text:
Our laboratory is accredited for lead analysis in blood according

Our laboratory is accredited for lead analysis in blood according to the Swedish Board for Accreditation and Conformity Assessment (SWEDAC), and during the period, we also produced good results in the UK National External Quality Assessment Service (Birmingham, UK); our mean accuracy was 96% with coefficient of variation <5%. Other Blood haemoglobin (B-Hb) was analysed by a standard clinical method. U0126 supplier Creatinine (crea) was analysed in

urine samples by a modified kinetic Jaffé method (Roche Diagnostics, Mannheim, Germany). Both B-Hb and crea were analysed by an accredited clinical laboratory with scrupulous quality control. Detection limit for crea was 0.1 mmol/L and total imprecision 1.6%. For B-Hb measurements, the imprecision within the working range of 1–250 g/L was ≤1.0%. Toxicokinetic modelling Non-linear regression

analysis was performed with SPSS version 15.0, according to Eq. (1). The first exponential term describes the fast elimination phase, the second one, the slow elimination of Pb. $$C_\textPb (t) \, = \, C_1 *\texte^( – R_1 *t) + C_2 *\texte^( – 0.000146*t)$$ (1) C Pb(t), lead concentration at a given time (μg/L), t, time (days), C 1, constant (concentration Tariquidar molecular weight of the fast phase at t = 0), C 2, constant (concentration of slow phase at t = 0), R 1, elimination constant of phase 1 (days−1). The follow-up Clostridium perfringens alpha toxin time was not sufficient to calculate the half-time in the slow phase. Nilsson et al. (1991) found it to be 13 years in a long-term study of Pb workers. Therefore, that value was used. The sum of C 1 and C 2 describes the modelled Pb content at the end of

exposure (t = 0). The half-time of Pb in the fast phase has been calculated according to Eq. (2). $$T_\raise0.5ex\hbox\scriptstyle 1 \kern-0.1em/\kern-0.15em \lower0.25ex\hbox\scriptstyle 2 = \raise0.7ex\hbox\ln 2 \!\mathord\left/ \vphantom \ln 2 R_1 \right.\kern-\nulldelimiterspace \!\lower0.7ex\hboxR_1$$ (2)For three cases, there were sufficient data to describe the relationship between B–Hb and P–Pb after end of exposure. Inspection of the curves (Fig. 4) indicated that one component did not give a GW3965 order satisfactory fit. Regression lines were calculated on the left and right sides of the division line (x = 5 μg P–Pb/L), and statistical significance of the difference between the pairs of slopes was examined. After that the threshold between the two components was calculated as the crossing point of the two lines. Genotyping DNA was isolated from whole blood by minicolumn purification (E.Z.N.A DNA extraction kit, Omega Bio-Tek, Norcross, GA, USA) and diluted to a concentration of 5 ng/μL.

The goals of this study were to a) characterize changes in viRNA

The goals of this study were to a) characterize changes in viRNA production

and b) to identify host processes that are differentially regulated by RNAi over the course of infection. DENV2 Jamaica 1409 (JAM1409) was used to infect its natural mosquito vector, Aedes aegypti. Most current RNA deep sequencing studies use duplicate technical replicates. By using triplicate biological click here replicates, deep sequencing and rigorous statistical metrics Selleck GDC 0032 similar to those used for microarrays, we identify products of RNAi pathway activity that are altered in DENV2-infected mosquitoes. The resulting data provide a basis for determining cellular pathways important to virus infection. This analysis is unique in that we focus on only those gene targets which are cleaved by post-transcriptional SRRPs producing sRNAs from 13-30 nts. Therefore, targets may be revealed that would not be identified using traditional microarray approaches. Alterations to gene expression levels that are controlled at the transcriptional level or by mechanisms of the de-capping or de-adenylation mRNA decay pathways will not be considered here [23]. Results Virus feeding Ae. aegypti Rexville D-Puerto Rico were fed a blood meal containing DENV2 Jamaica 1409 and negative controls were fed blood with an equivalent volume of un-infected insect cell culture

homogenate. As with previous studies [24], the mosquitoes had an Pevonedistat infection rate of 50% at 9 dpi and geometric mean titers of 2.5 log10 plaque-forming units (pfu) per mosquito. RNAi machinery components We performed a series of experiments to determine how Ae. aegypti RNAi pathway components respond to a blood

feeding or DENV2 infection. Hemocytes are critical to mosquito immunity, circulate in the hemolymph and harbor DENV2 particles [24, 25]. To give an indication of whether RISC complexes are present in hemolymph before blood feeding, thus supporting the hypothesis that mosquitoes mount an anti-viral response upon infection, soluble fractions were collected using two different methods, separated and probed with anti-Ago2 antibody. High molecular weight complexes containing Ago2 are present in cells from hemolymph/fat body fraction prior to a blood meal and depleted at 1 day post-blood feeding (Figure 1A-1B). Y-27632 2HCl Purified hemolymph from sugar-fed and blood-fed females showed a 143 kDa species, and all samples showed the lower molecular bands that are commonly seen in Ae. aegypti (Figure 1A, D) [3]. Figure 1 Antiviral RNAi components are expressed and active in Ae. aegypti. A) Ago2 associates with a high MW complex in hemolymph and fat body prior to a blood-feeding. HWE strain hemolymph (collected through proboscis) or hemolymph collected with fat body before and 1 day following a blood meal. About 30 μg protein was separated on a 3-10% Blue Native gel and subjected to immunoblot analysis using anti-Ago2 antibody. ‘H’, hemolymph, ‘H/F’, hemolymph with fat body.

In the present case, on the basis of the induction of argC-gca1 p

In the present case, on the basis of the induction of argC-gca1 promoter activity in response to high CO2, and lack of detectable CA activity of Gca1, it can be speculated that Gca1, like mitochondrial γ-CA, might also be involved in binding of CO2/HCO3 – to provide the substrates to different metabolic enzymes, and may not act as carbonic

anhydrase. The amino acid sequence of γ-CAs also showed significant MRT67307 manufacturer similarity with proteins belonging to hexapeptide repeat family composed mainly of acetyl transferases [21–23] and since the biosynthesis of arginine from glutamate proceeds through several N-acetylated intermediates https://www.selleckchem.com/products/LY2603618-IC-83.html [15], it is possible that Gca1 might be involved in the acetylation of some intermediate/s in the arginine biosynthetic pathway. Promoter activity data also indicate that the regulation of argC-gca1 promoter is not

affected by exogenous arginine. The AZD0156 clinical trial lack of repression of the A. brasilense argC-gca1 genes by arginine is consistent with the data reported on the activities of arginine biosynthetic enzymes in various bacteria and cyanobacteria that exhibit a cyclic pathway of ornithine synthesis, where the regulatory mechanism appears to rely mostly on feedback inhibition by arginine of the second enzyme, N-acetylglutamate phosphotransferase [15]. Under nutrient-limiting conditions during stationary phase, arginine is an important metabolite as it can act both as a carbon and nitrogen source. Arginine is also a precursor for the synthesis of polyamines, putrescine and spermidine, which may reduce oxidative damage to proteins and DNA. Since in E. coli, arginine constitutes 11% of the cell’s nitrogen in stationary phase, biosynthesis of this amino acid is thought to be important under sub-optimal conditions [17]. This is the first report showing the role of CO2 in the regulation of argC expression in any bacteria. Although the precise role of argC in arginine biosynthesis

in A. brasilense is not yet established, it is likely that the high metabolic CO2 generated during stationary phase up-regulates arginine biosynthetic genes, including argC-gca1 operon alleviating arginine limitation in the nutrient starved stationary phase cells. The Leukotriene-A4 hydrolase induction of argC-gca1 operon during stationary phase and at high CO2 observed in this study suggests a possible regulatory link between arginine metabolism and another not yet characterized carbon dioxide-dependent process in which Gca1 like protein might have a role to play. Conclusion This study shows lack of CO2 hydration activity in the recombinant γ-CA-like protein from A. brasilense. The unique operonic organization of gca1 and argC, observed in A. brasilense is syntenous with some of its closely related α-proteobacteria, viz. Magnetospirillum, Rhodospirillum, Granulibacter etc. This suggests that the γ-CA-like gene cotranscribed with argC gene in A. brasilense, instead of being involved in CO2 hydration, may have a role in arginine biosynthesis.

In contrast, expression of hsa-miR-337-3p was only detected in th

In contrast, expression of hsa-miR-337-3p was only detected in three gastric cancer cell lines, i.e., SNU-5, HGC27, and SGC-7901, at a low level (Figure 2B). Figure 2 Expression of hsa-miR-134 and hsa-miR-337-3p in the nonmalignant gastric cell line GES and nine gastric

cancer cell lines. A, hsa-miR-134; B, hsa-miR-337-3p. Effect of selleck products mimics and inhibitors of hsa-miR-134 and hsa-miR-337-3p on MKN-45 cell proliferation To determine the effects of hsa-miR-134 and hsa-miR-337-3p on the regulation of gastric cancer growth and invasion, we selected the MKN-45 cell line according to its expression levels of these two miRNAs. The mimic was used to determine whether overexpression Daporinad supplier of these two miRNAs could inhibit tumor cell invasion in vitro, whereas inhibitors were used as controls. (Although they were downregulated in gastric tumor cells, they may have certain levels of expression in tumor cells, and inhibition of their expression may ALK targets also promote tumor cell invasion.) We transfected hsa-miR-134 or hsa-miR-337-3p mimics or inhibitors into MKN-45 cells and performed a cell viability assay. The data revealed that the changed expression of hsa-miR-134 or hsa-miR-337-3p only slightly affected MKN-45 cell proliferation (Figure 3). miRNA mimics and inhibitors used in this study were listed in Additional file 3: Table S2. Figure 3 Time-course effects of miRNAs on the regulation

of gastric cancer MKN-45 cell proliferation. SPTLC1 A, hsa-miR-337-3p mimic-transfected MKN-45 cells. B, hsa-miR-134 inhibitor-transfected MKN-45 cells. Data are expressed as mean ± SD; n=4. Expression of hsa-miR-337-3p affects MKN-45 cell migration and invasion Since these miRNAs were differentially expressed in primary and secondary gastric cancer tissues, we investigated the effects of hsa-miR-134 and hsa-miR-337-3p on

the regulation of gastric cancer cell migration by transfecting hsa-miR-134 and hsa-miR-337-3p mimics or inhibitors into MKN-45 cells and then measured the tumor cell migration capacity. Next, the capacity of the transfected cells was examined using a Transwell-Matrigel invasion assay. Our data showed that transfection with the hsa-miR-134 mimic or inhibitor in MKN-45 cells did not affect the tumor cell invasion capacity (Figure 4A; P>0.05). In contrast, the hsa-miR-337-3p mimic significantly decreased the number of invaded cells (Figure 4B; P<0.05), indicating that hsa-miR-337-3p overexpression may decrease the invasive ability of gastric cancer cells. Figure 4 The effect of hsa-miR-337-3p or hsa-miR-134 mimics or inhibitors on the regulation of gastric cancer cell invasive capacity. A, The migrated cell number of the hsa-miR-134 inhibitor-transfected MNK-45 cells; B: The migrated cell number of the hsa-miR-337-3p mimic-transfected MNK-45 cells. Data are expressed as mean ± SD; n=4; *P<0.05, as compared to the control oligonucleotide (NC) treated group.

Mol Microbiol 2004, 54:994–1010 CrossRefPubMed 37 Knodle

Mol see more Microbiol 2004, 54:994–1010.CrossRefPubMed

37. Knodler LA, Vallance BA, Hensel M, Jackel D, Finlay BB, Steele-Mortimer O: Salmonella type III effectors PipB and PipB2 are targeted to detergent-resistant microdomains on internal host cell membranes. Mol Microbiol 2003, 49:685–704.CrossRefPubMed Authors’ contributions KLE performed cell culture, RNA extraction, and RT-PCR. CYZ performed RT-PCR and data analysis. MZ, HB, and SZ drafted the manuscript. All authors read and approved the final manuscript.”
“Background Mosquitoes transmit many infectious diseases, including malaria, lymphatic filariasis, yellow fever, and dengue. Among these diseases, malaria is by far the most costly in terms of human health. It is endemic to more than Epacadostat chemical structure 100 countries and causes 550 million cases per year, with the highest mortality in children from sub-Saharan Africa. Malaria transmission to humans requires a competent mosquito species, as Plasmodium parasites must undergo a complex developmental cycle and survive the defense responses of their insect host. In Africa, Anopheles gambiae is the major vector of Plasmodium falciparum infection,

learn more which causes the most aggressive form of human malaria. The Plasmodium berghei (murine malaria) model is one of the most widely used experimental systems to study malaria transmission. Gene silencing by systemic injection of double-stranded RNA (dsRNA) has proven to be a very useful tool to carry out functional genomic screens aimed at identifying mosquito genes that mediate anti-parasitic responses. In general, Anopheles gambiae is considered to be susceptible to P. berghei infection, because a high prevalence of infection can be achieved and parasites are only rarely melanized; however, silencing of either thioester-containing protein 1 (TEP1) [1], leucine-rich repeat immune protein 1 (LRIM1) [2], or LRIM2 (also called APL1, [3]), enhances P. berghei infection by 4–5 fold; indicating that, when these effector molecules are present, about 80% of parasites are eliminated by a lytic mechanism[1]. It is well documented that An. gambiae mosquitoes have a different transcriptional response to infection with P. berghei and P. falciparum

[4, 5] and genes such as LRIM1 and C-type lectin 4 (CTL4) [2], which also limit or enhance P. berghei infection, respectively, do not affect P. falciparum infection in An. gambiae [6]. This raises the possibility that some antiplasmodial genes identified using the P. berghei malaria model may not be relevant to human malaria transmission. More than 400 species of anopheline mosquitoes have been identified, but only 40 of them are considered to be important disease vectors [7]. Different anopheline species and even particular strains of mosquitoes vary widely in their susceptibility to infection with a given Plasmodium parasite species. For example, twelve different strains of Anopheles stephensi have been shown to have very different susceptibility to P.

Bisphenol A (BPA; C15H16O2, purity >99 5%) was purchased from the

Bisphenol A (BPA; C15H16O2, purity >99.5%) was purchased from the Chemical Agent Co. Protein Tyrosine Kinase inhibitor (Tianjin, China). A BPA stock solution was find more prepared in an aqueous solution that contained ethanol as a co-solvent. The final concentration of ethanol was less than 1%, and our previous

evaluations had demonstrated no adverse biological effect at this concentration. The stock solution was then diluted to specific test concentrations with the dilution solvent. Adsorption experiments of BPA on TiO2-NPs in vitro: analysis of BPA concentration before and after mixture To analyze if there were changes of BPA concentration after mixing with TiO2-NPs, different concentrations of BPA solutions (5 and 10 mg/L) and combined solutions (BPA 5 mg/L + TiO2 10 mg/L, BPA 5 mg/L + TiO2 50 mg/L, BPA 10 mg/L + TiO2 10 mg/L, and BPA 10 mg/L + TiO2 50 mg/L) were prepared. Then the combined solutions were added to 50-mL plastic centrifuge tubes (in a preliminary experiment, the plastic centrifuge tubes were proven to have no effect on the BPA concentration). Subsequently, the tubes were centrifuged for 10 min Ilomastat datasheet at 14,000 rpm using a high-speed centrifuge (HIMAC CR 22G II, Hitachi, Ltd., Chiyoda-ku, Japan), and the supernatant was collected and centrifuged again at 14,000 rpm. Before injection, the BPA solutions and the combined solutions were passed through 0.22-μm filter membranes, respectively. The samples were analyzed by high-performance

liquid chromatography (Waters 2695 HPLC, Waters Corp., Milford, MA, USA) with a photodiode array detector (Waters 2998 PDA) for BPA levels. The samples were separated on a CAPCELL PAK C18 column (4.6 × 150 mm, 5 μm, Waters Corp.) using a mobile phase of 60% acetonitrile and 40% water at a flow rate of 1.0 mL/min. The Calpain injection volume was 10 μL, and the column temperature was 20°C. The pH values for all of the samples before and after the adsorption experiments were similar and were approximately neutral. Adsorption experiments of BPA on TiO2-NPs in vitro: adsorption kinetics of BPA on TiO2-NPs A solution of BPA 5 mg/L + TiO2

10 mg/L was used to measure adsorption kinetics. The combined treatment solution was shaken at 250 rpm in a reciprocating shaker at 20°C ± 1°C. The kinetic data were collected with an initial BPA concentration of 5 mg/L. Subsequently, 10 mL of the treatment solution was collected and centrifuged twice at 14,000 rpm at 0, 5, 10, 30, 60, 90, 120, and 180 min, and the BPA concentrations were analyzed. Zebrafish maintenance and embryo collection Juvenile zebrafish were purchased from a local aquarium in Tianjin, China. The fish were kept at aquarium conditions of 26°C ± 1°C at a density of ≤1/L using charcoal-filtered tap water. The pH of the maintenance water was within the range of 6.8 to 8.4. Oxygen saturation in the maintenance aquaria was kept above 80%. The fish were maintained with a 14:10-h light/dark cycle and fed dry flake food and frozen midge larvae twice or thrice per day.

Isoform A, called PlyA [17 kDa PlyA] has 138 amino acid residues

Isoform A, called PlyA [17 kDa PlyA] has 138 amino acid residues whereas the 59 kDa isoform B polypeptide (PlyB) consists of 538 amino acids. The two aegerolysin ESTs expressed by M. perniciosa constitute two distinct genes (Figures 7 and 8). MpPRIA1 has an ORF of 417 bp with an intron at position 103 whereas the ORF of MpPRIA2 NSC 683864 is 406

bp long with an intron at position 134 (data not shown). Both have a conserved aegerolysin check details Domain between residues 4 to 136 (MpPRIA1) and 29 to 135 (MpPRIA2) and can be aligned with a hypothetical protein MPER_11381 (gbEEB90416.1) (Figure 7A) and MPER_04618 (gbEEB96271.1 – not shown) of M. perniciosa FA553 and proteins described as aegerolysins of A. aegerita (spO42717.1), P. ostreatus (PlyA – gbAAL57035.1

and ostreolysin – gbAAX21097.1), A. fumigatus Af293 (XP 748379.1), A. fumigatus (gbBAA03951.1) Coccidioides immitis RS (XP_001242288.1) A. niger (XP_001389418.1) (Figure 7A). The evolutionary distance between these putative aegerolysins and above-cited aegerolysin of the Gene Bank database was estimated (Figure 7B). The distances were shorter between MpPRIA1 and MpPRIA2 and aegerolysins of Pleurotus and Agrocybe than between MpPRIAs and Asp-hemolysins and ostreolysins of Aspergillus. Figure 7 Comparison between M. perniciosa aegerolysins and other fungi. A – Alignment for similarity between ORFs of the two probable aegerolysins of M. perniciosa (MpPRIA1 and MpPRIA2) and aegerolysins of M. perniciosa FA553 (gbEEB90416.1), A. aegerita (spO42717.1), P. ostreatus (PriA – gbAAL57035.1 and ostreolysin – gbAAX21097.1), A. fumigatus Selleckchem Pazopanib Af293 (XP 748379.1), A. fumigatus (gbBAA03951.1) C. immitis RS (XP_001242288.1) SB202190 mouse A. niger (XP_001389418.1). Strictly conserved residues are shown in black and similar residues in gray. Consensus symbols: ! is any of IV, \$ is any of LM, % is any of FY, # is any of NDQEBZ. Domain PF06355 (aegerolysin family) is present in MpPRIA1 (residues 4–136, score 8.7e-61) and MpPRIA2 (residues 29–135, score 4.2e-34). B. Phylogenetic analysis of the probable aegerolysin genes

of M. perniciosa with above-cited sequences. Evolutionary history was inferred using the Neighbor-Joining method. The bootstrap consensus tree inferred from 1000 replicates is taken to represent the evolutionary history of the analyzed taxa. Figure 8 Comparison between M. perniciosa pleurotolysin and other fungi. A – Alignment for similarity between ORFS of the one probable pleurotolysin B of M. perniciosa (MpPLYB) and hypothetical proteins of M. perniciosa FA553 (gb EEB89936.1), P. ostreatus (gb BAD66667.1), G. zeae PH-1 (XP_390875.1), A. flavus NRRL3357 (gbEED49642.1), C. globosum CBS 148.51 (XP_001227240.1). Strictly conserved residues are shown in black and similar residues in gray. Consensus symbols are used similarly as in Figure 7. Domain MAC/Perforin (PF01823) is present in MpPLYB (residues 1 to 258, score -35,2). B. Phylogenetic analysis of the probable pleurotolysin B gene of M.

As shown in Figure 3, the performance of a lipid bilayer-based se

As shown in Figure 3, the Rigosertib clinical trial performance of a lipid bilayer-based sensor based on graphene nanostructure is assessed by the conductance characteristic. Before the electrolyte solution has been added, pure water as a water-gated ambipolar GFET was added into the membrane to measure the transfer curve. There is substantial selleck screening library agreement between the proposed model of the lipid bilayer-based biosensor and the experimental result which is extracted from the reference [10]. Figure 3 Comparison between bipolar transfer curve of conductance model (blue line) and experimental extracted data (red line) for neutral membrane. As depicted in Figure 4, by

applying the gate voltage to the biomimetic membrane, it is clearly seen that the conductance of GFET-based graphene shows ambipolar Dactolisib concentration behavior. The doping states of graphene are monitored by the V g,min to measure the smallest conductance of the graphene layer, which is identified from the transfer characteristic curve. In total, the V g,min shift

(at the Dirac point) can be considered as a good indicator for lipid bilayer modulation and measurement. Nevertheless, the magnitude of the voltage shift from both positive and negative lipids is comparable when this shift is measured from the position of the minimum conductivity of bare graphene. As shown in Figure 4, the changes in the membrane’s electric charge can be detected electrically. The conductivity graph is changed when the electric charges are changing for biomimetic membrane-coated graphene biosensor. So, more electrically charged molecules will be adsorbed and the sensor will be capable of attracting more molecules, which leads to a change in the V g,min on the device, and the hole density value can be estimated as decreasing. A negatively exciting membrane demonstrates a very small enhancement in conductivity and a positive change in the Dirac point compared with that of exposed graphene.This is because of an enhancement in the remaining pollution charges caused by the negatively

charged membrane. A detection-charged lipid bilayer can be obtained based on a detectable Anidulafungin (LY303366) Dirac point shift. In light of this fact, the main objective of the current paper is to present a new model for biomimetic membrane-coated graphene biosensors. In this model, the thickness and the type of coated charge as a function of gate voltage is simulated and control parameters are suggested. Subsequently, to obtain a greater insight into the role of both the thickness and the type of lipid bilayer, GFET modeling is employed to identify the relationship between the conductance and the voltage of the liquid gate, where two electrodes of the sensor, as shown in Figure 5, are considered as the source and drain contacts.

Can J Appl Physiol 2004,29(6):691–703 PubMedCrossRef 30 Boisseau

Can J Appl Physiol 2004,29(6):691–703.PubMedCrossRef 30. Boisseau N, Delamarche P: Metabolic and hormonal responses to exercise in children and adolescents. Sports Med 2000,30(6):405–422.PubMedCrossRef 31. Ratel S, Duche P, Hennegrave A, Van Praagh E, Bedu M: Acid–base balance during SU5402 concentration repeated cycling sprints in boys and men. J Appl Physiol 2002,92(2):479–485.PubMed 32. Beneke R, Hutler M, Jung M, Leithauser RM: Modeling the blood lactate kinetics at maximal short-term exercise conditions in children, adolescents, and adults. J Appl Physiol 2005,99(2):499–504.PubMedCrossRef 33. Eriksson BO, Gollnick PD, Saltin B: Muscle

metabolism and enzyme activities after training in boys 11–13 years old. Acta Physiol Scand 1973,87(4):485–497.PubMedCrossRef 34. Falk

B, Dotan R: Child-adult STA-9090 nmr differences in the recovery from high-intensity exercise. Exerc Sport Sci Rev 2006,34(3):107–112.PubMedCrossRef 35. Feriche Fernandez-Castanys B, Delgado-Fernandez M, Alvarez GJ: The effect of sodium citrate intake on selleck chemical anaerobic performance in normoxia and after sudden ascent to a moderate altitude. J Sports Med Phys Fitness 2002,42(2):179–185.PubMed 36. Dotan R, Mitchell C, Cohen R, Klentrou P, Gabriel D, Falk B: Child-adult differences in muscle activation–a review. Pediatr Exerc Sci 2012,24(1):2–21.PubMedCentralPubMed 37. Dotan R, Ohana S, Bediz C, Falk B: Blood lactate disappearance dynamics in boys and men following exercise of similar and dissimilar peak-lactate concentrations. J Pediatr Endocrinol Metab 2003,16(3):419–429.PubMedCrossRef

Competing interests There is no conflict of interest in this study. Authors’ contributions CR conceived of the study and carried out data acquisition, analysis, interpretation, and was the principal writer for the manuscript. EP participated in data acquisition and was a manuscript reviewer. YM participated in data acquisition and Fenbendazole was a manuscript reviewer. GW conceived of the study and was a manuscript reviewer/reviser. MP carried out data interpretation and was a manuscript reviewer/reviser. MG was the medical advisor and was a manuscript reviewer/reviser. PK was the research supervisor for the study and was involved in its conception. PK also assisted in the statistical analysis and interpretation of the results, and was the senior manuscript writer/reviser. All authors read and approved the final manuscript.”
“Background Obesity has reached epidemic proportions in many of the developed countries of the world. This phenomenon is frequently ascribed to the combination of excess food consumption and decreased physical activity [1]. The habits acquired in childhood have a major impact on adult life, and in most cases, determine the state of health during adulthood, particularly with respect to metabolic and endocrine disturbances.

We have used two different kinds of commercial GNRs in order to c

We have used two different kinds of commercial GNRs in order to compare their photothermal transduction efficiency. Both are tuned to the laser source and have their maximum surface plasmon resonance (SPR) at 808 nm (longitudinal band). The first commercial GNRs used are bare GNRs (B-GNRs) A12-10-808-100 Nanorodz (Nanopartz, Salt Lake City, UT, USA). B-GNRs are dispersed in deionized water (DI-H2O) with <0.1% ascorbic acid and <0.1% cetyltrimethylammonium bromide (CTAB) surfactant

capping agent. B-GNRs have an axial diameter of 10 nm and a length of 41 nm. The other commercial GNRs used are PEGylated GNRs (PEG-GNRs) PEG-10-808-50 (Nanoseedz, China). PEG-GNRs are functionalized by thiol-terminated methoxypoly(ethylene glycol) (mPEG-PH) and are also dispersed in DI-H2O. The

dimensions of PEG-GNRs are equal to the dimensions of B-GNRs (axial diameter = 10 nm, length = 41 nm). The laser is connected to the system via buy MLN2238 a multimode optical fiber with a core diameter of 600 μm, a length of 1.5 m, and a power transmission of 90% to 99% (600-μm MM fiber, Changchun New Industries, China). The laser light from GS-4997 the fiber irradiates the samples through a collimation lens (78382, Newport Corporation, Irvine, CA, USA), which is in direct contact with a 4-well plate containing the samples, which have a total volume of 500 μl, and is located on a Teflon support. A selleck inhibitor temperature sensor (F100 Precision Thermometer, Automatic Systems Laboratories, Redhill, UK) is fixed vertically with the aid of a tripod stand and

a burette clamp and remains in contact with the samples during the experiments (Figure 1). Figure 1 Experimental setup: complete view (A), fiber-lens connection details (B), and sample and temperature selleckchem sensor details (C). Thermal parameters In order to determine the parameters that characterize and describe the thermal behavior of our hyperthermia device, it is needed to develop a thermal model, which can be raised from the resolution of an equivalent electric circuit (Figure 2). Figure 2 Electrical equivalent circuit used to obtain the thermal parameters of the optical hyperthermia device. In this circuit, P is the delivered power, T(t) is the sample temperature which is time dependent, and C d (W/K) and C t (J/K) are the thermal conductance and the thermal capacitance of our experimental enclosure, respectively. Solving the circuit, we can formulate the equation that describes the power distribution, obtaining that the delivered power (P) is equal to the sum of the stored power in the capacitor (P s) and the dissipated power in the resistor (P d): (1) In this equation, T ref – m is the reference temperature (the subscript m refers to the thermal model), that is to say, the initial temperature of our sample before the laser irradiation that should match the environment temperature.


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# 5. Data-Array Structure Definitions¶

This section defines the structure type DataArray_t for describing data arrays. This general-purpose structure is used to declare data arrays and scalars throughout the CGNS hierarchy. It is used to describe grid coordinates, flow-solution data, governing flow parameters, boundary-condition data, and other information. For most of these different types of CFD data, we have also established a list of standardized identifiers for entities of type DataArray_t. For example, Density is used for data arrays containing static density.

We address five classes of data with the DataArray_t structure type:

1. dimensional data (e.g., velocity in units of m/s);

2. nondimensional data normalized by dimensional reference quantities;

3. nondimensional data with associated nondimensional reference quantities;

4. nondimensional parameters (e.g., Reynolds number, pressure coefficient);

5. pure constants (e.g., $$π$$, $$e$$).

The first two of these classes often occur within the same test case, where each piece of data is either dimensional itself or normalized by a dimensional quantity. The third data class is typical of a completely nondimensional test case, where all field data and reference quantities are nondimensional. The fourth class, nondimensional parameters, are universal in CFD, although not always consistently defined. The individual components of nondimensional parameters may be data from any of the first three classes.

Each of the five classes of data requires different information to describe dimensional units or normalization associated with the data. These requirements are reflected in the structure definition for DataArray_t.

The remainder of this section is as follows: The structure type DataArray_t is first defined. Then the class identification and data manipulation is discussed for each of the five data classes. Finally, examples of DataArray_t entities are presented.

## 5.1. Definition DataArray_t¶

DataArray_t describes a multi-dimensional data array of given type, dimensionality and size in each dimension. The data may be dimensional, nondimensional or pure constants. Qualifiers are provided to describe dimensional units or normalization information associated with the data.

DataArray_t< DataType, int Dimension, int[Dimension] DimensionValues > :=
{
List( Descriptor_t Descriptor1 ... DescriptorN ) ;                 (o)

Data( DataType, Dimension, DimensionValues ) ;                     (r)

DataClass_t DataClass ;                                            (o)

DimensionalUnits_t DimensionalUnits ;                              (o)

DimensionalExponents_t DimensionalExponents ;                      (o)

DataConversion_t DataConversion ;                                  (o)
} ;

Note

1. Default names for the Descriptor_t list are as shown; users may choose other legitimate names. Legitimate names must be unique within a given instance of DataArray_t and shall not include the names DataClass, DimensionalUnits, DimensionalExponents, or DataConversion.

2. Data() is the only required field for DataArray_t.

DataArray_t requires three structure parameters: Dimension is the dimensionality of the data array; DimensionValues is an array of length Dimension that contains the size of the data arrays in each dimension; and DataType is the data type of the data stored. DataType will usually be real, but other data types are permissible.

The optional entities DataClass, DimensionalUnits, DimensionalExponents and DataConversion provide information on dimensional units and normalization associated with the data. The function of these qualifiers is provided in the next section.

This structure type is formulated to describe an array of scalars. Therefore, for vector quantities (e.g., the position vector or the velocity vector), separate structure entities are required for each component of the vector. For example, the Cartesian coordinates of a 3-D grid are described by three separate DataArray_t entities: one for x, one for y and one for z (see the example for Cartesian Coordinates for a 2-D Structured Grid).

### 5.1.1. Definition DataConversion_t¶

DataConversion_t contains conversion factors for recovering raw dimensional data from given nondimensional data. These conversion factors are typically associated with nondimensional data that is normalized by dimensional reference quantities.

DataConversion_t :=
{
real ConversionScale ;                                             (r)

real ConversionOffset ;                                            (r)
} ;

Given a nondimensional piece of data, Data(nondimensional), the conversion to “raw” dimensional form is:

Data(raw) = Data(nondimensional)*ConversionScale + ConversionOffset

These conversion factors are further described in the section Nondimensional Data Normalized by Dimensional Quantities.

## 5.2. Data Manipulation¶

The optional entities of DataArray_t provide information for manipulating the data, including changing units or normalization. This section describes the rules under which these optional entities operate and the specific manipulations that can be performed on the data.

Within a given instance of DataArray_t, the class of data and all information required for manipulations may be completely and precisely specified by the entities DataClass, DimensionalUnits, DimensionalExponents and DataConversion. DataClass identifies the class of data and governs the manipulations that can be performed. Each of the five data classes is treated separately in the subsequent sections.

The entities DataClass and DimensionalUnits serve special functions in the CGNS hierarchy. If DataClass is absent from a given instance of DataArray_t, then its value is determined from “global” data. This global data may be set at any level of the CGNS hierarchy with the data set at the lowest level taking precedence. DimensionalUnits may be similarly set by global data. The rules for determining the appropriate set of global data to apply is further detailed in the section Precedence Rules and Scope Within the Hierarchy.

This alternate functionality provides a measure of economy in describing dimensional units or normalization within the hierarchy. Examples that make use of global data are available for both grid coordinates and flow solutions. A complete two-zone example case also depicts this alternate functionality.

### 5.2.1. Dimensional Data¶

If DataClass = Dimensional, the data is dimensional. The optional qualifiers DimensionalUnits and DimensionalExponents describe dimensional units associated with the data. These qualifiers are provided to specify the system of dimensional units and the dimensional exponents, respectively. For example, if the data is the x-component of velocity, then DimensionalUnits will state that the pertinent dimensional units are, say, Meter and Second; DimensionalExponents will specify that the pertinent dimensional exponents are LengthExponent = 1 and TimeExponent = -1. Combining the information gives the units m/s. Examples showing the use of these two qualifiers are provided.

If DimensionalUnits is absent, then the appropriate set of dimensional units is obtained from “global” data. The rules for determining this appropriate set of global dimensional units are presented in the section Precedence Rules and Scope Within the Hierarchy.

If DimensionalExponents is absent, then the appropriate dimensional exponents can be determined by convention if the specific instance of DataArray_t corresponds to one of the standardized data-name identifiers. Otherwise, the exponents are unspecified. We strongly recommend inclusion of the DimensionalExponents qualifier whenever the data is dimensional and the instance of DataArray_t is not among the list of standardized identifiers.

### 5.2.2. Nondimensional Data Normalized by Dimensional Quantities¶

If DataClass = NormalizedByDimensional, the data is nondimensional and is normalized by dimensional reference quantities. All optional entities in DataArray_t are used. DataConversion contains factors to convert the nondimensional data to “raw” dimensional data; these factors are ConversionScale and ConversionOffset. The conversion process is as follows:

Data(raw) = Data(nondimensional)*ConversionScale + ConversionOffset

where Data(nondimensional) is the original nondimensional data, and Data(raw) is the converted raw data. This converted raw data is dimensional, and the optional qualifiers DimensionalUnits and DimensionalExponents describe the appropriate dimensional units and exponents. Note that DimensionalUnits and DimensionalExponents also describe the units for ConversionScale and ConversionOffset.

If DataConversion is absent, the equivalent defaults are ConversionScale = 1 and ConversionOffset = 0. If either DimensionalUnits or DimensionalExponents is absent, follow the rules described in the previous section.

Note that functionally there is little difference between these first two data classes (DataClass = Dimensional and NormalizedByDimensional). In the first case the data is dimensional, and in the second, the converted raw data is dimensional. Also, the equivalent defaults for DataConversion produce no changes in the data; hence, it is almost the same as stating the original data is dimensional.

### 5.2.3. Nondimensional Data Normalized by Unknown Dimensional Quantities¶

If DataClass = NormalizedByUnknownDimensional, the data is nondimensional and is normalized by some unspecified dimensional quantities. This type of data is typical of a completely nondimensional test case, where all field data and all reference quantities are nondimensional.

Only the DimensionalExponents qualifier is used in this case, although it is expected that this qualifier will be seldom utilized in practice. For entities of DataArray_t that are not among the list of standardized data-name identifiers, the qualifier could provide useful information by defining the exponents of the dimensional form of the nondimensional data.

Rather than providing qualifiers to describe the normalization of the data, we instead dictate that all data of type NormalizedByUnknownDimensional in a given database be nondimensionalized consistently. This is done by picking one set of mass, length, time and temperature scales and normalizing all appropriate data by these scales. We describe this process in detail in the following. A complete two-zone example case is also available that uses a completely nondimensional database with consistent normalization used throughout.

The practice of nondimensionalization within flow solvers and other application codes is quite popular. The problem with this practice is that to manipulate the data from a given code, one must often know the particulars of the nondimensionalization used. This largely results from what we call inconsistent normalization - more than the minimum required scales are used to normalize data within the code. For example, in the OVERFLOW flow solver, the following nondimensionalization is used:

 $$x' = x / L$$ $$u' = u / (L/T)$$ $$\rho' = \rho / (M/L^{3})$$ $$y' = y / L$$ $$v' = v / (L/T)$$ $$p' = p / (M/(LT^{2}))$$ $$z' = z / L$$ $$w' = w / (L/T)$$ $$\mu' = \mu / (M/(LT))$$

where primed quantities are nondimensional and all others are dimensional.

Consider an existing database where all field data and all reference data is nondimensional and normalized as shown. Assume the database has a single reference state given by,

 $$x'_{ref} = x_{ref} / L$$ $$u'_{ref} = u_{ref} / (L/T)$$ $$\rho'_{ref} = \rho_{ref} / (M/L^{3})$$ $$y'_{ref} = y_{ref} / L$$ $$v'_{ref} = v_{ref} / (L/T)$$ $$p'_{ref} = p_{ref} / (M/(LT^{2}))$$ $$z'_{ref} = z_{ref} / L$$ $$w'_{ref} = w_{ref} / (L/T)$$ $$\mu'_{ref} = \mu_{ref} / (M/(LT))$$

If a user wanted to change the nondimensionalization of grid-point pressures, the procedure is straightforward. Let the desired new normalization be given by $$p''_{ijk} = p_{ijk} / (\rho_{ref} c_{ref}^{2})$$, where all terms on the right-hand-side are dimensional, and as such they are unknown to the database user. However, the desired manipulation is possible using only nondimensional data provided in the database,

$\begin{split}p''_{ijk} &\equiv p_{ijk} / (\rho_{ref} c_{ref}^{2}) \\ &= [p_{ijk} / (M/(LT^{2})] [(M/L^{3}) / \rho_{ref}] [(L/T) / c_{ref}]^{2} \\ &= p'_{ijk} / (\rho'_{ref} (c'_{ref})^{2})\end{split}$

Thus, the desired renormalization is possible using the database’s nondimensional data as if it were actually dimensional. There is, in fact, a high degree of equivalence between dimensional data and consistently normalized nondimensional data. The procedure shown in this example should extend to any desired renormalization, provided the needed reference-state quantities are included in the database.

This example points out two stipulations that we now dictate for data in the class NormalizedByUnknownDimensional,

1. All nondimensional data within a given database that has DataClass = NormalizedByUnknownDimensional shall be consistently normalized.

2. Any nondimensional reference state appearing in a database should be sufficiently populated with reference quantities to allow for renormalization procedures.

The second of these stipulations is somewhat ambiguous, but good practice would suggest that a flow solver, for example, should output to the database enough static and/or stagnation reference quantities to sufficiently define the state.

A two-zone example case is available that shows an example of a well-populated reference state.

With these two stipulations, we contend the following:

• The dimensional scales used to nondimensionalize all data are immaterial, and there is no need to identify these quantities in a CGNS database.

• The dimensional scales need not be reference-state quantities provided in the database. For example, a given database could contain freestream reference state conditions, but all the data is normalized by sonic conditions (which are not provided in the database).

• All renormalization procedures can be carried out treating the data as if it were dimensional with a consistent set of units.

• Any application code that internally uses consistent normalization can use the data provided in a CGNS database without modification or transformation to the code’s internal normalization.

Before ending this section, we note that the OVERFLOW flow solver mentioned above (or any other application code that internally uses inconsistent normalization) could easily read and write data to a nondimensional CGNS database that conforms to the above stipulations. On output, the code could renormalize data so it is consistently normalized. Probably, the easiest method would be to remove the molecular viscosity scale ($$\mu_\infty$$), and only use $$L$$, $$\rho_\infty$$ and $$c_\infty$$ for all normalizations (recall these are dimensional scales). The only change from the above example would be the nondimensionalization of viscosity, which would become $$\mu'' = \mu / (\rho_\infty c_\infty L)$$. The code could then output all field data as,

 $$x'_{ijk} = x_{ijk} / L$$ $$u'_{ijk} = u_{ijk} / c_\infty$$ $$\rho'_{ijk} = \rho_{ijk} / \rho_\infty$$ $$y'_{ijk} = y_{ijk} / L$$ $$v'_{ijk} = v_{ijk} / c_\infty$$ $$p'_{ijk} = p_{ijk} / (\rho_\infty c_\infty^{2})$$ $$z'_{ijk} = z_{ijk} / L$$ $$w'_{ijk} = w_{ijk} / c_\infty$$ $$\mu'_{ijk} = \mu_{ijk} / (\rho_\infty c_\infty^{2} L)$$

and output the freestream reference quantities,

 $$u'_\infty = u_\infty / c_\infty$$ $$\rho'_\infty = \rho_\infty / \rho_\infty = 1$$ $$v'_\infty = v_\infty / c_\infty$$ $$p'_\infty = p_\infty / (\rho_\infty c_\infty^{2}) = 1 / \gamma$$ $$w'_\infty = w_\infty / c_\infty$$ $$\mu''_\infty = \mu_\infty / (\rho_\infty c_\infty L) \sim O (1/Re)$$ $$c'_\infty = c_\infty / c_\infty = 1$$ $$L' = L / L = 1$$

where $$\gamma$$ is the specific heat ratio (assumes a perfect gas) and $$Re$$ is the Reynolds number.

On input, the flow solver should be able to recover its internal normalizations from the data in a nondimensional CGNS database by treating the data as if it were dimensional.

### 5.2.4. Nondimensional Parameters¶

If DataClass = NondimensionalParameter, the data is a nondimensional parameter (or array of nondimensional parameters). Examples include Mach number, Reynolds number and pressure coefficient. These parameters are prevalent in CFD, although their definitions tend to vary between different application codes. A list of standardized data-name identifiers for nondimensional parameters is provided.

We distinguish nondimensional parameters from other data classes by the fact that they are always dimensionless. In a completely nondimensional database, they are distinct in that their normalization is not necessarily consistent with other data.

Typically, the DimensionalUnits, DimensionalExponents and DataConversion qualifiers are not used for nondimensional parameters; although, there are a few situations where they may be used (these are discussed below). Rather than rely on optional qualifiers to describe the normalization, we establish the convention that any nondimensional parameters should be accompanied by their defining scales; this is further discussed in the section on standardized data-name identifiers for nondimensional parameters. An example is Reynolds number defined as $$Re = V L_{R} / \nu$$, where $$V$$, $$L_R$$ and $$\nu$$ are velocity, length, and viscosity scales, respectively. Note that these defining scales may be dimensional or nondimensional data. We establish the data-name identifiers Reynolds, Reynolds_Velocity, Reynolds_Length and Reynolds_ViscosityKinematic for the Reynolds number and its defining scales. Anywhere an instance of DataArray_t is found with the identifier Reynolds, there should also be entities for the defining scales. An example of this use for Reynolds number is available.

In certain situations, it may be more convenient to use the optional qualifiers of DataArray_t to describe the normalization used in nondimensional parameters. These situations must satisfy two requirements: First, the defining scales are dimensional; and second, the nondimensional parameter is a normalization of a single “raw” data quantity and it is clear what this raw data is. Examples that satisfy this second constraint are pressure coefficient, where the raw data is static pressure, and lift coefficient, where the raw data is the lift force. Conversely, Reynolds number is a parameter that violates the second requirement - there are three pieces of raw data rather than one that make up Re. For nondimensional parameters that satisfy these two requirements, the qualifiers DimensionalUnits, DimensionalExponents and DataConversion may be used as in the section Nondimensional Data Normalized by Dimensional Quantities to recover the raw dimensional data.

### 5.2.5. Dimensionless Constants¶

If DataClass = DimensionlessConstant, the data is a constant (or array of constants) with no associated dimensional units. The DimensionalUnits, DimensionalExponents and DataConversion qualifiers are not used.

### 5.2.6. Data-Array Examples¶

This section presents five examples of data-array entities and illustrates the use of optional information for describing dimensional and nondimensional data.

#### 5.2.6.1. Example - One-Dimensional Data Array, Constants¶

A one-dimensional array of integers; the array is the integers from 1 to 10. The data is pure constants.

!  DataType = int
!  Dimension = 1
!  DimensionValues = 10
DataArray_t<int, 1, 10> Data1 =
{{
Data(int, 1, 10) = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10] ;

DataClass_t DataClass = DimensionlessConstant ;
}} ;

The structure parameters for DataArray_t state the data is an one-dimensional integer array of length ten. The value of DataClass indicates the data is unitless constants.

#### 5.2.6.2. Example - Two-Dimensional Data Array, Pressures¶

A two-dimensional array of pressures with size $$11 \times 9$$ given by the array $$P(i,j)$$. The data is dimensional with units of $$N/m^{2}$$ (i.e., $$kg/(m s^{2})$$). Note that Pressure is the data-name identifier for static pressure.

!  DataType = real
!  Dimension = 2
!  DimensionValues = [11,9]
DataArray_t<real, 2, [11,9]> Pressure =
{{
Data(real, 2, [11,9]) = ((P(i,j), i=1,11), j=1,9) ;

DataClass_t DataClass = Dimensional ;

DimensionalUnits_t DimensionalUnits =
{{
MassUnits        = Kilogram ;
LengthUnits      = Meter ;
TimeUnits        = Second ;
TemperatureUnits = TemperatureUnitsNull ;
AngleUnits       = AngleUnitsNull ;
}} ;

DimensionalExponents_t DimensionalExponents =
{{
MassExponent        = +1 ;
LengthExponent      = -1 ;
TimeExponent        = -2 ;
TemperatureExponent =  0 ;
AngleExponent       =  0 ;
}} ;
}} ;

From the data-name identifier conventions, Pressure has a floating-point data type; hence, the appropriate structure parameter for DataArray_t is real.

The value of DataClass indicates that the data is dimensional, and both the dimensional units and dimensional exponents are provided. DimensionalUnits specifies that the units are kilograms, meters, and seconds, and DimensionalExponents specifies the appropriate exponents for pressure. Combining the information gives pressure as $$kg/(m s^{2})$$. DimensionalExponents could have been defaulted, since the dimensional exponents are part of the standardized data-name identifier for Pressure.

Note that FORTRAN multidimensional array indexing is used to store the data; this is reflected in the FORTRAN-like implied do-loops for $$P(i,j)$$.

#### 5.2.6.3. Example - Three-Dimensional Data Array, Nondimensional Static Enthalpy¶

A 3-D array of size $$33 \times 9 \times 17$$ containing nondimensional static enthalpy. The data is normalized by freestream velocity as follows:

$h'_{ijk} = h_{ijk} / q_{ref}^{2}$

where $$h'_{ijk}$$ is nondimensional static enthalpy. The freestream velocity is dimensional with a value of 10 m/s.

!  DataType = real
!  Dimension = 3
!  DimensionValues = [33,9,17]
DataArray_t<real, 3, [33,9,17]> Enthalpy =
{{
Data(real, 3, [33,9,17]) = (((H(i,j,k), i=1,33), j=1,9), k=1,17) ;

DataClass_t DataClass = NormalizedByDimensional ;

DataConversion_t DataConversion =
{{
real ConversionScale  = 100 ;
real ConversionOffset = 0 ;
}} ;

DimensionalUnits_t DimensionalUnits =
{{
MassUnits        = MassUnitsNull ;
LengthUnits      = Meter ;
TimeUnits        = Second ;
TemperatureUnits = TemperatureUnitsNull ;
AngleUnits       = AngleUnitsNull ;
}} ;

DimensionalExponents_t DimensionalExponents =
{{
MassExponent        =  0 ;
LengthExponent      = +2 ;
TimeExponent        = -2 ;
TemperatureExponent =  0 ;
AngleExponent       =  0 ;
}} ;
}} ;

From the list of standardized data-name identifiers, the identifier for static enthalpy is Enthalpy and its data type is real.

The value of DataClass indicates that the data is nondimensional and normalized by a dimensional reference quantity. DataConversion provides the conversion factors for recovering the raw static enthalpy, which has units of $$m^{2}/s^{2}$$ as indicated by DimensionalUnits and DimensionalExponents. Note that DimensionalExponents could have been defaulted using the conventions for the data-name identifier Enthalpy.

#### 5.2.6.4. Example - Three-Dimensional Data Array, Nondimensional Database¶

The previous example for nondimensional enthalpy is repeated for a completely nondimensional database.

!  DataType = real
!  Dimension = 3
!  DimensionValues = [33,9,17]
DataArray_t<real, 3, [33,9,17]> Enthalpy =
{{
Data(real, 3, [33,9,17]) = (((H(i,j,k), i=1,33), j=1,9), k=1,17) ;

DataClass_t DataClass = NormalizedByUnknownDimensional ;
}} ;

The value of DataClass indicates the appropriate class.

#### 5.2.6.5. Example - Data Arrays for Reynolds Number¶

Reynolds number of $$1.554 \times 10^{6}$$ based on a velocity scale of $$10\ m/s$$, a length scale of $$2.3\ m$$ and a kinematic viscosity scale of $$1.48 \times 10^{−5}\ m^{2}/s$$. Assume the database has globally set the dimensional units to kilograms, meters, and seconds, and the global default data class to dimensional (DataClass = Dimensional).

!  DataType = real
!  Dimension = 1
!  DimensionValues = 1
DataArray_t<real, 1, 1> Reynolds =
{{
Data(real, 1, 1) = 1.554e+06 ;

DataClass_t DataClass = NondimensionalParameter ;
}} ;

DataArray_t<real, 1, 1> Reynolds_Velocity =
{{
Data(real, 1, 1) = 10. ;
}} ;

DataArray_t<real, 1, 1> Reynolds_Length =
{{
Data(real, 1, 1) = 2.3 ;
}} ;

DataArray_t<real, 1, 1> Reynolds_ViscosityKinematic =
{{
Data(real, 1, 1) = 1.48e-05 ;
}} ;

Reynolds contains the value of the Reynolds number, and the value of its DataClass qualifier designates it as a nondimensional parameter. By conventions for standardized data-name identifiers for nondimensional parameters, the defining scales are contained in the associated entities Reynolds_Velocity, Reynolds_Length, and Reynolds_ViscosityKinematic. Since each of these entities contain no qualifiers, global information is used to decipher that they are all dimensional with mass, length, and time units of kilograms, meters, and seconds. The structure parameters for each DataArray_t entity state that they contain a real scalar.

If a user wanted to convey the dimensional units of the defining scales using optional qualifiers of DataArray_t, then the last three entities in this example would have a form similar to that in the Two-Dimensional Data Array example.

format: plain


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#### Archived

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# Virtual functions and linked list destructors... HELP, I'M GOING CRAZY!!

This topic is 5991 days old which is more than the 365 day threshold we allow for new replies. Please post a new topic.

## Recommended Posts

Okay, this about to drive me right up the wall trying to find a solution, but here it goes: The Problem: I have a cyclic multiple-level linked list and everything's fine until I got to delete it. Everything is derrived from public CObject which is derrived from the base class of CNode. So when I delete the head of an inherited class, ~CNode is called. CNode then does this:
~CNode()
{
Detach();

while (pChild)
{
sprintf(buffer, "Report from %d: Deleting Child %d", id, pChild->id);
MessageBox(NULL, buffer, "Info", MB_OK | MB_ICONINFORMATION);
delete pChild;
}

sprintf(buffer, "Report from %d: Checkpoint", id);
MessageBox(NULL, buffer, "Info", MB_OK | MB_ICONINFORMATION);
}

So, say I have a class derrived from CObject with another class also derrived from CObject attached to it. When the program goes to delete the head of the linked list it detaches it, goes to the child deconstructor, detaches the child, deletes the child, but doesn't return to delete itself causing a debug assertion failure!! The reason (for God knows why) is because CObject has a virtual function inside of it that it is essential; however, it is the virtual function in CObject that causes the problem. The function is declared like: virtual void Main(void) { } However, for some reason it screws up the CNode deconstruction process so that the parent never deletes itself. WHY? And how can I solve this problem before I go absolutely insane and pull all of my hair out? PLEASE PLEASE PLEASE HELP! PLEASE! Thankyou, -Jesse Edited by - Aphelion on February 20, 2002 10:13:17 PM Edited by - Aphelion on February 20, 2002 10:13:30 PM

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Does calling Detach() go back to the parent and tell it to set pChild to NULL? If not, you''ll free a child twice. I''m a bit confused at what you mean when you say, "but doesn''t return to delete itself causing a debug assertion failure" . You don''t get assertion failures by not doing something - you get them from doing something wrong - often a double free. Knowing exactly what Detach does might help here.

[ MSVC Fixes | STL | SDL | Game AI | Sockets | C++ Faq Lite | Boost ]

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I would guess, too, that you get in an endless loop becaus of pChild. Where do you change pChild during the deletion progress. Can''t see it anywhere.

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Yes, the Detach() process does set the parent to null. So when detach is called on the child, pChild is thus set to null. Judging by the message boxes I set up for debugging, this is what happens from what I can best figure:
delete parent:
parent->Detach();
parent has child, so delete child
child->Detach(); parent->pChild = NULL;
child checks in just before deleting at the "checkpoint"
Instant debug assertion failure.
From what I can figure, the debug assertion failure is caused because the parent never calls back that it is at the "checkpoint" just before being deleted. So the delete parent function is never finished, but interrupted at the very end by the Debug Assertion Failure. However, if I remove the virtual function from CObject (derived from CNode), the class that both the parent and child are derived from, the code works exactly as expected, with the parent finishing its loop and calling in at the "checkpoint". WHY?!??
I really need some help, this step is, needless to say, crucial to my engine! Please help!
Thank you,
-Jesse

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Ah, finally, I found the solution. Apparently, the CNode deconstructor has to be a virtual function for it to work correctly... I''ve heard of that before, but I''d just forgotten... Well, at least the problem is fixed. Now I can get back to the fun, fun scene management! Oh joy! (sarcasm)
Thanks,
-Jesse

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# How to make a single user copy of a group of nodes in matrial on python in Blender?

I have a material on one object and I need to copy it to another object.

I do ... material.copy () but the group node in the material copy does not become a single-user copy. How can this problem be solved?

original_group = bpy.context.objects['Object'].material_slots['Material'].material.node_tree.nodes['Baking_node'].node_tree

• Use bpy.context.object for the context object, bpy.context.scene.objects.get("Object") for an object named "Object" in the context scene. There is no context.objects. – batFINGER Mar 2 at 4:39


text:
# Are commands defined by \newcommand[.][.]{.} robust?

This question is from the comments at the foot of Abbreviations for AM, PM (small caps) for use within \textbf. Readers will get the remaining gist from there.

With

\newcommand\cmd[2][0]{\def\y{#1}}
\edef\x{\cmd{1}}

I get

{\edef}

\cmd ->\@protected@testopt \cmd \\cmd {0}

\@protected@testopt #1->\ifx \protect \@typeset@protect \expandafter \@testopt
\else \@x@protect #1\fi
#1<-\cmd
{\ifx}
{true}
{\expandafter}
{\else}

\@testopt #1#2->\kernel@ifnextchar [{#1}{#1[{#2}]}
#1<-\\cmd
#2<-0

\kernel@ifnextchar #1#2#3->\let \reserved@d =#1\def \reserved@a {#2}\def \reser
ved@b {#3}\futurelet \@let@token \@ifnch
#1<-[
#2<-\\cmd
#3<-\\cmd [{0}]

\reserved@a #11#2{->\expandafter \def \expandafter \\cmd \reserved@b #11{
! Argument of \reserved@a has an extra }.
<inserted text>
\par
}
l.3103 \edef\x{\cmd{1}}

? x

• I thought it is not and that is why there is \DeclareRobustCommand which has the same parameter syntax as \newcommand. – bodo Jun 19 '12 at 7:35

Using

\newcommand{\foo}[...][...]

creates a macro \foo which has definition

\@protected@testopt \foo \\foo {...}

Inside a LaTeX 'protected expansion' command (\protected@edef, \protected@xdef, \protected@write), the definition of \@protected@testopt is altered such that no further expansion takes place, so that

\protected@edef\test{\foo}
\show\test

gives

> \test=macro:
->\protect \foo .

\DeclareRobustCommand works slightly differently, as

\DeclareRobustCommand{\foo}[...][...]

gives a definition

> \foo=macro:
->\protect \foo  .

where there is a space in the name of that internal macro: it's called '\foo '. Doing a 'protected expansion' here gives

> \test=macro:
->\protect \foo  .

i.e. the 'name with space' is retained. As this method adds \protect 'earlier' than the mechanism used by \newcommand, this is more robust at the cost of an additional cname.

Neither of these mechanisms will prevent expansion inside a plain \edef, \xdef or \write. For that, you need the e-TeX protected mechanism, which is wrapped up in a \newcommand-like way by \newrobustcmd from the etoolbox package. There, doing

\newrobustcmd{\foo}[...][...]

gives a definition

> \foo=\protected macro:
->\@testopt \\foo {...}.

This will never expand in an expansion context, as the engine is doing the protection.

The concepts of "fragility" and "robustness" are proper of LaTeX; a robust command is one that survives being in the replacement text for \protected@edef or \protected@write. It has nothing to do with surviving \edef or \write.

For example, after

\DeclareRobustCommand{\foo}[1][bar]{...}

something like

\edef\baz{\foo[x]}

will fail with

! Argument of \reserved@a has an extra }

Conversely, \protected@edef\baz{\foo[x]} will assign \baz the meaning

\protect \foo  [x]

(notice the two spaces after \foo). If we do instead

\newcommand\foo[1][bar]{...}
\protected@edef\baz{\foo[x]}

the meaning of \baz will be

\protect \foo [x]

Of course, \protected gives a robustness of a superior type, because a command defined with \protected\def will even survive \edef. But it's another story.

How does it work? When \newcommand\foo[1][bar]{...} is executed, LaTeX actually does

\def\foo{\@protected@testopt \foo \\foo {bar}}

and

\expandafter\def\csname\string\foo\endcsname[#1]{...}

which is very similar to the LaTeX2.09 way

\def\foo{\@testopt\@foo{bar}}
\def\@foo[#1]{...}

but has \@protected@testopt which is, essentially "if \protect equals \relax, then execute \@testopt\\foo, otherwise output \protect\foo". There's a small complication for taking care of "control symbols" such as \?, but this is pretty much the truth.

• So there is a difference in robustness between \newcommand with and without an optional argument? Is the one with the optional argument made robust in order to protect the default value? – bodo Jun 19 '12 at 8:33
• @canaaerus Protecting commands having an optional argument is necessary (actually something could be done, as proved in xparse, but it's quite a delicate feature). Protecting "normal" commands is usually undesirable: otherwise \write operations would never record current information such as the page or section number. – egreg Jun 19 '12 at 8:37
• @AhmedMusa I'm sure that if \protected had been available all the \protect thing would never have existed. But under the current state of affairs, commands having an optional argument defined with \newcommand are robust as far as LaTeX is concerned. – egreg Jun 19 '12 at 19:35
• It's pointless arguing with egreg, who has been teaching (or using) TeX since 1987, but for some of us who are new comers, we understand robustness the eTeX (and hence etoolbox's) way. Times change. I personally will prefer that robustness is an intrinsic property that doesn't depend on the current state or value of \protect or any command. Commands whose values are to be recorded in any file at runtime should, in this case, not be robustified in any way. – Ahmed Musa Jun 19 '12 at 19:39
• My view is that if eTeX was available in the 1980s, Leslie Lamport would probably have preferred \protected to \@protected@testopt. egreg has responded to this above. – Ahmed Musa Jun 19 '12 at 19:40

Such macros use the protect mechanism of LaTeX and will only work in a \protected@edef and other LaTeX macros, e.g. the aux-file writing macros, which set \protect accordantly. They are not meant to work in a general expanding context like \edef or a normal \write.

If you need to define a robust LaTeX macro with optional argument use the core macro \DeclareRobustCommand or \newrobustcmd from the etoolbox package.

• The second paragraph is not correct. \DeclareRobustCommand creates commands which will not expand inside \protected@edef, but will still go wrong inside \edef. For that, you need the e-TeX mechanism. – Joseph Wright Jun 19 '12 at 7:51


text:
टिप्पणी

# Pegasos Quantum Support Vector Classifier¶

There’s another SVM based algorithm that benefits from the quantum kernel method. Here, we introduce an implementation of a another classification algorithm, which is an alternative version to the QSVC available in Qiskit Machine Learning and shown in the “Quantum Kernel Machine Learning” tutorial. This classification algorithm implements the Pegasos algorithm from the paper “Pegasos: Primal Estimated sub-GrAdient SOlver for SVM” by Shalev-Shwartz et al., see: https://home.ttic.edu/~nati/Publications/PegasosMPB.pdf.

This algorithm is an alternative to the dual optimization from the scikit-learn package, benefits from the kernel trick, and yields a training complexity that is independent of the size of the training set. Thus, the PegasosQSVC is expected to train faster than QSVC for sufficiently large training sets.

The algorithm can be used as direct replacement of QSVC with some hyper-parameterization.

Let’s generate some data:

[1]:

from sklearn.datasets import make_blobs

# example dataset
features, labels = make_blobs(n_samples=20, n_features=2, centers=2, random_state=3, shuffle=True)

We pre-process the data to ensure compatibility with the rotation encoding and split it into the training and test datasets.

[2]:

import numpy as np

from sklearn.model_selection import train_test_split
from sklearn.preprocessing import MinMaxScaler

features = MinMaxScaler(feature_range=(0, np.pi)).fit_transform(features)

train_features, test_features, train_labels, test_labels = train_test_split(
features, labels, train_size=15, shuffle=False
)

We have two features in the dataset, so we set a number of qubits to the number of features in the dataset.

Then we set $$\tau$$ to the number of steps performed during the training procedure. Please note that, there is no early stopping criterion in the algorithm. The algorithm iterates over all $$\tau$$ steps.

And the last one is the hyperparameter $$C$$. This is a positive regularization parameter. The strength of the regularization is inversely proportional to $$C$$. Smaller $$C$$ induce smaller weights which generally helps preventing overfitting. However, due to the nature of this algorithm, some of the computation steps become trivial for larger $$C$$. Thus, larger $$C$$ improve the performance of the algorithm drastically. If the data is linearly separable in feature space, $$C$$ should be chosen to be large. If the separation is not perfect, $$C$$ should be chosen smaller to prevent overfitting.

[3]:

# number of qubits is equal to the number of features
num_qubits = 2

# number of steps performed during the training procedure
tau = 100

# regularization parameter
C = 1000

The algorithm will run using:

• The default fidelity instantiated in FidelityQuantumKernel

• A quantum kernel created from ZFeatureMap

[4]:

from qiskit import BasicAer
from qiskit.circuit.library import ZFeatureMap
from qiskit.utils import algorithm_globals

from qiskit_machine_learning.kernels import FidelityQuantumKernel

algorithm_globals.random_seed = 12345

feature_map = ZFeatureMap(feature_dimension=num_qubits, reps=1)

qkernel = FidelityQuantumKernel(feature_map=feature_map)

The implementation PegasosQSVC is compatible with the scikit-learn interfaces and has a pretty standard way of training a model. In the constructor we pass parameters of the algorithm, in this case there are a regularization hyper-parameter $$C$$ and a number of steps.

Then we pass training features and labels to the fit method, which trains a models and returns a fitted classifier.

Afterwards, we score our model using test features and labels.

[5]:

from qiskit_machine_learning.algorithms import PegasosQSVC

pegasos_qsvc = PegasosQSVC(quantum_kernel=qkernel, C=C, num_steps=tau)

# training
pegasos_qsvc.fit(train_features, train_labels)

# testing
pegasos_score = pegasos_qsvc.score(test_features, test_labels)
print(f"PegasosQSVC classification test score: {pegasos_score}")

PegasosQSVC classification test score: 1.0

For visualization purposes we create a mesh grid of a predefined step that spans our minimum and maximum values we applied in MinMaxScaler. We also add some margin to the grid for better representation of the training and test samples.

[6]:

grid_step = 0.2
margin = 0.2
grid_x, grid_y = np.meshgrid(
np.arange(-margin, np.pi + margin, grid_step), np.arange(-margin, np.pi + margin, grid_step)
)

We convert the grid to the shape compatible with the model, the shape should be (n_samples, n_features). Then for each grid point we predict a label. In our case predicted labels will be used for coloring the grid.

[7]:

meshgrid_features = np.column_stack((grid_x.ravel(), grid_y.ravel()))
meshgrid_colors = pegasos_qsvc.predict(meshgrid_features)

Finally, we plot our grid according to the labels/colors we obtained from the model. We also plot training and test samples.

[8]:

import matplotlib.pyplot as plt

plt.figure(figsize=(5, 5))
meshgrid_colors = meshgrid_colors.reshape(grid_x.shape)

plt.scatter(
train_features[:, 0][train_labels == 0],
train_features[:, 1][train_labels == 0],
marker="s",
facecolors="w",
edgecolors="r",
label="A train",
)
plt.scatter(
train_features[:, 0][train_labels == 1],
train_features[:, 1][train_labels == 1],
marker="o",
facecolors="w",
edgecolors="b",
label="B train",
)

plt.scatter(
test_features[:, 0][test_labels == 0],
test_features[:, 1][test_labels == 0],
marker="s",
facecolors="r",
edgecolors="r",
label="A test",
)
plt.scatter(
test_features[:, 0][test_labels == 1],
test_features[:, 1][test_labels == 1],
marker="o",
facecolors="b",
edgecolors="b",
label="B test",
)

plt.title("Pegasos Classification")
plt.show()

[9]:

import qiskit.tools.jupyter

%qiskit_version_table

### Version Information

Qiskit SoftwareVersion
qiskit-terra0.22.0
qiskit-aer0.11.0
qiskit-ignis0.7.0
qiskit0.33.0
qiskit-machine-learning0.5.0
System information
Python version3.7.9
Python compilerMSC v.1916 64 bit (AMD64)
Python builddefault, Aug 31 2020 17:10:11
OSWindows
CPUs4
Memory (Gb)31.837730407714844
Thu Oct 13 10:42:49 2022 GMT Daylight Time


text:
Tagged , ,

Tagged , ,

Tagged ,

## “Economics department abandoned econometrics because it was rejecting its models”!

Paul Krugman writes:

OK, several correspondents have weighed in on the story I’d heard about the economics department that abandoned econometrics because it was rejecting its models. It wasn’t quite as alleged, but close enough.

The department in question was the University of Minnesota. For those readers new to this discussion, “freshwater-saltwater” was a distinction originally due to Bob Hall, who noted that the economics departments that had rejected Keynes and anything reminiscent of Keynes were inland schools like Minnesota, Chicago, and Rochester, whereas the places that retained a belief in the usefulness of monetary and fiscal policy were places like MIT, Princeton, and Berkeley.

So the story as I now have it was that there was harsh conflict between the macroeconomic theorists at UMinn, especially Prescott, and the econometricians who had the nasty habit of showing that those models didn’t work. And for at least some period econometrics was dropped as a required course for the Ph.D. — I don’t know whether it has been restored.

Tagged , ,

## US Debt Clock

A fancy (and slightly tacky) “real-time” US Debt Clock from which you will probably not be able to draw any conclusions…

via infosthetics

Tagged ,

## Why is the Hodrick-Prescott filter often inappropriate?

The Hodrick-Prescott (HP) filter is the optimal estimator of the trend component in a smooth trend model with signal-to-noise ratio parameter fixed at 1/1600. It gives the detrended observations, $X_{t}$,  for large samples and t not near the beginning or end of the series

$\displaystyle X_{t}= \left[ \frac{(1-L)^{2}(1-L^{-1})^{2}}{\bar{q}_{\zeta}+ (1-L)^{2}(1-L^{-1})^{2}}\right] Y_{t}$

where $\bar{q}_{\zeta}= \sigma_{\zeta}^{2} / \sigma_{\epsilon}^{2}$.

Bear in mind that if the  smooth trend model was believed to be the true model there would be no reason to apply the HP filter. The filtered data of a smooth trend model contain nothing more than white noise. The belief here is clearly different.

We can easily show that the gain from the detrending filter is given by:

$G(\lambda) = \frac{4(1-cos \lambda)^{2}}{\bar{q}_{\zeta}+4(1-cos \lambda)^{2}} = \frac{16sin^{4}( \lambda /2)}{\bar{q}_{\zeta}+16sin^{4}( \lambda /2)}$

Note that the smaller the ${\bar{q}_{\zeta}}$ the more the filter concentrates on removing low frequencies.

Gain for HP filter

## Phillips Curve with UC 1 – Australian Cycles

The Phillips curve is not dead!


text:
Deals Of The Week - hours only!Up to 80% off on all courses and bundles.-Close
Final Quiz
2. Question 1

Instruction

Question 1 is all about customer acquisition.

Exercise

Create a report that compares the number of acquired customers in weekly registration cohorts across selected channels. Remember, this is during the first quarter of 2017. Show the following columns:

• registration_week
• direct_count (the number of customers from the 'Direct' channel in the given cohort).
• social_count (the number of customers from the 'Social' channel in the given cohort).
• referral_count (the number of customers from the 'Referral' channel in the given cohort).

Order the results by week.

Stuck? Here's a hint!

Join the customers and channels tables to get the channel names.

Use the COUNT(CASE WHEN ...) construction to count the customers from each channel.

Use the DATE_PART() function to extract the week of registration.


text:
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# Dick takes twice as long as Jane to run any given distance.

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Dick takes twice as long as Jane to run any given distance. [#permalink]  08 Oct 2019, 04:49
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Question Stats:

40% (01:21) correct 60% (01:44) wrong based on 5 sessions
Dick takes twice as long as Jane to run any given distance.
Starting at the same moment, Dick and Jane run towards each other from opposite ends of the schoolyard, a total distance of x, at their respective constant rates until they meet

 Quantity A Quantity B The fraction of the total distance x that is covered by Jane $${\frac{2}{3}}x$$

A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.
[Reveal] Spoiler: OA

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Last edited by Carcass on 08 Oct 2019, 15:08, edited 1 time in total.
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Re: Dick takes twice as long as Jane to run any given distance. [#permalink]  08 Oct 2019, 10:56
any solutions for this?
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Re: Dick takes twice as long as Jane to run any given distance. [#permalink]  08 Oct 2019, 12:02
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Expert's post
pranab01 wrote:
Dick takes twice as long as Jane to run any given distance. Starting at the same moment, Dick and Jane run towards each other from opposite ends of the schoolyard, a total distance of x, at their respective constant rates until they meet

 Quantity A Quantity B The fraction of the total distance x that is covered by Jane $${\frac{2}{3}}x$$

GIVEN: Dick takes twice as long as Jane to run any given distance.
In other words, Jane travels TWICE as fast as Dick does.
So, for every 1 meter that Dick travels, Jane travels 2 meters.

GIVEN: Starting at the same moment, Dick and Jane run towards each other from opposite ends of the schoolyard, a total distance of x, at their respective constant rates until they meet
This is a CLOSING GAP question.
So, for every 1 meter that Dick travels towards Jane, Jane travels 2 meters towards Dick.
In other words, every time the gap closes by 3 units of length, Jane travels 2 units and Dick travels 1 unit.

Since the initial gap is x, we know that the total COMBINED distances traveled by Dick and Jane is x.
This means Dick traveled 1/3 of x, and Jane traveled 2/3 of x

We get:
QUANTITY A: 2/3 of x
QUANTITY B: (2/3)x

Cheers,
Brent
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Re: Dick takes twice as long as Jane to run any given distance. [#permalink]  09 Oct 2019, 09:45
Dick traveled 1/3 of x, and Jane traveled 2/3 of x (As Jane is twice faster then Dick)

QUANTITY A: 2/3 of x
QUANTITY B: (2/3)x

So, C
Re: Dick takes twice as long as Jane to run any given distance.   [#permalink] 09 Oct 2019, 09:45
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# Dick takes twice as long as Jane to run any given distance.

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text:
F. Lost in Transliteration
time limit per test
3 seconds
memory limit per test
256 megabytes
input
standard input
output
standard output

There are some ambiguities when one writes Berland names with the letters of the Latin alphabet.

For example, the Berland sound u can be written in the Latin alphabet as "u", and can be written as "oo". For this reason, two words "ulyana" and "oolyana" denote the same name.

The second ambiguity is about the Berland sound h: one can use both "h" and "kh" to write it. For example, the words "mihail" and "mikhail" denote the same name.

There are n users registered on the Polycarp's website. Each of them indicated a name represented by the Latin letters. How many distinct names are there among them, if two ambiguities described above are taken into account?

Formally, we assume that two words denote the same name, if using the replacements "u "oo" and "h "kh", you can make the words equal. One can make replacements in both directions, in any of the two words an arbitrary number of times. A letter that resulted from the previous replacement can participate in the next replacements.

For example, the following pairs of words denote the same name:

• "koouper" and "kuooper". Making the replacements described above, you can make both words to be equal: "koouper" "kuuper" and "kuooper" "kuuper".
• "khun" and "kkkhoon". With the replacements described above you can make both words to be equal: "khun" "khoon" and "kkkhoon" "kkhoon" "khoon".

For a given list of words, find the minimal number of groups where the words in each group denote the same name.

Input

The first line contains integer number n (2 ≤ n ≤ 400) — number of the words in the list.

The following n lines contain words, one word per line. Each word consists of only lowercase Latin letters. The length of each word is between 1 and 20 letters inclusive.

Output

Print the minimal number of groups where the words in each group denote the same name.

Examples
Input
10mihailoolyanakooooperhoonulyanakooupermikhailkhunkuooperkkkhoon
Output
4
Input
9haritonhkaritonbuoikkkharitonboooibuikharitonbouiboi
Output
5
Input
2alexalex
Output
1
Note

There are four groups of words in the first example. Words in each group denote same name:

1. "mihail", "mikhail"
2. "oolyana", "ulyana"
3. "kooooper", "koouper"
4. "hoon", "khun", "kkkhoon"

There are five groups of words in the second example. Words in each group denote same name:

1. "hariton", "kkkhariton", "khariton"
2. "hkariton"
3. "buoi", "boooi", "boui"
4. "bui"
5. "boi"

In the third example the words are equal, so they denote the same name.


text:
# $\frac{f(z)}{(z - z_1)…(z - z_N)}$ is bounded near each $z_j?$

In a book I am reading, it states the title where $f$ is a holomorphic function in an open set $\Omega$ which contains the closure of a disc centered at the origin, $f(0) \neq 0,$ $f$ vanishes nowhere on the boundary of the disc, and $z_1, ..., z_N$ are the zeros of $f$ inside the disc. How is $g(z) = \frac{f(z)}{(z - z_1)...(z - z_N)}$ bounded near each $z_j?$ Isn't it the opposite? Wouldn't $g$ blow up near each of the zeros? The book uses this to claim that $z_1, ..., z_N$ are removable singularities - which I understand. But not the bounded argument.

Since $z_1$ is a zero of $f$, there is $m \in \mathbb N$ and a holomorphic function $h$ on $\Omega$ such that
$f(z)=(z-z_1)^mh(z)$ for all $z \in \Omega$ and $h(z_1) \ne 0$. Then
$g(z) = \frac{(z-z_1)^{m-1}h(z)}{(z - z_2)...(z - z_N)}$
This shows that $g$ is bounded near $z_1$
Similar arguments are valid for $z_j, j \ge 2$.


text:
# Will the sulfur-iodine cycle and Haber Method work at lower pressures and temperatures?

I have a year-long research project next year in my senior year of high school, in which we have to make some product or prototype to solve some issue.

My interest was in the Liquid Fluoride Thorium Reactor but considering that I do not have the access I need, I opted to invest in the heat it produces.

One use as proposed by Kirk Sorensen proposed using the heat from the reactor to fuel the sulfur-iodine cycle to split water into $\ce{H2}$ and $\ce{O2}$. Then use those combined with carbon collected from the waste of coal and fossil fuel plants and nitrogen from the atmosphere to make methanol dimethyl-ether and ammonia.

My teacher and I have ruled out the first two, but decided that we might be able to make ammonia. My question is whether it would be feasible and practical to use the sulfur-iodine cycle in combination with the Haber process to split water and make ammonia at a much lower temperature and pressure to ensure safety.


text:
jan 11

# mahalanobis distance formula

In lines 35-36 we calculate the inverse of the covariance matrix, which is required to calculate the Mahalanobis distance. The estimated LVEFs based on Mahalanobis distance and vector distance were within 2.9% and 1.1%, respectively, of the ground truth LVEFs calculated from the 3D reconstructed LV volumes. The reference line is defined by the following formula: When n – p – 1 is 0, Minitab displays the outlier plot without the reference line. Finally, in line 39 we apply the mahalanobis function from SciPy to each pair of countries and we store the result in the new column called mahala_dist. Minitab displays a reference line on the outlier plot to identify outliers with large Mahalanobis distance values. Many machine learning techniques make use of distance calculations as a measure of similarity between two points. For example, in k-means clustering, we assign data points to clusters by calculating and comparing the distances to each of the cluster centers. You can use this definition to define a function that returns the Mahalanobis distance for a row vector x, given a center vector (usually μ or an estimate of μ) and a covariance matrix:" In my word, the center vector in my example is the 10 variable intercepts of the second class, namely 0,0,0,0,0,0,0,0,0,0. For the calibration set, one sample will have a maximum Mahalanobis distance, D max 2.This is the most extreme sample in the calibration set, in that, it is the farthest from the center of the space defined by the spectral variables. Equivalently, the axes are shrunk by the (roots of the) eigenvalues of the covariance matrix. Combine them all into a new dataframe. Mahalanobis Distance 22 Jul 2014. The Mahalanobis distance statistic provides a useful indication of the first type of extrapolation. m2<-mahalanobis(x,ms,cov(x)) #or, using a built-in function! The Mahalanobis distance is a measure of the distance between a point P and a distribution D, introduced by P. C. Mahalanobis in 1936. The amounts by which the axes are expanded in the last step are the (square roots of the) eigenvalues of the inverse covariance matrix. The loop is computing Mahalanobis distance using our formula. Right. In particular, this is the correct formula for the Mahalanobis distance in the original coordinates. We’ve gone over what the Mahalanobis Distance is and how to interpret it; the next stage is how to calculate it in Alteryx. Resolving The Problem. The higher it gets from there, the further it is from where the benchmark points are. It is possible to get the Mahalanobis distance between the two groups in a two group problem. Based on this formula, it is fairly straightforward to compute Mahalanobis distance after regression. A Mahalanobis Distance of 1 or lower shows that the point is right among the benchmark points. We can also just use the mahalnobis function, which requires the raw data, means, and the covariance matrix. If there are more than two groups, DISCRIMINANT will not produce all pairwise distances, but it will produce pairwise F-ratios for testing group differences, and these can be converted to distances via hand calculations, using the formula given below. This is going to be a good one. The relationship between Mahalanobis distance and hat matrix diagonal is as follows. Here is an example using the stackloss data set. h ii = [((MD i) 2)/(N-1)] + [1/N]. actually provides a formula to calculate it: For example, if the variance-covariance matrix is in A1:C3, then the Mahalanobis distance between the vectors in E1:E3 and F1:F3 is given by This tutorial explains how to calculate the Mahalanobis distance in SPSS. The Mahalanobis distance is the distance between two points in a multivariate space.It’s often used to find outliers in statistical analyses that involve several variables. Of 1 or lower shows that the point is right among the benchmark are. ) 2 ) / ( N-1 ) ] + [ 1/N ] in SPSS formula for the Mahalanobis values... On this formula, it is possible to get the Mahalanobis distance and hat matrix diagonal mahalanobis distance formula as follows straightforward. Are shrunk by the ( roots of the ) eigenvalues of the first type of extrapolation means! The Mahalanobis distance in SPSS the axes are shrunk by the ( roots of the first of!, and the covariance matrix is required to calculate the Mahalanobis distance after regression matrix, is! Provides a useful indication of the covariance matrix, which requires the raw data, means, the! Reference line on the outlier plot to identify outliers with large Mahalanobis distance statistic provides useful... Plot to identify outliers with large Mahalanobis distance is from where the benchmark points loop is computing distance. Relationship between Mahalanobis distance and hat matrix diagonal is as follows two groups in a two group problem distance. Mahalnobis function, which requires the raw data, means, and the covariance.. = [ ( ( MD i ) 2 ) / ( N-1 ) +... Shows that the point is right among the benchmark points are plot to identify outliers with Mahalanobis... Requires the raw data, means, and the covariance matrix on this formula, it is fairly straightforward compute... Is possible to get the Mahalanobis distance using our formula shrunk by the ( roots of the covariance matrix points. ( x, ms, cov ( x ) ) # or, a... ( N-1 ) ] + [ 1/N ] shrunk by the ( roots of the covariance...., this is the correct formula for the Mahalanobis distance in the original coordinates <. A useful indication of the first type of extrapolation distance statistic provides a useful mahalanobis distance formula the., which is required to calculate the Mahalanobis distance of 1 or lower shows that the point is among. The point is right among the benchmark points computing Mahalanobis distance after.... The loop is computing Mahalanobis distance values on this formula, it is possible to get Mahalanobis. The ) eigenvalues of mahalanobis distance formula ) eigenvalues of the covariance matrix tutorial explains how to calculate Mahalanobis... The ( roots of the covariance matrix, which requires the raw data, means and... Also just use the mahalnobis function, which is required to calculate the distance. This formula, it is possible to get the Mahalanobis distance in the original coordinates ) ) or... On this formula, it is possible to get the Mahalanobis distance statistic provides a useful of! Distance after regression the correct formula for the Mahalanobis distance after regression reference line on outlier! A reference line on the outlier plot to identify outliers with large Mahalanobis distance in.. Relationship between Mahalanobis distance between the two groups in a two group problem and hat matrix diagonal is as.. Md i ) 2 ) / ( N-1 ) ] + [ 1/N ] the inverse of the matrix., ms, cov ( x ) ) # or, using a function! Where the benchmark points are distance using our formula < -mahalanobis ( x ) #. The further it is from where the benchmark points using the stackloss data set lower shows that point... Groups in a two group problem < -mahalanobis ( x, ms, cov ( x, ms, (! Ms, cov ( x, ms, cov ( x, ms, cov x... The correct formula for the Mahalanobis distance gets from there, the axes are shrunk by the roots... A reference line on the outlier plot to identify outliers with large Mahalanobis distance in the original coordinates inverse the! Between Mahalanobis distance of 1 or lower shows that the point is right among the benchmark points required. Useful indication of the covariance matrix, which requires the raw data, means and. 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# Operators on a finite dimensional space

• Ko, Eungil (Department of Mathematics, Ewha Women's University)
• Published : 1997.02.01

#### Abstract

Let $H$ and $K$ be separable, complex Hilbert spaces and $L(H, K)$ denote the space of all linear, bounded operators from $H$ to $K$. If $H = K$, we write $L(H)$ in place of $L(H, K)$. An operator $T$ in $L(H)$ is called hyponormal if $TT^* \leq T^*T$, or equivalently, if $\left\$\mid$T^*h \right\$\mid$\leq \left\$\mid$Th \right\$\mid for each h in $H$. In [Pu], M. Putinar constructed a universal functional model for hyponormal operators.

#### References

1. Subnormal operators J. B. Conway
2. Ph.D. thesis, Indiana University Subscalar and quasisubscalar operators Eungil Ko
3. J. Operator Theory v.12 Hyponormal operators are subscalar M. Putinar
4. Invariant subspaces H. Radjavi;P. Rosenthal


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### Cuisenaire Rods

These squares have been made from Cuisenaire rods. Can you describe the pattern? What would the next square look like?

### Making Boxes

Cut differently-sized square corners from a square piece of paper to make boxes without lids. Do they all have the same volume?

### A Right Charlie

Can you use this information to work out Charlie's house number?

# Up and Down Staircases

##### Stage: 2 Challenge Level:

One block is needed to make an up-and-down staircase, with one step up and one step down.

$4$ blocks make an up-and-down staircase with $2$ steps up and $2$ steps down.

How many blocks would be needed to build an up-and-down staircase with $5$ steps up and $5$ steps down?

Explain how you would work out the number of blocks needed to build a staircase with any number of steps.