Comparative study between powers of sigmoid functions, MLP-backpropagation and polynomials in function approximation problems

Function approximation is a very important task in environments where the computation has to be based on extracting information from data samples in real world processes. So, the development of new mathematical model is a very important activity to guarantee the evolution of the function approximation area. In this sense, we will present the Polynomials Powers of Sigmoid (PPS) as a linear neural network. In this paper, we will introduce one series of practical results for the Polynomials Powers of Sigmoid, where we will show some advantages of the use of the powers of sigmiod functions in relationship the traditional MLP-Backpropagation and Polynomials in functions approximation problems.

Enduring effects of evidence-based psychotherapies in acute depression and anxiety disorders versus treatment as usual at follow-up — A longitudinal meta-analysis

This meta-analysis examined the enduring efficacy of evidence-based psychotherapies (EBP) in comparison to treatment as usual (TAU) by examining effects from termination to follow-up for acute anxiety and depression in an adult outpatient population. It was hypothesized that EBPs might extend their efficacy at follow-up assessment (Tolin, 2010). METHOD: Longitudinal multilevel meta-analyses were conducted that examined the magnitude of difference between EBP and TAU. Targeted (disorder-specific) outcomes were examined, along with dropout rates at follow-up assessments. RESULTS: A total of 15 comparisons (including 30 repeated effect sizes [ES]) were included in this meta-analysis (average of 8.9 month follow-up). Small to moderate ES differences were found to be in favor of EBPs at 0-4 month assessments (Hedges' g=0.40) and up to 12-18 month assessments (g=0.20), indicating no extended efficacy at follow-up. However, the TAU-conditions were heterogeneous, ranging from absence of minimal mental health treatment to legitimate psychotherapeutic interventions provided by trained professionals, the latter of which resulted in smaller ES differences. Furthermore, samples where substance use comorbidities were not actively excluded indicated smaller ES differences. TAU-conditions produced slightly higher dropout rates than EBP-conditions. CONCLUSION: Findings indicate small and no extended superiority of EBP for acute depression and anxiety disorders in comparison to TAU at follow-up assessment. There are a limited number of studies investigating the transportability and lasting efficacy of EBP compared to TAU, especially to TAU with equivalent conditions between treatment groups.

The enduring effects of psychodynamic treatments vis-à-vis alternative treatments: A multilevel longitudinal meta-analysis

Although evidence suggests that the benefits of psychodynamic treatments are sustained over time, presently it is unclear whether these sustained benefits are superior to non-psychodynamic treatments. Additionally, the extant literature comparing the sustained benefits of psychodynamic treatments compared to alternative treatments is limited with methodological shortcomings. The purpose of the current study was to conduct a rigorous test of the growth of the benefits of psychodynamic treatments relative to alternative treatments across distinct domains of change (i.e., all outcome measures, targeted outcome measures, non-targeted outcome measures, and personality outcome measures). To do so, the study employed strict inclusion criteria to identify randomized clinical trials that directly compared at least one bona fide psychodynamic treatment and one bona fide non-psychodynamic treatment. Hierarchical linear modeling (Raudenbush, Bryk, Cheong, Congdon, & du Toit, 2011) was used to longitudinally model the impact of psychodynamic treatments compared to non-psychodynamic treatments at post-treatment and to compare the growth (i.e., slope) of effects beyond treatment completion. Findings from the present meta-analysis indicated that psychodynamic treatments and non-psychodynamic treatments were equally efficacious at post-treatment and at follow-up for combined outcomes (k=20), targeted outcomes (k=19), non-targeted outcomes (k=17), and personality outcomes (k=6). Clinical implications, directions for future research, and limitations are discussed.

Power of attorney for Joseph Chip, 1804 December 21

Handwritten draft of a power of attorney, in Croswell's hand, authorizing John Jones to act for mariner Joseph Chip.

Power of Attorney, [?] Wellington for Thomas Durant, Sept. 22, 1787

Signed by Thomas Durant and witnessed by Ebenezer Bradish. It is possible that Shapleigh used this document as a guide when drafting his own power of attorney documents.

Power of Attorney, Samuel Shapleigh for Thomas Adams, Jan. 12, 1791

Signed by Thomas Adams and witnessed by Abraham Biglow and Daniel Clarke Sanders.

Power of Attorney, Samuel Shapleigh for James Otis Prentiss, Aug. 18, 1791

Document also contains what appears to be a bill for medical services rendered by Prentiss, a doctor, to William Boman.

[Power of attorney between Stephen Sewall and Thomas Wigglesworth], 1794 August 21

This one-page printed form appoints Thomas Wigglesworth as the "true and lawful Attorney" for Stephen Sewall. The form is notarized by Samuel Barrett and witnessed by Barrett and his daughter Peggy Barrett.

Power of Attorney, Samuel Shapleigh for Thomas Thompson, May 18, 1791

Signed by Thomas Thompson and witnessed by Thaddeus Mason Harris and Otis(?) Clarke.

Power of attorney for Thomas Whippo, 1798 October 10

A handwritten translation of a power of attorney, on two folio-sized leaves, certified by Francis Sales and dated October 10, 1798. The power of attorney authorizes Isaac Whippo, an American citizen living in Bordeaux, France to act as the attorney general and special for his brother, Thomas Whippo, also an American citizen and captain of the ship the Ganges of New York. The power of attorney was created in the Office of Gabriel Duprat in Bordeaux, with William Henry Vernon translating for Thomas Whippo and was notarized by Joseph Fenwick, Consol of the United States of America on April 14, 1798.