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

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

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

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

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

Driving vascular endothelial cell fate of human multipotent Isl1+ heart progenitors with VEGF modified mRNA

Distinct families of multipotent heart progenitors play a central role in the generation of diverse cardiac, smooth muscle and endothelial cell lineages during mammalian cardiogenesis. The identification of precise paracrine signals that drive the cell-fate decision of these multipotent progenitors, and the development of novel approaches to deliver these signals in vivo, are critical steps towards unlocking their regenerative therapeutic potential. Herein, we have identified a family of human cardiac endothelial intermediates located in outflow tract of the early human fetal hearts (OFT-ECs), characterized by coexpression of Isl1 and CD144/vWF. By comparing angiocrine factors expressed by the human OFT-ECs and non-cardiac ECs, vascular endothelial growth factor (VEGF)-A was identified as the most abundantly expressed factor, and clonal assays documented its ability to drive endothelial specification of human embryonic stem cell (ESC)-derived Isl1+ progenitors in a VEGF receptor-dependent manner. Human Isl1-ECs (endothelial cells differentiated from hESC-derived ISL1+ progenitors) resemble OFT-ECs in terms of expression of the cardiac endothelial progenitor- and endocardial cell-specific genes, confirming their organ specificity. To determine whether VEGF-A might serve as an in vivo cell-fate switch for human ESC-derived Isl1-ECs, we established a novel approach using chemically modified mRNA as a platform for transient, yet highly efficient expression of paracrine factors in cardiovascular progenitors. Overexpression of VEGF-A promotes not only the endothelial specification but also engraftment, proliferation and survival (reduced apoptosis) of the human Isl1+ progenitors in vivo. The large-scale derivation of cardiac-specific human Isl1-ECs from human pluripotent stem cells, coupled with the ability to drive endothelial specification, engraftment, and survival following transplantation, suggest a novel strategy for vascular regeneration in the heart

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

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