Classical Walker Research Articles

Kardar-Parisi-Zhang Physics and Phase Transition in a Classical Single Random Walker under Continuous Measurement.

We introduce and study a new model consisting of a single classical random walker undergoing continuous monitoring at rate γ on a discrete lattice. Although such a continuous measurement cannot affect physical observables, it has a nontrivial effect on the probability distribution of the random walker. At small γ, we show analytically that the time evolution of the latter can be mapped to the stochastic heat equation. In this limit, the width of the log-probability thus follows a Family-Vicsek scaling law, N^{α}f(t/N^{α/β}), with roughness and growth exponents corresponding to the Kardar-Parisi-Zhang (KPZ) universality class, i.e., α_{KPZ}^{1D}=1/2 and β_{KPZ}^{1D}=1/3, respectively. When γ is increased outside this regime, we find numerically in 1D a crossover from the KPZ class to a new universality class characterized by exponents α_{M}^{1D}≈1 and β_{M}^{1D}≈1.4. In 3D, varying γ beyond a critical value γ_{M}^{c} leads to a phase transition from a smooth phase that we identify as the Edwards-Wilkinson class to a new universality class with α_{M}^{3D}≈1.

Analytical design and performance analysis of LEO mega chain satellite constellation

With the development of microsatellite technology and the growth of ground reconnaissance demand, the rapid design of a LEO constellation with minimum satellite number, low revisit time (within 10 minutes), and permanent inter-satellite links has become a hotspot and difficulty in constellation design. Aiming at the problem to use the minimum satellite number to achieve low revisit time coverage, a LEO (low earth orbit) Walker-chain constellation and its design method is proposed. The difference between the chain constellation and the classical Walker constellation is that it has one or more closed chain configurations. According to the coverage requirements and sensor field of view angle, the analytical design method is derived. A LEO chain constellation containing 132 satellites is designed for the ground reconnaissance mission. Comparing with the classical Walker-δ constellation and repeat ground track constellation, the chain constellation has fewer satellites, lower revisit time and the permanent inter-satellite links.

Novel Tyrosine Kinase-Mediated Phosphorylation With Dual Specificity Plays a Key Role in the Modulation of Streptococcus pyogenes Physiology and Virulence.

Streptococcus pyogenes (Group A Streptococcus, GAS) genomes do not contain a gene encoding a typical bacterial-type tyrosine kinase (BY-kinase) but contain an orphan gene-encoding protein Tyr-phosphatase (SP-PTP). Hence, the importance of Tyr-phosphorylation is underappreciated and not recognized for its role in GAS pathophysiology and pathogenesis. The fact that SP-PTP dephosphorylates Abl-tyrosine kinase-phosphorylated myelin basic protein (MBP), and SP-STK (S. pyogenes Ser/Thr kinase) also autophosphorylates its Tyr101-residue prompted us to identify a putative tyrosine kinase and Tyr-phosphorylation in GAS. Upon a genome-wide search of kinases possessing a classical Walker motif, we identified a non-canonical tyrosine kinase M5005_Spy_1476, a ∼17 kDa protein (153 aa) (SP-TyK). The purified recombinant SP-TyK autophosphorylated in the presence of ATP. In vitro and in vivo phosphoproteomic analyses revealed two key phosphorylated tyrosine residues located within the catalytic domain of SP-TyK. An isogenic mutant lacking SP-TyK derived from the M1T1 strain showed a retarded growth pattern. It displayed defective cell division and long chains with multiple parallel septa, often resulting in aggregates. Transcriptomic analysis of the mutant revealed 287 differentially expressed genes responsible for GAS pathophysiology and pathogenesis. SP-TyK also phosphorylated GAS CovR, WalR, SP-STP, and SDH/GAPDH proteins with dual specificity targeting their Tyr/Ser/Thr residues as revealed by biochemical and mass-spectrometric-based phosphoproteomic analyses. SP-TyK-phosphorylated CovR bound to PcovR efficiently. The mutant displayed sustained release of IL-6 compared to TNF-α during co-culturing with A549 lung cell lines, attenuation in mice sepsis model, and significantly reduced ability to adhere to and invade A549 lung cells and form biofilms on abiotic surfaces. SP-TyK, thus, plays a critical role in fine-tuning the regulation of key cellular functions essential for GAS pathophysiology and pathogenesis through post-translational modifications and hence, may serve as a promising target for future therapeutic developments.

Uncertainty Relation between Detection Probability and Energy Fluctuations.

A classical random walker starting on a node of a finite graph will always reach any other node since the search is ergodic, namely it fully explores space, hence the arrival probability is unity. For quantum walks, destructive interference may induce effectively non-ergodic features in such search processes. Under repeated projective local measurements, made on a target state, the final detection of the system is not guaranteed since the Hilbert space is split into a bright subspace and an orthogonal dark one. Using this we find an uncertainty relation for the deviations of the detection probability from its classical counterpart, in terms of the energy fluctuations.

A stochastic approach for automated brain MRI segmentation

This paper presents an approach to segment lesions from brain magnetic resonance images in a fully automatic manner. The proposed idea leverages the strength of classical random walker algorithm and graph cut optimization technique in a single framework. We demonstrate that formulating a “prior” from a stochastic model can ameliorate the need of manually selected seed selection process in the random walker framework, thus making the algorithm fully automatic in a generic manner. By analytically solving a linear system of equations in the random walk process, initial labelling ∈ [0, 1] of each pixel in the image are computed to obtain the likelihood probability. These probabilities are then used to compute the likelihood for the data fidelity term in the energy function to compute the final segmentation, which is minimized by min cut max flow algorithm. Experimental results show the superiority of the proposed method over the state-of-the-art techniques on publicly available datasets.

Quantum walks with quantum chaotic coins: Loschmidt echo, classical limit, and thermalization.

Coined discrete-time quantum walks are studied using simple deterministic dynamical systems as coins whose classical limit can range from being integrable to chaotic. It is shown that a Loschmidt echo-like fidelity plays a central role, and when the coin is chaotic this is approximately the characteristic function of a classical random walker. Thus the classical binomial distribution arises as a limit of the quantum walk and the walker exhibits diffusive growth before eventually becoming ballistic. The coin-walker entanglement growth is shown to be logarithmic in time as in the case of many-body localization and coupled kicked rotors, and saturates to a value that depends on the relative coin and walker space dimensions. In a coin-dominated scenario, the chaos can thermalize the quantum walk to typical random states such that the entanglement saturates at the Haar averaged Page value, unlike in a walker-dominated case when atypical states seem to be produced.

Return probability for the Anderson model on the random regular graph

We study the return probability for the Anderson model on the random regular graph and give evidence of the existence of two distinct phases: a fully ergodic and nonergodic one. In the ergodic phase, the return probability decays polynomially with time with oscillations, being the attribute of the Wigner-Dyson-like behavior, while in the nonergodic phase the decay follows a stretched exponential decay.We give a phenomenological interpretation of the stretched exponential decay in terms of a classical random walker. Furthermore, comparing typical and mean values of the return probability, we show how to differentiate an ergodic phase from a nonergodic one. We benchmark this method first in two random matrix models, the power-law random banded matrices, and the Rosenzweig-Porter matrices, which host both phases. Second, we apply this method to the Anderson model on the random regular graph to give further evidence of the existence of the two phases.

Stopping time of a one-dimensional bounded quantum walk**Project supported by the National Natural Science Foundation of China (Grant Nos. 11222430, 11434011, and 11474049), the National Basic Research Program of China (Grant No. 2012CB922104), the Fundamental Research Funds for the Central Universities, China, and the Research Funds of Renmin University of China (Grant No. 16XNLQ03).

The stopping time of a one-dimensional bounded classical random walk (RW) is defined as the number of steps taken by a random walker to arrive at a fixed boundary for the first time. A quantum walk (QW) is a non-trivial generalization of RW, and has attracted a great deal of interest from researchers working in quantum physics and quantum information. In this paper, we develop a method to calculate the stopping time for a one-dimensional QW. Using our method, we further compare the properties of stopping time for QW and RW. We find that the mean value of the stopping time is the same for both of these problems. However, for short times, the probability for a walker performing a QW to arrive at the boundary is larger than that for a RW. This means that, although the mean stopping time of a quantum and classical walker are the same, the quantum walker has a greater probability of arriving at the boundary earlier than the classical walker.

Quantum random walks on congested lattices and the effect of dephasing.

We consider quantum random walks on congested lattices and contrast them to classical random walks. Congestion is modelled on lattices that contain static defects which reverse the walker’s direction. We implement a dephasing process after each step which allows us to smoothly interpolate between classical and quantum random walks as well as study the effect of dephasing on the quantum walk. Our key results show that a quantum walker escapes a finite boundary dramatically faster than a classical walker and that this advantage remains in the presence of heavily congested lattices.

Occlusal caries detection using random walker algorithm: a graph approach.

The aim of this work is to present a modification of the Random Walker algorithm for the segmentation of occlusal caries from photographic color images. The modification improves the detection and time execution performance of the classical Random Walker algorithm and also deals with the limitations and difficulties that the specific type of images impose to the algorithm. The proposed modification consists of eight steps: 1) definition of the seed points, 2) conversion of the image to gray scale, 3) application of watershed transformation, 4) computation of the centroid of each region, 5) construction of the graph, 6) application of the Random Walker algorithm, 7) smoothing and extraction of the perimeter of the regions of interest and 8) overlay of the results. The algorithm was evaluated using a set of 96 images where 339 areas of interest were manually segmented by an expert. The obtained segmentation accuracy is 93%.

An Image Positioning Method of Automatic Random Walker Based on IFS Edge Detection

The segmentation method of classical random walker needs to select seed points artificially, and may cause incomplete or inaccurate segmentation. In view of these problems, this paper presents an image positioning method of automatic random walker based on IFS (Intuitionistic Fuzzy Set). IFS edge detection method is used to get the edge information of image, and then the connected domains are found out in image edge using the morphology method. Select the central pixels of each connected domain as seed points for automatic random walker, and then segment the IFS edge image by random walker. Experimental results show that the proposed method overcomes the application limitation of semi-automatic random walker algorithm, and improves the accuracy of image positioning.

Inflammatory aortic abdominal aneurysm - immunophenotypic characterization of inflammatory infiltrate.

Inflammatory aortic abdominal aneurysm - immunophenotypic characterization of inflammatory infiltrate.

Degree Distribution in Quantum Walks on Complex Networks

Google's search engine algorithmically determines the relative importance of the world's webpages by exploiting the physics of a classical random walker on the complex network of nodes (pages) and links (hyperlinks). What happens if the classical random walker is replaced by a quantum one? Researchers develop and investigate a simple model of a quantum walker on a complex network, uncovering interesting quantum-classical correspondence as well as fundamentally intriguing differences.

Imaging the Fine Structure of a Magnetic Domain Wall in a Ni Nanocylinder

We present the first experimental imaging of the internal DW structure in 55 and 85 nm diameter Ni nanocylinders, using electron holography combined with micromagnetic calculations. We demonstrate the magnetic transition from a hybrid magnetic state with both vortex and transverse DW in 85 nm diameter Ni nanocylinders to a pure transverse wall in thinner nanowires. This is particularly important as DWs in nanocylinders are model systems to go beyond the classical Walker limit.

Biochemical characterization of C4 protein of Cotton Leaf Curl Kokhran Virus-Dabawali

BackgroundCotton leaf curl Kokhran Virus-Dabawali (CLCuKV-Dab) is a monopartite begomovirus encoding two proteins V1 and V2 in the virion sense and four proteins C1, C2, C3 and C4 in the complementary sense. The C4 protein of monopartite begomoviruses has been implicated to play a role in symptom determination and virus movement. The present work aims at the biochemical characterization of this protein. MethodsThe C4 protein of CLCuKV-Dab was purified in fusion with GST and tested for the ability to hydrolyze ATP and other phosphate containing compounds. ATPase activity was assayed by using radiolabeled γ-[32P]-ATP and separating the product of reaction by thin layer chromatography. The hydrolysis of other compounds was monitored by the formation of a blue colored phosphomolybdate complex which was estimated by measuring the absorbance at 655nm. ResultsThe purified GST-C4 protein exhibited metal ion dependent ATPase and inorganic pyrophosphatase activities. Deletion of a sequence resembling the catalytic motif present in phosphotyrosine phosphatases resulted in 70% reduction in both the activities. Mutational analysis suggested arginine 13 to be catalytically important for the ATPase and cysteine 8 for the pyrophosphatase activity of GST-C4. Interaction of V2 with GST-C4 resulted in an increase in both the enzymatic activities of GST-C4. ConclusionsThe residues important for the enzymatic activities of GST-C4 are present in a motif different from the classical Walker motifs and the non-classical ATP binding motifs reported so far. General significanceThe C4 protein of CLCuKV-Dab, a putative natively unfolded protein, exhibits enzymatic activities.

N-Acetyl-d-glucosamine 2-epimerase from Anabaena sp. CH1 contains a novel ATP-binding site required for catalytic activity

ATP is required as a structural activator for the reversible epimerization of N-acetyl-d-glucosamine to N-acetyl-d-mannosamine by N-acetyl-d-glucosamine 2-epimerase (AGE); however, the ATP-binding site on AGE has not been clearly identified. This study aimed to investigate the specific region of Anabaena sp. CH1 AGE (bAGE) that is required for ATP binding. In the absence of ATP, tryptic digest of bAGE resulted in the production of 2 segments of 17 and 26kDa, while in the presence of 1mM ATP, the enzyme was resistant to trypsin. ADP also displayed protective effects against trypsin digestion. A trypsin-mediated ATP-footprinting assay identified a deviant ATP-protected region, 156-GKYTK-160, which is located within the flexible loop of bAGE. Site-directed mutagenesis of residues in the loop region was performed, and both K151A and K160A variants greatly decreased the enzymatic activity as well as the ATP-binding ability of bAGE, indicating that residues K151 and K160 may be critical for ATP binding. This study demonstrated that the ATP-binding site (151-KDNPKGKYTK-160) of bAGE was a novel rather than a classical Walker motif A. This is the first ATP-binding site reported for AGEs.

Mutational analysis of human NOD1 and NOD2 NACHT domains reveals different modes of activation

Nucleotide-binding oligomerization domain-containing protein (NOD)1 and NOD2 are intracellular pattern recognition receptors (PRRs) of the nucleotide-binding domain and leucine-rich repeat containing (NLR) gene family involved in innate immune responses. Their centrally located NACHT domain displays ATPase activity and is necessary for activation and oligomerization leading to inflammatory signaling responses. Mutations affecting key residues of the ATPase domain of NOD2 are linked to severe auto-inflammatory diseases, such as Blau syndrome and early-onset sarcoidosis. By mutational dissection of the ATPase domain function, we show that the NLR-specific extended Walker B box (DGhDE) can functionally replace the canonical Walker B sequence (DDhWD) found in other ATPases. A requirement for an intact Walker A box and the magnesium-co-ordinating aspartate of the classical Walker B box suggest that an initial ATP hydrolysis step is necessary for activation of both NOD1 and NOD2. In contrast, a Blau-syndrome associated mutation located in the extended Walker B box of NOD2 that results in higher autoactivation and ligand-induced signaling does not affect NOD1 function. Moreover, mutation of a conserved histidine in the NACHT domain also has contrasting effects on NOD1 and NOD2 mediated NF-κB activation. We conclude that these two NLRs employ different modes of activation and propose distinct models for activation of NOD1 and NOD2.

Diffusion on a heptagonal lattice

We study the diffusion phenomena on the negatively curved surface made up of congruent heptagons. Unlike the usual two-dimensional plane, this structure makes the boundary increase exponentially with the distance from the center, and hence the displacement of a classical random walker increases linearly in time. The diffusion of a quantum particle put on the heptagonal lattice is also studied in the framework of the tight-binding model Hamiltonian, and we again find the linear diffusion like the classical random walk. A comparison with diffusion on complex networks is also made.

A Simple Multicloud Parameterization for Convectively Coupled Tropical Waves. Part II: Nonlinear Simulations

Abstract Observations in the Tropics point to the important role of three cloud types, congestus, stratiform, and deep convective clouds, besides ubiquitous shallow boundary layer clouds for both the climatology and large-scale organized anomalies such as convectively coupled Kelvin waves, two-day waves, and the Madden–Julian oscillation. Recently, the authors have developed a systematic model convective parameterization highlighting the dynamic role of the three cloud types through two baroclinic modes of vertical structure: a deep convective heating mode and a second mode with lower troposphere heating and cooling corresponding respectively to congestus and stratiform clouds. The model includes both a systematic moisture equation where the lower troposphere moisture increases through detrainment of shallow cumulus clouds, evaporation of stratiform rain, and moisture convergence and decreases through deep convective precipitation and also a nonlinear switch that favors either deep or congestus convection depending on whether the lower middle troposphere is moist or dry. Here these model convective parameterizations are applied to a 40 000-km periodic equatorial ring without rotation, with a background sea surface temperature (SST) gradient and realistic radiative cooling mimicking a tropical warm pool. Both the emerging “Walker cell” climatology and the convectively coupled wave fluctuations are analyzed here while various parameters in the model are varied. The model exhibits weak congestus moisture coupled waves outside the warm pool in a turbulent bath that intermittently amplify in the warm pool generating convectively coupled moist gravity wave trains propagating at speeds ranging from 15 to 20 m s−1 over the warm pool, while retaining a classical Walker cell in the mean climatology. The envelope of the deep convective events in these convectively coupled wave trains often exhibits large-scale organization with a slower propagation speed of 3–5 m s−1 over the warm pool and adjacent region. Occasional much rarer intermittent deep convection also occurs outside the warm pool. The realistic parameter regimes in the multicloud model are identified as those with linearized growth rates for large scale instabilities roughly in the range of 0.5 K day−1.

A random walk approach to quantum algorithms

The development of quantum algorithms based on quantum versions of random walks is placed in the context of the emerging field of quantum computing. Constructing a suitable quantum version of a random walk is not trivial; pure quantum dynamics is deterministic, so randomness only enters during the measurement phase, i.e. when converting the quantum information into classical information. The outcome of a quantum random walk is very different from the corresponding classical random walk owing to the interference between the different possible paths. The upshot is that quantum walkers find themselves further from their starting point than a classical walker on average, and this forms the basis of a quantum speed up, which can be exploited to solve problems faster. Surprisingly, the effect of making the walk slightly less than perfectly quantum can optimize the properties of the quantum walk for algorithmic applications. Looking to the future, even with a small quantum computer available, the development of quantum walk algorithms might proceed more rapidly than it has, especially for solving real problems.