Pair Of Indices Research Articles

Excision-preserving cubical approach to the algorithmic computation of the discrete Conley index

We introduce a new approach to the algorithmic computation of the Conley index for continuous maps. We use the technique of splitting an index pair into two layers which is inspired by the work of Mrozek, Reineck and Srzednicki [M. Mrozek, J.F. Reineck, R. Srzednicki, The Conley index over a base, Trans. Amer. Math. Soc. 352 (2000) 4171–4194]. The main advantage of our construction over the approach based directly on the one introduced by Mischaikow, Mrozek and Pilarczyk [K. Mischaikow, M. Mrozek, P. Pilarczyk, Graph approach to the computation of the homology of continuous maps, Found. Comput. Math. 5 (2005) 199–229] is that our cubical sets have the excision property. Moreover, our solution has some advantages in comparison to the approach recently proposed by Mrozek [M. Mrozek, Index pair algorithms, Found. Comput. Math. 6 (2006) 457–493].

Comparison between pulsed‐wave Doppler‐ and tissue Doppler‐derived Tei indices in fetuses with and without congenital heart disease

The aim of this study was to compare the right (RV) and left (LV) ventricular Tei indices obtained by pulsed-wave Doppler (PD) and tissue Doppler (TD) methods in fetuses with structurally normal and abnormal hearts. This was a retrospective cross-sectional study of 147 fetuses that had a fetal echocardiogram and Tei index measured during a 2-year period. The RV and LV Tei indices were measured using both PD and TD methods. The difference between the two methods of Tei index measurement was tested using paired sample t-test, Pearson correlation coefficient was used to examine their relationship, and the agreement between the methods was tested using Bland-Altman analysis. A total of 87 fetuses had normal hearts and 60 had a congenital heart defect. Both PD and TD Tei indices were measured successfully from at least one ventricle in 123 cases and from both ventricles in 110 cases. The mean TD Tei index was significantly higher than the mean PD Tei index for both ventricles (P < 0.0001). There was a weak but statistically significant correlation between the PD and TD Tei indices of the right ventricle (r = 0.20, P = 0.029), whereas the PD and TD Tei indices of the left ventricle did not correlate significantly (r = 0.04, P = 0.684). When pairs of Tei indices measured by two different methods (123 pairs for the right ventricle and 111 for the left ventricle) were tested with Bland-Altman analysis, the bias and precision were 0.147 and 0.254, respectively, for the right ventricle, and 0.299 and 0.276, respectively, for the left ventricle. Correlation between Tei indices measured by PD and TD methods is weak and the agreement between individual measurements is poor. Therefore, they should not be used interchangeably in the assessment of fetal cardiac function.

Incidence of Tuberculosis and the Predictive Value of ELISPOT and Mantoux Tests in Gambian Case Contacts

BackgroundStudies of Tuberculosis (TB) case contacts are increasingly being utilised for understanding the relationship between M. tuberculosis and the human host and for assessing new interventions and diagnostic tests. We aimed to identify the incidence rate of new TB cases among TB contacts and to relate this to their initial Mantoux and ELISPOT test results.Methods and FindingsAfter initial Mantoux and ELISPOT tests and exclusion of co-prevalent TB cases, we followed 2348 household contacts of sputum smear positive TB cases. We visited them at 3 months, 6 months, 12 months, 18 months and 24 months, and investigated those with symptoms consistent with TB. Those who were diagnosed separately at a government clinic had a chest x-ray. Twenty six contacts were diagnosed with definite TB over 4312 person years of follow-up (Incidence rate 603/100,000 person years; 95% Confidence Interval, 370–830). Nine index and secondary case pairs had cultured isolates available for genotyping. Of these, 6 pairs were concordant and 3 were discordant. 2.5% of non-progressors were HIV positive compared to 12% of progressors (HR 6.2; 95% CI 1.7–22.5; p = 0.010). 25 secondary cases had initial Mantoux results, 14 (56%) were positive ; 21 had initial ELISPOT results, 11 (52%) were positive; 15 (71%) of 21 tested were positive by one or the other test. Of the 6 contacts who had concordant isolates with their respective index case, 4 (67%) were Mantoux positive at recruitment, 3 (50%) were ELISPOT positive; 5 (83%) were positive by one or other of the two tests. ELISPOT positive contacts, and those with discordant results, had a similar rate of progression to those who were Mantoux positive. Those negative on either or both tests had the lowest rate of progression.ConclusionsThe incidence rate of TB disease in Gambian TB case contacts, after screening for co-prevalent cases, was 603/100,000 person years. Since initial ELISPOT test and Mantoux tests were each positive in only just over half of cases, but 71% were positive by one or other test, positivity by either might be the best indication for preventive treatment. These data do not support the replacement of the Mantoux test by an ELISPOT test in The Gambia or similar settings.

Extreme US stock market fluctuations in the wake of 9/11

AbstractWe apply extreme value analysis to US sectoral stock indices in order to assess whether tail risk measures like value‐at‐risk and extremal linkages were significantly altered by 9/11. We test whether semi‐parametric quantile estimates of ‘downside risk’ and ‘upward potential’ have increased after 9/11. The same methodology allows one to estimate probabilities of joint booms and busts for pairs of sectoral indices or for a sectoral index and a market portfolio. The latter probabilities measure the sectoral response to macro shocks during periods of financial stress (so‐called ‘tail‐βs’). Taking 9/11 as the sample midpoint we find that tail‐βs often increase in a statistically and economically significant way. This might be due to perceived risk of new terrorist attacks. Copyright © 2008 John Wiley &amp; Sons, Ltd.

The noncommutative geometry of k-graph C*-algebras

AbstractThis paper is comprised of two related parts. First we discuss which k-graph algebras have faithful traces. We characterise the existence of a faithful semifinite lower-semicontinuous gauge-invariant trace on C* (Λ) in terms of the existence of a faithful graph trace on Λ.Second, for k-graphs with faithful gauge invariant trace, we construct a smooth (k,∞)-summable semifinite spectral triple. We use the semifinite local index theorem to compute the pairing with K-theory. This numerical pairing can be obtained by applying the trace to a KK-pairing with values in the K-theory of the fixed point algebra of the Tk action. As with graph algebras, the index pairing is an invariant for a finer structure than the isomorphism class of the algebra.

A density tensor hierarchy for open system dynamics: retrieving the noise

We develop a density tensor hierarchy for open system dynamics that recovers information about fluctuations (or ‘noise’) lost in passing to the reduced density matrix. For the case of fluctuations arising from a classical probability distribution, the hierarchy is formed from expectations of products of pure state density matrix elements and can be compactly summarized by a simple generating function. For the case of quantum fluctuations arising when a quantum system interacts with a quantum environment in an overall pure state, the corresponding hierarchy is defined as the environmental trace of products of system matrix elements of the full density matrix. Whereas all members of the classical noise hierarchy are system observables, only the lowest member of the quantum noise hierarchy is directly experimentally measurable. The unit trace and idempotence properties of the pure state density matrix imply descent relations for the tensor hierarchies, that relate the order n tensor, under contraction of appropriate pairs of tensor indices, to the order n − 1 tensor. As examples to illustrate the classical probability distribution formalism, we consider a spatially isotropic ensemble of spin-1/2 pure states, a quantum system evolving by an Itô stochastic Schrödinger equation and a quantum system evolving by a jump process Schrödinger equation. As examples to illustrate the corresponding trace formalism in the quantum fluctuation case, we consider the tensor hierarchies for collisional Brownian motion of an infinite mass Brownian particle and for the weak coupling Born–Markov master equation. In different specializations, the latter gives the hierarchies generalizing the quantum optical master equation and the Caldeira–Leggett master equation. As a further application of the density tensor, we contrast stochastic Schrödinger equations that reduce and that do not reduce the state vector, and discuss why a quantum system coupled to a quantum environment behaves like the latter. The descent relations for our various examples are checked in a series of appendices.

Bivariate and higher-order terms in models of international equity returns

Nonsynchronous measurement induces significant higher-order auto and serial cross correlations in observed bivariate returns and squared returns to international equity indices. In order to investigate the statistical and economic significance of bivariate and higher-order terms in conditional models of international equity returns, we fit a VMA(2)–EGARCH(2,2) model with normal errors and a constant conditional correlation using MSCI index pairs for Japan, the UK and the USA. First-order univariate and bivariate conditional mean and volatility terms are statistically significant in each series. Second-order own- and cross-volatility terms also are significant, although second-order conditional mean terms are not. We investigate the economic significance of bivariate and second-order terms by comparing the return and volatility predictions of various models using out-of-sample regressions of returns or squared returns on conditional means or volatilities. Bivariate terms significantly improve return predic...

Bulk perturbations ofN= 2 branes

The evolution of supersymmetric A-type D-branes under the bulk renormalization group flow between two different N=2 minimal models is studied. Using the Landau-Ginzburg description we show that a specific set of branes decouples from the infrared theory, and we make detailed predictions for the behavior of the remaining branes. The Landau-Ginzburg picture is then checked against a direct conformal field theory analysis. In particular we construct a natural index pairing which is preserved by the RG flow, and show that the branes that decouple have vanishing index with the surviving branes.

Quantifying positional importance in food webs: A comparison of centrality indices

Conservation biology should focus more on the importance rather than the rarity of species, although the definition and quantification of importance are not easy. One approach involves measuring the positional importance (e.g. centrality) of species in ecological interaction networks to provide a basis for species ranking. However, there are many centrality indices, each reflecting a particular aspect of positional importance and therefore giving a rank order of species different from those provided by alternative formulations. Thus, there is a strong need for comparing the available indices and for examining their relative merits in network analysis. In this paper, we apply 13 centrality indices to the “species” (trophic components) of methodologically comparable trophic flow networks, in order to answer the following questions: (1) What is the disagreement between different indices regarding the rank of a given species in a given network? (2) How is this disagreement in performance influenced by the choice of the network? (3) What is the overall relationship among these indices and, in particular, which are the most similar to degree (the simplest index of all, being equal to the number of links pertaining to a given node)? We compare the 13 indices based on the data of nine networks using metric and rank statistics and multivariate analysis procedures. We conclude that (1) different centrality ranks differ in each network; (2) different webs can be characterized by different relationships between ranks but there is a robust pattern of relationships among the indices, some index pairs behaving very similarly in all networks; and (3) it is the index of closeness centrality which provides a rank most similar to that based on degree.

Interdependence between Eastern and Western European stock markets: Evidence from intraday data

We analyze comovements among three stock markets in Central and Eastern Europe and, in addition, interdependence which may exist between Western European (DAX, CAC, UKX) and Central and Eastern European (BUX, PX-50, WIG-20) stock markets. The novelty of our paper rests mainly on the use of 5-min tick intraday price data from mid-2003 to early 2005 for stock indices and on the wide range of econometric techniques employed. We find no robust cointegration relationship for any of the stock index pairs or for any of the extended specifications. There are signs of short-term spillover effects both in terms of stock returns and stock price volatility. Granger causality tests show the presence of bidirectional causality for returns as well as volatility series. The results based on a VAR framework indicate a more limited number of short-term relationships among the stock markets.

Algorithmic computation of the Conley index

The Conley index of an isolated invariant set with respect to some flow in is defined in terms of a so-called index pair. Therefore, determining a suitable index pair is crucial for the computation of the Conley index. We develop a procedure that enables us to construct an index pair, which can be replaced by a topological equivalent pair of simplicial complexes in a finite number of steps. This is possible by a special triangulation and by formulating sufficient contractibility conditions for the topological equivalence. Our procedure also works in cases where there is no isolating block corresponding to the invariant set available. We demonstrate the power of this procedure by applying it to a Hopf bifurcation problem.

Atomic-Resolution Dynamic Force Microscopy/Spectroscopy of Individual Single-Walled Carbon Nanotube

We report the atomic-resolution imaging of an individual single-walled carbon nanotube and quantitative measurements of forces above specific atomic sites by dynamic force microscopy and three-dimensional force field spectroscopy at low temperatures. The detailed structure, i.e., the pair of indices (n,m) corresponding to a chiral angle φ and diameter d, is derived from atomic resolution images. Through the evaluation of short-range forces, the chemical reactivity of nanotube surface is found to be very weak when the interatomic short-range van der Waals forces are dominant.

Index Pairs Algorithms

We introduce some modifications and extensions of the concept of index pair in the Conley index theory. We then show how these concepts may be used to overcome some difficulties in obtaining efficient algorithms computing the Conley index. We also present examples of applications to computer assisted proofs in dynamics.

Hierarchical organisation of neuro-anatomical constraints in interlimb coordination

Based on the observation that bimanual finger tapping movements tend toward mirror symmetry with respect to the body midline, despite the synchronous activation of non-homologous muscles, F. Mechsner, D. Kerzel, G. Knoblich, and W. Prinz (2001) [Perceptual basis of bimanual coordination. Nature, 414, 69–73] suggested that the basis of rhythmic coordination is purely spatial/perceptual in nature, and independent of the neuro-anatomical constraints of the motor system. To investigate this issue further, we employed a four finger tapping task similar to that used by F. Mechsner and G. Knoblich (2004) [Do muscle matter in bimanual coordination? Journal of Experimental Psychology: Human Perception and Performance, 30, 490–503] in which six male participants were required to alternately tap combinations of adjacent pairs of index (I), middle (M) and ring (R) fingers of each hand in time with an auditory metronome. The metronome pace increased continuously from 1Hz to 3Hz over the course of a 30-s trial. Each participant performed three blocks of trials in which finger combination for each hand (IM or MR) and mode of coordination (mirror or parallel) were presented in random order. Within each block, the right hand was placed in one of three orientations; prone, neutral and supine. The order of blocks was counterbalanced across the six participants. The left hand maintained a prone position throughout the experiment. On the basis of discrete relative phase analyses between synchronised taps, the time at which the initial mode of coordination was lost was determined for each trial. When the right hand was prone, transitions occurred only from parallel symmetry to mirror symmetry, regardless of finger combination. In contrast, when the right hand was supine, transitions occurred only from mirror symmetry to parallel but no transitions were observed in the opposite direction. In the right hand neutral condition, mirror and parallel symmetry are insufficient to describe the modes of coordination since the hands are oriented orthogonally. When defined anatomically, however, the results in each of the three right hand orientations are consistent. That is, synchronisation of finger tapping is determined by a hierarchy of control of individual fingers based on their intrinsic neuro-mechanical properties rather than on the basis of their spatial orientation.

Homology index braids in infinite-dimensional Conley index theory

We extend the notion of a categorial Conley-Morse index, as defined in [K. P. rybakowski, The Morse index, repeller-attractor pairs and the connection index for semiflows on noncompact spaces , J. Differential Equations 47 (1987), 66–98], to the case based on a more general concept of an index pair introduced in [R. D. Franzosa and K. Mischaikow, The connection matrix theory for semiflows on (not necessarily locally compact) metric spaces , J. Differential Equations 71 (1988), 270–287]. We also establish a naturality result of the long exact sequence of attractor-repeller pairs with respect to the choice of index triples. In particular, these results immediately give a complete and rigorous existence result for homology index braids in infinite dimensional Conley index theory. Finally, we describe some general regular and singular continuation results for homology index braids obtained in our recent papers [M. C. Carbinatto and K. P. Rybakowski, Nested sequences of index filtrations and continuation of the connection matrix , J. Differential Equations 207 (2004), 458–488] and [M. C. Carbinatto and K. P. Rybakowski, Continuation of the connection matrix in singular perturbation problems ].

IMPACT: A twin-index framework for efficient moving object query processing

With the rapid advancement in wireless communications and positioning techniques, it is now feasible to track the positions of moving objects. However, existing indexes and associated algorithms, which are usually disk-based, are unable to keep up with the high update rate while providing speedy retrieval at the same time. Since main memory is much faster than disk, efficient management of moving-object database can be achieved through aggressive use of main memory. In this paper, we propose an integrated memory partitioning and activity conscious twin-index (IMPACT) framework where the moving object database is indexed by a pair of indexes based on the properties of the objects’ movement—a main-memory structure manages active objects while a disk-based index handles inactive objects. As objects become active (or inactive), they dynamically migrate from one structure to the other. In the worst case that each time an object need to be migrated to the disk, which means each update may incur a disk access, the performance of IMPACT degrades to be the same as the disk-based index structures. Moreover, the main memory is also organized into two partitions—one for the main memory index, and the other as buffers for the frequently accessed nodes of the disk-based index. We also presented the detailed algorithms for different operations and a cost model to estimate the optimal memory allocation. Our analytical and experimental results show that the proposed IMPACT framework achieves significant performance improvement over the traditional indexing scheme.

A study on performance of introducing ERP to semiconductor related industries in Taiwan

Enterprise resource planning (ERP) has become critical to enhancing the competitiveness of the semiconductor industry in Taiwan by applying information technology to integrate internal information as well as external service capability of an enterprise to increase the flow speed and values and reduce the costs of human and managerial resources, manufacturing, management, and marketing. The success of ERP implementation depends on several factors, such as space, time, location, industry, and the like. It is critically important to collect information on the successful factors of ERP implementation and evaluate the performance of ERP in semiconductor-related industries in Taiwan. A statistical method based on Parasuraman et al. was applied to ERP implementation by providing a pair of performance indices, i.e., action and importance. In addition, a performance evaluation matrix, originally proposed by Lambert and Sharman, was revised to set up a standard by providing performance upper and lower control limits with the emphases of the Taguchi method and Shewhart control charts. Finally, quality function deployment (QFD) was used to remedy the weaknesses and develop corporate strategies to improve the ERP implementation.

Contagion Across and Integration of Central and Eastern European Stock Markets: Evidence from Intraday Data

We analyze interrelations between three stock markets in Central and Eastern Europe and, in addition, interconnections which may exist between Western European (DAX, CAC, UKX) and Central and Eastern European stock markets (BUX, PX-50, WIG20). The novelty of our paper rests mainly on the use of the five-minute tick intraday price data from the mid-2003 to the early 2005 for stock indices and on the wide range of econometric techniques employed. We find no robust cointegration relationship for any of the stock index pairs or for any of the extended specifications. There are signs of short-term spillover effects both in terms of stock returns and stock price volatility. Granger causality tests show the presence of bidirectional causality for returns as well as volatility series. The results based on a VAR framework indicate a more limited number of short-term relationships between the stock markets. In general, it appears that spillover effects are stronger from volatility to volatility than contagion effects from return to return series.

Solar EUV and UV spectral irradiances and solar indices

Several experiments have measured solar EUV/UV flux in the last 10–15 years including SUSIM UARS, SOHO CELIAS SEM, and SOHO EIT and have generated multi-year spectral irradiance time series. Empirical models of these important sources of radiant energy are often based on solar activity proxies, most often, the solar 10.7 cm radio flux ( F 10.7 ). The short- and long-term correspondence of four solar activity index time series International Sunspot Number, the He 1083 Equivalent Width, F 10.7 , and the Mg II core-to-wing ratio are analyzed. All of these show well-correlated long-term behavior with F 10.7 and Mg II showing the greatest long-term agreement among all of the index pairs. However, during the recent maximum period of solar cycle 23, both the ISN and He 1083 have diverged significantly from the others. Recent UV and EUV measurements are compared with Mg II and F 10.7 to assess their value as solar activity proxies. In every case, Mg II was found to correlate more strongly than F 10.7 with the UV and EUV time series which correspond to a range of solar atmospheric temperatures of 4000K–2 MK. This correspondence indicates that the mechanisms underlying irradiances changes from upper photospheric chromospheric, transition region, and lower coronal solar atmospheric layers are closely linked.

Orthogonal Zonal, Tesseral and Sectorial Wavelets on the Sphere for the Analysis of Satellite Data

The spherical harmonics Y n,k } n=0,1,...;k=−n,...,n represent a standard complete orthonormal system in ℒ2(Ω), where Ω is the unit sphere. In view of present and future satellite missions (e.g., for the determination of the Earth's gravity field) it is of particular importance to treat the different accuracies and sizes of data in dependence of the index pairs (n,k). It is, e.g., known that the GOCE mission yields essentially less accurate data in the zonal (k=0) case. Therefore, this paper presents new ways of constructing multiresolutions for a Sobolev space of functions on Ω allowing the separate treatment of certain classes of pairs (n,k) and, in particular, the separate treatment of different orders k. Orthogonal bandlimited as well as non-bandlimited detail and scale spaces adapted to certain (geo)scientific problems and to the character of the given data can now be used. Finally, an explicit representation of a non-bandlimited wavelet on Ω yielding an orthogonal decomposition of the function space is calculated for the first time.