7,432 research outputs found
Mathematical analysis and simulations of the neural circuit for locomotion in lamprey
We analyze the dynamics of the neural circuit of the lamprey central pattern generator. This analysis provides insight into how neural interactions form oscillators and enable spontaneous oscillations in a network of damped oscillators, which were not apparent in previous simulations or abstract phase oscillator models. We also show how the different behavior regimes (characterized by phase and amplitude relationships between oscillators) of forward or backward swimming, and turning, can be controlled using the neural connection strengths and external inputs
Lie monads and dualities
We study dualities between Lie algebras and Lie coalgebras, and their
respective (co)representations. To allow a study of dualities in an
infinite-dimensional setting, we introduce the notions of Lie monads and Lie
comonads, as special cases of YB-Lie algebras and YB-Lie coalgebras in additive
monoidal categories. We show that (strong) dualities between Lie algebras and
Lie coalgebras are closely related to (iso)morphisms between associated Lie
monads and Lie comonads. In the case of a duality between two Hopf algebras -in
the sense of Takeuchi- we recover a duality between a Lie algebra and a Lie
coalgebra -in the sense defined in this note- by computing the primitive and
the indecomposables elements, respectively.Comment: 27 pages, v2: some examples added and minor change
Performance of the sleep-mode mechanism of the new IEEE 802.16m proposal for correlated downlink traffic
There is a considerable interest nowadays in making wireless telecommunication more energy-efficient. The sleep-mode mechanism in WiMAX (IEEE 802.16e) is one of such energy saving measures. Recently, Samsung proposed some modifications on the sleep-mode mechanism, scheduled to appear in the forthcoming IEEE 802.16m standard, aimed at minimizing the signaling overhead. In this work, we present a performance analysis of this proposal and clarify the differences with the standard mechanism included in IEEE 802.16e. We also propose some special algorithms aimed at reducing the computational complexity of the analysis
Carbon nanotube chirality determines properties of encapsulated linear carbon chain
Long linear carbon chains encapsulated inside carbon nanotubes are a very
close realization of carbyne, the truly one-dimensional allotrope of carbon.
Here we study individual pairs of double-walled carbon nanotubes and
encapsulated linear carbon chains by tip-enhanced Raman scattering. We observe
that the radial breathing mode of the inner nanotube correlates with the
frequency of the carbon chain's Raman mode, revealing that the nanotube
chirality determines the vibronic and electronic properties of the encapsulated
carbon chain. We provide the missing link that connects the properties of the
encapsulated long linear carbon chain with the structure of the host nanotube.Comment: keywords: linear carbon chains; carbyne; carbon nanotubes;
tip-enhanced Raman scattering; TERS; Significant changes compared to first
version of the manuscript. Current version includes Supporting Informatio
Spatial clustering method for geographic data
In the process of visualizing quantitative spatial data, it is necessary to
classify attribute values into some class divisions. In a previous paper, the author
proposed a classification method for minimizing the loss of information contained in
original data. This method can be considered as a kind of smoothing method that
neglects the characteristics of spatial distribution. In order to understand the
spatial structure of data, it is also necessary to construct another smoothing method
considering the characteristics of the distribution of the spatial data. In this paper,
a spatial clustering method based on Akaike’s Information Criterion is proposed.
Furthermore, numerical examples of its application are shown using actual spatial
data for the Tokyo Metropolitan area
Computational Complexity of the Interleaving Distance
The interleaving distance is arguably the most prominent distance measure in
topological data analysis. In this paper, we provide bounds on the
computational complexity of determining the interleaving distance in several
settings. We show that the interleaving distance is NP-hard to compute for
persistence modules valued in the category of vector spaces. In the specific
setting of multidimensional persistent homology we show that the problem is at
least as hard as a matrix invertibility problem. Furthermore, this allows us to
conclude that the interleaving distance of interval decomposable modules
depends on the characteristic of the field. Persistence modules valued in the
category of sets are also studied. As a corollary, we obtain that the
isomorphism problem for Reeb graphs is graph isomorphism complete.Comment: Discussion related to the characteristic of the field added. Paper
accepted to the 34th International Symposium on Computational Geometr
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