Should Pruning be a Pre-Processor of any Linear System?

There are many real-world problems whose mathematical models turn out to be linear systems Ax = b, where A is an m x n matrix. Each equation of the linear system is an information. An information, in a physical problem, such as 4 mangoes, 6 bananas, and 5 oranges cost $10, is mathematically modeled as an equation 4x(sub 1) + 6x(sub 2) + 5x(sub 3) = 10 , where x(sub 1), x(sub 2), x(sub 3) are each cost of one mango, that of one banana, and that of one orange, respectively. All the information put together in a specified context, constitutes the physical problem and need not be all distinct. Some of these could be redundant, which cannot be readily identified by inspection. The resulting mathematical model will thus have equations corresponding to this redundant information and hence are linearly dependent and thus superfluous. Consequently, these equations once identified should be better pruned in the process of solving the system. The benefits are (i) less computation and hence less error and consequently a better quality of solution and (ii) reduced storage requirements. In literature, the pruning concept is not in vogue so far although it is most desirable. It is assumed that at least one information, i.e. one equation is known to be correct and which will be our first equation. In a numerical linear system, the system could be slightly inconsistent or inconsistent of varying degree. If the system is too inconsistent, then we should fall back on to the physical problem (PP), check the correctness of the PP derived from the material universe, modify it, if necessary, and then check the corresponding mathematical model (MM) and correct it. In nature/material universe, inconsistency is completely nonexistent. If the MM becomes inconsistent, it could be due to error introduced by the concerned measuring device and/or due to assumptions made on the PP to obtain an MM which is relatively easily solvable or simply due to human error. No measuring device can usually measure a quantity with an accuracy greater that 0.005% or, equivalently with a relative error less than 0.005%. Hence measurement error is unavoidable in a numerical linear system when the quantities are continuous (or even discrete with extremely large number). Assumptions, though not desirable, are usually made when we find the problem sufficiently difficult to be solved within the available means/tools/resources and hence distort the PP and the corresponding MM. The . error thus introduced in the system could (not always necessarily though) make the system somewhat inconsistent. If the inconsistency (contradiction) is too much then one should definitely not proceed to solve the system in terms of getting a least-squares solution or the minimum-norm least-squares solution. All these solutions will be invariably of no real-world use. If, on the other hand, inconsistency is reasonably low, i.e. the system is near-consistent or, equivalently, has near-linearly-dependent rows, then the foregoing solutions are useful. Pruning in such a near-consistent system should be performed based on the desired accuracy and on the definition of near-linear dependence. In this article, we discuss pruning over various kinds of linear systems and strongly suggest its use as a pre-processor or as a part of an algorithm. Ideally pruning should (i) be a part of the solution process (algorithm) of the system, (ii) reduce both computational error and complexity of the process, and (iii) take into account the numerical zero defined in the context. These are precisely what we achieve through our proposed O(mn2) algorithm presented in Matlab, that uses a subprogram of solving a single linear equation and that has embedded in it the pruning

Polaronic state and nanometer-scale phase separation in colossal magnetoresistive manganites

High resolution topographic images obtained by scanning tunneling microscope in the insulating state of Pr0.68Pb0.32MnO3 single crystals showed regular stripe-like or zigzag patterns on a width scale of 0.4 - 0.5 nm confirming a high temperature polaronic state. Spectroscopic studies revealed inhomogeneous maps of zero-bias conductance with small patches of metallic clusters on length scale of 2 - 3 nm only within a narrow temperature range close to the metal-insulator transition. The results give a direct observation of polarons in the insulating state, phase separation of nanometer-scale metallic clusters in the paramagnetic metallic state, and a homogeneous ferromagnetic state

Effect of Microwave Pretreatment on Extraction Yield and Quality of Catfish Oil in Northern Thailand

The effect of microwave pretreatment of catfish processing waste on oil recovery and quality was investigated. Fish oil was extracted using the enzymatic hydrolysis using alcalase enzyme after the microwave pretreatment. The effect of microwave power and microwave pretreatment times was evaluated. The results revealed that a highest yield of 9.25% when catfish waste was treated at 110 W for 60 s. This condition was found as the most appropriate condition of microwave pretreatment since it decreased the extraction time from 150 min to up to 30 min. Analysis of oil quality indices (e.g. acid value, p-anisidine value, peroxide value) extracted by microwave pretreatment and non-pretreatment indicated that catfish oil from both processes has comparatively similar fatty acids composition. In addition, catfish oil was extracted by microwave pretreatment and enzymatic hydrolysis had lower lipid oxidation compared to several standards

International Nosocomial Infection Control Consortium report, data summary of 50 countries for 2010-2015: Device-associated module

•We report INICC device-associated module data of 50 countries from 2010-2015.•We collected prospective data from 861,284 patients in 703 ICUs for 3,506,562 days.•DA-HAI rates and bacterial resistance were higher in the INICC ICUs than in CDC-NHSN's.•Device utilization ratio in the INICC ICUs was similar to CDC-NHSN's. Background: We report the results of International Nosocomial Infection Control Consortium (INICC) surveillance study from January 2010-December 2015 in 703 intensive care units (ICUs) in Latin America, Europe, Eastern Mediterranean, Southeast Asia, and Western Pacific. Methods: During the 6-year study period, using Centers for Disease Control and Prevention National Healthcare Safety Network (CDC-NHSN) definitions for device-associated health care-associated infection (DA-HAI), we collected prospective data from 861,284 patients hospitalized in INICC hospital ICUs for an aggregate of 3,506,562 days. Results: Although device use in INICC ICUs was similar to that reported from CDC-NHSN ICUs, DA-HAI rates were higher in the INICC ICUs: in the INICC medical-surgical ICUs, the pooled rate of central line-associated bloodstream infection, 4.1 per 1,000 central line-days, was nearly 5-fold higher than the 0.8 per 1,000 central line-days reported from comparable US ICUs, the overall rate of ventilator-associated pneumonia was also higher, 13.1 versus 0.9 per 1,000 ventilator-days, as was the rate of catheter-associated urinary tract infection, 5.07 versus 1.7 per 1,000 catheter-days. From blood cultures samples, frequencies of resistance of Pseudomonas isolates to amikacin (29.87% vs 10%) and to imipenem (44.3% vs 26.1%), and of Klebsiella pneumoniae isolates to ceftazidime (73.2% vs 28.8%) and to imipenem (43.27% vs 12.8%) were also higher in the INICC ICUs compared with CDC-NHSN ICUs. Conclusions: Although DA-HAIs in INICC ICU patients continue to be higher than the rates reported in CDC-NSHN ICUs representing the developed world, we have observed a significant trend toward the reduction of DA-HAI rates in INICC ICUs as shown in each international report. It is INICC's main goal to continue facilitating education, training, and basic and cost-effective tools and resources, such as standardized forms and an online platform, to tackle this problem effectively and systematically