The ideal energy of classical lattice dynamics

We define, as local quantities, the least energy and momentum allowed by quantum mechanics and special relativity for physical realizations of some classical lattice dynamics. These definitions depend on local rates of finite-state change. In two example dynamics, we see that these rates evolve like classical mechanical energy and momentum.Comment: 12 pages, 4 figures, includes revised portion of arXiv:0805.335

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

On the probability of occurrence of rogue waves

A number of extreme and rogue wave studies have been conducted theoretically, numerically, experimentally and based on field data in the last years, which have significantly advanced our knowledge of ocean waves. So far, however, consensus on the probability of occurrence of rogue waves has not been achieved. The present investigation is addressing this topic from the perspective of design needs. Probability of occurrence of extreme and rogue wave crests in deep water is here discussed based on higher order time simulations, experiments and hindcast data. Focus is given to occurrence of rogue waves in high sea states

The biochemical basis of interactions between Glucocerebrosidase and alpha‐synuclein in GBA1 mutation carriers

The discovery of genes involved in familial as well as sporadic forms of Parkinson disease (PD) constitutes an important milestone in understanding this disorder's pathophysiology and potential treatment. Among these genes, GBA1 is one of the most common and well-studied, but it is still unclear how mutations in GBA1 translate into an increased risk for developing PD. In this review, we provide an overview of the biochemical and structural relationship between GBA1 and PD to help understand the recent advances in the development of PD therapies intended to target this pathway

Targeting the GBA1 pathway to slow Parkinson disease: Insights into clinical aspects, pathogenic mechanisms and new therapeutic avenues

The GBA1 gene encodes the lysosomal enzyme glucocerebrosidase (GCase), which is involved in sphingolipid metabolism. Biallelic variants in GBA1 cause Gaucher disease (GD), a lysosomal storage disorder characterised by loss of GCase activity and aberrant intracellular accumulation of GCase substrates. Carriers of GBA1 variants have an increased risk of developing Parkinson disease (PD), with odds ratio ranging from 2.2 to 30 according to variant severity. GBA1 variants which do not cause GD in homozygosis can also increase PD risk. Patients with PD carrying GBA1 variants show a more rapidly progressive phenotype compared to non-carriers, emphasising the need for disease modifying treatments targeting the GBA1 pathway. Several mechanisms secondary to GCase dysfunction are potentially responsible for the pathological changes leading to PD. Misfolded GCase proteins induce endoplasmic reticulum stress and subsequent unfolded protein response and impair the autophagy-lysosomal pathway. This results in α-synuclein accumulation and spread, and promotes neurodegenerative changes. Preclinical evidence also shows that products of GCase activity can promote accumulation of α-synuclein, however there is no convincing evidence of substrate accumulation in GBA1-PD brains. Altered lipid homeostasis secondary to loss of GCase activity could also contribute to PD pathology. Treatments that target the GBA1 pathway could reverse these pathological processes and halt/slow the progression of PD. These range from augmentation of GCase activity via GBA1 gene therapy, restoration of normal intracellular GCase trafficking via molecular chaperones, and substrate reduction therapy. This review discusses the pathways associated with GBA1-PD and related novel GBA1-targeted interventions for PD treatment

Energy Transport in an Ising Disordered Model

We introduce a new microcanonical dynamics for a large class of Ising systems isolated or maintained out of equilibrium by contact with thermostats at different temperatures. Such a dynamics is very general and can be used in a wide range of situations, including disordered and topologically inhomogenous systems. Focusing on the two-dimensional ferromagnetic case, we show that the equilibrium temperature is naturally defined, and it can be consistently extended as a local temperature when far from equilibrium. This holds for homogeneous as well as for disordered systems. In particular, we will consider a system characterized by ferromagnetic random couplings $J_{ij} \in [ 1 - \epsilon, 1 + \epsilon ]$. We show that the dynamics relaxes to steady states, and that heat transport can be described on the average by means of a Fourier equation. The presence of disorder reduces the conductivity, the effect being especially appreciable for low temperatures. We finally discuss a possible singular behaviour arising for small disorder, i.e. in the limit $\epsilon \to 0$.Comment: 14 pages, 8 figure

Modulational instability and wave amplification in finite water depth

The modulational instability of a uniform wave train to side band perturbations is one of the most plausible mechanisms for the generation of rogue waves in deep water. In a condition of finite water depth, however, the interaction with the sea floor generates a wave-induced current that subtracts energy from the wave field and consequently attenuates the instability mechanism. As a result, a plane wave remains stable under the influence of collinear side bands for relative depths <i>kh</i> &leq; 1.36 (where <i>k</i> is the wavenumber of the plane wave and <i>h</i> is the water depth), but it can still destabilise due to oblique perturbations. Using direct numerical simulations of the Euler equations, it is here demonstrated that oblique side bands are capable of triggering modulational instability and eventually leading to the formation of rogue waves also for <i>kh</i> &leq; 1.36. Results, nonetheless, indicate that modulational instability cannot sustain a substantial wave growth for <i>kh</i> < 0.8

A simple trapped-ion architecture for high-fidelity Toffoli gates

We discuss a simple architecture for a quantum Toffoli gate implemented using three trapped ions. The gate, which in principle can be implemented with a single laser-induced operation, is effective under rather general conditions and is strikingly robust (within any experimentally realistic range of values) against dephasing, heating and random fluctuations of the Hamiltonian parameters. We provide a full characterization of the unitary and noise-affected gate using three-qubit quantum process tomography

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