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  • 1.
    Ardelius, John
    et al.
    RISE, Swedish ICT, SICS.
    Aurell, Erik
    Krishnamurthy, Supriya
    RISE, Swedish ICT, SICS.
    Clustering of solutions in hard satisfiability problems2007In: Journal of Statistical Mechanics: Theory and Experiment, ISSN 1742-5468, E-ISSN 1742-5468Article in journal (Refereed)
    Abstract [en]

    We study the structure of the solution space and behavior of local search methods on random 3-SAT problems close to the SAT/UNSAT transition. Using the overlap measure of similarity between different solutions found on the same problem instance we show that the solution space is shrinking as a function of alpha. We consider chains of satisfiability problems, where clauses are added sequentially. In each such chain, the overlap distribution is first smooth, and then develops a tiered structure, indicating that the solutions are found in well separated clusters. On chains of not too large instances, all solutions are eventually observed to be in only one small cluster before vanishing. This condensation transition point is estimated to be alpha_c = 4.26. The transition approximately obeys finite-size scaling with an apparent critical exponent of about 1.7. We compare the solutions found by a local heuristic, ASAT, and the Survey Propagation algorithm up to alpha_c.

  • 2.
    Ardonne, Eddy
    et al.
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita).
    Bergholtz, Emil J.
    Stockholm University, Faculty of Science, Department of Physics.
    Kailasvuori, Janik
    Wikberg, Emma
    Stockholm University, Faculty of Science, Department of Physics.
    Degeneracy of non-Abelian quantum Hall states on the torus: domain walls and conformal field theory2008In: Journal of Statistical Mechanics: Theory and Experiment, ISSN 1742-5468, E-ISSN 1742-5468, p. P04016-Article in journal (Refereed)
    Abstract [en]

    We analyze the non-Abelian Read–Rezayi quantum Hall states on the torus, where it is natural to employ a mapping of the many-body problem onto a one-dimensional lattice model. On the thin torus—the Tao–Thouless (TT) limit—the interacting many-body problem is exactly solvable. The Read–Rezayi states at filling ν = k/(kM+2) are known to be exact ground states of a local repulsive k+1-body interaction, and in the TT limit this is manifested in that all states in the ground state manifold have exactly k particles on any kM+2 consecutive sites. For M \neq 0 the two-body correlations of these states also imply that there is no more than one particle on M adjacent sites. The fractionally charged quasiparticles and quasiholes appear as domain walls between the ground states, and we show that the number of distinct domain wall patterns gives rise to the nontrivial degeneracies, required by the non-Abelian statistics of these states. In the second part of the paper we consider the quasihole degeneracies from a conformal field theory (CFT) perspective, and show that the counting of the domain wall patterns maps one to one on the CFT counting via the fusion rules. Moreover we extend the CFT analysis to topologies of higher genus

  • 3. Battistin, C.
    et al.
    Hertz, John
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA. Niels Bohr Institute, Denmark .
    Tyrcha, J.
    Roudi, Yasser
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA. Centre for Neural Computation, Norway.
    Belief propagation and replicas for inference and learning in a kinetic Ising model with hidden spins2015In: Journal of Statistical Mechanics: Theory and Experiment, ISSN 1742-5468, E-ISSN 1742-5468, no 5, article id P05021Article in journal (Refereed)
    Abstract [en]

    We propose a new algorithm for inferring the state of hidden spins and reconstructing the connections in a synchronous kinetic Ising model, given the observed history. Focusing on the case in which the hidden spins are conditionally independent of each other given the state of observable spins, we show that calculating the likelihood of the data can be simplified by introducing a set of replicated auxiliary spins. Belief propagation (BP) and susceptibility propagation (SusP) can then be used to infer the states of hidden variables and to learn the couplings. We study the convergence and performance of this algorithm for networks with both Gaussian-distributed and binary bonds. We also study how the algorithm behaves as the fraction of hidden nodes and the amount of data are changed, showing that it outperforms the Thouless-Anderson-Palmer (TAP) equations for reconstructing the connections.

  • 4. Battistin, Claudia
    et al.
    Hertz, John
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita). Niels Bohr Institute, Denmark.
    Tyrcha, Joanna
    Stockholm University, Faculty of Science, Department of Mathematics.
    Roudi, Yasser
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita). Kavli Institute for Systems Neuroscience/Centre for Neural Computation, Norway.
    Belief propagation and replicas for inference and learning in a kinetic Ising model with hidden spins2015In: Journal of Statistical Mechanics: Theory and Experiment, ISSN 1742-5468, E-ISSN 1742-5468, article id P05021Article in journal (Refereed)
    Abstract [en]

    We propose a new algorithm for inferring the state of hidden spins and reconstructing the connections in a synchronous kinetic Ising model, given the observed history. Focusing on the case in which the hidden spins are conditionally independent of each other given the state of observable spins, we show that calculating the likelihood of the data can be simplified by introducing a set of replicated auxiliary spins. Belief propagation (BP) and susceptibility propagation (SusP) can then be used to infer the states of hidden variables and to learn the couplings. We study the convergence and performance of this algorithm for networks with both Gaussian-distributed and binary bonds. We also study how the algorithm behaves as the fraction of hidden nodes and the amount of data are changed, showing that it outperforms the Thouless-Anderson-Palmer (TAP) equations for reconstructing the connections.

  • 5.
    Bernhardsson, Sebastian
    et al.
    Umeå University, Faculty of Science and Technology, Department of Physics.
    Baek, Seung Ki
    Umeå University, Faculty of Science and Technology, Department of Physics.
    Minnhagen, Petter
    Umeå University, Faculty of Science and Technology, Department of Physics.
    A Paradoxical Property of the Monkey Book2011In: Journal of Statistical Mechanics: Theory and Experiment, ISSN 1742-5468, E-ISSN 1742-5468, p. P07013-Article in journal (Refereed)
    Abstract [en]

    A 'monkey book' is a book consisting of a random sequence of letters and blanks, where a group of letters surrounded by two blanks is defined as a word. We compare the statistics of the word distribution for a monkey book to real books. It is shown that the word distribution statistics for the monkey book is different and quite distinct from a typical real book. In particular, the monkey book obeys Heaps' power law to an extraordinarily good approximation, in contrast to the word distributions for real books, which deviate from Heaps' law in a characteristic way. This discrepancy is traced to the different properties of a 'spiked' distribution and its smooth envelope. The somewhat counter-intuitive conclusion is that a 'monkey book' obeys Heaps' power law precisely because its word-frequency distribution is not a smooth power law, contrary to the expectation based on simple mathematical arguments that if one is a power law, so is the other.

  • 6.
    Bo, Stefano
    et al.
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA. Max Planck Inst Phys Komplexer Syst, Nothnitzer Str 38, DE-01187 Dresden, Germany. ; Stockholm Univ, Roslagstullsbacken 23, SE-10691 Stockholm, Sweden.
    Lim, Soon Hoe
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA. Stockholm Univ, Roslagstullsbacken 23, SE-10691 Stockholm, Sweden.
    Eichhorn, Ralf
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA. Stockholm Univ, Roslagstullsbacken 23, SE-10691 Stockholm, Sweden.
    Functionals in stochastic thermodynamics: how to interpret stochastic integrals2019In: Journal of Statistical Mechanics: Theory and Experiment, ISSN 1742-5468, E-ISSN 1742-5468, article id 084005Article in journal (Refereed)
    Abstract [en]

    In stochastic thermodynamics standard concepts from macroscopic thermodynamics, such as heat, work, and entropy production, are generalized to small fluctuating systems by defining them on a trajectory-wise level. In Langevin systems with continuous state-space such definitions involve stochastic integrals along system trajectories, whose specific values depend on the discretization rule used to evaluate them (i.e. the 'interpretation' of the noise terms in the integral). Via a systematic mathematical investigation of this apparent dilemma, we corroborate the widely used standard interpretation of heat-and work-like functionals as Stratonovich integrals. We furthermore recapitulate the anomalies that are known to occur for entropy production in the presence of temperature gradients.

  • 7.
    Bo, Stefano
    et al.
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita).
    Lim, Soon Hoe
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita).
    Eichhorn, Ralf
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita).
    Functionals in stochastic thermodynamics: how to interpret stochastic integrals2019In: Journal of Statistical Mechanics: Theory and Experiment, ISSN 1742-5468, E-ISSN 1742-5468, article id 084005Article in journal (Refereed)
    Abstract [en]

    In stochastic thermodynamics standard concepts from macroscopic thermodynamics, such as heat, work, and entropy production, are generalized to small fluctuating systems by defining them on a trajectory-wise level. In Langevin systems with continuous state-space such definitions involve stochastic integrals along system trajectories, whose specific values depend on the discretization rule used to evaluate them (i.e. the 'interpretation' of the noise terms in the integral). Via a systematic mathematical investigation of this apparent dilemma, we corroborate the widely used standard interpretation of heat-and work-like functionals as Stratonovich integrals. We furthermore recapitulate the anomalies that are known to occur for entropy production in the presence of temperature gradients.

  • 8.
    Diaz-Mendez, Rogelio
    et al.
    KTH, School of Engineering Sciences (SCI), Physics.
    Lidmar, Jack
    KTH, School of Engineering Sciences (SCI), Physics.
    Wallin, Mats
    KTH, School of Engineering Sciences (SCI), Physics.
    Scaling of the magnetic permeability at the Berezinskii–Kosterlitz–Thouless transition from Coulomb gas simulations2018In: Journal of Statistical Mechanics: Theory and Experiment, ISSN 1742-5468, E-ISSN 1742-5468, Vol. 2018, no 12, article id 123203Article in journal (Refereed)
    Abstract [en]

    A new approach to the Berezinskii–Kosterlitz–Thouless transition in the two-dimensional Coulomb gas model is explored by Monte Carlo simulation and finite size scaling. The usual mapping of a neutral two-dimensional superconductor in zero magnetic field to a Coulomb gas leads to an unscreened logarithmic interaction between the vortices, and with periodic boundary conditions vortex configurations are always vorticity neutral with an equal number of plus and minus vortices. We demonstrate that relaxing the neutrality condition has certain advantages. It leads to non-neutral vortex configurations that can appear in real systems with open boundary conditions and permits calculation of the compressibility, which for thin film superconductors corresponds to the magnetic permeability. The vortex-number fluctuation has remarkable scaling properties at and below the Berezinskii–Kosterlitz–Thouless transition. The fugacity variable becomes dangerously irrelevant in the low-temperature phase and leads to a multiplicative scaling correction to the mean-square vortex-number fluctuation and to the magnetic permeability. This multiplicative correction strongly affects the scaling properties of the vorticity fluctuation at and below the transition. Consequences of these findings are demonstrated using Monte Carlo simulations. Inclusion of the next-higher order correction to scaling is found to play an important role in the analysis of numerical data for the vortex number fluctuation and permits accurate determination of the critical properties.

  • 9. Foda, O.
    et al.
    Zarembo, Konstantin
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA. Stockholm Univ., Sweden.
    Overlaps of partial Neel states and Bethe states2016In: Journal of Statistical Mechanics: Theory and Experiment, ISSN 1742-5468, E-ISSN 1742-5468, article id 023107Article in journal (Refereed)
    Abstract [en]

    Partial Neel states are generalizations of the ordinary Neel (classical anti-ferromagnet) state that can have arbitrary integer spin. We study overlaps of these states with Bethe states. We first identify this overlap with a partial version of reflecting-boundary domain-wall partition function, and then derive various determinant representations for off-shell and on-shell Bethe states.

  • 10. Foda, O.
    et al.
    Zarembo, Konstantin
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita). Uppsala University, Sweden.
    Overlaps of partial Neel states and Bethe states2016In: Journal of Statistical Mechanics: Theory and Experiment, ISSN 1742-5468, E-ISSN 1742-5468, article id 023107Article in journal (Refereed)
    Abstract [en]

    Partial Neel states are generalizations of the ordinary Neel (classical anti-ferromagnet) state that can have arbitrary integer spin. We study overlaps of these states with Bethe states. We first identify this overlap with a partial version of reflecting-boundary domain-wall partition function, and then derive various determinant representations for off-shell and on-shell Bethe states.

  • 11.
    Foda, O.
    et al.
    Univ Melbourne, Sch Math & Stat, Parkville, Vic 3010, Australia..
    Zarembo, Konstantin
    Uppsala University, Disciplinary Domain of Science and Technology, Physics, Department of Physics and Astronomy, Theoretical Physics. KTH Royal Inst Technol, NORDITA, Roslagstullsbacken 23, SE-10691 Stockholm, Sweden.;Stockholm Univ, Roslagstullsbacken 23, SE-10691 Stockholm, Sweden..
    Overlaps of partial Néel states and Bethe states2016In: Journal of Statistical Mechanics: Theory and Experiment, ISSN 1742-5468, E-ISSN 1742-5468, article id 023107Article in journal (Refereed)
    Abstract [en]

    Partial Neel states are generalizations of the ordinary Neel (classical anti-ferromagnet) state that can have arbitrary integer spin. We study overlaps of these states with Bethe states. We first identify this overlap with a partial version of reflecting-boundary domain-wall partition function, and then derive various determinant representations for off-shell and on-shell Bethe states.

  • 12.
    Freyhult, Lisa
    et al.
    Uppsala University, Disciplinary Domain of Science and Technology, Physics, Department of Physics and Astronomy, Theoretical Physics.
    Rej, Adam
    Staudacher, Matthias
    A generalized scaling function for AdS/CFT2008In: Journal of Statistical Mechanics: Theory and Experiment, ISSN 1742-5468, E-ISSN 1742-5468, p. P07015-Article in journal (Refereed)
    Abstract [en]

    We study a refined large spin limit for twist operators in the sl(2) sector of AdS/CFT. We derive a novel non-perturbative equation for the generalized two-parameter scaling function associated with this limit, and analyze it for weak coupling. It is expected to smoothly interpolate between weakly coupled gauge theory and string theory for strong coupling.

  • 13. Gulikers, Lennart
    et al.
    Evers, Joep
    Muntean, Adrian
    Eindhoven University of Technology.
    Lyulin, Alexey
    The effect of perception anisotropy on particle systems describing pedestrian flows in corridors2013In: Journal of Statistical Mechanics: Theory and Experiment, ISSN 1742-5468, E-ISSN 1742-5468, Vol. 2013, no 4Article in journal (Refereed)
    Abstract [en]

    We consider a microscopic model (a system of self-propelled particles) to study the behaviour of a large group of pedestrians walking in a corridor. Our point of interest is the effect of anisotropic interactions on the global behaviour of the crowd. The anisotropy we have in mind reflects the fact that people do not perceive (i.e. see, hear, feel or smell) their environment equally well in all directions. The dynamics of the individuals in our model follow from a system of Newton-like equations in the overdamped limit. The instantaneous velocity is modelled in such a way that it accounts for the angle at which an individual perceives another individual. We investigate the effects of this perception anisotropy by means of simulations, very much in the spirit of molecular dynamics. We define a number of characteristic quantifiers (including the polarization index and Morisita index) that serve as measures, for example, for organization and clustering, and we use these indices to investigate the influence of anisotropy on the global behaviour of the crowd. The goal of the paper is to investigate the potential of this model; extensive statistical analysis of simulation data and reproducing any specific real-life situation are beyond its scope.

  • 14.
    Innocenti, Nicolas
    et al.
    KTH, School of Computer Science and Communication (CSC), Computational Biology, CB.
    Aurell, Erik
    KTH, School of Computer Science and Communication (CSC), Computational Biology, CB.
    Lognormality and oscillations in the coverage of high-throughput transcriptomic data towards gene ends2013In: Journal of Statistical Mechanics: Theory and Experiment, ISSN 1742-5468, E-ISSN 1742-5468, Vol. 2013, no 10, p. P10013-Article in journal (Refereed)
    Abstract [en]

    High-throughput transcriptomics experiments have reached the stage where the count of the number of reads alignable to a given position can be treated as an almost-continuous signal. This allows us to ask questions of biophysical/biotechnical nature, but which may still have biological implications. Here we show that when sequencing RNA fragments from one end, as is the case on most platforms, an oscillation in the read count is observed at the other end. We further show that these oscillations can be well described by Kolmogorov's 1941 broken stick model. We investigate how the model can be used to improve predictions of gene ends (3' transcript ends), but conclude that with present data the improvement is only marginal. The results highlight subtle effects in high-throughput transcriptomics experiments which do not have a biological origin, but which may still be used to obtain biological information.

  • 15.
    Jia, Tao
    et al.
    Högskolan i Gävle.
    Jiang, Bin
    Högskolan i Gävle.
    Carling, Kenneth
    Dalarna University, School of Technology and Business Studies, Statistics.
    Bohlin, Magnus
    Dalarna University, School of Technology and Business Studies, Human Geography.
    Ban, Yifang
    KTH.
    An empirical study on human mobility and its agent-based modeling2012In: Journal of Statistical Mechanics: Theory and Experiment, ISSN 1742-5468, E-ISSN 1742-5468, article id P11024Article in journal (Refereed)
    Abstract [en]

    This paper aims to analyze the GPS traces of 258 volunteers for a better understanding of both the human mobility patterns and the mechanism. We report the regular and scaling properties of human mobility from several aspects, and importantly we find its levy flight characteristic which is consistent with the previous studies. We further assume two factors that may govern the levy flight property: (1) the scaling and hierarchical properties of the purpose clusters which serve as the underlying spatial structure, and (2) the individual preferential behavior. To verify the assumptions, we implement an agent-based model with the two factors, and the simulated agents indeed reproduce the same levy flight pattern as the observed one. In order to enable the model to reproduce more mobility patterns, we add the model a third factor, the jumping factor which means the probability that one person may cancel the regular mobility schedule and visit a random place. With this factor, our model could cover a relatively wide range of human mobility patterns with exponent values from 1.55 to 2.05.

  • 16.
    Jia, Tao
    et al.
    KTH, School of Architecture and the Built Environment (ABE), Urban Planning and Environment, Geodesy and Geoinformatics.
    Jiang, Bin
    University of Gävle.
    Carling, Kenneth
    Dalarna University.
    Bolin, Magnus
    Dalarna University.
    Ban, Yifang
    KTH, School of Architecture and the Built Environment (ABE), Urban Planning and Environment, Geodesy and Geoinformatics.
    An empirical study on human mobility and its agent-based modeling2012In: Journal of Statistical Mechanics: Theory and Experiment, ISSN 1742-5468, E-ISSN 1742-5468, Vol. 2012, no 11, p. P11024-Article in journal (Refereed)
    Abstract [en]

    This paper aims to analyze the GPS traces of 258 volunteers for a better understanding of both the human mobility patterns and the mechanism. We report the regular and scaling properties of human mobility from several aspects, and importantly we identify its levy flight characteristic which is consistent with the previous studies. We further assume two factors that may govern the levy flight property: (1) the scaling and hierarchical properties of the purpose clusters which serve as the underlying spatial structure, and (2) the individual preferential behavior. To verify the assumptions, we implement an agent-based model with the two factors, and the simulated results indeed capture the same levy flight pattern as the observed one. In order to enable the model to reproduce more mobility patterns, we add the model a third factor, the jumping factor which means the probability that one person may cancel the regular mobility schedule and explore a random place. With this factor, our model could cover a relatively wide range of human mobility patterns with scaling exponent values from 1.55 to 2.05.

  • 17.
    Jia, Tao
    et al.
    University of Gävle, Faculty of Engineering and Sustainable Development, Department of Industrial Development, IT and Land Management, Urban and regional planning/GIS-institute. Division of Geoinformatics, Royal Institute of Technology (KTH), Stockholm, Sweden .
    Jiang, Bin
    University of Gävle, Faculty of Engineering and Sustainable Development, Department of Industrial Development, IT and Land Management, Urban and regional planning/GIS-institute.
    Carling, Kenneth
    School of Technology and Business Studies, Dalarna University, Borlänge, Sweden .
    Bolin, Magnus
    School of Technology and Business Studies, Dalarna University, Borlänge, Sweden .
    Ban, Yifang
    Division of Geoinformatics, Royal Institute of Technology (KTH), Stockholm, Sweden.
    An empirical study on human mobility and its agent-based modeling2012In: Journal of Statistical Mechanics: Theory and Experiment, ISSN 1742-5468, E-ISSN 1742-5468, no 11, p. P11024-Article in journal (Refereed)
    Abstract [en]

    This paper aims to analyze the GPS traces of 258 volunteers in order to obtain a better understanding of both the human mobility patterns and the mechanism. We report the regular and scaling properties of human mobility for several aspects, and importantly we identify its Levy flight characteristic, which is consistent with those from previous studies. We further assume two factors that may govern the Levy flight property: (1) the scaling and hierarchical properties of the purpose clusters which serve as the underlying spatial structure, and (2) the individual preferential behaviors. To verify the assumptions, we implement an agent-based model with the two factors, and the simulated results do indeed capture the same Levy flight pattern as is observed. In order to enable the model to reproduce more mobility patterns, we add to the model a third factor: the jumping factor, which is the probability that one person may cancel their regular mobility schedule and explore a random place. With this factor, our model can cover a relatively wide range of human mobility patterns with scaling exponent values from 1.55 to 2.05.

  • 18. Jiang, Bin
    et al.
    Zhao, Sijian
    Yin, Junjun
    Self-organized natural roads for predicting traffic flow: a sensitivity study2008In: Journal of Statistical Mechanics: Theory and Experiment, ISSN 1742-5468, E-ISSN 1742-5468, no July, article id P07008Article in journal (Refereed)
  • 19.
    Kabashima, Yoshiyuki
    et al.
    Department of Computational Intelligence and Systems Science, Tokyo Institute of Technology.
    Vehkaperä, Mikko
    KTH, School of Electrical Engineering (EES), Communication Theory. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Chatterjee, Saikat
    KTH, School of Electrical Engineering (EES), Communication Theory. KTH, School of Electrical Engineering (EES), Centres, ACCESS Linnaeus Centre.
    Typical l(1)-recovery limit of sparse vectors represented by concatenations of random orthogonal matrices2012In: Journal of Statistical Mechanics: Theory and Experiment, ISSN 1742-5468, E-ISSN 1742-5468, Vol. 2012, no 12, p. P12003-Article in journal (Refereed)
    Abstract [en]

    We consider the problem of recovering an N-dimensional sparse vector x from its linear transformation y = Dx of M (<N) dimensions. Minimization of the l(1)-norm of x under the constraint y = Dx is a standard approach for the recovery problem, and earlier studies report that the critical condition for typically successful l(1)-recovery is universal over a variety of randomly constructed matrices D. To examine the extent of the universality, we focus on the case in which D is provided by concatenating T = N/M matrices O-1, O-2,O- ... ,O-T drawn uniformly according to the Haar measure on the M x M orthogonal matrices. By using the replica method in conjunction with the development of an integral formula to handle the random orthogonal matrices, we show that the concatenated matrices can result in better recovery performance than that predicted by the universality when the density of non-zero signals is not uniform among the T matrix modules. The universal condition is reproduced for the special case of uniform non-zero signal densities. Extensive numerical experiments support the theoretical predictions.

  • 20.
    Kardell, Mikael
    et al.
    Stockholm University, Faculty of Science, Department of Physics.
    Karlhede, Anders
    Stockholm University, Faculty of Science, Department of Physics.
    Exclusion statistics for quantum Hall states in the Tao-Thouless limit2011In: Journal of Statistical Mechanics: Theory and Experiment, ISSN 1742-5468, E-ISSN 1742-5468, article id P02037Article in journal (Refereed)
    Abstract [en]

    We consider spin-polarized Abelian quantum Hall states in the Tao-Thouless limit, i.e. on a thin torus. For any filling factor nu = p/q a well-defined sector of low energy states is identified and the exclusion statistics of the excitations is determined. We study numerically, at and near nu = 1/3 and 2/5, how the low energy states develop as one moves away from the Tao-Thouless limit towards the physical regime. We find that the lowest energy states in the physical regime develop from states in the low energy sector but that the exclusion statistics is modified.

  • 21.
    Kish, Laszlo B.
    et al.
    Texas A&M Univ, Dept Elect & Comp Engn, TAMUS 3128, College Stn, TX 77843 USA..
    Niklasson, Gunnar A.
    Uppsala University, Disciplinary Domain of Science and Technology, Technology, Department of Engineering Sciences, Solid State Physics.
    Granqvist, Claes-Göran
    Uppsala University, Disciplinary Domain of Science and Technology, Technology, Department of Engineering Sciences, Solid State Physics.
    Zero-point term and quantum effects in the Johnson noise of resistors: a critical appraisal2016In: Journal of Statistical Mechanics: Theory and Experiment, ISSN 1742-5468, E-ISSN 1742-5468, article id 054006Article in journal (Refereed)
    Abstract [en]

    There is a longstanding debate about the zero-point term in the Johnson noise voltage of a resistor. This term originates from a quantum-theoretical treatment of the fluctuation-dissipation theorem (FDT). Is the zero-point term really there, or is it only an experimental artifact, due to the uncertainty principle, for phase-sensitive amplifiers? Could it be removed by renormalization of theories? We discuss some historical measurement schemes that do not lead to the effect predicted by the FDT, and we analyse new features that emerge when the consequences of the zero-point term are measured via the mean energy and force in a capacitor shunting the resistor. If these measurements verify the existence of a zero-point term in the noise, then two types of perpetual motion machines can be constructed. Further investigation with the same approach shows that, in the quantum limit, the Johnson-Nyquist formula is also invalid under general conditions even though it is valid for a resistor-antenna system. Therefore we conclude that in a satisfactory quantum theory of the Johnson noise, the FDT must, as a minimum, include also the measurement system used to evaluate the observed quantities. Issues concerning the zero-point term may also have implications for phenomena in advanced nanotechnology.

  • 22.
    Kjall, J.
    et al.
    Stockholm Univ, AlbaNova Univ Ctr, Dept Phys, SE-10691 Stockholm, Sweden..
    Ardonne, E.
    Stockholm Univ, AlbaNova Univ Ctr, Dept Phys, SE-10691 Stockholm, Sweden..
    Dwivedi, V.
    Univ Cologne, Inst Theoret Phys, D-50937 Cologne, Germany..
    Hermanns, M.
    Univ Cologne, Inst Theoret Phys, D-50937 Cologne, Germany.;Univ Gothenburg, Dept Phys, SE-41296 Gothenburg, Sweden..
    Hansson, T. H.
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA. Stockholm Univ, AlbaNova Univ Ctr, Dept Phys, SE-10691 Stockholm, Sweden..
    Matrix product state representation of quasielectron wave functions2018In: Journal of Statistical Mechanics: Theory and Experiment, ISSN 1742-5468, E-ISSN 1742-5468, article id 053101Article in journal (Refereed)
    Abstract [en]

    Matrix product state techniques provide a very efficient way to numerically evaluate certain classes of quantum Hall wave functions that can be written as correlators in two-dimensional conformal field theories. Important examples are the Laughlin and Moore-Read ground states and their quasihole excitations. In this paper, we extend the matrix product state techniques to evaluate quasielectron wave functions, a more complex task because the corresponding conformal field theory operator is not local. We use our method to obtain density profiles for states with multiple quasielectrons and quasiholes, and to calculate the (mutual) statistical phases of the excitations with high precision. The wave functions we study are subject to a known difficulty: the position of a quasielectron depends on the presence of other quasiparticles, even when their separation is large compared to the magnetic length. Quasielectron wave functions constructed using the composite fermion picture, which are topologically equivalent to the quasielectrons we study, have the same problem. This flaw is serious in that it gives wrong results for the statistical phases obtained by braiding distant quasiparticles. We analyze this problem in detail and show that it originates from an incomplete screening of the topological charges, which invalidates the plasma analogy. We demonstrate that this can be remedied in the case when the separation between the quasiparticles is large, which allows us to obtain the correct statistical phases. Finally, we propose that a modification of the Laughlin state, that allows for local quasielectron operators, should have good topological properties for arbitrary configurations of excitations.

  • 23.
    Kjäll, Jonas
    et al.
    Stockholm University, Faculty of Science, Department of Physics.
    Ardonne, Eddy
    Stockholm University, Faculty of Science, Department of Physics.
    Dwivedi, V.
    Hermanns, M.
    Hansson, Thors Hans
    Stockholm University, Faculty of Science, Department of Physics. Stockholm University, Nordic Institute for Theoretical Physics (Nordita).
    Matrix product state representation of quasielectron wave functions2018In: Journal of Statistical Mechanics: Theory and Experiment, ISSN 1742-5468, E-ISSN 1742-5468, article id 053101Article in journal (Refereed)
    Abstract [en]

    Matrix product state techniques provide a very efficient way to numerically evaluate certain classes of quantum Hall wave functions that can be written as correlators in two-dimensional conformal field theories. Important examples are the Laughlin and Moore-Read ground states and their quasihole excitations. In this paper, we extend the matrix product state techniques to evaluate quasielectron wave functions, a more complex task because the corresponding conformal field theory operator is not local. We use our method to obtain density profiles for states with multiple quasielectrons and quasiholes, and to calculate the (mutual) statistical phases of the excitations with high precision. The wave functions we study are subject to a known difficulty: the position of a quasielectron depends on the presence of other quasiparticles, even when their separation is large compared to the magnetic length. Quasielectron wave functions constructed using the composite fermion picture, which are topologically equivalent to the quasielectrons we study, have the same problem. This flaw is serious in that it gives wrong results for the statistical phases obtained by braiding distant quasiparticles. We analyze this problem in detail and show that it originates from an incomplete screening of the topological charges, which invalidates the plasma analogy. We demonstrate that this can be remedied in the case when the separation between the quasiparticles is large, which allows us to obtain the correct statistical phases. Finally, we propose that a modification of the Laughlin state, that allows for local quasielectron operators, should have good topological properties for arbitrary configurations of excitations.

  • 24.
    Krishnamurthy, Supriya
    et al.
    Stockholm University, Faculty of Science, Department of Physics.
    Sumedha,
    On the behaviour of random K-SAT on trees2012In: Journal of Statistical Mechanics: Theory and Experiment, ISSN 1742-5468, E-ISSN 1742-5468, p. P05009-Article in journal (Refereed)
    Abstract [en]

    We consider the K-satisfiability problem on a regular d-ary rooted tree. For this model, we demonstrate how we can calculate in closed form the moments of the total number of solutions as a function of d and K, where the average is over all realizations for a fixed assignment of the surface variables. We find that different moments pick out different 'critical' values of d, below which they diverge as the total number of variables on the tree -> infinity and above which they decay. We show that K-SAT on the random graph also behaves similarly. We also calculate exactly the fraction of instances that have solutions for all K. On the tree, this quantity decays to 0 (as the number of variables increases) for any d > 1. However, the recursion relations for this quantity have a non-trivial fixed point solution which indicates the existence of a different transition in the interior of an infinite rooted tree.

  • 25.
    Krishnamurthy, Supriya
    et al.
    KTH, School of Computer Science and Communication (CSC), Theoretical Computer Science, TCS.
    Sumedha, Sumedha
    Natl Inst Sci Educ & Res, Inst Phys Campus, Bhubaneswar, India .
    On the behaviour of random K-SAT on trees2012In: Journal of Statistical Mechanics: Theory and Experiment, ISSN 1742-5468, E-ISSN 1742-5468, Vol. 2012, no 5, p. P05009-Article in journal (Refereed)
    Abstract [en]

    We consider the K-satisfiability problem on a regular d-ary rooted tree. For this model, we demonstrate how we can calculate in closed form the moments of the total number of solutions as a function of d and K, where the average is over all realizations for a fixed assignment of the surface variables. We find that different moments pick out different 'critical' values of d, below which they diverge as the total number of variables on the tree and above which they decay. We show that K-SAT on the random graph also behaves similarly. We also calculate exactly the fraction of instances that have solutions for all K. On the tree, this quantity decays to 0 (as the number of variables increases) for any d > 1. However, the recursion relations for this quantity have a non-trivial fixed point solution which indicates the existence of a different transition in the interior of an infinite rooted tree.

  • 26. Marsili, Matteo
    et al.
    Mastromatteo, Iacopo
    Roudi, Yasser
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita). Norwegian University of Science & Technology.
    On sampling and modeling complex systems2013In: Journal of Statistical Mechanics: Theory and Experiment, ISSN 1742-5468, E-ISSN 1742-5468, p. P09003-Article in journal (Refereed)
    Abstract [en]

    The study of complex systems is limited by the fact that only a few variables are accessible for modeling and sampling, which are not necessarily the most relevant ones to explain the system behavior. In addition, empirical data typically undersample the space of possible states. We study a generic framework where a complex system is seen as a system of many interacting degrees of freedom, which are known only in part, that optimize a given function. We show that the underlying distribution with respect to the known variables has the Boltzmann form, with a temperature that depends on the number of unknown variables. In particular, when the influence of the unknown degrees of freedom on the known variables is not too irregular, the temperature decreases as the number of variables increases. This suggests that models can be predictable only when the number of relevant variables is less than a critical threshold. Concerning sampling, we argue that the information that a sample contains on the behavior of the system is quantified by the entropy of the frequency with which different states occur. This allows us to characterize the properties of maximally informative samples: within a simple approximation, the most informative frequency size distributions have power law behavior and Zipf's law emerges at the crossover between the under sampled regime and the regime where the sample contains enough statistics to make inferences on the behavior of the system. These ideas are illustrated in some applications, showing that they can be used to identify relevant variables or to select the most informative representations of data, e.g. in data clustering.

  • 27. Marsili, Matteo
    et al.
    Mastromatteo, Iacopo
    Roudi, Yasser
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA.
    On sampling and modeling complex systems2013In: Journal of Statistical Mechanics: Theory and Experiment, ISSN 1742-5468, E-ISSN 1742-5468, Vol. 2013, no 9Article in journal (Refereed)
    Abstract [en]

    The study of complex systems is limited by the fact that only a few variables are accessible for modeling and sampling, which are not necessarily the most relevant ones to explain the system behavior. In addition, empirical data typically undersample the space of possible states. We study a generic framework where a complex system is seen as a system of many interacting degrees of freedom, which are known only in part, that optimize a given function. We show that the underlying distribution with respect to the known variables has the Boltzmann form, with a temperature that depends on the number of unknown variables. In particular, when the influence of the unknown degrees of freedom on the known variables is not too irregular, the temperature decreases as the number of variables increases. This suggests that models can be predictable only when the number of relevant variables is less than a critical threshold. Concerning sampling, we argue that the information that a sample contains on the behavior of the system is quantified by the entropy of the frequency with which different states occur. This allows us to characterize the properties of maximally informative samples: within a simple approximation, the most informative frequency size distributions have power law behavior and Zipf's law emerges at the crossover between the under sampled regime and the regime where the sample contains enough statistics to make inferences on the behavior of the system. These ideas are illustrated in some applications, showing that they can be used to identify relevant variables or to select the most informative representations of data, e.g. in data clustering.

  • 28.
    Rocha, Luis E C
    Umeå University, Faculty of Science and Technology, Department of Physics.
    Structural evolution of the Brazilian airport network2009In: Journal of Statistical Mechanics: Theory and Experiment, ISSN 1742-5468, E-ISSN 1742-5468, p. 04020-Article in journal (Refereed)
    Abstract [en]

    The aviation sector is profitable, but sensitive to economic fluctuations, geopolitical constraints and governmental regulations. As for other means of transportation, the relation between origin and destination results in a complex map of routes, which can be complemented with information associated with the routes themselves, for instance, frequency, traffic load and distance. The theory of networks provides a natural framework for investigating the dynamics on the resulting structure. Here, we investigate the structure and evolution of the Brazilian airport network (BAN) as regards several quantities: routes, connections, passengers and cargo. Some structural features are in accordance with previous results for other airport networks. The analysis of the evolution of the BAN shows that its structure is dynamic, with changes in the relative relevance of some airports and routes. The results indicate that the connections converge to specific routes. The network shrinks at the route level but grows in number of passengers and amount of cargo, which more than doubled during the period studied.

  • 29. Tyrcha, Joanna
    et al.
    Roudi, Yasser
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA.
    Marsili, Matteo
    Hertz, John
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA.
    The effect of nonstationarity on models inferred from neural data2013In: Journal of Statistical Mechanics: Theory and Experiment, ISSN 1742-5468, E-ISSN 1742-5468, p. P03005-Article in journal (Refereed)
    Abstract [en]

    Neurons subject to a common nonstationary input may exhibit a correlated firing behavior. Correlations in the statistics of neural spike trains also arise as the effect of interaction between neurons. Here we show that these two situations can be distinguished with machine learning techniques, provided that the data are rich enough. In order to do this, we study the problem of inferring a kinetic Ising model, stationary or nonstationary, from the available data. We apply the inference procedure to two data sets: one from salamander retinal ganglion cells and the other from a realistic computational cortical network model. We show that many aspects of the concerted activity of the salamander retinal neurons can be traced simply to the external input. A model of non-interacting neurons subject to a nonstationary external field outperforms a model with stationary input with couplings between neurons, even accounting for the differences in the number of model parameters. When couplings are added to the nonstationary model, for the retinal data, little is gained: the inferred couplings are generally not significant. Likewise, the distribution of the sizes of sets of neurons that spike simultaneously and the frequency of spike patterns as a function of their rank (Zipf plots) are well explained by an independent-neuron model with time-dependent external input, and adding connections to such a model does not offer significant improvement. For the cortical model data, robust couplings, well correlated with the real connections, can be inferred using the nonstationary model. Adding connections to this model slightly improves the agreement with the data for the probability of synchronous spikes but hardly affects the Zipf plot.

  • 30.
    Tyrcha, Joanna
    et al.
    Stockholm University, Faculty of Science, Department of Mathematics.
    Roudi, Yasser
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita). Kavli Institute for Systems Neuroscience, NTNU, Norway.
    Marsili, Matteo
    Hertz, John
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita). Niels Bohr Institute, Denmark.
    The effect of nonstationarity on models inferred from neural data2013In: Journal of Statistical Mechanics: Theory and Experiment, ISSN 1742-5468, E-ISSN 1742-5468, article id P03005Article in journal (Refereed)
    Abstract [en]

    Neurons subject to a common nonstationary input may exhibit a correlated firing behavior. Correlations in the statistics of neural spike trains also arise as the effect of interaction between neurons. Here we show that these two situations can be distinguished with machine learning techniques, provided that the data are rich enough. In order to do this, we study the problem of inferring a kinetic Ising model, stationary or nonstationary, from the available data. We apply the inference procedure to two data sets: one from salamander retinal ganglion cells and the other from a realistic computational cortical network model. We show that many aspects of the concerted activity of the salamander retinal neurons can be traced simply to the external input. A model of non-interacting neurons subject to a nonstationary external field outperforms a model with stationary input with couplings between neurons, even accounting for the differences in the number of model parameters. When couplings are added to the nonstationary model, for the retinal data, little is gained: the inferred couplings are generally not significant. Likewise, the distribution of the sizes of sets of neurons that spike simultaneously and the frequency of spike patterns as a function of their rank (Zipf plots) are well explained by an independent-neuron model with time-dependent external input, and adding connections to such a model does not offer significant improvement. For the cortical model data, robust couplings, well correlated with the real connections, can be inferred using the nonstationary model. Adding connections to this model slightly improves the agreement with the data for the probability of synchronous spikes but hardly affects the Zipf plot.

  • 31.
    Wikberg, Emma
    et al.
    Stockholm University, Faculty of Science, Department of Physics.
    Bergholtz, Emil J.
    Karlhede, Anders
    Stockholm University, Faculty of Science, Department of Physics.
    Spin chain description of rotating bosons at v = 12009In: Journal of Statistical Mechanics: Theory and Experiment, ISSN 1742-5468, E-ISSN 1742-5468, p. P07038-Article in journal (Refereed)
    Abstract [en]

    We consider bosons at Landau level filling ν = 1 on a thin torus. In analogy with previous work on fermions at filling ν = 1/2, we map the low-energy sector onto a spin-1/2 chain. While the fermionic system may realize the gapless XY phase, we show that typically this does not happen for the bosonic system. Instead, both delta function and Coulomb interaction lead to gapped phases in the bosonic system, and in particular we identify a phase corresponding to the non-Abelian Moore–Read state. In the spin language, the Hamiltonian is dominated by a ferromagnetic next-nearest-neighbor interaction, which leads to a description consistent with the non-trivial degeneracies of the ground and excited states of this phase of matter. In addition we comment on the similarities and differences of the two systems mentioned above and fermions at ν = 5/2.

1 - 31 of 31
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