Typical kernel size and number of sparse random matrices over Galois fields: a statistical physics approach

Using methods of statistical physics, we study the average number and kernel size of general sparse random matrices over GF(q), with a given connectivity profile, in the thermodynamical limit of large matrices. We introduce a mapping of GF(q) matrices onto spin systems using the representation of the cyclic group of order q as the q-th complex roots of unity. This representation facilitates the derivation of the average kernel size of random matrices using the replica approach, under the replica symmetric ansatz, resulting in saddle point equations for general connectivity distributions. Numerical solutions are then obtained for particular cases by population dynamics. Similar techniques also allow us to obtain an expression for the exact and average number of random matrices for any general connectivity profile. We present numerical results for particular distributions.

Experimental studies of lobe growth in the lichen Parmelia conspersa (Ehrh. Ex Ach.) Ach.

The radial growth of individual lobes of the foliose lichen, Parmelia conspersa (Ehrh. Ex Ach.) Ach. was studied to determine whether (1) adjacent lobes exchange carbohydrate and (2) marginal competition between lobes influences radial growth. In a survey of thalli of different size, the number of marginal lobes was linearly related to thallus circumference. However, the relationship between mean lobe width and thallus circumference was fitted by a second order polynomial. Hence, mean lobe width may reach a maximum in thalli approx. 3 cm in diameter. The interactions between marginal lobes were studied by either painting single lobes with acrylic paint or by removing lobes from the thallus. Painting the whole lobe virtually stopped its radial growth while partially painted lobes grew less than control lobes. The radial growth of a lobe was unaffected by either completely painting or removing its neighbour. Removal of both neighbouring lobes did not influence the radial growth of a lobe but severing the lobe from the thallus reduced its radial growth. In addition, lobe width increased significantly when both neighbouring lobes were removed. These results suggest that adjacent lobes have a considerable degree of independence and that there is little exchange of carbohydrate between them. In addition, marginal competition between adjacent lobes may restrict the lateral extension of the lobe and this may maintain a more constant mean lobe width in larger thalli. It is possible that the intensity of marginal competition between adjacent lobes may vary with thallus size and this could be a factor determining the growth curve of a foliose lichen throughout its life.

Some aspects of system design for production management in the rolling-mill industry

Case studies in copper-alloy rolling mill companies showed that existing planning systems suffer from numerous shortcomings. Where computerised systems are in use, these tend to simply emulate older manual systems and still rely heavily on modification by experienced planners on the shopfloor. As the size and number of orders increase, the task of process planners, while seeking to optimise the manufacturing objectives and keep within the production constraints, becomes extremely complicated because of the number of options for mixing or splitting the orders into batches. This thesis develops a modular approach to computerisation of the production management and planning functions. The full functional specification of each module is discussed, together with practical problems associated with their phased implementation. By adapting the Distributed Bill of Material concept from Material Requirements Planning (MRP) philosophy, the production routes generated by the planning system are broken down to identify the rolling stages required. Then to optimise the use of material at each rolling stage, the system generates an optimal cutting pattern using a new algorithm that produces practical solutions to the cutting stock problem. It is shown that the proposed system can be accommodated on a micro-computer, which brings it into the reach of typical companies in the copper-alloy rolling industry, where profit margins are traditionally low and the cost of widespread use of mainframe computers would be prohibitive.

Planning and decision-making for energy recovery from waste at the sub-regional level

This research project has developed a novel decision support system using Geographical Information Systems and Multi Criteria Decision Analysis and used it to develop and evaluate energy-from-waste policy options. The system was validated by applying it to the UK administrative areas of Cornwall and Warwickshire. Different strategies have been defined by the size and number of the facilities, as well as the technology chosen. Using sensitivity on the results from the decision support system, it was found that key decision criteria included those affected by cost, energy efficiency, transport impacts and air/dioxin emissions. The conclusions of this work are that distributed small-scale energy-from-waste facilities score most highly overall and that scale is more important than technology design in determining overall policy impact. This project makes its primary contribution to energy-from-waste planning by its development of a Decision Support System that can be used to assist waste disposal authorities to identify preferred energy-from-waste options that have been tailored specifically to the socio-geographic characteristics of their jurisdictional areas. The project also highlights the potential of energy-from-waste policies that are seldom given enough attention to in the UK, namely those of a smaller-scale and distributed nature that often have technology designed specifically to cater for this market.

Supply chain optimisation of pyrolysis plant deployment using goal programming

This paper presents a goal programming model to optimise the deployment of pyrolysis plants in Punjab, India. Punjab has an abundance of waste straw and pyrolysis can convert this waste into alternative bio-fuels, which will facilitate the provision of valuable energy services and reduce open field burning. A goal programming model is outlined and demonstrated in two case study applications: small scale operations in villages and large scale deployment across Punjab's districts. To design the supply chain, optimal decisions for location, size and number of plants, downstream energy applications and feedstocks processed are simultaneously made based on stakeholder requirements for capital cost, payback period and production cost of bio-oil and electricity. The model comprises quantitative data obtained from primary research and qualitative data gathered from farmers and potential investors. The Punjab district of Fatehgarh Sahib is found to be the ideal location to initially utilise pyrolysis technology. We conclude that goal programming is an improved method over more conventional methods used in the literature for project planning in the field of bio-energy. The model and findings developed from this study will be particularly valuable to investors, plant developers and municipalities interested in waste to energy in India and elsewhere. © 2014 Elsevier Ltd. All rights reserved.

Modeling contention based bandwidth request scheme for IEEE 802.16 networks

IEEE 802.16 standard specifies a contention based bandwidth request scheme for best-effort and non-real time polling services in Point-to-MultiPoint (PMP) architecture. In this letter we propose an analytical model for the scheme and study how the performances of bandwidth efficiency and channel access delay change with the contention window size, the number of contending subscriber stations, the number of slots allocated for bandwidth request and data transmission. Simulations validate its high accuracy. © 2007 IEEE.

Shortest node-disjoint paths on random graphs

A localized method to distribute paths on random graphs is devised, aimed at finding the shortest paths between given source/destination pairs while avoiding path overlaps at nodes. We propose a method based on message-passing techniques to process global information and distribute paths optimally. Statistical properties such as scaling with system size and number of paths, average path-length and the transition to the frustrated regime are analyzed. The performance of the suggested algorithm is evaluated through a comparison against a greedy algorithm. © 2014 IOP Publishing Ltd and SISSA Medialab srl.

Size frequency distribution of prion protein (PrP) aggregates in variant Creutzfeldt-Jakob disease (vCJD)

The frequency distribution of aggregate size of the diffuse and florid-type prion protein (PrP) plaques was studied in various brain regions in cases of variant Creutzfeldt-Jakob disease (vCJD). The size distributions were unimodal and positively skewed and resembled those of β-amyloid (Aβ) deposits in Alzheimer's disease (AD) and Down's syndrome (DS). The frequency distributions of the PrP aggregates were log-normal in shape, but there were deviations from the expected number of plaques in specific size classes. More diffuse plaques were observed in the modal size class and fewer in the larger size classes than expected and more florid plaques were present in the larger size classes compared with the log-normal model. It was concluded that the growth of the PrP aggregates in vCJD does not strictly follow a log-normal model, diffuse plaques growing to within a more restricted size range and florid plaques to larger sizes than predicted. © Springer-Verlag 2005.

Alzheimer's disease: size class frequency distribution of senile plaques: do they indicate when a brain tissue was affected?

The size class frequency distribution of a sample of senile plaques (SP) was determined in a total of 20 brain regions from 5 elderly cases of Alzheimer's disease (AD). The purpose of the study was to determine whether a comparison of the frequency distributions could be used to determine the chronology of SP development in the AD brain. SP from 10 microns to a maximum diameter of 160 microns were present in the tissue and the size class frequency distributions were positively skewed. The frequency distributions varied between brain regions in: (1) the size class containing the mode, (2) the degree of positive skew, and (3) the ratio of large to small SP. In most patients the ratio of large to small SP was higher in the hippocampus or adjacent gyrus compared with temporal, parietal and frontal neocortex. If the diameter of a SP reflects its age in the tissue than the data suggest that SP formed earlier either in the hippocampus or adjacent gyrus compared with the other neocortical tissues. However, this conclusion rests on a number of assumptions including: (1) that SP diameter is directly related to age, (2) that SP development occurs at similar rates in different brain regions and (3) that, once formed, SP are not removed from the tissue by astrocytes.

What determines the size frequency distribution of β-amyloid (Aβ) deposits in Alzheimer's disease patients?

The factors determining the size of individual β-amyloid (A,8) deposits and their size frequency distribution in tissue from Alzheimer's disease (AD) patients have not been established. In 23/25 cortical tissues from 10 AD patients, the frequency of Aβ deposits declined exponentially with increasing size. In a random sample of 400 Aβ deposits, 88% were closely associated with one or more neuronal cell bodies. The frequency distribution of (Aβ) deposits which were associated with 0,1,2,...,n neuronal cell bodies deviated significantly from a Poisson distribution, suggesting a degree of clustering of the neuronal cell bodies. In addition, the frequency of Aβ deposits declined exponentially as the number of associated neuronal cell bodies increased. Aβ deposit area was positively correlated with the frequency of associated neuronal cell bodies, the degree of correlation being greater for pyramidal cells than smaller neurons. These data suggested: (1) the number of closely adjacent neuronal cell bodies which simultaneously secrete Aβ was an important factor determining the size of an Aβ deposit and (2) the exponential decline in larger Aβ deposits reflects the low probability that larger numbers of adjacent neurons will secrete Aβ simultaneously to form a deposit. © 1995.

Serial innovators in the UK:does size matter?

This article aims to shed light on the presence and importance of a significant number of small firms amongst serial innovators. Contrary to the common expectation in the innovative persistence literature, we posit that small serial innovators also benefit from operating within patterns of creative accumulation. However, it is in the quality of the technology and in the very nature of the knowledge accumulation process that the differences between small and large serial innovators can be found. Using a sample of 811 UK-based, highly innovative companies that patented over 66,000 inventions from 1990 to 2006, we find evidence in support of our theory. While large serial innovators experience higher innovation rates due to the scale of their innovation efforts, small serial innovators benefit more from processes of search depth characterized by the internal recombination of their previous knowledge. We find that important differences exist also in the very nature of the technologies being developed by small and large serial innovators.

Effects of grain size and microstructure on threshold values and near threshold crack growth in powder-formed Ni-base superalloy

Threshold stress intensity values, ranging from ∼6 to 16 MN m −3/2 can be obtained in powder-formed Nimonic AP1 by changing the microstructure. The threshold and low crack growth rate behaviour at room temperature of a number of widely differing API microstructures, with both ‘necklace’ and fully recrystallized grain structures of various sizes and uniform and bimodal γ′-distributions, have been investigated. The results indicate that grain size is an important microstructural parameter which can control threshold behaviour, with the value of threshold stress intensity increasing with increasing grain size, but that the γ′-distribution is also important. In this Ni-base alloy, as in many others, near threshold fatigue crack growth occurs in a crystallographic manner along {111} planes. This is due to the development of a dislocation structure involving persistent slip bands on {111} planes in the plastic zone, caused by the presence of ordered shearable precipitates in the microstructure. However, as the stress intensity range is increased, a striated growth mode takes over. The results presented show that this transition from faceted to striated growth is associated with a sudden increase in crack propagation rate and occurs when the size of the reverse plastic zone at the crack tip becomes equal to the grain size, independent of any other microstructural variables.

Portfolio size, non-trading frequency and portfolio return autocorrelation

In this paper we re-examine the relationship between non-trading frequency and portfolio return autocorrelation. We show that in portfolios where security specific effects have not been completely diversified, portfolio autocorrelation will not increase monotonically with increasing non-trading, as indicated in Lo and MacKinlay (1990). We show that at high levels of non-trading, portfolio autocorrelation will become a decreasing function of non-trading probability and may take negative values. We find that heterogeneity among the means, variances and betas of the component securities in a portfolio can act to increase the induced autocorrelation, particularly in portfolios containing fewer stocks. Security specific effects remain even when the number of securities in the portfolio is far in excess of that considered necessary to diversify security risk. © 2014 Elsevier B.V.

The correlation of indentation size effect experiments with pyramidal and spherical indenters

Experiments were conducted in annealed iridium using pyramidal and spherical indenters over a wide range of load. For a Berkovich pyramidal indenter, the hardness increased with decreasing depth of penetration. However, for spherical indenters, hardness increased with decreasing sphere radius. Based on the number of geometrically necessary dislocations generated during indentation, a theory that takes into account the work hardening differences between pyramidal and spherical indenters is developed to correlate the indentation size effects measured with the two indenters. The experimental results verify the theoretical correlation.

Exploring the optimum step size for defocus curves

Purpose: To evaluate the effect of reducing the number of visual acuity measurements made in a defocus curve on the quality of data quantified. Setting: Midland Eye, Solihull, United Kingdom. Design: Evaluation of a technique. Methods: Defocus curves were constructed by measuring visual acuity on a distance logMAR letter chart, randomizing the test letters between lens presentations. The lens powers evaluated ranged between +1.50 diopters (D) and -5.00 D in 0.50 D steps, which were also presented in a randomized order. Defocus curves were measured binocularly with the Tecnis diffractive, Rezoom refractive, Lentis rotationally asymmetric segmented (+3.00 D addition [add]), and Finevision trifocal multifocal intraocular lenses (IOLs) implanted bilaterally, and also for the diffractive IOL and refractive or rotationally asymmetric segmented (+3.00 D and +1.50 D adds) multifocal IOLs implanted contralaterally. Relative and absolute range of clear-focus metrics and area metrics were calculated for curves fitted using 0.50 D, 1.00 D, and 1.50 D steps and a near add-specific profile (ie, distance, half the near add, and the full near-add powers). Results: A significant difference in simulated results was found in at least 1 of the relative or absolute range of clear-focus or area metrics for each of the multifocal designs examined when the defocus-curve step size was increased (P<.05). Conclusion: Faster methods of capturing defocus curves from multifocal IOL designs appear to distort the metric results and are therefore not valid. Financial Disclosure: No author has a financial or proprietary interest in any material or method mentioned. © 2013 ASCRS and ESCRS.