Why 'scaffolding' is the wrong metaphor : the cognitive usefulness of mathematical representations.

The metaphor of scaffolding has become current in discussions of the cognitive help we get from artefacts, environmental affordances and each other. Consideration of mathematical tools and representations indicates that in these cases at least (and plausibly for others), scaffolding is the wrong picture, because scaffolding in good order is immobile, temporary and crude. Mathematical representations can be manipulated, are not temporary structures to aid development, and are refined. Reflection on examples from elementary algebra indicates that Menary is on the right track with his ‘enculturation’ view of mathematical cognition. Moreover, these examples allow us to elaborate his remarks on the uniqueness of mathematical representations and their role in the emergence of new thoughts.Peer reviewe

From Euclidean Geometry to Knots and Nets

This document is the Accepted Manuscript of an article accepted for publication in Synthese. Under embargo until 19 September 2018. The final publication is available at Springer via https://doi.org/10.1007/s11229-017-1558-x.This paper assumes the success of arguments against the view that informal mathematical proofs secure rational conviction in virtue of their relations with corresponding formal derivations. This assumption entails a need for an alternative account of the logic of informal mathematical proofs. Following examination of case studies by Manders, De Toffoli and Giardino, Leitgeb, Feferman and others, this paper proposes a framework for analysing those informal proofs that appeal to the perception or modification of diagrams or to the inspection or imaginative manipulation of mental models of mathematical phenomena. Proofs relying on diagrams can be rigorous if (a) it is easy to draw a diagram that shares or otherwise indicates the structure of the mathematical object, (b) the information thus displayed is not metrical and (c) it is possible to put the inferences into systematic mathematical relation with other mathematical inferential practices. Proofs that appeal to mental models can be rigorous if the mental models can be externalised as diagrammatic practice that satisfies these three conditions.Peer reviewe

Quantum lattice gases and their invariants

The one particle sector of the simplest one dimensional quantum lattice gas automaton has been observed to simulate both the (relativistic) Dirac and (nonrelativistic) Schroedinger equations, in different continuum limits. By analyzing the discrete analogues of plane waves in this sector we find conserved quantities corresponding to energy and momentum. We show that the Klein paradox obtains so that in some regimes the model must be considered to be relativistic and the negative energy modes interpreted as positive energy modes of antiparticles. With a formally similar approach--the Bethe ansatz--we find the evolution eigenfunctions in the two particle sector of the quantum lattice gas automaton and conclude by discussing consequences of these calculations and their extension to more particles, additional velocities, and higher dimensions.Comment: 19 pages, plain TeX, 11 PostScript figures included with epsf.tex (ignore the under/overfull \vbox error messages

Current Trends in Urinary Diversion in Men

Prior to the introduction of the ileal conduit more than four decades ago, the options for urinary diversion after cystectomy were extremely limited. Direct cutaneous anastomoses of the collecting system (cutaneous pyelostomies, ureterostomies) offered patients a short-term diversion, but the benefits were outweighed by significant complications: recession or stenosis of the stoma. The first choice of diversion was the ureterosigmoidostomy with or without antireflux technique. Then it fell in popularity and was replaced with continent/non-continent uretero-ileo-cutaneous diversions. Only in the last years the continent orthotopic neobladder has been widely employed as first procedure choice. At present, patients can be offered a non-continent cutaneous diversion, a continent cutaneous diversion or an orthotopic neobladder urinary reconstructio

AI-based Ecological Monitoring of Handwriting to Early Detect Cognitive Decline

The early detection of Mild Cognitive Impairment (MCI) is fundamental to initiate treatments for delaying the onset of dementia. Currently, the Mini Mental State Examination (MMSE) is one of the most common clinical scales used by geriatricians to assess cognitive function. A deviation of 1 to 3 points from the maximum score (30) is considered as sign of relevant cognitive decline. However, objective and affordable tools are needed to complement the screening process. The quantitative analysis of handwriting represents a suitable solution, as the gesture is significantly impaired in MCI subjects in terms of time, speed, fluency and applied pressure. This works presents the development and testing of classification models able to separate subjects at risk of cognitive decline (MMSE <= 28) from controls (MMSE > 28), starting from free-content handwriting data acquired with a smart ink pen, used on paper, from which 36 indicators were computed. Data were collected in 2 phases. The former involved 45 subjects and served for models training. In the latter, data were acquired from 23 subjects in a domestic longitudinal framework and were partially used for model refinement, but mainly for testing. Three different algorithms were tried (support vector machine, random forest and Catboost) The best test performances on the longitudinal data were obtained by a Catboost classifier, achieving accuracy 93.33%, precision 88.89%, recall 100% and f1 score 94.12%. The results support the use of computerized handwriting analysis as screening tool for cognitive decline detection

Density Functional Theory for the Photoionization Dynamics of Uracil

Photoionization dynamics of the RNA base Uracil is studied in the framework of Density Functional Theory (DFT). The photoionization calculations take advantage of a newly developed parallel version of a multicentric approach to the calculation of the electronic continuum spectrum which uses a set of B-spline radial basis functions and a Kohn-Sham density functional hamiltonian. Both valence and core ionizations are considered. Scattering resonances in selected single-particle ionization channels are classified by the symmetry of the resonant state and the peak energy position in the photoelectron kinetic energy scale; the present results highlight once more the site specificity of core ionization processes. We further suggest that the resonant structures previously characterized in low-energy electron collision experiments are partly shifted below threshold by the photoionization processes. A critical evaluation of the theoretical results providing a guide for future experimental work on similar biosystems

Collaborative Computation in Self-Organizing Particle Systems

Many forms of programmable matter have been proposed for various tasks. We use an abstract model of self-organizing particle systems for programmable matter which could be used for a variety of applications, including smart paint and coating materials for engineering or programmable cells for medical uses. Previous research using this model has focused on shape formation and other spatial configuration problems (e.g., coating and compression). In this work we study foundational computational tasks that exceed the capabilities of the individual constant size memory of a particle, such as implementing a counter and matrix-vector multiplication. These tasks represent new ways to use these self-organizing systems, which, in conjunction with previous shape and configuration work, make the systems useful for a wider variety of tasks. They can also leverage the distributed and dynamic nature of the self-organizing system to be more efficient and adaptable than on traditional linear computing hardware. Finally, we demonstrate applications of similar types of computations with self-organizing systems to image processing, with implementations of image color transformation and edge detection algorithms

A Two-Player Game of Life

We present a new extension of Conway's game of life for two players, which we call p2life. P2life allows one of two types of token, black or white, to inhabit a cell, and adds competitive elements into the birth and survival rules of the original game. We solve the mean-field equation for p2life and determine by simulation that the asymptotic density of p2life approaches 0.0362.Comment: 7 pages, 3 figure

Directional Soliton and Breather Beams

Solitons and breathers are nonlinear modes that exist in a wide range of physical systems. They are fundamental solutions of a number of nonlinear wave evolution equations, including the uni-directional nonlinear Schr\"odinger equation (NLSE). We report the observation of slanted solitons and breathers propagating at an angle with respect to the direction of propagation of the wave field. As the coherence is diagonal, the scale in the crest direction becomes finite, consequently, a beam dynamics forms. Spatio-temporal measurements of the water surface elevation are obtained by stereo-reconstructing the positions of the floating markers placed on a regular lattice and recorded with two synchronized high-speed cameras. Experimental results, based on the predictions obtained from the (2D+1) hyperbolic NLSE equation, are in excellent agreement with the theory. Our study proves the existence of such unique and coherent wave packets and has serious implications for practical applications in optical sciences and physical oceanography. Moreover, unstable wave fields in this geometry may explain the formation of directional large amplitude rogue waves with a finite crest length within a wide range of nonlinear dispersive media, such as Bose-Einstein condensates, plasma, hydrodynamics and optics

Sex disparities in efficacy in covid-19 vaccines: A systematic review and meta-analysis

Sex differences in adaptive and innate immune responses have been shown to occur and anecdotal reports suggest that vaccine efficacy and safety may be sex-dependent. We investigated the influence of sex on the efficacy of COVID-19 vaccines through a systematic review and meta-analysis of clinical trials on COVID-19 vaccines. The safety profile of COVID-19 vaccines was also investigated. A systematic review included eligible articles published in three databases and three websites. A meta-analysis of available data, stratified by sex, was conducted. Statistical analysis was performed using the Hartung\u2013Knapp\u2013Sidik\u2013Jonkman method, as well as influence and heterogeneity analysis. Pooled analysis showed significantly higher efficacy, measured as the rate of new COVID-19 cases, in men compared to women in the vaccine group (OR = 0.67, 95% CI 0.48\u20130.94). No sex differences were found in the rate of new cases in the control group (OR = 0.92, 95% CI 0.78\u20131.09). Safety profiles derived from pharmacovigilance reports appear to indicate increased toxicity in women. In conclusion, evidence of a potential role of sex in COVID-19 vaccine efficacy was described. It strengthens the need to include sex as a core variable in the clinical trial design of COVID-19 vaccines