LU Factorization of Non-standard Forms and Direct Multiresolution Solvers

AbstractIn this paper we introduce the multiresolution LU factorization of non-standard forms (NS-forms) and develop fastdirect multiresolutionmethods for solving systems of linear algebraic equations arising in elliptic problems.The NS-form has been shown to provide a sparse representation for a wide class of operators, including those arising in strictly elliptic problems. For example, Green's functions of such operators (which are ordinarily represented by dense matrices, e.g., of sizeNbyN) may be represented by −log ϵ·Ncoefficients, where ϵ is the desired accuracy.The NS-form is not an ordinary[fn9] matrix representation and the usual operations such as multiplication of a vector by the NS-form are different from the standard matrix–vector multiplication. We show that (up to a fixed but arbitrary accuracy) the sparsity of the LU factorization is maintained on any finite number of scales for self-adjoint strictly elliptic operators and their inverses. Moreover, the condition number of matrices for which we compute the usual LU factorization at different scales isO(1). The direct multiresolution solver presents, therefore, an alternative to a multigrid approach and may be interpreted as a multigrid method with a single V-cycle.For self-adjoint strictly elliptic operators the multiresolution LU factorization requires onlyO((−log ϵ)2·N) operations. Combined withO(N) procedures of multiresolution forward and back substitutions, it yields a fast direct multiresolution solver. We also describe direct methods for solving matrix equations and demonstrate how to construct the inverse inO(N) operations (up to a fixed but arbitrary accuracy). We present several numerical examples which illustrate the algorithms developed in the paper. Finally, we outline several directions for generalization of our algorithms. In particular, we note that the multidimensional versions of the multiresolution LU factorization maintain sparsity, unlike the usual LU factorization

Acute-on-chronic liver failure in cirrhosis

The definition of acute-on-chronic liver failure (ACLF) remains contested. In Europe and North America, the term is generally applied according to the European Association for the Study of the Liver-Chronic Liver Failure (EASL-CLIF) Consortium guidelines, which defines this condition as a syndrome that develops in patients with cirrhosis and is characterized by acute decompensation, organ failure and high short-term mortality. One-third of patients who are hospitalized for acute decompensation present with ACLF at admission or develop the syndrome during hospitalization. ACLF frequently occurs in a closed temporal relationship to a precipitating event, such as bacterial infection or acute alcoholic, drug-induced or viral hepatitis. However, no precipitating event can be identified in approximately 40% of patients. The mechanisms of ACLF involve systemic inflammation due to infections, acute liver damage and, in cases without precipitating events, probably intestinal translocation of bacteria or bacterial products. ACLF is graded into three stages (ACLF grades 1–3) on the basis of the number of organ failures, with higher grades associated with increased mortality. Liver and renal failures are the most common organ failures, followed by coagulation, brain, circulatory and respiratory failure. The 28-day mortality rate associated with ACLF is 30%. Depending on the grade, ACLF can be reversed using standard therapy in only 16–51% of patients, leaving a considerable proportion of patients with ACLF that remains steady or progresses. Liver transplantation in selected patients with ACLF grade 2 and ACLF grade 3 increases the 6-month survival from 10% to 80%

Acute-on-Chronic Liver Failure: Definition, Diagnosis, and Clinical Characteristics

Acute-on-chronic liver failure (ACLF) is a recently recognized syndrome in cirrhosis characterized by acute decompensation (AD), organ failure(s), and high short-term mortality. Organ failure(s) is defined by the Chronic Liver Failure-Sequential Organ Failure (CLIF-SOFA) score or by its simplified version Chronic Liver Failure-Organ Failure Assessment (CLIF-OF) score. They include six types of organ failure: liver, renal, coagulation, cerebral, respiratory, and circulatory. One third of patients hospitalized with AD present with ACLF at admission or develop ACLF during hospitalization. Acute-on-chronic liver failure frequently occurs in a closed relationship to a precipitating event. According to the number of organ failures, ACLF is graded into three stages: ACLF-1 = single renal failure or single nonrenal organ failure if associated with renal dysfunction and/or cerebral dysfunction; ACLF-2 = two organ failures; and ACLF-3 = three to six organ failures, with increasing 28-day mortality rate (from 23%–74%). Acute-on-chronic liver failure may develop at any phase during the clinical course of the disease. Patients without prior AD develop a severe form of ACLF

Higher education and unemployment in Europe : an analysis of the academic subject and national effects

This paper examines the impact of an academic degree and field of study on short and long-term unemployment across Europe (EU15). Labour Force Survey (LFS) data on over half a million individuals are utilised for that purpose. The harmonized LFS classification of level of education and field of study overcomes past problems of comparability across Europe. The study analyses (i) the effect of an academic degree at a European level, (ii) the specific effect of 14 academic subjects and (iii) country specific effects. The results indicate that an academic degree is more effective on reducing the likelihood of short-term than long-term unemployment. This general pattern even though it is observed for most of the academic subjects its levels show significant variation across disciplines and countries

Synthetic routes, characterization and photophysical properties of luminescent, surface functionalized nanodiamonds

The functionalization of small diameter (ca. 50 nm) polycarboxylated nanodiamond particles using amide coupling methodologies in both water and acetonitrile solvent has been investigated. In this manner, the surfaces of nanodiamond particles were adorned with different luminescent moieties, including a green fluorescent 1,8-naphthalimide species (Nap-1), and a red emitting ruthenium(II) tris-bipyridine complex (Ru-1), as well as dual functionalization with both luminophores. Comprehensive characterization of the surface functionalized nanodiamonds has been achieved using a combination of dynamic light scattering, nanoparticle tracking analysis, transmission electron microscopy, X-ray photoelectron spectroscopy, zeta potential measurements, microwave plasma atomic emission spectroscopy and time-resolved photophysics. The tendency of the functionalized nanodiamonds to aggregate reflects the degree of surface substitution, yielding small aggregates with typical particle sizes ca. 150 nm. This is likely to be driven by the reduction of the zeta potential, concomitant with the conversion of surface charged carboxylate groups to neutral amide functions. The results show that luminescent nanodiamond materials can be synthesised with tuneable photophysical properties

Ground-Based Ultraviolet-Radiation Measurements during Springtime in the Southern Hemisphere

We report the first measurements obtained by a network of UV-B detectors established through Argentina and Chile, at locations covering latitudes extending from 53°S to 18° S. Evidence that UVB increases are detected at these latitudes during the Austral spring 1993 is presented

Ground-based ultraviolet-radiation measurements during springtime in the Southern hemisphere

We report the first measurements obtained by a network of UV-B detectors established through Argentina and Chile, at locations covering latitudes extending from 53°S to 18° S. Evidence that UVB increases are detected at these latitudes during the Austral spring 1993 is presented. The destruction of the stratospheric ozone layer is generally considered one of the most serious environmental problems. It has been recently published that during October 1998 the ozone hole has been the deepest ever recorded. Reduction of the stratospheric ozone layer was un ambiguously detected about two decades ago in the Antarctic continent. Since then it has been systematically monitored by different means (satellite, balloon soundings and ground station observations. One of the most serious content reduction is the increase of biologically effective ultraviolet doses, particularly the so-called ultraviolet B radiation (280-320 nm) received at the Earth surface, with multiple possible hazards for living species. Despite these consequences, ground stations to check the UV Sun radiation are not very numerous, particularly outside the circumpolar area in the Southern Hemisphere. With the aim of studying whether the ozone depletion over the Antarctic area has extended further, and whether the possibility that UV radiation increase may begin to affect inhabited regions, a network of UVB detectors has been established through Argentina and Chile, at locations covering latitudes extending from 53°S to 18° S. Here we report the first measurements obtained by this network providing evidence that UVB increases are detected at these latitudes during the last Austral spring.Facultad de Ciencias Exacta

Characteristics, Diagnosis and Prognosis of Acute-on-Chronic Liver Failure in Cirrhosis Associated to Hepatitis B

The study was supported by National Natural Science Foundation of China (NSFC), grant number: 30770962, 30971333, 81170421, 81470869 and Chinese High Technology “863” programme, grant number: 2006AA02A411 (Hai.Li); The CLIF Consortium Data Management Center is supported by an unrestricted grant from Grifols