Nonlocal Structure Research Articles

Topological Strata of Weighted Complex Networks.

The statistical mechanical approach to complex networks is the dominant paradigm in describing natural and societal complex systems. The study of network properties, and their implications on dynamical processes, mostly focus on locally defined quantities of nodes and edges, such as node degrees, edge weights and –more recently– correlations between neighboring nodes. However, statistical methods quickly become cumbersome when dealing with many-body properties and do not capture the precise mesoscopic structure of complex networks. Here we introduce a novel method, based on persistent homology, to detect particular non-local structures, akin to weighted holes within the link-weight network fabric, which are invisible to existing methods. Their properties divide weighted networks in two broad classes: one is characterized by small hierarchically nested holes, while the second displays larger and longer living inhomogeneities. These classes cannot be reduced to known local or quasilocal network properties, because of the intrinsic non-locality of homological properties, and thus yield a new classification built on high order coordination patterns. Our results show that topology can provide novel insights relevant for many-body interactions in social and spatial networks. Moreover, this new method creates the first bridge between network theory and algebraic topology, which will allow to import the toolset of algebraic methods to complex systems.

Structure of nonlocality of plasma turbulence

Various indications on the weakly nonlocal character of turbulent plasma transport both from experimental fluctuation measurements from Tore Supra and observations from the full-f, flux-driven gyrokinetic code GYSELA are reported. A simple Fisher equation model of this weakly nonlocal dynamics can be formulated in terms of an evolution equation for the turbulent entropy density, which contains the basic phenomenon of radial turbulence spreading in addition to avalanche-like dynamics via coupling to profile modulations. A derivation of this model, which contains the so-called beach effect, a diffusive and convective flux components for the flux of turbulence intensity, in addition to linear group propagation is given, starting from the drift-kinetic equation. The proposed model has the form of a transport equation for turbulence intensity, and may be considered as an addition to transport modelling. The kinetic fluxes given, can be computed using model closures, or local gyrokinetics. The model is also used in a particular setup that represents the near edge region as a relatively stable zone between the core and edge region where the energy injection is locally more substantial. It is observed that with constant, physical coefficients, the model gives a convincing qualitative profile of fluctuation intensity when the turbulence is coming from the core region with either a group velocity or a convective flux.

Towards the fast scrambling conjecture

Many proposed quantum mechanical models of black holes include highly nonlocal interactions. The time required for thermalization to occur in such models should reflect the relaxation times associated with classical black holes in general relativity. Moreover, the time required for a particularly strong form of thermalization to occur, sometimes known as scrambling, determines the time scale on which black holes should start to release information. It has been conjectured that black holes scramble in a time logarithmic in their entropy, and that no system in nature can scramble faster. In this article, we address the conjecture from two directions. First, we exhibit two examples of systems that do indeed scramble in logarithmic time: Brownian quantum circuits and the antiferromagnetic Ising model on a sparse random graph. Unfortunately, both fail to be truly ideal fast scramblers for reasons we discuss. Second, we use Lieb-Robinson techniques to prove a logarithmic lower bound on the scrambling time of systems with finite norm terms in their Hamiltonian. The bound holds in spite of any nonlocal structure in the Hamiltonian, which might permit every degree of freedom to interact directly with every other one.

Effects of Interface Resistance Asymmetry on Local and Non-local Magnetoresistance Structures

Spin injection and detection are very sensitive to the interface properties between ferromagnet and semiconductor. Because the interface properties such as a tunneling resistance and a polarization factor can be chosen independently between the injection and detection sides, the magnetic transport properties are considered to depend on the asymmetry of the two interfaces. We theoretically investigate the effect of the asymmetric interfaces of the injection side and the detection side on both the local and non-local magnetoresistance measurements. The results show the magnetoresistance ratio of local measurement structure has its maximum at the symmetric structure, and the effect of the asymmetry is very weak for the non-local measurement structure.

A Principled Approach to Grammars for Controlled Natural Languages and Predictive Editors

Controlled natural languages (CNL) with a direct mapping to formal logic have been proposed to improve the usability of knowledge representation systems, query interfaces, and formal specifications. Predictive editors are a popular approach to solve the problem that CNLs are easy to read but hard to write. Such predictive editors need to be able to "look ahead" in order to show all possible continuations of a given unfinished sentence. Such lookahead features, however, are difficult to implement in a satisfying way with existing grammar frameworks, especially if the CNL supports complex nonlocal structures such as anaphoric references. Here, methods and algorithms are presented for a new grammar notation called Codeco, which is specifically designed for controlled natural languages and predictive editors. A parsing approach for Codeco based on an extended chart parsing algorithm is presented. A large subset of Attempto Controlled English (ACE) has been represented in Codeco. Evaluation of this grammar and the parser implementation shows that the approach is practical, adequate and efficient.

Thermodynamics of string field theory motivated nonlocal models

We investigate the thermodynamic properties of the nonlocal tachyon motivated by their nonlocal structure in string field theory. We use previously developed perturbative methods for nonlocal fields to calculate the partition function and the equation of state in the high temperature limit. We find that in these models the tachyons undergo a second order phase transition. We compare our results with those of ordinary scalar field theory. We also calculate the one loop finite temperature effective potential.

Calculation of Nonlocal Spin Transfer Torque

We microscopically derive the spin-transfer torque due to diffusive spin current arising from nonequilibrium spin accumulation as realized in systems with nonlocal spin valve structure. Spin relaxation effects in spin transport is taken into account by introducing magnetic impurities.

Local and Nonlocal Preserving Projection for Bearing Defect Classification and Performance Assessment

The sensitivity of various physical features that are characteristics of bearing performance may vary significantly under different working conditions. Thus, it is critical to extract the most effective information from the original physical features generated from vibration signals for bearing defect classification and performance degradation assessment. This paper proposes a local and nonlocal preserving projection (LNPP)-based feature extraction algorithm, which is different from principal component analysis that aims to discover the global structure of Euclidean space and regular manifold learning algorithms that attempt to preserve local structure in data. LNPP is capable of discovering both local and nonlocal structures of data manifold. This may enable LNPP to find the meaningful low-dimensional information hidden in the high-dimensional feature set and then to serve as a preprocessor for defect classification. Furthermore, an LNPP-based quantification index is proposed for the assessment of bearing performance degradation. An LNPP-based contribution plot for feature selection is developed to improve the degradation detection sensitiveness and to reduce false alarms. A dynamic LNPP for bearing performance assessment is further developed to consider inherent autocorrelation existing in vibration data. Detailed results are very promising and are reported in this paper. This paper will provide guidance for the applications of manifold learning algorithms (e.g., LNPP) in machine fault diagnosis and performance prognostics.

Two-vortex structure of electron, nonlocality and Dirac equation

The dimensionless electromagnetic coupling constant α=e2/ℏc may have three interpretations: as the well-known ratio between the electron charge radius e2/mc2 and the Compton wavelength of an electron λc=ℏ/mc, as the ratio of two angular momenta since the Planck constant has the dimension of angular momentum and as the ratio of two flux quanta e and hc/e . The anomalous part of the electron magnetic moment together with the unified picture of the three interpretations of α is suggested to have deep physical significance. The electric charge is proposed to be a new quantum of flux that leads to a new model of the electron envisaging a two-vortex structure. In analogy with quantum conditions, we postulate sub-quantum conditions applicable in a region of the order of λc replacing ℏ by a universal constant f=e2/2πc and we apply it to the Dirac equation in internal space that gives rise to the anomalous magnetic moment of an electron. The Dirac spinor and two-spinor representations for the vortex structure of an electron in the single-particle Dirac framework are discussed. The role of sub-quantum rules and internal variables in developing the present ideas is also discussed. A critical discussion of past attempts at giving fundamental importance to magnetism and flux quantum is presented in order to delineate the new ideas in the present work.

Non-local adaptive structure tensors: Application to anisotropic diffusion and shock filtering

Structure tensors are used in several PDE-based methods to estimate information on the local structure in the image, such as edge orientation. They have become a common tool in many image processing applications. To integrate the local data information, the structure tensor is based on a local regularization of a tensorial product. In this paper, we propose a new regularization model based on the non-local properties of the tensor product. The resulting non-local structure tensor is effective in the restitution of the non homogeneity of the local orientation of the structures. It is particularly efficient in texture regions where patches repeat non locally. The new tensor regularization also offers the advantage of automatically adapting the smoothing parameter to the local structures of the tensor product. Finally, we explain how this new adaptive structure tensor can be plugged into two PDEs: an anisotropic diffusion and a shock filter. Comparisons with other tensor regularization methods and other PDEs demonstrate the clear advantage of using the non-local structure tensor.

Aromatic–Aromatic Interactions in Proteins: Beyond the Dimer

Aromatic residues are key widespread elements of protein structures and have been shown to be important for structure stability, folding, protein-protein recognition, and ligand binding. The interactions of pairs of aromatic residues (aromatic dimers) have been extensively studied in protein structures. Isolated aromatic molecules tend to form higher order clusters, like trimers, tetramers, and pentamers, that adopt particular well-defined structures. Taking this into account, we have surveyed protein structures deposited in the Protein Data Bank in order to find clusters of aromatic residues in proteins larger than dimers and characterized them. Our results show that larger clusters are found in one of every two unique proteins crystallized so far, that the clusters are built adopting the same trimer motifs found for benzene clusters in vacuum, and that they are clearly nonlocal brining primary structure distant sites together. We extensively analyze the trimers and tetramers conformations and found two main cluster types: a symmetric cluster and an extended ladder. Finally, using calmodulin as a test case, we show aromatic clsuters possible role in folding and protein-protein interactions. All together, our study highlights the relevance of aromatic clusters beyond the dimer in protein function, stability, and ligand recognition.

Nonequilibrium frequency-dependent noise through a quantum dot: A real-time functional renormalization group approach

We construct a real time current-conserving functional renormalization group (RG) scheme on the Keldysh contour to study frequency-dependent transport and noise through a quantum dot in the local moment regime. We find that the current vertex develops a nontrivial nonlocal structure in time that is governed by a new set of RG equations. Solving these RG equations, we compute the complete frequency and temperature dependence of the noise spectrum. For voltages that are large compared to the Kondo temperature (i.e., $\mathit{eV}\ensuremath{\gg}{k}_{B}{T}_{K}$), two sharp antiresonances are found in the noise spectrum at frequencies $\ensuremath{\hbar}\ensuremath{\omega}=\ifmmode\pm\else\textpm\fi{}eV$ and, correspondingly, two Kondo-assisted peaks appear in the ac conductance through the dot.

Compatible metrics and the diagonalizability of nonlocally bi-Hamiltonian systems of hydrodynamic type

We study bi-Hamiltonian systems of hydrodynamic type with nonsingular (semisimple) nonlocal bi-Hamiltonian structures. We prove that all such systems of hydrodynamic type are diagonalizable and that the metrics of the bi-Hamiltonian structure completely determine the complete set of Riemann invariants constructed for any such system. Moreover, we prove that for an arbitrary nonsingular (semisimple) nonlocally bi-Hamiltonian system of hydrodynamic type, there exist local coordinates (Riemann invariants) such that all matrix differential-geometric objects related to this system, namely, the matrix (affinor) V j i (u) of this system of hydrodynamic type, the metrics g ij (u) and g ij (u), the affinor υ j i (u) = g is (u)g 2,sj(u), and also the affinors (w 1,n) j i (u) and (w 2,n) j i (u) of the nonsingular nonlocal bi-Hamiltonian structure of this system, are diagonal in these special “diagonalizing” local coordinates (Riemann invariants of the system). The proof is a natural corollary of the general results of our previously developed theories of compatible metrics and of nonlocal bi-Hamiltonian structures; we briefly review the necessary notions and results in those two theories.

Case assignment, case concord, and the quantificational case construction

Abstract This paper examines a controversial and particularly complex case phenomenon called quantificational case attested in a number of historically unrelated Slavonic and Finno-Ugric languages, and attempts to establish certain novel cross-linguistic generalizations and conclusions. In particular, it will be argued that (i) instead of standard one-to-one case assignment, in which one case assigner is case-related to one case assignee, a many-to-many case flow is attested; (ii) nominal case is not a privilege of full DPs, arguments or thematic roles; (iii) case reflects either local or nonlocal functional structure, whether in the verbal or nominal domain; and that (iv) there is no distinction between case assignment and case concord. An analysis is provided using the probe–goal system of recent minimalist theory, although some modifications to this system are required. In particular, the system is generalized to cover the reported instances of many-to-many case assignment in which one probe can affect several goals and several probes can affect the case features of the one and the same goal.

Nonvolatile multiple-valued memory device using lateral spin valve

The authors propose a nonvolatile multiple-valued memory based on a nonlocal spin valve structure. Multibit informations are formed by changing the magnetization configuration in a nonlocal voltage probe consisting of a magnetic multilayer. A simple calculation method for the spin-accumulation voltage induced in lateral ferromagnetic/nonmagnetic multilayered hybrid structures is also developed on the basis of the spin resistance model. The developed model enables us to find the thickness of each ferromagnetic layer for the optimized operation of the multiple-valued memory.

On the Degradation of Cell-Centered Diffusive Preconditioners for Accelerating SN Transport Calculations in the Periodic Horizontal Interface Configuration

We investigate the degraded effectiveness of diffusion-based acceleration schemes in terms of the adjacent-cell preconditioner (AP) in a periodically heterogeneous limit devised for the two-dimensional (2-D) periodic horizontal interface (PHI) configuration. Specifically, we demonstrate that the diffusive low-order operator employed in the AP scheme lacks the structure of the integral transport operator in the above asymptotic limit since it (1) ignores cross-derivative coupling and (2) incorrectly estimates the strength of intra-layer coupling in the optically thin layers. In order to prove propositions 1 and 2, we derive expressions for the elements of the matrix representing a certain angular (SN) and spatially discretized form of the 2-D neutron transport integral operator. This is the transport operator that produces the full scalar flux solution if it is directly inverted on the once-collided particle source. The properties of this operator’s elements are then investigated in the asymptotic limit for PHI. The results of the asymptotic analysis point to a sparse but nonlocal matrix structure due to long-range coupling of a cell’s average flux with its neighboring cells, independent of the distance between the cells in the spatial mesh. In particular, for a cell in a thin layer, cross-derivative coupling of the cell’s flux to its diagonal neighbors is of the same asymptotic order as self-coupling and coupling with its north/south Cartesian neighbors. Similarly, its coupling with the fluxes in the same thin layer is of the same order, independent of the distance between the cells in the layer, as the coupling with the east/west Cartesian neighbors.We also show that modifying the standard diffusion-based AP can lead to effective acceleration in PHI. Specifically, we devise three novel acceleration schemes, named APB, Optimized-AP (OAP), and Hybrid-AP (HAP), obtained by modifying the original AP formalism in 2-D. In the APB the five-point AP operator is extended to a nine-point stencil that accounts for cross-derivative coupling by including the matrix elements of the integral transport operator B, which couple a cell-averaged scalar flux to its first diagonal neighbors. In the OAP the five-point stencil of the original AP operator is retained while optimizing the value of the elements in the preconditioner that affect the coupling of a cell with its east/west Cartesian neighbors. Specifically, the optimum elements are obtained by minimizing the iteration’s spectral radius and offer a more correct estimate of the strength of intra-layer coupling in a thin layer. Finally, the nine-point HAP operator represents a “hybrid” of the APB and OAP approaches, in the sense that the spectral properties of the optimized five-point OAP are further improved via the inclusion of cross-derivative terms. Fourier analysis of the novel acceleration schemes indicates that robustness of the accelerated iterations can be recovered, in spite of sharp material discontinuities, by accounting for cross-derivative coupling and by optimizing the preconditioner elements. The new acceleration schemes have also been implemented in a 2-D transport code, and numerical tests successfully verify the predictions of the Fourier analysis. However, it is important to emphasize that the modifications attempted in this work are specific to the selected asymptotic limit for PHI and do not translate into new low-order operators for the general heterogeneous-material case. Rather, the above modified operators suggest that it may be possible to eventually derive such a general low-order unconditionally robust operator.

Linear gyrokinetic simulation of high-n toroidal Alfvén eigenmodes in a burning plasma

A hybrid gyrokinetic ions/massless fluid electron model is used to study the stability of high-n toroidal Alfvén eigenmodes (TAEs) in ITER [M. Shimada et al., Nucl. Fusion 47, S1 (2007)]. The hybrid model has been implemented in the particle-in-cell turbulence simulation code GEM [Y. Chen and S. E. Parker, J. Comput. Phys. 220, 839 (2007)]. The adequacy of the hybrid model for simulating TAEs has been previously demonstrated [J. Lang et al., Phys. Plasmas 16, 102101 (2009)] by comparing the simulated TAE mode frequency and structure with an eigenmode analysis, and the thermal ion kinetic damping effect with analytic theory. By using a global particle-in-cell code the effects of large orbit width and nonlocal mode structures can be accurately included. Damping rate due to numerical filtering is carefully monitored, and convergence with respect to particle number, grid resolution, etc., is thoroughly tested. The simulations show that the most unstable modes in ITER lie in the rage of 10<n<20. Thermal ion pressure effect and alpha particle nonperturbative effect are important in determining the mode radial location and stability threshold. The thermal ion Landau damping rate and radiative damping rate from the simulations are compared with analytical estimates. The thermal ion Landau damping is the dominant damping mechanism. Plasma elongation has a strong stabilizing effect on the alpha driven TAEs. The central alpha particle pressure threshold for the most unstable n=15 mode is about βα(0)=0.7% for the fully shaped ITER equilibrium.

Domain-Wall Depinning Assisted by Pure Spin Currents

We study the depinning of domain walls by pure diffusive spin currents in a nonlocal spin valve structure based on two ferromagnetic Permalloy elements with copper as the nonmagnetic spin conduit. The injected spin current is absorbed by the second Permalloy structure with a domain wall, and from the dependence of the wall depinning field on the spin current density we find an efficiency of 6×10{-14} T/(A/m{2}), which is more than an order of magnitude larger than for conventional current induced domain-wall motion. Theoretically we find that this high efficiency arises from the surface torques exerted by the absorbed spin current that lead to efficient depinning.

A descriptive study of a manual therapy intervention within a randomised controlled trial for hamstring and lower limb injury prevention

BackgroundThere is little literature describing the use of manual therapy performed on athletes. It was our purpose to document the usage of a sports chiropractic manual therapy intervention within a RCT by identifying the type, amount, frequency, location and reason for treatment provided. This information is useful for the uptake of the intervention into clinical settings and to allow clinicians to better understand a role that sports chiropractors offer.MethodsAll treatment rendered to 29 semi-elite Australian Rules footballers in the sports chiropractic intervention group of an 8 month RCT investigating hamstring and lower-limb injury prevention was recorded. Treatment was pragmatically and individually determined and could consist of high-velocity, low-amplitude (HVLA) manipulation, mobilization and/or supporting soft tissue therapies. Descriptive statistics recorded the treatment rendered for symptomatic or asymptomatic benefit, delivered to joint or soft tissue structures and categorized into body regions. For the joint therapy, it was recorded whether treatment consisted of HVLA manipulation, HVLA manipulation and mobilization, or mobilization only. Breakdown of the HVLA technique was performed.ResultsA total of 487 treatments were provided (mean 16.8 consultations/player) with 64% of treatment for asymptomatic benefit (73% joint therapies, 57% soft tissue therapies). Treatment was delivered to approximately 4 soft tissue and 4 joint regions each consultation. The most common asymptomatic regions treated with joint therapies were thoracic (22%), knee (20%), hip (19%), sacroiliac joint (13%) and lumbar (11%). For soft tissue therapies it was gluteal (22%), hip flexor (14%), knee (12%) and lumbar (11%). The most common symptomatic regions treated with joint therapies were lumbar (25%), thoracic (15%) and hip (14%). For soft tissue therapies it was gluteal (22%), lumbar (15%) and posterior thigh (8%). Of the joint therapy, 56% was HVLA manipulation only, 36% high-HVLA and mobilization and 9% mobilization only. Of the HVLA manipulation, 63% was manually performed and 37% mechanically assisted.ConclusionsThe intervention applied was multimodal and multi-regional. Most treatment was for asymptomatic benefit, particularly for joint based therapies, which consisted largely of HVLA manipulation techniques. Most treatment was applied to non-local hamstring structures, in particular the knee, hip, pelvis and spine.

Purely nonlocal Hamiltonian formalism for systems of hydrodynamic type

We study purely nonlocal Hamiltonian structures for systems of hydrodynamic type. In the case of a semi-Hamiltonian system, we show that such structures are related to quadratic expansions of the diagonal metrics naturally associated with the system.