Statistical mechanics of temporal association in neural networks with transmission delays

We study the representation of static patterns and temporal sequences in neural networks with signal delays and a stochastic parallel dynamics. For a wide class of delay distributions, the asymptotic network behavior can be described by a generalized Gibbs distribution, generated by a novel Lyapunov functional for the determination dynamics. We extend techniques of equilibrium statistical mechanics so as to deal with time-dependent phenomena, derive analytic results for both retrieval quality and storage capacity, and compare them with numerical simulations

On the Fourier transform of the characteristic functions of domains with C1C^1 -smooth boundary

We consider domains $D\subseteq\mathbb R^n$ with $C^1$ -smooth boundary and study the following question: when the Fourier transform $\hat{1_D}$ of the characteristic function $1_D$ belongs to $L^p(\mathbb R^n)$?Comment: added two references; added footnotes on pages 6 and 1

Variational Lie algebroids and homological evolutionary vector fields

We define Lie algebroids over infinite jet spaces and establish their equivalent representation through homological evolutionary vector fields.Comment: Int. Workshop "Nonlinear Physics: Theory and Experiment VI" (Gallipoli, Italy; June-July 2010). Published v3 = v2 minus typos, to appear in: Theoret. and Mathem. Phys. (2011) Vol.167:3 (168:1), 18 page

Humalog Mix25 improves 24-hour plasma glucose profiles compared with the human insulin mixture 30/70 in patients with type 2 diabetes mellitus

Objective. To compare the effects of Humalog Mix25 (Humalog Mix75/25 in the USA) (Mix25) and human insulin 30/70 (30/70) on the 24-hour inpatient plasma glucose (PG) profile in patients with type 2 diabetes mellitus (T2DM). Design. A randomised, open-label, 8-week crossover study. Study insulins were injected twice daily, 5 minutes before breakfast and dinner. Setting. Four-week outpatient (dose-adjustment) treatment phase, and 3-day inpatient (test) phase. Patients. Twenty-five insulin-treated patients with T2DM (ages 40 - 66 years), mean (± standard error of the mean) (SEM) HbA1c 7.7% ± 0.23%, and body mass index (BMI) 29.3 ± 0.83 kg/m2. Outcome measures. 24-hour PG profiles, PG excursions after meals, PG area under the curve (AUC), and 30-day hypoglycaemia rate. Results. The 2-hour PG excursions following breakfast (5.5 ± 0.34 v. 7.2 ± 0.34 mmol/l, p = 0.002) and dinner (2.4 ± 0.27 v. 3.4 ± 0.27 mmol/l, p = 0.018) were smaller with Mix25 than with 30/70. PG AUC between breakfast and lunch was smaller with Mix25 than with 30/70 (77.6 ± 3.8 v. 89.5 ± 4.3 mmol/h/ml, p = 0.001). PG AUC between lunch and dinner, dinner and bedtime, and bedtime and breakfast did not differ between treatments. Pre-meal and nocturnal PG were comparable. The postprandial insulin requirement for lunch meals was supplied equally by the two insulin treatments. The thirty-day hypoglycaemia rate was low (Mix25 0.049 ± 0.018 v. 30/70 0.100 ± 0.018 episodes/patient/30 days, p = 0.586) for both treatments. Conclusion. In patients with T2DM, Mix25 improved the 24-hour PG profile with lower postprandial PG excursions than with human insulin 30/70. (South African Medical Journal: 2003 93(3): 219-223

Harmonic lattice behavior of two-dimensional colloidal crystals

Using positional data from video-microscopy and applying the equipartition theorem for harmonic Hamiltonians, we determine the wave-vector-dependent normal mode spring constants of a two-dimensional colloidal model crystal and compare the measured band-structure to predictions of the harmonic lattice theory. We find good agreement for both the transversal and the longitudinal mode. For $q\to 0$, the measured spring constants are consistent with the elastic moduli of the crystal.Comment: 4 pages, 3 figures, submitte

Lorentz angle measurements in irradiated silicon detectors between 77 K and 300 K

Future experiments are using silicon detectors in a high radiation environment and in high magnetic fields. The radiation tolerance of silicon improves by cooling it to temperatures below 180 K. At low temperatures the mobility increases, which leads to larger deflections of the charge carriers by the Lorentz force. A good knowledge of the Lorentz angle is needed for design and operation of silicon detectors. We present measurements of the Lorentz angle between 77 K and 300 K before and after irradiation with a primary beam of 21 MeV protons.Comment: 13 pages, 9 figures, submitted to ICHEP2000, Osaka, Japa

Noncommutative Figa-Talamanca-Herz algebras for Schur multipliers

We introduce a noncommutative analogue of the Fig\'a-Talamanca-Herz algebra $A_p(G)$ on the natural predual of the operator space $\frak{M}_{p,cb}$ of completely bounded Schur multipliers on Schatten space $S_p$. We determine the isometric Schur multipliers and prove that the space $\frak{M}_{p}$ of bounded Schur multipliers on Schatten space $S_p$ is the closure in the weak operator topology of the span of isometric multipliers.Comment: 24 pages; corrected typo

Exciton bimolecular annihilation dynamics in supramolecular nanostructures of conjugated oligomers

We present femtosecond transient absorption measurements on $\pi$-conjugated supramolecular assemblies in a high pump fluence regime. Oligo(\emph{p}-phenylenevinylene) monofunctionalized with ureido-\emph{s}-triazine (MOPV) self-assembles into chiral stacks in dodecane solution below 75$^{\circ}$C at a concentration of $4\times 10^{-4}$ M. We observe exciton bimolecular annihilation in MOPV stacks at high excitation fluence, indicated by the fluence-dependent decay of $1^1$B$_{u}$-exciton spectral signatures, and by the sub-linear fluence dependence of time- and wavelength-integrated photoluminescence (PL) intensity. These two characteristics are much less pronounced in MOPV solution where the phase equilibrium is shifted significantly away from supramolecular assembly, slightly below the transition temperature. A mesoscopic rate-equation model is applied to extract the bimolecular annihilation rate constant from the excitation fluence dependence of transient absorption and PL signals. The results demonstrate that the bimolecular annihilation rate is very high with a square-root dependence in time. The exciton annihilation results from a combination of fast exciton diffusion and resonance energy transfer. The supramolecular nanostructures studied here have electronic properties that are intermediate between molecular aggregates and polymeric semiconductors

Hypermatrix factors for string and membrane junctions

The adjoint representations of the Lie algebras of the classical groups SU(n), SO(n), and Sp(n) are, respectively, tensor, antisymmetric, and symmetric products of two vector spaces, and hence are matrix representations. We consider the analogous products of three vector spaces and study when they appear as summands in Lie algebra decompositions. The Z3-grading of the exceptional Lie algebras provide such summands and provides representations of classical groups on hypermatrices. The main natural application is a formal study of three-junctions of strings and membranes. Generalizations are also considered.Comment: 25 pages, 4 figures, presentation improved, minor correction