Explicit Construction of Optimal Exact Regenerating Codes for Distributed Storage

Erasure coding techniques are used to increase the reliability of distributed storage systems while minimizing storage overhead. Also of interest is minimization of the bandwidth required to repair the system following a node failure. In a recent paper, Wu et al. characterize the tradeoff between the repair bandwidth and the amount of data stored per node. They also prove the existence of regenerating codes that achieve this tradeoff. In this paper, we introduce Exact Regenerating Codes, which are regenerating codes possessing the additional property of being able to duplicate the data stored at a failed node. Such codes require low processing and communication overheads, making the system practical and easy to maintain. Explicit construction of exact regenerating codes is provided for the minimum bandwidth point on the storage-repair bandwidth tradeoff, relevant to distributed-mail-server applications. A sub-space based approach is provided and shown to yield necessary and sufficient conditions on a linear code to possess the exact regeneration property as well as prove the uniqueness of our construction. Also included in the paper, is an explicit construction of regenerating codes for the minimum storage point for parameters relevant to storage in peer-to-peer systems. This construction supports a variable number of nodes and can handle multiple, simultaneous node failures. All constructions given in the paper are of low complexity, requiring low field size in particular.

Voltage delay during constant-current or constant-resistance discharge of Mg-MnO2 dry cells: A comparative study

A theoretical approach has been developed to relate the voltage delay transients of the Mg-MnO2 dry cell observed during discharge by two commonly employed modes, viz., (1) at constant current, and (2) across a constant resistance. The approach has been verified by comparison of experimentally obtained transients with those generated from theory. The method may be used to predict the delay parameters of the Mg-MnO2 dry cell under the two modes of discharge and can, in principle, be extended to lithium batteries.

Quantum Error Correction via Codes over GF(2)

It is well known that n-length stabilizer quantum error correcting codes (QECCs) can be obtained via n-length classical error correction codes (CECCs) over GF(4), that are additive and self-orthogonal with respect to the trace Hermitian inner product. But, most of the CECCs have been studied with respect to the Euclidean inner product. In this paper, it is shown that n-length stabilizer QECCs can be constructed via 371 length linear CECCs over GF(2) that are self-orthogonal with respect to the Euclidean inner product. This facilitates usage of the widely studied self-orthogonal CECCs to construct stabilizer QECCs. Moreover, classical, binary, self-orthogonal cyclic codes have been used to obtain stabilizer QECCs with guaranteed quantum error correcting capability. This is facilitated by the fact that (i) self-orthogonal, binary cyclic codes are easily identified using transform approach and (ii) for such codes lower bounds on the minimum Hamming distance are known. Several explicit codes are constructed including two pure MDS QECCs.

Isoscalar axial-vector renormalization constant and polarized proton structure function

The isoscalar axial-vector renormalization constant is reevaluated using the QCD sum-rule method. It is found to be substantially different from the anomaly-free octet axial-vector u¯γμγ5+d¯γμγ5-2s¯γμγ5 coupling. Combining this determination with the known values of the isovector coupling GA and the F/D ratio for the octet current, we find the integral of the polarized proton structure function to be Gp=Fgp1(x)dx=0.135, in agreement with recent measurement by the European Muon Collaboration.

Purification and characterization of endo-1,4-β-xylanase from Paecilomyces varioti Bainier

An endo-xylanase (1,4-β-d-xylanxylanohydrolase EC 3.2.1.8) was isolated from the culture filtrate of Paecilomyces varioti Bainier. The enzyme was purified 3.2 fold with a 60% yield by gel filtration and ion exchange chromatography. The purified enzyme had a molecular weight of 25,000 with a sedimentation coefficient of 2.2 S. The isoelectric point of the enzyme was 3.9. The enzyme was obtained in crystalline form. The optimum pH range was 5.5–7.0 and the temperature, 65°C. The Michaelis constant was 2.5 mg larchwood xylan/ml. The enzyme was found to degrade xylan by an endo mechanism producing arabinose, xylobiose, xylo- and arabinosylxylo-oligosaccharides, during the initial stages of hydrolysis. On prolonged incubation, xylotriose, arabinosylxylotriose and xylobiose were the major products with traces of xylotetraose, xylose and arabinose.

Convolutional Codes for Network-Error Correction

In this work, we introduce convolutional codes for network-error correction in the context of coherent network coding. We give a construction of convolutional codes that correct a given set of error patterns, as long as consecutive errors are separated by a certain interval. We also give some bounds on the field size and the number of errors that can get corrected in a certain interval. Compared to previous network error correction schemes, using convolutional codes is seen to have advantages in field size and decoding technique. Some examples are discussed which illustrate the several possible situations that arise in this context.

Diesel Engine Driven Stand-Alone Variable Speed Constant Frequency Slip Ring Induction Generator - Theory and Experimental Results

The operation of a stand-alone, as opposed to grid connected generation system, using a slip-ring induction machine as the electrical generator, is considered. In contrast to an alternator, a slip-ring induction machine can run at variable speed and still deliver constant frequency power to loads. This feature enables optimization of the system when the prime mover is inherently variable speed in nature eg. wind turbines, as well as diesel driven systems, where there is scope for economizing on fuel consumption. Experimental results from a system driven by a 44 bhp diesel engine are presented. Operation at subsynchronous as well as super-synchronous speeds is examined. The measurement facilitates the understanding of the system as well as its design.

On BCH codes over arbitrary integer rings

Bose-C-Hocquenghem (BCH) atdes with symbols from an arbitrary fhite integer ring are derived in terms of their generator polynomials. The derivation is based on the factohation of x to the power (n) - 1 over the unit ring of an appropriate extension of the fiite integer ring. lke eomtruetion is thus shown to be similar to that for BCH codes over fink flelda.

Studies on follicular growth in the immature rat and hamster: Effect of a single injection of gonadotropin or estrogen on the rate of3H-thymidine incorporation into ovarian DNAin vitro

Initiation of follicular growth by specific hormonal stimuli in ovaries of immature rats and hamsters was studied by determining the rate of incorporation of3H-thymidine into ovarian DNAin vitro. Incorporation was considered as an index of DNA synthesis and cell multiplication. A single injection of pregnant mare serum gonadotropin could thus maximally stimulate by 18 hr3H-thymidine incorporation into DNA of the ovary of immature hamsters. Neutralization of pregnant mare serum gonadotropin by an antiserum to ovine follicle stimulating hormone only during the initial 8–10 hr and not later could inhibit the increase in3H-thymidine incorporationin vitro observed at 18 hr, suggesting that the continued presence of gonadotropin stimulus was not necessary for this response. The other indices of follicular growth monitored such as ovarian weight, serum estradiol and uterine weight showed discernible increase at periods only after the above initial event. A single injection of estrogen (diethyl stilbesterol or estradiol-l7β) could similarly cause 18 hr later, a stimulation in the rate of incorporation of3H-thymidine into DNAin vitro in ovaries of immature rats. The presence of endogenous gonadotropins, however, was obligatory for observing this response to estrogen. Evidence in support of the above was two-fold: (i) administration of antiserum to follicle stimulating hormone or luteinizing hormone along with estrogen completely inhibited the increase in3H-thymidine incorporation into ovarian DNAin vitro; (ii) a radioimmunological measurement revealed following estrogen treatment, the presence of a higher concentration of endogenous follicle stimulating hormone in the ovary. Finally, administration of varying doses of ovine follicle stimulating hormone along with a constant dose of estrogen to immature rats produced a dose-dependent increment in the incorporation of3H-thymidine into ovarian DNAin vitro. These observations suggested the potentiality of this system for developing a sensitive bioassay for follicle stimulating hormone.

Antioxidants, weight change and risk of type 2 diabetes

The incidence of type 2 diabetes has increased rapidly worldwide. Obesity is one of the most important modifiable risk factors of type 2 diabetes: weight gain increases and weight loss decreases the risk. However, the effects of weight fluctuation are unclear. Reactive oxygen species are presumably part of the complicated mechanism for the development of insulin resistance and beta-cell destruction in the pancreas. The association of antioxidants with the risk of incident type 2 diabetes has been studied in longitudinal prospective human studies, but so far there is no clear conclusion about protective effect of dietary or of supplementary antioxidants on diabetes risk. The present study examined 1) weight change and fluctuation as risk factors for incident type 2 diabetes; 2) the association of baseline serum alpha-tocopherol or beta-carotene concentration and dietary intake of antioxidants with the risk of type 2 diabetes; 3) the effect of supplementation with alpha-tocopherol or beta-carotene on the risk of incident type 2 diabetes; and on macrovascular complications and mortality among type 2 diabetics. This investigation was part of the Alpha-Tocopherol, Beta-Carotene Cancer Prevention (ATBC) Study, a randomized, double-blind, placebo-controlled prevention trial, which has undertaken to examine the effect of alpha-tocopherol and beta-carotene supplementation on the development of lung cancer, other cancers, and cardiovascular diseases in male smokers aged 50-69 years at baseline. Participants were assigned to receive either 50 mg alpha-tocopherol, 20mg beta-carotene, both, or placebo daily in a 2 x 2 factorial design experiment during 1985-1993. Cases of incident diabetes were identified through a nationwide register of drug reimbursements of the Social Insurance Institution. At baseline 1700 men had a history of diabetes. Among those (n = 27 379) with no diabetes at baseline 305 new cases of type 2 diabetes were recognized during the intervention period and 705 during the whole follow-up to 12.5 years. Weight gain and weight fluctuation measured over a three year period were independent risk factors for subsequent incident type 2 diabetes. Relative risk (RR) was 1.77 (95% confidence interval [CI] 1.44-2.17) for weight gain of at least 4 kg compared to those with a weight change of less than 4 kg. The RR in the highest weight fluctuation quintile compared to the lowest was 1.64 (95% CI 1.24-2.17). Dietary tocopherols and tocotrienols as well as dietary carotenoids, flavonols, flavones and vitamin C were not associated with the risk of type 2 diabetes. Baseline serum alpha-tocopherol and beta-carotene concentrations were not associated with the risk of incident diabetes. Neither alpha-tocopherol nor beta-carotene supplementation affected the risk of diabetes. The relative risks for participants who received alpha-tocopherol compared with nonrecipients and for participants who received beta-carotene compared with nonrecipients were 0.92 (95% CI 0.79-1.07) and 0.99 (95% CI 0.85-1.15), respectively. Furthermore, alpha-tocopherol or beta-carotene supplementation did not affect the risk of macrovascular complications or mortality of diabetic subjects during the 19 years follow-up time. In conclusion, in this study of older middle-aged male smokers, weight gain and weight fluctuation were independent risk factors for type 2 diabetes. Intake of antioxidants or serum alpha-tocopherol or beta-carotene concentrations were not associated with the risk of type 2 diabetes. Supplementation with of alpha-tocopherol or beta-carotene did not prevent type 2 diabetes. Neither did they prevent macrovascular complications, or mortality among diabetic subjects.

Preterm birth and risk factors for chronic disease : Helsinki Study of Very Low Birth Weight Adults

Background: The improved prognosis of early preterm birth has created a generation of surviving very low birth weight (< 1500 g, VLBW) infants whose health risks in adulthood are poorly known. Of every 1000 live-born infants in Finland, about 8 are born at VLBW. Variation in birth weight, even within the normal range, relates to considerable variation in the risk for several common adult disorders, including cardiovascular disease and osteoporosis. Small preterm infants frequently exhibit severe postnatal or prenatal growth retardation, or both. Much reason for concern thus exists, regarding adverse health effects in surviving small preterm infants later lives. We studied young adults, aiming at exploring whether VLBW birth and postnatal events after such a birth are associated with higher levels of risk factors for cardiovascular disease or osteoporosis. Subjects and Methods: A follow-up study for VLBW infants began in 1978; by the end of 1985, 335 VLBW survivors at Helsinki University Central Hospital participated in the follow-up. Their gestational ages ranged from 24 to 35 weeks, mean 29.2 and standard deviation 2.2 weeks. In 2004, we invited for a clinic visit 255 subjects, aged 18 to 27, who still lived in the greater Helsinki area. From the same birth hospitals, we also invited 314 term-born controls of similar age and sex. These two study groups underwent measurements of body size and composition, function of brachial arterial endothelium (flow-mediated dilatation, FMD) and carotid artery intima-media thickness (cIMT) by ultrasound. In addition, we measured plasma lipid concentrations, ambulatory blood pressure, fasting insulin, glucose tolerance and, by dual-energy x-ray densitometry, bone-mineral density. Results: 172 control and 166 VLBW participants underwent lipid measurements and a glucose tolerance test. VLBW adults fasting insulin (adjusted for body mass index) was 12.6% (95% confidence interval, 0.8 to 25.8) higher than that of the controls. The glucose and insulin concentrations 120 minutes after 75 g glucose ingestion showed similar differences (N=332) (I). VLBW adults had 3.9 mmHg (1.3 to 6.4) higher office systolic blood pressure, 3.5 mmHg (1.7 to 5.2) higher office diastolic blood pressure (I), and, when adjusted for body mass index and height, 3.1 mmHg (0.5 to 5.5) higher 24-hour mean systolic blood pressure (N=238) (II). VLBW birth was associated neither with HDL- or total cholesterol nor triglyceride concentrations (N=332) (I), nor was it associated with a low FMD or a high cIMT (N=160) (III). VLBW adults had 0.51-unit (0.28 to 0.75) lower lumbar spine Z scores and 0.56-unit (0.34 to 0.78) lower femoral neck Z scores (N=283). Adjustments for size attenuated the differences, but only partially (IV). Conclusions: These results imply that those born at VLBW, although mostly healthy as young adults, already bear several risk factors for chronic adult disease. The significantly higher fasting insulin level in adults with VLBW suggests increased insulin resistance. The higher blood pressure in young adults born at VLBW may indicate they later are at risk for hypertension, although their unaffected endothelial function may be evidence for some form of protection from cardiovascular disease. Lower bone mineral density around the age of peak bone mass may suggest increased risk for later osteoporotic fractures. Because cardiovascular disease and osteoporosis are frequent, and their prevention is relatively cheap and safe, one should focus on prevention now. When initiated early, preventive measures are likely to have sufficient time to be effective in preventing or postponing the onset of chronic disease.

Design of Constant Accuracy Linear Proportional Weir

Five different shaped weirs were designed and pertinent data for their use are given. One of these weir shapes had the least “sharp edge” at the junction of the base weir and “complementary weir.” Two other types of weirs had equal slopes at the junction of the base weir and complementary weir. Another shape, for which neither the indication accuracy was constant nor the slope was equal at the junction of the base weir and complementary weir, was also tested. The results of the four weir shapes hydraulically tested give consistent values for the coefficient of discharge varying between 0.625 to 0.631. The indication accuracies of all the previously designed linear proportional weirs (includig Sutro weir) are neither constant nor unity, as is believed.

Regenerating Codes for Distributed Storage Networks

In a storage system where individual storage nodes are prone to failure, the redundant storage of data in a distributed manner across multiple nodes is a must to ensure reliability. Reed-Solomon codes possess the reconstruction property under which the stored data can be recovered by connecting to any k of the n nodes in the network across which data is dispersed. This property can be shown to lead to vastly improved network reliability over simple replication schemes. Also of interest in such storage systems is the minimization of the repair bandwidth, i.e., the amount of data needed to be downloaded from the network in order to repair a single failed node. Reed-Solomon codes perform poorly here as they require the entire data to be downloaded. Regenerating codes are a new class of codes which minimize the repair bandwidth while retaining the reconstruction property. This paper provides an overview of regenerating codes including a discussion on the explicit construction of optimum codes.

Preterm birth and risk factors for chronic disease : Helsinki Study of Very Low Birth Weight Adults

Background: The improved prognosis of early preterm birth has created a generation of surviving very low birth weight (PIENEMPI KUIN 1500 g, VLBW) infants whose health risks in adulthood are poorly known. Of every 1000 live-born infants in Finland, about 8 are born at VLBW. Variation in birth weight, even within the normal range, relates to considerable variation in the risk for several common adult disorders, including cardiovascular disease and osteoporosis. Small preterm infants frequently exhibit severe postnatal or prenatal growth retardation, or both. Much reason for concern thus exists, regarding adverse health effects in surviving small preterm infants later lives. We studied young adults, aiming at exploring whether VLBW birth and postnatal events after such a birth are associated with higher levels of risk factors for cardiovascular disease or osteoporosis. Subjects and Methods: A follow-up study for VLBW infants began in 1978; by the end of 1985, 335 VLBW survivors at Helsinki University Central Hospital participated in the follow-up. Their gestational ages ranged from 24 to 35 weeks, mean 29.2 and standard deviation 2.2 weeks. In 2004, we invited for a clinic visit 255 subjects, aged 18 to 27, who still lived in the greater Helsinki area. From the same birth hospitals, we also invited 314 term-born controls of similar age and sex. These two study groups underwent measurements of body size and composition, function of brachial arterial endothelium (flow-mediated dilatation, FMD) and carotid artery intima-media thickness (cIMT) by ultrasound. In addition, we measured plasma lipid concentrations, ambulatory blood pressure, fasting insulin, glucose tolerance and, by dual-energy x-ray densitometry, bone-mineral density. Results: 172 control and 166 VLBW participants underwent lipid measurements and a glucose tolerance test. VLBW adults fasting insulin (adjusted for body mass index) was 12.6% (95% confidence interval, 0.8 to 25.8) higher than that of the controls. The glucose and insulin concentrations 120 minutes after 75 g glucose ingestion showed similar differences (N=332) (I). VLBW adults had 3.9 mmHg (1.3 to 6.4) higher office systolic blood pressure, 3.5 mmHg (1.7 to 5.2) higher office diastolic blood pressure (I), and, when adjusted for body mass index and height, 3.1 mmHg (0.5 to 5.5) higher 24-hour mean systolic blood pressure (N=238) (II). VLBW birth was associated neither with HDL- or total cholesterol nor triglyceride concentrations (N=332) (I), nor was it associated with a low FMD or a high cIMT (N=160) (III). VLBW adults had 0.51-unit (0.28 to 0.75) lower lumbar spine Z scores and 0.56-unit (0.34 to 0.78) lower femoral neck Z scores (N=283). Adjustments for size attenuated the differences, but only partially (IV). Conclusions: These results imply that those born at VLBW, although mostly healthy as young adults, already bear several risk factors for chronic adult disease. The significantly higher fasting insulin level in adults with VLBW suggests increased insulin resistance. The higher blood pressure in young adults born at VLBW may indicate they later are at risk for hypertension, although their unaffected endothelial function may be evidence for some form of protection from cardiovascular disease. Lower bone mineral density around the age of peak bone mass may suggest increased risk for later osteoporotic fractures. Because cardiovascular disease and osteoporosis are frequent, and their prevention is relatively cheap and safe, one should focus on prevention now. When initiated early, preventive measures are likely to have sufficient time to be effective in preventing or postponing the onset of chronic disease.

Microscopic expression for frequency and wave vector dependent dielectric constant of a dipolar liquid

A microscopic expression for the frequency and wave vector dependent dielectric constant of a dense dipolar liquid is derived starting from the linear response theory. The new expression properly takes into account the effects of the translational modes in the polarization relaxation. The longitudinal and the transverse components of the dielectric constant show vastly different behavior at the intermediate values of the wave vector k. We find that the microscopic structure of the dense liquid plays an important role at intermediate wave vectors. The continuum model description of the dielectric constant, although appropriate at very small values of wave vector, breaks down completely at the intermediate values of k. Numerical results for the longitudinal and the transverse dielectric constants are obtained by using the direct correlation function from the mean‐spherical approximation for dipolar hard spheres. We show that our results are consistent with all the limiting expressions known for the dielectric function of matter.