Evaporative Cooling and Self‐Thermalization in an Open System of Interacting Fermions

Depletion dynamics of an open system of weakly interacting fermions with two‐body random interactions is studied. In this model, fermions are escaping from the high‐energy one‐particle orbitals, that mimics the evaporation process used in laboratory experiments with neutral atoms to cool them to ultra‐low temperatures. It is shown that due to self‐thermalization the system instantaneously adjusts to the new temperature which decreases with the course of time.     

N-phenyl-6-chloro-4-hydroxy-2-quinolone-3-carboxamides: Molecular Docking,Synthesis, and Biological Investigation as Anticancer Agents

Cancer is a multifactorial disease and the second leading cause of death worldwide. Diverse factors induce carcinogenesis, such as diet, smoking, radiation, and genetic defects. The phosphatidylinositol 3-kinase (PI3Kα) has emerged as an attractive target for anticancer drug design. Eighteen derivatives of N-phenyl-6-chloro-4-hydroxy-2-quinolone-3-carboxamide were synthesized and characterized using FT-IR, NMR (¹H and ¹³C), and high-resolution mass spectra (HRMS). The series exhibited distinct antiproliferative activity (IC₅₀ µM) against human epithelial colorectal adenocarcinoma (Caco-2) and colon carcinoma (HCT-116) cell lines, respectively: compounds 16 (37.4, 8.9 µM), 18 (50.9, 3.3 µM), 19 (17.0, 5.3 µM), and 21 (18.9, 4.9 µM). The induced-fit docking (IFD) studies against PI3Kαs showed that the derivatives occupy the PI3Kα binding site and engage with key binding residues.     

Raman-induced localization in Kerr waveguide arrays

We show that during the spatiotemporal compression in a periodic Kerr waveguide array, stimulated Raman scattering can effectively balance the effects of self-phase modulation, diffraction, and group-velocity dispersion, eliminating collapse and breakup over a wide range of input powers and leading to stable propagation in a single site.     

Direct observation of protein motion during the photochemical reaction cycle of bacteriorhodopsin

Platinum-coated, conductive atomic force microscope cantilevers were used to deposit electrophoretically purple membranes from Halobacterium salinarum on the bottom part of the cantilevers. By illuminating the bacteriorhodopsin-containing purple membranes, the protein goes through its photochemical reaction cycle, during which a conformational change happens in the protein, changing its shape and size. The size change of the protein acts upon the cantilever by causing its deflection, which can be monitored by the detection system of the atomic force microscope. The shape of the signal, the action spectrum of the deflection amplitude, and the blue light inhibition of the deflection all prove that the origin of the signal is the conformational change arising in the bacteriorhodopsin during the photocycle. From the size of the signal, the magnitude of the protein motion could be estimated. Using polarized light, the orientation of the motion was determined, relative to the transition moment of the retinal.     

Quantum particle trajectories and geometric phase

Particle trajectories are defined as integrable dx _μ dp ^μ=0 paths in projective space. Quantum states evolving on such trajectories, open or closed, do not delocalize in (x, p) projection, the phase associated with the trajectories related to the geometric (Berry) phase and the classical mechanics action. Properties at high energies of the states evolving on particle trajectories are discussed.     

Sampling and refinement protocols for template-based macrocycle docking: 2018 D3R Grand Challenge 4

We describe a new template-based method for docking flexible ligands such as macrocycles to proteins. It combines Monte-Carlo energy minimization on the manifold, a fast manifold search method, with BRIKARD for complex flexible ligand searching, and with the MELD accelerator of Replica-Exchange Molecular Dynamics simulations for atomistic degrees of freedom. Here we test the method in the Drug Design Data Resource blind Grand Challenge competition. This method was among the best performers in the competition, giving sub-angstrom prediction quality for the majority of the targets.     

*-Quantizations of Fourier–Mukai Transforms

We study deformations of Fourier–Mukai transforms in general complex analytic settings. Suppose X and Y are complex manifolds, and let P be a coherent sheaf on X ×  Y. Suppose that the Fourier–Mukai transform ${\Phi}$ Φ given by the kernel P is an equivalence between the coherent derived categories of X and of Y. Suppose also that we are given a formal *-quantization ${\mathbb{X}}$ X of X. Our main result is that ${\mathbb{X}}$ X gives rise to a unique formal *-quantization ${\mathbb{Y}}$ Y of Y. For the statement to hold, *-quantizations must be understood in the framework of stacks of algebroids. The quantization ${\mathbb{Y}}$ Y is uniquely determined by the condition that ${\Phi}$ Φ deforms to an equivalence between the derived categories of ${\mathbb{X}}$ X and ${\mathbb{Y}}$ Y . Equivalently, the condition is that P deforms to a coherent sheaf ${\tilde{P}}$ P ~ on the formal *-quantization ${\mathbb{X} \times\mathbb{Y}^{op}}$ X × Y o p of X × Y; here ${\mathbb{Y}^{op}}$ Y o p is the opposite of the quantization ${\mathbb{Y}}$ Y .     

Spectral properties of Google matrix of Wikipedia and other networks

We study the properties of eigenvalues and eigenvectors of the Google matrix of the Wikipedia articles hyperlink network and other real networks. With the help of the Arnoldi method, we analyze the distribution of eigenvalues in the complex plane and show that eigenstates with significant eigenvalue modulus are located on well defined network communities. We also show that the correlator between PageRank and CheiRank vectors distinguishes different organizations of information flow on BBC and Le Monde web sites.     

When is the self-intersection of a subvariety a fibration?

We provide a necessary and sufficient condition for the derived self-intersection of a smooth subscheme inside a smooth scheme to be a fibration over the subscheme. As a consequence we deduce a generalized HKR isomorphism. We also investigate the relationship of our result to path spaces in homotopy theory, Buchweitz–Flenner formality in algebraic geometry, and draw parallels with similar results in Lie theory and symplectic geometry.