A New Improved Adomian Decomposition Method for Solving Emden{Fowler Type Equations of Higher{Order

In this paper, we present a suggested modification for Adomain decomposition method to solve Emden{Fowler Types Equations of higher-order ordinary differential equations. The proposed method can be applied to linear and non-linear problems. By using some illustrative examples, we tested the reliability and effectiveness of the proposed method and we found that the obtained results approximate the exact solution. Thus, we can conclude that this proposed method is efficient and reliable .

Modified Mathematical Model of Tumor Treatment by Radiotherapy

In this research, a mathematical model of tumor treatment by radiotherapy is studied and a new modification for the model is proposed as well as introducing the check for the suggested modification. Also the stability of the modified model is analyzed in the last section.

Problems and Prospects with the Scientonomic Workflow

While the scientonomic workflow guiding the development of a general theory of scientific change has been practiced for nearly four years, it has yet to be formally evaluated. The goal of this paper is to fill this gap with a critical appraisal of the practice and theoretical underpinnings of the workflow currently used in scientonomy. First, we consider the traditional workflow which uses publications as the primary vehicle for substantive epistemic change and find that it fails to be sufficiently transparent or inclusive and is ambiguous at decisive points. Conversely, as we argue, the scientonomic workflow has the potential to succeed where the traditional workflow fails and thus provides a promising alternative workflow. We then go on to note a number of practical and theoretical problems that have arisen upon reflection on the scientonomic workflow and suggest some modifications to the workflow and to our practices. This paper takes the first steps in improving the workflow to reach its maximum potential. Suggested Modifications [Sciento-2019-0001]: Accept that the goal of peer-reviews in the scientonomic workflow is evaluation for pursuitworthiness rather than acceptability. [Sciento-2019-0002]: Accept that the discussions concerning a suggested modification are to be published once a communal verdict is available. The discussions are to be published in the journal as special commentary articles co-authored by all participants of the discussion or in special edited collections. [Sciento-2019-0003]: Accept that the commentators of suggested modifications are allowed to suggest reformulations of the original formulations. Also accept that, by default, the new formulation should bear the original author’s name, unless the author decides to give credit to those who significantly contributed to the new reformulation. This should be decided collegially by the author, the commentators, and the editors on a case-by-case basis. [Sciento-2019-0004]: Accept that an annual book prize is to be offered for extensive participation on the encyclopedia. The winner(s) are to be decided by the encyclopedia editors. [Sciento-2019-0005]: Accept that star-ratings are to be introduced for commentators who comment on suggested modifications on the encyclopedia. [Sciento-2019-0006]: Accept that the encyclopedia editors are to be granted official housekeeping rights to handle the ripple effects. Also accept that if the additional required changes are implicit in the suggested modification, the editors should create and alter encyclopedia pages to ensure that the accepted body of scientonomic knowledge is properly documented; if it is conceivable to accept the modification without accepting the ripple effect change in question, the editors should register these changes as new suggested modifications so that the community can discuss and evaluate them in an orderly fashion. [Sciento-2019-0007]: Accept that the verdict on suggested modifications is to be decided by a communal vote that will follow the discussion period. Have a communal discussion and decide as to what percentage of votes it should take for a modification to be accepted – a simple majority (50% +1), or supermajority of three fifths (60%), two thirds (67%), or three quarters (75%). Also discuss to decide as to how long the discussion period and the voting period should be. This modification is incompatible with modification [Sciento-2019-0008]. [Sciento-2019-0008]: Accept that a countdown mechanism is to be introduced, where a modification is accepted by default if there are no objections within a 90-day period following its publication. This modification is incompatible with modification [Sciento-2019-0007].

Suggested modification of presentation of stroke trial results

The modified Rankin Scale (mRS) at 90 days after stroke onset has become the preferred outcome measure in acute stroke trials, including recent trials of interventional therapies. Reporting the range of modified Rankin Scale scores as a paired horizontal stacked bar graph (colloquially known as “Grotta bars”) has become the conventional method of visualizing modified Rankin Scale results. Grotta bars readily illustrate the levels of the ordinal modified Rankin Scale in which benefit may have occurred. However, complementing the available graphical information by including additional features to convey statistical significance may be advantageous. We propose a modification of the horizontal stacked bar graph with illustrative examples. In this suggested modification, the line joining the segments of the bar graph (e.g. modified Rankin Scale 1–2 in treatment arm to modified Rankin Scale 1–2 in control arm) is given a color and thickness based on the p-value of the result at that level (in this example, the p-value of modified Rankin Scale 0–1 vs. 2–6)—a thick green line for p-values <0.01, thin green for p-values of 0.01 to <0.05, gray for 0.05 to <0.10, thin red for 0.10 to <0.90, and thick red for p-values ≥0.90 or outcome favoring the control group. Illustrative examples from four recent trials (ESCAPE, SWIFT-PRIME, IST-3, ASTER) are shown to demonstrate the range of significant and non-significant effects that can be captured using this proposed method. By formalizing a display of outcomes which includes statistical tests of all possible dichotomizations of the Rankin scale, this approach also encourages pre-specification of such hypotheses. Prespecifying tests of all six dichotomizations of the Rankin scale provides all possible statistical information in an a priori fashion. Since the result of our proposed approach is six distinct dichotomized tests in addition to a primary test, e.g. of the ordinal Rankin shift, it may be prudent to account for multiplicity in testing by using dichotomized p-values only after adjustment, such as by the Bonferroni or Hochberg-Holm methods. Whether p-values are nominal or adjusted may be left to the discretion of the presenter as long as the presence or absence is clearly stated in the statistical methods. Our proposed modification results in a visually intuitive summary of both the size of the effect—represented by the matched bars and their connecting segments—as well as its statistical relevance.