Estimation of the variance in any point of an electron-density map for any space group

In a recent paper [Giacovazzo & Mazzone (2011). Acta Cryst. A67, 210-218] a mathematical expression of the variance at any point of the unit cell has been described. The formulas were derived in P1 for any type of Fourier synthesis (observed, difference and hybrid) under the following hypothesis: the current phases are distributed on the trigonometric circle about the correct values according to von Mises distributions. This general hypothesis allows the variance expressions to be valid at any stage of the phasing process. In this paper the method has been extended to any space group, no matter whether centric or acentric. The properties of the variance generated by space-group symmetry are described; in particular it is shown that the variance is strictly connected with the implication transformations, which are basic for Patterson deconvolution. General formulas simultaneously taking into account phase uncertainty and measurement errors have been obtained, valid no matter what the quality of the model

Detecting Neutrino Magnetic Moments with Conducting Loops

It is well established that neutrinos have mass, yet it is very difficult to measure those masses directly. Within the standard model of particle physics, neutrinos will have an intrinsic magnetic moment proportional to their mass. We examine the possibility of detecting the magnetic moment using a conducting loop. According to Faraday's Law of Induction, a magnetic dipole passing through a conducting loop induces an electromotive force, or EMF, in the loop. We compute this EMF for neutrinos in several cases, based on a fully covariant formulation of the problem. We discuss prospects for a real experiment, as well as the possibility to test the relativistic formulation of intrinsic magnetic moments.Comment: 6 pages, 4 b/w figures, uses RevTe

Random projections and the optimization of an algorithm for phase retrieval

Iterative phase retrieval algorithms typically employ projections onto constraint subspaces to recover the unknown phases in the Fourier transform of an image, or, in the case of x-ray crystallography, the electron density of a molecule. For a general class of algorithms, where the basic iteration is specified by the difference map, solutions are associated with fixed points of the map, the attractive character of which determines the effectiveness of the algorithm. The behavior of the difference map near fixed points is controlled by the relative orientation of the tangent spaces of the two constraint subspaces employed by the map. Since the dimensionalities involved are always large in practical applications, it is appropriate to use random matrix theory ideas to analyze the average-case convergence at fixed points. Optimal values of the gamma parameters of the difference map are found which differ somewhat from the values previously obtained on the assumption of orthogonal tangent spaces.Comment: 15 page

Analytical evaluation of atomic form factors: application to Rayleigh scattering

Atomic form factors are widely used for the characterization of targets and specimens, from crystallography to biology. By using recent mathematical results, here we derive an analytical expression for the atomic form factor within the independent particle model constructed from nonrelativistic screened hydrogenic wavefunctions. The range of validity of this analytical expression is checked by comparing the analytically obtained form factors with the ones obtained within the Hartee-Fock method. As an example, we apply our analytical expression for the atomic form factor to evaluate the differential cross section for Rayleigh scattering off neutral atoms.Comment: 7 pages, 1 figur

Effects of caloric restriction on neuropathic pain, peripheral nerve degeneration and inflammation in normometabolic and autophagy defective prediabetic Ambra1 mice

There is a growing interest on the role of autophagy in diabetes pathophysiology, where development of neuropathy is one of the most frequent comorbidities. We have previously demonstrated that neuropathic pain after nerve damage is exacerbated in autophagy-defective heterozygous Ambra1 mice. Here, we show the existence of a prediabetic state in Ambra1 mice, characterized by hyperglycemia, intolerance to glucose and insulin resistance. Thus, we further investigate the hypothesis that prediabetes may account for the exacerbation of allodynia and chronic pain and that counteracting the autophagy deficit may relieve the neuropathic condition. We took advantage from caloric restriction (CR) able to exert a double action: a powerful increase of autophagy and a control on the metabolic status. We found that CR ameliorates neuropathy throughout anti-inflammatory and metabolic mechanisms both in Ambra1 and in WT animals subjected to nerve injury. Moreover, we discovered that nerve lesion represents, per se, a metabolic stressor and CR reinstates glucose homeostasis, insulin resistance, incomplete fatty acid oxidation and energy metabolism. As autophagy inducer, CR promotes and anticipates Schwann cell autophagy via AMP-activated protein kinase (AMPK) that facilitates remyelination in peripheral nerve. In summary, we provide new evidence for the role of autophagy in glucose metabolism and identify in energy depletion by dietary restriction a therapeutic approach in the fight against neuropathic pain

Passive immunotherapy for N-truncated tau ameliorates the cognitive deficits in two mouse AD models

Clinical and neuropathological studies have shown that tau pathology better correlates with the severity of dementia than amyloid plaque burden, making tau an attractive target for the cure of Alzheimer\u2019s disease. We have explored whether passive immunization with the 12A12 monoclonal antibody (26\u201336aa of tau protein) could improve the Alzheimer\u2019s disease phenotype of two well-established mouse models, Tg2576 and 3xTg mice. 12A12 is a cleavage-specific monoclonal antibody which selectively binds the pathologically relevant neurotoxic NH226-230 fragment (i.e. NH2htau) of tau protein without cross-reacting with its full-length physiological form(s). We found out that intravenous administration of 12A12 monoclonal antibody into symptomatic (6 months old) animals: (i) reaches the hippocampus in its biologically active (antigen-binding competent) form and successfully neutralizes its target; (ii) reduces both pathological tau and amyloid precursor protein/amyloid\u3b2 metabolisms involved in early disease-associated synaptic deterioration; (iii) improves episodic-like type of learning/memory skills in hippocampal-based novel object recognition and object place recognition behavioural tasks; (iv) restores the specific up-regulation of the activity-regulated cytoskeleton-associated protein involved in consolidation of experience-dependent synaptic plasticity; (v) relieves the loss of dendritic spine connectivity in pyramidal hippocampal CA1 neurons; (vi) rescues the Alzheimer\u2019s disease-related electrophysiological deficits in hippocampal long-term potentiation at the CA3-CA1 synapses; and (vii) mitigates the neuroinflammatory response (reactive gliosis). These findings indicate that the 20\u201322 kDa NH2-terminal tau fragment is crucial target for Alzheimer\u2019s disease therapy and prospect immunotherapy with 12A12 monoclonal antibody as safe (normal tau-preserving), beneficial approach in contrasting the early Amyloid\u3b2-dependent and independent neuropathological and cognitive alterations in affected subject