Topological Signatures Research Articles

Topological Signature of Deterministic Chaos in Short Nonstationary Signals from an Optical Parametric Oscillator

Although deterministic chaos has been predicted to occur in the triply resonant optical parametric oscillator (TROPO) 15 years ago, experimental evidence of chaotic behavior in this system has been lacking so far, in marked contrast with most nonlinear systems, where chaos has been actively tracked and found. This situation is probably linked to the high sensitivity of the TROPO to perturbations, which adversely affects stationary operation at high power. We report the experimental observation in this system of a burst of irregular behavior of duration 80 micros. Although the system is highly nonstationary over this time interval, a topological analysis allows us to extract a clear-cut signature of deterministic chaos from a time series segment of only nine base cycles (3 micros). This result suggests that nonstationarity is not necessarily an obstacle to the characterization of chaos.

Conjugacy, Involutions, and Reversibility for Real Homeomorphisms

The classification up to conjugacy of the homeomorphisms of the real line onto itself is well-understood by the experts, but there does not appear to be an exposition in print. In other words, it is mathematical folklore. In this expository paper, we give a complete but concise account of the classification, in terms of a suitable topological signature concept. A topological signature is a kind of pattern of signs. We provide similar classifications for homeomorphisms that fix a given subset, and for germs of homeomorphisms at a point. For direction-reversing homeomorphisms, we show that the signature of the compositional square is antisymmetric. We go on to apply the conjugacy classification and signatures to reprove recent results of Jarczyk on the composition of involutions. His results classify the reversible homeomorphisms (the composition of two involutions), and show that each homeomorphism is the composition of at most four involutions. The reversible direction-preserving homeomorphisms have symmetric signatures.

DNA repair community connects at Cortona: researchers focus on protein networks, network topology and molecular signatures

DNA repair community connects at Cortona: researchers focus on protein networks, network topology and molecular signatures

Robustness of the long-range structure in denatured staphylococcal nuclease to changes in amino acid sequence.

A nativelike low-resolution structure has been shown to persist in the Delta 131 Delta denatured fragment of staphylococcal nuclease, even in the presence of 8 M urea. In this report, the physical-chemical basis of this structure is addressed by monitoring changes in structure reflected in residual dipolar couplings and diffusion coefficients as a function of changes in amino acid sequence. Ten large hydrophobic residues, previously shown to play dominant roles in the stability of the native state, are replaced with polar residues of similar shape. Modest increases in the Stokes radius determined by NMR methods result from replacement of five isoleucine/valine residues with threonine, one leucine with glutamine, and oxidation of four methionines to the sulfoxides. Yet in the presence of all ten hydrophobic to polar substitutions and 8 M urea, the NMR signature of a native-like topology is still largely intact. In addition, removal of 30 residues from either the N-terminus (which deletes a three-strand beta meander) or C-terminus (a long extended segment and the final alpha helix) produces only very small changes in long-range structure. These data indicate that both the general shape of the denatured state and the angular relationships of individual bond angles to the axes describing the spatial distribution of the protein chain are insensitive to large changes in the amino acid sequence, a finding consistent with the conclusion that the long-range structure of denatured proteins is encoded primarily by local steric interactions between side chains and the polypeptide backbone.

A topologicalsignature in cosmic topology

Two procedures for obtaining (extracting and constructing) thetopologicalsignature of any multiply connected Robertson-Walker (RW) universearepresented. It is shown through computer-aided simulations that bothapproaches give rise to the same topological signature for a multiplyconnected flat RW universe. The strength of these approaches isillustrated by extracting the topological signatures of a flat(k = 0), an elliptic (k = 1) and a hyperbolic (k = -1) multiply connected RW universes. We also show howseparated contributions of thecovering isometries add up to form the topological signature of a RWflat universe. From our theoretical results andsimulations it is found that the topological signature arises(in the mean) even when there are just a few images for each object.It isalso shown that the mean pair separation histogram technique works,andthat it is a suitable approach for studying the topologicalsignatures ofRW universes as well as the role of non-translational isometries.

SIGNATURE FOR THE SHAPE OF THE UNIVERSE

If the universe has a nontrivial shape (topology) the sky may show multiple correlated images of cosmic objects. These correlations can be couched in terms of distance correlations. We propose a statistical quantity which can be used to reveal the topological signature of any Robertson–Walker (RW) spacetime with nontrivial topology. We also show through computer-aided simulations how one can extract the topological signatures of flat, elliptic, and hyperbolic RW universes with nontrivial topology.

Spikes in cosmic crystallography II: topological signature of compact flat universes

We study the topological signature of euclidean isometries in pair separations histograms (PSH) and elucidate some unsettled issues regarding distance correlations between cosmic sources in cosmic crystallography. Reducing the noise of individual PSHs using mean pair separations histograms we show how to distinguish between topological and statistical spikes. We report results of simulations that evince that topological spikes are not enough to distinguish between manifolds with the same set of Clifford translations in their covering groups, and that they are not the only signature of topology in PSHs corresponding to euclidean small universes. We also show how to evince the topological signature due to non-translational isometries.

DISTINGUISHING MARKS OF SIMPLY-CONNECTED UNIVERSES

A statistical quantity suitable for distinguishing simply-connected Robertson–Walker (RW) universes is introduced, and its explicit expressions for the three possible classes of simply-connected RW universes with an uniform distribution of matter are determined. Graphs of the distinguishing mark for each class of RW universes are presented and analyzed. There sprout from our results an improvement on the procedure to extract the topological signature of multiply-connected RW universes, and a refined understanding of that topological signature of these universes studied in previous works.

Topological Signatures of Medium Range Order in Amorphous Semiconductor Models

ABSTRACTThe topological local cluster (or Schläfli cluster) concept of Marians and Hobbs is used to detect topologically crystalline regions in models of disordered tetrahedral semiconductors. We present simple algorithms for detecting both Wells-type shortest circuits and O'Keeffe-type rings, which can be used to delineate alternative forms of the Schläfli cluster in models.

Concept, design and performance of the second level triggers of the H1 detector

Since the end of the 1995 HERA running period the second level (L2) trigger system of the H1 experiment has been in operation. The L2 decision is presently derived from a combination of two independent hardware systems; one is based on the output of neural networks while the other decides on the grounds of topological event signatures in the detector. In contrast to the first level trigger (L1), which is fully pipelined and operates at the HERA bunch crossing rate of 10.4 MHz, the decision of the L2 systems is delivered within 20 /spl mu/s of the preceding L1 keep signal, allowing sufficient time for transmission of trigger information and computation of the L2 trigger response. This scheme significantly reduces the trigger rate, with minimal impact on detector deadtime for L1 rates below 1 kHz. The L2 trigger has proven to be flexible and highly effective in isolating physics processes from background.

Supersymmetry at LEP, experimental review

The current status of experimental searches for supersymmetry is reviewed. After a brief exposition of the assumptions determining the mass spectrum of the supersymmetric particles, the signatures corresponding to two supersymmetry breaking mechanisms (gravity and gauge mediated) are analysed. The status of standard topological signatures and standard gauge mediated breaking model signatures is reviewed as well as the experimental effort to cover `singular' areas of the parameter space where degeneracies and/or dynamical suppression of standard topologies exists. The complementarities of different searches is explored and the effort to obtain a model-independent lower experimental limit of the neutralino mass is described.

Observations of flux rope − associated particle bursts with GEOTAIL in the distant tail

Abstract. Geotail energetic particle, magnetic field data and plasma observations (EPIC, MGF and CPI experiments) have been examined for a number of energetic particle bursts in the distant tail (120Re<|XGSM|< 130 Re), associated with moving magnetic field structures, following substorm onsets. The features obtained from this data analysis are consistent with the distant magnetotail dynamics determined first by ISEE3 observations and explained in terms of the neutral line model. At the onset of the bursts, before plasma sheet entrance, energetic electrons appear as a field-aligned beam flowing in the tailward direction, followed by anisotropic ions. Within the flux rope region, suprathermal ions exhibit a convective anisotropy, which allows determination of the plasma flow velocity, assuming that the anisotropy arises from the Compton-Getting effect. The velocities thus determined in the plasma sheet are estimated to be 200–650 km/s, and compare favourably with the velocities derived from the CPI electron and proton experiment. The estimated length of magnetic field structures varies between 28 and 56 Re and depends on the strength of the westward electrojet intensification. Finally, the three structures reported here show clear magnetic field signatures of flux rope topology. The existence of a strong magnetic field aligned approximately along the Y-axis and centred on the north-to-south excursion of the field, and the bipolar signature in both By and/or Bz components, is consistent with the existence of closed field lines extending from Earth and wrapping around the core of the flux rope structure.Key words. Magnetospheric configuration and dynamics · Magnetotail

The complete inventory of the yeast Saccharomyces cerevisiae P-type transport ATPases

A total of sixteen open reading frames encoding for P-type ATPases have been identified in the complete genome sequence of Saccharomyces cerevisiae. Phylogenetic analysis distinguishes 6 distinct families. Topology predictions, identification of aminoacid sequence motifs and phenotype analysis of the available mutants suggest that these families correspond to ATPases transporting either H + (2 members), Ca 2+ (2 members), Na + (3 members), heavy metals (2 members), possibly aminophospholipids (5 members including 4 new ones) or unknown substrates (2 new members). It is proposed that the latter family which has homologs in Tetrahymena thermophila, Plasmodium falciparum and Caenorhabditis elegans constitutes a new group called P4-ATPases with characteristic topology and aminoacid signatures.

Signals for the minimal gauge-mediated supersymmetry-breaking model at the Fermilab Tevatron collider

We investigate the experimental implications of the minimal gauge-mediated low energy supersymmetry breaking (GMLESB) model for Fermilab Tevatron collider experiments. We map out the regions of parameter space of this model that have already been excluded by collider searches and by limits on $b\to s\gamma$. We use ISAJET to compute the cross sections for a variety of topological signatures which include photons in assocation with multiple leptons, jets and missing transverse energy. The reach in the parameter $\Lambda$, which fixes the scale of sparticle masses, is estimated to be $\sim 60$, 100 and 135 TeV for Tevatron integrated luminosities of 0.1, 2 and 25 fb$^{-1}$, respectively. The largest signals occur in photon(s) plus lepton(s) plus multi-jet channels; jet-free channels containing just photons plus leptons occur at much smaller rates, at least within this minimal framework.

Electron and ion signatures of field line topology at the low‐shear magnetopause

Electrons above 50 eV are a sensitive indicator of field line topology at the magnetopause, particularly when the solar wind dynamic pressure is high and the shear across the boundary is low. AMPTE/CCE electron observations under conditions when these criteria are fulfilled indicate a clear topological transition from the magnetosheath to open field lines threading the magnetopause in the magnetosheath boundary layer (MSBL). Once across the magnetopause and in the low latitude boundary layer (LLBL), the fast moving electrons are no longer a good indicator of magnetic field topology. In particular, the counterstreaming electron observations in this region are not an indicator of a closed magnetic topology. Rather, the field topology continues to be open, and the counterstreaming occurs because electrons from the magnetopause region move rapidly enough along the LLBL magnetic field to make it to the ionosphere, mirror, and return to the observation point Slower moving ions provide important additional information on magnetic field topology in the LLBL. CCE observations discussed here indicate that two types of solar wind ion distributions are observed in this layer. One type consists of a single, heated distribution which resembles somewhat the electron distribution in the layer. The field‐aligned velocity of this distribution is near zero. The other type consists of a unidirectional streaming distribution. The field‐aligned velocity of this distribution is higher than in the adjacent magnetosheath. Combining these observations with magnetospheric ion observations (e.g., O+) in the LLBL and with electron observations in the MSBL, two distinct magnetic field topologies emerge for the low‐shear magnetopause. The first, which gives rise to single, low‐parallel‐velocity and heated solar wind ion distributions in the LLBL, is magnetic reconnection poleward of the cusp. The second, which gives rise to unidirectional streaming solar wind ion distributions in the LLBL, is magnetic reconnection equatorward of the cusp. This type of component reconnection may not be sustained in a quasi‐steady fashion.

Particle signatures of magnetic topology at the magnetopause: AMPTE/CCE observations

Electron distributions at energies above 50 eV have been found to be a sensitive indicator of magnetic topology for magnetopause crossings of the AMPTE/CCE spacecraft. Progressing from the magnetosheath to the magnetosphere two abrupt transitions occur. First, the magnetosheath electron population directed either parallel or antiparallel to the magnetic field is replaced by a streaming, heated magnetosheath electron population. The other half of the distribution is unchanged. The region with unidirectional, heated magnetosheath electrons is identified as the magnetosheath boundary layer (MSBL). Second, the unheated magnetosheath electron population is replaced by a heated population nearly identical to the population encountered in the MSBL, resulting in a symmetric counterstreaming distribution. The region populated by the bidirectional heated magnetosheath electrons is identified as the low‐latitude boundary layer (LLBL). The MSBL and LLBL identified by the electron transitions are the same as the regions identified using ion composition measurements. The magnetosheath‐MSBL transition reflects a change in magnetic topology from a solar wind field line to one that threads the magnetopause, and the existence of a magnetosheath‐MSBL transition implies that the magnetopause is open. When the current layer is easily identified, the MSBL‐LLBL transition coincides with the magnetopause current layer, indicating that the magnetosheath electrons are heated in the current layer. Both magnetosheath‐MSBL and MSBL‐LLBL transitions are observed for low as well as high magnetic shears. Moreover, the transitions are particularly clear for low shear implying that magnetic topology boundaries are sharp even when abrupt changes in the field and other plasma parameters are absent. Furthermore, for low magnetic shear, solar wind ions with low parallel drift speeds make up the majority of the LLBL population indicating that the magnetosheath plasma has convected directly across the magnetopause. These observations are consistent with quasi‐steady, high‐latitude reconnection and indicate that the signatures of this reconnection geometry are commonly present in the subsolar region.

On the dynamics of a plasma vortex street and its topological signatures

A plasma vortex street configuration can evolve when two velocity and one magnetic shear layer interact strongly. A study of the interaction between two- and three-dimensional plasma modes and a mean sheared magnetic field is undertaken using a three-dimensional magnetohydrodynamic spectral Galerkin computation. The initial state is a simple magnetic shear in a plane perpendicular to the plasma velocity shear plane. In a very weak magnetic field, secondary instabilities (three-dimensional modes), expressed by the kinking of vortex tubes, lead to plasma flow along and around the axes of the vortex cores, creating characteristic patterns of kinetic helicity and linkages between vortex filaments. Three-dimensionality leads to the vortex breakdown process. A strong sheared magnetic field inhibits the kinking of vortex tubes, maintaining two-dimensionality. This inhibits vortex breakdown over long dynamical times. There is an anticorrelation in time between linkage indices of the vortex filament (related to kinetic helicity), suggesting that the ellipticity axes of the vortex cores along the street undergo a global inphase evolution. This anticorrelation has a dynamical interpretation. It extends to a relaxing plasma in the Navier–Stokes flow notion that helical regions of opposite helicities interact and screen each other off so that the global helicity remains bounded.

Field‐aligned currents associated with substorms in the vicinity of synchronous orbit: 1. The July 5, 1979, substorm observed by SCATHA, GOES 3, and GOES 2

Magnetic field topology and field‐aligned current signatures in the vicinity of synchronous orbit are examined for a substorm on July 5, 1979. Changes from taillike to dipolar field geometry propagate earthward near the midnight meridian during the substorm. The major field‐aligned currents producing a negative D perturbation at and around synchronous orbit are downward currents flowing into the auroral ionosphere on L shells greater than the synchronous spacecraft L shell. Although these currents are located initially on higher L shells, they shift toward the lower L shells as the change from taillike to dipolar fields propagates earthward. There may exist upward field‐aligned currents located on smaller L shells in the limited longitudinal region near the meridian where mid‐latitude D perturbations change their sign.

Identifying heavy flavours with vertex detectors via unusual decay topologies

Although top-flavoured hadrons decay too quickly to leave detectable tracks, multibranch cascade decays offer distinctive topological signatures with multiple b-, c- and τ-decay vertices emanating from a top decay. These modes are relatively copious for tt and (bt) systems produced at e+e− and hadron colliders, and should be recognizable by micro-vertex detectors with impact distance resolutions of order 20 μm or better. Multibranch cascade decay topologies are also relevant to the study of b-quarks and possible heavy quarks, charged leptons and neutrinos of the fourth generation; they occur too in multiple heavy quark production via jet fragmentation or Higgs bremsstrahlung.