Bounds on isoperimetric values of trees

Let G = (V, E) be a finite, simple and undirected graph. For S subset of V, let delta(S, G) = {(u, v) is an element of E : u is an element of S and v is an element of V - S} be the edge boundary of S. Given an integer i, 1 <= i <= vertical bar V vertical bar, let the edge isoperimetric value of G at i be defined as b(e)(i, G) = min(S subset of V:vertical bar S vertical bar=i)vertical bar delta(S, G)vertical bar. The edge isoperimetric peak of G is defined as b(e)(G) = max(1 <= j <=vertical bar V vertical bar)b(e)(j, G). Let b(v)(G) denote the vertex isoperimetric peak defined in a corresponding way. The problem of determining a lower bound for the vertex isoperimetric peak in complete t-ary trees was recently considered in [Y. Otachi, K. Yamazaki, A lower bound for the vertex boundary-width of complete k-ary trees, Discrete Mathematics, in press (doi: 10.1016/j.disc.2007.05.014)]. In this paper we provide bounds which improve those in the above cited paper. Our results can be generalized to arbitrary (rooted) trees. The depth d of a tree is the number of nodes on the longest path starting from the root and ending at a leaf. In this paper we show that for a complete binary tree of depth d (denoted as T-d(2)), c(1)d <= b(e) (T-d(2)) <= d and c(2)d <= b(v)(T-d(2)) <= d where c(1), c(2) are constants. For a complete t-ary tree of depth d (denoted as T-d(t)) and d >= c log t where c is a constant, we show that c(1)root td <= b(e)(T-d(t)) <= td and c(2)d/root t <= b(v) (T-d(t)) <= d where c(1), c(2) are constants. At the heart of our proof we have the following theorem which works for an arbitrary rooted tree and not just for a complete t-ary tree. Let T = (V, E, r) be a finite, connected and rooted tree - the root being the vertex r. Define a weight function w : V -> N where the weight w(u) of a vertex u is the number of its successors (including itself) and let the weight index eta(T) be defined as the number of distinct weights in the tree, i.e eta(T) vertical bar{w(u) : u is an element of V}vertical bar. For a positive integer k, let l(k) = vertical bar{i is an element of N : 1 <= i <= vertical bar V vertical bar, b(e)(i, G) <= k}vertical bar. We show that l(k) <= 2(2 eta+k k)

Normative values for corneal nerve morphology assessed using corneal confocal microscopy: A multinational normative data set

OBJECTIVE Corneal confocal microscopy is a novel diagnostic technique for the detection of nerve damage and repair in a range of peripheral neuropathies, in particular diabetic neuropathy. Normative reference values are required to enable clinical translation and wider use of this technique. We have therefore undertaken a multicenter collaboration to provide worldwide age-adjusted normative values of corneal nerve fiber parameters. RESEARCH DESIGN AND METHODS A total of 1,965 corneal nerve images from 343 healthy volunteers were pooled from six clinical academic centers. All subjects underwent examination with the Heidelberg Retina Tomograph corneal confocal microscope. Images of the central corneal subbasal nerve plexus were acquired by each center using a standard protocol and analyzed by three trained examiners using manual tracing and semiautomated software (CCMetrics). Age trends were established using simple linear regression, and normative corneal nerve fiber density (CNFD), corneal nerve fiber branch density (CNBD), corneal nerve fiber length (CNFL), and corneal nerve fiber tortuosity (CNFT) reference values were calculated using quantile regression analysis. RESULTS There was a significant linear age-dependent decrease in CNFD (-0.164 no./mm(2) per year for men, P < 0.01, and -0.161 no./mm(2) per year for women, P < 0.01). There was no change with age in CNBD (0.192 no./mm(2) per year for men, P = 0.26, and -0.050 no./mm(2) per year for women, P = 0.78). CNFL decreased in men (-0.045 mm/mm(2) per year, P = 0.07) and women (-0.060 mm/mm(2) per year, P = 0.02). CNFT increased with age in men (0.044 per year, P < 0.01) and women (0.046 per year, P < 0.01). Height, weight, and BMI did not influence the 5th percentile normative values for any corneal nerve parameter. CONCLUSIONS This study provides robust worldwide normative reference values for corneal nerve parameters to be used in research and clinical practice in the study of diabetic and other peripheral neuropathies.

Plasma biochemistry and hematologic values for wild-caught flying foxes (Pteropus giganteus) in India

Although bats of the genus Pteropus are important ecologically as pollinators and natural hosts for zoonotic pathogens, little is known about their basic physiology. Hematology and plasma biochemistries were determined from wild-caught flying foxes (Pteropus giganteus) in northern India (n = 41). Mean lymphocyte differential count was higher for juveniles than adults. Mean platelet count was lower than previously reported. No hemoparasites were observed. No differences were observed between plasma biochemistry values of male and female bats, juveniles and adults, or lactating and nonlactating females. Variation in aspartate aminotransferase (AST) was seen based on body condition score. Blood urea nitrogen and cholesterol concentrations were lower in P. giganteus than other mammalian groups, but were consistent with those reported from other Pteropus species. Alanine aminotransferase and AST concentrations were higher than those reported for Pteropus vampyrus, a closely related species. This study provides basic physiologic information that can be used in future health and disease studies of Indian flying foxes.

Design of high-order filters with restricted component values

The feasibility of realising a high-order LC filter with a small set of different capacitor values, without sacrificing the frequency response specifications, is indicated. This idea could be conveniently adopted in other filter structures also—for example the FDNR transformed filter realisations.

Ethical values and the global carbon integrity system

There are many excellent books on climate justice and ethics, and their theorizing is a crucial and natural step in moving towards a justified response to this urgent problem. However, the purpose of this book lies elsewhere; it explores how ethical values can and should work in driving and structuring the global carbon integrity system.

Calorimetric values of composite solid propellants

The calorimetric values of composite solid propellant based on polystyrene, polyphenolformaldehyde, poly(vinyl chloride) and carboxy-terminated polybutadiene were determined using combustion calorimetry in order to assess the uncertainities in their measurements. The dependence of the calorimetric values on various propellant composition was obtained. The stoichiometry of oxidizer and fuel in the propellant for complete combustion obtained experimentally were compared with the theoretical stoichiometry calculated based on the oxidizer decomposition.

Precise Values of the "C Component Vicinal Coupling Constants for Calculating Side-Chain Conformations in Amino Acids

From consideration of 'H-lH vicinal coupling constants and '"G'H long-range coupling constants in a series of amino acid derivatives, the precise values of uC component vicinal coupling constants have been calculated for the three minimum energy staggered rotamers for the C(or)H-C(P)H, side-chains of amino acids.

New method of calculating calorific values from elemental compositions of fossil fuels

A new method of calculating the calorific values of fossil fuels from their chemical composition has been developed, based on the concept that heats of reaction of stoichiometric fuel-oxidizer systems are rectilinearly related with the total oxidizing or reducing valancies of the mixture. The calorific value of fossil fuels has been shown to be directly related to the net reducing valencies of the fuel. The proposed method is simple and compares favourably with the other prominent methods reported in the literature.

Prediction of breeding values for average fruit weight in mango using a multivariate individual mixed model

Mango is an important horticultural fruit crop and breeding is a key strategy to improve ongoing sustainability. Knowledge of breeding values of potential parents is important for maximising progress from breeding. This study successfully employed a mixed linear model methods incorporating a pedigree to predict breeding values for average fruit weight from highly unbalanced data for genotypes planted over three field trials and assessed over several harvest seasons. Average fruit weight was found to be under strong additive genetic control. There was high correlation between hybrids propagated as seedlings and hybrids propagated as scions grafted onto rootstocks. Estimates of additive genetic correlation among trials ranged from 0.69 to 0.88 with correlations among harvest seasons within trials greater than 0.96. These results suggest that progress from selection for broad adaptation can be achieved, particularly as no repeatable environmental factor that could be used to predict G x E could be identified. Predicted breeding values for 35 known cultivars are presented for use in ongoing breeding programs.

Soil phosphorus–crop response calibration relationships and criteria for winter cereal crops grown in Australia

Soil testing is the most widely used tool to predict the need for fertiliser phosphorus (P) application to crops. This study examined factors affecting critical soil P concentrations and confidence intervals for wheat and barley grown in Australian soils by interrogating validated data from 1777 wheat and 150 barley field treatment series now held in the BFDC National Database. To narrow confidence intervals associated with estimated critical P concentrations, filters for yield, crop stress, or low pH were applied. Once treatment series with low yield (<1 t/ha), severe crop stress, or pHCaCl2 <4.3 were screened out, critical concentrations were relatively insensitive to wheat yield (>1 t/ha). There was a clear increase in critical P concentration from early trials when full tillage was common compared with those conducted in 1995–2011, which corresponds to a period of rapid shift towards adoption of minimum tillage. For wheat, critical Colwell-P concentrations associated with 90 or 95% of maximum yield varied among Australian Soil Classification (ASC) Orders and Sub-orders: Calcarosol, Chromosol, Kandosol, Sodosol, Tenosol and Vertosol. Soil type, based on ASC Orders and Sub-orders, produced critical Colwell-P concentrations at 90% of maximum relative yield from 15 mg/kg (Grey Vertosol) to 47 mg/kg (Supracalcic Calcarosols), with other soils having values in the range 19–27 mg/kg. Distinctive differences in critical P concentrations were evident among Sub-orders of Calcarosols, Chromosols, Sodosols, Tenosols, and Vertosols, possibly due to differences in soil properties related to P sorption. However, insufficient data were available to develop a relationship between P buffering index (PBI) and critical P concentration. In general, there was no evidence that critical concentrations for barley would be different from those for wheat on the same soils. Significant knowledge gaps to fill to improve the relevance and reliability of soil P testing for winter cereals were: lack of data for oats; the paucity of treatment series reflecting current cropping practices, especially minimum tillage; and inadequate metadata on soil texture, pH, growing season rainfall, gravel content, and PBI. The critical concentrations determined illustrate the importance of recent experimental data and of soil type, but also provide examples of interrogation pathways into the BFDC National Database to extract locally relevant critical P concentrations for guiding P fertiliser decision-making in wheat and barley.

Resistance to Fusarium oxysporum f. sp fragariae and Predicted Breeding Values in Strawberry

Fusarium wilt of strawberry, incited by Fusarium oxysporum f. sp. fragariae (Fof), is a major disease of the cultivated strawberry (Fragaria xananassa) worldwide. An increase in disease outbreaks of the pathogen in Western Australia and Queensland plus the search for alternative disease management strategies place emphasis on the development of resistant cultivars. In response, a partial incomplete diallel cross involving four parents was performed for use in glasshouse resistance screenings. The resulting progeny were evaluated for their susceptibility to Fof. Best-performing progeny and suitability of progenies as parents were determined using data from disease severity ratings and analyzed using a linear mixed model incorporating a pedigree to produce best linear unbiased predictions of breeding values. Variation in disease response, ranging from highly susceptible to resistant, indicates a quantitative effect. The estimate of the narrow-sense heritability was 0.49 +/- 0.04 (SE), suggesting the population should be responsive to phenotypic recurrent selection. Several progeny genotypes have predicted breeding values higher than any of the parents. Knowledge of Fof resistance derived from this study can help select best parents for future crosses for the development of new strawberry cultivars with Fof resistance.

Samoa’s education policy: Negotiating a hybrid space for values

This paper analyses the education policy of Samoa to examine the values that are presented within as relevant to the education system. Drawing on the theory of postcolonialism and globalization, we illustrate how the global and local interact within the education policy to create a hybrid, heterogeneous mix of values and, while the policy acknowledges the significance of Samoan values, it is principally directed towards universal values being incorporated into the education system. We undertake a critical policy analysis to illustrate how the hybrid set of values are indicative of a neo-colonial discourse and argue that universal values are required, however, these need to be equally matched with local Samoan values for the education policy to be highly relevant, authentic and applicable to the Samoan education context.

In response: UV–vis light transmittance through tinted contact lenses and the effect of color on values

In the study, we used the Agilent 8453 spectrophotometer (which is equipped with a limiting aperture that restricts the light beam to the central 5 mm of the contact lens), to measure the transmittance of various coloured contact lenses including the one Day Acuvue define manufactured by Johnson and Johnson which the authors represent. We measured the instrument baseline before the transmittance spectra of lenses were tested. The values of lens transmittances were thus the difference between baseline and lens measurement at each time. The transmittance measurements were obtained at 0.5 nm intervals, from 200 to 700 nm after a soak in saline to remove the influence of any surface active agents within the packaging products. The technique used in our study was not very different from how other research studies [2], [3], [4], [5] and [6] have measured the spectra transmittances of contact lenses...

Diagnostic values for skin temperature assessment to detect diabetes-related foot complications

Background Skin temperature assessment is a promising modality for early detection of diabetic foot problems, but its diagnostic value has not been studied. Our aims were to investigate the diagnostic value of different cutoff skin temperature values for detecting diabetes-related foot complications such as ulceration, infection, and Charcot foot and to determine urgency of treatment in case of diagnosed infection or a red-hot swollen foot. Materials and Methods The plantar foot surfaces of 54 patients with diabetes visiting the outpatient foot clinic were imaged with an infrared camera. Nine patients had complications requiring immediate treatment, 25 patients had complications requiring non-immediate treatment, and 20 patients had no complications requiring treatment. Average pixel temperature was calculated for six predefined spots and for the whole foot. We calculated the area under the receiver operating characteristic curve for different cutoff skin temperature values using clinical assessment as reference and defined the sensitivity and specificity for the most optimal cutoff temperature value. Mean temperature difference between feet was analyzed using the Kruskal–Wallis tests. Results The most optimal cutoff skin temperature value for detection of diabetes-related foot complications was a 2.2°C difference between contralateral spots (sensitivity, 76%; specificity, 40%). The most optimal cutoff skin temperature value for determining urgency of treatment was a 1.35°C difference between the mean temperature of the left and right foot (sensitivity, 89%; specificity, 78%). Conclusions Detection of diabetes-related foot complications based on local skin temperature assessment is hindered by low diagnostic values. Mean temperature difference between two feet may be an adequate marker for determining urgency of treatment.

Absolute values of instantaneous corrosion rates by faradaic rectification

Doss and Agarwal 1 discovered the "redoxokinetic effect" which is now familiarly known as faradaic rectification. Subsequently, the theory and applications of faradaic rectification due to a single electrode reaction have been developed by several workers 2-5. The theory and application of faradaic rectification in the case of a corrosion cell sustaining mixed electrode reactions on a corroding metal was reported recently 6"7. This led to the development of a new electrochemical method of corrosion rate determination. It was shown that changes in the instantaneous corrosion rates of a metal are readily evaluated by faradaic rectification measurements at the corrosion potential of the metal in a given medium. The aim of the present work is to show that absolute values of instantaneous corrosion rates may also be obtained by the new method under certain conditions. The practical advantages that arise from this development are pointed out.