Zeta Functions and Monodromy for Surfaces that are General for a Toric Idealistic Cluster

In this article, we consider surfaces that are general withrespect to a three-dimensional toric idealistic cluster. Inparticular, this means that blowing up a toric constellationprovides an embedded resolution of singularities for these surfaces.First we give a formula for the topological zeta function directlyin terms of the cluster. Then we study the eigenvalues of monodromy.In particular, we derive a useful criterion to be an eigenvalue.In a third part, we prove the monodromy and the holomorphy conjecturefor these surfaces.     

Suppressing decoherence of quantum algorithms by jump codes

The stabilizing properties of one-error correcting jump codes are explored under the realistic non-ideal condition of finite recovery times. For this purpose the quantum algorithm of the tent-map is decomposed into a universal set of Hamiltonian quantum gates which ensure perfect correction of spontaneous decay processes under ideal circumstances even if they occur during a gate operation. An entanglement gate is presented which is capable of entangling any two logical qubits of different one-error correcting code spaces. With the help of this gate simultaneous spontaneous decay processes affecting physical qubits of different code spaces can be corrected and decoherence can be suppressed significantly.     

Receiving beam patterns in the horizontal plane of a harbor porpoise (Phocoena phocoena)

Receiving beam patterns of a harbor porpoise were measured in the horizontal plane, using narrow-band frequency modulated signals with center frequencies of 16, 64, and 100 kHz. Total signal duration was 1000 ms, including a 200 ms rise time and 300 ms fall time. The harbor porpoise was trained to participate in a psychophysical test and stationed itself horizontally in a specific direction in the center of a 16-m-diameter circle consisting of 16 equally-spaced underwater transducers. The animal's head and the transducers were in the same horizontal plane, 1.5 m below the water surface. The go/no-go response paradigm was used; the animal left the listening station when it heard a sound signal. The method of constants was applied. For each transducer the 50% detection threshold amplitude was determined in 16 trials per amplitude, for each of the three frequencies. The beam patterns were not symmetrical with respect to the midline of the animal's body, but had a deflection of 3-7 degrees to the right. The receiving beam pattern narrowed with increasing frequency. Assuming that the pattern is rotation-symmetrical according to an average of the horizontal beam pattern halves, the receiving directivity indices are 4.3 at 16 kHz, 6.0 at 64 kHz, and 11.7 dB at 100 kHz. The receiving directivity indices of the porpoise were lower than those measured for bottlenose dolphins. This means that harbor porpoises have wider receiving beam patterns than bottlenose dolphins for the same frequencies. Directivity of hearing improves the signal-to-noise ratio and thus is a tool for a better detection of certain signals in a given ambient noise condition.     

Effect of spermine and DNase on DNA release from bacteriophage T5

Bacterial viruses (bacteriophages) consist of nucleic acid protected by a protein envelope called capsid. At the start of infection, the phage genome is translocated into the bacterial cytoplasm. In vitro (and also in vivo), this DNA release can be triggered by binding a specific receptor protein to the phage tail. The force responsible for the release arises from energy stored in the capsid due to strong confinement of the DNA. We show that this force can be modified by adding molecules like spermine that affect DNA conformation. The tetravalent cation spermine can reduce the pressure inside the capsid and induce condensation of the released DNA. We examine the effect of spermine on DNA ejection from phage T5 by using light scattering and gel electrophoresis to measure the amount of DNA remaining in the capsid at the end of ejection. We discuss the results in terms of free energy minimization and we demonstrate that the presence of a DNA condensate outside the phage generates an additional force pulling passively on the DNA remaining inside the capsid.     

The multiple-scale transport equation in one space dimension

This study examines the behavior of the one-dimensional non-homogeneous transport equation of the form u_t= u_x+f, «1. The solution consists of behavior which changes on two different time scales, one rapid and one slow. This time scale behavior is known. Additionally, however, we find here that because of the presence of the non-homogeneous forcing termf, and large wave speed 1/, there is a component of the solution which will vary only on a very large spatial scale. This large space-scale solution persists throughout all time, even after the source term of the solution has been shut off. The analysis of this large spacescale behavior is the focus of this paper. Numerical experiments highlight some of our results. These results have applications in fields such as meteorology, and other areas where multiple time scales are of interest.This work was supported in part by NSF grant NSF-DMS93-21728.     

Existence and fractional regularity of solutions for a doubly nonlinear differential inclusion

This article considers the issues of existence and regularity of solutions to the following doubly nonlinear differential inclusion $$\omega_t+\alpha (\omega_t)-\Delta \omega-\Delta_p{\omega} \ni f$$ where α is a maximal monotone operator in ${\mathbb{R}^2}$ and Δ _p denotes the p-Laplacian with p > 2. The investigation on fractional regularity is based on the Galerkin method combined with a suitable basis for W ^1,p , which we exhibit as a preliminary result. This approach also allows the obtaining of estimates in the so-called Nikolskii spaces, since it balances the interplay between the maximal monotone operator with the appearing higher order nonlinear terms.     

Burstiness and fractional diffusion on complex networks

Many dynamical processes on real world networks display complex temporal patterns as, forinstance, a fat-tailed distribution of inter-events times, leading to heterogeneouswaiting times between events. In this work, we focus on distributions whose averageinter-event time diverges, and study its impact on the dynamics of random walkers onnetworks. The process can naturally be described, in the long time limit, in terms ofRiemann-Liouville fractional derivatives. We show that all the dynamical modes possess, inthe asymptotic regime, the same power law relaxation, which implies that the dynamics doesnot exhibit time-scale separation between modes, and that no mode can be neglected versusanother one, even for long times. Our results are then confirmed by numericalsimulations.     

Persistence stability for geometric complexes

In this paper we study the properties of the homology of different geometric filtered complexes (such as Vietoris–Rips, ?ech and witness complexes) built on top of totally bounded metric spaces. Using recent developments in the theory of topological persistence, we provide simple and natural proofs of the stability of the persistent homology of such complexes with respect to the Gromov–Hausdorff distance. We also exhibit a few noteworthy properties of the homology of the Rips and ?ech complexes built on top of compact spaces.     

Critical exponents for Fréedericskz transition in nematics between concentric cylinders

The equilibrium tilt angle profile in a cell limited by two concentric cylinders filled with nematic liquid crystals is determined for strong homeotropic anchoring at the surfaces. The anchoring condition is such that the nematic director is perpendicular to the cylinder axes and a radial nonuniform electric field is applied to investigate a Fréedericksz transition. The distortions induced by the field remain in the plane perpendicular to the cylinder axes, and a threshold field is analytically determined indicating a transition from a pure splay to a splay-bend conformation of the director. It is shown that this transition can be induced by the thickness of the region between the two cylinders, and can be detected even in the absence of an external field. If the maximum value of the tilt angle is assumed as an order parameter, its behavior near to the transition can be used to obtain the critical exponent, which is the same as the one obtained in the mean field approximation. These results are indications that nontrivial consequences may occur when complex fluids are subject to non-planar geometries.