Magic Mirrors, Dense Diameters, Baire Category

Abstract. An old result of Zamfirescu says that for most convex curves C in the plane most points in R 2 lie on infinitely many normals to C, where most is meant in Baire category sense. We strengthen this result by showing that ‘infinitely many’ can be replaced by ‘continuum many’ in the statement. We present further theorems in the same spirit

Neural representations of sensorimotor memory- and digit position-based load force adjustments before the onset of dexterous object manipulation

Anticipatory load forces for dexterous object manipulation in humans are modulated based on visual object properties cues, sensorimotor memories of previous experiences with the object, and, when digit positioning varies from trial-to-trial, the integrating of this sensed variability with force modulation. Studies of the neural representations encoding these anticipatory mechanisms have not considered these mechanisms separately from each other or from feedback mechanisms emerging after lift onset. Representational similarity analyses of fMRI data were used to identify neural representations of sensorimotor memories and the sensing and integration of digit position. Cortical activity and movement kinematics were measured as 20 human subjects (11 women) minimized tilt of a symmetrically-shaped object with a concealed asymmetric center of mass (CoM, left- and right-sided) - this required generating compensatory torques in opposite directions which, without helpful visual CoM cues, relied primarily on sensorimotor memories of the same object and CoM. Digit position was constrained or unconstrained, the latter of which required modulating forces beyond what can be recalled from sensorimotor memories to compensate for digit position variability. Ventral premotor (PMv), somatosensory, and cerebellar lobule regions (CrusII, VIIIa) were sensitive to anticipatory behaviors that reflect sensorimotor memory content, as shown by larger voxel pattern differences for unmatched than matched CoM conditions. Cerebellar lobule I-IV, Broca area 44 and PMv showed greater voxel pattern differences for unconstrained than constrained grasping, which suggests their sensitivity to monitor the online coincidence of planned and actual digit positions and correct for a mismatch by force modulation.Michelle Marneweck, Deborah A. Barany, Marco Santello and Scott T. Grafto

Corrigendum to ‘Dietary aflatoxin B1 (AFB1) reduces growth performance, impacting growth axis, metabolism, and tissue integrity in juvenile gilthead sea bream (Sparus aurata)’. Aquaculture, volume 533, 25 February 2021, 736189

The authors regret the errors in a few table references within the text. Specifically, it should reads as follows within the following subsections/ page: 3.2. Blood analysis (page 5)info:eu-repo/semantics/publishedVersio

On the equivalence of strong formulations for capacitated multi-level lot sizing problems with setup times

Several mixed integer programming formulations have been proposed for modeling capacitated multi-level lot sizing problems with setup times. These formulations include the so-called facility location formulation, the shortest route formulation, and the inventory and lot sizing formulation with (l,S) inequalities. In this paper, we demonstrate the equivalence of these formulations when the integrality requirement is relaxed for any subset of binary setup decision variables. This equivalence has significant implications for decomposition-based methods since same optimal solution values are obtained no matter which formulation is used. In particular, we discuss the relax-and-fix method, a decomposition-based heuristic used for the efficient solution of hard lot sizing problems. Computational tests allow us to compare the effectiveness of different formulations using benchmark problems. The choice of formulation directly affects the required computational effort, and our results therefore provide guidelines on choosing an effective formulation during the development of heuristic-based solution procedures

A computational analysis of lower bounds for big bucket production planning problems

In this paper, we analyze a variety of approaches to obtain lower bounds for multi-level production planning problems with big bucket capacities, i.e., problems in which multiple items compete for the same resources. We give an extensive survey of both known and new methods, and also establish relationships between some of these methods that, to our knowledge, have not been presented before. As will be highlighted, understanding the substructures of difficult problems provide crucial insights on why these problems are hard to solve, and this is addressed by a thorough analysis in the paper. We conclude with computational results on a variety of widely used test sets, and a discussion of future research

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

Potential energy threshold for nano-hillock formation by impact of slow highly charged ions on a CaF2_2(111) surface

We investigate the formation of nano-sized hillocks on the (111) surface of CaF$_2$ single crystals by impact of slow highly charged ions. Atomic force microscopy reveals a surprisingly sharp and well-defined threshold of potential energy carried into the collision of about 14 keV for hillock formation. Estimates of the energy density deposited suggest that the threshold is linked to a solid-liquid phase transition (``melting'') on the nanoscale. With increasing potential energy, both the basal diameter and the height of the hillocks increase. The present results reveal a remarkable similarity between the present predominantly potential-energy driven process and track formation by the thermal spike of swift ($\sim$ GeV) heavy ions.Comment: 10 pages, 2 figure

Unusual reactivity of N-acyl imides: N-aroyl-1,2,4-dithiazolidine-3,5-diones as acyl isocyanate equivalents.

Crystalline samples of three N-aroyl-1,2,4-dithiazolidine-3,5-diones have been prepared as the first examples of a novel class of compound that displays the reactivity of an acyl isocyanate when treated with nucleophiles