Globally enumerating unstable periodic orbits for observed data using symbolic dynamics

The unstable periodic orbits of a chaotic system provide an important skeleton of the dynamics in a chaotic system, but they can be difficult to find from an observed time series. We present a global method for finding periodic orbits based on their symbolic dynamics, which is made possible by several recent methods to find good partitions for symbolic dynamics from observed time series. The symbolic dynamics are approximated by a Markov chain estimated from the sequence using information-theoretical concepts. The chain has a probabilistic graph representation, and the cycles of the graph may be exhaustively enumerated with a classical deterministic algorithm, providing a global, comprehensive list of symbolic names for its periodic orbits. Once the symbolic codes of the periodic orbits are found, the partition is used to localize the orbits back in the original state space. Using the periodic orbits found, we can estimate several quantities of the attractor such as the Lyapunov exponent and topological entropy.     

Enhanced (13)C PFG NMR for the study of hydrodynamic dispersion in porous media

PFG NMR methods are frequently used as a means of probing both coherent and incoherent molecular motions of fluids contained within heterogeneous porous media. The time scale over which molecular displacements can be probed in a conventional PFG NMR experiment is limited by the relaxation characteristics of (1)H - the nucleus that is typically observed. In multiphase systems, due to its sensitivity to susceptibility gradients and interactions with surfaces,(1)H signal is frequently characterized by rapid T(1) and T(2) relaxation. In this work, a heteronuclear approach to PFG NMR is demonstrated which allows the study of molecular displacement over extended time scales (and, consequently, length scales) by exploiting the longer relaxation time of (13)C. The method presented employs the DEPT technique of polarization transfer in order to enhance both the sensitivity and efficiency of (13)C detection. This hybrid coherence transfer PFG technique has been used to acquire displacement propagators for flow through a bead pack with an observation time of up to 35 s.     

Spectral editing in solid-state MAS NMR of quadrupolar nuclei using selective satellite inversion

A sensitivity enhancement method based on selective adiabatic inversion of a satellite transition has been employed in a (pi/2)CT-(pi)ST1-(pi/2)CT spectral editing sequence to both enhance and resolve multisite NMR spectra of quadrupolar nuclei. In addition to a total enhancement of 2.5 times for spin 3/2 nuclei, enhancements up to 2.0 times is reported for the edited sites in a mixture of rubidium salts.     

Spectroscopic imaging with volume selection by unpaired adiabatic pi pulses: theory and application

In NMR spectroscopy, volume selection can be advantageously achieved using adiabatic pi pulses, which enable high bandwidth and B(1) insensitivity. In order to avoid the generation of non-linear phase profiles and the subsequent signal loss caused by incoherent averaging, adiabatic pi pulses are usually used in pairs for volume selection in each spatial dimension. Alternatively, when performing spectroscopic imaging (SI), a high enough spatial resolution results in negligible phase dispersion within each pixel. This allows using only one pulse per selected spatial dimension, resulting in a reduced echo-time and reduced power deposition. In this work, the feasibility of such an approach is explored theoretically and numerically, allowing the derivation of explicit conditions to obtain SI images without artifact. Adequate spatial and spectral post-processing procedures are described to compensate for the effect of non-linear phase profiles. These developments are applied to SI in the rat brain at 9.4 T, using a new adiabatic sequence named Pseudo-LASER.     

A mini-landscape of exact MSSM spectra in heterotic orbifolds

We explore a “fertile patch” of the heterotic landscape based on a Z₆-II${\mathbb{Z}}_6\text{-II}$ orbifold with SO(10) and E₆ local GUT structures. We search for models allowing for the exact MSSM spectrum. Our result is that of order 100 out of a total 3×¹⁰⁴$3\times {10}^4$ inequivalent models satisfy this requirement.     

Measurability of vacuum fluctuations and dark energy

Vacuum fluctuations of the electromagnetic field induce current fluctuations in resistively shunted Josephson junctions that are measurable in terms of a physically relevant power spectrum. In this paper we investigate under which conditions vacuum fluctuations can be gravitationally active, thus contributing to the dark energy density of the universe. Our central hypothesis is that vacuum fluctuations are gravitationally active if and only if they are measurable   in terms of a physical power spectrum in a suitable macroscopic or mesoscopic detector. This hypothesis is consistent with the observed dark energy density in the universe and offers a resolution of the cosmological constant problem. Using this hypothesis we show that the observable vacuum energy density _ρvac${\rho }_{\mathit{vac}}$ in the universe is related to the largest possible critical temperature _Tc$T_c$ of superconductors through _ρvac=σ·(_kTc)⁴/?³c³${\rho }_{\mathit{vac}}=\sigma ·({\mathit{kT}}_c{)}^4/{?}^3{c}^3$, where σ$\sigma$ is a small constant of the order 10^-3${10}^{-3}$. This relation can be regarded as an analog of the Stefan–Boltzmann law for dark energy. Our hypothesis is testable in Josephson junctions where we predict there should be a cutoff in the measured spectrum at 1.7 THz if the hypothesis is true.     

Special tensors in the deformation theory of quadratic algebras for the classical Lie algebras

Using deformation theory, Braverman and Joseph constructed certain primitive ideals in the enveloping algebras of the simple Lie algebras. Except in the case sl(2,C)$\mathfrak{s}\mathfrak{l}(2,\mathbb{C})$, there is a special value of the deformation parameter giving an ideal of infinite codimension. For the classical Lie algebras, the uniqueness of the special value is equivalent to the existence of tensors with very particular properties. The existence of these tensors was concluded abstractly by Braverman and Joseph but here we present explicit formulae. This allows a rather direct computation of the special value of the deformation parameter.     

Microporated PEG Spheres for Fluorescent Analyte Detection

Poly(ethylene glycol) (PEG) hydrogels have been used to encapsulate fluorescently labeled molecules in order to detect a variety of analytes. The hydrogels are designed with a mesh size that will retain the sensing elements while allowing for efficient diffusion of small analytes. Some sensing assays, however, require a conformational change or binding of large macromolecules, which may be sterically prohibited in a dense polymer matrix. A process of hydrogel microporation has been developed to create cavities within PEG microspheres to contain the assay components in solution. This arrangement provides improved motility for large sensing elements, while limiting leaching and increasing sensor lifetime. Three hydrogel compositions, 100% PEG, 50% PEG, and microporated 100% PEG, were used to create pH-sensitive microspheres that were tested for response time and stability. In order to assess motility, a second, more complex sensor, namely a FITC-dextran/TRITC-Con A glucose-specific assay was encapsulated within the microspheres.     

Low Temperature Metal-Enhanced Fluorescence

In this short letter, we describe the effects of low temperature on the Metal-Enhanced Fluorescence (MEF) phenomenon. Fluorophores close to Silver Island Films (SiFs) show on average two- to ten-fold enhancements in their fluorescence signatures at room temperature. However, at 77 K, we have observed that MEF is even more pronounced as compared to an identical glass control sample. We also demonstrate that the further enhancements in MEF occur at low temperature over a range of visible wavelengths for different fluorophores, for both SiFs and 20 nm surface deposited gold colloids.     

Match statistics for sequence-based alleles in profiles from forensic PCR-mps kits

The first autosomal sequence-based allele (aka SNP-STR haplotype) frequency database for forensic massively parallel sequencing (MPS) has been published, thereby removing one of the remaining barriers to implementing MPS in casework. The database was developed using a specific set of flank trim sites. If different trim sites or different kits with different primers are used for casework, then SNP-STR haplotypes may be detected that do not have frequencies in the database. We describe a procedure to address calculation of match probabilities when casework samples are generated using an MPS kit with different trim sites than those present in the relevant population frequency database. The procedure provides a framework for comparison of any MPS kit or database combination while also accommodating comparison of MPS and CE profiles.