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.

Controlling air solubility to maintain `'Cassie'' state for sustained drag reduction

`'Cassie'' state of wetting can be established by trapping air pockets on the crevices of textured hydrophobic surfaces, leading to significant drag reduction. However, this drag reduction cannot be sustained due to gradual dissolution of trapped air into water. In this paper, we explore the possibility of sustaining the underwater Cassie state of wetting in a microchannel by controlling the solubility of air in water; the solubility being changed by controlling the local absolute pressure near the surface. We show that using this method, we can in fact make the water locally supersaturated with air thus encouraging the growth of trapped air pockets on the surface. In this case, the water acts as a pumping medium, delivering air to the crevices of the hydrophobic surface in the microchannel, where the presence of air pockets is most beneficial from the drag reduction perspective. In our experiments, the air trapped on a textured surface is visualized using total internal reflection based technique, at different local absolute pressures with the pressure drop (or drag) also being simultaneously measured. We find that, by controlling the pressure and hence the solubility close to the surface, we can either shrink or grow the trapped air bubbles, uniformly over a large surface area. The experiments show that, by precisely controlling the pressure and hence the solubility we can sustain the `'Cassie state'' over extended periods of time. This method thus provides a means of getting sustained drag reduction from a textured hydrophobic surface in channel flows. (C) 2014 Elsevier B.V. All rights reserved.

On the stability of the L-p-norm of the Riemannian curvature tensor

We consider the Riemannian functional defined on the space of Riemannian metrics with unit volume on a closed smooth manifold M where R(g) and dv (g) denote the corresponding Riemannian curvature tensor and volume form and p a (0, a). First we prove that the Riemannian metrics with non-zero constant sectional curvature are strictly stable for for certain values of p. Then we conclude that they are strict local minimizers for for those values of p. Finally generalizing this result we prove that product of space forms of same type and dimension are strict local minimizer for for certain values of p.

Performance of OFDM Systems With Best-m Feedback, Scheduling, and Delays for Uniformly Correlated Subchannels

Contemporary cellular standards, such as Long Term Evolution (LTE) and LTE-Advanced, employ orthogonal frequency-division multiplexing (OFDM) and use frequency-domain scheduling and rate adaptation. In conjunction with feedback reduction schemes, high downlink spectral efficiencies are achieved while limiting the uplink feedback overhead. One such important scheme that has been adopted by these standards is best-m feedback, in which every user feeds back its m largest subchannel (SC) power gains and their corresponding indices. We analyze the single cell average throughput of an OFDM system with uniformly correlated SC gains that employs best-m feedback and discrete rate adaptation. Our model incorporates three schedulers that cover a wide range of the throughput versus fairness tradeoff and feedback delay. We show that, for small m, correlation significantly reduces average throughput with best-m feedback. This result is pertinent as even in typical dispersive channels, correlation is high. We observe that the schedulers exhibit varied sensitivities to correlation and feedback delay. The analysis also leads to insightful expressions for the average throughput in the asymptotic regime of a large number of users.

Throughput Analysis of Best-m Feedback in OFDM Systems with Uniformly Correlated Subchannels

Practical orthogonal frequency division multiplexing (OFDM) systems, such as Long Term Evolution (LTE), exploit multi-user diversity using very limited feedback. The best-m feedback scheme is one such limited feedback scheme, in which users report only the gains of their m best subchannels (SCs) and their indices. While the scheme has been extensively studied and adopted in standards such as LTE, an analysis of its throughput for the practically important case in which the SCs are correlated has received less attention. We derive new closed-form expressions for the throughput when the SC gains of a user are uniformly correlated. We analyze the performance of the greedy but unfair frequency-domain scheduler and the fair round-robin scheduler for the general case in which the users see statistically non-identical SCs. An asymptotic analysis is then developed to gain further insights. The analysis and extensive numerical results bring out how correlation reduces throughput.

On Locally Gabriel Geometric Graphs

Let be a set of points in the plane. A geometric graph on is said to be locally Gabriel if for every edge in , the Euclidean disk with the segment joining and as diameter does not contain any points of that are neighbors of or in . A locally Gabriel graph(LGG) is a generalization of Gabriel graph and is motivated by applications in wireless networks. Unlike a Gabriel graph, there is no unique LGG on a given point set since no edge in a LGG is necessarily included or excluded. Thus the edge set of the graph can be customized to optimize certain network parameters depending on the application. The unit distance graph(UDG), introduced by Erdos, is also a LGG. In this paper, we show the following combinatorial bounds on edge complexity and independent sets of LGG: (i) For any , there exists LGG with edges. This improves upon the previous best bound of . (ii) For various subclasses of convex point sets, we show tight linear bounds on the maximum edge complexity of LGG. (iii) For any LGG on any point set, there exists an independent set of size .

Mixed norm estimates for the Riesz transforms on the Heisenberg group

In this paper we prove weighted mixed norm estimates for Riesz transforms on the Heisenberg group and Riesz transforms associated to the special Hermite operator. From these results vector-valued inequalities for sequences of Riesz transforms associated to generalised Grushin operators and Laguerre operators are deduced.

MIXED NORM ESTIMATES FOR THE RIESZ TRANSFORMS ON SU (2)

In this paper we prove mixed norm estimates for Riesz transforms on the group SU(2). From these results vector valued inequalities for sequences of Riesz transforms associated to Jacobi differential operators of different types are deduced.

Preliminary investigation on growth responses of Cyprinus carpio L. fed on locally formulated artificial diets

The growth rate and feed conversion ratios of the common carp, Cyprinus carpio were measured for five test diets in 14-day replicate laboratory studies. The young carp were fed with artificial test diets with crude protein contents ranging from 14.50 to 21.42 per cent. Within this range of feed characteristic optimum growth rates were obtained with diets containing 20.25 and 21.42 per cent crude protein. The study of the effect of varying ration levels showed that growth rates increased with increases of ration size, but the food conversion efficiency and protein efficiency ratios decreased markedly as ration size was increased

The use of locally available materials in fish feed production

In Nigeria, the culture of fish is gaining importance, but local fish farmers face a set back because of the stoppage on importation of fish feed. Locally available raw materials such as yam, plantain, banana, cowpeas, macuna, maize, cassava, millet, sorghum, groundnut, sunnhemp seed and brewery wastes are considered as potential materials for fish feed. These have been examined on their minimum protein contributions since this is the most expensive part of the fish feed. Alternative sources to animal proteins are also examined. Plant protein from groundnut, melon, mucuna and others compare favourably with bloodmeal mixture and thus can be used to replace the more expensive animal proteins. Pellet feed can be produced on a small scale or commercial basis from the locally available raw materials and the fish farmer is advised to seek assistance from qualified fisheries personnel

A Wide Band Strong Acoustic Absorption in a Locally Network Anechoic Coating

Composite materials with interpenetrating network structures usually exhibit unexpected merit due to the cooperative interaction. Locally resonant phononic crystals (LRPC) exhibit excellent sound attenuation performance based on a periodical arrangement of sound wave scatters. Inspired by the interpenetrating network structure and the LRPC concept, we develop a locally network anechoic coating (LNAC) that can achieve a wide band of underwater strong acoustic absorption. The experimental results show that the LNAC possesses an excellent underwater acoustic absorbing capacity in a wide frequency range. Moreover, in order to investigate the impact of the interpenetrating network structure, we fabricate a faultage structure sample and the network is disconnected by hard polyurethane (PU). The experimental comparison between the LNAC and the faultage structure sample shows that the interpenetrating network structure of the LNAC plays an important role in achieving a wide band strong acoustic absorption.

Locally resonant phononic woodpile: A wide band anomalous underwater acoustic absorbing material

To meet the demand of modern acoustic absorbing material for which acoustic absorbing frequency region can be readily tailored, we introduced woodpile structure into locally resonant phononic crystal (LRPC) and fabricated an underwater acoustic absorbing material, which is called locally resonant phononic woodpile (LRPW). Experimental results show that LRPW has a strong capability of absorbing sound in a wide frequency range. Further theoretical research revealed that LRPC units and woodpile structure in LRPW play an important role in realization of wide band underwater strong acoustic absorption.

Effect of locally available spices on the organoleptic and storage periods of Heterotis niloticus

Investigation were carried out on the effect of some locally available species in the enhancement of the organoleptic quality and the storage periods of smoked Heterotis niloticus using Pprosopis africana as common smoke sources. Samples of fresh H. niloticus were bought, cut into chunks while extract juice from pepper, ginger rhizomes, garlic, onion bulb were used as sources of spices. Samples of fish were divided randomly into five (5) batches dipped into spice extract juices for 10 minutes drained and smoked with common firewood. Treatment without spice extract juice served as control. Each batch of fish was smoked for 7 hours on a drum-made smoking kiln products were individually packaged in polythene bag stored at room temperature and used for sensory evaluation and microbial analysis. Results of the sensory evaluation indicated that there was significant difference (P<0.005) for taste, appearance, colour and overall acceptance for the treatments. Ginger juice extract had the best overall acceptance. Similarly there was significant difference (P>0.05) in the microbial analysis. The garlic juice extract had the longest storage period with minimum total plate and mould count after 8 weeks