On t-designs and bounds relating query complexity to error resilience in locally correctable codes

An n-length block code C is said to be r-query locally correctable, if for any codeword x ∈ C, one can probabilistically recover any one of the n coordinates of the codeword x by querying at most r coordinates of a possibly corrupted version of x. It is known that linear codes whose duals contain 2-designs are locally correctable. In this article, we consider linear codes whose duals contain t-designs for larger t. It is shown here that for such codes, for a given number of queries r, under linear decoding, one can, in general, handle a larger number of corrupted bits. We exhibit to our knowledge, for the first time, a finite length code, whose dual contains 4-designs, which can tolerate a fraction of up to 0.567/r corrupted symbols as against a maximum of 0.5/r in prior constructions. We also present an upper bound that shows that 0.567 is the best possible for this code length and query complexity over this symbol alphabet thereby establishing optimality of this code in this respect. A second result in the article is a finite-length bound which relates the number of queries r and the fraction of errors that can be tolerated, for a locally correctable code that employs a randomized algorithm in which each instance of the algorithm involves t-error correction.

Low-complexity near-optimal signal detection in underdetermined large-MIMO systems

In this paper, we consider signal detection in nt × nr underdetermined MIMO (UD-MIMO) systems, where i) nt >; nr with a overload factor α = nt over nr >; 1, ii) nt symbols are transmitted per channel use through spatial multiplexing, and iii) nt, nr are large (in the range of tens). A low-complexity detection algorithm based on reactive tabu search is considered. A variable threshold based stopping criterion is proposed which offers near-optimal performance in large UD-MIMO systems at low complexities. A lower bound on the maximum likelihood (ML) bit error performance of large UD-MIMO systems is also obtained for comparison. The proposed algorithm is shown to achieve BER performance close to the ML lower bound within 0.6 dB at an uncoded BER of 10-2 in 16 × 8 V-BLAST UD-MIMO system with 4-QAM (32 bps/Hz). Similar near-ML performance results are shown for 32 × 16, 32 × 24 V-BLAST UD-MIMO with 4-QAM/16-QAM as well. A performance and complexity comparison between the proposed algorithm and the λ-generalized sphere decoder (λ-GSD) algorithm for UD-MIMO shows that the proposed algorithm achieves almost the same performance of λ-GSD but at a significantly lesser complexity.

Low complexity joint estimation of synchronization impairments in sparse channel for MIMO-OFDM system

Low complexity joint estimation of synchronization impairments and channel in a single-user MIMO-OFDM system is presented in this paper. Based on a system model that takes into account the effects of synchronization impairments such as carrier frequency offset, sampling frequency offset, and symbol timing error, and channel, a Maximum Likelihood (ML) algorithm for the joint estimation is proposed. To reduce the complexity of ML grid search, the number of received signal samples used for estimation need to be reduced. The conventional channel estimation techniques using Least-Squares (LS) or Maximum a posteriori (MAP) methods fail for the reduced sample under-determined system, which results in poor performance of the joint estimator. The proposed ML algorithm uses Compressed Sensing (CS) based channel estimation method in a sparse fading scenario, where the received samples used for estimation are less than that required for an LS or MAP based estimation. The performance of the estimation method is studied through numerical simulations, and it is observed that CS based joint estimator performs better than LS and MAP based joint estimator. (C) 2013 Elsevier GmbH. All rights reserved.

SIRT6 Promotes COX-2 Expression and Acts as an Oncogene in Skin Cancer

SIRT6 is a SIR2 family member that regulates multiple molecular pathways involved in metabolism, genomic stability, and aging. It has been proposed previously that SIRT6 is a tumor suppressor in cancer. Here, we challenge this concept by presenting evidence that skin-specific deletion of SIRT6 in the mouse inhibits skin tumorigenesis. SIRT6 promoted expression of COX-2 by repressing AMPK signaling, thereby increasing cell proliferation and survival in the skin epidermis. SIRT6 expression in skin keratinocytes was increased by exposure to UVB light through activation of the AKT pathway. Clinically, we found that SIRT6 was upregulated in human skin squamous cell carcinoma. Taken together, our results provide evidence that SIRT6 functions as an oncogene in the epidermis and suggest greater complexity to its role in epithelial carcinogenesis. (C) 2014 AACR.

Exploring the Crystal Structure Landscape with a Heterosynthon Module: Fluorobenzoic Acid:1,2-Bis(4-pyridyl)ethylene 2:1 Cocrystals

The crystal structure landscape of the 2:1 benzoic acid:dipyridylethylene cocrystal (BA:DPE-I) is explored experimentally with fluoro-substituted benzoic acids and extended with studies employing the Cambridge Structural Database (CSD). The interpretation of the cocrystal landscape is facilitated by considering the kinetically favored and robust acidpyridine heterosynthon as a modular unit. Information based on high-throughput crystallography shows that polymorphs and pseudopolymorphs may belong to the same landscape but arise from different crystallization pathways because of complex and different kinetic features, and secondary synthon preferences. Using the CSD as a guide, the coformer was changed from 1,2-bis(4-pyridyl)ethylene (DPE-I) to 1,2-bis(4-pyridyl)ethane (DPE-II) and this provides an extended interpretation of the BA:DPE-I cocrystal landscape, also highlighting the complexity of the kineticthermodynamic dichotomy during the molecule-to-crystal progression.

Efficient QR Decomposition Using Low Complexity Column-wise Givens Rotation (CGR)

QR decomposition (QRD) is a widely used Numerical Linear Algebra (NLA) kernel with applications ranging from SONAR beamforming to wireless MIMO receivers. In this paper, we propose a novel Givens Rotation (GR) based QRD (GR QRD) where we reduce the computational complexity of GR and exploit higher degree of parallelism. This low complexity Column-wise GR (CGR) can annihilate multiple elements of a column of a matrix simultaneously. The algorithm is first realized on a Two-Dimensional (2 D) systolic array and then implemented on REDEFINE which is a Coarse Grained run-time Reconfigurable Architecture (CGRA). We benchmark the proposed implementation against state-of-the-art implementations to report better throughput, convergence and scalability.

On the Parameterized Complexity of Finding Separators with Non-Hereditary Properties

We study the problem of finding small s-t separators that induce graphs having certain properties. It is known that finding a minimum clique s-t separator is polynomial-time solvable (Tarjan in Discrete Math. 55:221-232, 1985), while for example the problems of finding a minimum s-t separator that induces a connected graph or forms an independent set are fixed-parameter tractable when parameterized by the size of the separator (Marx et al. in ACM Trans. Algorithms 9(4): 30, 2013). Motivated by these results, we study properties that generalize cliques, independent sets, and connected graphs, and determine the complexity of finding separators satisfying these properties. We investigate these problems also on bounded-degree graphs. Our results are as follows: Finding a minimum c-connected s-t separator is FPT for c=2 and W1]-hard for any ca parts per thousand yen3. Finding a minimum s-t separator with diameter at most d is W1]-hard for any da parts per thousand yen2. Finding a minimum r-regular s-t separator is W1]-hard for any ra parts per thousand yen1. For any decidable graph property, finding a minimum s-t separator with this property is FPT parameterized jointly by the size of the separator and the maximum degree. Finding a connected s-t separator of minimum size does not have a polynomial kernel, even when restricted to graphs of maximum degree at most 3, unless .

Keeping Research Data Safe 2 (KRDS2)

Data has always been fundamental to many areas of research but in recent years it has become central to more disciplines and inter-disciplinary projects and grown substantially in scale and complexity. There is increasing awareness of its strategic importance as a resource in addressing modern global challenges and the possibilities being unlocked by rapid technological advances and their application in research (NAS2009). The first Keeping Research Data Safe study funded by JISC made a major contribution to understanding of long-term preservation costs for research data by developing a cost model and identifying cost variables for preserving research data in UK universities (Beagrie et al, 2008). The Keeping Research Data Safe 2 (KRDS2) project has built on this work.

Ordinary mod p representations of the metaplectic cover of p-adic SL_2

We classify the genuine ordinary mod p representations of the metaplectic group SL(2,F)-tilde, where F is a p-adic field, and compute its genuine mod p spherical and Iwahori Hecke algebras. The motivation is an interest in a possible correspondence between genuine mod p representations of SL(2,F)-tilde and mod p representations of the dual group PGL(2,F), so we also compare the two Hecke algebras to the mod p spherical and Iwahori Hecke algebras of PGL(2,F). We show that the genuine mod p spherical Hecke algebra of SL(2,F)-tilde is isomorphic to the mod p spherical Hecke algebra of PGL(2,F), and that one can choose an isomorphism which is compatible with a natural, though partial, correspondence of unramified ordinary representations via the Hecke action on their spherical vectors. We then show that the genuine mod p Iwahori Hecke algebra of SL(2,F)-tilde is a subquotient of the mod p Iwahori Hecke algebra of PGL(2,F), but that the two algebras are not isomorphic. This is in contrast to the situation in characteristic 0, where by work of Savin one can recover the local Shimura correspondence for representations generated by their Iwahori fixed vectors from an isomorphism of Iwahori Hecke algebras.

Complexity of rupture propagation in large earthquakes in relation to tectonic environment

Complexity in the earthquake rupture process can result from many factors. This study investigates the origin of such complexity by examining several recent, large earthquakes in detail. In each case the local tectonic environment plays an important role in understanding the source of the complexity.

Several large shallow earthquakes (M_s > 7.0) along the Middle American Trench have similarities and differences between them that may lead to a better understanding of fracture and subduction processes. They are predominantly thrust events consistent with the known subduction of the Cocos plate beneath N. America. Two events occurring along this subduction zone close to triple junctions show considerable complexity. This may be attributable to a more heterogeneous stress environment in these regions and as such has implications for other subduction zone boundaries.

An event which looks complex but is actually rather simple is the 1978 Bermuda earthquake (M_s ~ 6). It is located predominantly in the mantle. Its mechanism is one of pure thrust faulting with a strike N 20°W and dip 42°NE. Its apparent complexity is caused by local crustal structure. This is an important event in terms of understanding and estimating seismic hazard on the eastern seaboard of N. America.

A study of several large strike-slip continental earthquakes identifies characteristics which are common to them and may be useful in determining what to expect from the next great earthquake on the San Andreas fault. The events are the 1976 Guatemala earthquake on the Motagua fault and two events on the Anatolian fault in Turkey (the 1967, Mudurnu Valley and 1976, E. Turkey events). An attempt to model the complex P-waveforms of these events results in good synthetic fits for the Guatemala and Mudurnu Valley events. However, the E. Turkey event proves to be too complex as it may have associated thrust or normal faulting. Several individual sources occurring at intervals of between 5 and 20 seconds characterize the Guatemala and Mudurnu Valley events. The maximum size of an individual source appears to be bounded at about 5 x 10²⁶ dyne-cm. A detailed source study including directivity is performed on the Guatemala event. The source time history of the Mudurnu Valley event illustrates its significance in modeling strong ground motion in the near field. The complex source time series of the 1967 event produces amplitudes greater by a factor of 2.5 than a uniform model scaled to the same size for a station 20 km from the fault.

Three large and important earthquakes demonstrate an important type of complexity --- multiple-fault complexity. The first, the 1976 Philippine earthquake, an oblique thrust event, represents the first seismological evidence for a northeast dipping subduction zone beneath the island of Mindanao. A large event, following the mainshock by 12 hours, occurred outside the aftershock area and apparently resulted from motion on a subsidiary fault since the event had a strike-slip mechanism.

An aftershock of the great 1960 Chilean earthquake on June 6, 1960, proved to be an interesting discovery. It appears to be a large strike-slip event at the main rupture's southern boundary. It most likely occurred on the landward extension of the Chile Rise transform fault, in the subducting plate. The results for this event suggest that a small event triggered a series of slow events; the duration of the whole sequence being longer than 1 hour. This is indeed a "slow earthquake".

Perhaps one of the most complex of events is the recent Tangshan, China event. It began as a large strike-slip event. Within several seconds of the mainshock it may have triggered thrust faulting to the south of the epicenter. There is no doubt, however, that it triggered a large oblique normal event to the northeast, 15 hours after the mainshock. This event certainly contributed to the great loss of life-sustained as a result of the Tangshan earthquake sequence.

What has been learned from these studies has been applied to predict what one might expect from the next great earthquake on the San Andreas. The expectation from this study is that such an event would be a large complex event, not unlike, but perhaps larger than, the Guatemala or Mudurnu Valley events. That is to say, it will most likely consist of a series of individual events in sequence. It is also quite possible that the event could trigger associated faulting on neighboring fault systems such as those occurring in the Transverse Ranges. This has important bearing on the earthquake hazard estimation for the region.

Implications of substrate complexity and kelp variability for south-central Alaskan nearshore fish communities

Understanding the interactions between kelp beds and nearshore fish is essential because anthropogenic changes and natural variability in these beds may affect available habitat for fishes. In this study fish communities were investigated in south-central Alaska kelp beds characterized by a range of substrate complexity and varying densities of both perennial understory kelps and annual canopy kelps. Many of the observed fish species, as well as understory and canopy kelps, were positively associated with structurally complex substratum. Targeted canopy and understory kelp beds supported seasonal populations of adult and juvenile Pacific cod (Gadus macrocephalus), rockfishes (Sebastes spp.), and year-round populations of greenlings (Hexagrammos spp.). Monthly changes in kelp and fish communities ref lected seasonal changes; the densities of some species were greatest during periods with higher temperatures. This work illustrates the importance of structurally complex kelp beds with persistent understory kelp populations as important fish habitat for several commercially and recreationally important fishes.

Measurement of the Interaction Between Recombinant I-domain from Integrin alpha 2 beta 1 and a Triple Helical Collagen Peptide with the GFOGER Binding Motif Using Molecular Force Spectroscopy.

The role of the collagen-platelet interaction is of crucial importance to the haemostatic response during both injury and pathogenesis of the blood vessel wall. Of particular interest is the high affinity interaction of the platelet transmembrane receptor, alpha 2 beta 1, responsible for firm attachment of platelets to collagen at and around injury sites. We employ single molecule force spectroscopy (SMFS) using the atomic force microscope (AFM) to study the interaction of the I-domain from integrin alpha 2 beta 1 with a synthetic collagen related triple-helical peptide containing the high-affinity integrin-binding GFOGER motif, and a control peptide lacking this sequence, referred to as GPP. By utilising synthetic peptides in this manner we are able to study at the molecular level subtleties that would otherwise be lost when considering cell-to-collagen matrix interactions using ensemble techniques. We demonstrate for the first time the complexity of this interaction as illustrated by the complex multi-peaked force spectra and confirm specificity using control blocking experiments. In addition we observe specific interaction of the GPP peptide sequence with the I-domain. We propose a model to explain these observations.