The correspondence between augmentations and rulings for Legendrian knots

We strengthen the link between holomorphic and generating-function invariants of Legendrian knots by establishing a formula relating the number of augmentations of a knot's contact homology to the complete ruling invariant of Chekanov and Pushkar.Comment: v2: 10 pages, 3 figures; minor revisions, to appear in Pacific J. Mat

Slow subcarrier-hopped Space Division Multiple Access OFDM systems

Recently Space Division Multiple Access (SDMA) assisted Multi-Input-Multi-Output (MIMO) OFDM systems invoking Multi-User Detection (MUD) techniques have attracted substantial research interests, which are capable of exploiting both transmitter multiplexing gain and receiver diversity gain. Furthermore, the classic Frequency-Hopping (FH) technique can be effectively amalgamated with SDMA-OFDM systems, resulting in Frequency-Hopped (FH) SDMA-OFDM. In this paper we devise a Turbo Trellis Coded Modulation (TTCM) assisted subcarrier-based FH/SDMA-OFDM scheme, which may be able to fully exploit the attainable frequency diversity, while exhibiting a high Multi-User-Interference (MUI) resistance. In the high-throughput scenario investigated, the proposed Uniform Slow-SubCarrier-Hopped (USSCH) SDMA-OFDM system was capable of achieving 6dB Eb=N0 gain at the BER of 10¡4 over the conventional SDMA-OFDM system, while maintaining a similar complexity

TCM, TTCM, BICM and BICM-ID Assisted MMSE Multi-User Detected SDMA-OFDM Using Walsh-Hadamard Spreading

Space Division Multiple Access (SDMA) aided Orthogonal Frequency Division Multiplexing (OFDM) systems assisted by efficient Multi-User Detection (MUD) techniques have recently attracted intensive research interests. Forward Error Correction (FEC) schemes and frequency-domain spreading techniques can be efficiently amalgamated with SDMA-OFDM systems for the sake of improving the achievable performance. In this contribution a Coded Modulation (CM) assisted and Minimum Mean-Square Error (MMSE) multi-user detected SDMA-OFDM system combined with Walsh-Hadamard-Transform-Spreading (WHTS) across a number of subcarriers is proposed. The various CM schemes used are Trellis Coded Modulation (TCM), Turbo TCM (TTCM), Bit-Interleaved Coded Modulation (BICM) and Iteratively Decoded BICM (BICM-ID), which constitute bandwidth efficient schemes that combine the functions of coding and modulation. Invoking the WHTS technique is capable of further improving the average Bit Error Rate (BER) performance of the CM-SDMA-OFDM system, since the bursty error effects imposed by the frequency-domain fading encountered are spread over the entire WHT block length, therefore increasing the chances of correcting the transmission errors by the CM decoders

Hybrid Iterative Multiuser Detection for Channel Coded Space Division Multiple Access OFDM Systems

Space division multiple access (SDMA) aided orthogonal frequency division multiplexing (OFDM) systems assisted by efficient multiuser detection (MUD) techniques have recently attracted intensive research interests. The maximum likelihood detection (MLD) arrangement was found to attain the best performance, although this was achieved at the cost of a computational complexity, which increases exponentially both with the number of users and with the number of bits per symbol transmitted by higher order modulation schemes. By contrast, the minimum mean-square error (MMSE) SDMA-MUD exhibits a lower complexity at the cost of a performance loss. Forward error correction (FEC) schemes such as, for example, turbo trellis coded modulation (TTCM), may be efficiently combined with SDMA-OFDM systems for the sake of improving the achievable performance. Genetic algorithm (GA) based multiuser detection techniques have been shown to provide a good performance in MUD-aided code division multiple access (CDMA) systems. In this contribution, a GA-aided MMSE MUD is proposed for employment in a TTCM assisted SDMA-OFDM system, which is capable of achieving a similar performance to that attained by its optimum MLD-aided counterpart at a significantly lower complexity, especially at high user loads. Moreover, when the proposed biased Q-function based mutation (BQM) assisted iterative GA (IGA) MUD is employed, the GA-aided system’s performance can be further improved, for example, by reducing the bit error ratio (BER) measured at 3 dB by about five orders of magnitude in comparison to the TTCM assisted MMSE-SDMA-OFDM benchmarker system, while still maintaining modest complexity

Coded Modulation Assisted Radial Basis Function Aided Turbo Equalisation for Dispersive Rayleigh Fading Channels

In this contribution a range of Coded Modulation (CM) assisted Radial Basis Function (RBF) based Turbo Equalisation (TEQ) schemes are investigated when communicating over dispersive Rayleigh fading channels. Specifically, 16QAM based Trellis Coded Modulation (TCM), Turbo TCM (TTCM), Bit-Interleaved Coded Modulation (BICM) and iteratively decoded BICM (BICM-ID) are evaluated in the context of an RBF based TEQ scheme and a reduced-complexity RBF based In-phase/Quadrature-phase (I/Q) TEQ scheme. The Least Mean Square (LMS) algorithm was employed for channel estimation, where the initial estimation step-size used was 0.05, which was reduced to 0.01 for the second and the subsequent TEQ iterations. The achievable coding gain of the various CM schemes was significantly increased, when employing the proposed RBF-TEQ or RBF-I/Q-TEQ rather than the conventional non-iterative Decision Feedback Equaliser - (DFE). Explicitly, the reduced-complexity RBF-I/Q-TEQ-CM achieved a similar performance to the full-complexity RBF-TEQ-CM, while attaining a significant complexity reduction. The best overall performer was the RBF-I/Q-TEQ-TTCM scheme, requiring only 1.88~dB higher SNR at BER=10-5, than the identical throughput 3~BPS uncoded 8PSK scheme communicating over an AWGN channel. The coding gain of the scheme was 16.78-dB

Reestimation of the production spectra of cosmic ray secondary positrons and electrons in the ISM

A detailed calculation of the production spectra of charged hadrons produced by interactions of cosmic rays in the interstellar medium is presented along with a thorough treatment of pion and muon decays. Newly parameterized inclusive cross sections of hadrons were used and exact kinematic limitations were taken into account. Single parametrized expressions for the production spectra of both secondary positrons and electrons in the energy range .1 to 100 GeV are presented. The results are compared with other authors' predictions. Equilibrium spectra using various models are also presented

Performance Analysis of Iteratively Decoded Variable-Length Space-Time Coded Modulation

It is demonstrated that iteratively Decoded Variable Length Space Time Coded Modulation (VL-STCM-ID) schemes are capable of simultaneously providing both coding gain as well as multiplexing and diversity gain. The VL-STCM-ID arrangement is a jointly designed iteratively decoded scheme combining source coding, channel coding, modulation as well as spatial diversity/multiplexing. In this contribution, we analyse the iterative decoding convergence of the VL-STCM-ID scheme using symbol-based three-dimensional EXIT charts. The performance of the VL-STCM-ID scheme is shown to be about 14.6 dB better than that of the Fixed Length STCM (FL-STCM) benchmarker at a source symbol error ratio of 10?4, when communicating over uncorrelated Rayleigh fading channels. The performance of the VL-STCM-ID scheme when communicating over correlated Rayleigh fading channels using imperfect channel state information is also studied

Invariants of Legendrian Knots and Coherent Orientations

We provide a translation between Chekanov's combinatorial theory for invariants of Legendrian knots in the standard contact R^3 and a relative version of Eliashberg and Hofer's Contact Homology. We use this translation to transport the idea of ``coherent orientations'' from the Contact Homology world to Chekanov's combinatorial setting. As a result, we obtain a lifting of Chekanov's differential graded algebra invariant to an algebra over Z[t,t^{-1}] with a full Z grading.Comment: 32 pages, 17 figures; small technical corrections to proof of Thm 3.7 and example 4.

Gravitational energy as dark energy: Concordance of cosmological tests

We provide preliminary quantitative evidence that a new solution to averaging the observed inhomogeneous structure of matter in the universe [gr-qc/0702082, arxiv:0709.0732], may lead to an observationally viable cosmology without exotic dark energy. We find parameters which simultaneously satisfy three independent tests: the match to the angular scale of the sound horizon detected in the cosmic microwave background anisotropy spectrum; the effective comoving baryon acoustic oscillation scale detected in galaxy clustering statistics; and type Ia supernova luminosity distances. Independently of the supernova data, concordance is obtained for a value of the Hubble constant which agrees with the measurement of the Hubble Key team of Sandage et al [astro-ph/0603647]. Best-fit parameters include a global average Hubble constant H_0 = 61.7 (+1.2/-1.1) km/s/Mpc, a present epoch void volume fraction of f_{v0} = 0.76 (+0.12/-0.09), and an age of the universe of 14.7 (+0.7/-0.5) billion years as measured by observers in galaxies. The mass ratio of non-baryonic dark matter to baryonic matter is 3.1 (+2.5/-2.4), computed with a baryon-to-photon ratio that concords with primordial lithium abundances.Comment: 4 pages, 2 figures; v2 improved statistics, references added, to appear in ApJ Letter

Measuring the star formation rate with gravitational waves from binary black holes

A measurement of the history of cosmic star formation is central to understand the origin and evolution of galaxies. The measurement is extremely challenging using electromagnetic radiation: significant modeling is required to convert luminosity to mass, and to properly account for dust attenuation, for example. Here we show how detections of gravitational waves from inspiraling binary black holes made by proposed third-generation detectors can be used to measure the star formation rate of massive stars with high precision up to redshifts of ~10. Depending on the time-delay model, the predicted detection rates ranges from ~1400 to ~16000 per month with the current measurement of local merger rate density. With three months of observations, parameters describing the volumetric star formation rate can be constrained at the few percent level, and the volumetric merger rate can be directly measured to 3% at z~2. Given a parameterized star formation rate, the characteristic delay time between binary formation and merger can be measured to ~60%.Comment: 7 pages, 1 table, 4 fig