Palindromic complexity of trees

We consider finite trees with edges labeled by letters on a finite alphabet $\varSigma$. Each pair of nodes defines a unique labeled path whose trace is a word of the free monoid $\varSigma^*$. The set of all such words defines the language of the tree. In this paper, we investigate the palindromic complexity of trees and provide hints for an upper bound on the number of distinct palindromes in the language of a tree.Comment: Submitted to the conference DLT201

Long Wave Infrared Type II Superlattice Focal Plane Array Detector

The XBn/XBp family of barrier detectors enables diffusion limited dark currents comparable with HgxCd1-xTe Rule-07 and high quantum efficiencies. SCD’s XBp type II superlattice (T2SL) detector contains InAs/GaSb and InAs/AlSb T2SLs, and was designed for the long wave infrared (LWIR) atmospheric window using k · p based modeling of the energy bands and photo-response. Wafers are grown by molecular beam epitaxy and are fabricated into focal plane array (FPA) detectors using standard FPA processes, including wet and dry etching, indium bump hybridisation, under-fill, and back-side polishing. The 640 × 512 pixel, 15 μm pitch, detector goes by the name of ‘Pelican-D LW’ and exhibits a quantum efficiency of ~ 50 per cent with background limited performance at an operating temperature of 77 K. It has a cut-off wave length of ~ 9.5 μm, with a pixel operability of above 99 per cent. The detector gives a very stable image with a residual non uniformity of below 0.04 per cent over its useful dynamic range. A new digital read-out integrated circuit has been designed so that the complete detector closely follows the configuration of SCD’s MWIR Pelican-D detector

Benefit from preoperative radiotherapy in rectal cancer treatment: disease-free patients' and oncologists' preferences

Preoperative radiotherapy (PRT) in resectable rectal cancer improves local control but increases probability of faecal incontinence and sexual dysfunction. Consensus was reached in 2001 in the Netherlands on a guideline advising PRT to new patients. Purpose was to assess at what benefit oncologists and rectal cancer patients prefer PRT followed by surgery to surgery alone, and how oncologists and patients value various treatment outcomes. Sixty-six disease-free patients and 60 oncologists (surgical, radiation, medical) were interviewed. Minimally desired benefit from PRT (local control) was assessed using the Treatment Tradeoff Method. Importance of survival, local control, faecal incontinence, and sexual dysfunction in determining treatment outcome preferences was assessed using Adaptive Conjoint Analysis. The range of required benefit from PRT varied widely within participant groups. Seventeen percent of patients would choose PRT at a 0% benefit; 11% would not choose PRT for the maximum benefit of 11%. Mean minimally desired benefit excluding these two groups was 4%. For oncologists, the required benefit was 5%. Also, how strongly participants valued treatment outcomes varied widely within groups. Of the four outcomes, participants considered incontinence most often as most important. Relative treatment outcome importance differed between specialties. Patients considered sexual functioning more important than oncologists. Large differences in treatment preferences exist between individual patients and oncologists. Oncologists should adequately inform their patients about the risks and benefits of PRT, and elicit patient preferences regarding treatment outcomes

Individualized decision aid for diverse women with lupus nephritis (IDEA-WON): A randomized controlled trial.

BackgroundTreatment decision-making regarding immunosuppressive therapy is challenging for individuals with lupus. We assessed the effectiveness of a decision aid for immunosuppressive therapy in lupus nephritis.Methods and findingsIn a United States multicenter, open-label, randomized controlled trial (RCT), adult women with lupus nephritis, mostly from racial/ethnic minority backgrounds with low socioeconomic status (SES), seen in in- or outpatient settings, were randomized to an individualized, culturally tailored, computerized decision aid versus American College of Rheumatology (ACR) lupus pamphlet (1:1 ratio), using computer-generated randomization. We hypothesized that the co-primary outcomes of decisional conflict and informed choice regarding immunosuppressive medications would improve more in the decision aid group. Of 301 randomized women, 298 were analyzed; 47% were African-American, 26% Hispanic, and 15% white. Mean age (standard deviation [SD]) was 37 (12) years, 57% had annual income of <$40,000, and 36% had a high school education or less. Compared with the provision of the ACR lupus pamphlet (n = 147), participants randomized to the decision aid (n = 151) had (1) a clinically meaningful and statistically significant reduction in decisional conflict, 21.8 (standard error [SE], 2.5) versus 12.7 (SE, 2.0; p = 0.005) and (2) no difference in informed choice in the main analysis, 41% versus 31% (p = 0.08), but clinically meaningful and statistically significant difference in sensitivity analysis (net values for immunosuppressives positive [in favor] versus negative [against]), 50% versus 35% (p = 0.006). Unresolved decisional conflict was lower in the decision aid versus pamphlet groups, 22% versus 44% (p < 0.001). Significantly more patients in the decision aid versus pamphlet group rated information to be excellent for understanding lupus nephritis (49% versus 33%), risk factors (43% versus 27%), medication options (50% versus 33%; p ≤ 0.003 for all); and the ease of use of materials was higher in the decision aid versus pamphlet groups (51% versus 38%; p = 0.006). Key study limitations were the exclusion of men, short follow-up, and the lack of clinical outcomes, including medication adherence.ConclusionsAn individualized decision aid was more effective than usual care in reducing decisional conflict for choice of immunosuppressive medications in women with lupus nephritis.Trial registrationClinicaltrials.gov, NCT02319525

A Cauchy-Dirac delta function

The Dirac delta function has solid roots in 19th century work in Fourier analysis and singular integrals by Cauchy and others, anticipating Dirac's discovery by over a century, and illuminating the nature of Cauchy's infinitesimals and his infinitesimal definition of delta.Comment: 24 pages, 2 figures; Foundations of Science, 201

Leibniz's Infinitesimals: Their Fictionality, Their Modern Implementations, And Their Foes From Berkeley To Russell And Beyond

Many historians of the calculus deny significant continuity between infinitesimal calculus of the 17th century and 20th century developments such as Robinson's theory. Robinson's hyperreals, while providing a consistent theory of infinitesimals, require the resources of modern logic; thus many commentators are comfortable denying a historical continuity. A notable exception is Robinson himself, whose identification with the Leibnizian tradition inspired Lakatos, Laugwitz, and others to consider the history of the infinitesimal in a more favorable light. Inspite of his Leibnizian sympathies, Robinson regards Berkeley's criticisms of the infinitesimal calculus as aptly demonstrating the inconsistency of reasoning with historical infinitesimal magnitudes. We argue that Robinson, among others, overestimates the force of Berkeley's criticisms, by underestimating the mathematical and philosophical resources available to Leibniz. Leibniz's infinitesimals are fictions, not logical fictions, as Ishiguro proposed, but rather pure fictions, like imaginaries, which are not eliminable by some syncategorematic paraphrase. We argue that Leibniz's defense of infinitesimals is more firmly grounded than Berkeley's criticism thereof. We show, moreover, that Leibniz's system for differential calculus was free of logical fallacies. Our argument strengthens the conception of modern infinitesimals as a development of Leibniz's strategy of relating inassignable to assignable quantities by means of his transcendental law of homogeneity.Comment: 69 pages, 3 figure

Ten Misconceptions from the History of Analysis and Their Debunking

The widespread idea that infinitesimals were "eliminated" by the "great triumvirate" of Cantor, Dedekind, and Weierstrass is refuted by an uninterrupted chain of work on infinitesimal-enriched number systems. The elimination claim is an oversimplification created by triumvirate followers, who tend to view the history of analysis as a pre-ordained march toward the radiant future of Weierstrassian epsilontics. In the present text, we document distortions of the history of analysis stemming from the triumvirate ideology of ontological minimalism, which identified the continuum with a single number system. Such anachronistic distortions characterize the received interpretation of Stevin, Leibniz, d'Alembert, Cauchy, and others.Comment: 46 pages, 4 figures; Foundations of Science (2012). arXiv admin note: text overlap with arXiv:1108.2885 and arXiv:1110.545