053–3063, 2003     

Simply connected coset complexes for rank 1 groups of Lie type

This work was partially supported by BSF 92-00320     

Composite quarks and leptons in supersymmetric grand unification

Chirality under SUSY-GUT is suggested as a sufficient condition for composites to be massless, in addition to the necessary anomaly matching á la 't Hooft. This results in a very stringent set of self-consistency requirements, which dictates also the number and structure of the generations. As an illustration I present an [SU(3)]³×[SUSY] model. It involves three generations (2 light + 1 heavy) and some other realistic features.     

Spatial encoding strategies for ultrafast multidimensional nuclear magnetic resonance

Multidimensional spectroscopy plays a central role in contemporary magnetic resonance. A general feature of multidimensional NMR is its inherent multiscan nature, stemming from the methodology's reliance on a series of independent acquisitions to sample the spins' evolutions throughout the indirect time domains. Contrasting this traditional feature, an acquisition scheme has recently been reported that enables the collection of complete of multidimensional NMR data sets within one single scan. Provided that the signals to be observed are sufficiently strong, this new "ultrafast" protocol can thus shorten the acquisition times of multidimensional NMR experiments by several orders of magnitude. This new methodology operates by departing from temporal encoding principles used since the advent of Fourier-transform NMR, replacing them with a spatial encoding of the spin interactions. Spatial encoding operates in turn on the basis of novel radiofrequency irradiation and magnetic field gradient waveform manipulations, designed so as to impart on the sample a coherent spin magnetization pattern that reflects the internal interactions to be measured. Given the central role played by this new kind of spectroscopic-oriented manipulations in ultrafast NMR, we devote this review to surveying different variants that have hitherto been proposed for their implementation. These include both discrete and continuous versions, real- and constant-time implementations, as well as amplitude- and phase-modulated alternatives. The principles underlying these various spatial encoding approaches are treated, their operation is graphically illustrated as well as formally derived within suitable theoretical frameworks, and an in-depth comparison of their line shape characteristics is discussed.