557 research outputs found
Topographic VAEs learn Equivariant Capsules
In this work we seek to bridge the concepts of topographic organization and
equivariance in neural networks. To accomplish this, we introduce the
Topographic VAE: a novel method for efficiently training deep generative models
with topographically organized latent variables. We show that such a model
indeed learns to organize its activations according to salient characteristics
such as digit class, width, and style on MNIST. Furthermore, through
topographic organization over time (i.e. temporal coherence), we demonstrate
how predefined latent space transformation operators can be encouraged for
observed transformed input sequences -- a primitive form of unsupervised
learned equivariance. We demonstrate that this model successfully learns sets
of approximately equivariant features (i.e. "capsules") directly from sequences
and achieves higher likelihood on correspondingly transforming test sequences.
Equivariance is verified quantitatively by measuring the approximate
commutativity of the inference network and the sequence transformations.
Finally, we demonstrate approximate equivariance to complex transformations,
expanding upon the capabilities of existing group equivariant neural networks
Extensive Tonotopic Mapping across Auditory Cortex Is recapitulated by spectrally directed attention and systematically related to Cortical Myeloarchitecture
Auditory selective attention is vital in natural soundscapes. But, it is unclear how attentional focus on the primary dimension of auditory representation - acoustic frequency - might modulate basic auditory functional topography during active listening. In contrast to visual selective attention, which is supported by motor-mediated optimization of input across saccades and pupil dilation, the primate auditory system has fewer means of differentially sampling the world. This makes spectrally-directed endogenous attention a particularly crucial aspect of auditory attention. Using a novel functional paradigm combined with quantitative MRI, we establish in male and female listeners that human frequency-band-selective attention drives activation in both myeloarchitectonically-estimated auditory core, and across the majority of tonotopically-mapped non-primary auditory cortex. The attentionally-driven best-frequency maps show strong concordance with sensory-driven maps in the same subjects across much of the temporal plane, with poor concordance in areas outside traditional auditory cortex. There is significantly greater activation across most of auditory cortex when best frequency is attended, versus ignored; the same regions do not show this enhancement when attending to the least-preferred frequency band. Finally, the results demonstrate that there is spatial correspondence between the degree of myelination and the strength of the tonotopic signal across a number of regions in auditory cortex. Strong frequency preferences across tonotopically-mapped auditory cortex spatially correlate with R1-estimated myeloarchitecture, indicating shared functional and anatomical organization that may underlie intrinsic auditory regionalization
Adiabatic spin pumping through a quantum dot with a single orbital level
We investigate an adiabatic spin pumping through a quantum dot with a single
orbital energy level under the Zeeman effect. Electron pumping is produced by
two periodic time dependent parameters, a magnetic field and a difference of
the dot-lead coupling between the left and right barriers of the dot. The
maximum charge transfer per cycle is found to be , the unit charge in the
absence of a localized moment in the dot. Pumped charge and spin are different,
and spin pumping is possible without charge pumping in a certain situation.
They are tunable by changing the minimum and maximum value of the magnetic
field.Comment: RevTeX4, 5 pages, 3 figure
Flux-quantum-modulated Kondo conductance in a multielectron quantum dot
We investigate a lateral semiconductor quantum dot with a large number of
electrons in the limit of strong coupling to the leads. A Kondo effect is
observed and can be tuned in a perpendicular magnetic field. This Kondo effect
does not exhibit Zeeman splitting. It shows a modulation with the periodicity
of one flux quantum per dot area at low temperatures. The modulation leads to a
novel, strikingly regular stripe pattern for a wide range in magnetic field and
number of electrons.Comment: 4 pages, 5 figure
Antiferromagnetic Domains and Superconductivity in UPt3
We explore the response of an unconventional superconductor to spatially
inhomogeneous antiferromagnetism (SIAFM). Symmetry allows the superconducting
order parameter in the E-representation models for UPt3 to couple directly to
the AFM order parameter. The Ginzburg-Landau equations for coupled
superconductivity and SIAFM are solved numerically for two possible SIAFM
configurations: (I) abutting antiferromagnetic domains of uniform size, and
(II) quenched random disorder of `nanodomains' in a uniform AFM background. We
discuss the contributions to the free energy, specific heat, and order
parameter for these models. Neither model provides a satisfactory account of
experiment, but results from the two models differ significantly. Our results
demonstrate that the response of an E_{2u} superconductor to SIAFM is strongly
dependent on the spatial dependence of AFM order; no conclusion can be drawn
regarding the compatibility of E_{2u} superconductivity with UPt3 that is
independent of assumptions on the spatial dependence of AFMComment: 12 pages, 13 figures, to appear in Phys. Rev.
Mixing Bandt-Pompe and Lempel-Ziv approaches: another way to analyze the complexity of continuous-states sequences
In this paper, we propose to mix the approach underlying Bandt-Pompe
permutation entropy with Lempel-Ziv complexity, to design what we call
Lempel-Ziv permutation complexity. The principle consists of two steps: (i)
transformation of a continuous-state series that is intrinsically multivariate
or arises from embedding into a sequence of permutation vectors, where the
components are the positions of the components of the initial vector when
re-arranged; (ii) performing the Lempel-Ziv complexity for this series of
`symbols', as part of a discrete finite-size alphabet. On the one hand, the
permutation entropy of Bandt-Pompe aims at the study of the entropy of such a
sequence; i.e., the entropy of patterns in a sequence (e.g., local increases or
decreases). On the other hand, the Lempel-Ziv complexity of a discrete-state
sequence aims at the study of the temporal organization of the symbols (i.e.,
the rate of compressibility of the sequence). Thus, the Lempel-Ziv permutation
complexity aims to take advantage of both of these methods. The potential from
such a combined approach - of a permutation procedure and a complexity analysis
- is evaluated through the illustration of some simulated data and some real
data. In both cases, we compare the individual approaches and the combined
approach.Comment: 30 pages, 4 figure
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