Thermodynamic curvature measures interactions

Thermodynamic fluctuation theory originated with Einstein who inverted the relation $S=k_B\ln\Omega$ to express the number of states in terms of entropy: $\Omega= \exp(S/k_B)$. The theory's Gaussian approximation is discussed in most statistical mechanics texts. I review work showing how to go beyond the Gaussian approximation by adding covariance, conservation, and consistency. This generalization leads to a fundamentally new object: the thermodynamic Riemannian curvature scalar $R$, a thermodynamic invariant. I argue that $|R|$ is related to the correlation length and suggest that the sign of $R$ corresponds to whether the interparticle interactions are effectively attractive or repulsive.Comment: 29 pages, 7 figures (added reference 27

Stevin numbers and reality

We explore the potential of Simon Stevin's numbers, obscured by shifting foundational biases and by 19th century developments in the arithmetisation of analysis.Comment: 22 pages, 4 figures. arXiv admin note: text overlap with arXiv:1104.0375, arXiv:1108.2885, arXiv:1108.420

Augmented Reality for People with Visual Impairments: Designing and Creating Audio-Tactile Content from Existing Objects

ISBN: 978-3-319-94273-5International audienceTactile maps and diagrams are widely used as accessible graphical media for people with visual impairments, in particular in the context of education. They can be made interactive by augmenting them with audio feedback. It is however complicated to create audio-tactile graphics that have rich and realistic tactile textures. To overcome these limitations, we propose a new augmented reality approach allowing novices to easily and quickly augment real objects with audio feedback. In our user study, six teachers created their own audio-augmentation of objects, such as a botanical atlas, within 30 minutes or less. Teachers found the tool easy to use and were confident about re-using it. The resulting augmented objects allow two modes: exploration mode provides feedback on demand about an element, while quiz mode provides questions and answers. We evaluated the resulting audio-tactile material with five visually impaired children. Participants found the resulting interactive graphics exciting to use independently of their mental imagery skills

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

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

A Burgessian critique of nominalistic tendencies in contemporary mathematics and its historiography

We analyze the developments in mathematical rigor from the viewpoint of a Burgessian critique of nominalistic reconstructions. We apply such a critique to the reconstruction of infinitesimal analysis accomplished through the efforts of Cantor, Dedekind, and Weierstrass; to the reconstruction of Cauchy's foundational work associated with the work of Boyer and Grabiner; and to Bishop's constructivist reconstruction of classical analysis. We examine the effects of a nominalist disposition on historiography, teaching, and research.Comment: 57 pages; 3 figures. Corrected misprint

A functional analysis of haptic feedback in digital musical instrument interactions

An experiment is presented that measured aspects of functionality, usability and user experience for four distinct types of device feedback. The goal was to analyse the role of haptic feedback in functional digital musical instrument (DMI) interactions. Quantitative and qualitative human–computer interaction analysis techniques were applied in the assessment of prototype DMIs that displayed unique elements of haptic feedback; specifically, full haptic (constant-force and vibrotactile) feedback, constant-force only, vibrotactile only and no feedback. From the analysis, data are presented that comprehensively quantify the effects of feedback in haptic interactions with DMI devices. The investigation revealed that the various types of haptic feedback applied had no significant functional effect upon device performance in pitch selection tasks; however, a number of significant effects were found upon the users’ perception of usability and their experiences with each of the different feedback types

Thermodynamic curvature and black holes

I give a relatively broad survey of thermodynamic curvature $R$, one spanning results in fluids and solids, spin systems, and black hole thermodynamics. $R$ results from the thermodynamic information metric giving thermodynamic fluctuations. $R$ has a unique status in thermodynamics as being a geometric invariant, the same for any given thermodynamic state. In fluid and solid systems, the sign of $R$ indicates the character of microscopic interactions, repulsive or attractive. $|R|$ gives the average size of organized mesoscopic fluctuating structures. The broad generality of thermodynamic principles might lead one to believe the same for black hole thermodynamics. This paper explores this issue with a systematic tabulation of results in a number of cases.Comment: 27 pages, 10 figures, 7 tables, 78 references. Talk presented at the conference Breaking of Supersymmetry and Ultraviolet Divergences in extended Supergravity, in Frascati, Italy, March 27, 2013. v2 corrects some small problem

Pathogenic variants in SQOR encoding sulfide:quinone oxidoreductase are a potentially treatable cause of Leigh disease

Hydrogen sulfide, a signaling molecule formed mainly from cysteine, is catabolized by sulfide:quinone oxidoreductase (gene SQOR). Toxic hydrogen sulfide exposure inhibits complex IV. We describe children of two families with pathogenic variants in SQOR. Exome sequencing identified variants; SQOR enzyme activity was measured spectrophotometrically, protein levels evaluated by western blotting, and mitochondrial function was assayed. In family A, following a brief illness, a 4- year- old girl presented comatose with lactic acidosis and multiorgan failure. After stabilization, she remained comatose, hypotonic, had neurostorming episodes, elevated lactate, and Leigh- like lesions on brain imaging. She died shortly after. Her 8- year- old sister presented with a rapidly fatal episode of coma with lactic acidosis, and lesions in the basal ganglia and left cortex. Muscle and liver tissue had isolated decreased complex IV activity, but normal complex IV protein levels and complex formation. Both patients were homozygous for c.637G- >- A, which we identified as a founder mutation in the Lehrerleut Hutterite with a carrier frequency of 1 in 13. The resulting p.Glu213Lys change disrupts hydrogen bonding with neighboring residues, resulting in severely reduced SQOR protein and enzyme activity, whereas sulfide generating enzyme levels were unchanged. In family B, a boy had episodes of encephalopathy and basal ganglia lesions. He was homozygous for c.446delT and had severely reduced fibroblast SQOR enzyme activity and protein levels. SQOR dysfunction can result in hydrogen sulfide accumulation, which, consistent with its known toxicity, inhibits complex IV resulting in energy failure. In conclusion, SQOR deficiency represents a new, potentially treatable, cause of Leigh disease.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/162807/2/jimd12232.pdfhttp://deepblue.lib.umich.edu/bitstream/2027.42/162807/1/jimd12232_am.pd