A novel approach to fractional calculus: utilizing fractional integrals and derivatives of the Dirac delta function

While the definition of a fractional integral may be codified by Riemann and Liouville, an agreed-upon fractional derivative has eluded discovery for many years. This is likely a result of integral definitions including numerous constants of integration in their results. An elimination of constants of integration opens the door to an operator that reconciles all known fractional derivatives and shows surprising results in areas unobserved before, including the appearance of the Riemann Zeta Function and fractional Laplace and Fourier Transforms. A new class of functions, known as Zero Functions and closely related to the Dirac Delta Function, are necessary for one to perform elementary operations of functions without using constants. The operator also allows for a generalization of the Volterra integral equation, and provides a method of solving for Riemann's "complimentary" function introduced during his research on fractional derivatives

Flow diagram describing literature search and selection of studies (PRISMA 2009 flow chart).

<p>Flow diagram describing literature search and selection of studies (PRISMA 2009 flow chart).</p

Sero-epidemiological studies using Ag-ELISA and/or EITB for human cysticercosis in Asia.

<p>Legend: YOP: Year of publication; Location: Corresponds to the Province, State, Region or Department in which the communities are located where the studies took place; Ag: Antigen detection based on Ag-ELISA results; Ab: Antibody detection based on EITB results; 95% CI: 95% Confidence Intervals; REMEP: Random Effects Model Estimated Prevalence</p><p>^a: Results obtained from B158/B60 Ag-ELISA</p><p>Sero-epidemiological studies using Ag-ELISA and/or EITB for human cysticercosis in Asia.</p

Sero-epidemiological studies using Ag-ELISA and/or EITB for human cysticercosis in Africa.

<p>Legend: YOP: Year of publication; Location: Corresponds to the Province, State, Region or Department in which the communities where the studies took place are located; Ag: Antigen detection based on Ag-ELISA results; Ab: Antibody detection based on EITB results; 95% CI: 95% Confidence Intervals; REMEP: Random Effects Model Estimated Prevalence; Dem. Rep. of Congo: Democratic Republic of Congo.</p><p>^a: Results obtained from B158/B60 Ag-ELISA</p><p>^b: Results obtained from HP10 Ag-ELISA.</p><p>Sero-epidemiological studies using Ag-ELISA and/or EITB for human cysticercosis in Africa.</p

Global distribution of the endemic countries where Ag-ELISA and/or EITB based epidemiological studies were held.

<p>Light yellow represents the countries confirmed as endemic by the World Health Organization (WHO) until 2012 [<a href="http://www.plosntds.org/article/info:doi/10.1371/journal.pntd.0003919#pntd.0003919.ref066" target="_blank">66</a>]. Circles represent the countries where Ag-ELISA based studies took place. Each color represents the average prevalence per country found from the selected articles in this review classified in 0 to 5 percent; 5 to 10 percent and more than 10 percent. Triangles represent the countries where EITB based studies took place. Each color represents the average prevalence per country found from the selected articles in this review classified in 0 to 5 percent; 5 to 10 percent and more than 10 percent.</p

Factors affecting serological variations of human cysticercosis infection and exposure to <i>T</i>. <i>solium</i> eggs.

<p>Factors affecting serological variations of human cysticercosis infection and exposure to <i>T</i>. <i>solium</i> eggs.</p

Sero-epidemiological studies using Ag-ELISA and/or EITB for human cysticercosis in Latin America.

<p>Legend: YOP: Year of publication; Location: Corresponds to the Province, State, Region or Department in which the communities are located where the studies took place; Ag: Antigen detection based on Ag-ELISA results; Ab: Antibody detection based on EITB results; 95% CI: 95% Confidence Intervals; REMEP: Random Effects Model Estimated Prevalence</p><p>^a: Results obtained from B158/B60 Ag-ELISA</p><p>^b: Results obtained from HP10 Ag-ELISA</p><p>N.A.: Not available.</p><p>Sero-epidemiological studies using Ag-ELISA and/or EITB for human cysticercosis in Latin America.</p

data_sheet_1.xlsx

<p>The increasing occurrence of human cysticercosis, a zoonotic neglected disease, is challenging the traditional prevention and control paradigm and calling for One Health (OH) solutions in industrialized countries. OH solutions for health interventions are increasingly being used to capture expected and unexpected outcomes across people, animals, and the environment. The Network for Evaluation of One Health (NEOH) proposes an evidence-based framework, relying on systems and mixed methods approaches to evaluate the One Health-ness. In this case study, this tool is used to evaluate the design of the Observatory of Taeniasis and Cysticercosis, as an example of intersectorial collaboration for surveillance in Portugal. The OH Initiative (drivers and expected outcomes) and its system (boundaries, aim, dimensions, actors, and stakeholders) were described. The different aspects of this Initiative were scored with values from 0 (=no OH approach) to 1 (=perfect OH approach). The OH index was 0.31. Its OH ratio is 1.98. Overall scores were as follows: OH thinking 0.75; OH planning 0.60; OH working 0.60; OH sharing 0.35; OH learning 0.50; and systemic organization 0.50. Operational levels of the Initiative are the main strengths, indicating a comprehensive multidimensional innovative approach and transdisciplinarity. Critical issues in the supporting infrastructure were observed, related to communication, learning and organizational gaps in the project, with the evaluation being conducted as the project is being designed and implemented. The strengths and weaknesses detected may be used to refine the Initiative. This case study therefore exemplifies and supports OH assessment also for ongoing projects, at design and early implementation stages for guiding and guaranteeing an OH-oriented perspective.</p

Taeniasis reports from Africa, Latin America and Asia.

<p>Legend: FECT: Formalin-ether concentration technique; KATO: Kato-Katz technique; MSFT: Magnesium sulphate flotation technique; PCR-RFLP: Polymerase chain reaction-restriction fragment length polymorphism; ELISA: Enzyme-Linked Immunosorbent Assay; Copro-Ag ELISA: Coproantigen ELISA; EITB: Enzyme-linked Immunoelectrotransfer Blot; Dem. Rep. of Congo: Democratic Republic of Congo.</p><p>^a: Fecal samples were provided voluntarily from participants when not specified otherwise</p><p>*: One sided 97.5% confidence interval</p><p>**: Technique applied in fecal samples from seropositive subjects for <i>T</i>. <i>solium</i> antibodies or circulating antigens</p><p>Coprology†: Technique not defined</p><p>Taeniasis reports from Africa, Latin America and Asia.</p

Seroconversion rates of human cysticercosis in function of sex for both circulating antigen and specific antibody analyses.

<p>P1 stands for period 1 (between Round 1 and Round 2, 6 months), P2 for period 2 (between Round 2 and 3, 6 months) and P3 for period 3 (between Round 1 and 3, 12 months). Ag-ELISA: detection of circulating cysticercus antigen in serum; EITB: detection of specific antibodies in serum.</p