Modeling spatial patterns in the visual cortex

Daza, Yudy Carolina; Tauro, Carolina B.; Tamarit, Francisco A.; Gleiser, Pablo M.

doi:10.1103/physreve.90.042818

Cited by 3 publications

(7 citation statements)

References 31 publications

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“…The anomaly originates from the SO(2,1) symmetry of the classical action that is broken in the quantized theory. A substantial theoretical effort has been made to quantify the anomalous corrections of the breathing mode frequency ω B both at zero [5,19,20,22] and finite [7,23,25] temperature.For two-component Fermi gases anomalous shifts up to 10 % are expected that show a strong dependence on both interaction strength and temperature. At zero temperature a rather large shift to frequencies above 2ω R is predicted [5,22] while pertubative solutions at finite temperatures show significantly reduced shifts on the order of 1 − 2 % that even go below the scale invariant value of 2ω R in the strongly interacting region [7,23].Experimentally scale invariance has been studied with arXiv:1803.08879v3 [cond-mat.quant-gas]…”

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confidence: 99%

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Anomalous Breaking of Scale Invariance in a Two-Dimensional Fermi Gas

et al. 2018

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The frequency of the breathing mode of a two-dimensional Fermi gas with zero-range interactions in a harmonic confinement is fixed by the scale invariance of the Hamiltonian. Scale invariance is broken in the quantized theory by introducing the two-dimensional scattering length as a regulator. This is an example of a quantum anomaly in the field of ultracold atoms and leads to a shift of the frequency of the collective breathing mode of the cloud. In this work, we study this anomalous frequency shift for a two component Fermi gas in the strongly interacting regime. We measure significant upwards shifts away from the scale invariant result that show a strong interaction dependence. This observation implies that scale invariance is broken anomalously in the strongly interacting two-dimensional Fermi gas.Symmetries are an indispensable ingredient to any attempt of formulating a fundamental theory of nature. Yet, it is not allways true that one can make accurate predictions about the behaviour of some complex system based on the symmetries of its Hamiltonian alone. The fundamental reason behind this is the concept of symmetry breaking [1]. Symmetry violations often have drastic effects on the state of the system, for example when some metal breaks rotational invariance and becomes ferromagnetic. There are three different mechanisms through which a given system may violate some of the symmetries of its Hamiltonian: explicit, spontaneous and anomalous symmetry breaking [2].Quantum anomalies are violations of an exact symmetry of a classical action in the corresponding quantized theory [3]. They may occur when a cut-off has to be introduced to regularize divergent terms. This regulator may explicitly break some symmetry of the theory. If this symmetry is not restored even after the cut-off is removed at the end of the renormalization procedure, the symmetry is broken anomalously.Quantum anomalies are ubiquitous in quantum field theories and provide, important constraints on physical gauge theories like the standard model [4, 5] or on string theories [6, 7]. Whereas the formalisms of explicit and spontaneous symmetry breaking are frequently applied across many fields in physics [8][9][10], anomalous symmetry breaking is typically associated only with high energy physics. One exception was found in molecular physics [11,12] and here we report an observation of a quantum anomaly in the field of cold atom physics.A particular class of anomalies, called conformal anomalies, break the scale invariance of a theory, that is invariance of the Hamiltonian under r → λr. The most prominent examples are found in field theories like QED or QCD where the renormalized coupling constants depend on the energy scale and thus break scale invariance explicitly. In ordinary quantum mechanics the 1/r 2 -and the δ 2 -potential in 2D are well-known examples of conformal anomalies [13,14].Notably, the δ 2 -potential is used to model contact in-teractions in cold atom gases in two-dimensions as V int ∝ g 0 δ 2 (r i − r j ). Including the kinetic...

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confidence: 99%

Anomalous Breaking of Scale Invariance in a Two-Dimensional Fermi Gas

et al. 2018

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“…Our results show that even with this simple approximation the model is still able to capture the main ingredients of the cortical organization. In fact, with only a few parameters, the model allows for the emergence of clustered or striped patterns that quantitatively resemble experimental patterns observed in infant macaques, monkeys, and ferrets [3].…”

Section: Modelmentioning

confidence: 68%

“…This is usually approximated by using a scale-free power-law degree distribution. In fact, recently we showed that using a scale-free network and also distance-dependent competing interactions we were able to obtain clustered or striped patterns that quantitatively resemble experimental patterns observed in infant macaques, monkeys, and ferrets [3]. In this section we will take this into account and, as in Ref.…”

Section: Scale-free Topologymentioning

confidence: 83%

“…This allows for the introduction of an interaction function that varies with distance. Recently, we proposed a simple model that includes this characteristic, and allows for the emergence of patterns like the ones observed in the visual cortex [2,3]. In particular, we analyzed the behavior of a Kuramoto model of coupled phase oscillators [27][28][29] with competing interactions in a complex network embedded in two-dimensional Euclidean space [3].…”

Section: Modelmentioning

confidence: 99%

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Interplay of network structure and dynamics in functional organization of the visual cortex

Gleiser

Tamarit

2018

Phys. Rev. E

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The functional patterns of the visual cortex observed in some mammals such as cats, primates, and humans has allowed us to understand basic principles of organization in the structure of the cortex. However, the observation of different kinds of functional arrangement in other animals such as mice, rats, rabbits, and squirrels, called salt and pepper patterns, raise questions about which of these principles can be transferred to the understanding of visual processing in general. In order to gain insight into these basic principles, in this work we propose a simple model for the formation of spatiotemporal patterns in the visual cortex. The model is based on coupled phase oscillators that interact through an evolving complex network that is embedded in a two-dimensional Euclidean space. In this way we are able to explore the relation between network structure and functional organization. We find that the model allows for the emergence of clustered synchronized states that are spatially segregated as some orientation maps, and also synchronized states that are spatially interspersed, resembling salt and pepper organizational maps.

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KurSL: Model of Anharmonic Coupled Oscillations Based on Kuramoto Coupling and Sturm–Liouville Problem

Laszuk

Cadenas

Nasuto

2018

Adv. Data Sci. Adapt. Data Anal.

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Physiological signaling is often oscillatory and shows nonlinearity due to complex interactions of underlying processes or signal propagation delays. This is particularly evident in case of brain activity which is subject to various feedback loop interactions between different brain structures, that coordinate their activity to support normal function. In order to understand such signaling in health and disease, methods are needed that can deal with such complex oscillatory phenomena. In this paper, a data-driven method for analyzing anharmonic oscillations is introduced. The KurSL model incorporates two well-studied components, which in the past have been used separately to analyze oscillatory behavior. The Sturm–Liouville equations describe a form of a general oscillation, and the Kuramoto coupling model represents a set of oscillators interacting in the phase domain. Integration of these components provides a flexible framework for capturing complex interactions of oscillatory processes of more general form than the most commonly used harmonic oscillators. The paper introduces a mathematical framework of the KurSL model and analyzes its behavior for a variety of parameter ranges. The significance of the model follows from its ability to provide information about coupled oscillators’ phase dynamics directly from the time series. KurSL offers a novel framework for analyzing a wide range of complex oscillatory behaviors, such as the ones encountered in physiological signals.

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Modeling spatial patterns in the visual cortex

Cited by 3 publications

References 31 publications

Anomalous Breaking of Scale Invariance in a Two-Dimensional Fermi Gas

Anomalous Breaking of Scale Invariance in a Two-Dimensional Fermi Gas

Interplay of network structure and dynamics in functional organization of the visual cortex

KurSL: Model of Anharmonic Coupled Oscillations Based on Kuramoto Coupling and Sturm–Liouville Problem

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