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  • George Stoica added an answer in Stochastic Differential Equations:
    How can I consider asymptotic behavior of a dynamical system of stochastic differential equations?

    Analytic or numerical asymptotic behavior of a SDE system is of interest. The system has finite dimension and its symmetric positive definite diffusion matrix multiplied by a vector of independent Wiener processes. The stability of such system (not stability of numerical methods for solving it) is also required.

    every comments or references is appreciated.

    George Stoica

    Dear Mahmood,

    A brief but good reference is:


    Also see chapter 11 in


    Sincerely, George

  • Rahim Abdur added an answer in Cellulose Nanocrystals:
    How can I perform SEM on cellulose nanocrystal film without burning on sample?

    My CNC film was prepared by evaporating in petri dish. Then, it was sputtered with Pt and Pd for 60 sec. And I try to get SEM image at high magnification (i.e. > 150,000x) but the sample always was burn. Actually, my CNC-film start burning at 30,000x. I try to adjust parameters : both "High Voltage" (from 30, 20 and 10 kV) and "Spot" (from 3.0, 2.0, 1.5, 1.0) but useless. 

    Anyone can tell me the technique to overcome this thing ?

    Rahim Abdur

    I have measured polymer films after pt coating using JEOL-7401F many times. Initially I also had that problem. 

    You can use lower acceleration voltage, lower prob current, closer distance and less focusing time as well as faster scan to get the image.

    I think you have try each of these to get the optimum image. Good luck. 

  • Pablo German added an answer in RNAlater:
    Has anyone used RNAlater for whole insect storage?

    Dear all:
    I'm currentlly trying to achieve some infections with Rhodnius prolixus in Trypanosoma cruzi-infected mice and I need to save the infected insects for later. I'm working with R.p fourth instar nymph and I'm interested in knowing if anyone has ever efectivly storage arthropods this size in RNAlater.
    Thank you so much.

    Pablo German

    Hi Melina, there are two related questions and answers in the two links provided. I'm also planning to store an arthropod in RNAlater and wonder whether the RNAlater will penetrate the cuticle fast enough to preserve the RNA.

    + 1 more attachment

  • Abdus Salam Sarkar added an answer in Graphene Quantum Dots:
    How can I differ between a graphene quantum dot and carbon dot?

    How can I differ between a graphene quantum dot and carbon dot?

    Abdus Salam Sarkar

    Syam Sai Ravuri thank you for the reference.

  • Liting Ji asked a question in RNA Probes:
    I am new to in situ hybridisation. I am wondering how can I prepare linearized DNA to make RNA probe?

    How can I prepare the linearized DNA template to generate RNA probe for in situ hybridization? Thank you!

  • Bhim Dahal asked a question in FLAC3D:
    Could anybody please recommend the best software for modelling of surface and sub-surface deformation due to underground excavation (tunnel)?

    Actually I am new in the field of modelling. I have options in software's availability i.e.  Abacus or Flac3D. I am trying to model layered soft-soil and shallow tunnel/deep excavation in urban area and its effect in surface and subsurface structures.

  • Liting Ji added an answer in In Situ Hybridization:
    What is the most sensitive non-radioactive protocol for in situ hybridization to detect mRNA in brain or spinal cord tissue sections?

    Preferably using fluorescence and suitable for double labelling.

    Liting Ji

    Hello,I am new to in situ hybridisation. I am wondering how can I prepare linearized DNA to make RNA probe? Thank you.

  • Rafik Karaman added an answer in Ordination:
    Can we apply the Cliff's delta for Matched Ordinal Data to Calculate Clinical Significance? If not then which tests would be more appropriate?

    Clinical Significance, Cliff's Delta, Matched or Paired Ordinal Data

    Rafik Karaman

    Dear Devangini,

    The answer yes; we can. Please read the following text: In addition, attached please find an important publication on this topic.

    Meyer NE. Clinical usefulness of Cliff's δ

    Authors : MEYER* Nicolas E.1
    & Sauleau Erik-André2
    Affiliations : 1 Laboratoire de Biostatistique, Département de Santé Publique,
    Faculté de Médecine, 4, rue Kirschleger, 67085 Strasbourg
    Service des Etudes et des Applications de l’Information Médicale,
    Hôpital du Hasenrain, BP 1070, 87, Avenue d'Altkirch
    Email: Nicolas.Meyer@medecine.u-strasbg.fr; Sauleauea@ch-mulhouse.fr
    Phone: +333 90 24 32 62 and +333 89 64 79 95; Fax:+333 88 11 61 59 and +333 89 64 79 71
    Corresponding author: MEYER NE.
    Key-Words : effect size, null hypothesis, delta, clinical significance.
    Topic area : Miscellaneous topics related to Stastistics in Health
    Medical research rests largely on hypothesis testing, enabling comparisons of a set of groups on a qualitative or quantitative criterion. These tests are based on the computation of a test statistic which is converted in a probability, usually noted p, that measures the probability to observe a difference as important or more important than the observed one. This p-value is frequently called the significance of the test. Since Fisher and Neymann-Pearson (NP), a controversy aroused over the role of the p-value in the scientific decision process and the relevance of the use of a significance threshold as a criterion to reject null hypothesis. The present prevailing attitude follows the NP concept, owing mainly to its ease of application. It
    is based on a null hypothesis H0 and its logical counterpart, the alternative hypothesis H1. H0 is rejected whenever p ≤ α, where α is the test nominal level. This attitude is prone to criticism, notably the lack of measure of the effect size by the choosen test. One knows the risk associated with the rejection of H0 but the amplitude of the difference is unevaluated. The information is more relevant when the confidence interval (CI) of the parameter of interest is used but CI being also build on an α level, the validity of the experimental conclusion is not changed. Due to the lack of effect size measure, statistical significance is not clinical   Clinical usefulness of Cliff's δ
    evidence: a powerful study makes possible to detect a clinicaly unuseful difference. The
    hypothesis test yields no information on the importance of the difference or the strength of the
    relationship between variables. It indicates rather the sample sizes since if p < 5%, the test is significant but if p > 5%, a sufficient power increase (that is a size increase) leads to significance. Four values are linked together: power, α level, size and effect size. When comparing the means of two independant groups, effect size can be measured by the part of variance explained by the groups, using either η², ω² or ε² [1] but the parameter typically used to measure effect size, under normality and homoscedasticity assumptions, is σ
    µ1 − µ2 D =
    [2], linked to the standardized increments described by Feinstein [3]. The standard deviation to be used is the standard deviation of the pooled groups [4,5]. But the estimation of D is problematical when confronted to heteroscedasticity. In this situation, many solutions have been proposed [6], like for instance, using the standard deviation of the control group [7], using the mean variance of the groups [2], transforming the data in order to egalise variances [8] or to see the effect size as a biserial point correlation coefficient [8]. From a larger point of view, robust methods have been proposed to take into account heteroscedasticity but also the
    absence of normality like using weighted standard deviation [9], interquartile ranges [10] or non parametric estimators [4,5]. Assuming the normality of underlying distributions is generaly not reasonable and furthermore heteroscedasticity is common in medical studies [11,12]. Moreover, homoscedasticity is difficult to test, tests being powerless. A more radical solution to circumvent these assumptions is to derive a distribution function for the effect size, rather than using it as a central tendency measure. An effect size measure can then be the probability that a subject being sampled at random in a group, will have a score that is superior to the score of any subject sampled in the other group. This probability is best estimated by the probability of superiority (PS) as defined by Grissom [13,14,15], which can
    be shown to exhibit the smallest variance of unbiased estimator of ( ) Pr X1 > X2 . PS is computed as the ratio of the number of measures of the first group being greater than measures in the second group, divided by the product of the sample sizes, that is the number of possible comparisons beween the two groups. If both groups are identical this probability equals 0.5. But when computing PS, ex-aequo poses problems. Cliff’s δ [16] statistic eliminates this difficulty, at the cost of a slightly greater complexity. If PS was writtten Pr( ) X1i>X2j , δ can be written as Pr( )( ) X1i>X2j −Pr X1i<X2j , and is estimated by Meyer NE. Clinical usefulness of Cliff's δ
    ( )( ) mn # x1i>x2j −# x1i<x2j (where m and n are sample sizes). δ varies from –1 (non overlapping distributions with X1 on the left) to 1 (non overlapping distributions with X1 on the right). It’s a form of Somer’s d [17], applied to the case of a dichotomic and a continuous variable. It is linked to the Mann-Whitney test U by δ=2U/mn-1, but, unlike the Mann-Whitney, δ does not need the homoscedasticity assumption. A CI can be derived under different methods [16].
    Apart from giving the position of a distribution relative to the other, an interest of δ lies also in the possibility to know the probability of the effect being greater than a predefined value (other than zero which corresponds to δ). Our goal is to show, through simulations in different situations, the usefulness of Cliff’s δ and of the measure of probability of different effect sizes, when comparing two means.
    Method We simulate in two samples a measure (admitted to be known without error) of a variable. We simulate these measures according to two gaussian distributions with the same mean (m=0) and with the same variance (σ = 1) or with variances ratio from 1 to 5, or following two lognormal distributions with the same mean (m=1) and with the same geometrical standard deviation or varying between 1 and 3. Samples sizes are set to 10, 20 and 50 for each group.
    For each sample, Cliff’s δ is computed with two different measures of its CI, along with the classical Student t-test (with and without Welch correction for heteroscedasticity). Those elements are computed for a shift between the two distributions of 0 (observed δ) and for different values until the two distributions are completely non overlapping. We draw 1,000 random samples for each combination of these parameters which are crossed with each other in order to get a set of 1,000⋅3⋅3⋅5⋅6 simulations for each type of distribution (normal or lognormal)
    for the homoscedasticity case. The same pattern of simulations is applied to
    heteroscedasticity case. All analyses are run under .
    For sample sizes of 50, a shift of 0.6 between the means, under standard gaussian distribution, a typical value of δ would be 0.24 with a p-value of 0.038, CI [0.004 – 0.442], while the matching Student p-value is 0.025. The empirical error rate is in agreement with the nominal level α = 0.05 under H0. In the situation of homoscedasticity, the probability of rejecting the null hypothesis of no effect, for a shift of 0, 0.6 and 1 between the groups, for a sample size of 50 in each group, are respectively for δ and for the Student t-test of 0.050, 0.862, 0.996 and of 0.050, 0.865 and 0.997. The agreement between δ and Student t-test results is higher than 93  Meyer NE. Clinical usefulness of Cliff's δ
    %, whatever the respective sample sizes and shift. The proportions of tests conclusions in concordance for those three situations are respectively of 0.986, 0.961, and 0.999. A δ value near 1 or –1 is more frequently significant than near zero values, in accordance with expected results. For a same rejected difference, δ gives an estimate of the clinical significance of the observed difference.
    The results in case of heteroscedasticity agree with the homoscedastic case. The agreement between δ and Welch test is never below 94 %. For example, the probability of rejecting the null hypothesis of no effect, for a shift of 0, 0.6 and 1 between the groups, for a sample size of 50 in each group, are respectively for δ and for the Welch t-test of 0.072, 0.277, 0.752 and of 0.056, 0.241 and 0.745, when the ratio of the variances of the two distributions is 4. This means that, when a distribution has a bigger variance than the other, but the same location, the
    α-level of the test is not pertubed. When a shift between the distributions is added, the probability of rejecting the null hypothesis of no effect increases with the shift, but less quickly when an heteroscedasticity exists than when not.
    Simulations are on the way to examine clear cut heteroscedastic situations (normal vs lognormal distributions).
    The results show that δ performs as well as the Student t-test in term of rejecting H0. It brings however an additional infomation which is the quantification of the superiority of the effect of a treament compared to an other. For a similar power, δ is thus more usefull than the t-test and should then be used as a substitute for it. δ is very common in social sciences. Its use in the biomedical field is however very sparse whereas it could find a wide range of applications :
    every treatment has an effect, however small is it, and in most cases, it is accompanied by an increase of the variance, that is the treatment affects the spread as well as the center of the distribution. The possibility to quantify the effect size instead of simply rejecting a null hypothesis, in a reliable way, even when faced with heteroscedasticity, must lead to a change in the use of statistical tests. Moreover, the possibility to estimate δ for a value greater than a predefined level of clinical interest, that is including a "usefullness" gap to the observed effect
    size is a clear benefit when compared to Student t-test. Actually, most of the times, a
    treatment is interesting only above a given limit while classical statistical tests are just able to reject the hypothesis of no effect which, sometimes, can be of non clinical significance. δ is a dimensionless value wich is to be interpreted in the same way than a correlation coefficient.
    Meyer NE. Clinical usefulness of Cliff's δ
    The use of δ is not straigthforward when comparing more than two groups because it is not transitive. A modification of δ, the Common Language Effet Size, contrarywise, can be applied to more than two groups [18].
    [1] Olejnik, S.; Algina J. Measures of effect size for comparative studies: applications,
    interpretations and limitations. Contemporary Educational Psychology, 2000, 25:241-86.
    [2] Cohen, J. Statistical power analysis for the behavorial sciences. Academic Press, New
    York (2nd Ed.) 1988.
    [3] Feinstein, A.R.. Indexes of constrat and quantitative significance for comparisons of two
    groups. Statistics in Medicine, 1999, 18:2557-81.
    [4] Hedges, L.V.; Olkin, I. Nonparametric estimators of effect size in meta-analysis.
    Psychological Bulletin, 1984, 96:573-80.
    [5] Hedges, L.V.; Olkin, I. Statistical methods for meta-analysis. Academic Press, San Diego,
    [6] Grissom, R.J.; Kim, J. Review of assumptions and problems in the appropriate
    conceptualization of effect size. Psychological Methods, 2001, 6:135-46.
    [7] Glass, G.V.; Mac Graw, B.; Smith, M.L. Meta-analysis in social research. Sage,
    Thousand Oaks, 1981.
    [8] Rosenthal, R. Meta-analytic procedures for social research. Sage, Newbury Park 1991.
    [9] Goldberg, K.M.; Iglewicz, B. Bivariate extension of the boxplot. Technometrics, 1992,
    [10] Laird, N.M.; Mosteller, F. Some statistical methods for combining experimental results.
    International Journal of Technology Assessment in Health Care, 1990, 6:5-30.
    [11] Grissom, R.J. Heterogeneity of variance in clinical data. Journal of Consulting and
    Clinical Psychology, 2000, 68:155-65.
    [12] Bryk, A.S.; Raudenbush, S.W. Heterogeneity of variance in experimental studies: a
    challenge to conventional interpretations. Psychological Bulletin, 1988, 104:396-404.
    [13] Grissom, R.J. Probability of the superior outcome of one tratment over another. Journal
    of Applied Psychology, 1994, 79:314-6.
    [14] Grissom, R.J. Statistical anlysis of ordinal categorical status after therapies. Journal of
    Consulting and Clinical Psychology, 1994, 62:281-4.

    Hoping this will be helpful,


  • Bindi Vanzella added an answer in Seedling:
    Has anyone had any success seed-drilling woody species in restoration sites dominated by pasture grasses?

    I'm interested to find out if anyone has had success seed-drilling woody species in restoration sites that are dominated by pasture grasses? If so, how have you prepared the site? How have you protected any resulting seedlings from being swamped by regrowth from the pasture grasses? 

    My first thought is that it is probably impractical given the vigorous growth of pasture grasses, even after spraying. However, I am still interested to find out what experiences researchers or restoration practitioners have had using this technique. 

    Bindi Vanzella

    Contact Graham Fifield from Greening Australia http://www.greeningaustralia.org.au/news/staff-profile-graham-Fifield

    Graham Fifield (GFifield@greeningaustralia.org.au)

  • Nobuhiro Takeuchi asked a question in Artificial Respiration:
    Is there any possibility that epidermis staphylococcus may be a cause of sepsis in a healthy individual?

    Here is the case that I need your advice. A 41-year-old female was brought to our emergency department with high fever and conscious disturbance. Her vital signs on admission suggested that she was in a state of septic shock. Laboratory data showed elevated liver and renal function, and coagulation abnormality. Two set of blood culture revealed the presence of coagulase-negative staphylococcus (afterwards the microbe turned out to be epidermis staphylococcus). Close inspection of the patient showed that she had scratched skin eruption in her legs and hands. Her past medical records did not include diabetes mellitus. She did not take steroids or anti-cancer drugs. She was not considered to be in a state of immunodeficiency. Intensive care, including artificial respirator, dialysis, and aggressive therapy of anti-bacterial drugs, saved her in the end. I learned that, basically, epidermis staphylococcus is a weak microbe which usually affects infants or immunosuppressive individuals. I could not find articles or researches which wrote about healthy individuals who were inflicted by sepsis resulted from epidermis staphylococcus. I believe that blood culture was not a contaminant. I suppose that microbes entered into bloodstream from the scratched wounds. Is there any possibility that epidermis staphylococcus may be a cause of bacteremia as well as sepsis in a healthy individual?

  • Satriyo Krido Wahono added an answer in Biogas Production:
    Can someone explain to me how to regenerate NaOH from Na2CO3 to NaOH again, because i use NaOH to purify CO2 from Biogas product?

    i use NaOH to purify Biogas , adsorb CO2 using NaOH, and then NaOH that used become Na2CO3, i want to regenerate Na2CO3  to NaOH again but i don't know how

    Satriyo Krido Wahono

    I think it will need more energy to release CO2 than to capture it, because naturally NaOH capture CO2. If you want to make it back to solid form NaOH, maybe you can try to heated more than boiling water temperature, but if you only need to make it back to NaOH solution, maybe 60-80 C is enough. I suggest you to try it or find suitable reference related CO2 release from Na2CO3.

  • Carolyn Wilshire asked a question in Digital:
    Does anyone know of any norms for the digit span task that breaks performance down according to digit position??

    We're looking for some norms for older individuals on the digit span task. Although there seem to be a lot of sources that report norms, very few report how accurate the participants were at the various different serial positions. We're especially interested in recency effects, so this information is crucial.

    Anyone know of anything?


  • ChuanBiao Zhang added an answer in Gromacs:
    How can I make a movie from gromacs trajectory file (200 ns)?

    VMD failed because of low memory of computer (16GB) for resolving this problem, Can I split .xtc files to two parts? How?

    ChuanBiao Zhang

    yes , trjconv of gromacs  will help you. 

  • Max Stanley Chartrand added an answer in Audiology:
    How effective are hearing aids in management of individuals with Auditory neuropathy from your personal experiences?
    Management of ANSD patients is still a challenge for audiologists. In countries where people can't afford CI, can hearing aids with proper fitting strategies employed benefit individuals with ANSD?
    Max Stanley Chartrand

    I noticed my comment of more than a year ago was voted down for some reason. Possibly, the reader thought I was downplaying the need for hearing aids in cases of auditory neuropathy. Of course, hearing aids appropriately fitted a given hearing loss are foundational to any viable auditory rehab program for such cases. My larger point was that the relevant health issues need addressed, also, meaning it becomes an allied professional effort often coordinated by the clinical audiologist or the attending otologist.

    Hans made a great point re SNR characterisitics and uncomfortable MPOs of the amplification. Cochlear distortions play into the equation when SNR are not optimal. That's where wireless excels, especially in large area or classroom listening.   

  • Satriyo Krido Wahono added an answer in Biogas:
    When do biogas digesters start to produce biogas?

    i made an experiment in 4 l digester with inoculum 10% V/V, the digester produced biogas in the first week but other researchers say its not possible to produce before about 21 day, any one have an explanation? 

    Satriyo Krido Wahono

    Based on my experience for cow dung biogas, It need 7-21 days to produce first biogas. It is depend on the environment conditions and raw material type/composition which is used.

  • Yusrifar K Tirta added an answer in Marine Ecology:
    Alternative to formalin for fixation of marine fauna?
    Formalin, a 4-5% solution of formaldehyde in seawater has traditionally been used in the marine biology for the fixation of benthic macrofauna samples.
    However the use of formaldehyde is no more recommended since this chemical is carcinogenic, poisonous, irritating to the skin, eyes and mucous membranes
    That’s why I seek an alternative protocol and/or compound to avoid the use of formalin.
    I did not find recent articles in literature that address the problem of formalin substitution in ecology.
    I heard about methods based on ethanol and freezing for the fixation of maxcroinvertebrates.
    Does anyone know an alternative to formalin for the fixation of benthic fauna samples from soft-sediments?
    Any suggestions are welcome.
    Yusrifar K Tirta

    dr. Shields, thank you for your elaborate answer.

    i'd like to ask a few question.

    You have said that Bouin fixative is not recommended for molecular studies and ethanol does the work much better. Let say what i am try to fixate is a parasite reside in the cephalopods body. First i need to fixate the liver for characterisation using microscopy and then i need to do molecular technique for the parasite itself for more analysis.

    1. What should i do for the sample preservation? In case  i need to bring it overseas.

    2. Is it really that bad to extract DNA from the bouin fixated tissues or parasite? so it is impossible then?

    Thank you. 

  • Hon Wing Yan added an answer in Chlorella Vulgaris:
    What are the pigments composition of Chlorella pyrenoidosa and Chlorella Vulgaris?

    Please give the % of contain by each pigment

    The answer sample as the following:

    Type: Mangosteen


    Cyanidin 3-o-sophoroside (76.1%)

    Pelargonidin 3-o-glucoside (6.2%)

    Cyanidin 3-o-glucoside (13.4%)

    Hon Wing Yan

    To ayşe Köse:

    My Chlorella vulgaris sample is BG-11 Medium and 12 hours dark & 12 hours light (White ligth) condition for 1 week.

  • Andreas Kalckert added an answer in White Matter Tract:
    Which white matter tracts are functionally associated with the insular cortex?

    That is, what would be a good region of interest to target to correlate DTI findings with a structural change affecting the insular cortex.

  • Tri Handoyo added an answer in Bacteria:
    How can I analyse bacteria lactase use of Syringaldehyde as a substrate?

    How can I analyse bacteria lactase use of Syringaldehyde as a substrate?

    Tri Handoyo

    To see the invitro activity of lactase, you can use a substitution substrate (ONPG=ortho-nitrophenyl-beta-galactoside). ONPG --------> Galactose + ONP was detected by spectrophotometer on 420 nm. You can observe a color change from colorless to yellow.

  • Xiong Yanshi asked a question in NCBI:
    Which genome size data( OR, 2C content )of maize(Zea mayz 'B73') should I use in my flow cytometry experiment?

    Hello, everyone! I am recently working on nuclear DNA content,or genome size estimation by flow cytometry, using whole genome sequenced Zea mayz "B73" as internal reference standard. But, I get confused about the real genome size of this genome sequenced species. Because more than ONE genome size data was used in different paper, such as:

    1): 1C = 2067.62 Mbp, the latest whole genome sequence data in NCBI website.

    2): 1C = 2.365 Gbp, the size used by the whole genome sequence project when building BAC library;

    3): 2C = 4.85 GBP, used as the genome size of internal standard species (Zea mayz "B73") in FCM;

    4): maybe more I didn't know.

    So, the question is: which one should I use?

    Thank you all guys, any suggestions will be appreciated!

    + 3 more attachments

  • Fang Yuan added an answer in Sputtering:
    Why is my Cu film black?

    I used DC magnetro sputtering  to deposite Cu film on glass. But the colour of the film is black. I want to know whic parameter effect the corlour, pressure, gas flu or power?

    Fang Yuan

    Now, the main reson is pressure.when pressure is too high, the colour become black

  • Jim Best added an answer in Social Theory:
    What stories of how complex adaptive systems "work" have you encountered?

    I have identified some 50 CAS concepts commonly used by authors in the paper.  They range from those derived thru chaos theory and agent-based modeling, to self-organization of agents as they interact and co-adapt, to emergence, etc. I have created one brief story that weaves together clusters of these concepts and then another brief story that weaves together the clusters.

    How important is it to have a coherent story as one applies the concepts to new areas of inquiry?  Is a universal story across domains necessary?  What is it?

    • Source
      [Show abstract] [Hide abstract]
      ABSTRACT: The study surveys 25 popular secondary sources (1992-2014) on complexity theory and complex adaptive systems (CAS) to develop a comprehensive framework of CAS attributes used when authors reference CAS theory. The attributes are analyzed using network analysis algorithms to determine if there are related clusters of concepts. A two level story of theoretical relationships is developed between the attributes within the clusters and between the clusters to augment the CAS Framework. The complete CAS Framework is used to map CAS theory representations from the sources so that comparisons and evaluations of focus and thoroughness can be easily made. The result is a tool that can be used to assess any representation of CAS theory in any context, but especially in the social sciences with human agents.
    Jim Best

    Thanks Haikai, for that interesting story of Peter A's insight.  Revealing the interconnections behind his discernment sounds fascinating.

  • Xiujun Wang added an answer in Eddy Covariance:
    How to know the CO2 concentration in water through satellite images?

    I have done two years of measuring eddy covariance flows in a tower eight meters, installed in the Caxiuanã bay, but I have no data on the concentration of CO2 in the water.

    Xiujun Wang

    Your study site has a complex system so your flux data may not be in  line with the calculation based on the difference in pCO2 between the atmosphere and water, which is often used for oceanic studies. Terrestrial processes can have large impacts on the CO2 flux at the bay.

  • Aleksey Nikolaevich Glebov added an answer in Graphs:
    On edge-disjoint spanning subgraph of a connected graph?

    Suppose there is a connected and undirected graph $G$ with n(n>=4) vertices. Let f(G') be the number of connected components of a graph $G'$. Then $f(G)=1$.

    Now under the condition that all  vertices of $G$ have at least 3 adjacent vertices (no loop),

    can we separate $G$ into two edge-disjoint spanning subgraph $G1$ and $G2$ satisfying that f(G1)+f(G2)<=[2n/3] ?

    I mean "separate"  the  edges into to parts, and "separate" the degree of vertices also.

    That is to say, if a subgraph   contain the edge $e$, then I consider it contain the vertices of $e$.

    I think the answer should be yes and the bound of  f(G1)+f(G2) may be lower but I have no idea how to prove it. Mathematical Induction seems to be no help. Can anyone help me? Thank you very much!

    Aleksey Nikolaevich Glebov

    It is not hard to prove that every simple graph G (with no multiple edges), which is not necessarily connected, with minimum degree >= 3, can be decomposed to G1 and G2 such that f(G1)+f(G2) <= n/2. This bound is sharp since it is attained on 3-regular graphs.

    Suppose G is a counterexample to this statement with the fewest edges. Then G is connected. Denote by D=D(G) the maximum degree of G.

    If G has two adjacent vertices of degree >=4, then removing edge between them yeilds a smaller counterexample, which contradicts to the minimality of G. So we can assume that any two vertices of degree >=4 are non-adjacent.

    If D<=4, then for every subset X of vertices in G the subgraph H induced by X has at most 2|X|-2 edges. Indeed, it is trivial if D(H)<=3, and if H has a 4-vertex, then all neighbours of this vertex have degree <=3, so the sum of degrees of all vertices of H is at most 4|X|-4, which implies that the number of edges is at most 2|X|-2. Therefore, by Nash-Williams Theorem, the set of edges of G can be partitioned into two forests F1 and F2. Since G has at least 3n/2 edges and a forest with m edges consists of precisely n-m connected components we have f(F1)+f(F2) <= 2n - 3n/2 = n/2.

    Finally, assume that D>=5. Let V be a vertex of degree D in G. Since all neighbours of V have degree 3, we can find two of them, say A and B, that are not joined by an edge. Insert an edge AB and remove edges VA and VB from G, i.e. set G' = G-{VA,VB}U{AB}. Note that G' is a simple graph with minimum degree 3 having fewer edges than G. Thus, G' has a desired 2-partition (= 2-colouring) of its edges. W.l.o.g. assume that AB is coloured 1. We take the colouring of G'-{AB} and we colour VA and VB by 1. In the resulting edge-colouring of G the set of connected components of colour 2 is the same as in G' and the number of components of colour 1 is not greater than in G'. Indeed, the number of components of colour 1 in G'-{AB} can be only by 1 greater than in G' and only if A and B are in different components of G'-{AB}. However, in G = (G'-{AB})U{VA,VB} the vertices A and B are joined by the path (A,V,B) of colour 1, so they are in the same component of colour 1. This implies that if we denote the subgraphs of G induced by colours 1 and 2 by G1 and G2 respectively, then f(G1)+f(G2) <= n/2, as desired.

    I believe that for graphs with minimum degree >=4 the bound can be improved to 2n/5, and I have an idea how to prove it.

  • Paul K Canavan added an answer in Knee Osteoarthritis:
    Are Physiotherapy interventions really capable to change the Pathology of Knee Osteoarthritis?

    Almost all the physiotherapy articles on OA  shows clinically significant in management osteoarthritis(Hip & Knee). Whether this significant changes are also capable of changing pathology of OA , so can we believe on each and every articles showing clinically significant ..............?

    Paul K Canavan

    A proper individualized rehabilitation program based upon each person's unique profile and prioritized needs along with compliance to skilled outpt. P.T. and compliance to a individualized Home Ex program can and has been shown to decrease individual's pain and improve function. The area of confusion comes when one analyzes cartilage thickness, joint spaces, K/L scores, and other static, non-dynamic tests. Thus, functional movements and understanding of flexibility, balance, gait patterns, strength, L.E. power all contribute for the dynamic ability and stability of the joint.

  • Jorge Molina-Gonzalez asked a question in Upconversion:
    Is the type of crystalline phase affects the luminescence of upconversion nanoparticles?

    For example, in a ceramic, the alpha or beta phase, Do they have an effect on the luminescence?, What is best for efficient luminescence?

  • Iqra Saleem asked a question in ANSYS:
    Is capillary diameter affect the convergence with hexahedral mesh?

    Hello everyone!
    I am simulating the problem in ANSYS Polyflow.
    Fluid ,which is non-newtonian, is flowing though a pipe having diameter 1mm and length 100mm.
    The problem is converged with tetrahedral mesh. But when I try to simulate the same problem with hexahedral mesh, the error occured that is " the solution component in fluid flow (Polyflow) does not contain all entity types advertised in its component tempelate, even after update".
    What does it mean??
    Is it due to capillary diameter?

  • Abdullah Ghawanmeh added an answer in Colchicine:
    Can we use Boron tribromide dimethyl sulfide complex to demethylate the methoxy groups on ring A of colchicine?

    Can we use Boron tribromide dimethyl sulfide complex to demethylate the methoxy groups on ring A of colchicine?

    Abdullah Ghawanmeh

    Actually it is not possible to get BBr3 from suppliers.

  • Pramudita Kumala Ardianti asked a question in Economic Valuation:
    Can any one explain to me how do economic valuation of public open space benefit?

    open public space benefit are comfort, aesthetics, reduce social conflict, etc

  • Anand Parkash asked a question in Biochemical Engineering:
    What are the latest research topics for PhD in the field of Chemical/Biochemical Engineering?

    Searching latest research topics for PhD in the field of Chemical/Biochemical Engineering.