New obstructions to symplectic embeddings

In this paper we establish new restrictions on symplectic embeddings of certain convex domains into symplectic vector spaces. These restrictions are stronger than those implied by the Ekeland-Hofer capacities. By refining an embedding technique due to Guth, we also show that they are sharp.Comment: 80 pages, 3 figures, v2: improved exposition and minor corrections, v3: Final version, expanded and improved exposition and minor corrections. The final publication is available at link.springer.co

Causation, Measurement Relevance and No-conspiracy in EPR

In this paper I assess the adequacy of no-conspiracy conditions employed in the usual derivations of the Bell inequality in the context of EPR correlations. First, I look at the EPR correlations from a purely phenomenological point of view and claim that common cause explanations of these cannot be ruled out. I argue that an appropriate common cause explanation requires that no-conspiracy conditions are re-interpreted as mere common cause-measurement independence conditions. In the right circumstances then, violations of measurement independence need not entail any kind of conspiracy (nor backwards in time causation). To the contrary, if measurement operations in the EPR context are taken to be causally relevant in a specific way to the experiment outcomes, their explicit causal role provides the grounds for a common cause explanation of the corresponding correlations.Comment: 20 pages, 1 figur

Chemical ordering and composition fluctuations at the (001) surface of the Fe-Ni Invar alloy

We report on a study of (001) oriented fcc Fe-Ni alloy surfaces which combines first-principles calculations and low-temperature STM experiments. Density functional theory calculations show that Fe-Ni alloy surfaces are buckled with the Fe atoms slightly shifted outwards and the Ni atoms inwards. This is consistent with the observation that the atoms in the surface layer can be chemically distinguished in the STM image: brighter spots (corrugation maxima with increased apparent height) indicate iron atoms, darker ones nickel atoms. This chemical contrast reveals a c2x2 chemical order (50% Fe) with frequent Fe-rich defects on Invar alloy surface. The calculations also indicate that subsurface composition fluctuations may additionally modulate the apparent height of the surface atoms. The STM images show that this effect is pronounced compared to the surfaces of other disordered alloys, which suggests that some chemical order and corresponding concentration fluctuations exist also in the subsurface layers of Invar alloy. In addition, detailed electronic structure calculations allow us to identify the nature of a distinct peak below the Fermi level observed in the tunneling spectra. This peak corresponds to a surface resonance band which is particularly pronounced in iron-rich surface regions and provides a second type of chemical contrast with less spatial resolution but one that is essentially independent of the subsurface composition.Comment: 7 pages, 5 figure

Isotope effects in underdoped cuprate superconductors: a quantum phenomenon

We show that the unusual doping dependence of the isotope effects on transition temperature and zero temperature in - plane penetration depth naturally follows from the doping driven 3D-2D crossover, the 2D quantum superconductor to insulator transition (QSI) in the underdoped limit and the change of the relative doping concentration upon isotope substitution. Close to the QSI transition both, the isotope coefficient of transition temperature and penetration depth approach the coefficient of the relative dopant concentration, and its divergence sets the scale. These predictions are fully consistent with the experimental data and imply that close to the underdoped limit the unusual isotope effect on transition temperature and penetration depth uncovers critical phenomena associated with the quantum superconductor to insulator transition in two dimensions.Comment: 6 pages, 3 figure

T1 Mapping Quantifies Spinal Cord Compression in Patients With Various Degrees of Cervical Spinal Canal Stenosis

Age-related degeneration of the cervical spinal column is the most common cause of spinal cord lesions. T1 mapping has been shown to indicate the grade and site of spinal cord compression in low grade spinal canal stenosis (SCS). Aim of our study was to further investigate the diagnostic potential of a novel T1 mapping method at 0.75 mm resolution and 4 s acquisition time in 31 patients with various grades of degenerative cervical SCS. T1 mapping was performed in axial sections of the stenosis as well as above and below. Included subjects received standard T2-weighted MRI of the cervical spine (including SCS-grading 0-III), electrophysiological, and clinical examination. We found that patients with cervical SCS showed a significant difference in T1 relaxation times within the stenosis (727 ± 66 ms, mean ± standard deviation) in comparison to non-stenotic segments above (854 ± 104 ms, p < 0.001) and below (893 ± 137 ms, p < 0.001). There was no difference in mean T1 in non-stenotic segments in patients (p = 0.232) or between segments in controls (p = 0.272). Mean difference of the T1 relaxation times was significantly higher in grade III stenosis (234 ± 45) vs. in grade II stenosis (176 ± 45, p = 0.037) vs. in grade I stenosis (90 ± 87 ms, p = 0.010). A higher difference in T1 relaxation time was associated with a central efferent conduction deficit. In conclusion, T1 mapping may be useful as a tool for SCS quantification in all grades of SCS, including high-grade stenosis with myelopathy signal in conventional T2-weighted imaging

High periventricular T1 relaxation times predict gait improvement after spinal tap in patients with idiopathic normal pressure hydrocephalus

Purpose:The diagnosis of idiopathic normal pressure hydrocephalus (iNPH) can be challenging. Aim of this study was to use a novel T1 mapping method to enrich the diagnostic work-up of patients with suspected iNPH.Methods:Using 3T magnetic resonance imaging (MRI) we prospectively evaluated rapid high-resolution T1 mapping at 0.5 mm resolution and 4 s acquisition time in 15 patients with suspected iNPH and 8 age-matched, healthy controls.T1 mapping in axial sections of the cerebrum, clinical and neuropsychological testing were performed prior to and after cerebrospinal fluid tap test (CSF-TT). T1 relaxation times were measured in 5 predefined periventricular regions.Results:All 15 patients with suspected iNPH showed gait impairment, 13 (86.6%) showed signs of cognitive impairment and 8 (53.3%) patients had urinary incontinence. Gait improvement was noted in 12 patients (80%) after CSF-TT. T1 relaxation times in all periventricular regions were elevated in patients with iNPH compared to controls with the most pronounced differences in the anterior (1006 ± 93 ms vs. 911 ± 77 ms; p = 0.023) and posterior horns (983 ± 103 ms vs. 893 ± 68 ms; p = 0.037) of the lateral ventricles. Montreal cognitive assessment (MoCA) scores at baseline were negatively correlated with T1 relaxation times (r 0.6 and p Conclusion:In iNPH-patients, periventricular T1 relaxation times are increased compared to age-matched controls and predict gait improvement after CSF-TT. T1 mapping might enrich iNPH work-up and might be useful to indicate permanent shunting

Coordinated analysis of age, sex, and education effects on change in MMSE scores

Objectives. We describe and compare the expected performance trajectories of older adults on the Mini-Mental Status Examination (MMSE) across six independent studies from four countries in the context of a collaborative network of longitudinal studies of aging. A coordinated analysis approach is used to compare patterns of change conditional on sample composition differences related to age, sex, and education. Such coordination accelerates evaluation of particular hypotheses. In particular, we focus on the effect of educational attainment on cognitive decline.Method. Regular and Tobit mixed models were fit to MMSE scores from each study separately. The effects of age, sex, and education were examined based on more than one centering point.Results. Findings were relatively consistent across studies. On average, MMSE scores were lower for older individuals and declined over time. Education predicted MMSE score, but, with two exceptions, was not associated with decline in MMSE over time.Conclusion. A straightforward association between educational attainment and rate of cognitive decline was not supported. Thoughtful consideration is needed when synthesizing evidence across studies, as methodologies adopted and sample characteristics, such as educational attainment, invariably differ. © 2012 The Author

On the notion of phase in mechanics

The notion of phase plays an esential role in both classical and quantum mechanics.But what is a phase? We show that if we define the notion of phase in phase (!) space one can very easily and naturally recover the Heisenberg-Weyl formalism; this is achieved using the properties of the Poincare-Cartan invariant, and without making any quantum assumption

The "Symplectic Camel Principle" and Semiclassical Mechanics

Gromov's nonsqueezing theorem, aka the property of the symplectic camel, leads to a very simple semiclassical quantiuzation scheme by imposing that the only "physically admissible" semiclassical phase space states are those whose symplectic capacity (in a sense to be precised) is nh + (1/2)h where h is Planck's constant. We the construct semiclassical waveforms on Lagrangian submanifolds using the properties of the Leray-Maslov index, which allows us to define the argument of the square root of a de Rham form.Comment: no figures. to appear in J. Phys. Math A. (2002

Invariant variational principle for Hamiltonian mechanics

It is shown that the action for Hamiltonian equations of motion can be brought into invariant symplectic form. In other words, it can be formulated directly in terms of the symplectic structure $\omega$ without any need to choose some 1-form $\gamma$, such that $\omega= d \gamma$, which is not unique and does not even generally exist in a global sense.Comment: final version; to appear in J.Phys.A; 17 pages, 2 figure