Numerical computation of an analytic singular value decomposition of a matrix valued function

This paper extends the singular value decomposition to a path of matricesE(t). An analytic singular value decomposition of a path of matricesE(t) is an analytic path of factorizationsE(t)=X(t)S(t)Y(t) T whereX(t) andY(t) are orthogonal andS(t) is diagonal. To maintain differentiability the diagonal entries ofS(t) are allowed to be either positive or negative and to appear in any order. This paper investigates existence and uniqueness of analytic SVD's and develops an algorithm for computing them. We show that a real analytic pathE(t) always admits a real analytic SVD, a full-rank, smooth pathE(t) with distinct singular values admits a smooth SVD. We derive a differential equation for the left factor, develop Euler-like and extrapolated Euler-like numerical methods for approximating an analytic SVD and prove that the Euler-like method converges.

Reliability, sufficiency, and the decomposition of proper scores

Scoring rules are an important tool for evaluating the performance of probabilistic forecasting schemes. A scoring rule is called strictly proper if its expectation is optimal if and only if the forecast probability represents the true distribution of the target. In the binary case, strictly proper scoring rules allow for a decomposition into terms related to the resolution and the reliability of a forecast. This fact is particularly well known for the Brier Score. In this article, this result is extended to forecasts for finite-valued targets. Both resolution and reliability are shown to have a positive effect on the score. It is demonstrated that resolution and reliability are directly related to forecast attributes that are desirable on grounds independent of the notion of scores. This finding can be considered an epistemological justification of measuring forecast quality by proper scoring rules. A link is provided to the original work of DeGroot and Fienberg, extending their concepts of sufficiency and refinement. The relation to the conjectured sharpness principle of Gneiting, et al., is elucidated.

Estimating reliability and resolution of probability forecasts through decomposition of the empirical score

References (20)Cited By (1)Export CitationAboutAbstract Proper scoring rules provide a useful means to evaluate probabilistic forecasts. Independent from scoring rules, it has been argued that reliability and resolution are desirable forecast attributes. The mathematical expectation value of the score allows for a decomposition into reliability and resolution related terms, demonstrating a relationship between scoring rules and reliability/resolution. A similar decomposition holds for the empirical (i.e. sample average) score over an archive of forecast–observation pairs. This empirical decomposition though provides a too optimistic estimate of the potential score (i.e. the optimum score which could be obtained through recalibration), showing that a forecast assessment based solely on the empirical resolution and reliability terms will be misleading. The differences between the theoretical and empirical decomposition are investigated, and specific recommendations are given how to obtain better estimators of reliability and resolution in the case of the Brier and Ignorance scoring rule.

A study of the microstructure and condition of thin sheets of painting support ivory using SEM and ESEM

This paper outlines a study of the microstructure of thin sheets of ivory used as a painting support for portrait miniatures. Warping of the ivory support is one of the main problems commonly found in portrait miniatures from the late eighteenth century and early nineteenth century. Portrait miniatures from this period are painted on very thin sheets of ivory that are often only 0.2 mm in thickness. Warping can lead to cracking of the ivory and can also accentuate flaking of the paint layer. The problem of warping in ivory has thus been of long-term interest to conservators who deal with portrait miniatures, including those at the Victoria and Albert (V&A) Museum. The causes of warping are complex. However, it should be noted that artists normally stuck the thin ivory sheets onto paper or card before commencing the painting. The possible causes of warping therefore are thought to relate to the differential reactions of the ivory/adhesive/paper or card layers to changes in relative humidity (RH). It is well known that ivory is hygroscopic and anisotropic.1 However, only a few scientific studies have been carried out related to this subject and systematic analyses of the morphological and microstructural changes due to changes in RH or moisture in such thin sheets of ivory have yet to be investigated.

Decomposition of surface electromyographic signal using Hidden Markov Model

The detection of physiological signals from the motor system (electromyographic signals) is being utilized in the practice clinic to guide the therapist in a more precise and accurate diagnosis of motor disorders. In this context, the process of decomposition of EMG (electromyographic) signals that includes the identification and classification of MUAP (Motor Unit Action Potential) of a EMG signal, is very important to help the therapist in the evaluation of motor disorders. The EMG decomposition is a complex task due to EMG features depend on the electrode type (needle or surface), its placement related to the muscle, the contraction level and the health of the Neuromuscular System. To date, the majority of researches on EMG decomposition utilize EMG signals acquired by needle electrodes, due to their advantages in processing this type of signal. However, relatively few researches have been conducted using surface EMG signals. Thus, this article aims to contribute to the clinical practice by presenting a technique that permit the decomposition of surface EMG signal via the use of Hidden Markov Models. This process is supported by the use of differential evolution and spectral clustering techniques. The developed system presented coherent results in: (1) identification of the number of Motor Units actives in the EMG signal; (2) presentation of the morphological patterns of MUAPs in the EMG signal; (3) identification of the firing sequence of the Motor Units. The model proposed in this work is an advance in the research area of decomposition of surface EMG signals.

Soils of contrasting pH affect the decomposition of buried mammalian (Ovis aries) skeletal muscle tissue

Little is known about the effect of edaphic conditions on the decomposition of buried mammalian tissues. To address this, we set up a replicated incubation study with three fresh soils of contrasting pH: a Podsol (acidic), a Cambisol (neutral), and a Rendzina (alkaline), in which skeletal muscle tissue (SMT) of known mass was allowed to decompose. Our results clearly demonstrated that soil type had a considerable effect on the decomposition of SMT buried in soil. Differences in the rate of decomposition were up to three times greater in the Podsol compared with the Rendzina. The rate of microbial respiration was correlated to the rate of soft tissue loss, which suggests that the decomposition of SMT is dependent on the microbial community present in the soil. Decompositional by-products caused the pH of the immediate soil environment to change, becoming more alkaline at first, before acidifying. Our results demonstrate the need for greater consideration of soil type in future taphonomic studies.

Temperature affects microbial decomposition of cadavers (Rattus rattus) in contrasting soils

The ecology of soils associated with dead mammals (i.e. cadavers) is poorly understood. Although temperature and soil type are well known to influence the decomposition of other organic resource patches, the effect of these variables on the degradation of cadavers in soil has received little experimental investigation. To address this, cadavers of juvenile rats (Rattus rattus) were buried in one of three contrasting soils (Sodosol, Rudosol, and Vertosol) from tropical savanna ecosystems in Queensland, Australia and incubated at 29 °C, 22 °C, or 15 °C in a laboratory setting. Cadavers and soils were destructively sampled at intervals of 7 days over an incubation period of 28 days. Measurements of decomposition included cadaver mass loss, carbon dioxide–carbon (CO2–C) evolution, microbial biomass carbon (MBC), protease activity, phosphodiesterase activity, and soil pH, which were all significantly positively affected by cadaver burial. A temperature effect was observed where peaks or differences in decomposition that at occurred at higher temperature would occur at later sample periods at lower temperature. Soil type also had an important effect on some measured parameters. These findings have important implications for a largely unexplored area of soil ecology and nutrient cycling, which are significant for forensic science, cemetery planning and livestock carcass disposal.

Microbial decomposition of skeletal muscle tissue (Ovis aries) in a sandy loam soil at different temperatures

A laboratory experiment was conducted to determine the effect of temperature (2, 12, 22 °C) on the rate of aerobic decomposition of skeletal muscle tissue (Ovis aries) in a sandy loam soil incubated for a period of 42 days. Measurements of decomposition processes included skeletal muscle tissue mass loss, carbon dioxide (CO2) evolution, microbial biomass, soil pH, skeletal muscle tissue carbon (C) and nitrogen (N) content and the calculation of metabolic quotient (qCO2). Incubation temperature and skeletal muscle tissue quality had a significant effect on all of the measured process rates with 2 °C usually much lower than 12 and 22 °C. Cumulative CO2 evolution at 2, 12 and 22 °C equaled 252, 619 and 905 mg CO2, respectively. A significant correlation (P<0.001) was detected between cumulative CO2 evolution and tissue mass loss at all temperatures. Q10s for mass loss and CO2 evolution, which ranged from 1.19 to 3.95, were higher for the lower temperature range (Q10(2– 12 °C)>Q10(12–22 °C)) in the Ovis samples and lower for the low temperature range (Q10(2–12 °C)decomposition was most efficient at 2 °C. These phenomena may be due to lower microbial catabolic requirements at lower temperature.

The use and impacts of bank support on UK small and medium-sized enterprises

This article examines an under-investigated area in relationship banking, i.e. the use of bank advice and support and its impacts on the financial conditions of small and medium-sized enterprises (SMEs). The findings indicate that the characteristics of businesses and entrepreneurs, among other factors, have determinant effects on the use of bank support by SMEs when they make financial decisions. SMEs can alleviate the severity of their financial problems significantly by using bank support more fully, through developing long-term relationships with banks as primary network partners. The article further recognises the value of advice from banks as a substitute for entrepreneurial human capital, especially when bankers use private information to determine the nature and level of financial and non-financial assistance that they are prepared to supply to their clients.

Decomposition in soil and chemical characteristics of pollen

The input to soils made by pollen and its subsequent mineralization has rarely been investigated from a soil microbiological point of view even though the small but significant quantities of C and N in pollen may make an important contribution to nutrient cycling. The relative resistance to decomposition of pollen exines (outer layers) has led to much of the focus of pollen in soil being on its preservation for archaeological and palaeo-ecological purposes. We have examined aspects of the chemical composition and decomposition of pollen from birch (Betula alba) and maize (Zea mays) in soil. The relatively large N contents, small C-to-N ratios and large water-soluble contents of pollen from both species indicated that they would be readily mineralized in soil. When added to soil and incubated at 16 degrees C an amount of C equivalent to 22-26% of the added pollen C was lost as CO2 within 22 days, with the Z. mays pollen decomposing faster. For B. alba pollen, the water-soluble fraction decomposed faster than the whole pollen and the insoluble fraction decomposed more slowly over 22 days. By contrast, there were no significant differences in the decomposition rates of the different fractions from Z. mays pollen. Solid-state C-13 nuclear magnetic resonance (NMR) revealed no gross chemical differences between the pollen of these two species, with strong resonances in the alkyl- and methyl-C region (0-45 p.p.m.) indicative of aliphatic compounds, the O-alkyl-C (60-90 p.p.m.) and the acetal- and ketal-C region (90-110 p.p.m.) indicative of polysaccharides, and the carbonyl-C region indicative of peptides and carboxylic acids. In addition, both pollens gave a small but distinct resonance at 55 p.p.m. attributed to N-alkyl-C. The resonances attributed to polysaccharides were lost completely or substantially reduced after decomposition.

Decomposition in soil and chemical characteristics of pollen

The input to soils made by pollen and its subsequent mineralization has rarely been investigated from a soil microbiological point of view even though the small but significant quantities of C and N in pollen may make an important contribution to nutrient cycling. The relative resistance to decomposition of pollen exines (outer layers) has led to much of the focus of pollen in soil being on its preservation for archaeological and palaeo-ecological purposes. We have examined aspects of the chemical composition and decomposition of pollen from birch (Betula alba) and maize (Zea mays) in soil. The relatively large N contents, small C-to-N ratios and large water-soluble contents of pollen from both species indicated that they would be readily mineralized in soil. When added to soil and incubated at 16 degrees C an amount of C equivalent to 22-26% of the added pollen C was lost as CO2 within 22 days, with the Z. mays pollen decomposing faster. For B. alba pollen, the water-soluble fraction decomposed faster than the whole pollen and the insoluble fraction decomposed more slowly over 22 days. By contrast, there were no significant differences in the decomposition rates of the different fractions from Z. mays pollen. Solid-state C-13 nuclear magnetic resonance (NMR) revealed no gross chemical differences between the pollen of these two species, with strong resonances in the alkyl- and methyl-C region (0-45 p.p.m.) indicative of aliphatic compounds, the O-alkyl-C (60-90 p.p.m.) and the acetal- and ketal-C region (90-110 p.p.m.) indicative of polysaccharides, and the carbonyl-C region indicative of peptides and carboxylic acids. In addition, both pollens gave a small but distinct resonance at 55 p.p.m. attributed to N-alkyl-C. The resonances attributed to polysaccharides were lost completely or substantially reduced after decomposition.

Time-resolved gas-phase kinetic and quantum chemical studies of the reaction of silylene with oxygen

Time-resolved kinetic studies of the reaction of silylene, SiH2, generated by laser flash photolysis of phenylsilane, have been carried out to obtain rate constants for its bimolecular reaction with O-2. The reaction was studied in the gas phase over the pressure range 1-100 Torr in SF6 bath gas, at five temperatures in the range 297-600 K. The second order rate constants at 10 Torr were fitted to the Arrhenius equation: log(k/cm(3) molecule(-1) s(-1)) = (-11.08 +/- 0.04) + (1.57 +/- 0.32 kJ mol(-1))/RT ln10 The decrease in rate constant values with increasing temperature, although systematic is very small. The rate constants showed slight increases in value with pressure at each temperature, but this was scarcely beyond experimental uncertainty. From estimates of Lennard-Jones collision rates, this reaction is occurring at ca. 1 in 20 collisions, almost independent of pressure and temperature. Ab initio calculations at the G3 level backed further by multi-configurational (MC) SCF calculations, augmented by second order perturbation theory (MRMP2), support a mechanism in which the initial adduct, H2SiOO, formed in the triplet state (T), undergoes intersystem crossing to the more stable singlet state (S) prior to further low energy isomerisation processes leading, via a sequence of steps, ultimately to dissociation products of which the lowest energy pair are H2O + SiO. The decomposition of the intermediate cyclo-siladioxirane, via O-O bond fission, plays an important role in the overall process. The bottleneck for the overall process appears to be the T -> S process in H2SiOO. This process has a small spin orbit coupling matrix element, consistent with an estimate of its rate constant of 1 x 10(9) s(-1) obtained with the aid of RRKM theory. This interpretation preserves the idea that, as in its reactions in general, SiH2 initially reacts at the encounter rate with O-2. The low values for the secondary reaction barriers on the potential energy surface account for the lack of an observed pressure dependence. Some comparisons are drawn with the reactions of CH2 + O-2 and SiCl2 + O-2.

A randomised clinical trial to assess the effect of total enteral and total parenteral nutritional support on metabolic, inflammatory and oxidative markers in patients with predicted severe acute pancreatitis (APACHE II >= 66)

Background: Total enteral nutrition (TEN) within 48 h of admission has recently been shown to be safe and efficacious as part of the management of severe acute pancreatitis. Our aim was to ascertain the safety of immediate TEN in these patients and the effect of TEN on systemic inflammation, psychological state, oxidative stress, plasma glutamine levels and endotoxaemia. Methods: Patients admitted with predicted severe acute pancreatitis (APACHE II score 15) were randomised to total enteral (TEN; n = 8) or total parenteral nutrition (TPN; n = 9). Measurements of systemic inflammation (C-reactive protein), fatigue ( visual analogue scale), oxidative stress ( plasma thiobarbituric acid- reactive substances), plasma glutamine and anti-endotoxin IgG and IgM antibody concentrations were made on admission and repeated on days 3 and 7 thereafter. Clinical progress was monitored using APACHE II score. Organ failure and complications were recorded. Results: All patients tolerated the feeding regime well with few nutrition-related complications. Fatigue improved in both groups but more rapidly in the TEN group. Oxidative stress was high on admission and rose by similar amounts in both groups. Plasma glutamine concentrations did not change significantly in either group. In the TPN group, 3 patients developed respiratory failure and 3 developed non-respiratory single organ failure. There were no such complications in the TEN group. Hospital stay was shorter in the TEN group [ 7 (4-14) vs. 10 (7-26) days; p = 0.05] as was time to passing flatus and time to opening bowels [1 (0-2) vs. 2 (1-5) days; p = 0.01]. The cost of TEN was considerably less than of TPN. Conclusion: Immediate institution of nutritional support in the form of TEN is safe in predicted severe acute pancreatitis. It is as safe and as efficacious as TPN and may be beneficial in the clinical course of this disease. Copyright (C) 2003 S. Karger AG, Basel and IAP.

Fruit and vegetables, and the role they have played in determining the EU’s aggregate measurement of support

In its periodic declarations of domestic support to the WTO, the EU has progressively reduced its amber-box declarations in line with its changing system of farm support. Surprisingly, however, in 2007/08 it managed to more than halve its amber box compared with that of the previous year, easily achieving the reduction targets being touted in the Doha Round. This was largely due to a change in the calculations for fresh fruits and vegetables. These had been linked to the entry price system, which was not affected by the 2008 fruit and vegetables reform. Why the EU chose to make this change during the ongoing Doha Round negotiations remains unclear.