A piecewise memory principle for fractional derivatives

2017 ◽  
Vol 20 (4) ◽  
Author(s):  
Chunye Gong ◽  
Weimin Bao ◽  
Jie Liu
Keyword(s):  
Fractional Derivatives ◽  
Numerical Approximation ◽  
Past History ◽  
Equal Weight ◽  
Crucial Point ◽  
Step Size ◽  
Memory Length ◽  
The Past ◽  
Length Step ◽  
Computing Accuracy

AbstractIn the numerical approximation of fractional order derivatives, the crucial point is to balance the computing complexity and the computing accuracy. We proposed a piecewise memory principle for fractional derivatives, in which the past history is divided into several segments instead of discarded. The piecewise approximation is performed on each segment. Error estimation of piecewise memory principle is analyzed also. Numerical examples show that the contradiction of computing accuracy and complexity is effectively relaxed and the piecewise memory principle is superior to the existing short, variable and equal-weight memory principles. The impacts of the memory length, step size and segment size are also discussed.

Initialization Issues of the Caputo Fractional Derivative

2005 ◽  
Author(s):  
B. N. Narahari Achar ◽  
Carl F. Lorenzo ◽  
Tom T. Hartley
Keyword(s):  
Differential Equation ◽  
Fractional Calculus ◽  
Fractional Derivative ◽  
Caputo Fractional Derivative ◽  
Fractional Derivatives ◽  
Past History ◽  
The Past ◽  
History Of ◽  
Fractional Differential ◽  
Generally True

The importance of proper initialization in taking into account the history of a system whose time evolution is governed by a differential equation of fractional order, has been established by Lorenzo and Hartley, who also gave the method of properly incorporating the effect of the past (history) by means of an initialization function for the Riemann-Liouville and the Grunwald formulations of fractional calculus. The present work addresses this issue for the Caputo fractional derivative and cautions that the commonly held belief that the Caputo formulation of fractional derivatives properly accounts for the initialization effects is not generally true when applied to the solution of fractional differential equations.

Obituary notices of fellows deceased

1877 ◽  
Vol 25 (171-178) ◽  
Keyword(s):  
Past History ◽  
The Past ◽  
The Earth ◽  
History Of ◽  
Reign Of Terror ◽  
Accurate Observation

George Poulett Scrope. It is scarcely possible at the present day to realize the conditions of that intellectual “reign of terror” which prevailed at the commencement of the present century, as the consequence of the unreasoning prejudice and wild alarm excited by the early progress of geological inquiry. At that period, every attempt to explain the past history of the earth by a reference to the causes still in operation upon it was met, not by argument, but by charges of atheism against its propounder; and thus Hutton’s masterly fragment of a ‘Theory of the Earth,’ Playfair’s persuasive‘ Illustrations,’ and Hall’s records of accurate observation and ingenious experiment had come to be inscribed m a social Index Expurgatorius ,and for a while, indeed, might have seemed to be consigned to total oblivion. Equally injurious suspicions were aroused against the geologist who dared to make allusion to the important part which igneous forces have undoubtedly played in the formation of certain rocks; for the authority of Werner had acquired an almost sacred cha­racter; and “ Vulcanists ” and “ Huttonians ” were equally objects of aversion and contempt. To two men who have very recently—and within a few months of one another—passed away from our midst, science is indebted for boldly en­countering and successfully overcoming this storm of prejudice. Hutton and his friends lived a generation too soon ; and thus it was reserved tor Lyell and Scrope to carry out the task which the great Scotch philosopher had failed to accomplish, namely, the removal of geology from the domain of speculation to that of inductive science.

Colonising the Past? History, Medicine, and Reality Television

2006 ◽  
Vol 8 (2) ◽  
pp. 124-146
Author(s):  
Susan Hardy ◽  
Anthony Corones
Keyword(s):  
Reality Television ◽  
Past History ◽  
The Past

Preserve the past [history - architecture]

2021 ◽  
Vol 16 (11) ◽  
pp. 46-49
Author(s):  
H. Pozniak
Keyword(s):  
Past History ◽  
The Past

scholarly journals The Old Greeks

2016 ◽  
Vol 22 (2) ◽  
Author(s):  
George Kouvaros
Keyword(s):  
Past History ◽  
The Past ◽  
Siegfried Kracauer ◽  
The Future ◽  
The Dead

In his final unfinished book on the writing of history, Siegfried Kracauer wonders about his increasing susceptibility to ‘the speechless plea of the dead’. ‘[T]he older one grows, the more he is bound to realize that his future is the future of the past—history.’ For the children of migrants, the question of how to speak well of the dead is distinguished by complex feelings of attachment and rejection, identification and denial that are expressed in a range of everyday interactions. ‘The Old Greeks’ examines the part played by photographic media in this process of memorialisation. It elaborates a series of propositions about the value of photographic media that are tested through a consideration of the events that surrounded the author’s first years in Australia.

Revisiting the Past: History and Historical Memory during the Leningrad Blockade

2011 ◽  
Vol 38 (2) ◽  
pp. 105-129
Author(s):  
Alexis Peri
Keyword(s):  
Civil War ◽  
Past History ◽  
Historical Memory ◽  
Crimean War ◽  
Collective Memories ◽  
The Past ◽  
Everyday Practices ◽  
The Everyday ◽  
Historical Reflection

AbstractThis article examines the everyday practices of historical reflection, recollection, and reconstruction as revealed in diaries of the Leningrad Blockade. In particular, it focuses on how Leningraders who chose to keep diaries of their experiences worked to make sense of the siege by situating it historically and comparing it to two other historical moments, the blockade of Petrograd during the Civil War and the siege of Sevastopol' during the Crimean War. Their evaluations of these historical analogies were based on a combination of personal and collective memories as well as on their understandings of state-sanctioned accounts of these events. Ultimately, these historical refl ections alerted the diarists to what they came to see as the unique and incomparable aspects of Blockade.

scholarly journals Genetic and linguistic histories in Central Asia inferred using approximate Bayesian computations

2017 ◽  
Vol 284 (1861) ◽  
pp. 20170706 ◽  
Author(s):  
Valentin Thouzeau ◽  
Philippe Mennecier ◽  
Paul Verdu ◽  
Frédéric Austerlitz
Keyword(s):  
Central Asia ◽  
Linguistic Diversity ◽  
Past History ◽  
Genetic Data ◽  
Human Populations ◽  
Language Diversity ◽  
Methodological Framework ◽  
The Past ◽  
Approximate Bayesian ◽  
Future Work

Linguistic and genetic data have been widely compared, but the histories underlying these descriptions are rarely jointly inferred. We developed a unique methodological framework for analysing jointly language diversity and genetic polymorphism data, to infer the past history of separation, exchange and admixture events among human populations. This method relies on approximate Bayesian computations that enable the identification of the most probable historical scenario underlying each type of data, and to infer the parameters of these scenarios. For this purpose, we developed a new computer program PopLingSim that simulates the evolution of linguistic diversity, which we coupled with an existing coalescent-based genetic simulation program, to simulate both linguistic and genetic data within a set of populations. Applying this new program to a wide linguistic and genetic dataset of Central Asia, we found several differences between linguistic and genetic histories. In particular, we showed how genetic and linguistic exchanges differed in the past in this area: some cultural exchanges were maintained without genetic exchanges. The methodological framework and the linguistic simulation tool developed here can be used in future work for disentangling complex linguistic and genetic evolutions underlying human biological and cultural histories.

scholarly journals P311 Detection and characterisation of extra-intestinal manifestations of IBD in clinical office notes using natural language processing

2020 ◽  
Vol 14 (Supplement_1) ◽  
pp. S309-S310
Author(s):  
R Stidham ◽  
D Yu ◽  
S Lahiri ◽  
V Vydiswaran
Keyword(s):  
Natural Language Processing ◽  
Natural Language ◽  
Language Processing ◽  
Past History ◽  
Model Development ◽  
Population Based ◽  
Equal Weight ◽  
Disease Experience ◽  
Status Classification ◽  
Therapeutic Decision Making

Abstract Background Extra-Intestinal Manifestations (EIM) occur in nearly 40% of patients with IBD and impact both disease experience and therapeutic decision-making, but are not well captured by administrative codes. We aimed to pilot computational natural language processing (NLP) methods to characterise EIMs using consultant notes. Methods Subjects with a diagnosis of IBD were identified in a single-centre retrospective review of electronic health records (EHR) between 2014–2017. Gastroenterology (GI) notes were annotated by two reviewers for the presence and activity of EIMs. EIM concepts were identified using NLP methods leveraging UMLS libraries and hand-crafted features. EIM characterisation occurred within a ±25-word window around identified EIMs with classifications including inactive concepts (negated, historical, resolved) and active concepts (improved, worsened, active but unchanged). Decisions on EIM status when repeatedly referenced in a document used section-based weighting for status inference, with greatest to least weight ranking for assessment/plan, subjective, past history, exam, and other, respectively. EIM status was classified as ambiguous when multiple conflicting references were present within the same document of approximately equal weight. Model development and testing used an 80/20 dataset split. Results In 4108 unique IBD patients, 1640 (39.9%) had at least 1 EIM identified. The mean age was 41.9 years, 47.2% were male, and 27.0% had biologic exposure. A total of 1240 manually annotated documents (first GI notes) were comprised of 51.1% arthritis, 16.5% ocular, 16.2% psoriasis, with erythema nodosum (EN), pyoderma gangrenosum (PG), and hidradenitis suppurativa (HS) together comprising 16.2% of the cohort. NLP models performed well for correctly classifying both EIM presence and status in a testing set, with overall accuracy, sensitivity, and specificity of 91.2%, 92.9% and 81.8% across all EIMs in notes automatically classified as non-ambiguous (Table 1). NLP methods identified EIM status classification as ambiguous in 38.9% of cases. Conclusion NLP methods can detect and classify EIMs with reasonable performance and efficiency compared with traditional manual chart review. Though source document variation and ambiguity present challenges, NLP offers exciting possibilities for population-based research and decision support.

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