Pub Date : 2020-02-25DOI: 10.1103/PhysRevX.11.021064
Christian Keup, Tobias Kühn, David Dahmen, M. Helias
Cortical neurons communicate with spikes, which are discrete events in time. Even if the timings of the individual events are strongly chaotic (microscopic chaos), the rate of events might still be non-chaotic or at the edge of what is known as rate chaos. Such edge-of-chaos dynamics are beneficial to the computational power of neuronal networks. We analyze both types of chaotic dynamics in densely connected networks of asynchronous binary neurons, by developing and applying a model-independent field theory for neuronal networks. We find a strongly size-dependent transition to microscopic chaos. We then expose the conceptual difficulty at the heart of the definition of rate chaos, identify two reasonable definitions, and show that for neither of them the binary network dynamics crosses a transition to rate chaos. The analysis of diverging trajectories in chaotic networks also allows us to study classification of linearly non-separable classes of stimuli in a reservoir computing approach. We show that microscopic chaos rapidly expands the dimensionality of the representation while, crucially, the number of dimensions corrupted by noise lags behind. This translates to a transient peak in the networks' classification performance even deeply in the chaotic regime, challenging the view that computational performance is always optimal near the edge of chaos. This is a general effect in high dimensional chaotic systems, and not specific to binary networks: We also demonstrate it in a continuous 'rate' network, a spiking LIF network, and an LSTM network. For binary and LIF networks, classification performance peaks rapidly within one activation per participating neuron, demonstrating fast event-based computation that may be exploited by biological neural systems, for which we propose testable predictions.
{"title":"Transient Chaotic Dimensionality Expansion by Recurrent Networks","authors":"Christian Keup, Tobias Kühn, David Dahmen, M. Helias","doi":"10.1103/PhysRevX.11.021064","DOIUrl":"https://doi.org/10.1103/PhysRevX.11.021064","url":null,"abstract":"Cortical neurons communicate with spikes, which are discrete events in time. Even if the timings of the individual events are strongly chaotic (microscopic chaos), the rate of events might still be non-chaotic or at the edge of what is known as rate chaos. Such edge-of-chaos dynamics are beneficial to the computational power of neuronal networks. We analyze both types of chaotic dynamics in densely connected networks of asynchronous binary neurons, by developing and applying a model-independent field theory for neuronal networks. We find a strongly size-dependent transition to microscopic chaos. We then expose the conceptual difficulty at the heart of the definition of rate chaos, identify two reasonable definitions, and show that for neither of them the binary network dynamics crosses a transition to rate chaos. \u0000The analysis of diverging trajectories in chaotic networks also allows us to study classification of linearly non-separable classes of stimuli in a reservoir computing approach. We show that microscopic chaos rapidly expands the dimensionality of the representation while, crucially, the number of dimensions corrupted by noise lags behind. This translates to a transient peak in the networks' classification performance even deeply in the chaotic regime, challenging the view that computational performance is always optimal near the edge of chaos. This is a general effect in high dimensional chaotic systems, and not specific to binary networks: We also demonstrate it in a continuous 'rate' network, a spiking LIF network, and an LSTM network. For binary and LIF networks, classification performance peaks rapidly within one activation per participating neuron, demonstrating fast event-based computation that may be exploited by biological neural systems, for which we propose testable predictions.","PeriodicalId":8438,"journal":{"name":"arXiv: Disordered Systems and Neural Networks","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2020-02-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80924372","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-02-07DOI: 10.1103/PHYSREVB.103.054202
A. Churkin, S. Matityahu, A. Maksymov, A. Burin, M. Schechter
Tunneling two-level systems (TLSs), generic to amorphous solids, dictate the low-energy properties of amorphous solids and dominate noise and decoherence in quantum nano-devices. The properties of the TLSs are generally described by the phenomenological standard tunneling model. Yet, significant deviations from the predictions of this model found experimentally suggest the need for a more precise model in describing the low-energy properties of amorphous solids. Here we show that the temperature dependence of the sound velocity, dielectric constant, specific heat, and thermal conductivity, can be explained using an energy-dependent TLS density of states. The reduction of the TLS density of states at low energies relates to the ratio between the strengths of the TLS-TLS interactions and the random potential, which is enhanced in systems with dominant electric dipolar interactions.
{"title":"Anomalous low-energy properties in amorphous solids and the interplay of electric and elastic interactions of tunneling two-level systems","authors":"A. Churkin, S. Matityahu, A. Maksymov, A. Burin, M. Schechter","doi":"10.1103/PHYSREVB.103.054202","DOIUrl":"https://doi.org/10.1103/PHYSREVB.103.054202","url":null,"abstract":"Tunneling two-level systems (TLSs), generic to amorphous solids, dictate the low-energy properties of amorphous solids and dominate noise and decoherence in quantum nano-devices. The properties of the TLSs are generally described by the phenomenological standard tunneling model. Yet, significant deviations from the predictions of this model found experimentally suggest the need for a more precise model in describing the low-energy properties of amorphous solids. Here we show that the temperature dependence of the sound velocity, dielectric constant, specific heat, and thermal conductivity, can be explained using an energy-dependent TLS density of states. The reduction of the TLS density of states at low energies relates to the ratio between the strengths of the TLS-TLS interactions and the random potential, which is enhanced in systems with dominant electric dipolar interactions.","PeriodicalId":8438,"journal":{"name":"arXiv: Disordered Systems and Neural Networks","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2020-02-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86562743","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-01-17DOI: 10.1007/978-3-030-60754-8_2
L. Arguin, C. Newman, D. Stein
{"title":"Ground State Stability in Two Spin Glass Models","authors":"L. Arguin, C. Newman, D. Stein","doi":"10.1007/978-3-030-60754-8_2","DOIUrl":"https://doi.org/10.1007/978-3-030-60754-8_2","url":null,"abstract":"","PeriodicalId":8438,"journal":{"name":"arXiv: Disordered Systems and Neural Networks","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2020-01-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73073355","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-01-14DOI: 10.1142/9789811215575_0009
S. Yannopoulos
The current critical review aims to be more than a simple summary and reproduction of previously published work. Many comprehensive reviews and collections can be found in the literature. The main intention is to provide an account of the progress made in selected aspects of photoinduced phenomena in non-crystalline chalcogenides, presenting the current understanding of the mechanisms underlying such effects. An essential motive for the present review article has been to assess critically published experimental work in the field.
{"title":"Athermal Photoelectronic Effects in Non-Crystalline Chalcogenides: Current Status and Beyond","authors":"S. Yannopoulos","doi":"10.1142/9789811215575_0009","DOIUrl":"https://doi.org/10.1142/9789811215575_0009","url":null,"abstract":"The current critical review aims to be more than a simple summary and reproduction of previously published work. Many comprehensive reviews and collections can be found in the literature. The main intention is to provide an account of the progress made in selected aspects of photoinduced phenomena in non-crystalline chalcogenides, presenting the current understanding of the mechanisms underlying such effects. An essential motive for the present review article has been to assess critically published experimental work in the field.","PeriodicalId":8438,"journal":{"name":"arXiv: Disordered Systems and Neural Networks","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2020-01-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89497506","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-01-09DOI: 10.1103/PHYSREVRESEARCH.2.033099
T. Wahl, B. B'eri
Many-body localized (MBL) systems are often described using their local integrals of motion, which, for spin systems, are commonly assumed to be a local unitary transform of the set of on-site spin-z operators. We show that this assumption cannot hold for topologically ordered MBL systems. Using a suitable definition to capture such systems in any spatial dimension, we demonstrate a number of features, including that MBL topological order, if present: (i) is the same for all eigenstates; (ii) is robust in character against any perturbation preserving MBL; (iii) implies that on topologically nontrivial manifolds a complete set of integrals of motion must include nonlocal ones in the form of local-unitary-dressed noncontractible Wilson loops. Our approach is well suited for tensor-network methods, and is expected to allow these to resolve highly-excited finite-size-split topological eigenspaces despite their overlap in energy. We illustrate our approach on the disordered Kitaev chain, toric code, and X-cube model.
{"title":"Local integrals of motion for topologically ordered many-body localized systems","authors":"T. Wahl, B. B'eri","doi":"10.1103/PHYSREVRESEARCH.2.033099","DOIUrl":"https://doi.org/10.1103/PHYSREVRESEARCH.2.033099","url":null,"abstract":"Many-body localized (MBL) systems are often described using their local integrals of motion, which, for spin systems, are commonly assumed to be a local unitary transform of the set of on-site spin-z operators. We show that this assumption cannot hold for topologically ordered MBL systems. Using a suitable definition to capture such systems in any spatial dimension, we demonstrate a number of features, including that MBL topological order, if present: (i) is the same for all eigenstates; (ii) is robust in character against any perturbation preserving MBL; (iii) implies that on topologically nontrivial manifolds a complete set of integrals of motion must include nonlocal ones in the form of local-unitary-dressed noncontractible Wilson loops. Our approach is well suited for tensor-network methods, and is expected to allow these to resolve highly-excited finite-size-split topological eigenspaces despite their overlap in energy. We illustrate our approach on the disordered Kitaev chain, toric code, and X-cube model.","PeriodicalId":8438,"journal":{"name":"arXiv: Disordered Systems and Neural Networks","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2020-01-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88086087","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2019-12-28DOI: 10.1103/physrevb.102.134212
S. Ganeshan, Kartiek Agarwal, Kartiek Agarwal, R. Bhatt, R. Bhatt
We investigate the localization properties of driven models that exhibit a sub-extensive number of extended states in the static setting. We consider instances where the extended modes are or are not protected by topological considerations. To this end, we contrast the strongly driven disordered lowest Landau level, which we refer to as the random Landau model (RLM), with the random dimer model (RDM); the latter also has a sub-extensive set of delocalized modes in the middle of the spectrum whose origin is not topological. We map the driven models on to a higher dimensional effective model and numerically compute the localization length as a function of disorder strength, drive amplitude and frequency using the recursive Green's function method. Our numerical results indicate that in the presence of a strong drive (low frequency and/or large drive amplitude), the topologically protected RLM continues to exhibit a spectrum with both localized and delocalized (or critical) modes, but the spectral range of delocalized modes is enhanced by the driving. This occurs due to an admixture of the localized modes with extended modes arising due to the topologically protected critical energy in the middle of the spectrum. On the other hand, in the RDM, a weak drive immediately localizes the entire spectrum. This occurs in contrast to the naive expectation from perturbation theory that mixing between localized and delocalized modes generically enhances the delocalization of all modes. Our work highlights the importance of the origin of the delocalized modes in the localization properties of the corresponding Floquet model.
{"title":"Floquet dynamics of disordered bands with isolated critical energies","authors":"S. Ganeshan, Kartiek Agarwal, Kartiek Agarwal, R. Bhatt, R. Bhatt","doi":"10.1103/physrevb.102.134212","DOIUrl":"https://doi.org/10.1103/physrevb.102.134212","url":null,"abstract":"We investigate the localization properties of driven models that exhibit a sub-extensive number of extended states in the static setting. We consider instances where the extended modes are or are not protected by topological considerations. To this end, we contrast the strongly driven disordered lowest Landau level, which we refer to as the random Landau model (RLM), with the random dimer model (RDM); the latter also has a sub-extensive set of delocalized modes in the middle of the spectrum whose origin is not topological. We map the driven models on to a higher dimensional effective model and numerically compute the localization length as a function of disorder strength, drive amplitude and frequency using the recursive Green's function method. Our numerical results indicate that in the presence of a strong drive (low frequency and/or large drive amplitude), the topologically protected RLM continues to exhibit a spectrum with both localized and delocalized (or critical) modes, but the spectral range of delocalized modes is enhanced by the driving. This occurs due to an admixture of the localized modes with extended modes arising due to the topologically protected critical energy in the middle of the spectrum. On the other hand, in the RDM, a weak drive immediately localizes the entire spectrum. This occurs in contrast to the naive expectation from perturbation theory that mixing between localized and delocalized modes generically enhances the delocalization of all modes. Our work highlights the importance of the origin of the delocalized modes in the localization properties of the corresponding Floquet model.","PeriodicalId":8438,"journal":{"name":"arXiv: Disordered Systems and Neural Networks","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2019-12-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74433377","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2019-12-20DOI: 10.1103/PHYSREVRESEARCH.2.023283
Yi Zhang, P. Ginsparg, Eun-Ah Kim
There has been growing excitement over the possibility of employing artificial neural networks (ANNs) to gain new theoretical insight into the physics of quantum many-body problems. "Interpretability" remains a concern: can we understand the basis for the ANN's decision-making criteria in order to inform our theoretical understanding? "Interpretable" machine learning in quantum matter has to date been restricted to linear models, such as support vector machines, due to the greater difficulty of interpreting non-linear ANNs. Here we consider topological quantum phase transitions in models of Chern insulator, $mathbb{Z}_2$ topological insulator, and $mathbb{Z}_2$ quantum spin liquid, each using a shallow fully connected feed-forward ANN. The use of quantum loop topography, a "domain knowledge"-guided approach to feature selection, facilitates the construction of faithful phase diagrams. Due to the relative simplicity of the ANN, its learning can be interpreted in each of the three cases. To identify the topological phases, the ANNs learn physically meaningful features, such as topological invariants and deconfinement of loops. The interpretability in these cases suggests hope for theoretical progress based on future uses of ANN-based machine learning on quantum many-body problems.
{"title":"Interpreting machine learning of topological quantum phase transitions","authors":"Yi Zhang, P. Ginsparg, Eun-Ah Kim","doi":"10.1103/PHYSREVRESEARCH.2.023283","DOIUrl":"https://doi.org/10.1103/PHYSREVRESEARCH.2.023283","url":null,"abstract":"There has been growing excitement over the possibility of employing artificial neural networks (ANNs) to gain new theoretical insight into the physics of quantum many-body problems. \"Interpretability\" remains a concern: can we understand the basis for the ANN's decision-making criteria in order to inform our theoretical understanding? \"Interpretable\" machine learning in quantum matter has to date been restricted to linear models, such as support vector machines, due to the greater difficulty of interpreting non-linear ANNs. Here we consider topological quantum phase transitions in models of Chern insulator, $mathbb{Z}_2$ topological insulator, and $mathbb{Z}_2$ quantum spin liquid, each using a shallow fully connected feed-forward ANN. The use of quantum loop topography, a \"domain knowledge\"-guided approach to feature selection, facilitates the construction of faithful phase diagrams. Due to the relative simplicity of the ANN, its learning can be interpreted in each of the three cases. To identify the topological phases, the ANNs learn physically meaningful features, such as topological invariants and deconfinement of loops. The interpretability in these cases suggests hope for theoretical progress based on future uses of ANN-based machine learning on quantum many-body problems.","PeriodicalId":8438,"journal":{"name":"arXiv: Disordered Systems and Neural Networks","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2019-12-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84135188","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2019-12-20DOI: 10.1142/9789811216220_0004
N. Lebovka, Y. Tarasevich
This chapter is devoted to the analysis of jamming and percolation behavior of two-dimensional systems of elongated particles. We consider both continuous and discrete spaces (with the special attention to the square lattice), as well the systems with isotropically deposited and aligned particles. Overviews of different analytical and computational methods and main results are presented.
{"title":"Two-Dimensional Systems of Elongated Particles: From Diluted to Dense","authors":"N. Lebovka, Y. Tarasevich","doi":"10.1142/9789811216220_0004","DOIUrl":"https://doi.org/10.1142/9789811216220_0004","url":null,"abstract":"This chapter is devoted to the analysis of jamming and percolation behavior of two-dimensional systems of elongated particles. We consider both continuous and discrete spaces (with the special attention to the square lattice), as well the systems with isotropically deposited and aligned particles. Overviews of different analytical and computational methods and main results are presented.","PeriodicalId":8438,"journal":{"name":"arXiv: Disordered Systems and Neural Networks","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2019-12-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73773890","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2019-12-19DOI: 10.1103/PHYSREVB.102.024201
D. S. Bhakuni, Ritu Nehra, Auditya Sharma
We study the phenomenon of many-body localization (MBL) in an interacting system subjected to a combined DC as well as a square wave AC electric field. First, the condition for the dynamical localization, coherent destruction of Wannier-Stark localization and super Bloch oscillations in the non-interacting limit, are obtained semi-classically. In the presence of interactions (and a confining/disordered potential), a static field alone leads to ``Stark many-body localization", for sufficiently large field strengths. We find that in the presence of an additional high-frequency AC field, there are two ways of maintaining the MBL intact: either by resonant drive where the ratio of amplitude to the frequency of the drive ($A/omega$) is tuned at the dynamical localization point of the non-interacting limit or by off-resonant drive. Remarkably, resonant drive with $A/omega$ tuned away from the dynamical localization point leads to a emph{coherent destruction of Stark-MBL}. Moreover, a pure (high-frequency) AC field can also give rise to the MBL phase if $A/omega$ is tuned at the dynamical localization point of the zero dc field problem.
{"title":"Drive-induced many-body localization and coherent destruction of Stark many-body localization","authors":"D. S. Bhakuni, Ritu Nehra, Auditya Sharma","doi":"10.1103/PHYSREVB.102.024201","DOIUrl":"https://doi.org/10.1103/PHYSREVB.102.024201","url":null,"abstract":"We study the phenomenon of many-body localization (MBL) in an interacting system subjected to a combined DC as well as a square wave AC electric field. First, the condition for the dynamical localization, coherent destruction of Wannier-Stark localization and super Bloch oscillations in the non-interacting limit, are obtained semi-classically. In the presence of interactions (and a confining/disordered potential), a static field alone leads to ``Stark many-body localization\", for sufficiently large field strengths. We find that in the presence of an additional high-frequency AC field, there are two ways of maintaining the MBL intact: either by resonant drive where the ratio of amplitude to the frequency of the drive ($A/omega$) is tuned at the dynamical localization point of the non-interacting limit or by off-resonant drive. Remarkably, resonant drive with $A/omega$ tuned away from the dynamical localization point leads to a emph{coherent destruction of Stark-MBL}. Moreover, a pure (high-frequency) AC field can also give rise to the MBL phase if $A/omega$ is tuned at the dynamical localization point of the zero dc field problem.","PeriodicalId":8438,"journal":{"name":"arXiv: Disordered Systems and Neural Networks","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2019-12-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84072977","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2019-12-17DOI: 10.13130/DI-GIOACCHINO-ANDREA_PHD2019-12-17
Andrea Di Gioacchino
tutor and supervisor: S. Caracciolo ; co-supervisor: L. G. Molinari ; director of the school: M. Paris
导师:S. Caracciolo;共同主管:L. G. Molinari;校长:帕里斯先生
{"title":"EUCLIDEAN CORRELATIONS IN COMBINATORIAL OPTIMIZATION PROBLEMS: A STATISTICAL PHYSICS APPROACH","authors":"Andrea Di Gioacchino","doi":"10.13130/DI-GIOACCHINO-ANDREA_PHD2019-12-17","DOIUrl":"https://doi.org/10.13130/DI-GIOACCHINO-ANDREA_PHD2019-12-17","url":null,"abstract":"tutor and supervisor: S. Caracciolo ; co-supervisor: L. G. Molinari ; director of the school: M. Paris","PeriodicalId":8438,"journal":{"name":"arXiv: Disordered Systems and Neural Networks","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2019-12-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87369382","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
京公网安备 11010802042870号
京ICP备2023020795号-1
扫码关注我们
求助内容：
应助结果提醒方式：