On regular and random two-dimensional packing of crosses

Packing problems, even of objects with regular geometries, are in general non-trivial. For few special shapes, the features of crystalline as well as random, irregular two-dimensional (2D) packing structures are known. The packing of 2D crosses does not yet belong to the category of solved problems. We demonstrate in experiments with crosses of different aspect ratios (arm width to length) which packing fractions are actually achieved by random packing, and we compare them to densest regular packing structures. We determine local correlations of the orientations and positions after ensembles of randomly placed crosses were compacted in the plane until they jam. Short-range orientational order is found over 2 to 3 cross lengths. Similarly, correlations in the spatial distributions of neighbors extend over 2 to 3 crosses. There is no simple relation between the geometries of the crosses and the peaks in the spatial correlation functions, but some features of the orientational correlations can be traced to typical local configurations.

Stellar Population and Elemental Abundance Gradients of Early-type Galaxies*

The evolution of galaxies is imprinted on their stellar populations. Several stellar population properties in massive early-type galaxies have been shown to correlate with intrinsic galaxy properties such as the galaxy’s central velocity dispersion, suggesting that stars formed in an initial collapse of gas (z ∼ 2). However, stellar populations change as a function of galaxy radius, and it is not clear how local gradients of individual galaxies are influenced by global galaxy properties and galaxy environment. In this paper, we study the stellar populations of eight early-type galaxies as a function of radius. We use optical spectroscopy (∼4000–8600 Å) and full spectral fitting to measure stellar population age, metallicity, slope of the initial mass function (IMF), and nine elemental abundances (O, Mg, Si, Ca, Ti, C, N, Na, and Fe) out to 1 R e for each galaxy individually. We find a wide range of properties, with ages ranging from 3–13 Gyr. Some galaxies have a radially constant, Salpeter-like IMF, and other galaxies have a super-Salpeter IMF in the center, decreasing to a sub-Salpeter IMF at ∼0.5 R e . We find a global correlation of the central [Z/H] with the central IMF and the radial gradient of the IMF for the eight galaxies, but local correlations of the IMF slope with other stellar population parameters hold only for subsets of the galaxies in our sample. Some elemental abundances also correlate locally with each other within a galaxy, suggesting a common production channel. These local correlations appear only in subsets of our galaxies, indicating variations of the stellar content among different galaxies.

Resting-state functional MRI signal fluctuations are correlated with brain amyloid-β deposition

Mounting evidence suggests that amyloid-β (Aβ) and vascular etiologies are intertwined in the pathogenesis of Alzheimer′s disease. Spontaneous fluctuations of the brain blood-oxygen-level-dependent (BOLD) signal, as measured by resting-state functional MRI (rs-fMRI), have been shown to be associated with neuronal activities as well as cerebrovascular hemodynamics. Nevertheless, it is unclear if rs-fMRI BOLD fluctuations are associated with brain Aβ deposition in individuals with an elevated risk of Alzheimer's disease. We recruited 33 patients with amnestic mild cognitive impairment who underwent rs-fMRI and positron emission tomography (PET). The Aβ standardized uptake value ratio (SUVR) was calculated with cortical white matter as the reference region to improve sensitivity for cortical Aβ quantification. We calculated the amplitudes of low-frequency fluctuations (ALFF) of local BOLD signals in the frequency band of 0.01-0.08 Hz. Applying physiological/vascular signal regression in stepwise increasing levels on the rs-fMRI data, we examined whether local correlations between ALFF and brain Aβ deposition were driven by vascular hemodynamics, spontaneous neuronal activities, or both. We found that ALFF and Aβ SUVR were negatively correlated in brain regions involving the default-mode and visual networks, with peak correlation at the precuneus, and angular, lingual, and fusiform gyri. Regions with higher ALFF had less Aβ accumulation. The correlated cluster sizes in MNI space were reduced from 3018 mm3 with no physiological/vascular regression to 1072 mm3 with strong physiological/vascular regression, with mean cluster r values at approximately -0.47. Results demonstrate that both vascular hemodynamics and neuronal activities, as reflected by BOLD fluctuations, are negatively associated with brain Aβ deposition. These findings further imply that local brain blood fluctuations due to either vascular hemodynamics or neuronal activities can affect Aβ homeostasis.

The Operational Choi–Jamiołkowski Isomorphism

In this article, I use an operational formulation of the Choi–Jamiołkowski isomorphism to explore an approach to quantum mechanics in which the state is not the fundamental object. I first situate this project in the context of generalized probabilistic theories and argue that this framework may be understood as a means of drawing conclusions about the intratheoretic causal structure of quantum mechanics which are independent of any specific ontological picture. I then give an operational formulation of the Choi–Jamiołkowski isomorphism and show that, in an operational theory which exhibits this isomorphism, several features of the theory which are usually regarded as properties of the quantum state can be derived from constraints on non-local correlations. This demonstrates that there is no need to postulate states to be the bearers of these properties, since they can be understood as consequences of a fundamental equivalence between multipartite and temporal correlations.