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Markov NT, Ercsey-Ravasz MM, Ribeiro Gomes AR, Lamy C, Magrou L, Vezoli J, Misery P, Falchier A, Quilodran R, Gariel MA, Sallet J, Gamanut R, Huissoud C, Clavagnier S, Giroud P, Sappey-Marinier D, Barone P, Dehay C, Toroczkai Z, Knoblauch K, Van Essen DC, Kennedy H. A weighted and directed interareal connectivity matrix for macaque cerebral cortex. ACTA ACUST UNITED AC 2012; 24:17-36. [PMID: 23010748 PMCID: PMC3862262 DOI: 10.1093/cercor/bhs270] [Citation(s) in RCA: 504] [Impact Index Per Article: 42.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/22/2023]
Abstract
Retrograde tracer injections in 29 of the 91 areas of the macaque cerebral cortex revealed 1,615 interareal pathways, a third of which have not previously been reported. A weight index (extrinsic fraction of labeled neurons [FLNe]) was determined for each area-to-area pathway. Newly found projections were weaker on average compared with the known projections; nevertheless, the 2 sets of pathways had extensively overlapping weight distributions. Repeat injections across individuals revealed modest FLNe variability given the range of FLNe values (standard deviation <1 log unit, range 5 log units). The connectivity profile for each area conformed to a lognormal distribution, where a majority of projections are moderate or weak in strength. In the G29 × 29 interareal subgraph, two-thirds of the connections that can exist do exist. Analysis of the smallest set of areas that collects links from all 91 nodes of the G29 × 91 subgraph (dominating set analysis) confirms the dense (66%) structure of the cortical matrix. The G29 × 29 subgraph suggests an unexpectedly high incidence of unidirectional links. The directed and weighted G29 × 91 connectivity matrix for the macaque will be valuable for comparison with connectivity analyses in other species, including humans. It will also inform future modeling studies that explore the regularities of cortical networks.
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Affiliation(s)
- N T Markov
- Stem cell and Brain Research Institute, INSERM U846, 69500 Bron, France
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Markov NT, Misery P, Falchier A, Lamy C, Vezoli J, Quilodran R, Gariel MA, Giroud P, Ercsey-Ravasz M, Pilaz LJ, Huissoud C, Barone P, Dehay C, Toroczkai Z, Van Essen DC, Kennedy H, Knoblauch K. Weight consistency specifies regularities of macaque cortical networks. ACTA ACUST UNITED AC 2010; 21:1254-72. [PMID: 21045004 PMCID: PMC3097985 DOI: 10.1093/cercor/bhq201] [Citation(s) in RCA: 281] [Impact Index Per Article: 20.1] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/04/2022]
Abstract
To what extent cortical pathways show significant weight differences and whether these differences are consistent across animals (thereby comprising robust connectivity profiles) is an important and unresolved neuroanatomical issue. Here we report a quantitative retrograde tracer analysis in the cynomolgus macaque monkey of the weight consistency of the afferents of cortical areas across brains via calculation of a weight index (fraction of labeled neurons, FLN). Injection in 8 cortical areas (3 occipital plus 5 in the other lobes) revealed a consistent pattern: small subcortical input (1.3% cumulative FLN), high local intrinsic connectivity (80% FLN), high-input form neighboring areas (15% cumulative FLN), and weak long-range corticocortical connectivity (3% cumulative FLN). Corticocortical FLN values of projections to areas V1, V2, and V4 showed heavy-tailed, lognormal distributions spanning 5 orders of magnitude that were consistent, demonstrating significant connectivity profiles. These results indicate that 1) connection weight heterogeneity plays an important role in determining cortical network specificity, 2) high investment in local projections highlights the importance of local processing, and 3) transmission of information across multiple hierarchy levels mainly involves pathways having low FLN values.
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Affiliation(s)
- N T Markov
- Stem Cell and Brain Research Institute, Institut National de la Sante et de la Recherche Medicale U846, 18 avenue du Doyen Lepine, Bron, France
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Abstract
We study the statistics and scaling of extreme fluctuations in noisy task-completion landscapes, such as those emerging in synchronized distributed-computing networks, or generic causally constrained queuing networks, with scale-free topology. In these networks the average size of the fluctuations becomes finite (synchronized state) and the extreme fluctuations typically diverge only logarithmically in the large system-size limit ensuring synchronization in a practical sense. Provided that local fluctuations in the network are short tailed, the statistics of the extremes are governed by the Gumbel distribution. We present large-scale simulation results using the exact algorithmic rules, supported by mean-field arguments based on a coarse-grained description.
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Affiliation(s)
- H Guclu
- Center for Nonlinear Studies, Theoretical Division, Los Alamos National Laboratory, MS-B258, Los Alamos, New Mexico 87545, USA
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Guclu H, Korniss G, Novotny MA, Toroczkai Z, Rácz Z. Synchronization landscapes in small-world-connected computer networks. Phys Rev E Stat Nonlin Soft Matter Phys 2006; 73:066115. [PMID: 16906922 DOI: 10.1103/physreve.73.066115] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/26/2005] [Indexed: 05/11/2023]
Abstract
Motivated by a synchronization problem in distributed computing we studied a simple growth model on regular and small-world networks, embedded in one and two dimensions. We find that the synchronization landscape (corresponding to the progress of the individual processors) exhibits Kardar-Parisi-Zhang-like kinetic roughening on regular networks with short-range communication links. Although the processors, on average, progress at a nonzero rate, their spread (the width of the synchronization landscape) diverges with the number of nodes (desynchronized state) hindering efficient data management. When random communication links are added on top of the one and two-dimensional regular networks (resulting in a small-world network), large fluctuations in the synchronization landscape are suppressed and the width approaches a finite value in the large system-size limit (synchronized state). In the resulting synchronization scheme, the processors make close-to-uniform progress with a nonzero rate without global intervention. We obtain our results by "simulating the simulations," based on the exact algorithmic rules, supported by coarse-grained arguments.
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Affiliation(s)
- H Guclu
- Department of Physics, Applied Physics, and Astronomy, Rensselaer Polytechnic Institute, 110 8th Street, Troy, New York, 12180-3590, USA
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Finn JM, Goettee JD, Toroczkai Z, Anghel M, Wood BP. Estimation of entropies and dimensions by nonlinear symbolic time series analysis. Chaos 2003; 13:444-456. [PMID: 12777107 DOI: 10.1063/1.1555471] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/24/2023]
Abstract
Symbolic nonlinear time series analysis methods have the potential for analyzing nonlinear data efficiently with low sensitivity to noise. In symbolic nonlinear time series analysis a time series for a fixed delay is partitioned into a small number (called the alphabet size) of cells labeled by symbols, creating a symbolic time series. Symbolic methods involve computing the statistics of words made from the symbolic time series. Specifically, the Shannon entropy of the distribution of possible words for a range of word lengths is computed. The rate of increase of the entropy with word length is the metric (Kolmogorov-Sinai) entropy. Methods of computing the metric entropy for flows as well as for maps are shown. A method of computing the information dimension appropriate to symbolic analysis is proposed. In terms of this formulation, the information dimension is determined by the scaling of entropy as alphabet size is modestly increased, using the information obtained from large word length. We discuss the role of sampling time and the issue of using these methods when there may be no generating partition.
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Affiliation(s)
- J M Finn
- Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
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Abstract
In a parallel discrete-event simulation (PDES) scheme, tasks are distributed among processing elements (PEs) whose progress is controlled by a synchronization scheme. For lattice systems with short-range interactions, the progress of the conservative PDES scheme is governed by the Kardar-Parisi-Zhang equation from the theory of nonequilibrium surface growth. Although the simulated (virtual) times of the PEs progress at a nonzero rate, their standard deviation (spread) diverges with the number of PEs, hindering efficient data collection. We show that weak random interactions among the PEs can make this spread nondivergent. The PEs then progress at a nonzero, near-uniform rate without requiring global synchronizations.
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Affiliation(s)
- G Korniss
- Department of Physics, Applied Physics, and Astronomy, Rensselaer Polytechnic Institute, 110 8th Street, Troy, NY 12180, USA.
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Benczik IJ, Toroczkai Z, Tél T. Selective sensitivity of open chaotic flows on inertial tracer advection: catching particles with a stick. Phys Rev Lett 2002; 89:164501. [PMID: 12398726 DOI: 10.1103/physrevlett.89.164501] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/30/2002] [Indexed: 05/24/2023]
Abstract
We investigate the effects of finite size and inertia of a small spherical particle immersed in an open unsteady flow which, for ideal tracers, generates transiently chaotic trajectories. The inertia effects may strongly modify the chaotic motion to the point that attractors may appear in the configuration space. These studies are performed in a model of the two-dimensional flow past a cylindrical obstacle. The relevance to modeling efforts of biological pathogen transport in large-scale flows is discussed. Since the tracer dynamics is sensitive to the particle inertia and size, simple geometric setups in such flows could be used as a particle mixture segregator separating and trapping particles.
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Affiliation(s)
- I J Benczik
- Institute for Theoretical Physics, Eötvös University, P.O. Box 32, H-1518 Budapest, Hungary
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Das Sarma S, Punyindu Chatraphorn P, Toroczkai Z. Universality class of discrete solid-on-solid limited mobility nonequilibrium growth models for kinetic surface roughening. Phys Rev E Stat Nonlin Soft Matter Phys 2002; 65:036144. [PMID: 11909202 DOI: 10.1103/physreve.65.036144] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/16/2001] [Revised: 10/09/2001] [Indexed: 05/23/2023]
Abstract
We investigate, using the noise reduction technique, the asymptotic universality class of the well-studied nonequilibrium limited mobility atomistic solid-on-solid surface growth models introduced by Wolf and Villain (WV) and Das Sarma and Tamborenea (DT) in the context of kinetic surface roughening in ideal molecular beam epitaxy. We find essentially all the earlier conclusions regarding the universality class of DT and WV models to be severely hampered by slow crossover and extremely long-lived transient effects. We identify the correct asymptotic universality class(es) that differs from earlier conclusions in several instances.
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Affiliation(s)
- S Das Sarma
- Department of Physics, University of Maryland, College Park, Maryland 20742-4111, USA
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Toroczkai Z, Korniss G. Comment on "extremal-point densities of interface fluctuations in a quenched random medium". Phys Rev E Stat Nonlin Soft Matter Phys 2001; 64:048101. [PMID: 11690187 DOI: 10.1103/physreve.64.048101] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/05/2001] [Indexed: 05/23/2023]
Abstract
Lam and Tan [Phys. Rev. E 62, 6246 (2000)] recently studied the extremal-point densities of interface fluctuations in a quenched random medium. In this Comment we show that their results for systems on a lattice contain algebraic errors leading to invalid conclusions. Further, while most of their calculations for the continuum case are correct, they misinterpret the result to come to an agreement with the (erroneous) lattice calculations. We derive the correct expressions for the lattice, which agree with the correct interpretation of the continuum case.
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Affiliation(s)
- Z Toroczkai
- Theoretical Division and Center for Nonlinear Studies, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
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Abstract
We investigate the reaction kinetics of small spherical particles with inertia, obeying coalescence type of reaction, B+B-->B, and being advected by hydrodynamical flows with time-periodic forcing. In contrast to passive tracers, the particle dynamics is governed by the strongly nonlinear Maxey-Riley equations, which typically create chaos in the spatial component of the particle dynamics, appearing as filamental structures in the distribution of the reactants. Defining a stochastic description supported on the natural measure of the attractor, we show that, in the limit of slow reaction, the reaction kinetics assumes a universal behavior exhibiting a t(-1) decay in the amount of reagents, which become distributed on a subset of dimension D2, where D2 is the correlation dimension of the chaotic flow.
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Affiliation(s)
- T Nishikawa
- Department of Mathematics, Arizona State University, Tempe, Arizona 85287, USA
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Abstract
Hydrodynamical phenomena play a keystone role in the population dynamics of passively advected species such as phytoplankton and replicating macromolecules. Recent developments in the field of chaotic advection in hydrodynamical flows encourage us to revisit the population dynamics of species competing for the same resource in an open aquatic system. If this aquatic environment is homogeneous and well-mixed then classical studies predict competitive exclusion of all but the most perfectly adapted species. In fact, this homogeneity is very rare, and the species of the community (at least on an ecological observation time scale) are in nonequilibrium coexistence. We argue that a peculiar small-scale, spatial heterogeneity generated by chaotic advection can lead to coexistence. In open flows this imperfect mixing lets the populations accumulate along fractal filaments, where competition is governed by an "advantage of rarity" principle. The possibility of this generic coexistence sheds light on the enrichment of phytoplankton and the information integration in early macromolecule evolution.
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Affiliation(s)
- G Károlyi
- Department of Civil Engineering Mechanics, Technical University of Budapest, Müegyetem rkp. 3, H-1521 Budapest, Hungary
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Toroczkai Z, Korniss G, Zia RK. Extremal-point densities of interface fluctuations. Phys Rev E Stat Phys Plasmas Fluids Relat Interdiscip Topics 2000; 62:276-294. [PMID: 11088461 DOI: 10.1103/physreve.62.276] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/16/2000] [Indexed: 05/23/2023]
Abstract
We introduce and investigate the stochastic dynamics of the density of local extrema (minima and maxima) of nonequilibrium surface fluctuations. We give a number of analytic results for interface fluctuations described by linear Langevin equations, and for on-lattice, solid-on-solid surface-growth models. We show that, in spite of the nonuniversal character of the quantities studied, their behavior against the variation of the microscopic length scales can present generic features, characteristic of the macroscopic observables of the system. The quantities investigated here provide us with tools that give an unorthodox approach to the dynamics of surface morphologies: a statistical analysis from the short-wavelength end of the Fourier decomposition spectrum. In addition to surface-growth applications, our results can be used to solve the asymptotic scalability problem of massively parallel algorithms for discrete-event simulations, which are extensively used in Monte Carlo simulations on parallel architectures.
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Affiliation(s)
- Z Toroczkai
- Department of Physics, University of Maryland, College Park, Maryland 20742-4111 and Center for Nonlinear Science and Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87544, USA
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Korniss G, Toroczkai Z, Novotny MA, Rikvold PA. From massively parallel algorithms and fluctuating time horizons to nonequilibrium surface growth. Phys Rev Lett 2000; 84:1351-1354. [PMID: 11017516 DOI: 10.1103/physrevlett.84.1351] [Citation(s) in RCA: 15] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/07/1999] [Indexed: 05/23/2023]
Abstract
We study the asymptotic scaling properties of a massively parallel algorithm for discrete-event simulations where the discrete events are Poisson arrivals. The evolution of the simulated time horizon is analogous to a nonequilibrium surface. Monte Carlo simulations and a coarse-grained approximation indicate that the macroscopic landscape in the steady state is governed by the Edwards-Wilkinson Hamiltonian. Since the efficiency of the algorithm corresponds to the density of local minima in the associated surface, our results imply that the algorithm is asymptotically scalable.
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Affiliation(s)
- G Korniss
- Supercomputer Computations Research Institute, Florida State University, Tallahassee, Florida 32306-4130, USA
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Toroczkai Z, Newman TJ, Das Sarma S. Sign-time distributions for interface growth. Phys Rev E Stat Phys Plasmas Fluids Relat Interdiscip Topics 1999; 60:R1115-8. [PMID: 11969931 DOI: 10.1103/physreve.60.r1115] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/27/1998] [Revised: 05/11/1999] [Indexed: 04/18/2023]
Abstract
We apply the recently introduced distribution of sign-times (DST) to nonequilibrium interface growth dynamics. We are able to treat within a unified picture the persistence properties of a large class of relaxational and noisy linear growth processes, and prove the existence of a nontrivial scaling relation. A critical dimension is found, relating to the persistence properties of these systems. We also illustrate, by means of numerical simulations, the different types of DST to be expected in both linear and nonlinear growth mechanisms.
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Affiliation(s)
- Z Toroczkai
- Department of Physics, Virginia Polytechnic Institute and State University, Blacksburg Virginia 24061, USA
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Károlyi G, Péntek A, Toroczkai Z, Tél T, Grebogi C. Chemical or biological activity in open chaotic flows. Phys Rev E Stat Phys Plasmas Fluids Relat Interdiscip Topics 1999; 59:5468-81. [PMID: 11969526 DOI: 10.1103/physreve.59.5468] [Citation(s) in RCA: 48] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/05/1998] [Indexed: 11/07/2022]
Abstract
We investigate the evolution of particle ensembles in open chaotic hydrodynamical flows. Active processes of the type A+B-->2B and A+B-->2C are considered in the limit of weak diffusion. As an illustrative advection dynamics we consider a model of the von Kármán vortex street, a time-periodic two-dimensional flow of a viscous fluid around a cylinder. We show that a fractal unstable manifold acts as a catalyst for the process, and the products cover fattened-up copies of this manifold. This may account for the observed filamental intensification of activity in environmental flows. The reaction equations valid in the wake are derived either in the form of dissipative maps or differential equations depending on the regime under consideration. They contain terms that are not present in the traditional reaction equations of the same active process: the decay of the products is slower while the productivity is much faster than in homogeneous flows. Both effects appear as a consequence of underlying fractal structures. In the long time limit, the system locks itself in a dynamic equilibrium state synchronized to the flow for both types of reactions. For particles of finite size an emptying transition might also occur leading to no products left in the wake.
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Affiliation(s)
- G Károlyi
- Department of Civil Engineering Mechanics, Technical University of Budapest, Muegyetem rkp. 3, H-1521 Budapest, Hungary
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Péntek Á, Toroczkai Z, Tél T, Grebogi C, Yorke JA. Fractal boundaries in open hydrodynamical flows: Signatures of chaotic saddles. Phys Rev E Stat Phys Plasmas Fluids Relat Interdiscip Topics 1995; 51:4076-4088. [PMID: 9963118 DOI: 10.1103/physreve.51.4076] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
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Péntek Á, Toroczkai Z, Mayer DH, Tél T. Kac model from a dynamical system's point of view. Phys Rev E Stat Phys Plasmas Fluids Relat Interdiscip Topics 1994; 49:2026-2040. [PMID: 9961443 DOI: 10.1103/physreve.49.2026] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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Toroczkai Z, Péntek Á. Classification criterion for dynamical systems in intermittent chaos. Phys Rev E Stat Phys Plasmas Fluids Relat Interdiscip Topics 1993; 48:136-146. [PMID: 9960575 DOI: 10.1103/physreve.48.136] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
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