Kafka on the Shore

Kafka On The Shore consists of three simple concrete letterforms floating on a gallery wall. Reminiscent of minimalist sculpture, the mathematical expression of the letterforms states that ‘r’ is greater than ‘g’. Despite this material simplicity, the solemn presentation of the formula suggests a sense of foreboding, a quiet menace. The work was created as a response to the economic theories of Thomas Piketty presented in his book Capital in the Twenty-First Century. The primary finding of Piketty’s data-driven research is the formula presented by the work; that historically, wealth and inequity both flourish when the rate of return on capital (r) is greater than the rate of economic growth (g). With this simple mathematical summary the book acts as a sobering indictment on the present state of economic inequality.

Stationary crack tip fields in elastic-plastic solids: an overview of recent numerical simulations

In this paper, an overview of some recent numerical simulations of stationary crack tip fields in elastic-plastic solids is presented. First, asymptotic analyses carried out within the framework of 2D plane strain or plane stress conditions in both pressure insensitive and pressure sensitive plastic solids are reviewed. This is followed by discussion of salient results obtained from recent computational studies. These pertain to 3D characteristics of elastic-plastic near-front fields under mixed mode loading, mechanics of fracture and simulation of near-tip shear banding process of amorphous alloys and influence of crack tip constraint on the structure of near-tip fields in ductile single crystals. These results serve to illustrate several important features associated with stress and strain distributions near the crack tip and provide the foundation for understanding the operative failure mechanisms. The paper concludes by highlighting some of the future prospects for this field of study.

Nd2O3 : Eu3+ nanocrystalline phosphor - a new potential thermoluminescing material for dosimetry

Nanoparticles of trivalent Eu3+-doped Nd2O3 phosphors have been prepared using a low-temperature solution combustion method with metal nitrate as precursor and oxalyldihydrazide as a fuel at a fairly low temperature (<500 degrees C) and in a very short time (<5 min). A powder X-ray diffraction pattern reveals that cubic Nd2O3 : Eu3+ crystallites are directly obtained without the requirement of further calcinations. The crystallite size, evaluated from Scherer's formula, was found to be in the range of 20-30 nm. The microstructure and morphology were studied by scanning electron microscopy, which showed the phosphor to be foamy and fluffy in nature. Thermoluminescence characteristics of the Nd2O3 : Eu3+ have been studied using gamma irradiation. These demonstrate that the phosphor is suitable for use as a dosimeter.

Entire Solutions of Hydrodynamical Equations with Exponential Dissipation

We consider a modification of the three-dimensional Navier-Stokes equations and other hydrodynamical evolution equations with space-periodic initial conditions in which the usual Laplacian of the dissipation operator is replaced by an operator whose Fourier symbol grows exponentially as e(vertical bar k vertical bar/kd) at high wavenumbers vertical bar k vertical bar. Using estimates in suitable classes of analytic functions, we show that the solutions with initially finite energy become immediately entire in the space variables and that the Fourier coefficients decay faster than e-(C(k/kd) ln(vertical bar k vertical bar/kd)) for any C < 1/(2 ln 2). The same result holds for the one-dimensional Burgers equation with exponential dissipation but can be improved: heuristic arguments and very precise simulations, analyzed by the method of asymptotic extrapolation of van der Hoeven, indicate that the leading-order asymptotics is precisely of the above form with C = C-* = 1/ ln 2. The same behavior with a universal constant C-* is conjectured for the Navier-Stokes equations with exponential dissipation in any space dimension. This universality prevents the strong growth of intermittency in the far dissipation range which is obtained for ordinary Navier-Stokes turbulence. Possible applications to improved spectral simulations are briefly discussed.

Low loss and frequency (1 kHz-1 MHz) independent dielectric characteristics of 3BaO-3TiO(2)-B2O3 glasses

X-ray powder diffraction along with differential thermal analysis carried out on the as-quenched samples in the 3BaO-3TiO(2)-B2O3 system confirmed their amorphous and glassy nature, respectively. The dielectric constants in the 1 kHz-1 MHz frequency range were measured as a function of temperature (323-748 K). The dielectric constant and loss were found to be frequency independent in the 323-473 K temperature range. The temperature coefficient of dielectric constant was estimated using Havinga's formula and found to be 16 ppm K-1. The electrical relaxation was rationalized using the electric modulus formalism. The dielectric constant and loss were 17 +/- 0.5 and 0.005 +/- 0.001, respectively at 323 K in the 1 kHz-1 MHz frequency range which may be of considerable interest to capacitor industry.

Convergence analysis of the Newton algorithm and a pseudo-time marching scheme for diffuse correlation tomography

We propose a self-regularized pseudo-time marching scheme to solve the ill-posed, nonlinear inverse problem associated with diffuse propagation of coherent light in a tissuelike object. In particular, in the context of diffuse correlation tomography (DCT), we consider the recovery of mechanical property distributions from partial and noisy boundary measurements of light intensity autocorrelation. We prove the existence of a minimizer for the Newton algorithm after establishing the existence of weak solutions for the forward equation of light amplitude autocorrelation and its Frechet derivative and adjoint. The asymptotic stability of the solution of the ordinary differential equation obtained through the introduction of the pseudo-time is also analyzed. We show that the asymptotic solution obtained through the pseudo-time marching converges to that optimal solution provided the Hessian of the forward equation is positive definite in the neighborhood of optimal solution. The superior noise tolerance and regularization-insensitive nature of pseudo-dynamic strategy are proved through numerical simulations in the context of both DCT and diffuse optical tomography. (C) 2010 Optical Society of America.

Delamination of Surfactant-Intercalated Brucite-Like Hydroxy Salts of Cobalt and Copper and Solvothermal Decomposition of the Resultant Colloidal Dispersions

Surfactant anion intercalated hydroxy salts of copper and cobalt of the formula M(OH)(2-x)(surf)(x)center dot mH(2)O [M = Cu, Co; surf = dodecyl sulfate. dodecyl benzene sulfonate. and x = 0.5 for Cu and 0.67 for Co] delaminate readily in 1-butanol to give translucent colloidal dispersions that are stable for months. The extent of delamination and the colloidal dispersion observed in these solids is higher than what had been observed for layered double hydroxides. The dispersions yield the corresponding nanoparticulate oxides on solvothermal decomposition. While the copper hydroxy salt forms similar to 300 nm dendrimer-like CuO nanostructures comprising nanorods of similar to 10 nm diameter, the cobalt analogue forms similar to 20 nm superparamagnetic particles of Co3O4.

Boson-fermion duality in SU(m vertical bar n) supersymmetric Haldane-Shastry spin chain

By using the Y(gl(m|n)) super Yangian symmetry of the SU(m|n) supersymmetric Haldane-Shastry spin chain, we show that the partition function of this model satisfies a duality relation under the exchange of bosonic and fermionic spin degrees of freedom. As a byproduct of this study of the duality relation, we find a novel combinatorial formula for the super Schur polynomials associated with some irreducible representations of the Y(gl(m|n)) Yangian algebra. Finally, we reveal an intimate connection between the global SU(m|n) symmetry of a spin chain and the boson-fermion duality relation. (C) 2007 Elsevier B.V. All rights reserved.

Dynamics of Barrierless and Activated Chemical Reactions in a Dispersive Medium within the Fractional Diffusion Equation Approach

Barrierless chemical reactions have often been modeled as a Brownian motion on a one-dimensional harmonic potential energy surface with a position-dependent reaction sink or window located near the minimum of the surface. This simple (but highly successful) description leads to a nonexponential survival probability only at small to intermediate times but exponential decay in the long-time limit. However, in several reactive events involving proteins and glasses, the reactions are found to exhibit a strongly nonexponential (power law) decay kinetics even in the long time. In order to address such reactions, here, we introduce a model of barrierless chemical reaction where the motion along the reaction coordinate sustains dispersive diffusion. A complete analytical solution of the model can be obtained only in the frequency domain, but an asymptotic solution is obtained in the limit of long time. In this case, the asymptotic long-time decay of the survival probability is a power law of the Mittag−Leffler functional form. When the barrier height is increased, the decay of the survival probability still remains nonexponential, in contrast to the ordinary Brownian motion case where the rate is given by the Smoluchowski limit of the well-known Kramers' expression. Interestingly, the reaction under dispersive diffusion is shown to exhibit strong dependence on the initial state of the system, thus predicting a strong dependence on the excitation wavelength for photoisomerization reactions in a dispersive medium. The theory also predicts a fractional viscosity dependence of the rate, which is often observed in the reactions occurring in complex environments.

Spherical means with centers on a hyperplane in even dimensions

Given a real-valued function on R-n we study the problem of recovering the function from its spherical means over spheres centered on a hyperplane. An old paper of Bukhgeim and Kardakov derived an inversion formula for the odd n case with great simplicity and economy. We apply their method to derive an inversion formula for the even n case. A feature of our inversion formula, for the even n case, is that it does not require the Fourier transform of the mean values or the use of the Hilbert transform, unlike the previously known inversion formulas for the even n case. Along the way, we extend the isometry identity of Bukhgeim and Kardakov for odd n, for solutions of the wave equation, to the even n case.

1-[5-Acetyl-4-(4-bromophenyl)-2,6-dimethyl-1,4-dihydropyridin-3-yl]eth anone monohydrate

The 1,4-dihydropyridine ring in the title hydrate, C17H18BrNO2 center dot H2O, has a flattened-boat conformation, and the benzene ring is occupies a position orthogonal to this [dihedral angle: 82.19 (16)degrees]. In the crystal packing, supramolecular arrays mediated by N-H center dot center dot center dot O-water and O-water-H center dot center dot center dot O-carbonyl hydrogen bonding are formed in the bc plane. A highly disordered solvent molecule is present within a molecular cavity defined by the organic and water molecules. Its contribution to the electron density was removed from the observed data in the final cycles of refinement and the formula, molecular weight and density are given without taking into account the contribution of the solvent molecule.

New insights from a fixed-point analysis of single cell IEEE 802.11 WLANs

We study a fixed-point formalization of the well-known analysis of Bianchi. We provide a significant simplification and generalization of the analysis. In this more general framework, the fixed-point solution and performance measures resulting from it are studied. Uniqueness of the fixed point is established. Simple and general throughput formulas are provided. It is shown that the throughput of any flow will be bounded by the one with the smallest transmission rate. The aggregate throughput is bounded by the reciprocal of the harmonic mean of the transmission rates. In an asymptotic regime with a large number of nodes, explicit formulas for the collision probability, the aggregate attempt rate, and the aggregate throughput are provided. The results from the analysis are compared with ns2 simulations and also with an exact Markov model of the backoff process. It is shown how the saturated network analysis can be used to obtain TCP transfer throughputs in some cases.

Bayesian estimation of small effects in exercise and sports science

The aim of this paper is to provide a Bayesian formulation of the so-called magnitude-based inference approach to quantifying and interpreting effects, and in a case study example provide accurate probabilistic statements that correspond to the intended magnitude-based inferences. The model is described in the context of a published small-scale athlete study which employed a magnitude-based inference approach to compare the effect of two altitude training regimens (live high-train low (LHTL), and intermittent hypoxic exposure (IHE)) on running performance and blood measurements of elite triathletes. The posterior distributions, and corresponding point and interval estimates, for the parameters and associated effects and comparisons of interest, were estimated using Markov chain Monte Carlo simulations. The Bayesian analysis was shown to provide more direct probabilistic comparisons of treatments and able to identify small effects of interest. The approach avoided asymptotic assumptions and overcame issues such as multiple testing. Bayesian analysis of unscaled effects showed a probability of 0.96 that LHTL yields a substantially greater increase in hemoglobin mass than IHE, a 0.93 probability of a substantially greater improvement in running economy and a greater than 0.96 probability that both IHE and LHTL yield a substantially greater improvement in maximum blood lactate concentration compared to a Placebo. The conclusions are consistent with those obtained using a ‘magnitude-based inference’ approach that has been promoted in the field. The paper demonstrates that a fully Bayesian analysis is a simple and effective way of analysing small effects, providing a rich set of results that are straightforward to interpret in terms of probabilistic statements.

Cow's milk allergy and the development of tolerance

Aims: To gain insight on the immunological processes behind cow’s milk allergy (CMA) and the development of oral tolerance. To furthermore investigate the associations of HLA II and filaggrin genotypes with humoral responses to early oral antigens. Methods: The study population was from a cohort of 6209 healthy, full-term infants who in a double-blind randomized trial received supplementary feeding at maternity hospitals (mean duration 4 days): cow’s milk (CM) formula, extensively hydrolyzed whey formula or donor breast milk. Infants who developed CM associated symptoms that subsided during elimination diet (n=223) underwent an open oral CM challenge (at mean age 7 months). The challenge was negative in 112, and in 111 it confirmed CMA, which was IgE-mediated in 83. Patients with CMA were followed until recovery, and 94 of them participated in a follow-up study at age 8-9 years. We investigated serum samples at diagnosis (mean age 7 months, n=111), one year later (19 months, n=101) and at follow-up (8.6 years, n=85). At follow-up, also 76 children randomly selected from the original cohort and without CM associated symptoms were included. We measured CM specific IgE levels with UniCAP (Phadia, Uppsala, Sweden), and β-lactoglobulin, α-casein and ovalbumin specific IgA, IgG1, IgG4 and IgG levels with enzyme-linked immunosorbent assay in sera. We applied a microarray based immunoassay to measure the binding of IgE, IgG4 and IgA serum antibodies to sequential epitopes derived from five major CM proteins at the three time points in 11 patients with active IgE-mediated CMA at age 8-9 years and in 12 patients who had recovered from IgE-mediated CMA by age 3 years. We used bioinformatic methods to analyze the microarray data. We studied T cell expression profile in peripheral blood mononuclear cell (PBMC) samples from 57 children aged 5-12 years (median 8.3): 16 with active CMA, 20 who had recovered from CMA by age 3 years, 21 non-atopic control subjects. Following in vitro β-lactoglobulin stimulation, we measured the mRNA expression in PBMCs of 12 T-cell markers (T-bet, GATA-3, IFN-γ, CTLA4, IL-10, IL-16, TGF-β, FOXP3, Nfat-C2, TIM3, TIM4, STIM-1) with quantitative real time polymerase chain reaction, and the protein expression of CD4, CD25, CD127, FoxP3 with flow cytometry. To optimally distinguish the three study groups, we performed artificial neural networks with exhaustive search for all marker combinations. For genetic associations with specific humoral responses, we analyzed 14 HLA class II haplotypes, the PTPN22 1858 SNP (R620W allele) and 5 known filaggrin null mutations from blood samples of 87 patients with CMA and 76 control subjects (age 8.0-9.3 years). Results: High IgG and IgG4 levels to β-lactoglobulin and α-casein were associated with the HLA (DR15)-DQB1*0602 haplotype in patients with CMA, but not in control subjects. Conversely, (DR1/10)-DQB1*0501 was associated with lower IgG and IgG4 levels to these CM antigens, and to ovalbumin, most significantly among control subjects. Infants with IgE-mediated CMA had lower β -lactoglobulin and α-casein specific IgG1, IgG4 and IgG levels (p<0.05) at diagnosis than infants with non-IgE-mediated CMA or control subjects. When CMA persisted beyond age 8 years, CM specific IgE levels were higher at all three time points investigated and IgE epitope binding pattern remained stable (p<0.001) compared with recovery from CMA by age 3 years. Patients with persisting CMA at 8-9 years had lower serum IgA levels to β-lactoglobulin at diagnosis (p=0.01), and lower IgG4 levels to β-lactoglobulin (p=0.04) and α-casein (p=0.05) at follow-up compared with patients who recovered by age 3 years. In early recovery, signal of IgG4 epitope binding increased while that of IgE decreased over time, and binding patterns of IgE and IgG4 overlapped. In T cell expression profile in response to β –lactoglobulin, the combination of markers FoxP3, Nfat-C2, IL-16, GATA-3 distinguished patients with persisting CMA most accurately from patients who had become tolerant and from non-atopic subjects. FoxP3 expression at both RNA and protein level was higher in children with CMA compared with non-atopic children. Conclusions: Genetic factors (the HLA II genotype) are associated with humoral responses to early food allergens. High CM specific IgE levels predict persistence of CMA. Development of tolerance is associated with higher specific IgA and IgG4 levels and lower specific IgE levels, with decreased CM epitope binding by IgE and concurrent increase in corresponding epitope binding by IgG4. Both Th2 and Treg pathways are activated upon CM antigen stimulation in patients with CMA. In the clinical management of CMA, HLA II or filaggrin genotyping are not applicable, whereas the measurement of CM specific antibodies may assist in estimating the prognosis.

Performance of Quantized Equal Gain Transmission With Noisy Feedback Channels

In this paper, new results and insights are derived for the performance of multiple-input, single-output systems with beamforming at the transmitter, when the channel state information is quantized and sent to the transmitter over a noisy feedback channel. It is assumed that there exists a per-antenna power constraint at the transmitter, hence, the equal gain transmission (EGT) beamforming vector is quantized and sent from the receiver to the transmitter. The loss in received signal-to-noise ratio (SNR) relative to perfect beamforming is analytically characterized, and it is shown that at high rates, the overall distortion can be expressed as the sum of the quantization-induced distortion and the channel error-induced distortion, and that the asymptotic performance depends on the error-rate behavior of the noisy feedback channel as the number of codepoints gets large. The optimum density of codepoints (also known as the point density) that minimizes the overall distortion subject to a boundedness constraint is shown to be the same as the point density for a noiseless feedback channel, i.e., the uniform density. The binary symmetric channel with random index assignment is a special case of the analysis, and it is shown that as the number of quantized bits gets large the distortion approaches the same as that obtained with random beamforming. The accuracy of the theoretical expressions obtained are verified through Monte Carlo simulations.