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.

Influence of check and field size on the visual evoked magnetic response to a pattern shift stimulus

A decrease in the check size of a pattern shift stimulus increases the latency and amplitude of the visual evoked potential (VEP) P100. In addition, for a given check size, decreasing the size of the stimulus field increases the latency and amplitude of the P100. These results imply that the central regions of the retina make a significant contribution to the generation of the electrical P100. However, the corresponding magnetic P100m may have a different origin. We have studied the effects of check and field size on the P100m in five normal subjects using a DC-Squid, second-order gradiometer. Magnetic responses were recorded at the positive maximum of the P100m over the occipital scalp to six check sizes (10-100') presented in a large (13 degrees 34') and small (5 degrees 14') field and to a large check (100') presented in seven field sizes (1 degree 45' - 15 degrees 10'). No responses were recorded to any check size with a small field. Decreasing the check size presented in a large field increased latency of the P100m by approx. 30 ms while the amplitude of the response decreased with the largest reduction occurring between 70' and 12' checks. Using a large check, latency increased and amplitude decreased as the field size was reduced. The latency changes in response to check and field size were similar to those described for the VEP although the magnitudes of the magnetic changes were greater. Unlike the VEP, amplitude responses were maximal when large checks were presented in a large stimulus field. This suggests that regions outside the central retina make a more significant contribution to the visual evoked magnetic response than they do to the VEP, and that the P100m may be useful clinically in the study of diseases that affect the more peripheral regions of the retina.

Size frequency distribution of beta-amyloid (Abeta) deposits in dementia with Lewy bodies

In Alzheimer's disease (AD) and Down's syndrome (DS), the size frequency distribution of the beta-amyloid (Abeta) deposits can be described by a log-normal model and may indictae the growth of the deposits. This study determined the size frequency distribution of the Abeta deposits in the temporal lobe in 8 casaes of dementia with Lewy bodies (DLB) with associated AD pathology (DLB/AD. The size distributions of Abeta deposits were unimodal and positively skewed; the mean size of deposi and the degree of skew varying with deposit type and brain region. Size distributions of the primitive deposits had lower means and were less skewed compared with the diffuse and classic deposits. In addition, size distributions in the hippocampus and parahippocampal gyrus (PHG) had larger means and a greater degree of skew compared with other cortical gyri. All size distributions deviated significantly from a log-normal model. There were more Abeta deposits than expected in the smaller size classes and fewer than expected near the mean and in the larger size classes. The data suggest thatthe pattern of growth of the Abeta deposits in DLB/AD depends both on deposit morphology and brain area. In addition, Abeta deposits in DLB appear to grow to within a more restricted size range than predicted and hence, to have less potential for growth compared with cases of 'pure' AD and DS.

The size frequency distributions of beta-amyloid deposit subtypes in Alzheimer's disease

The size frequency distributions of diffuse, primitive and classic beta/A4 deposits was studied in single sections in the hippocampus, parahippocampal gyrus (PHG) and lateral occipitotemporal gyrus (LOT) in five cases of Alzheimer's disease. In most brain regions, the size distribution of the diffuse deposits was significantly different from that of the primitive and classic deposits. The data suggested that larger diffuse deposits appeared to be converted less often into primitive and classic deposits. Significant differences in the size distribution of primitive deposits were commonly observed between brain regions in which there was no difference in the size distribution of the diffuse deposits. Hence, local brain factors may influence the size of diffuse deposit which can be converted into mature amyloid deposit.

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.

Size frequency distributions of β-amyloid (Aβ) deposits:a comparative study of four neurodegenerative disorders

Deposition of ß-amyloid (Aß ), a 'signature' pathological lesion of Alzheimer's disease (AD), is also characteristic of Down's syndrome (DS), and has been observed in dementia with Lewy bodies (DLB) and corticobasal degeneration (CBD). To determine whether the growth of Aß deposits was similar in these disorders, the size frequency distributions of the diffuse ('pre-amyloid'), primitive ('neuritic'), and classic ('dense-cored') A ß deposits were compared in AD, DS, DLB, and CBD. All size distributions had essentially the same shape, i.e., they were unimodal and positively skewed. Mean size of Aß deposits, however, varied between disorders. Mean diameters of the diffuse, primitive, and classic deposits were greatest in DS, DS and CBD, and DS, respectively, while the smallest deposits, on average, were recorded in DLB. Although the shape of the frequency distributions was approximately log-normal, the model underestimated the frequency of smaller deposits and overestimated the frequency of larger deposits in all disorders. A 'power-law' model fitted the size distributions of the primitive deposits in AD, DS, and DLB, and the diffuse deposits in AD. The data suggest: (1) similarities in size distributions of Aß deposits among disorders, (2) growth of deposits varies with subtype and disorder, (3) different factors are involved in the growth of the diffuse/primitive and classic deposits, and (4) log-normal and power-law models do not completely account for the size frequency distributions.

The roles of inducer size and distance in the Ebbinghaus illusion (Titchener circles)

Although the Ebbinghaus illusion is commonly used as an example of a simple size-contrast effect, previous studies have emphasised its complexity by identifying many factors that potentially influence the magnitude of the illusion. Here, in a series of three experiments, we attempt to simplify this complexity. In each trial, subjects saw a display comprising, on one side, a target stimulus surrounded by inducers and, on the other, an isolated probe stimulus. Their task was to indicate whether the probe appeared larger or smaller than the target. Probe size was adjusted with a one-up, one-down staircase procedure to find the point of subjective equality between probe and target. From these experiments, we argue that the apparent effects of inducer size are often confounded by the relative completeness of the inducing surround and that factors such as the similarity of the inducers and target are secondary. We suggest a simple model that can explain most of the data in terms of just two primary and independent factors: the relative size of the inducers and target, and the distance between the inducers and the target. The balance between these two factors determines whether the size of the target is underestimated or overestimated. © 2005 a Pion publication.

Dynamic measurement of accommodation and pupil size using the portable Grand Seiko FR-5000 autorefractor

PURPOSE. The purpose of this study was to evaluate the potential of the portable Grand Seiko FR-5000 autorefractor to allow objective, continuous, open-field measurement of accommodation and pupil size for the investigation of the visual response to real-world environments and changes in the optical components of the eye. METHODS. The FR-5000 projects a pair of infrared horizontal and vertical lines on either side of fixation, analyzing the separation of the bars in the reflected image. The measurement bars were turned on permanently and the video output of the FR-5000 fed into a PC for real-time analysis. The calibration between infrared bar separation and the refractive error was assessed over a range of 10.0 D with a model eye. Tolerance to longitudinal instrument head shift was investigated over a ±15 mm range and to eye alignment away from the visual axis over eccentricities up to 25.0°. The minimum pupil size for measurement was determined with a model eye. RESULTS. The separation of the measurement bars changed linearly (r = 0.99), allowing continuous online analysis of the refractive state at 60 Hz temporal and approximately 0.01 D system resolution with pupils >2 mm. The pupil edge could be analyzed on the diagonal axes at the same rate with a system resolution of approximately 0.05 mm. The measurement of accommodation and pupil size were affected by eccentricity of viewing and instrument focusing inaccuracies. CONCLUSIONS. The small size of the instrument together with its resolution and temporal properties and ability to measure through a 2 mm pupil make it useful for the measurement of dynamic accommodation and pupil responses in confined environments, although good eye alignment is important. Copyright © 2006 American Academy of Optometry.

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.

Changes in Caribbean paleoproductivity, diversity and benthic foraminiferal test size caused by the Neogene closing of the tropical Atlantic-Pacific ocean gateway

The purpose of this study was to test 3 hypotheses: (a) that late Miocene to early Pliocene constriction and complete closure of the Central American Seaway (CAS), connecting tropical Atlantic and East Equatorial Pacific (EEP) oceans, caused decreased productivity in the Caribbean, due to reduced coastal upwelling and an end to the connection with high-productivity Pacific waters, (b) reduced paleoproductivity resulted in decreased diversity in the Caribbean and, (c) this decreased availability of food (reduced paleoproductivity) was responsible for larger mean test size in the three most common benthic foraminiferal species Epistominella exigua, Oridorsalis umbonatus and Globocassidulina subglobosa. ^ These are tested by applying correlation analysis to 7 groups of paleoceanographic proxies, 3 indices of diversity measures and mean test size data from the Caribbean Ocean Drilling Project Site 999, to 47 core samples for the interval between 8.3-2.5 Ma. Results are compared with published Caribbean and Pacific deep-sea records. ^ The Caribbean, between 8.3-7.9 Ma, experienced reduced current velocity and lower ventilation of bottom waters. Thereafter, until 4.2 Ma, the seasonality of phytodetritus input increased and ventilation further reduced. From 4.2-2.5 Ma, paleoproductivity decreased, current velocity reduced, ventilation improved, and the seasonality of phytodetrital input decreased dramatically. The benthic foraminiferal diversity followed the same trend as paleoproductivity. Individual correlation analysis between mean test size of benthic foraminiferal species Epistominella exigua, Oridorsalis umbonatus and Globocassidulina subglobosa and paleoceanographic proxies yielded a positive and significant relationship with paleoproductivity. However, a combined datasets of all 3 species yielded a negative and significant relationship with species abundance. ^ Thus, the study concludes that (a) the gradual closure of the CAS led Caribbean diversity and paleoproductivity to decrease abruptly at 7.9 Ma, when the nutrient-rich Pacific deep waters were cut off, and then, again with the complete closure of the seaway at 4.2 Ma, (b) diversity and paleoproductivity are positively correlated in the Caribbean and (c) that the availability of food is an overriding factor that influences mean test size; lower availability of food and decreased abundance leads to larger test size. ^

Does Financial Performance Depend on Hotel Size? Analysis of the Financial Profile of the U.S. Lodging Industry

This research presents a financial profile of the U.S. Lodging Industry based on an analysis of 2,091 financial statements (fiscal year 2011) for individual hotels ranging in asset size of $500 thousand to $250 million. The study analyzes summary results of the financial position and profitability of hotels based on a common size analysis of Balance Sheets and Income Statements. Furthermore, the study analyzes 10 key performance benchmarks as measured by Liquidity, Solvency and Operating Ratios. The results of the study show a divergence in the hotel industry’s financial performance based on the size of the hotel and by upper, median and lower quartiles of the study sample.

Size distribution of Holocene planktic foraminifer assemblages

The size of any organism is influenced by the surrounding ecological conditions. In this study, we investigate the effects of such factors on the size spectra of planktic foraminiferal assemblages from Holocene surface sediments. We analyzed assemblages from 69 Holocene samples, which cover the major physical and chemical gradients of the oceans. On a global scale, the range of sizes in assemblages triples from the poles to the tropics. This general temperature-related size increase is interrupted by smaller sizes at temperatures characteristic of the polar and subtropical fronts, at 2°C and 17°C, respectively, as well as in upwelling areas. On a regional scale, surface water stratification, seasonality and primary productivity are highly correlated with the size patterns. Such environmentally controlled size changes are not only characteristic for entire assemblage, but also for the dominant single species.

Grain size distribution and bulk chemistry of eolian dust

Atmospheric dust samples collected along a transect off the West African coast have been investigated for their physical (grain-size distribution), mineralogical, and chemical (major elements) composition. On the basis of these data the samples were grouped into sets of samples that most likely originated from the same source area. In addition, shipboard-collected atmospheric meteorological data, modeled 4-day back trajectories for each sampling day and location, and Total Ozone Mapping Spectrometer aerosol index data for the time period of dust collection (February-March 1998) were combined and used to reconstruct the sources of the groups of dust samples. On the basis of these data we were able to determine the provenance of the various dust samples. It appears that the bulk of the wind-blown sediments that are deposited in the proximal equatorial Atlantic Ocean are transported in the lower level (>~900 hPa) NE trade wind layer, which is a very dominant feature north of the Intertropical Convergence Zone (ITCZ). However, south of the surface expression of the ITCZ, down to 5°S, where surface winds are southwesterly, we still collected sediments that originated from the north and east, carried there by the NE trade wind layer, as well as by easterly winds from higher altitudes. The fact that the size of the wind-blown dust depends not only on the wind strength of the transporting agent but also on the distance to the source hampers a direct comparison of the dust's size distributions and measured wind strengths. However, a comparison between eolian dust and terrigenous sediments collected in three submarine sediment traps off the west coast of NW Africa shows that knowledge of the composition of eolian dust is a prerequisite for the interpretation of paleorecords obtained from sediment cores in the equatorial Atlantic.

LINEUP SIZE AND NUMBER OF CUES: WHEN BIGGER ISN’T BETTER

Larger lineups could protect innocent suspects from being misidentified; however, they can also decrease correct identifications. Bertrand (2006) investigated whether the decrease in correct identifications could be prevented by adding more cues, in the form of additional views of lineup members’ faces, to the lineup. Adding these cues was successful to an extent. The current series of studies attempted to replicate Bertrand’s (2006) findings while addressing some methodological issues—namely, the inconsistency in image size as lineup size increased. First, I investigated whether image size could affect face recognition (Chapter 2) and found it could, but that it also affected previously-seen (“old”) versus previously-unseen (“new”) faces differently. Specifically, smaller image sizes at exposure lowered accuracy for old faces, while these same image sizes at recognition lowered accuracy for new faces. Although these results indicate that target recognition would be unaffected by image size at recognition (i.e., during a lineup), lineups are also comprised of previously-unseen faces, in the form of fillers and innocent suspects. Because image size could affect lineup decisions, as it could become more difficult to realize fillers are previously-unseen, I decided to replicate Bertrand (2006) while keeping image size constant in Chapters 3 (simultaneous lineups) and 4 (simultaneous-presentation, sequential decisions). In both Chapters, the integral findings were the same: correct identification rates decreased as lineup size increased from 6- to 24-person lineups, but adding cues had no effect. The inability to replicate Bertrand (2006) could mean that the original finding was due to chance, but alternate explanations also exist, such as the overall size of the array, the degree to which additional cues overlap, and the length of the target exposure. These alternate explanations, along with directions for future research, are discussed in the following Chapters.

The influence of simulated exploitation onPatella vulgatapopulations: protandric sex change is size-dependent

Grazing mollusks are used as a food resource worldwide, and limpets are harvested commercially for both local consumption and export in several countries. This study describes a field experiment to assess the effects of simulated human exploitation of limpets Patella vulgata on their population ecology in terms of protandry (age-related sex change from male to female), growth, recruitment, migration, and density regulation. Limpet populations at two locations in southwest England were artificially exploited by systematic removal of the largest individuals for 18 months in plots assigned to three treatments at each site: no (control), low, and high exploitation. The shell size at sex change (L50: the size at which there is a 50:50 sex ratio) decreased in response to the exploitation treatments, as did the mean shell size of sexual stages. Size-dependent sex change was indicated by L50 occurring at smaller sizes in treatments than controls, suggesting an earlier switch to females. Mean shell size of P. vulgata neuters changed little under different levels of exploitation, while males and females both decreased markedly in size with exploitation. No differences were detected in the relative abundances of sexual stages, indicating some compensation for the removal of the bigger individuals via recruitment and sex change as no migratory patterns were detected between treatments. At the end of the experiment, 0–15 mm recruits were more abundant at one of the locations but no differences were detected between treatments. We conclude that sex change in P. vulgata can be induced at smaller sizes by reductions in density of the largest individuals reducing interage class competition. Knowledge of sex-change adaptation in exploited limpet populations should underpin strategies to counteract population decline and improve rocky shore conservation and resource management.