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

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

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

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

An Inquiry into the Practice of Proving in Low-Dimensional Topology

The aim of this article is to investigate specific aspects connected with visualization in the practice of a mathematical subfield: low-dimensional topology. Through a case study, it will be established that visualization can play an epistemic role. The background assumption is that the consideration of the actual practice of mathematics is relevant to address epistemological issues. It will be shown that in low-dimensional topology, justifications can be based on sequences of pictures. Three theses will be defended. First, the representations used in the practice are an integral part of the mathematical reasoning. As a matter of fact, they convey in a material form the relevant transitions and thus allow experts to draw inferential connections. Second, in low-dimensional topology experts exploit a particular type of manipulative imagination which is connected to intuition of two- and three-dimensional space and motor agency. This imagination allows recognizing the transformations which connect different pictures in an argument. Third, the epistemic—and inferential—actions performed are permissible only within a specific practice: this form of reasoning is subject-matter dependent. Local criteria of validity are established to assure the soundness of representationally heterogeneous arguments in low-dimensional topology

Multi-valued Logic Gates for Quantum Computation

We develop a multi-valued logic for quantum computing for use in multi-level quantum systems, and discuss the practical advantages of this approach for scaling up a quantum computer. Generalizing the methods of binary quantum logic, we establish that arbitrary unitary operations on any number of d-level systems (d > 2) can be decomposed into logic gates that operate on only two systems at a time. We show that such multi-valued logic gates are experimentally feasible in the context of the linear ion trap scheme for quantum computing. By using d levels in each ion in this scheme, we reduce the number of ions needed for a computation by a factor of log d.Comment: Revised version; 8 pages, 3 figures; to appear in Physical Review

CDK4/6 Inhibitors in Breast Cancer Treatment: Potential Interactions with Drug, Gene, and Pathophysiological Conditions

Palbociclib, ribociclib, and abemaciclib belong to the third generation of cyclin-dependent kinases inhibitors (CDKis), an established therapeutic class for advanced and metastatic breast cancer. Interindividual variability in the therapeutic response of CDKis has been reported and some individuals may experience increased and unexpected toxicity. This narrative review aims at identifying the factors potentially concurring at this variability for driving the most appropriate and tailored use of CDKis in the clinic. Specifically, concomitant medications, pharmacogenetic profile, and pathophysiological conditions could influence absorption, distribution, metabolism, and elimination pharmacokinetics. A personalized therapeutic approach taking into consideration all factors potentially contributing to an altered pharmacokinetic/pharmacodynamic profile could better drive safe and effective clinical use

The Effect Of Microscopic Correlations On The Information Geometric Complexity Of Gaussian Statistical Models

We present an analytical computation of the asymptotic temporal behavior of the information geometric complexity (IGC) of finite-dimensional Gaussian statistical manifolds in the presence of microcorrelations (correlations between microvariables). We observe a power law decay of the IGC at a rate determined by the correlation coefficient. It is found that microcorrelations lead to the emergence of an asymptotic information geometric compression of the statistical macrostates explored by the system at a faster rate than that observed in absence of microcorrelations. This finding uncovers an important connection between (micro)-correlations and (macro)-complexity in Gaussian statistical dynamical systems.Comment: 12 pages; article in press, Physica A (2010)

Constructing Qubits in Physical Systems

The notion of a qubit is ubiquitous in quantum information processing. In spite of the simple abstract definition of qubits as two-state quantum systems, identifying qubits in physical systems is often unexpectedly difficult. There are an astonishing variety of ways in which qubits can emerge from devices. What essential features are required for an implementation to properly instantiate a qubit? We give three typical examples and propose an operational characterization of qubits based on quantum observables and subsystems.Comment: 16 pages, no figures; IoP LaTeX2e style. Submitted to J. Phys. A: Math. Ge

Influences of Psychological Traits and PROP Taster Status on Familiarity with and Choice of Phenol-Rich Foods and Beverages

Plant phenolics are powerful antioxidants and free radical scavengers that can contribute to the healthy functional properties of plant-based food and beverages. Thus, dietary behaviours rich in plant-based food and beverages are encouraged. However, it is well-known that the bitter taste and other low-appealing sensory properties that characterize vegetables and some other plant-based foods act as an innate barrier for their acceptance. The aim of this study was to investigate the influence of psychological traits and PROP status (the responsiveness to bitter taste of 6-n- propylthiouracil) on the choice of and familiarity with phenol-rich vegetables and beverages varying in recalled level of bitterness and astringency. Study 1 aimed at assessing the variations of the sensory properties of vegetable and coffee/tea items with two check-all-that-apply (CATA) questionnaires (n = 201 and n = 188 individuals, respectively). Study 2 aimed at investigating how sensitivity to punishment, to reward, and to disgust, food neophobia, private body consciousness, alexithymia, and PROP responsiveness affect choice and familiarity with phenol-rich foods (n = 1200 individuals). A Choice Index was calculated for vegetables (CV) and coffee/tea (CC) as a mean of the choices of the more bitter/astringent option of the pairs and four Familiarity Indices were computed for vegetables (FV) and coffee/tea (FC), higher (+) or lower (-) in bitterness and astringency. Subjects higher in food neophobia, sensitivity to punishment or sensitivity to disgust reported significantly lower choice indices than individuals lower in these traits, meaning that they systematically opted for the least bitter/astringent option within the pairs. Familiarity with vegetables was lower in individuals high in sensitivity to punishment, in food neophobia and in alexithymia, irrespective of their sensory properties. The Familiarity Index with coffee/tea characterized by higher bitterness and astringency was lower in individuals high in food neophobia, sensitivity to disgust, and alexithymia. No significant effect of PROP was found on any indices. The proposed approach based on product grouping according to differences in bitterness and astringency allowed the investigation of the role of individual differences in chemosensory perception and of psychological traits as modulators of phenol-rich foods preference and consumption