Compatibility of radial, Lorenz and harmonic gauges

We observe that the radial gauge can be consistently imposed \emph{together} with the Lorenz gauge in Maxwell theory, and with the harmonic traceless gauge in linearized general relativity. This simple observation has relevance for some recent developments in quantum gravity where the radial gauge is implicitly utilized.Comment: 9 pages, minor changes in the bibliograph

Many-nodes/many-links spinfoam: the homogeneous and isotropic case

I compute the Lorentzian EPRL/FK/KKL spinfoam vertex amplitude for regular graphs, with an arbitrary number of links and nodes, and coherent states peaked on a homogeneous and isotropic geometry. This form of the amplitude can be applied for example to a dipole with an arbitrary number of links or to the 4-simplex given by the compete graph on 5 nodes. All the resulting amplitudes have the same support, independently of the graph used, in the large j (large volume) limit. This implies that they all yield the Friedmann equation: I show this in the presence of the cosmological constant. This result indicates that in the semiclassical limit quantum corrections in spinfoam cosmology do not come from just refining the graph, but rather from relaxing the large j limit.Comment: 8 pages, 4 figure

Advanced 3D Models of Human Brain Tissue Using Neural Cell Lines: State-of-the-Art and Future Prospects

Human-relevant three-dimensional (3D) models of cerebral tissue can be invaluable tools to boost our understanding of the cellular mechanisms underlying brain pathophysiology. Nowadays, the accessibility, isolation and harvesting of human neural cells represents a bottleneck for obtaining reproducible and accurate models and gaining insights in the fields of oncology, neurodegenerative diseases and toxicology. In this scenario, given their low cost, ease of culture and reproducibility, neural cell lines constitute a key tool for developing usable and reliable models of the human brain. Here, we review the most recent advances in 3D constructs laden with neural cell lines, highlighting their advantages and limitations and their possible future applications

A Smart Region-Growing Algorithm for Single-Neuron Segmentation From Confocal and 2-Photon Datasets

Accurately digitizing the brain at the micro-scale is crucial for investigating brain structure-function relationships and documenting morphological alterations due to neuropathies. Here we present a new Smart Region Growing algorithm (SmRG) for the segmentation of single neurons in their intricate 3D arrangement within the brain. Its Region Growing procedure is based on a homogeneity predicate determined by describing the pixel intensity statistics of confocal acquisitions with a mixture model, enabling an accurate reconstruction of complex 3D cellular structures from high-resolution images of neural tissue. The algorithm’s outcome is a 3D matrix of logical values identifying the voxels belonging to the segmented structure, thus providing additional useful volumetric information on neurons. To highlight the algorithm’s full potential, we compared its performance in terms of accuracy, reproducibility, precision and robustness of 3D neuron reconstructions based on microscopic data from different brain locations and imaging protocols against both manual and state-of-the-art reconstruction tools

Asymptotics of LQG fusion coefficients

The fusion coefficients from SO(3) to SO(4) play a key role in the definition of spin foam models for the dynamics in Loop Quantum Gravity. In this paper we give a simple analytic formula of the EPRL fusion coefficients. We study the large spin asymptotics and show that they map SO(3) semiclassical intertwiners into $SU(2)_L\times SU(2)_R$ semiclassical intertwiners. This non-trivial property opens the possibility for an analysis of the semiclassical behavior of the model.Comment: 14 pages, minor change

Gotta trace ‘em all: A mini-review on tools and procedures for segmenting single neurons toward deciphering the structural connectome

Decoding the morphology and physical connections of all the neurons populating a brain is necessary for predicting and studying the relationships between its form and function, as well as for documenting structural abnormalities in neuropathies. Digitizing a complete and high-fidelity map of the mammalian brain at the micro-scale will allow neuroscientists to understand disease, consciousness, and ultimately what it is that makes us humans. The critical obstacle for reaching this goal is the lack of robust and accurate tools able to deal with 3D datasets representing dense-packed cells in their native arrangement within the brain. This obliges neuroscientist to manually identify the neurons populating an acquired digital image stack, a notably time-consuming procedure prone to human bias. Here we review the automatic and semi-automatic algorithms and software for neuron segmentation available in the literature, as well as the metrics purposely designed for their validation, highlighting their strengths and limitations. In this direction, we also briefly introduce the recent advances in tissue clarification that enable significant improvements in both optical access of neural tissue and image stack quality, and which could enable more efficient segmentation approaches. Finally, we discuss new methods and tools for processing tissues and acquiring images at sub-cellular scales, which will require new robust algorithms for identifying neurons and their sub-structures (e.g., spines, thin neurites). This will lead to a more detailed structural map of the brain, taking twenty-first century cellular neuroscience to the next level, i.e., the Structural Connectome

Spinfoams in the holomorphic representation

We study a holomorphic representation for spinfoams. The representation is obtained via the Ashtekar-Lewandowski-Marolf-Mour\~ao-Thiemann coherent state transform. We derive the expression of the 4d spinfoam vertex for Euclidean and for Lorentzian gravity in the holomorphic representation. The advantage of this representation rests on the fact that the variables used have a clear interpretation in terms of a classical intrinsic and extrinsic geometry of space. We show how the peakedness on the extrinsic geometry selects a single exponential of the Regge action in the semiclassical large-scale asymptotics of the spinfoam vertex.Comment: 10 pages, 1 figure, published versio

Intertwiner dynamics in the flipped vertex

We continue the semiclassical analysis, started in a previous paper, of the intertwiner sector of the flipped vertex spinfoam model. We use independently both a semi-analytical and a purely numerical approach, finding the correct behavior of wave packet propagation and physical expectation values. In the end, we show preliminary results about correlation functions.Comment: 12 pages, 7 figure

Asymptotics of Spinfoam Amplitude on Simplicial Manifold: Euclidean Theory

We study the large-j asymptotics of the Euclidean EPRL/FK spin foam amplitude on a 4d simplicial complex with arbitrary number of simplices. We show that for a critical configuration (j_f, g_{ve}, n_{ef}) in general, there exists a partition of the simplicial complex into three regions: Non-degenerate region, Type-A degenerate region and Type-B degenerate region. On both the non-degenerate and Type-A degenerate regions, the critical configuration implies a non-degenerate Euclidean geometry, while on the Type-B degenerate region, the critical configuration implies a vector geometry. Furthermore we can split the Non-degenerate and Type-A regions into sub-complexes according to the sign of Euclidean oriented 4-simplex volume. On each sub-complex, the spin foam amplitude at critical configuration gives a Regge action that contains a sign factor sgn(V_4(v)) of the oriented 4-simplices volume. Therefore the Regge action reproduced here can be viewed as a discretized Palatini action with on-shell connection. The asymptotic formula of the spin foam amplitude is given by a sum of the amplitudes evaluated at all possible critical configurations, which are the products of the amplitudes associated to different type of geometries.Comment: 27 pages, 5 figures, references adde

The EPRL intertwiners and corrected partition function

Do the SU(2) intertwiners parametrize the space of the EPRL solutions to the simplicity constraint? What is a complete form of the partition function written in terms of this parametrization? We prove that the EPRL map is injective for n-valent vertex in case when it is a map from SO(3) into SO(3)xSO(3) representations. We find, however, that the EPRL map is not isometric. In the consequence, in order to be written in a SU(2) amplitude form, the formula for the partition function has to be rederived. We do it and obtain a new, complete formula for the partition function. The result goes beyond the SU(2) spin-foam models framework.Comment: RevTex4, 15 pages, 5 figures; theorem of injectivity of EPRL map correcte