Generalized LIL for geometrically weighted random series in Banach spaces

AbstractLet {X,Xn;n⩾0} be a sequence of independent and identically distributed random variables, taking values in a separable Banach space B with topological dual B⁎. Considering the geometrically weighted series ξ(β)=∑n=0∞βnXn for 0<β<1, motivated by Einmahl and Li (2005, 2008), a general law of the iterated logarithm for ξ(β) is established

A Solvable Model for Discrete Time Crystal Enforced by Nonsymmorphic Dynamical Symmetry

Discrete time crystal is a class of nonequilibrium quantum systems exhibiting subharmonic responses to external periodic driving. Here we propose a class of discrete time crystals enforced by nonsymmorphic dynamical symmetry. We start with a system with nonsymmorphic dynamical symmetry, in which the instantaneous eigenstates become M\"obius twisted, hence doubling the period of the instantaneous state. The exact solution of the time-dependent Schr\"odinger equation shows that the system spontaneously exhibits a period extension without undergoing quantum superposition states for a series of specifc evolution frequencies or in the limit of long evolution period. Moreover, in such case the system gains a {\pi} Berry phase after two periods' evolution. Finally, we show that the subharmonic response is stable even when many-body interactions are introduced, indicating a DTC phase in the thermodynamic limit.Comment: 5 pages, 4 figure

NUMERICAL STUDY ON PROPULSIVE FACTORS IN REGULAR HEAD AND OBLIQUE WAVES

This paper applies Reynolds-averaged Navier-Stokes (RANS) method to study propulsion performance in head and oblique waves. Finite volume method (FVM) is employed to discretize the governing equations and SST k-ω model is used for modeling the turbulent flow. The free surface is solved by volume of fluid (VOF) method. Sliding mesh technique is used to enable rotation of propeller. Propeller open water curves are determined by propeller open water simulations. Calm water resistance and wave added resistances are obtained from towing computations without propeller. Self-propulsion simulations in calm water and waves with varying loads are performed to obtain self-propulsion point and thrust identify method is use to predict propulsive factors. Regular head waves with wavelengths varying from 0.6 to 1.4 times the length of ship and oblique waves with incident directions varying from 0° to 360° are considered. The influence of waves on propulsive factors, including thrust deduction and wake fraction, open water, relative rotative, hull and propulsive efficiencies are discussed

In silico design of potentially functional artificial metallo-haloalkane dehalogenase containing catalytic zinc

Artificial metalloenzymes are unique as they combine the good features of homogeneous and enzymatic catalysts, and they can potentially improve some difficult catalytic assays. This study reports a method that can be used to create an artificial metal-binding site prior to proving it to be functional in a wet lab. Haloalkane dehalogenase was grafted into a metal-binding site to form an artificial metallo-haloalkane dehalogenase and was studied for its potential functionalities in silico. Computational protocols regarding dynamic metal docking were studied using native metalloenzymes and functional artificial metalloenzymes. Using YASARA Structure, a simulation box covering template structure was created to be filled with water molecules followed by one mutated water molecule closest to the metal-binding site to metal ion. A simple energy minimization step was subsequently run using an AMBER force field to allow the metal ion to interact with the metal-binding residues. Long molecular dynamic simulation using YASARA Structure was performed to analyze the stability of the metal-binding site and the distance between metal-binding residues. Metal ions fluctuating around 2.0 Å across a 20 ns simulation indicated a stable metal-binding site. Metal-binding energies were predicted using FoldX, with a native metalloenzyme (carbonic anhydrase) scoring 18.0 kcal/mol and the best mutant model (C1a) scoring 16.4 kcal/mol. Analysis of the metal-binding site geometry was performed using CheckMyMetal, and all scores for the metalloenzymes and mutant models were in an acceptable range. Like native metalloenzymes, the metal-binding site of C1a was supported by residues in the second coordination shell to maintain a more coordinated metal-binding site. Short-chain multihalogenated alkanes (1,2-dibromoethane and 1,2,3-trichloropropane) were able to dock in the active site of C1a. The halides of the substrate were in contact with both the metal and halide-stabilizing residues, thus indicating a better stabilization of the substrate. The simple catalytic mechanism proposed is that the metal ion interacted with halogen and polarized the carbon–halogen bond, thus making the alpha carbon susceptible to attack by nucleophilic hydroxide. The interaction between halogen in the metal ion and halide-stabilizing residues may help to improve the stabilization of the substrate–enzyme complex and reduce the activation energy. This study reports a modified dynamic metal-docking protocol and validation tests to verify the metal-binding site. These approaches can be applied to design different kinds of artificial metalloenzymes or metal-binding sites

3-Fluoro-4-nitro­phenyl 4-methyl­benzene­sulfonate

In the title compound, C13H10FNO5S, the dihedral angle between the benzene rings is 47.63 (14)°. In the crystal, π–π stacking occurs between nearly parallel benzene rings of adjacent mol­ecules, the centroid–centroid distance being 3.7806 (16) Å. Weak inter­molecular C—H⋯O hydrogen bonding is also present in the crystal structure

Vessel Extraction for AS-OCT Angiography

In this work, we propose a filter-based vessel segmentation method for Anterior Segment Optical Coherence Tomography Angiography image. In our method, the bandpass filter is utilized to suppress the horizontal noise lines caused by eye movement, while the curvedsupport Gaussian filter is utilized to enhance the vessel and generate the probability map