Reshaping cortical connectivity in traumatic spinal cord injury: a novel effect of hyperbaric oxygen therapy

Introduction: Spinal cord injuries (SCIs) represent a severe neuro-traumatic occurrence and an excruciating social burden. Though the hyperbaric oxygen (HBO2) has been credited as a first line therapeutic resource for SCIs, its mechanism of action in the spine is only partially known, while the impingement upon other areas of the nervous system deserves additional investigation. In this study we deem to describe a novel effect of HBO2 in a subject affected by SCI who, along with the clinical improvement, showed a reshaped connectivity in cortical sensory-motor areas. Case presentation: A 45 years male presenting severe sensory-motor symptoms following a spinal lesion partially involving the C1 segment was successfully treated with HBO2 cycles. After the dramatic improvement reflected by an excellent optimization of the single performances, it has been investigated whether this result would reveal not only an intrinsic effect upon the spinal cord, but also a better connectivity strength in sensory-motor cortical regions. The results obtained by implementing EEG recordings with EEGLAB auto regressive vector plugins indeed suggest a substantial reshaping of cortico-cortical connectivity after HBO2. Discussion: These results show a correlation between positive clinical evolution and a new modulation of cortical connectivity. Though further clinical investigations would clarify as to whether HBO2 might be directly or epiphenomenally involved in this aspect of the network architecture, our report suggests that a comparison between clinical results and the study of brain connectivity represent a holistic approach in investigating the physiopathology of SCIs and in monitoring the treatment

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

Stereotactic body radiation therapy for liver tumours using flattening filter free beam: dosimetric and technical considerations

Purpose: To report the initial institute experience in terms of dosimetric and technical aspects in stereotactic body radiation therapy (SBRT) delivered using flattening filter free (FFF) beam in patients with liver lesions.Methods and Materials: From October 2010 to September 2011, 55 consecutive patients with 73 primary or metastatic hepatic lesions were treated with SBRT on TrueBeam using FFF beam and RapidArc technique. Clinical target volume (CTV) was defined on multi-phase CT scans, PET/CT, MRI, and 4D-CT. Dose prescription was 75 Gy in 3 fractions to planning target volume (PTV). Constraints for organs at risk were: 700 cc of liver free from the 15 Gy isodose, D max < 21 Gy for stomach and duodenum, D max < 30 Gy for heart, D 0.1 cc < 18 Gy for spinal cord, V 15 Gy < 35% for kidneys. The dose was downscaled in cases of not full achievement of dose constraints. Daily cone beam CT (CBCT) was performed.Results: Forty-three patients with a single lesion, nine with two lesions and three with three lesions were treated with this protocol. Target and organs at risk objectives were met for all patients. Mean delivery time was 2.8 ± 1.0 min. Pre-treatment plan verification resulted in a Gamma Agreement Index of 98.6 ± 0.8%. Mean on-line co-registration shift of the daily CBCT to the simulation CT were: -0.08, 0.05 and -0.02 cm with standard deviations of 0.33, 0.39 and 0.55 cm in, vertical, longitudinal and lateral directions respectively.Conclusions: SBRT for liver targets delivered by means of FFF resulted to be feasible with short beam on time. © 2012 Mancosu et al; licensee BioMed Central Ltd

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

Explanation in mathematics: Proofs and practice

Mathematicians distinguish between proofs that explain their results and those that merely prove. This paper explores the nature of explanatory proofs, their role in mathematical practice, and some of the reasons why philosophers should care about them. Among the questions addressed are the following: what kinds of proofs are generally explanatory (or not)? What makes a proof explanatory? Do all mathematical explanations involve proof in an essential way? Are there really such things as explanatory proofs, and if so, how do they relate to the sorts of explanation encountered in philosophy of science and metaphysics

Cauchy's infinitesimals, his sum theorem, and foundational paradigms

Cauchy's sum theorem is a prototype of what is today a basic result on the convergence of a series of functions in undergraduate analysis. We seek to interpret Cauchy's proof, and discuss the related epistemological questions involved in comparing distinct interpretive paradigms. Cauchy's proof is often interpreted in the modern framework of a Weierstrassian paradigm. We analyze Cauchy's proof closely and show that it finds closer proxies in a different modern framework. Keywords: Cauchy's infinitesimal; sum theorem; quantifier alternation; uniform convergence; foundational paradigms.Comment: 42 pages; to appear in Foundations of Scienc