Neighboring Steps Research Articles

Asymptotics of noncolliding q-exchangeable random walks

We consider a process of noncolliding q-exchangeable random walks on making steps 0 (‘straight’) and −1 (‘down’). A single random walk is called q-exchangeable if under an elementary transposition of the neighboring steps the probability of the trajectory is multiplied by a parameter . Our process of m noncolliding q-exchangeable random walks is obtained from the independent q-exchangeable walks via the Doob’s h-transform for a nonnegative eigenfunction h (expressed via the q-Vandermonde product) with the eigenvalue less than 1. The system of m walks evolves in the presence of an absorbing wall at 0. The repulsion mechanism is the q-analogue of the Coulomb repulsion of random matrix eigenvalues undergoing Dyson Brownian motion. However, in our model, the particles are confined to the positive half-line and do not spread as Brownian motions or simple random walks. We show that the trajectory of the noncolliding q-exchangeable walks started from an arbitrary initial configuration forms a determinantal point process, and express its kernel in a double contour integral form. This kernel is obtained as a limit from the correlation kernel of q-distributed random lozenge tilings of sawtooth polygons. In the limit as , with γ > 0 fixed, and under a suitable scaling of the initial data, we obtain a limit shape of our noncolliding walks and also show that their local statistics are governed by the incomplete beta kernel. The latter is a distinguished translation invariant ergodic extension of the two-dimensional discrete sine kernel.

Mechanical properties and damage behavior of tapered unidirectional CFRP laminates

An understanding of damage mechanisms induced by drop-off plies in tapered composite laminates is crucial. This study investigated the mechanical properties and damage behaviors of asymmetric tapered unidirectional carbon fiber-reinforced plastic laminates. Damage observations of laminates with simultaneous tapered and staggered tapered structures under monotonic and cyclic tensile loads were done by an optical microscope and X-ray radiography. Based on the results, matrix cracks in the resin pocket and delamination occurred earliest in the simultaneous tapered specimen due to a greater stress concentration in a single large resin pocket in the structure. Intralaminar damages in the staggered tapered specimen with a shorter step spacing occurred mainly in the lower dropped ply as there was a more significant interaction between the neighboring steps in the specimen. The drastic decrease in the stress concentration after the occurrence of damages in the neighboring step(s) then suppressed the occurrence of intralaminar damages in the upper dropped ply. This is in contrast to the specimen with a longer step spacing where the intralaminar damages occurred in both dropped plies due to the distributed stress distribution. Delamination propagated between the dropped plies and continuous (belt and core) plies for both staggered laminates regardless of the length of the step spacing at higher applied stress levels. The results showed that internal ply-drop configuration and step spacing in staggered tapered structures contribute to significant differences in the mechanical properties and damage behavior in the laminates.

Mastering the Cahn–Hilliard equation and Camassa–Holm equation with cell-average-based neural network method

In this paper, we develop cell-average-based neural network (CANN) method to approximate solutions of nonlinear Cahn–Hilliard equation and Camassa–Holm equation. The CANN method is motivated by the finite volume scheme and evolved from the integral or weak formulation of partial differential equations. The major idea of cell-average-based neural network method is to explore a neural network to approximate the solution average difference or evolution between two neighboring time steps. Unlike traditional numerical methods, CANN method is not limited by the CFL restriction and can adapt large time steps for solution evolution, which is a significant advantage that classical numerical methods do not have. Once well trained, this method can be implemented as an fixed explicit finite volume scheme and applied to certain groups of initial value conditions for Cahn–Hilliard equation and Camassa–Holm equation without retraining the neural network. Furthermore, the CANN method also performs very well in handling data with corruption or low-quality data generated by Gaussian white noise. Numerical examples are presented to demonstrate effectiveness, accuracy and capability of the proposed method.

God the Mother Speaks of Xenia

I AM the children sleeping under mylar in a Texas warehouse.I AM the fathers lifting toddlers to their shoulders on our journeyto safety and rest. I'm safety and rest. But I'm mostly the motherswho'd rather not lug the heavy memory of the twelve-year-old boycut to fit in a sack, ditched on the neighbor's steps. I hold his ghost hand,a pale flower. Some call us vermin, an infestation. We're waitingfor recognition's spark, milk of kindness, hoping for something to hope.Even a goddess like me needs birds to perch in the soul. Even Irequire feathers, the tune that never stops. Don't look for me in the guards,or their guns. I'm not in the false borders, the fenced miles or razor wire.Haven't I taught you better? Even the body arrives by crossingover. Sperm into egg. Then uterine guestroom. Then cervical gate.Each life a light-chip, hard & bright, I slip into like second skin. So,I will walk with, as, in them. My names rhyme with exile & asylum.I wear boots, steel-toed. I wear running shoes. I wear these cracked, bloody soles.

Femtosecond Dynamics of a Polariton Bosonic Cascade at Room Temperature.

Whispering gallery modes in a microwire are characterized by a nearly equidistant energy spectrum. In the strong exciton-photon coupling regime, this system represents a bosonic cascade: a ladder of discrete energy levels that sustains stimulated transitions between neighboring steps. Here, by using a femtosecond angle-resolved spectroscopic imaging technique, the ultrafast dynamics of polaritons in a bosonic cascade based on a one-dimensional ZnO whispering gallery microcavity are explicitly visualized. Clear ladder-form build-up processes from higher to lower energy branches of the polariton condensates are observed, which are well reproduced by modeling using rate equations. Remarkably, a pronounced superbunching feature, which could serve as solid evidence for bosonic cascades, is demonstrated by the measured second-order time correlation factor. In addition, the nonlinear polariton parametric scattering dynamics on a time scale of hundreds of femtoseconds are revealed. Our understandings pave the way toward ultrafast coherent control of polaritons at room temperature.

Adiabatic Molecular Orbital Tracking in Ab Initio Molecular Dynamics.

The ab initio molecular dynamics (AIMD) method provides a computational route for the real-time simulation of reactive chemistry. An often-overlooked capability of this approach is the opportunity to examine the electronic evolution of a chemical system. For AIMD trajectories based on Hartree-Fock or density functional theory methods, the real-time evolution of single-particle molecular orbitals (MOs) can provide detailed insights into the time-dependent electronic structure of molecules. The evolving electronic Hamiltonians at each MD step pose problems for tracking and visualizing a given MO's character, ordering, and associated phase throughout an MD trajectory, however. This report presents and assesses a simple algorithm for correcting these deficiencies by exploiting similarity projections of the electronic structure between neighboring MD steps. Two aspects bring this analysis beyond a simple step-to-step projection scheme. First, the challenging case of coincidental orbital degeneracies is resolved via a quadrupole-field perturbation that nonetheless rigorously preserves energy conservation. Second, the resulting orbitals are shown to evolve adiabatically, in spite of the "preservation of character" concept that undergirds a projection of neighboring steps' MOs. The method is tested on water clusters, which exhibit considerable dynamic degeneracies, as well as a classic organic nucleophilic substitution reaction, in which the adiabatic evolution of the bonding orbitals clarifies textbook interpretations of the electronic structure during this reactive collision.

Species richness and beta diversity patterns of multiple taxa along an elevational gradient in pastured grasslands in the European Alps

To understand how diversity is distributed in space is a fundamental aim for optimizing future species and community conservation. We examined in parallel species richness and beta diversity components of nine taxonomic groups along a finite space, represented by pastured grasslands along an elevational gradient. Beta diversity, which is assumed to bridge local alpha diversity to regional gamma diversity was partitioned into the two components turnover and nestedness and analyzed at two levels: from the lowest elevation to all other elevations, and between neighboring elevations. Species richness of vascular plants, butterflies, beetles, spiders and earthworms showed a hump-shaped relationship with increasing elevation, while it decreased linearly for grasshoppers and ants, but increased for lichens and bryophytes. For most of the groups, turnover increased with increasing elevational distance along the gradient while nestedness decreased. With regard to step-wise beta diversity, rates of turnover or nestedness did not change notably between neighboring steps for the majority of groups. Our results support the assumption that species communities occupying the same habitat significantly change along elevation, however transition seems to happen continuously and is not detectable between neighboring steps. Our findings, rather than delineating levels of major diversity losses, indicate that conservation actions targeting at a preventive protection for species and their environment in mountainous regions require the consideration of entire spatial settings.

Implementations of parallel software for crack analyses based on the improved XFEM

The extended finite element method (XFEM) has been a state-of-the-art tool for crack analyses. However, the method has been long hampered in engineering applications by two major issues. One is the global stiffness matrix in static analyses being highly ill-conditioned. The other one is the inconsistent energy transfer between the neighboring time steps in dynamic analyses. The first issue leads to bad convergence in large-scale engineering applications where iterative equation solvers are mainly used. The second issue causes poor accuracy and difficulties in implementations of dynamic analyses. In order to overcome these two issues, the improved XFEM is proposed, based on an extra-dof-free PU approximation. Thereby, parallel software for crack analyses, PANDA_Fracture, is developed based on the proposed method with an HPC framework for numerical applications—JAUMIN. As numerical examples indicate, the software PANDA_Fracture has several distinguished features. Firstly, it introduces highly accurate crack tip enrichment and supports arbitrary crack propagation. Secondly, it supports both implicit and explicit dynamic analyses. Thirdly, it supports multiple crack analyses with high efficiency. Fourthly, it scales up to one thousand CPU cores for high-performance simulations.

A Design Approach for High-Q FBARs With a Dual-Step Frame.

This paper presents a new approach for the design of film bulk acoustic resonators (FBARs) with high-quality factor ${Q}_{a}$ at antiresonant frequency ${f}_{a}$ . Lamb waves are among the main contributors to the loss of energy at ${f}_{a}$ and the deterioration of ${Q}_{a}$ . The targeted approach is an optimization process of a dual-step frame structure to alleviate the problem with Lamb waves at ${f}_{a}$ . Such a frame is a combination of two neighboring steps that have different acoustic impedances reflecting the two Lamb modes that carry the largest amount of energy. The dimensions of these steps are computed using the diffraction grating method. To do so, the dispersion curves of Lamb waves and their associated power flows are calculated using a global matrix method and the acoustic Poynting's Theorem. This results in an enhancement in ${Q}_{a}$ of nearly 82% for an FBAR with a dual-step frame in comparison with an FBAR with no frame, as well as a smoother electrical response, at frequencies above ${f}_{a}$ but below the resonant frequency ${f}_{r}$ spurious resonances are moderately increased.

Echo state kernel recursive least squares algorithm for machine condition prediction

Abstract Kernel adaptive filter (KAF) has been widely utilized for time series prediction due to its online adaptation scheme, universal approximation capability and convexity. Nevertheless, KAF’s ability to handle temporal tasks is limited, because it is essentially a feed-forward neural network that lacks dynamic characteristics. Traditionally, a sliding widow that contains consecutive data points is constructed to deal with the temporal dependency between data points at neighboring time steps, but the restricted widow length may be incapable of capturing temporal patterns on a larger time scale. To manage this issue, a novel sequential learning approach called echo state KRLS (ES-KRLS) algorithm is proposed by incorporating a dynamic reservoir into kernel recursive least squares (KRLS) algorithm. The reservoir, consisting of a large number of sparsely interconnected hidden units, is treated as a temporal function that transforms the history of the time series into a high-dimensional reservoir state space. Subsequently, the spatial relationship between the reservoir state and the target output is effectively approximated by KRLS algorithm. With the utilization of the fixed reservoir, our novel method not only maintains the simplicity of the learning process but also leads to a significant improvement in the capability of modeling dynamic systems. Numerical results on benchmark tasks demonstrate the excellent performance of the novel method with respect to long-term prediction. Finally, an online prognostic method that combines ES-KRLS and a Bayesian technique is developed for tracking the health status of a degraded system and predicting remaining useful life (RUL). This prognostic method is applied to a turbofan engine degradation dataset to demonstrate its effectiveness.

Effect of Methylation on Local Mechanics and Hydration Structure of DNA

Cytosine methylation affects mechanical properties of DNA and potentially alters the hydration fingerprint for recognition by proteins. The atomistic origin for these effects is not well understood, and we address this via all-atom molecular dynamics simulations. We find that the stiffness of the methylated dinucleotide step changes marginally, whereas the neighboring steps become stiffer. Stiffening is further enhanced for consecutively methylated steps, providing a mechanistic origin for the effect of hypermethylation. Steric interactions between the added methyl groups and the nonpolar groups of the neighboring nucleotides are responsible for the stiffening in most cases. By constructing hydration maps, we found that methylation also alters the surface hydration structure in distinct ways. Its resistance to deformation may contribute to the stiffening of DNA for deformational modes lacking steric interactions. These results highlight the sequence- and deformational-mode-dependent effects of cytosine methylation.

Received signal strength difference–based tracking estimation method for arbitrarily moving target in wireless sensor networks

The surveillance system, which is mainly used for detecting and tracking moving targets, is one of the most significant applications of wireless sensor networks. Up to present, received signal strength indicator is the most common measuring mean for estimating the distance in sensor networks. However, in the presence of noise, it is impossible to gain the accurate distance based on received signal strength indicator. In this article, we propose a new tracking scheme based on received signal strength difference, which is the difference value of received signal strength indicators between two neighboring sampling steps. Supposing the noise has a certain degree of correlation in a certain time interval, received signal strength difference can effectively reduce the negative impact from noise. The tracking algorithm based on received signal strength difference is built: The sensor nodes collectively estimate a possible zone of the target via the signs of received signal strength difference. Next, the possible zone is further immensely shrunk to the refined zone via the absolute values of received signal strength difference. Finally, we determine the target’s final location by choosing the reference dot with the minimum norm in the refined zone. The simulation results demonstrate that the proposed tracking method achieves higher localization accuracy than the typical received signal strength indicator–based scheme. The received signal strength difference–based method also has good generality and robustness with respect to the noises with different deviation values and the target following arbitrarily state model.

A dynamic causal topic model for mining activities from complex videos

In this paper, a novel probabilistic topic model is proposed for mining activities from complex video surveillance scenes. In order to handle the temporal nature of the video data, we devise a dynamical causal topic model (DCTM) that can detect the latent topics and causal interactions between them. The model is based on the assumption that all temporal relationships between latent topics at neighboring time steps follow a noisy-OR distribution. And the parameter of the noisy-OR distribution is estimated by a data driven approach based on the idea of nonparametric Granger causality statistic. Furthermore, for convergence analysis during model learning process, the Kullback-Leibler between the prior and the posterior distributions is calculated. At last, using the causality matrix learned by DCTM, the total causal influence of each topic is measured. We evaluate the proposed model through experimentations on several challenging datasets and demonstrate that our model can identify the high influence activity in crowded scenes.

Investigation of Growth Mechanisms of Sodium Chlorate Crystals from Aqueous Solutions

Difficulties in determining the crystal growth mechanism from growth rate versus solution supersaturation dependence are discussed. Obtained results indicate that in the supersaturation range of 0.66–1.56%, sodium chlorate crystals grow in accordance with the spiral growth model. It is shown that in the supersaturation range of 0.44–1.32%, the growth mechanism depends on crystal growth history. Namely, the exponent n in the power law R = Kσn depends on the manner of supersaturation changes (varied from 1.3 to 1.9%). This indicates that the overlapping of diffusion fields of neighboring steps depends on growth history.

Excited Random Walks with Non-nearest Neighbor Steps

Let W be an integer-valued random variable satisfying \(E[W] =: \delta \ge 0\) and \(P(W 0\), and consider a self-interacting random walk that behaves like a simple symmetric random walk with the exception that on the first visit to any integer \(x\in \mathbb Z\), the size of the next step is an independent random variable with the same distribution as W. We show that this self-interacting random walk is recurrent if \(\delta \le 1\) and transient if \(\delta >1\). This is a special case of our main result which concerns the recurrence and transience of excited random walks (or cookie random walks) with non-nearest neighbor jumps.

Faceting diagram for sticky steps

Faceting diagrams for the step-faceting zone, the step droplet zone, and the Gruber-Mullins-Pokrovsky-Talapov (GMPT) zone for a crystal surface are obtained by using the density matrix renormalization group method to calculate the surface tension. The model based on these calculations is the restricted solid-on-solid (RSOS) model with a point-contact-type step-step attraction (p-RSOS model) on a square lattice. The point-contact-type step-step attraction represents the energy gain obtained by forming a bonding state with orbital overlap at the meeting point of the neighboring steps. In the step-faceting zone, disconnectedness in the surface tension leads to the formation of a faceted macrostep on a vicinal surface at equilibrium. The disconnectedness in the surface tension also causes the first-order shape transition for the equilibrium shape of a crystal droplet. The lower zone boundary line (ZBL), which separates the step-faceting zone and the step droplet zone, is obtained by the condition γ1=limn→∞γn/n, where γn is the step tension of the n-th merged step. The upper ZBL, which separates the GMPT zone and the step droplet zone, is obtained by the condition Aq,eff = 0 and Bq,eff = 0, where Aq,eff and Bq,eff represent the coefficients for the |q→|2 term and the |q→|3 term, respectively, in the |q→|-expanded form of the surface free energy feff(q→). Here, q→ is the surface gradient relative to the (111) surface. The reason why the vicinal surface inclined in the 〈101〉 direction does not exhibit step-faceting is explained in terms of the one-dimensional spinless quasi-impenetrable attractive bosons at absolute zero.

ANALYSIS OF STEP-LOADED OPEN RECTANGULAR GRATING SLOW-WAVE STRUCTURES FOR MM-WAVE TRAVELING-WAVE TUBES

The open rectangular grating with step-loaded slow-wave structure (SWS), a type of allmetal SWS for high power wide band mm-wave wave traveling wave tubes (TWT) is presented in this paper. By using the jumping conditions at the interface of two neighboring steps and single-mode approximation (SMA) field matching theory, the dispersion equation and coupling impedance of this SWS were obtained. Then the obtained complex dispersion equation was numerically calculated, and the slow-wave characteristics of the fundamental wave of this structure were discussed. Moreover, the calculation results by our theory were accordant with the simulation data obtained by the 3D electromagnetic simulation software HFSS. The numerical calculation results show that the dispersion characteristics and coupling impedance are notably improved by loading the steps. And the working bandwidth may be the widest when the thickness of the step is about equal to the thickness of the groove depth. The proper design parameters can be optimized to meet the needs of high frequency characteristics with wide bandwidth and high output power. The present study will be useful for further research and design of this kind of high frequency system.

Rectification and phase locking of graphite

Rectification phenomena and the phase locking in a two-dimensional overdamped Frenkel–Kontorova model with a graphite periodic substrate were studied. The presence of dc and ac forces in the longitudinal direction causes the appearance of dynamicalmode locking and the steps in the response function of the system. On the other hand, the presence of an ac force in the transverse direction causes the appearance of rectification,even though there is no net dc force in the transverse direction. It is found that whereas the longitudinal velocity increases in a series of steps, rectification in the transverse direction can occur only between two neighbor steps. The amplitude and phase of the external ac driving force affect the depinning force,rectification of the system and particles trajectories.

Identifying Change Points in a Covariate Effect on Time-to-Event Analysis with Reduced Isotonic Regression

Isotonic regression is a useful tool to investigate the relationship between a quantitative covariate and a time-to-event outcome. The resulting non-parametric model is a monotonic step function of a covariate X and the steps can be viewed as change points in the underlying hazard function. However, when there are too many steps, over-fitting can occur and further reduction is desirable. We propose a reduced isotonic regression approach to allow combination of small neighboring steps that are not statistically significantly different. In this approach, a second stage, the reduction stage, is integrated into the usual monotonic step building algorithm by comparing the adjacent steps using appropriate statistical testing. This is achieved through a modified dynamic programming algorithm. We implemented the approach with the simple exponential distribution and then its extension, the Weibull distribution. Simulation studies are used to investigate the properties of the resulting isotonic functions. We apply this methodology to the Diabetes Control and Complication Trial (DCCT) data set to identify potential change points in the association between HbA1c and the risk of severe hypoglycemia.

Unraveling the sequence-dependent polymorphic behavior of d(CpG) steps in B-DNA.

We have made a detailed study of one of the most surprising sources of polymorphism in B-DNA: the high twist/low twist (HT/LT) conformational change in the d(CpG) base pair step. Using extensive computations, complemented with database analysis, we were able to characterize the twist polymorphism in the d(CpG) step in all the possible tetranucleotide environment. We found that twist polymorphism is coupled with BI/BII transitions, and, quite surprisingly, with slide polymorphism in the neighboring step. Unexpectedly, the penetration of cations into the minor groove of the d(CpG) step seems to be the key element in promoting twist transitions. The tetranucleotide environment also plays an important role in the sequence-dependent d(CpG) polymorphism. In this connection, we have detected a previously unexplored intramolecular C-H···O hydrogen bond interaction that stabilizes the low twist state when 3′-purines flank the d(CpG) step. This work explains a coupled mechanism involving several apparently uncorrelated conformational transitions that has only been partially inferred by earlier experimental or theoretical studies. Our results provide a complete description of twist polymorphism in d(CpG) steps and a detailed picture of the molecular choreography associated with this conformational change.