Infinite Simple 3D Cubic Lattice of Identical Resistors (Two Missing Bonds)

An infinite regular three-dimensional network is composed of identical resistors each of resistance joining adjacent nodes. What is the equivalent resistance between the lattice site and the lattice site, when two bonds are removed from the perfect network? Three cases are considered here, and some numerical values are calculated. Finally, the asymptotic behavior of the equivalent resistance is studied for large distances between the two sites.Comment: 11 pages, 3 figures, published in EPJ-A

Searching for the extra-tidal stars of globular clusters using high-dimensional analysis and a core particle spray code

Three-body interactions can eject stars from the core of a globular cluster, causing them to enter the Galactic halo as extra-tidal stars. While finding extra-tidal stars is imperative for understanding cluster evolution, connecting isolated extra-tidal field stars back to their birth cluster is extremely difficult. In this work, we present a new methodology consisting of high-dimensional data analysis and a particle spray code to identify extra-tidal stars of any Galactic globular cluster using M3 as a case study. Using the t-Stochastic Neighbour Embedding (t-SNE) and Uniform Manifold Approximation and Projection (UMAP) machine learning dimensionality reduction algorithms, we first identify a set of 103 extra-tidal candidates in the APOGEE DR17 data catalogue with chemical abundances similar to M3 stars. To confirm each candidate's extra-tidal nature, we introduce Corespray; a new Python-based three-body particle spray code that simulates extra-tidal stars for any Galactic globular cluster. Using Gaia EDR3 proper motions and APOGEE DR17 radial velocities, we apply multivariate Gaussian modelling and an extreme deconvolution to identify the extra-tidal candidates that are more likely to be associated with a distribution of Corespray-simulated M3 extra-tidal stars than the field. Through these methods, we identify 13 new high-probability extra-tidal stars of M3. Future applications of Corespray will yield better understandings of core dynamics, star formation histories and binary fractions in globular clusters.Comment: 15 pages, 8 figures, 2 tables. Submitted to Monthly Notices of the Royal Astronomical Societ

Infinite Networks of Identical Capacitors

The capacitance between the origin and any other lattice site in an infinite square lattice of identical capacitors is studied. The method is generalized to infinite Simple Cubic (SC) lattice. We make use of the superposition principle and the symmetry of the infinite gridComment: 16 pages, 5 figures, 2 table

α8β1 integrin regulates nutrient absorption through an Mfge8-PTEN dependent mechanism.

Coordinated gastrointestinal smooth muscle contraction is critical for proper nutrient absorption and is altered in a number of medical disorders. In this work, we demonstrate a critical role for the RGD-binding integrin α8β1 in promoting nutrient absorption through regulation of gastrointestinal motility. Smooth muscle-specific deletion and antibody blockade of α8 in mice result in enhanced gastric antral smooth muscle contraction, more rapid gastric emptying, and more rapid transit of food through the small intestine leading to malabsorption of dietary fats and carbohydrates as well as protection from weight gain in a diet-induced model of obesity. Mechanistically, ligation of α8β1 by the milk protein Mfge8 reduces antral smooth muscle contractile force by preventing RhoA activation through a PTEN-dependent mechanism. Collectively, our results identify a role for α8β1 in regulating gastrointestinal motility and identify α8 as a potential target for disorders characterized by hypo- or hyper-motility