Local non-negative initial data scalar characterization of the Kerr solution

For any vacuum initial data set, we define a local, non-negative scalar quantity which vanishes at every point of the data hypersurface if and only if the data are Kerr initial data. Our scalar quantity only depends on the quantities used to construct the vacuum initial data set which are the Riemannian metric defined on the initial data hypersurface and a symmetric tensor which plays the role of the second fundamental form of the embedded initial data hypersurface. The dependency is algorithmic in the sense that given the initial data one can compute the scalar quantity by algebraic and differential manipulations, being thus suitable for an implementation in a numerical code. The scalar could also be useful in studies of the non-linear stability of the Kerr solution because it serves to measure the deviation of a vacuum initial data set from the Kerr initial data in a local and algorithmic way.

Hot-dip galvanized steel dip-coatedwith ureasilicate hybrid in simulated concrete pore solution: Assessment of coating morphology and corrosion protection efficiency

The barrier effect and the performance of an organic–inorganic hybrid (OIH) sol–gel coating are highlydependent on the coating deposition method as well as processing conditions. In this work, studies onthe influence of experimental parameters using the dip coating method were performed. Factors suchas residence time (Rt), a curing step between each dip step and the number of layers of sol–gel OIHfilms deposited on HDGS to prevent corrosion in highly alkaline environments were studied. These OIHcoatings were obtained using a functionalized siloxane, 3-isociantepropyltriethoxysilane that reactedwith a diamino-functionalized oligopolymer (Jeffamine®D-230). The barrier efficiency of OIH coatings insimulated concrete pore solutions (SCPS) was assessed in the first moments of contact, by electrochemicalimpedance spectroscopy and potentiodynamic methods. The durability and stability of the OIH coatings inSCPS was monitored during eight days by macrocell current density. The morphological characterizationof the surface was performed by scanning electronic microscopy before and after exposure to SCPS.Glow discharge optical emission spectroscopy was used to obtain quantitative composition profiles toinvestigate the thickness of the OIH coatings as a function of the number of layers deposited and theinfluence of the Rt in the coating thickness.

Ureasilicate hybrid coatings for corrosion protection of galvanized steel in chloride-contaminated simulated concrete pore solution

Organic-inorganic hybrid (OIH) sol-gel coatings based on ureasilicates (U(X)) have promising properties for use as eco-friendly coatings on hot dip galvanized steel (HDGS) and may be considered potential substitutes for pre-treatment systems containing Cr(VI). These OIH coatings reduce corrosion activity during the initial stages of contact of the HDGS samples with highly alkaline environments (cementitious media) and allow the mitigation of harmful effects of an initial excessive reaction between cement pastes and the zinc layer. However, the behavior of HDGS coated with U(X) in the presence of chloride ions has never been reported. In this paper, the performance of HDGS coated with five different U(X) coatings was assessed by electrochemical measurements in chloride-contaminated simulated concrete pore solution (SCPS). U(X) sol-gel coatings were produced and deposited on HDGS by a dip coating method. The coatings performance was evaluated by electrochemical impedance spectroscopy, potentiodynamic polarization curves measurements, macrocell current density and polarization resistance in contact with chloride-contaminated SCPS. The SEM/EDS analyses of the coatings before and after the tests were also performed. The results showed that the HDGS samples coated with the OIH coatings exhibited enhanced corrosion resistance to chloride ions when compared to uncoated galvanized steel.

Singularities of the dynamical structure factors of the spin-1/2 XXX chain at finite magnetic field

We study the longitudinal and transverse spin dynamical structure factors of the spin-1/2 XXX chain at finite magnetic field h, focusing in particular on the singularities at excitation energies in the vicinity of the lower thresholds. While the static properties of the model can be studied within a Fermi-liquid like description in terms of pseudoparticles, our derivation of the dynamical properties relies on the introduction of a form of the ‘pseudofermion dynamical theory’ (PDT) of the 1D Hubbard model suitably modified for the spin-only XXX chain and other models with two pseudoparticle Fermi points. Specifically, we derive the exact momentum and spin-density dependences of the exponents ζτ(k) controlling the singularities for both the longitudinal  and transverse (τ = t) dynamical structure factors for the whole momentum range  , in the thermodynamic limit. This requires the numerical solution of the integral equations that define the phase shifts in these exponents expressions. We discuss the relation to neutron scattering and suggest new experiments on spin-chain compounds using a carefully oriented crystal to test our predictions.

Desarrollo de sistemas nano/micro-particulados con aplicación en la fotodegradación selectiva de contaminantes orgánicos en solución. Development of nano / micro-particles systems with application to selective photodegradation of organic pollutants in solution.

IDENTIFICACIÓN DEL PROBLEMA DE ESTUDIO. Las sustancias orgánicas solubles en agua no biodegradables tales como ciertos herbicidas, colorantes industriales y metabolitos de fármacos de uso masivo son una de las principales fuentes de contaminación en aguas subterráneas de zonas agrícolas y en efluentes industriales y domésticos. Las reacciones fotocatalizadas por irradiación UV-visible y sensitizadores orgánicos e inorgánicos son uno de los métodos más económicos y convenientes para la descomposición de contaminantes en subproductos inocuos y/o biodegradables. En muchas aplicaciones es deseable un alto grado de especificidad, efectividad y velocidad de degradación de un dado agente contaminante que se encuentra presente en una mezcla compleja de sustancias orgánicas en solución. En particular son altamente deseables sistemas nano/micro -particulados que formen suspensiones acuosas estables debido a que estas permiten una fácil aplicación y una eficaz acción descontaminante en grandes volúmenes de fluidos. HIPÓTESIS Y PLANTEO DE LOS OBJETIVOS. El objetivo general de este proyecto es desarrollar sistemas nano/micro particulados formados por polímeros de impresión molecular (PIMs) y foto-sensibilizadores (FS). Un PIMs es un polímero especialmente sintetizado para que sea capaz de reconocer específicamente un analito (molécula plantilla) determinado. La actividad de unión específica de los PIMs en conjunto con la capacidad fotocatalizadora de los sensibilizadores pueden ser usadas para lograr la fotodescomposición específica de moléculas “plantilla” (en este caso un dado contaminante) en soluciones conteniendo mezclas complejas de sustancias orgánicas. MATERIALES Y MÉTODOS A UTILIZAR. Se utilizaran técnicas de polimerización en mini-emulsión para sintetizar los sistemas nano/micro PIM-FS para buscar la degradación de ciertos compuestos de interés. Para caracterizar eficiencias, mecanismos y especificidad de foto-degradación en dichos sistemas se utilizan diversas técnicas espectroscópicas (estacionarias y resueltas en el tiempo) y de cromatografía (HPLC y GC). Así mismo, para medir directamente distribuciones de afinidades de unión y eficiencia de foto-degradación se utilizaran técnicas de fluorescencia de molécula/partícula individual. Estas determinaciones permitirán obtener resultados importantes al momento de analizar los factores que afectan la eficiencia de foto-degradación (nano/micro escala), tales como cantidad y ubicación de foto- sensibilizadores en las matrices poliméricas y eficiencia de unión de la plantilla y los productos de degradación al PIM. RESULTADOS ESPERADOS. Los estudios propuestos apuntan a un mejor entendimiento de procesos foto-iniciados en entornos nano/micro-particulados para aplicar dichos conocimientos al diseño de sistemas optimizados para la foto-destrucción selectiva de contaminantes acuosos de relevancia social; tales como herbicidas, residuos industriales, metabolitos de fármacos de uso masivo, etc. IMPORTANCIA DEL PROYECTO. Los sistemas nano/micro-particulados PIM-FS que se propone desarrollar en este proyecto se presentan como candidatos ideales para tratamientos específicos de efluentes industriales y domésticos en los cuales se desea lograr la degradación selectiva de compuestos orgánicos. Los conocimientos adquiridos serán indispensables para construir una plataforma versátil de sistemas foto-catalíticos específicos para la degradación de diversos contaminantes orgánicos de interés social. En lo referente a la formación de recursos humanos, el proyecto propuesto contribuirá en forma directa a la formación de 3 estudiantes de postgrado y 2 estudiantes de grado. En las capacidades institucionales se contribuirá al acondicionamiento del Laboratorio para Microscopía Óptica Avanzada (LMOA) en el Dpto. de Química de la UNRC y al montaje de un sistema de microscopio de fluorescencia que permitirá la aplicación de técnicas avanzadas de espectroscopia de fluorescencia de molecula individual. Water-soluble organic molecules such as certain non-biodegradable herbicides, industrial dyes and metabolites of widespread use drugs are a major source of pollution in groundwater from agricultural areas and in industrial and domestic effluents. Photo-catalytic reactions by UV-visible irradiation and organic sensitizers are one of the most economical and convenient methods for the decomposition of pollutants into harmless byproducts. In many applications it is highly desirable a high degree of specificity, effectiveness and speed of degradation of specific pollutants present in a complex mixture. In particular nano/micro-particles systems that form stable aqueous suspensions are highly desirable because they allow for easy application and effective decontamination of large volumes of fluids. Herein we propose the development of nano/micro particles composed by molecularly imprinted polymers (MIP) and photo-sensitizers (PS). The specific binding of MIP and the photo-catalytic ability of the sensitizers are used to achieve the photo-decomposition of specific "template" molecules in complex mixtures. Mini-emulsion polymerization techniques will be used to synthesize nano/micro MIP-FS systems. Spectroscopy (steady-state and time resolved) and chromatography (GC and HPLC) will be used to characterize efficiency, mechanisms and specificity of photo-degradation in these systems. In addition single molecule/particle fluorescence spectroscopy techniques will be used to directly measure distributions of binding affinities and photo-degradation efficiency in individual particles. The proposed studies point to a more detailed understanding of the factors affecting the photo-degradation efficiency in nano/micro-particles and to apply that knowledge in the design of optimized systems for photo-selective destruction of socially relevant aqueous pollutants.

A determinação dos números de indivíduos mínimos necessários na experimentação genética

The main object of the present paper consists in giving formulas and methods which enable us to determine the minimum number of repetitions or of individuals necessary to garantee some extent the success of an experiment. The theoretical basis of all processes consists essentially in the following. Knowing the frequency of the desired p and of the non desired ovents q we may calculate the frequency of all possi- ble combinations, to be expected in n repetitions, by expanding the binomium (p-+q)n. Determining which of these combinations we want to avoid we calculate their total frequency, selecting the value of the exponent n of the binomium in such a way that this total frequency is equal or smaller than the accepted limit of precision n/pª{ 1/n1 (q/p)n + 1/(n-1)| (q/p)n-1 + 1/ 2!(n-2)| (q/p)n-2 + 1/3(n-3) (q/p)n-3... < Plim - -(1b) There does not exist an absolute limit of precision since its value depends not only upon psychological factors in our judgement, but is at the same sime a function of the number of repetitions For this reasen y have proposed (1,56) two relative values, one equal to 1-5n as the lowest value of probability and the other equal to 1-10n as the highest value of improbability, leaving between them what may be called the "region of doubt However these formulas cannot be applied in our case since this number n is just the unknown quantity. Thus we have to use, instead of the more exact values of these two formulas, the conventional limits of P.lim equal to 0,05 (Precision 5%), equal to 0,01 (Precision 1%, and to 0,001 (Precision P, 1%). The binominal formula as explained above (cf. formula 1, pg. 85), however is of rather limited applicability owing to the excessive calculus necessary, and we have thus to procure approximations as substitutes. We may use, without loss of precision, the following approximations: a) The normal or Gaussean distribution when the expected frequency p has any value between 0,1 and 0,9, and when n is at least superior to ten. b) The Poisson distribution when the expected frequecy p is smaller than 0,1. Tables V to VII show for some special cases that these approximations are very satisfactory. The praticai solution of the following problems, stated in the introduction can now be given: A) What is the minimum number of repititions necessary in order to avoid that any one of a treatments, varieties etc. may be accidentally always the best, on the best and second best, or the first, second, and third best or finally one of the n beat treatments, varieties etc. Using the first term of the binomium, we have the following equation for n: n = log Riim / log (m:) = log Riim / log.m - log a --------------(5) B) What is the minimun number of individuals necessary in 01der that a ceratin type, expected with the frequency p, may appaer at least in one, two, three or a=m+1 individuals. 1) For p between 0,1 and 0,9 and using the Gaussean approximation we have: on - ó. p (1-p) n - a -1.m b= δ. 1-p /p e c = m/p } -------------------(7) n = b + b² + 4 c/ 2 n´ = 1/p n cor = n + n' ---------- (8) We have to use the correction n' when p has a value between 0,25 and 0,75. The greek letters delta represents in the present esse the unilateral limits of the Gaussean distribution for the three conventional limits of precision : 1,64; 2,33; and 3,09 respectively. h we are only interested in having at least one individual, and m becomes equal to zero, the formula reduces to : c= m/p o para a = 1 a = { b + b²}² = b² = δ2 1- p /p }-----------------(9) n = 1/p n (cor) = n + n´ 2) If p is smaller than 0,1 we may use table 1 in order to find the mean m of a Poisson distribution and determine. n = m: p C) Which is the minimun number of individuals necessary for distinguishing two frequencies p1 and p2? 1) When pl and p2 are values between 0,1 and 0,9 we have: n = { δ p1 ( 1-pi) + p2) / p2 (1 - p2) n= 1/p1-p2 }------------ (13) n (cor) We have again to use the unilateral limits of the Gaussean distribution. The correction n' should be used if at least one of the valors pl or p2 has a value between 0,25 and 0,75. A more complicated formula may be used in cases where whe want to increase the precision : n (p1 - p2) δ { p1 (1- p2 ) / n= m δ = δ p1 ( 1 - p1) + p2 ( 1 - p2) c= m / p1 - p2 n = { b2 + 4 4 c }2 }--------- (14) n = 1/ p1 - p2 2) When both pl and p2 are smaller than 0,1 we determine the quocient (pl-r-p2) and procure the corresponding number m2 of a Poisson distribution in table 2. The value n is found by the equation : n = mg /p2 ------------- (15) D) What is the minimun number necessary for distinguishing three or more frequencies, p2 p1 p3. If the frequecies pl p2 p3 are values between 0,1 e 0,9 we have to solve the individual equations and sue the higest value of n thus determined : n 1.2 = {δ p1 (1 - p1) / p1 - p2 }² = Fiim n 1.2 = { δ p1 ( 1 - p1) + p1 ( 1 - p1) }² } -- (16) Delta represents now the bilateral limits of the : Gaussean distrioution : 1,96-2,58-3,29. 2) No table was prepared for the relatively rare cases of a comparison of threes or more frequencies below 0,1 and in such cases extremely high numbers would be required. E) A process is given which serves to solve two problemr of informatory nature : a) if a special type appears in n individuals with a frequency p(obs), what may be the corresponding ideal value of p(esp), or; b) if we study samples of n in diviuals and expect a certain type with a frequency p(esp) what may be the extreme limits of p(obs) in individual farmlies ? I.) If we are dealing with values between 0,1 and 0,9 we may use table 3. To solve the first question we select the respective horizontal line for p(obs) and determine which column corresponds to our value of n and find the respective value of p(esp) by interpolating between columns. In order to solve the second problem we start with the respective column for p(esp) and find the horizontal line for the given value of n either diretly or by approximation and by interpolation. 2) For frequencies smaller than 0,1 we have to use table 4 and transform the fractions p(esp) and p(obs) in numbers of Poisson series by multiplication with n. Tn order to solve the first broblem, we verify in which line the lower Poisson limit is equal to m(obs) and transform the corresponding value of m into frequecy p(esp) by dividing through n. The observed frequency may thus be a chance deviate of any value between 0,0... and the values given by dividing the value of m in the table by n. In the second case we transform first the expectation p(esp) into a value of m and procure in the horizontal line, corresponding to m(esp) the extreme values om m which than must be transformed, by dividing through n into values of p(obs). F) Partial and progressive tests may be recomended in all cases where there is lack of material or where the loss of time is less importent than the cost of large scale experiments since in many cases the minimun number necessary to garantee the results within the limits of precision is rather large. One should not forget that the minimun number really represents at the same time a maximun number, necessary only if one takes into consideration essentially the disfavorable variations, but smaller numbers may frequently already satisfactory results. For instance, by definition, we know that a frequecy of p means that we expect one individual in every total o(f1-p). If there were no chance variations, this number (1- p) will be suficient. and if there were favorable variations a smaller number still may yield one individual of the desired type. r.nus trusting to luck, one may start the experiment with numbers, smaller than the minimun calculated according to the formulas given above, and increase the total untill the desired result is obtained and this may well b ebefore the "minimum number" is reached. Some concrete examples of this partial or progressive procedure are given from our genetical experiments with maize.

Exact Riemann solutions to two selected resonant hyperbolic systems

Magdeburg, Univ., Fak. für Mathematik, Diss., 2013

Sôbre u'a modificação do meio de Monteverde

It is well known that the culture media used in the presumptive diagnosis of suspiciuous colonies from plates inoculated with stools for isolation of enteric organisms do not always correctly indicate the major groups of enterobacteria. In an effort to obtain a medium affording more exact indications, several media (1-9) have been tested. Modifications of some of these media have also been tested with the result that a satisfactory modification of Monteverde's medium was finaly selected. This proved to be most satisfactory, affording, as a result of only one inoculation, a complete series of basic indications. The modification involves changes in the formula, in the method of preparation and in the manner of storage. The formulae are: A. Thymol blue indicator: NaOH 0.1/N .............. 34.4 ml; Thymol blue .............. 1.6 g; Water .................... 65.6 ml. B. Andrade's indicator. C. Urea and sugar solution: Urea ..................... 20 g; Lactose ................... 30 g; Sucrose ................... 30 g; Water .................... 100 ml. The mixture (C.) should be warmed slightly in order to dissolve the ingredients rapidly. Sterilise by filtration (Seitz). Keep stock in refrigeratior. The modification of Monteverde's medium is prepared in two parts. Semi-solid part - Peptone (Difco) 2.0 g; NaCl 0.5 g; Agar 0.5 g; Water 100.0 ml. Boil to dissolve the ingredients. Adjust pH with NaOH to 7.3-7.4. Boil again for precipitation. Filter through cotton. Ad indicators "A" 0.3 ml and "B" 1.0 ml. Sterilise in autoclave 115ºC, 15 minutes in amounts not higher than 200 ml. Just before using, add solution "C" asseptically in amounts of 10 ml to 200 ml of the melted semi-solid medium, maintained at 48-50ºC. Solid part - Peptone (Difco) 1.5 g; Trypticase (BBL) 0.5 g; Agar 2.0 g; Water 100,00 ml. Boil to dissolve the ingredients. Adjust pH with NaOH to 7.3-7.4. Boils again. Filter through cotton. Add indicators "A" 0.3 ml and "B" 1.0 ml; ferrous ammonium sulfate 0.02 g; sodiun thiosulfate 0.02 g. Sterilise in autoclave 115ºC, 15 minutes in amounts not higher than 200 ml. Just before using, add solution "C" asseptically in amounts of 10 ml to 200 ml of the melted solid medium, maintained at 48-50ºC. Final medium - The semi-solid part is dispensed first (tubes about 12 x 120 mm) in 2.5 ml amounts and left to harden at room temperature, in vertical position. The solid part is dispensed over the hardened semi-solid one in amounts from 2.0 ml to 2.5 ml and left to harden in slant position, affording a butt of 12 to 15 mm. The tubes of medium should be subjected to a sterility test in the incubator, overnight. Tubes showing spontaneous gas bubbles (air) should then be discarded. The medium should be stored in the incubator (37ºC), for not more than 2 to 4 days. Storage of the tubes in the ice-box produces the absorption of air which is released as bubbles when the tubes are incubated at 37ºC after inoculation. This fact confirmed the observation of ARCHAMBAULT & McCRADY (10) who worked with liquid media and the aplication of their observation was found to be essential to the proper working conditions of this double-layer medium. Inoculation - The inoculation is made by means of a long straight needle, as is usually done on the triple sugar, but the needel should penetrate only to about half of the height of the semi-solid column. Indol detection - After inoculation, a strip of sterelized filter papaer previously moistened with Ehrlich's reagent, is suspended above the surface of the medium, being held between the cotton plug and the tube. Indications given - In addition to providing a mass of organisms on the slant for serological invetigations, the medium gives the following indications: 1. Acid from lactose and/or sucrose (red, of yellowsh with strains which reduce the indicators). 2. Gas from lactose and/or sucrose (bubbles). 3. H[2]S production, observed on the solid part (black). 4. Motility observed on the semi-solid part (tubidity). 5. Urease production, observed on solid and semi-solid parts (blue). 6. Indol production, observed on the strip of filter paper (red or purplish). Indol production is not observed with indol positive strains which rapidly acidify the surface o the slant, and the use of oxalic acid has proved to give less sensitive reaction (11). Reading of results - In most cases overnight incubation is enough; sometimes the reactions appear within only a few hours of incubation, affording a definitive orientation of the diagnosis. With some cultures it is necessary to observe the medium during 48 hours of incubation. A description showing typical differential reaction follows: Salmonella: Color of the medium unchanged, with blackening of the solid part when H[2]S is positive. The slant tends to alkalinity (greenish of bluish). Gas always absent. Indol negative. Motility positive or negative. Shigella: Color of the medium unchanged at the beginning of incubation period, but acquiring a red color when the strain is late lactose/sucrose positive. Slant tending to alkalinity (greenish or purplish). Indol positive or negative. Motility, gas and H[2]S always negative. Proteus: Color of the medium generally changes entirely to blue or sometimes to green (urease positive delayed), with blackening of solid part when H[2]S is positive. Motility positive of negative. Indol positive. Gas positive or negative. The strains which attack rapidly sucrose may give a yellow-greenish color to the medium. Sometimes the intense blue color of the medium renders difficult the reading of the H[2]S production. Escherichiae and Klebsiellae: Color of the medium red or yellow (acid) with great and rapid production of gas. Motility positive or negative. Indol generally impossible to observe. Paracoli: Those lactose of sucrose positive give the same reaction as Esherichia. Those lactose or sucrose negatives give the same reactions as Salmonellae. Sometimes indol positive and H[2]S negative. Pseudomonas: Color of the medium unchanged. The slant tends to alkalinity. It is impossible to observe motility because there is no growth in the bottom. Alkaligenes: Color of the medium unchanged. The slant tends to alkalinity. The medium does not alter the antigenic properties of the strains and with the mass of organisms on the slant we can make the serologic diagnosis. It is admitted that this medium is somewhat more laborious to prepare than others used for similar purposes. Nevertheless it can give informations generally obtained by two or three other media. Its use represents much saving in time, labor and material, and we suggest it for routine laboratory work in which a quick presumptive preliminary grouping of enteric organisms is needed.

Purification and activity standardisation of a (166m)Ho solution.

As part of a project to use the long-lived (T(1/2)=1200a) (166m)Ho as reference source in its reference ionisation chamber, IRA standardised a commercially acquired solution of this nuclide using the 4pibeta-gamma coincidence and 4pigamma (NaI) methods. The (166m)Ho solution supplied by Isotope Product Laboratories was measured to have about 5% Europium impurities (3% (154)Eu, 0.94% (152)Eu and 0.9% (155)Eu). Holmium had therefore to be separated from europium, and this was carried out by means of ion-exchange chromatography. The holmium fractions were collected without europium contamination: 162h long HPGe gamma measurements indicated no europium impurity (detection limits of 0.01% for (152)Eu and (154)Eu, and 0.03% for (155)Eu). The primary measurement of the purified (166m)Ho solution with the 4pi (PC) beta-gamma coincidence technique was carried out at three gamma energy settings: a window around the 184.4keV peak and gamma thresholds at 121.8 and 637.3keV. The results show very good self-consistency, and the activity concentration of the solution was evaluated to be 45.640+/-0.098kBq/g (0.21% with k=1). The activity concentration of this solution was also measured by integral counting with a well-type 5''x5'' NaI(Tl) detector and efficiencies computed by Monte Carlo simulations using the GEANT code. These measurements were mutually consistent, while the resulting weighted average of the 4pi NaI(Tl) method was found to agree within 0.15% with the result of the 4pibeta-gamma coincidence technique. An ampoule of this solution and the measured value of the concentration were submitted to the BIPM as a contribution to the Système International de Référence.

A Modulated Closed Form solution for Quantitative Susceptibility Mapping - A thorough evaluation and comparison to iterative methods based on edge prior knowledge.

The aim of this study is to perform a thorough comparison of quantitative susceptibility mapping (QSM) techniques and their dependence on the assumptions made. The compared methodologies were: two iterative single orientation methodologies minimizing the l2, l1TV norm of the prior knowledge of the edges of the object, one over-determined multiple orientation method (COSMOS) and anewly proposed modulated closed-form solution (MCF). The performance of these methods was compared using a numerical phantom and in-vivo high resolution (0.65mm isotropic) brain data acquired at 7T using a new coil combination method. For all QSM methods, the relevant regularization and prior-knowledge parameters were systematically changed in order to evaluate the optimal reconstruction in the presence and absence of a ground truth. Additionally, the QSM contrast was compared to conventional gradient recalled echo (GRE) magnitude and R2* maps obtained from the same dataset. The QSM reconstruction results of the single orientation methods show comparable performance. The MCF method has the highest correlation (corrMCF=0.95, r(2)MCF =0.97) with the state of the art method (COSMOS) with additional advantage of extreme fast computation time. The l-curve method gave the visually most satisfactory balance between reduction of streaking artifacts and over-regularization with the latter being overemphasized when the using the COSMOS susceptibility maps as ground-truth. R2* and susceptibility maps, when calculated from the same datasets, although based on distinct features of the data, have a comparable ability to distinguish deep gray matter structures.

The analysis of approximate quickselect and related problems

Approximate Quickselect, a simple modification of the well known Quickselect algorithm for selection, can be used to efficiently find an element with rank k in a given range [i..j], out of n given elements. We study basic cost measures of Approximate Quickselect by computing exact and asymptotic results for the expected number of passes, comparisons and data moves during the execution of this algorithm. The key element appearing in the analysis of Approximate Quickselect is a trivariate recurrence that we solve in full generality. The general solution of the recurrence proves to be very useful, as it allows us to tackle several related problems, besides the analysis that originally motivated us. In particular, we have been able to carry out a precise analysis of the expected number of moves of the ith element when selecting the jth smallest element with standard Quickselect, where we are able to give both exact and asymptotic results. Moreover, we can apply our general results to obtain exact and asymptotic results for several parameters in binary search trees, namely the expected number of common ancestors of the nodes with rank i and j, the expected size of the subtree rooted at the least common ancestor of the nodes with rank i and j, and the expected distance between the nodes of ranks i and j.