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

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

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

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

Sensory and chemical profile of a phenolic extract from olive mill waste waters in plant-base food with varied macro-composition

Phenols from olive mill waste water (OMWW) represent valuable functional ingredients. The negative impact on sensory quality limits their use in functional food formulations. Chemical interactions phenols/biopolymers and their consequences on bioactivity in plant-base foods have been widely investigated, but no studies to date have explored the variation of bitterness, astringency and pungency induced by OMWW phenols as a function of the food composition. The aim of the paper was to profile the sensory and chemical properties of phenols from OMWW in plant-base foods varied in their macro-composition. Four phenol concentrations were selected (0.44, 1.00, 2.25, 5.06 g/kg) to induce significant variations of bitterness, sourness, astringency and pungency in three plant-base food: proteins/neutral pH \u2013 bean pur\ue9e (BP), starch/neutral pH \u2013 potato pur\ue9e (PP), fiber/low pH \u2013 tomato juice (TJ). The macro-composition affected the amount of the phenols recovered from functionalized food. The highest recovery was from TJ and the lowest from BP. Two groups of 29 and 27 subjects, trained to general Labelled Magnitude Scale and target sensations, participated in the evaluation of psychophysical curves of OMWW phenols and of functionalized plant-base foods, respectively. Target sensations were affected by the food macro-composition. Bitterness increased with phenol concentration in all foods. Astringency and sourness slightly increased with concentration, reaching the weak-moderate intensity at the highest phenol concentration in PP and TJ only. Pungency was suppressed in BP and perceived at weak-moderate intensity in PP and TJ sample at the highest phenol concentration. Proteins/neutral pH plant-food (BP) resulted more appropriate to counteract the impact of added phenol on negative sensory properties thus allowing to optimize the balance between health and sensory properties

Sensory and chemical profile of a phenolic extract from olive mill waste waters in plant-base food with varied macro-composition

Phenols from olive mill waste water (OMWW) represent valuable functional ingredients. The negative impact on sensory quality limits their use in functional food formulations. Chemical interactions phenols/biopolymers and their consequences on bioactivity in plant-base foods have been widely investigated, but no studies to date have explored the variation of bitterness, astringency and pungency induced by OMWW phenols as a function of the food composition. The aim of the paper was to profile the sensory and chemical properties of phenols from OMWW in plant-base foods varied in their macro-composition. Four phenol concentrations were selected (0.44, 1.00, 2.25, 5.06 g/kg) to induce significant variations of bitterness, sourness, astringency and pungency in three plant-base food: proteins/neutral pH \u2013 bean pur\ue9e (BP), starch/neutral pH \u2013 potato pur\ue9e (PP), fiber/low pH \u2013 tomato juice (TJ). The macro-composition affected the amount of the phenols recovered from functionalized food. The highest recovery was from TJ and the lowest from BP. Two groups of 29 and 27 subjects, trained to general Labelled Magnitude Scale and target sensations, participated in the evaluation of psychophysical curves of OMWW phenols and of functionalized plant-base foods, respectively. Target sensations were affected by the food macro-composition. Bitterness increased with phenol concentration in all foods. Astringency and sourness slightly increased with concentration, reaching the weak-moderate intensity at the highest phenol concentration in PP and TJ only. Pungency was suppressed in BP and perceived at weak-moderate intensity in PP and TJ sample at the highest phenol concentration. Proteins/neutral pH plant-food (BP) resulted more appropriate to counteract the impact of added phenol on negative sensory properties thus allowing to optimize the balance between health and sensory properties

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