Congruences for Overpartitions with Restricted Odd Differences

In recent work, Bringmann et al. used q-difference equations to compute a two-variable q-hypergeometric generating function for the number of overpartitions where (i) the difference between two successive parts may be odd only if the larger of the two is overlined, and (ii) if the smallest part is odd then it is overlined, given by t ¯ ( n ) . They also established the two-variable generating function for the same overpartitions where (i) consecutive parts differ by a multiple of ( k + 1 ) unless the larger of the two is overlined, and (ii) the smallest part is overlined unless it is divisible by k + 1 , enumerated by t ¯ ( k ) ( n ) . As an application they proved that t ¯ ( n ) = 0 ( mod 3 ) if n is not a square. In this paper, we extend the study of congruence properties of t ¯ ( n ) , and we prove congruences modulo 3 and 6 for t ¯ ( n ) , congruences modulo 2 and 4 for t ¯ ( 3 ) ( n ) and t ¯ ( 7 ) ( n ) , congruences modulo 4 and 5 for t ¯ ( 4 ) ( n ) , and congruences modulo 3, 6 and 12 for t ¯ ( 8 ) ( n )

Sustainable utilization of discarded foundry sand and crushed brick masonry aggregate in the production of lightweight concrete

Nowadays, there is a considerable shortage in the availability of river sand and natural stone aggregate for the construction activities all around the globe and the way out is being worked out by the use of discarded foundry sand and crushed brick masonry aggregate for construction purposes. In the present study, river sand was partly replaced by the discarded foundry sand procured from steel moulding industries and the crushed brick masonry aggregate was used as coarse aggregate for the production of lightweight concrete. The experimental program involved casting of six distinct mixes with 0%, 20%, 40%, 60%, 80% & 100% replacement of fine aggregate by discarded foundry sand. The mechanical and durability properties of the lightweight concrete were assessed for each of the six diverse blends. Even though the 80% and 100% replacement mixes were found to be less dense than the rest of the mix, the blend of 40% replacement acquired desirable mechanical and durability properties when compared to that of all other mixes. The optimum replacement level of the discarded foundry sand by mass to the river sand was 40%. The lightweight concrete produced by utilizing crushed brick masonry aggregate and discarded foundry sand (40% substitution level) can be employed in all major structural lightweight construction aspects and is ideally suited for sloped roof slabs and making architectural or decorative concrete blocks

Investigation of concrete produced using recycled aluminium dross for hot weather concreting conditions

Aluminium dross is a by-product obtained from the aluminium smelting process. Currently, this dross is processed in rotary kilns to recover the residual aluminium, and the resultant salt cake is sent to landfills. The present study investigates the utilization of recycled aluminium dross in producing concrete, which is suitable for hot weather concreting condition. The primary objectives of the experimental study are to examine the feasibility of using concrete blended with recycled aluminium dross under hot weather concreting situations and then to evaluate the strength and durability aspects of the produced concrete. From the experimental results it is observed that the initial setting time of the recycled aluminium dross concrete extended by about 30 minutes at 20% replacement level. This property of recycled aluminium dross concrete renders it to be suitable for hot weather concreting conditions. Based on the results obtained, the replacement of cement with 20% of Al dross yields superior mechanical and durability characteristics

CGHScan: finding variable regions using high-density microarray comparative genomic hybridization data

BACKGROUND: Comparative genomic hybridization can rapidly identify chromosomal regions that vary between organisms and tissues. This technique has been applied to detecting differences between normal and cancerous tissues in eukaryotes as well as genomic variability in microbial strains and species. The density of oligonucleotide probes available on current microarray platforms is particularly well-suited for comparisons of organisms with smaller genomes like bacteria and yeast where an entire genome can be assayed on a single microarray with high resolution. Available methods for analyzing these experiments typically confine analyses to data from pre-defined annotated genome features, such as entire genes. Many of these methods are ill suited for datasets with the number of measurements typical of high-density microarrays. RESULTS: We present an algorithm for analyzing microarray hybridization data to aid identification of regions that vary between an unsequenced genome and a sequenced reference genome. The program, CGHScan, uses an iterative random walk approach integrating multi-layered significance testing to detect these regions from comparative genomic hybridization data. The algorithm tolerates a high level of noise in measurements of individual probe intensities and is relatively insensitive to the choice of method for normalizing probe intensity values and identifying probes that differ between samples. When applied to comparative genomic hybridization data from a published experiment, CGHScan identified eight of nine known deletions in a Brucella ovis strain as compared to Brucella melitensis. The same result was obtained using two different normalization methods and two different scores to classify data for individual probes as representing conserved or variable genomic regions. The undetected region is a small (58 base pair) deletion that is below the resolution of CGHScan given the array design employed in the study. CONCLUSION: CGHScan is an effective tool for analyzing comparative genomic hybridization data from high-density microarrays. The algorithm is capable of accurately identifying known variable regions and is tolerant of high noise and varying methods of data preprocessing. Statistical analysis is used to define each variable region providing a robust and reliable method for rapid identification of genomic differences independent of annotated gene boundaries

Occurrence of macro plastic in the stomach of flat needlefish

On 6th January 2016, biological samples ofAblennes hians were collected from the hook andline fishing boats based at Munambam FishingHarbour, Kochi. While analysing the gut contents inthe laboratory, the stomach of one specimen (weight380 gm, total length 687 mm) contained macroplastic material having about 0.02 gm weight.Stomach also contained partially digested shrimps,sea snails (Diacavolinia longirostris, Cavoliniatridentata) and digested matter

Emergent complex neural dynamics

A large repertoire of spatiotemporal activity patterns in the brain is the basis for adaptive behaviour. Understanding the mechanism by which the brain's hundred billion neurons and hundred trillion synapses manage to produce such a range of cortical configurations in a flexible manner remains a fundamental problem in neuroscience. One plausible solution is the involvement of universal mechanisms of emergent complex phenomena evident in dynamical systems poised near a critical point of a second-order phase transition. We review recent theoretical and empirical results supporting the notion that the brain is naturally poised near criticality, as well as its implications for better understanding of the brain

Failure of adaptive self-organized criticality during epileptic seizure attacks

Critical dynamics are assumed to be an attractive mode for normal brain functioning as information processing and computational capabilities are found to be optimized there. Recent experimental observations of neuronal activity patterns following power-law distributions, a hallmark of systems at a critical state, have led to the hypothesis that human brain dynamics could be poised at a phase transition between ordered and disordered activity. A so far unresolved question concerns the medical significance of critical brain activity and how it relates to pathological conditions. Using data from invasive electroencephalogram recordings from humans we show that during epileptic seizure attacks neuronal activity patterns deviate from the normally observed power-law distribution characterizing critical dynamics. The comparison of these observations to results from a computational model exhibiting self-organized criticality (SOC) based on adaptive networks allows further insights into the underlying dynamics. Together these results suggest that brain dynamics deviates from criticality during seizures caused by the failure of adaptive SOC.Comment: 7 pages, 5 figure

Avalanches in a Stochastic Model of Spiking Neurons

Neuronal avalanches are a form of spontaneous activity widely observed in cortical slices and other types of nervous tissue, both in vivo and in vitro. They are characterized by irregular, isolated population bursts when many neurons fire together, where the number of spikes per burst obeys a power law distribution. We simulate, using the Gillespie algorithm, a model of neuronal avalanches based on stochastic single neurons. The network consists of excitatory and inhibitory neurons, first with all-to-all connectivity and later with random sparse connectivity. Analyzing our model using the system size expansion, we show that the model obeys the standard Wilson-Cowan equations for large network sizes ( neurons). When excitation and inhibition are closely balanced, networks of thousands of neurons exhibit irregular synchronous activity, including the characteristic power law distribution of avalanche size. We show that these avalanches are due to the balanced network having weakly stable functionally feedforward dynamics, which amplifies some small fluctuations into the large population bursts. Balanced networks are thought to underlie a variety of observed network behaviours and have useful computational properties, such as responding quickly to changes in input. Thus, the appearance of avalanches in such functionally feedforward networks indicates that avalanches may be a simple consequence of a widely present network structure, when neuron dynamics are noisy. An important implication is that a network need not be “critical” for the production of avalanches, so experimentally observed power laws in burst size may be a signature of noisy functionally feedforward structure rather than of, for example, self-organized criticality