1,316 research outputs found
Spherical Principal Curves
This paper presents a new approach for dimension reduction of data observed
in a sphere. Several dimension reduction techniques have recently developed for
the analysis of non-Euclidean data. As a pioneer work, Hauberg (2016) attempted
to implement principal curves on Riemannian manifolds. However, this approach
uses approximations to deal with data on Riemannian manifolds, which causes
distorted results. In this study, we propose a new approach to construct
principal curves on a sphere by a projection of the data onto a continuous
curve. Our approach lies in the same line of Hastie and Stuetzle (1989) that
proposed principal curves for Euclidean space data. We further investigate the
stationarity of the proposed principal curves that satisfy the self-consistency
on a sphere. Results from real data analysis with earthquake data and
simulation examples demonstrate the promising empirical properties of the
proposed approach
Einstein Manifolds As Yang-Mills Instantons
It is well-known that Einstein gravity can be formulated as a gauge theory of
Lorentz group where spin connections play a role of gauge fields and Riemann
curvature tensors correspond to their field strengths. One can then pose an
interesting question: What is the Einstein equations from the gauge theory
point of view? Or equivalently, what is the gauge theory object corresponding
to Einstein manifolds? We show that the Einstein equations in four dimensions
are precisely self-duality equations in Yang-Mills gauge theory and so Einstein
manifolds correspond to Yang-Mills instantons in SO(4) = SU(2)_L x SU(2)_R
gauge theory. Specifically, we prove that any Einstein manifold with or without
a cosmological constant always arises as the sum of SU(2)_L instantons and
SU(2)_R anti-instantons. This result explains why an Einstein manifold must be
stable because two kinds of instantons belong to different gauge groups,
instantons in SU(2)_L and anti-instantons in SU(2)_R, and so they cannot decay
into a vacuum. We further illuminate the stability of Einstein manifolds by
showing that they carry nontrivial topological invariants.Comment: v4; 17 pages, published version in Mod. Phys. Lett.
Baryonic Matter in the Hidden Local Symmetry Induced from Holographic QCD Models
Baryonic matter is studied in the Skyrme model by taking into account the
roles of , and mesons through the hidden local symmetry
up to terms including the homogeneous Wess-Zumino (hWZ)
terms. Using the master formulas for the low energy constants derived from
holographic QCD models the skyrmion matter properties can be quantitatively
calculated with the input values of the pion decay constant and the
vector meson mass . We find that the hWZ terms are responsible for
the repulsive interactions of the meson. In addition, the
self-consistently included terms with the hWZ terms is found
to increase the half skyrmion phase transition point above the normal nucleon
density.Comment: Contribution to SCGT12 "KMI-GCOE Workshop on Strong Coupling Gauge
Theories in the LHC Perspective", 4-7 Dec. 2012, Nagoya Universit
Recommended from our members
Real-time observations of TRIP-induced ultrahigh strain hardening in a dual-phase CrMnFeCoNi high-entropy alloy.
Strategies involving metastable phases have been the basis of the design of numerous alloys, yet research on metastable high-entropy alloys is still in its infancy. In dual-phase high-entropy alloys, the combination of local chemical environments and loading-induced crystal structure changes suggests a relationship between deformation mechanisms and chemical atomic distribution, which we examine in here in a Cantor-like Cr20Mn6Fe34Co34Ni6 alloy, comprising both face-centered cubic (fcc) and hexagonal closed packed (hcp) phases. We observe that partial dislocation activities result in stable three-dimensional stacking-fault networks. Additionally, the fraction of the stronger hcp phase progressively increases during plastic deformation by forming at the stacking-fault network boundaries in the fcc phase, serving as the major source of strain hardening. In this context, variations in local chemical composition promote a high density of Lomer-Cottrell locks, which facilitate the construction of the stacking-fault networks to provide nucleation sites for the hcp phase transformation
Human dopamine receptor nanovesicles for gate-potential modulators in high-performance field-effect transistor biosensors
The development of molecular detection that allows rapid responses with high sensitivity and selectivity remains challenging. Herein, we demonstrate the strategy of novel bio-nanotechnology to successfully fabricate high-performance dopamine (DA) biosensor using DA Receptor-containing uniform-particle-shaped Nanovesicles-immobilized Carboxylated poly(3,4-ethylenedioxythiophene) (CPEDOT) NTs (DRNCNs). DA molecules are commonly associated with serious diseases, such as Parkinson's and Alzheimer's diseases. For the first time, nanovesicles containing a human DA receptor D1 (hDRD1) were successfully constructed from HEK-293 cells, stably expressing hDRD1. The nanovesicles containing hDRD1 as gate-potential modulator on the conducting polymer (CP) nanomaterial transistors provided high-performance responses to DA molecule owing to their uniform, monodispersive morphologies and outstanding discrimination ability. Specifically, the DRNCNs were integrated into a liquid-ion gated field-effect transistor (FET) system via immobilization and attachment processes, leading to high sensitivity and excellent selectivity toward DA in liquid state. Unprecedentedly, the minimum detectable level (MDL) from the field-induced DA responses was as low as 10โ
pM in real- time, which is 10 times more sensitive than that of previously reported CP based-DA biosensors. Moreover, the FET-type DRNCN biosensor had a rapid response time (<1โ
s) and showed excellent selectivity in human serum
Geomagnetic field influences probabilistic abstract decision-making in humans
To resolve disputes or determine the order of things, people commonly use
binary choices such as tossing a coin, even though it is obscure whether the
empirical probability equals to the theoretical probability. The geomagnetic
field (GMF) is broadly applied as a sensory cue for various movements in many
organisms including humans, although our understanding is limited. Here we
reveal a GMF-modulated probabilistic abstract decision-making in humans and the
underlying mechanism, exploiting the zero-sum binary stone choice of Go game as
a proof-of-principle. The large-scale data analyses of professional Go matches
and in situ stone choice games showed that the empirical probabilities of the
stone selections were remarkably different from the theoretical probability. In
laboratory experiments, experimental probability in the decision-making was
significantly influenced by GMF conditions and specific magnetic resonance
frequency. Time series and stepwise systematic analyses pinpointed the
intentionally uncontrollable decision-making as a primary modulating target.
Notably, the continuum of GMF lines and anisotropic magnetic interplay between
players were crucial to influence the magnetic field resonance-mediated
abstract decision-making. Our findings provide unique insights into the impact
of sensing GMF in decision-makings at tipping points and the quantum mechanical
mechanism for manifesting the gap between theoretical and empirical probability
in 3-dimensional living space.Comment: 32 pages, 5 figures, 4 supplementary figures, 2 supplementary tables,
and separate 15 ancillary file
Hidden Local Symmetry and Infinite Tower of Vector Mesons for Baryons
In an effort to access dense baryonic matter relevant for compact stars in a
unified framework that handles both single baryon and multibaryon systems on
the same footing, we first address a holographic dual action for a single
baryon focusing on the role of the infinite tower of vector mesons
deconstructed from five dimensions. To leading order in 't Hooft coupling
, one has the Bogomol'nyi-Prasad-Sommerfield (BPS)
Skyrmion that results when the warping of the bulk background and the
Chern-Simons term in the Sakai-Sugimoto D4/D8- model are
ignored. The infinite tower was found by Sutcliffe to induce flow to a
conformal theory, i.e., the BPS. We compare this structure to that of the SS
model consisting of a 5D Yang-Mills action in warped space and the Chern-Simons
term in which higher vector mesons are integrated out while preserving hidden
local symmetry and valid to and in the chiral counting.
We point out the surprisingly important role of the meson that figures
in the Chern-Simons term that encodes chiral anomaly in the baryon structure
and that may be closely tied to short-range repulsion in nuclear interactions.Comment: 9 pages, REVTeX, to be published in Phys. Rev.
- โฆ