Nuclear masses set bounds on quantum chaos

It has been suggested that chaotic motion inside the nucleus may significantly limit the accuracy with which nuclear masses can be calculated. Using a power spectrum analysis we show that the inclusion of additional physical contributions in mass calculations, through many-body interactions or local information, removes the chaotic signal in the discrepancies between calculated and measured masses. Furthermore, a systematic application of global mass formulas and of a set of relationships among neighboring nuclei to more than 2000 nuclear masses allows one to set an unambiguous upper bound for the average errors in calculated masses, which turn out to be almost an order of magnitude smaller than estimated chaotic components.     

Consistent discretization and loop quantum geometry

We apply the "consistent discretization" approach to general relativity leaving the spatial slices continuous. The resulting theory is free of the diffeomorphism and Hamiltonian constraints, but one can impose the diffeomorphism constraint to reduce its space of solutions and the constraint is preserved exactly under the discrete evolution. One ends up with a theory that has as physical space what is usually considered the kinematical space of loop quantum geometry, given by diffeomorphism invariant spin networks endowed with appropriate rigorously defined diffeomorphism invariant measures and inner products. The dynamics can be implemented as a unitary transformation and the problem of time explicitly solved or at least reduced to a numerical problem. We exhibit the technique explicitly in (2+1)-dimensional gravity.     

Empirical modeling of human face kinematics during speech using motion clustering

In this paper we present an algorithm for building an empirical model of facial biomechanics from a set of displacement records of markers located on the face of a subject producing speech. Markers are grouped into clusters, which have a unique primary marker and a number of secondary markers with an associated weight. Motion of the secondary markers is computed as the weighted sum of the primary markers of the clusters to which they belong. This model may be used to produce facial animations, by driving the primary markers with measured kinematic signals.     

Fermi-like behavior of weakly vibrated granular matter

Vertical movement of zirconia-yttria stabilized 2 mm balls is measured by a laser facility at the surface of a vibrated 3D granular matter under gravity. Realizations z(t) are measured from the top of the container by tuning the fluidized gap with a 1D measurement window in the direction of the gravity. The statistics obeys a Fermi-like configurational approach which is tested by the relation between the dispersions in amplitude and velocity. We introduce a generalized equipartition law to characterize the ensemble of particles which cannot be described in terms of a Brownian motion. The relation between global granular temperature and the external excitation frequency is established.     

Macrocycle-Derived Functional Xanthenes and Progress Towards Concurrent Detection of Glucose and Fructose

The detection of saccharides in biological media is of great current importance for the monitoring of disease states. We have previously reported that solutions of boronic acid-functionalized macrocycles form acyclic oligomeric materials in situ. The oligomers contain fluorescent xanthene moieties. Current efforts are aimed at modulating the spectroscopic responses of these materials for the analysis of specific sugars. We describe conditions whereby the xanthene boronic acids exhibit high colorimetric fructose selectivity. In contrast, at physiological levels selective glucose monitoring can be achieved via fluorescence. Additionally, we describe a method which exhibits promise for detecting both glucose and fructose at dual wavelengths in the UV-Vis region. Mechanistic rationale for each of these findings is presented.     

EPR spectroscopy of protein microcrystals oriented in a liquid crystalline polymer medium

Correlation of the g-tensor of a paramagnetic active center of a protein with its structure provides a unique experimental information on the electronic structure of the metal site. To address this problem, we made solid films containing metalloprotein (Desulfovibrio gigas cytochrome c(3)) microcrystals. The microcrystals in a liquid crystalline polymer medium (water/hydroxypropylcellulose) were partially aligned by a shear flow. A strong orientation effect of the metalloprotein was observed by EPR spectroscopy and polarizing optical microscopy. The EPR spectra of partially oriented samples were simulated, allowing for molecular orientation distribution function determination. The observed effect results in enhanced sensitivity and resolution of the EPR spectra and provides a new approach towards the correlation of spectroscopic data, obtained by EPR or some other technique, with the three-dimensional structure of a protein or a model compound.     

Ultrasensitive ATP detection using firefly luciferase entrapped in sugar-modified sol-gel-derived silica

Firefly luciferase (FL) was entrapped in sol-gel-derived silica containing precursors based on covalent linkage of d-gluconolactone or d-maltonolactone to (aminopropyl)triethoxysilane to form N-(3-triethoxysilylpropyl)gluconamide or N-(3-triethoxysilylpropyl)maltonamide. The enzyme was active and stable in this material and showed catalytic constants close to those in solution. As little as 20 amol ATP could be detected with the entrapped FL, and the entrapped enzyme could be used over several cycles.     

Nontrivial Solutions for a Semilinear Dirichlet Problem with Nonlinearity Crossing Multiple Eigenvalues

In this paper we prove that a semilinear elliptic boundary value problem has at least three nontrivial solutions when the range of the derivative of the nonlinearity includes at least the first two eigenvalues of the Laplacian and all solutions are nondegenerate. A pair are of one sign (positive and negative, respectively). The one sign solutions are of Morse index less than or equal to 1 and the third solution has Morse index greater than or equal to 2. Extensive use is made of the mountain pass theorem, and Morse index arguments of the type Lazer–Solimini (see Lazer and Solimini, Nonlinear Anal. 12(8), 761–775, 1988). Our result extends and complements a theorem of Cossio and Veléz, Rev. Colombiana Mat. 37(1), 25–36, 2003.AMS Subject classification: 35J20; 35J25; 35J60.Dedicated to Professor Shui-Nee Chow on the occasion of his 60th birthday.     

High focal depth with fractional-power wave fronts

We explore the use of phase profiles with fractional power for tailoring modulation transfer functions with high focal depth at high pupil apertures. We present numerical simulations of the images that can be obtained with certain fractional-power profiles.