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1,803.09267
|
Frobenius Degenerations of Preprojective Algebras
|
In this paper, we study a preprojective algebra for quivers decorated with
$k$-algebras and bimodules, which generalizes work of Gabriel for ordinary
quivers, work of Dlab and Ringel for $k$-species, and recent work of de
Thanhoffer de V\"olcsey and Presotto, which has recently appeared from a
different perspective in work of K\"ulshammer. As for undecorated quivers, we
show that its moduli space of representations recovers the Hamiltonian
reduction of the cotangent bundle over the space of representations of the
decorated quiver. These algebras yield degenerations of ordinary preprojective
algebras, by folding the quiver and then degenerating the decorations. We prove
that these degenerations are flat in the Dynkin case, and conjecture, based on
computer results, that this extends to arbitrary decorated quivers.
|
math.RA math.RT math.SG
|
in this paper we study a preprojective algebra for quivers decorated with kalgebras and bimodules which generalizes work of gabriel for ordinary quivers work of dlab and ringel for kspecies and recent work of de thanhoffer de volcsey and presotto which has recently appeared from a different perspective in work of kulshammer as for undecorated quivers we show that its moduli space of representations recovers the hamiltonian reduction of the cotangent bundle over the space of representations of the decorated quiver these algebras yield degenerations of ordinary preprojective algebras by folding the quiver and then degenerating the decorations we prove that these degenerations are flat in the dynkin case and conjecture based on computer results that this extends to arbitrary decorated quivers
|
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|
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|
1,803.09268
|
On the non-vanishing of $p$-adic heights on CM abelian varieties, and
the arithmetic of Katz $p$-adic $L$-functions
|
Let $B$ be a simple CM abelian variety over a CM field $E$, $p$ a rational
prime. Suppose that $B$ has potentially ordinary reduction above $p$ and is
self-dual with root number $-1$. Under some further conditions, we prove the
generic non-vanishing of (cyclotomic) $p$-adic heights on $B$ along
anticyclotomic $\Z_{p}$-extensions of $E$. This provides evidence towards
Schneider's conjecture on the non-vanishing of $p$-adic heights. For CM
elliptic curves over $\Q$, the result was previously known as a consequence of
work of Bertrand, Gross--Zagier and Rohrlich in the 1980s. Our proof is based
on non-vanishing results for Katz $p$-adic $L$-functions and a Gross--Zagier
formula relating the latter to families of rational points on $B$.
|
math.NT
|
let b be a simple cm abelian variety over a cm field e p a rational prime suppose that b has potentially ordinary reduction above p and is selfdual with root number 1 under some further conditions we prove the generic nonvanishing of cyclotomic padic heights on b along anticyclotomic z_pextensions of e this provides evidence towards schneiders conjecture on the nonvanishing of padic heights for cm elliptic curves over q the result was previously known as a consequence of work of bertrand grosszagier and rohrlich in the 1980s our proof is based on nonvanishing results for katz padic lfunctions and a grosszagier formula relating the latter to families of rational points on b
|
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|
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|
1,803.09269
|
Pathwise integration and change of variable formulas for continuous
paths with arbitrary regularity
|
We construct a pathwise integration theory, associated with a change of
variable formula, for smooth functionals of continuous paths with arbitrary
regularity defined in terms of the notion of $p$-th variation along a sequence
of time partitions. For paths with finite $p$-th variation along a sequence of
time partitions, we derive a change of variable formula for $p$ times
continuously differentiable functions and show pointwise convergence of
appropriately defined compensated Riemann sums. Results for functions are
extended to regular path-dependent functionals using the concept of vertical
derivative of a functional. We show that the pathwise integral satisfies an
`isometry' formula in terms of $p$-th order variation and obtain a `signal plus
noise' decomposition for regular functionals of paths with strictly increasing
$p$-th variation. For less regular ($C^{p-1}$) functions we obtain a
Tanaka-type change of variable formula using an appropriately defined notion of
local time. These results extend to multidimensional paths and yield a natural
higher-order extension of the concept of `reduced rough path'. We show that,
while our integral coincides with a rough-path integral for a certain rough
path, its construction is canonical and does not involve the specification of
any rough-path superstructure.
|
math.PR math.CA
|
we construct a pathwise integration theory associated with a change of variable formula for smooth functionals of continuous paths with arbitrary regularity defined in terms of the notion of pth variation along a sequence of time partitions for paths with finite pth variation along a sequence of time partitions we derive a change of variable formula for p times continuously differentiable functions and show pointwise convergence of appropriately defined compensated riemann sums results for functions are extended to regular pathdependent functionals using the concept of vertical derivative of a functional we show that the pathwise integral satisfies an isometry formula in terms of pth order variation and obtain a signal plus noise decomposition for regular functionals of paths with strictly increasing pth variation for less regular cp1 functions we obtain a tanakatype change of variable formula using an appropriately defined notion of local time these results extend to multidimensional paths and yield a natural higherorder extension of the concept of reduced rough path we show that while our integral coincides with a roughpath integral for a certain rough path its construction is canonical and does not involve the specification of any roughpath superstructure
|
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|
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|
1,803.0927
|
An exact formula for $\mathrm{U}(3)$ Vafa-Witten invariants on
$\mathbb{P}^2$
|
Topologically twisted $\mathcal{N} = 4$ super Yang-Mills theory has a
partition function that counts Euler numbers of instanton moduli spaces. On the
manifold $\mathbb{P}^2$ and with gauge group $\mathrm{U}(3)$ this partition
function has a holomorphic anomaly which makes it a mock modular form of depth
two. We employ the Circle Method to find a Rademacher expansion for the Fourier
coefficients of this partition function. This is the first example of the use
of Circle Method for a mock modular form of a higher depth.
|
math.NT hep-th math.AG
|
topologically twisted mathcaln 4 super yangmills theory has a partition function that counts euler numbers of instanton moduli spaces on the manifold mathbbp2 and with gauge group mathrmu3 this partition function has a holomorphic anomaly which makes it a mock modular form of depth two we employ the circle method to find a rademacher expansion for the fourier coefficients of this partition function this is the first example of the use of circle method for a mock modular form of a higher depth
|
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|
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|
1,803.09271
|
On the Schur function expansion of a symmetric quasi-symmetric function
|
Egge, Loehr, and Warrington proved a formula for the Schur function expansion
of a symmetric function in terms of its expansion in fundamental
quasi-symmetric functions. Their formula involves the coefficients of a
modified inverse Kostka matrix. Recently Garsia and Remmel gave a simpler
reformulation of Egge, Loehr, and Warrington's result, with a new proof. We
give here a simple proof of Garsia and Remmel's version, using a sign-reversing
involution.
|
math.CO
|
egge loehr and warrington proved a formula for the schur function expansion of a symmetric function in terms of its expansion in fundamental quasisymmetric functions their formula involves the coefficients of a modified inverse kostka matrix recently garsia and remmel gave a simpler reformulation of egge loehr and warringtons result with a new proof we give here a simple proof of garsia and remmels version using a signreversing involution
|
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|
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|
1,803.09272
|
Adaptive Sparse-grid Gauss-Hermite Filter
|
In this paper, a new nonlinear filter based on sparse-grid quadrature method
has been proposed. The proposed filter is named as adaptive sparse-grid
Gauss-Hermite filter (ASGHF). Ordinary sparse-grid technique treats all the
dimensions equally, whereas the ASGHF assigns a fewer number of points along
the dimensions with lower nonlinearity. It uses adaptive tensor product to
construct multidimensional points until a predefined error tolerance level is
reached. The performance of the proposed filter is illustrated with two
nonlinear filtering problems. Simulation results demonstrate that the new
algorithm achieves a similar accuracy as compared to sparse-grid Gauss-Hermite
filter (SGHF) and Gauss-Hermite filter (GHF) with a considerable reduction in
computational load. Further, in the conventional GHF and SGHF, any increase in
the accuracy level may result in an unacceptably high increase in the
computational burden. However, in ASGHF, a little increase in estimation
accuracy is possible with a limited increase in computational burden by varying
the error tolerance level and the error weighting parameter. This enables the
online estimator to operate near full efficiency with a predefined
computational budget.
|
eess.SP
|
in this paper a new nonlinear filter based on sparsegrid quadrature method has been proposed the proposed filter is named as adaptive sparsegrid gausshermite filter asghf ordinary sparsegrid technique treats all the dimensions equally whereas the asghf assigns a fewer number of points along the dimensions with lower nonlinearity it uses adaptive tensor product to construct multidimensional points until a predefined error tolerance level is reached the performance of the proposed filter is illustrated with two nonlinear filtering problems simulation results demonstrate that the new algorithm achieves a similar accuracy as compared to sparsegrid gausshermite filter sghf and gausshermite filter ghf with a considerable reduction in computational load further in the conventional ghf and sghf any increase in the accuracy level may result in an unacceptably high increase in the computational burden however in asghf a little increase in estimation accuracy is possible with a limited increase in computational burden by varying the error tolerance level and the error weighting parameter this enables the online estimator to operate near full efficiency with a predefined computational budget
|
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|
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|
1,803.09273
|
Symmetric and antisymmetric strain as continuous tuning parameters for
electronic nematic order
|
We report the separate response of the critical temperature of the nematic
phase transition $T_{\rm S}$ to symmetric and antisymmetric strains for the
prototypical underdoped iron pnictide Ba(Fe$_{0.975}$Co$_{0.025}$)$_2$As$_2$.
This decomposition is achieved by comparing the response of $T_{\rm S}$ to
uniaxial stress and hydrostatic pressure. In addition to quantifying the two
distinct linear responses to symmetric strains, we find a quadratic variation
of $T_{\rm S}$ as a response to antisymmetric strains $\epsilon_{\rm
B_{1g}}$=$\frac{1}{2}$($\epsilon_{\rm xx}$-$\epsilon_{\rm yy}$), exceeding the
non linear response to symmetric strains by at least two orders of magnitude.
These observations establish orthogonal antisymmetric strain as a powerful
tuning parameter for nematic order.
|
cond-mat.mtrl-sci
|
we report the separate response of the critical temperature of the nematic phase transition t_rm s to symmetric and antisymmetric strains for the prototypical underdoped iron pnictide bafe_0975co_0025_2as_2 this decomposition is achieved by comparing the response of t_rm s to uniaxial stress and hydrostatic pressure in addition to quantifying the two distinct linear responses to symmetric strains we find a quadratic variation of t_rm s as a response to antisymmetric strains epsilon_rm b_1gfrac12epsilon_rm xxepsilon_rm yy exceeding the non linear response to symmetric strains by at least two orders of magnitude these observations establish orthogonal antisymmetric strain as a powerful tuning parameter for nematic order
|
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|
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|
1,803.09274
|
Quantum nonlinear four-wave mixing with a single atom in an optical
cavity
|
Single atom cavity quantum electrodynamics grants access to nonclassical
photon statistics, while electromagnetically induced transparency exhibits a
dark state of long coherence time. The combination of the two produces a new
light field via four-wave mixing that shows long-lived quantum statistics. We
observe the new field in the emission from the cavity as a beat with the probe
light that together with the control beam and the cavity vacuum is driving the
four-wave mixing process. Moreover, the control field allows us to tune the new
light field from antibunching to bunching, demonstrating our all-optical
control over the photon-pair emission.
|
quant-ph
|
single atom cavity quantum electrodynamics grants access to nonclassical photon statistics while electromagnetically induced transparency exhibits a dark state of long coherence time the combination of the two produces a new light field via fourwave mixing that shows longlived quantum statistics we observe the new field in the emission from the cavity as a beat with the probe light that together with the control beam and the cavity vacuum is driving the fourwave mixing process moreover the control field allows us to tune the new light field from antibunching to bunching demonstrating our alloptical control over the photonpair emission
|
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|
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|
1,803.09275
|
Vacua and walls of mass-deformed K\"ahler nonlinear sigma models on
$Sp(N)/U(N)$
|
We study vacua and walls of mass-deformed K\"ahler nonlinear sigma models on
$Sp(N)/U(N)$. We identify elementary walls with the simple roots of $USp(2N)$
and discuss compressed walls, penetrable walls and multiwalls by using the
moduli matrix formalism.
|
hep-th
|
we study vacua and walls of massdeformed kahler nonlinear sigma models on spnun we identify elementary walls with the simple roots of usp2n and discuss compressed walls penetrable walls and multiwalls by using the moduli matrix formalism
|
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|
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|
1,803.09276
|
Internal shocks in microquasar jets with a continuous Lorentz factor
modulation
|
We perform relativistic hydrodynamic simulations of internal shocks formed in
microquasar jets by continuous variation of the bulk Lorentz factor, in order
to investigate the internal shock model. We consider one-, two-, and flicker
noise 20-mode variability. We observe emergence of a forward-reverse shock
structure for each peak of the Lorentz factor modulation. The high pressure in
the shocked layer launches powerful outflows perpendicular to the jet beam into
the ambient medium. These outflows dominate the details of the jet's kinetic
energy thermalization. They are responsible for mixing between the jet and
surrounding medium and generate powerful shocks in the latter. These results do
not concur with the popular picture of well-defined internal shells depositing
energy as they collide within the confines of the jet, in fact collisions
between internal shells themselves are quite rare in our continuous formulation
of the problem. For each of our simulations, we calculate the internal energy
deposited in the system, the "efficiency" of this deposition (defined as the
ratio of internal to total flow energy), and the maximum temperature reached in
order to make connections to emission mechanisms. We probe the dependence of
these diagnostics on the Lorentz factor variation amplitudes, modulation
frequencies, as well as the initial density ratio between the jet and the
ambient medium.
|
astro-ph.HE
|
we perform relativistic hydrodynamic simulations of internal shocks formed in microquasar jets by continuous variation of the bulk lorentz factor in order to investigate the internal shock model we consider one two and flicker noise 20mode variability we observe emergence of a forwardreverse shock structure for each peak of the lorentz factor modulation the high pressure in the shocked layer launches powerful outflows perpendicular to the jet beam into the ambient medium these outflows dominate the details of the jets kinetic energy thermalization they are responsible for mixing between the jet and surrounding medium and generate powerful shocks in the latter these results do not concur with the popular picture of welldefined internal shells depositing energy as they collide within the confines of the jet in fact collisions between internal shells themselves are quite rare in our continuous formulation of the problem for each of our simulations we calculate the internal energy deposited in the system the efficiency of this deposition defined as the ratio of internal to total flow energy and the maximum temperature reached in order to make connections to emission mechanisms we probe the dependence of these diagnostics on the lorentz factor variation amplitudes modulation frequencies as well as the initial density ratio between the jet and the ambient medium
|
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|
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|
1,803.09277
|
Serendipitous discovery of a strong-lensed galaxy in integral field
spectroscopy from MUSE
|
2MASX J04035024-0239275 is a bright red elliptical galaxy at redshift 0.0661
that presents two extended sources at 2\arcsec~to the north-east and
1\arcsec~to the south-west. The sizes and surface brightnesses of the two blue
sources are consistent with a gravitationally-lensed background galaxy. In this
paper we present MUSE observations of this galaxy from the All-weather MUse
Supernova Integral-field Nearby Galaxies (AMUSING) survey, and report the
discovery of a background lensed galaxy at redshift 0.1915, together with other
15 background galaxies at redshifts ranging from 0.09 to 0.9, that are not
multiply imaged. We have extracted aperture spectra of the lens and all the
sources and fit the stellar continuum with STARLIGHT to estimate their stellar
and emission line properties. A trace of past merger and active nucleus
activity is found in the lensing galaxy, while the background lensed galaxy is
found to be star-forming. Modeling the lensing potential with a singular
isothermal ellipsoid, we find an Einstein radius of 1\farcs45$\pm$0\farcs04,
which corresponds to 1.9 kpc at the redshift of the lens and it is much smaller
than its effective radius ($r_{\rm eff}\sim$ 9\arcsec). Comparing the Einstein
mass and the STARLIGHT stellar mass within the same aperture yields a dark
matter fraction of $18 \% \pm 8$ \% within the Einstein radius. The advent of
large surveys such as the Large Synoptic Survey Telescope (LSST) will discover
a number of strong-lensed systems, and here we demonstrate how wide-field
integral field spectroscopy offers an excellent approach to study them and to
precisely model lensing effects.
|
astro-ph.CO astro-ph.GA astro-ph.HE
|
2masx j040350240239275 is a bright red elliptical galaxy at redshift 00661 that presents two extended sources at 2arcsecto the northeast and 1arcsecto the southwest the sizes and surface brightnesses of the two blue sources are consistent with a gravitationallylensed background galaxy in this paper we present muse observations of this galaxy from the allweather muse supernova integralfield nearby galaxies amusing survey and report the discovery of a background lensed galaxy at redshift 01915 together with other 15 background galaxies at redshifts ranging from 009 to 09 that are not multiply imaged we have extracted aperture spectra of the lens and all the sources and fit the stellar continuum with starlight to estimate their stellar and emission line properties a trace of past merger and active nucleus activity is found in the lensing galaxy while the background lensed galaxy is found to be starforming modeling the lensing potential with a singular isothermal ellipsoid we find an einstein radius of 1farcs45pm0farcs04 which corresponds to 19 kpc at the redshift of the lens and it is much smaller than its effective radius r_rm effsim 9arcsec comparing the einstein mass and the starlight stellar mass within the same aperture yields a dark matter fraction of 18 pm 8 within the einstein radius the advent of large surveys such as the large synoptic survey telescope lsst will discover a number of stronglensed systems and here we demonstrate how widefield integral field spectroscopy offers an excellent approach to study them and to precisely model lensing effects
|
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|
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|
1,803.09278
|
Updated constraints on $f(T)$ models using direct and indirect
measurements of the Hubble parameter
|
We extract observational constraints on $f(T)$ gravity, using the recently
proposed statistical method which is not affected by the value of $H_0$ and
thus it bypasses the problem of the disagreement in its exact numerical value
between Planck and direct measurements. We use direct measurements of the
Hubble parameter with the corresponding covariance matrix, and for completeness
we perform a joint analysis using the latest data from Supernovae type Ia based
on JLA sample, quasi-stellar objects, and Cosmic Microwave Background shift
parameter from Planck. We analyze a large family of $f(T)$ models, and we
compare the fitting results with $\Lambda$CDM cosmology using the AIC
statistical test. Utilizing only the Hubble parameter data we find that in the
case of the power-law $f(T)$ model a small but non-zero deviation from
$\Lambda$CDM cosmology is slightly favored at 1-$\sigma$, nevertheless the
corresponding AIC value shows a statistical equivalence with it. Finally, the
join analysis reveals that all $f(T)$ models are very efficient and in very
good agreement with observations.
|
astro-ph.CO hep-ph hep-th
|
we extract observational constraints on ft gravity using the recently proposed statistical method which is not affected by the value of h_0 and thus it bypasses the problem of the disagreement in its exact numerical value between planck and direct measurements we use direct measurements of the hubble parameter with the corresponding covariance matrix and for completeness we perform a joint analysis using the latest data from supernovae type ia based on jla sample quasistellar objects and cosmic microwave background shift parameter from planck we analyze a large family of ft models and we compare the fitting results with lambdacdm cosmology using the aic statistical test utilizing only the hubble parameter data we find that in the case of the powerlaw ft model a small but nonzero deviation from lambdacdm cosmology is slightly favored at 1sigma nevertheless the corresponding aic value shows a statistical equivalence with it finally the join analysis reveals that all ft models are very efficient and in very good agreement with observations
|
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|
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|
1,803.09279
|
Enhanced Thermoelectric Properties in a New Silicon Crystal Si24 with
Intrinsic Nanoscale Porous Structure
|
Thermoelectric device is a promising next-generation energy solution owing to
its capability to transform waste heat into useful electric energy, which can
be realized in materials with high elec- tric conductivities and low thermal
conductivities. A recently synthesized silicon allotrope of Si$_{24}$ features
highly anisotropic crystal structure with nanometre-sized regular pores. Here,
based on first-principles study without any empirical parameter, we show that
the slightly doped Si$_{24}$ can pro- vide an order-of-magnitude enhanced
thermoelectric figure of merit at room temperature, compared with the cubic
diamond phase of silicon. We ascribe the enhancement to the intrinsic
nanostructure formed by the nanopore array, which effectively hinders heat
conduction while electric conductivity is maintained. This can be a viable
option to enhance the thermoelectric figure of merit without further forming an
extrinsic nanostructure. In addition, we propose a practical strategy to
further diminish the thermal conductivity without affecting electric
conductivity by confining rattling guest atoms in the pores.
|
cond-mat.mtrl-sci
|
thermoelectric device is a promising nextgeneration energy solution owing to its capability to transform waste heat into useful electric energy which can be realized in materials with high elec tric conductivities and low thermal conductivities a recently synthesized silicon allotrope of si_24 features highly anisotropic crystal structure with nanometresized regular pores here based on firstprinciples study without any empirical parameter we show that the slightly doped si_24 can pro vide an orderofmagnitude enhanced thermoelectric figure of merit at room temperature compared with the cubic diamond phase of silicon we ascribe the enhancement to the intrinsic nanostructure formed by the nanopore array which effectively hinders heat conduction while electric conductivity is maintained this can be a viable option to enhance the thermoelectric figure of merit without further forming an extrinsic nanostructure in addition we propose a practical strategy to further diminish the thermal conductivity without affecting electric conductivity by confining rattling guest atoms in the pores
|
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|
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|
1,803.0928
|
Generically nef vector bundles on ruled surfaces
|
The present paper concerns the invariants of generically nef vector bundles
on ruled surfaces. By Mehta - Ramanathan Restriction Theorem and by Miyaoka
characterization of semistable vector bundles on a curve, the generic nefness
can be considered as a weak form of semistability. We establish a Bogomolov
type inequality for generically nef vector bundles with nef general fiber
restriction on ruled surfaces with no negative section. This gives an
affermative answer in this case to a problem posed by Th. Peternell.
Concerning ruled surfaces with a negative section, we prove a a similar
result for generically nef vector bundles, with nef and balanced general fiber
restriction and with a numerical condition on first Chern class, which is
satisfied, for instance, if in its class there is a reduced divisor.
Finally, we use such results to bound the invariants of curve fibrations,
which factorize through finite covers of ruled surfaces.
|
math.AG
|
the present paper concerns the invariants of generically nef vector bundles on ruled surfaces by mehta ramanathan restriction theorem and by miyaoka characterization of semistable vector bundles on a curve the generic nefness can be considered as a weak form of semistability we establish a bogomolov type inequality for generically nef vector bundles with nef general fiber restriction on ruled surfaces with no negative section this gives an affermative answer in this case to a problem posed by th peternell concerning ruled surfaces with a negative section we prove a a similar result for generically nef vector bundles with nef and balanced general fiber restriction and with a numerical condition on first chern class which is satisfied for instance if in its class there is a reduced divisor finally we use such results to bound the invariants of curve fibrations which factorize through finite covers of ruled surfaces
|
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|
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|
1,803.09281
|
A position-dependent mass harmonic oscillator and deformed space
|
We consider canonically conjugated generalized space and linear momentum
operators $\hat{x}_q$ and $ \hat{p}_q$ in quantum mechanics, associated to a
generalized translation operator which produces infinitesimal deformed
displacements controlled by a deformation parameter $q$. A canonical
transformation $(\hat{x}, \hat{p}) \rightarrow (\hat{x}_q, \hat{p}_q)$ leads
the Hamiltonian of a position-dependent mass particle in usual space to another
Hamiltonian of a particle with constant mass in a conservative force field of
the deformed space. The equation of motion for the classical phase space $(x,
p)$ may be expressed in terms of the deformed (dual) $q$-derivative. We revisit
the problem of a $q$-deformed oscillator in both classical and quantum
formalisms. Particularly, this canonical transformation leads a particle with
position-dependent mass in a harmonic potential to a particle with constant
mass in a Morse potential. The trajectories in phase spaces $(x,p)$ and $(x_q,
p_q)$ are analyzed for different values of the deformation parameter. Lastly,
we compare the results of the problem in classical and quantum formalisms
through the principle of correspondence and the WKB approximation.
|
quant-ph
|
we consider canonically conjugated generalized space and linear momentum operators hatx_q and hatp_q in quantum mechanics associated to a generalized translation operator which produces infinitesimal deformed displacements controlled by a deformation parameter q a canonical transformation hatx hatp rightarrow hatx_q hatp_q leads the hamiltonian of a positiondependent mass particle in usual space to another hamiltonian of a particle with constant mass in a conservative force field of the deformed space the equation of motion for the classical phase space x p may be expressed in terms of the deformed dual qderivative we revisit the problem of a qdeformed oscillator in both classical and quantum formalisms particularly this canonical transformation leads a particle with positiondependent mass in a harmonic potential to a particle with constant mass in a morse potential the trajectories in phase spaces xp and x_q p_q are analyzed for different values of the deformation parameter lastly we compare the results of the problem in classical and quantum formalisms through the principle of correspondence and the wkb approximation
|
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|
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|
1,803.09282
|
Albert Einstein and the Marangoni family
|
The sixteen years old Albert Einstein made friend with Ernestina Marangoni in
the summer of 1895 in Pavia. We discuss in this article the unacknowledged link
between Albert Einstein and the physicist and professor Carlo Marangoni,
Ernestina's uncle, a specialist of capillarity effects.
|
physics.hist-ph
|
the sixteen years old albert einstein made friend with ernestina marangoni in the summer of 1895 in pavia we discuss in this article the unacknowledged link between albert einstein and the physicist and professor carlo marangoni ernestinas uncle a specialist of capillarity effects
|
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|
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|
1,803.09283
|
Stability Analysis of Inexact Solves in Model Reduction of Non-parametric Second-order Dynamical systems
|
Here, we focus on Model Order Reduction (MOR) of non-parametric second-order dynamical systems. In these MOR algorithms, sequences of large and sparse linear systems arise during the model reduction process. Solving such linear systems is the main computational bottleneck in efficient scaling of these MOR algorithms for reducing extremely large dynamical systems. Preconditioned iterative methods are often used for solving such linear systems.
These iterative methods introduce errors because they solve the linear systems up to a certain tolerance. Hence, our focus is to analyze the stability of these MOR algorithms when using inexact linear solves. Adaptive Iterative Rational Global Arnoldi (AIRGA) is a popular MOR algorithm belonging to this category. We prove that, under four mild conditions, the AIRGA algorithm is backward stable with respect to the errors introduced by these inexact linear solves. Our results easily extend to other MOR algorithms belonging to this category.
Our first condition enforces the use of a Ritz-Galerkin based linear solver, where the residual of a linear system is made orthogonal to the corresponding Krylov subspace. Our second condition requires satisfying few extra orthogonalities. We show how to modify the underlying linear solver to achieve these extra orthogonalities. We further demonstrate that using a recycling variant of the underlying linear solver helps us achieve these orthogonalities cheaply and with no code changes.
Our third condition involves existence and invertibility of a matrix mostly dependent upon the input dynamical system, with the norm of this matrix bounded by one. Our fourth and final condition involves being able to compute a perturbation from the derived expression and bounding its norm by one as well. The last two conditions are easily satisfied by all our models.
|
math.NA cs.NA
|
here we focus on model order reduction mor of nonparametric secondorder dynamical systems in these mor algorithms sequences of large and sparse linear systems arise during the model reduction process solving such linear systems is the main computational bottleneck in efficient scaling of these mor algorithms for reducing extremely large dynamical systems preconditioned iterative methods are often used for solving such linear systems these iterative methods introduce errors because they solve the linear systems up to a certain tolerance hence our focus is to analyze the stability of these mor algorithms when using inexact linear solves adaptive iterative rational global arnoldi airga is a popular mor algorithm belonging to this category we prove that under four mild conditions the airga algorithm is backward stable with respect to the errors introduced by these inexact linear solves our results easily extend to other mor algorithms belonging to this category our first condition enforces the use of a ritzgalerkin based linear solver where the residual of a linear system is made orthogonal to the corresponding krylov subspace our second condition requires satisfying few extra orthogonalities we show how to modify the underlying linear solver to achieve these extra orthogonalities we further demonstrate that using a recycling variant of the underlying linear solver helps us achieve these orthogonalities cheaply and with no code changes our third condition involves existence and invertibility of a matrix mostly dependent upon the input dynamical system with the norm of this matrix bounded by one our fourth and final condition involves being able to compute a perturbation from the derived expression and bounding its norm by one as well the last two conditions are easily satisfied by all our models
|
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|
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|
1,803.09284
|
Quasi-isometric invariance of continuous group $L^p$-cohomology, and
first applications to vanishings
|
We show that the continuous $L^p$-cohomology of locally compact second
countable groups is a quasi-isometric invariant. As an application, we prove
partial results supporting a positive answer to a question asked by M.~Gromov,
suggesting a classical behaviour of continuous $L^p$-cohomology of simple real
Lie groups. In addition to quasi-isometric invariance, the ingredients are a
spectral sequence argument and Pansu's vanishing results for real hyperbolic
spaces. In the best adapted cases of simple Lie groups, we obtain nearly half
of the relevant vanishings.
|
math.GR
|
we show that the continuous lpcohomology of locally compact second countable groups is a quasiisometric invariant as an application we prove partial results supporting a positive answer to a question asked by mgromov suggesting a classical behaviour of continuous lpcohomology of simple real lie groups in addition to quasiisometric invariance the ingredients are a spectral sequence argument and pansus vanishing results for real hyperbolic spaces in the best adapted cases of simple lie groups we obtain nearly half of the relevant vanishings
|
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|
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|
1,803.09285
|
Synthesizing Skeletons for Reactive Systems
|
We present an analysis technique for temporal specifications of reactive
systems that identifies, on the level of individual system outputs over time,
which parts of the implementation are determined by the specification, and
which parts are still open. This information is represented in the form of a
labeled transition system, which we call skeleton. Each state of the skeleton
is labeled with a three-valued assignment to the output variables: each output
can be true, false, or open, where true or false means that the value must be
true or false, respectively, and open means that either value is still
possible. We present algorithms for the verification of skeletons and for the
learning-based synthesis of skeletons from specifications in linear-time
temporal logic (LTL). The algorithm returns a skeleton that satisfies the given
LTL specification in time polynomial in the size of the minimal skeleton. Our
new analysis technique can be used to recognize and repair specifications that
underspecify critical situations. The technique thus complements existing
methods for the recognition and repair of overspecifications via the
identification of unrealizable cores.
|
cs.FL cs.LG
|
we present an analysis technique for temporal specifications of reactive systems that identifies on the level of individual system outputs over time which parts of the implementation are determined by the specification and which parts are still open this information is represented in the form of a labeled transition system which we call skeleton each state of the skeleton is labeled with a threevalued assignment to the output variables each output can be true false or open where true or false means that the value must be true or false respectively and open means that either value is still possible we present algorithms for the verification of skeletons and for the learningbased synthesis of skeletons from specifications in lineartime temporal logic ltl the algorithm returns a skeleton that satisfies the given ltl specification in time polynomial in the size of the minimal skeleton our new analysis technique can be used to recognize and repair specifications that underspecify critical situations the technique thus complements existing methods for the recognition and repair of overspecifications via the identification of unrealizable cores
|
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|
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|
1,803.09286
|
Phased-Locked Two-Color Single Soliton Microcombs in
Dispersion-Engineered Si3N4 Resonators
|
We propose and theoretically investigate a dispersion-engineered Si3N4
microring resonator, based on a cross-section containing a partially-etched
trench, that supports phase-locked, two-color soliton microcomb states. These
soliton states consist of a single circulating intracavity pulse with a
modulated envelope that sits on a continuous wave background. Such temporal
waveforms produce a frequency comb whose spectrum is spread over two
widely-spaced spectral windows, each exhibiting a squared hyperbolic secant
envelope, with the two windows phase-locked to each other via Cherenkov
radiation. The first spectral window is centered around the 1550 nm pump, while
the second spectral window is tailored based on straightforward geometric
control, and can be centered as short as 750 nm and as long as 3000 nm. We
numerically analyze the robustness of the design to parameter variation, and
consider its implications to self-referencing and visible wavelength comb
generation.
|
physics.optics
|
we propose and theoretically investigate a dispersionengineered si3n4 microring resonator based on a crosssection containing a partiallyetched trench that supports phaselocked twocolor soliton microcomb states these soliton states consist of a single circulating intracavity pulse with a modulated envelope that sits on a continuous wave background such temporal waveforms produce a frequency comb whose spectrum is spread over two widelyspaced spectral windows each exhibiting a squared hyperbolic secant envelope with the two windows phaselocked to each other via cherenkov radiation the first spectral window is centered around the 1550 nm pump while the second spectral window is tailored based on straightforward geometric control and can be centered as short as 750 nm and as long as 3000 nm we numerically analyze the robustness of the design to parameter variation and consider its implications to selfreferencing and visible wavelength comb generation
|
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|
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|
1,803.09287
|
Deformations and their controlling cohomologies of
$\mathcal{O}$-operators
|
$\mathcal{O}$-operators are important in broad areas in mathematics and
physics, such as integrable systems, the classical Yang-Baxter equation,
pre-Lie algebras and splitting of operads. In this paper, a deformation theory
of $\mathcal{O}$-operators is established in consistence with the general
principles of deformation theories. On the one hand, $\mathcal{O}$-operators
are shown to be characterized as the Maurer-Cartan elements in a suitable
graded Lie algebra. A given $\mathcal{O}$-operator gives rise to a differential
graded Lie algebra whose Maurer-Cartan elements characterize deformations of
the given $\mathcal{O}$-operator. On the other hand, a Lie algebra with a
representation is identified from an $\mathcal{O}$-operator $T$ such that the
corresponding Chevalley-Eilenberg cohomology controls deformations of $T$, thus
can be regarded as an analogue of the Andr\'e-Quillen cohomology for the
$\mathcal{O}$-operator. Thereafter, infinitesimal and formal deformations of
$\mathcal{O}$-operators are studied. In particular, the notion of Nijenhuis
elements is introduced to characterize trivial infinitesimal deformations.
Formal deformations and extendibility of order $n$ deformations of an
$\mathcal{O}$-operator are also characterized in terms of the new cohomology
theory. Applications are given to deformations of Rota-Baxter operators of
weight 0 and skew-symmetric $r$-matrices for the classical Yang-Baxter
equation. For skew-symmetric $r$-matrices, there is an independent
Maurer-Cartan characterization of the deformations as well as an analogue of
the Andr\'e-Quillen cohomology controlling the deformations, which turn out to
be equivalent to the ones obtained as $\mathcal{O}$-operators associated to the
coadjoint representations. Finally, infinitesimal deformations of
skew-symmetric $r$-matrices and their corresponding triangular Lie bialgebras
are studied.
|
math.QA math-ph math.KT math.MP
|
mathcalooperators are important in broad areas in mathematics and physics such as integrable systems the classical yangbaxter equation prelie algebras and splitting of operads in this paper a deformation theory of mathcalooperators is established in consistence with the general principles of deformation theories on the one hand mathcalooperators are shown to be characterized as the maurercartan elements in a suitable graded lie algebra a given mathcalooperator gives rise to a differential graded lie algebra whose maurercartan elements characterize deformations of the given mathcalooperator on the other hand a lie algebra with a representation is identified from an mathcalooperator t such that the corresponding chevalleyeilenberg cohomology controls deformations of t thus can be regarded as an analogue of the andrequillen cohomology for the mathcalooperator thereafter infinitesimal and formal deformations of mathcalooperators are studied in particular the notion of nijenhuis elements is introduced to characterize trivial infinitesimal deformations formal deformations and extendibility of order n deformations of an mathcalooperator are also characterized in terms of the new cohomology theory applications are given to deformations of rotabaxter operators of weight 0 and skewsymmetric rmatrices for the classical yangbaxter equation for skewsymmetric rmatrices there is an independent maurercartan characterization of the deformations as well as an analogue of the andrequillen cohomology controlling the deformations which turn out to be equivalent to the ones obtained as mathcalooperators associated to the coadjoint representations finally infinitesimal deformations of skewsymmetric rmatrices and their corresponding triangular lie bialgebras are studied
|
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|
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|
1,803.09288
|
The Geometry of Culture: Analyzing Meaning through Word Embeddings
|
We demonstrate the utility of a new methodological tool, neural-network word
embedding models, for large-scale text analysis, revealing how these models
produce richer insights into cultural associations and categories than possible
with prior methods. Word embeddings represent semantic relations between words
as geometric relationships between vectors in a high-dimensional space,
operationalizing a relational model of meaning consistent with contemporary
theories of identity and culture. We show that dimensions induced by word
differences (e.g. man - woman, rich - poor, black - white, liberal -
conservative) in these vector spaces closely correspond to dimensions of
cultural meaning, and the projection of words onto these dimensions reflects
widely shared cultural connotations when compared to surveyed responses and
labeled historical data. We pilot a method for testing the stability of these
associations, then demonstrate applications of word embeddings for
macro-cultural investigation with a longitudinal analysis of the coevolution of
gender and class associations in the United States over the 20th century and a
comparative analysis of historic distinctions between markers of gender and
class in the U.S. and Britain. We argue that the success of these
high-dimensional models motivates a move towards "high-dimensional theorizing"
of meanings, identities and cultural processes.
|
cs.CL
|
we demonstrate the utility of a new methodological tool neuralnetwork word embedding models for largescale text analysis revealing how these models produce richer insights into cultural associations and categories than possible with prior methods word embeddings represent semantic relations between words as geometric relationships between vectors in a highdimensional space operationalizing a relational model of meaning consistent with contemporary theories of identity and culture we show that dimensions induced by word differences eg man woman rich poor black white liberal conservative in these vector spaces closely correspond to dimensions of cultural meaning and the projection of words onto these dimensions reflects widely shared cultural connotations when compared to surveyed responses and labeled historical data we pilot a method for testing the stability of these associations then demonstrate applications of word embeddings for macrocultural investigation with a longitudinal analysis of the coevolution of gender and class associations in the united states over the 20th century and a comparative analysis of historic distinctions between markers of gender and class in the us and britain we argue that the success of these highdimensional models motivates a move towards highdimensional theorizing of meanings identities and cultural processes
|
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|
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|
1,803.09289
|
Minmax Centered k-Partitioning of Trees and Applications to Sink
Evacuation with Dynamic Confluent Flows
|
Let $T=(V,E)$ be a tree with associated costs on its subtrees. A minmax
$k$-partition of $T$ is a partition into $k$ subtrees, minimizing the maximum
cost of a subtree over all possible partitions. In the centered version of the
problem, the cost of a subtree cost is defined as the minimum cost of
"servicing" that subtree using a center located within it.
The problem motivating this work was the sink-evacuation problem on trees,
i.e., finding a collection of $k$-sinks that minimize the time required by a
confluent dynamic network flow to evacuate all supplies to sinks.
This paper provides the first polynomial-time algorithm for solving this
problem, running in $O\Bigl(\max(k,\log n) k n \log^4 n\Bigr)$ time. The
technique developed can be used to solve any Minmax Centered $k$-Partitioning
problem on trees in which the servicing costs satisfy some very general
conditions. Solutions can be found for both the discrete case, in which centers
must be on vertices, and the continuous case, in which centers may also be
placed on edges. The technique developed also improves previous results for
finding a minmax cost $k$-partition of a tree given the location of the sinks
in advance.
|
cs.DS
|
let tve be a tree with associated costs on its subtrees a minmax kpartition of t is a partition into k subtrees minimizing the maximum cost of a subtree over all possible partitions in the centered version of the problem the cost of a subtree cost is defined as the minimum cost of servicing that subtree using a center located within it the problem motivating this work was the sinkevacuation problem on trees ie finding a collection of ksinks that minimize the time required by a confluent dynamic network flow to evacuate all supplies to sinks this paper provides the first polynomialtime algorithm for solving this problem running in obiglmaxklog n k n log4 nbigr time the technique developed can be used to solve any minmax centered kpartitioning problem on trees in which the servicing costs satisfy some very general conditions solutions can be found for both the discrete case in which centers must be on vertices and the continuous case in which centers may also be placed on edges the technique developed also improves previous results for finding a minmax cost kpartition of a tree given the location of the sinks in advance
|
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|
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|
1,803.0929
|
Performance analysis of nanostructured Peltier coolers
|
Employing non-equilibrium quantum transport models, we investigate the
details and operating conditions of nano-structured Peltier coolers embedded
with an energy filtering barrier. Our investigations point out non-trivial
aspects of Peltier cooling which include an inevitable trade-off between the
cooling power and the coefficient of performance, the coefficient of
performance being high at a low voltage bias and subsequently deteriorating
with increasing voltage bias. We point out that there is an optimum energy
barrier height for nanowire Peltier coolers at which the cooling performance is
optimized. However, for bulk Peltier coolers, the cooling performance is
enhanced with the height of the energy filtering barrier. Exploring further, we
point out that a degradation in cooling performance with respect to bulk is
inevitable as a single moded nanowire transitions to a multi-moded one. The
results discussed here can provide theoretical insights for optimal design of
nano Peltier coolers.
|
physics.app-ph
|
employing nonequilibrium quantum transport models we investigate the details and operating conditions of nanostructured peltier coolers embedded with an energy filtering barrier our investigations point out nontrivial aspects of peltier cooling which include an inevitable tradeoff between the cooling power and the coefficient of performance the coefficient of performance being high at a low voltage bias and subsequently deteriorating with increasing voltage bias we point out that there is an optimum energy barrier height for nanowire peltier coolers at which the cooling performance is optimized however for bulk peltier coolers the cooling performance is enhanced with the height of the energy filtering barrier exploring further we point out that a degradation in cooling performance with respect to bulk is inevitable as a single moded nanowire transitions to a multimoded one the results discussed here can provide theoretical insights for optimal design of nano peltier coolers
|
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|
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|
1,803.09291
|
Duality for cohomology of curves with coefficients in abelian varieties
|
In this paper, we formulate and prove a duality for cohomology of curves over
perfect fields of positive characteristic with coefficients in Neron models of
abelian varieties. This is a global function field version of the author's
previous work on local duality and Grothendieck's duality conjecture. It
generalizes the perfectness of the Cassels-Tate pairing in the finite base
field case. The proof uses the local duality mentioned above, Artin-Milne's
global finite flat duality, the non-degeneracy of the height pairing and
finiteness of crystalline cohomology. All these ingredients are organized under
the formalism of the rational etale site developed earlier.
|
math.NT math.AG
|
in this paper we formulate and prove a duality for cohomology of curves over perfect fields of positive characteristic with coefficients in neron models of abelian varieties this is a global function field version of the authors previous work on local duality and grothendiecks duality conjecture it generalizes the perfectness of the casselstate pairing in the finite base field case the proof uses the local duality mentioned above artinmilnes global finite flat duality the nondegeneracy of the height pairing and finiteness of crystalline cohomology all these ingredients are organized under the formalism of the rational etale site developed earlier
|
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|
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|
1,803.09292
|
Boost invariant regulator for field theories
|
It is shown that by imposing the relativistic symmetries on the cutoff in
field theories one rules out all known non-perturbative regulators except the
point splitting. The relativistic cutoff dynamics is non-local in time and
thereby unstable, bringing the very existence of relativistic field theory into
question. It is argued within the context of a scalar field theory model that
the combination of the point splitting with a sufficiently fast suppression in
the field amplitude may lead to stable semiclassical dynamics and to a new kind
of realistic vacuum structure.
|
hep-th
|
it is shown that by imposing the relativistic symmetries on the cutoff in field theories one rules out all known nonperturbative regulators except the point splitting the relativistic cutoff dynamics is nonlocal in time and thereby unstable bringing the very existence of relativistic field theory into question it is argued within the context of a scalar field theory model that the combination of the point splitting with a sufficiently fast suppression in the field amplitude may lead to stable semiclassical dynamics and to a new kind of realistic vacuum structure
|
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|
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|
1,803.09293
|
Experimental evidence of accelerated seismic release without critical
failure in acoustic emissions of compressed nanoporous materials
|
The total energy of acoustic emission (AE) events in externally stressed
materials diverges when approaching macroscopic failure. Numerical and
conceptual models explain this accelerated seismic release (ASR) as the
approach to a critical point that coincides with ultimate failure. Here, we
report ASR during soft uniaxial compression of three silica-based (SiO$_2$)
nanoporous materials. Instead of a singular critical point, the distribution of
AE energies is stationary and variations in the activity rate are sufficient to
explain the presence of multiple periods of ASR leading to distinct brittle
failure events. We propose that critical failure is suppressed in the AE
statistics by dissipation and transient hardening. Some of the critical
exponents estimated from the experiments are compatible with mean field models,
while others are still open to interpretation in terms of the solution of
frictional and fracture avalanche models.
|
cond-mat.mtrl-sci physics.geo-ph
|
the total energy of acoustic emission ae events in externally stressed materials diverges when approaching macroscopic failure numerical and conceptual models explain this accelerated seismic release asr as the approach to a critical point that coincides with ultimate failure here we report asr during soft uniaxial compression of three silicabased sio_2 nanoporous materials instead of a singular critical point the distribution of ae energies is stationary and variations in the activity rate are sufficient to explain the presence of multiple periods of asr leading to distinct brittle failure events we propose that critical failure is suppressed in the ae statistics by dissipation and transient hardening some of the critical exponents estimated from the experiments are compatible with mean field models while others are still open to interpretation in terms of the solution of frictional and fracture avalanche models
|
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|
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|
1,803.09294
|
On an attempt to optically excite the nuclear isomer in Th-229
|
We aim to perform direct optical spectroscopy of the Th-229 nuclear isomer to
measure its energy and lifetime, and to demonstrate optical coupling to the
nucleus. To this end, we develop Th-doped CaF2 crystals, which are transparent
at the anticipated isomer wavelength. Such crystals are illuminated by tunable
VUV undulator radiation for direct excitation of the isomer. We scan a 5 sigma
region around the assumed isomer energy of 7.8(5) eV and vary the excitation
time in sequential scans between 30 and 600 seconds. Suffering from an
unforeseen strong photoluminescence of the crystal, the experiment is sensitive
only to radiative isomer lifetimes between 0.2 and 1.1 seconds. For this
parameter range, and assuming radiative decay as the dominant de-excitation
channel, we can exclude an isomer with energy between 7.5 and 10 eV at the 95%
confidence level.
|
physics.atom-ph nucl-ex
|
we aim to perform direct optical spectroscopy of the th229 nuclear isomer to measure its energy and lifetime and to demonstrate optical coupling to the nucleus to this end we develop thdoped caf2 crystals which are transparent at the anticipated isomer wavelength such crystals are illuminated by tunable vuv undulator radiation for direct excitation of the isomer we scan a 5 sigma region around the assumed isomer energy of 785 ev and vary the excitation time in sequential scans between 30 and 600 seconds suffering from an unforeseen strong photoluminescence of the crystal the experiment is sensitive only to radiative isomer lifetimes between 02 and 11 seconds for this parameter range and assuming radiative decay as the dominant deexcitation channel we can exclude an isomer with energy between 75 and 10 ev at the 95 confidence level
|
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|
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|
1,803.09295
|
Robin eigenvalues on domains with peaks
|
Let $\Omega\subset\mathbb{R}^N$, $N\ge 2,$ be a bounded domain with an
outward power-like peak which is assumed not too sharp in a suitable sense. We
consider the Laplacian $u\mapsto -\Delta u$ in $\Omega$ with the Robin boundary
condition $\partial_n u=\alpha u$ on $\partial\Omega$ with $\partial_n$ being
the outward normal derivative and $\alpha>0$ being a parameter. We show that
for large $\alpha$ the associated eigenvalues $E_j(\alpha)$ behave as
$E_j(\alpha)\sim -\epsilon_j \alpha^\nu$, where $\nu>2$ and $\epsilon_j>0$
depend on the dimension and the peak geometry. This is in contrast with the
well-known estimate $E_j(\alpha)=O(\alpha^2)$ for the Lipschitz domains.
|
math.AP math-ph math.MP math.SP
|
let omegasubsetmathbbrn nge 2 be a bounded domain with an outward powerlike peak which is assumed not too sharp in a suitable sense we consider the laplacian umapsto delta u in omega with the robin boundary condition partial_n ualpha u on partialomega with partial_n being the outward normal derivative and alpha0 being a parameter we show that for large alpha the associated eigenvalues e_jalpha behave as e_jalphasim epsilon_j alphanu where nu2 and epsilon_j0 depend on the dimension and the peak geometry this is in contrast with the wellknown estimate e_jalphaoalpha2 for the lipschitz domains
|
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|
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|
1,803.09296
|
A Hopf-Lax formula for Hamilton-Jacobi equations with Caputo time
derivative
|
We prove a representation formula of Hopf-Lax type for the solution of a
Hamilton-Jacobi equation involving Caputo time-fractional derivative. Equations
of these type are associated with optimal control problems where the controlled
dynamics is replaced by a time-changed stochastic process describing the
trajectory of a particle subject to random trapping effects.
|
math.AP math.NA math.OC
|
we prove a representation formula of hopflax type for the solution of a hamiltonjacobi equation involving caputo timefractional derivative equations of these type are associated with optimal control problems where the controlled dynamics is replaced by a timechanged stochastic process describing the trajectory of a particle subject to random trapping effects
|
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|
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|
1,803.09297
|
Proof nets and the instantiation overflow property
|
Instantiation overflow is the property of those second order types for which
all instances of full comprehension can be deduced from instances of atomic
comprehension. In other words, a type has instantiation overflow when one can
type, by atomic polymorphism, "expansion terms" which realize instances of the
full extraction rule applied to that type. This property was investigated in
the case of the types arising from the well-known Russell-Prawitz translation
of logical connectives into System F, but is not restricted to such types.
Moreover, it can be related to functorial polymorphism, a well-known categorial
approach to parametricity in System F. In this paper we investigate the
instantiation overflow property by exploiting the representation of derivations
by means of linear logic proof nets. We develop a geometric approach to
instantiation overflow yielding a deeper understanding of the structure of
expansion terms and Russell-Prawitz types. Our main result is a
characterization of the class of types of the form $\forall XA$, where $A$ is a
simple type, which enjoy the instantiation overflow property, by means of a
generalization of Russell-Prawitz types.
|
cs.LO math.LO
|
instantiation overflow is the property of those second order types for which all instances of full comprehension can be deduced from instances of atomic comprehension in other words a type has instantiation overflow when one can type by atomic polymorphism expansion terms which realize instances of the full extraction rule applied to that type this property was investigated in the case of the types arising from the wellknown russellprawitz translation of logical connectives into system f but is not restricted to such types moreover it can be related to functorial polymorphism a wellknown categorial approach to parametricity in system f in this paper we investigate the instantiation overflow property by exploiting the representation of derivations by means of linear logic proof nets we develop a geometric approach to instantiation overflow yielding a deeper understanding of the structure of expansion terms and russellprawitz types our main result is a characterization of the class of types of the form forall xa where a is a simple type which enjoy the instantiation overflow property by means of a generalization of russellprawitz types
|
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|
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|
1,803.09298
|
A high-order hybridizable discontinuous Galerkin method with fast
convergence to steady-state solutions of the gas kinetic equation
|
The mass flow rate of Poiseuille flow of rarefied gas through long ducts of
two-dimensional cross-sections with arbitrary shape are critical in the
pore-network modeling of gas transport in porous media. In this paper, for the
first time, the high-order hybridizable discontinuous Galerkin (HDG) method is
used to find the steady-state solution of the linearized Bhatnagar-Gross-Krook
equation on two-dimensional triangular meshes. The velocity distribution
function and its traces are approximated in the piecewise polynomial space (of
degree up to 4) on the triangular meshes and the mesh skeletons, respectively.
By employing a numerical flux that is derived from the first-order upwind
scheme and imposing its continuity on the mesh skeletons, global systems for
unknown traces are obtained with a few coupled degrees of freedom. To achieve
fast convergence to the steady-state solution, a diffusion-type equation for
flow velocity that is asymptotic-preserving into the fluid dynamic limit is
solved by the HDG simultaneously, on the same meshes. The proposed
HDG-synthetic iterative scheme is proved to be accurate and efficient.
Specifically, for flows in the near-continuum regime, numerical simulations
have shown that, to achieve the same level of accuracy, our scheme could be
faster than the conventional iterative scheme by two orders of magnitude, while
it is faster than the synthetic iterative scheme based on the finite difference
discretization in the spatial space by one order of magnitude. The
HDG-synthetic iterative scheme is ready to be extended to simulate rarefied gas
mixtures and the Boltzmann collision operator.
|
physics.comp-ph physics.flu-dyn
|
the mass flow rate of poiseuille flow of rarefied gas through long ducts of twodimensional crosssections with arbitrary shape are critical in the porenetwork modeling of gas transport in porous media in this paper for the first time the highorder hybridizable discontinuous galerkin hdg method is used to find the steadystate solution of the linearized bhatnagargrosskrook equation on twodimensional triangular meshes the velocity distribution function and its traces are approximated in the piecewise polynomial space of degree up to 4 on the triangular meshes and the mesh skeletons respectively by employing a numerical flux that is derived from the firstorder upwind scheme and imposing its continuity on the mesh skeletons global systems for unknown traces are obtained with a few coupled degrees of freedom to achieve fast convergence to the steadystate solution a diffusiontype equation for flow velocity that is asymptoticpreserving into the fluid dynamic limit is solved by the hdg simultaneously on the same meshes the proposed hdgsynthetic iterative scheme is proved to be accurate and efficient specifically for flows in the nearcontinuum regime numerical simulations have shown that to achieve the same level of accuracy our scheme could be faster than the conventional iterative scheme by two orders of magnitude while it is faster than the synthetic iterative scheme based on the finite difference discretization in the spatial space by one order of magnitude the hdgsynthetic iterative scheme is ready to be extended to simulate rarefied gas mixtures and the boltzmann collision operator
|
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|
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|
1,803.09299
|
Four-spin ring interaction as a source of unconventional magnetic orders
in orthorhombic perovskite manganites
|
We use ab initio electronic structure calculations in combination with Monte
Carlo simulations to investigate the magnetic and ferroelectric properties of
bulk orthorhombic HoMnO$_3$ and ErMnO$_3$. Our goals are to explain the
inconsistencies in the measured magnetic properties of the orthorhombic
perovskite manganites (o-$R$MnO$_3$) with small rare-earth ($R$) cations or Y,
as well as the contradictions between the directions and amplitudes of the
electric polarizations reported by different experimental groups. Our
computations stabilize several exotic magnetic orders (so-called w-spiral,
H-AFM and I-AFM), whose presence resolve the contradictions in the measured
magnetic and ferroelectric properties of o-$R$MnO$_3$. We show that these
orders emerge due to strong four-spin ring exchange interactions.
|
cond-mat.mtrl-sci
|
we use ab initio electronic structure calculations in combination with monte carlo simulations to investigate the magnetic and ferroelectric properties of bulk orthorhombic homno_3 and ermno_3 our goals are to explain the inconsistencies in the measured magnetic properties of the orthorhombic perovskite manganites ormno_3 with small rareearth r cations or y as well as the contradictions between the directions and amplitudes of the electric polarizations reported by different experimental groups our computations stabilize several exotic magnetic orders socalled wspiral hafm and iafm whose presence resolve the contradictions in the measured magnetic and ferroelectric properties of ormno_3 we show that these orders emerge due to strong fourspin ring exchange interactions
|
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|
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|
1,803.093
|
Monte Carlo Simulations of Novel Biaxial Ordering in Systems of
Uniaxially Interacting Rod-like Ellipsoids
|
The minimal ingredient to generate a biaxial liquid crystalline ordering is
usually considered to be the strongly biaxial interactions breaking the
cylindrical symmetry of the uniaxial molecules. Although there is no
fundamental reason to forbid a biaxial ordering of pure uniaxial origin, it has
been a long standing problem to find a robust demonstration of such phenomenon
in systems of rod-like particles. We report here off-lattice Monte Carlo
simulations of some new model systems of polar achiral rodlike ellipsoids which
spontaneously exhibit novel biaxial smectic phases of pure uniaxial origin. We
show that dipolar interactions can generate different biaxial phases of pure
uniaxial origin in systems of cylindrically symmetric Gay-Berne ellipsoids for
an wide variety of length-to-width ratios. The systems of ellipsoids with low
length-to-width ratios exhibit highly tilted biaxial smectic phases in the
presence of central axial dipoles. In case of ellipsoids having high
length-to-width ratio, the generation of a biaxial phase requires the presence
of two parallel axial terminal dipoles. In addition, the phases also exhibit
fascinating ferroelectric or striped ordering of the dipolar ellipsoids.
|
cond-mat.soft physics.chem-ph
|
the minimal ingredient to generate a biaxial liquid crystalline ordering is usually considered to be the strongly biaxial interactions breaking the cylindrical symmetry of the uniaxial molecules although there is no fundamental reason to forbid a biaxial ordering of pure uniaxial origin it has been a long standing problem to find a robust demonstration of such phenomenon in systems of rodlike particles we report here offlattice monte carlo simulations of some new model systems of polar achiral rodlike ellipsoids which spontaneously exhibit novel biaxial smectic phases of pure uniaxial origin we show that dipolar interactions can generate different biaxial phases of pure uniaxial origin in systems of cylindrically symmetric gayberne ellipsoids for an wide variety of lengthtowidth ratios the systems of ellipsoids with low lengthtowidth ratios exhibit highly tilted biaxial smectic phases in the presence of central axial dipoles in case of ellipsoids having high lengthtowidth ratio the generation of a biaxial phase requires the presence of two parallel axial terminal dipoles in addition the phases also exhibit fascinating ferroelectric or striped ordering of the dipolar ellipsoids
|
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|
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|
1,803.09301
|
Tate-Betti and Tate-Bass numbers
|
We define Tate-Betti and Tate-Bass invariants for modules over a commutative
noetherian local ring R. Then we show the periodicity of these invariants
provided that R is a hypersurface. In case R is also Gorenstein, we show that a
finitely generated R-module M and its Matlis dual have the same Tate-Betti and
Tate-Bass numbers.
|
math.KT math.AC
|
we define tatebetti and tatebass invariants for modules over a commutative noetherian local ring r then we show the periodicity of these invariants provided that r is a hypersurface in case r is also gorenstein we show that a finitely generated rmodule m and its matlis dual have the same tatebetti and tatebass numbers
|
[['we', 'define', 'tatebetti', 'and', 'tatebass', 'invariants', 'for', 'modules', 'over', 'a', 'commutative', 'noetherian', 'local', 'ring', 'r', 'then', 'we', 'show', 'the', 'periodicity', 'of', 'these', 'invariants', 'provided', 'that', 'r', 'is', 'a', 'hypersurface', 'in', 'case', 'r', 'is', 'also', 'gorenstein', 'we', 'show', 'that', 'a', 'finitely', 'generated', 'rmodule', 'm', 'and', 'its', 'matlis', 'dual', 'have', 'the', 'same', 'tatebetti', 'and', 'tatebass', 'numbers']]
|
[-0.26153643341735006, 0.015463143568485976, -0.127359659075737, 0.05516069055069238, -0.015515628978610039, -0.21751111892983319, -0.12371278455480933, 0.3786195207759738, -0.41626423709094523, -0.14101935712620617, 0.11997916377848014, -0.23707630321383477, -0.13646701058372857, 0.1791064801393077, -0.1558106709457934, -0.09473094276268966, 0.038836753945797685, 0.12339144868776203, -0.060247136214748025, -0.36229561891406775, 0.371331719905138, -0.018901514634490014, 0.1618101710313931, 0.06951199749484659, 0.12004030054435134, 0.006970387324690819, -0.03404833568260074, 0.11040717775002122, -0.22182242983166361, 0.0722219979390502, 0.31622623454779386, 0.11340509321540594, 0.1860801088437438, -0.354599049706012, -0.06275650104507804, 0.21708691285923123, 0.1588036141358316, -0.03336630769073963, -0.03112830296624452, -0.2158442997513339, 0.2553707672096789, -0.2510018203034997, -0.10317324992269278, -0.07840447336435317, 0.15687905153259635, 0.03969531545415521, -0.31151588171720507, -0.02170373253233265, 0.08139505811035633, 0.1775932520441711, -0.04208651260240003, -0.026607553977519273, -0.11858408196829259, 0.005089583499357104, -0.06901173803023994, -0.011893659895285964, 0.12102525885216892, -0.049106443226337435, -0.10230819103308023, 0.2982995247095823, -0.08933398261666298, -0.2456714877160266, 0.151217036023736, -0.23193862523883582, -0.10023809513892047, 0.058183341971598565, -0.030417274776846172, 0.20990579284727573, 0.025118215680122374, 0.26012413832941095, -0.20985475331544876, 0.08389599833637476, 0.09294363206252455, 0.0600439646281302, 0.19097797270864247, 0.05120742108672857, 0.06950343095290008, 0.12758029140532018, -0.011281803082674742, 0.09246796092018485, -0.37940328419208524, -0.24385319579392672, -0.17832444520667196, 0.15137763388454914, -0.09865631904365728, -0.09564103672280908, 0.4507320211082697, 0.12271752767264843, 0.15751929208636284, 0.1514087443239987, 0.22886179456021638, -0.025302054174244405, 0.059941024705767634, 0.11935521095991135, 0.09043089005630463, 0.18951016888022423, -0.007881202560383826, -0.09714254398830235, -0.0682645903993398, 0.19276195144280792]
|
1,803.09302
|
On the two-state problem for general differential operators
|
In this note we generalize the Ball-James rigidity theorem for gradient
differential inclusions to the setting of a general linear differential
constraint. In particular, we prove the rigidity for approximate solutions to
the two-state inclusion with incompatible states for merely
$\mathrm{L}^1$-bounded sequences. In this way, our theorem can be seen as a
result of compensated compactness in the linear-growth setting.
|
math.AP
|
in this note we generalize the balljames rigidity theorem for gradient differential inclusions to the setting of a general linear differential constraint in particular we prove the rigidity for approximate solutions to the twostate inclusion with incompatible states for merely mathrml1bounded sequences in this way our theorem can be seen as a result of compensated compactness in the lineargrowth setting
|
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|
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|
1,803.09303
|
Pseudo-Spectrum of the Resistive Magneto-hydrodynamics Operator:
Resolving the Resistive Alfven Paradox
|
The `Alfv\'en Paradox' is that as resistivity decreases, the discrete
eigenmodes do not converge to the generalized eigenmodes of the ideal Alfv\'en
continuum. To resolve the paradox, the $\epsilon$-pseudospectrum of the RMHD
operator is considered. It is proven that for any $\epsilon$, the $\epsilon$-
pseudospectrum contains the Alfv\'en continuum for sufficiently small
resistivity. Formal $\epsilon-pseudoeigenmodes$ are constructed using the
formal Wentzel-Kramers-Brillouin-Jeffreys solutions, and it is shown that the
entire stable half-annulus of complex frequencies with
$\rho{|\omega|^2}=|\bf{v} \cdot \bf{B}(x)|^2$ is resonant to order $\epsilon$,
i.e.~belongs to the $\epsilon-pseudospectrum$. The resistive eigenmodes are
exponentially ill-conditioned as a basis and the condition number is
proportional to $\exp(R_M^{1\over 2})$, where $R_M$ is the magnetic Reynolds
number.
|
physics.plasm-ph cs.NA math-ph math.MP math.NA math.SP physics.flu-dyn
|
the alfven paradox is that as resistivity decreases the discrete eigenmodes do not converge to the generalized eigenmodes of the ideal alfven continuum to resolve the paradox the epsilonpseudospectrum of the rmhd operator is considered it is proven that for any epsilon the epsilon pseudospectrum contains the alfven continuum for sufficiently small resistivity formal epsilonpseudoeigenmodes are constructed using the formal wentzelkramersbrillouinjeffreys solutions and it is shown that the entire stable halfannulus of complex frequencies with rhoomega2bfv cdot bfbx2 is resonant to order epsilon iebelongs to the epsilonpseudospectrum the resistive eigenmodes are exponentially illconditioned as a basis and the condition number is proportional to expr_m1over 2 where r_m is the magnetic reynolds number
|
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|
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|
1,803.09304
|
Spectral triples and wavelets for higher-rank graphs
|
In this paper, we present a new way to associate a finitely summable spectral
triple to a higher-rank graph $\Lambda$, via the infinite path space
$\Lambda^\infty$ of $\Lambda$. Moreover, we prove that this spectral triple has
a close connection to the wavelet decomposition of $\Lambda^\infty$ which was
introduced by Farsi, Gillaspy, Kang, and Packer in 2015. We first introduce the
concept of stationary $k$-Bratteli diagrams, in order to associate a family of
ultrametric Cantor sets, and their associated Pearson-Bellissard spectral
triples, to a finite, strongly connected higher-rank graph $\Lambda$. We then
study the zeta function, abscissa of convergence, and Dixmier trace associated
to the Pearson-Bellissard spectral triples of these Cantor sets, and show these
spectral triples are $\zeta$-regular in the sense of Pearson and Bellissard. We
obtain an integral formula for the Dixmier trace given by integration against a
measure $\mu$, and show that $\mu$ is a rescaled version of the measure $M$ on
$\Lambda^\infty$ which was introduced by an Huef, Laca, Raeburn, and Sims.
Finally, we investigate the eigenspaces of a family of Laplace-Beltrami
operators associated to the Dirichlet forms of the spectral triples. We show
that these eigenspaces refine the wavelet decomposition of $L^2(\Lambda^\infty,
M)$ which was constructed by Farsi et al.
|
math.OA math-ph math.FA math.MP
|
in this paper we present a new way to associate a finitely summable spectral triple to a higherrank graph lambda via the infinite path space lambdainfty of lambda moreover we prove that this spectral triple has a close connection to the wavelet decomposition of lambdainfty which was introduced by farsi gillaspy kang and packer in 2015 we first introduce the concept of stationary kbratteli diagrams in order to associate a family of ultrametric cantor sets and their associated pearsonbellissard spectral triples to a finite strongly connected higherrank graph lambda we then study the zeta function abscissa of convergence and dixmier trace associated to the pearsonbellissard spectral triples of these cantor sets and show these spectral triples are zetaregular in the sense of pearson and bellissard we obtain an integral formula for the dixmier trace given by integration against a measure mu and show that mu is a rescaled version of the measure m on lambdainfty which was introduced by an huef laca raeburn and sims finally we investigate the eigenspaces of a family of laplacebeltrami operators associated to the dirichlet forms of the spectral triples we show that these eigenspaces refine the wavelet decomposition of l2lambdainfty m which was constructed by farsi et al
|
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|
[-0.13120683517508905, 0.0680927549607265, -0.11337677258401742, 0.06923622744596045, -0.07928898669159948, -0.0671007629332541, 0.02528652649893531, 0.37141650243492547, -0.2965605730108293, -0.2301256859759924, 0.08983590654349827, -0.2829111120686522, -0.17175878093490754, 0.14194832701726903, -0.1239340187433483, 0.04221347151232397, 0.07915077957076942, 0.06816560977363381, -0.07069156432565614, -0.20773350917235284, 0.4164865667555536, 0.025349596932787318, 0.18004080242812268, 0.0370695752199519, 0.10052872433790506, 0.013489823619802964, -0.08207895954453795, -0.001554034005883815, -0.20784042455800641, 0.15838925457379455, 0.22299433289453607, 0.1175559534762385, 0.2507865719102653, -0.2700914032378789, -0.1474308492076753, 0.1634876195621204, 0.11009000321125309, -0.05197335887078673, 0.016856041350379, -0.30811524765538467, 0.13991326578947821, -0.1914612748728964, -0.12893510177350728, -0.09962600055139219, 0.0736131491323043, 0.032632545179806724, -0.28216360254084755, 0.018688551737500236, 0.11819819425659374, 0.048445057622822266, -0.06274024291156695, -0.09987143250159332, -0.04626915562127171, 0.0534970781793405, -0.042809813610264306, 0.01780402529502994, 0.016051533865958013, 0.00830619475859323, -0.1537399920824172, 0.30699322022798153, -0.10334570223914019, -0.18739850924400786, 0.1365557994390723, -0.1586641822276371, -0.17694819022630676, 0.09233290492901074, 0.07498305284973289, 0.13634166837179015, -0.11684346523392818, 0.1723618138196713, -0.09597479001896483, 0.11138950902142841, 0.14576616031553577, 0.006807303724218655, 0.12170815392469171, 0.05212734256334273, 0.0834441976329275, 0.1802521360180171, -0.03722414950894082, -0.012525127619433817, -0.28046809352622964, -0.20046983562006152, -0.20739238282890413, 0.09175638186520543, -0.09990237225852093, -0.23418074388549034, 0.3876570354117163, 0.10101101725256723, 0.22332981247452013, 0.07917325152485663, 0.1633798600119433, 0.13629089191262359, 0.03363424975865433, 0.06430345854900887, 0.10545966242040906, 0.20421166018940728, 0.04952578103913022, -0.1882357294674105, -0.038593967237596956, 0.20281357863651855]
|
1,803.09305
|
Arbitrary-order time-accurate semi-Lagrangian spectral approximations of
the Vlasov-Poisson system
|
The Vlasov-Poisson system, modeling the evolution of non-collisional plasmas
in the electrostatic limit, is approx- imated by a Semi-Lagrangian technique.
Spectral methods of periodic type are implemented through a collocation
approach. Groups of particles are represented by the Fourier Lagrangian basis
and evolve, for a single timestep, along an high-order accurate representation
of the local characteristic lines. The time-advancing technique is based on
Taylor developments that can be, in principle, of any order of accuracy, or by
coupling the phase space discretiza- tion with high-order accurate Backward
Differentiation Formulas (BDF) as in the method-of-lines framework. At each
timestep, particle displacements are reinterpolated and expressed in the
original basis to guarantee the order of accuracy in all the variables at
relatively low costs. Thus, these techniques combine excellent features of
spectral approximations with high-order time integration. Series of numerical
experiments are performed in order to assess the real performance. In
particular, comparisons with standard benchmarks are examined.
|
math.NA
|
the vlasovpoisson system modeling the evolution of noncollisional plasmas in the electrostatic limit is approx imated by a semilagrangian technique spectral methods of periodic type are implemented through a collocation approach groups of particles are represented by the fourier lagrangian basis and evolve for a single timestep along an highorder accurate representation of the local characteristic lines the timeadvancing technique is based on taylor developments that can be in principle of any order of accuracy or by coupling the phase space discretiza tion with highorder accurate backward differentiation formulas bdf as in the methodoflines framework at each timestep particle displacements are reinterpolated and expressed in the original basis to guarantee the order of accuracy in all the variables at relatively low costs thus these techniques combine excellent features of spectral approximations with highorder time integration series of numerical experiments are performed in order to assess the real performance in particular comparisons with standard benchmarks are examined
|
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|
[-0.10942970796372571, 0.058300969852199264, -0.09862389979470107, 0.041630076446868725, -0.02909226740369561, -0.08949232158354586, 0.0026116856462109128, 0.39252541189879375, -0.24541837341620837, -0.3007456103790235, 0.11077271806444437, -0.24089791323819193, -0.07694012586337824, 0.2077337380542779, -0.017531477428765, 0.09842971384866175, 0.10405804317298473, 0.0022867931877841165, -0.09867650360645866, -0.2264223209083129, 0.27383756332762926, 0.05663459187105688, 0.24798535117331674, -0.006702887961485733, 0.11740338312936764, -0.04431563494513968, -0.05825410325694951, 0.024378013084345843, -0.07429161359232833, 0.1255308025032647, 0.2501157120119756, 0.05492549232858556, 0.30401403878151984, -0.4501652670598108, -0.21688154150482292, 0.04617147392393973, 0.15999347245125892, 0.08406555336090474, -0.021712872850270393, -0.2650444405518618, 0.0718896169477185, -0.14588776510665377, -0.13502340075663394, -0.15072295156130994, -0.028340364174439504, 0.11337903985948442, -0.315479161400421, 0.09979840511383087, 0.01951228983675927, 0.08122644584406824, -0.034251879949390496, -0.095826417687836, -0.0071747731265240635, 0.10484306820595235, 0.0024210122547848943, 0.006181515728920893, 0.07505641497665518, -0.0814120308983024, -0.1258489412356022, 0.4117799243506263, -0.10845773520170303, -0.25320106036382806, 0.19393204683072718, -0.1315720864842506, -0.11791197778170112, 0.19414566591615237, 0.1817537342362544, 0.15225002525702996, -0.11765396001587433, 0.08645685643564112, 0.036221894131991644, 0.16127193965827377, 0.07847789107834056, 0.01638245171246429, 0.15626159648021404, 0.16945757071321732, 0.02752773053457145, 0.0510150990871183, -0.08091304594425643, -0.11210925345540387, -0.30096177737307706, -0.1564328289114082, -0.1812678164767491, -0.062368056157092545, -0.1309593522651471, -0.15521279715604203, 0.37941046384485816, 0.150018128131218, 0.14802577732826333, 0.059218173676164325, 0.31744173111308827, 0.1793367949252023, 0.050523910321085254, 0.046825226238058286, 0.20238388927114725, 0.12527075540761348, 0.08775692432510113, -0.22976355990501474, 0.04548862823772128, 0.1584984885005195]
|
1,803.09306
|
Simultaneous Diophantine approximation: sums of squares and homogeneous
polynomials
|
Let $f$ be a homogeneous polynomial with rational coefficients in $d$
variables. We prove several results concerning uniform simultaneous
approximation to points on the graph of $f$, as well as on the hypersurface
$\{f(x_1,\dots,x_d) = 1\}$. The results are first stated for the case
$f(x_1,\dots,x_d) = x_1^2+\dots+x_d^2,$ which is of particular interest.
|
math.NT math.DS
|
let f be a homogeneous polynomial with rational coefficients in d variables we prove several results concerning uniform simultaneous approximation to points on the graph of f as well as on the hypersurface fx_1dotsx_d 1 the results are first stated for the case fx_1dotsx_d x_12dotsx_d2 which is of particular interest
|
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|
[-0.1661839113969888, 0.04087264413888357, -0.052240196672477285, -0.004461965055623073, -0.0454892851792428, -0.11374178573451176, 0.0036241550530706134, 0.32287165777263593, -0.27121702589246693, -0.23451921179871626, 0.12728863060997075, -0.25565003242571743, -0.13614662405939734, 0.23795924502976087, -0.08549640086308426, 0.05231533072204614, 0.03814914244778302, 0.10469999111124448, -0.04966212435606487, -0.32460635131978127, 0.32905563183737047, -0.044338131456502845, 0.1603204325905868, 0.0769392818697177, 0.08424873087479144, 0.02737897696277621, -0.007123712735364632, 0.03541245109553696, -0.17509341344465407, 0.07724310197316263, 0.28210453278556163, 0.09171043546889357, 0.26009225328357855, -0.37059486630771843, -0.1947840093349924, 0.1755779321894658, 0.1274516618316423, 0.0006404105093976369, 0.021964052036328584, -0.24683522979006628, 0.12294923631968546, -0.08038431398418484, -0.1636167346328801, -0.0795465982614123, 0.04765752641180036, 0.10328959677444428, -0.3548267985294972, 0.038418367543086716, 0.11868103373289697, 0.09184026070015162, -0.05748524518721566, -0.17320120184473237, -0.002283284036746743, 0.06759419877139129, 0.02650844200742336, 0.10158148039208383, 0.03029436764440366, -0.07725822792521544, -0.11462935830029297, 0.38091022787349565, -0.09743362292647362, -0.24358673074415751, 0.13677356466270832, -0.17751826081729058, -0.15825140321323153, 0.04575017543167484, 0.16031025606682714, 0.16996574485484434, -0.04938562237182442, 0.16553704589795398, -0.13066803846432237, 0.09483177423458167, 0.10459886591083237, -0.009932192612667473, 0.10369048679095445, 0.056723163477430234, 0.10673697501877133, 0.1398426101481238, 0.0007099054221596036, -0.05675337104392903, -0.36811940371990204, -0.13444553790804076, -0.2248382691331968, 0.09880891907960176, -0.14164200984891884, -0.17357932584246202, 0.38107888556408637, 0.03590000017869229, 0.23513661203335742, 0.08992369862853036, 0.22267458823566533, 0.12720599785276063, -0.037947731605749956, 0.06672537464610472, 0.138233669463317, 0.17743587626942567, 0.015152972020512941, -0.09214797658769756, 0.07492020440630007, 0.13094856209900915]
|
1,803.09307
|
Multiplication of Weak Equivalence Classes May Be Discontinuous
|
For a countably infinite group $\Gamma$, let $\mathcal{W}_\Gamma$ denote the
space of all weak equivalence classes of measure-preserving actions of $\Gamma$
on atomless standard probability spaces, equipped with the compact metrizable
topology introduced by Ab\'{e}rt and Elek. There is a natural multiplication
operation on $\mathcal{W}_\Gamma$ (induced by taking products of actions) that
makes $\mathcal{W}_\Gamma$ an Abelian semigroup. Burton, Kechris, and Tamuz
showed that if $\Gamma$ is amenable, then $\mathcal{W}_\Gamma$ is a topological
semigroup, i.e., the product map $\mathcal{W}_\Gamma \times \mathcal{W}_\Gamma
\to \mathcal{W}_\Gamma \colon (\mathfrak{a}, \mathfrak{b}) \mapsto \mathfrak{a}
\times \mathfrak{b}$ is continuous. In contrast to that, we prove that if
$\Gamma$ is a Zariski dense subgroup of $\mathrm{SL}_d(\mathbb{Z})$ for some $d
\geqslant 2$ (for instance, if $\Gamma$ is a non-Abelian free group), then
multiplication on $\mathcal{W}_\Gamma$ is discontinuous, even when restricted
to the subspace $\mathcal{FW}_\Gamma$ of all free weak equivalence classes.
|
math.DS
|
for a countably infinite group gamma let mathcalw_gamma denote the space of all weak equivalence classes of measurepreserving actions of gamma on atomless standard probability spaces equipped with the compact metrizable topology introduced by abert and elek there is a natural multiplication operation on mathcalw_gamma induced by taking products of actions that makes mathcalw_gamma an abelian semigroup burton kechris and tamuz showed that if gamma is amenable then mathcalw_gamma is a topological semigroup ie the product map mathcalw_gamma times mathcalw_gamma to mathcalw_gamma colon mathfraka mathfrakb mapsto mathfraka times mathfrakb is continuous in contrast to that we prove that if gamma is a zariski dense subgroup of mathrmsl_dmathbbz for some d geqslant 2 for instance if gamma is a nonabelian free group then multiplication on mathcalw_gamma is discontinuous even when restricted to the subspace mathcalfw_gamma of all free weak equivalence classes
|
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|
[-0.1649188858761767, 0.20995142340767717, -0.04882346370036332, 0.05250165759160338, -0.09853157957868396, -0.15882453366547902, 0.025551140235934622, 0.412756882902744, -0.3544967560124376, -0.09958273925476795, 0.11613264572622402, -0.29068929258471843, -0.0899015517181737, 0.225191045505591, -0.15106162334299855, -0.04746182946314057, 0.06175686013524709, 0.1375510258157905, -0.0928573348465637, -0.21745558025436007, 0.38313000180872436, -0.07832074488962082, 0.18474107591783723, 0.01672308910102081, 0.13332716313947876, 0.025184445753157567, -0.005554825556631998, -0.0041214553607885705, -0.1520985310117081, 0.053516054814078395, 0.26923182101839843, 0.11816539428458153, 0.23475467179828197, -0.3161404257600042, -0.1490046944362011, 0.2919161327412727, 0.06474671499441853, -0.17147509469617184, -0.014234503879372647, -0.3318200061673955, 0.1797814734561516, -0.19447703445129258, -0.07385790854585257, -0.09057783797423509, 0.16686558427972545, -0.042258125250797265, -0.3336601175649239, -0.019582878969100524, 0.13692814912379003, 0.062118513925041224, -0.027252301562028073, -0.032413434846956524, -0.07066020264337175, 0.06260634550306336, -0.025850848286419356, 0.13909529056065054, 0.096754516283948, -0.033637258763552356, -0.10668591656655127, 0.40141255275862253, -0.06820756525953682, -0.2136880057116823, 0.14637236720580848, -0.20179679268877282, -0.18868320861415896, 0.15794686514803832, 0.0207354165479648, 0.13343778489117356, -0.017892393054588857, 0.3015678195582649, -0.15848251949432943, 0.10438473460016598, 0.07038238044265363, -0.03870011474803197, 0.04185155241309645, 0.09484281447689256, 0.150598415207091, 0.09798851506424425, 0.07013795675421737, 0.058690486601872115, -0.33839058833826574, -0.18953252501330145, -0.14050307775657772, 0.20812863921378102, -0.08695097356551434, -0.183093099379175, 0.31388747067988026, 0.017593921755152425, 0.12106844654228043, 0.1246496611526035, 0.19144239785357398, 0.05311277435871391, -0.0013327637801228238, 0.11266270678627753, 0.02615015361924562, 0.20930252438277114, -0.13335207029641102, -0.14614016023169693, 0.00026384790649088165, 0.23592509706538145]
|
1,803.09308
|
Phase shift of cyclotron orbits at type-I and type-II multi-Weyl nodes
|
Quantum oscillations of response functions in high magnetic fields tend to
reveal some of the most interesting properties of metals. In particular, the
oscillation phase shift is sensitive to topological band features, thereby
helping to identify the presence of Weyl fermions. In this work we predict
characteristic parameter dependence of the phase shift for Weyl fermions with
tilted and overtilted dispersion (type I and type II Weyl fermions) and an
arbitrary topological charge (multi-Weyl fermions). For type-II Weyl fermions
our calculations capture the case of magnetic breakthrough between the electron
and the hole part of the dispersion. Here the phase shift turns out to depend
only on the quantized topological charge due to cancellation of non-universal
contributions from the electron and the hole part.
|
cond-mat.mes-hall
|
quantum oscillations of response functions in high magnetic fields tend to reveal some of the most interesting properties of metals in particular the oscillation phase shift is sensitive to topological band features thereby helping to identify the presence of weyl fermions in this work we predict characteristic parameter dependence of the phase shift for weyl fermions with tilted and overtilted dispersion type i and type ii weyl fermions and an arbitrary topological charge multiweyl fermions for typeii weyl fermions our calculations capture the case of magnetic breakthrough between the electron and the hole part of the dispersion here the phase shift turns out to depend only on the quantized topological charge due to cancellation of nonuniversal contributions from the electron and the hole part
|
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|
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|
1,803.09309
|
Connectivity-Preserving Consensus of Multi-Agent Systems with Bounded
Actuation
|
This paper investigates the impact of bounded actuation on the
connectivity-preserving consensus of two classes of multi-agent systems, with
kinematic agents and with Euler- Lagrange agents. The investigation establishes
that: (1) there exists a class of gradient-based controls which drive kinematic
multi-agent systems to connectivity-preserving consensus even if they saturate;
(2) actuator saturation restricts the initial states from which Euler-Lagrange
multi-agent systems can be synchronized while preserving their local
connectivity; (3) Euler-Lagrange multi-agent systems with unbounded actuation
can achieve connectivity-preserving consensus without velocity measurements or
exact system dynamics; and (4) a proposed indirect coupling control strategy
drives Euler-Lagrange multi-agent systems with limited actuation and starting
from rest to connectivitypreserving consensus without requiring velocity
measurements and including in the presence of uncertain dynamics and
timevarying delays.
|
math.OC
|
this paper investigates the impact of bounded actuation on the connectivitypreserving consensus of two classes of multiagent systems with kinematic agents and with euler lagrange agents the investigation establishes that 1 there exists a class of gradientbased controls which drive kinematic multiagent systems to connectivitypreserving consensus even if they saturate 2 actuator saturation restricts the initial states from which eulerlagrange multiagent systems can be synchronized while preserving their local connectivity 3 eulerlagrange multiagent systems with unbounded actuation can achieve connectivitypreserving consensus without velocity measurements or exact system dynamics and 4 a proposed indirect coupling control strategy drives eulerlagrange multiagent systems with limited actuation and starting from rest to connectivitypreserving consensus without requiring velocity measurements and including in the presence of uncertain dynamics and timevarying delays
|
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|
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|
1,803.0931
|
Optimal shapes for general integral functionals
|
We consider shape optimization problems for general integral functionals of
the calculus of variations, defined on a domain $\Omega$ that varies over all
subdomains of a given bounded domain $D$ of ${\bf R}^d$. We show in a rather
elementary way the existence of a solution that is in general a quasi open set.
Under very mild conditions we show that the optimal domain is actually open and
with finite perimeter. Some counterexamples show that in general this does not
occur.
|
math.OC
|
we consider shape optimization problems for general integral functionals of the calculus of variations defined on a domain omega that varies over all subdomains of a given bounded domain d of bf rd we show in a rather elementary way the existence of a solution that is in general a quasi open set under very mild conditions we show that the optimal domain is actually open and with finite perimeter some counterexamples show that in general this does not occur
|
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|
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|
1,803.09311
|
On infinitely generated homology of Torelli groups
|
Let $\mathcal{I}_g$ be the Torelli group of an oriented closed surface $S_g$
of genus $g$, that is, the kernel of the action of the mapping class group on
the first integral homology group of $S_g$. We prove that the $k$th integral
homology group of $\mathcal{I}_g$ contains a free abelian subgroup of infinite
rank, provided that $g\ge 3$ and $2g-3\le k\le 3g-6$. Earlier the same property
was known only for $k=3g-5$ (Bestvina, Bux, Margalit, 2007) and in the special
case $g=k=3$ (Johnson, Millson, 1992). We also show that the hyperelliptic
involution acts on the constructed infinite system of linearly independent
homology classes in $\mathrm{H}_k(\mathcal{I}_g;\mathbb{Z})$ as multiplication
by $-1$, provided that $k+g$ is even, thus solving negatively a problem by
Hain. For $k=2g-3$, we show that the group
$\mathrm{H}_{2g-3}(\mathcal{I}_g;\mathbb{Z})$ contains a free abelian subgroup
of infinite rank generated by abelian cycles and we construct explicitly an
infinite system of abelian cycles generating such subgroup. As a consequence of
our results, we obtain that an Eilenberg--MacLane CW complex of type
$K(\mathcal{I}_g,1)$ cannot have a finite $(2g-3)$-skeleton. The proofs are
based on the study of the spectral sequence for the action of $\mathcal{I}_g$
on the complex of cycles constructed by Bestvina, Bux, and Margalit.
|
math.GR math.GT
|
let mathcali_g be the torelli group of an oriented closed surface s_g of genus g that is the kernel of the action of the mapping class group on the first integral homology group of s_g we prove that the kth integral homology group of mathcali_g contains a free abelian subgroup of infinite rank provided that gge 3 and 2g3le kle 3g6 earlier the same property was known only for k3g5 bestvina bux margalit 2007 and in the special case gk3 johnson millson 1992 we also show that the hyperelliptic involution acts on the constructed infinite system of linearly independent homology classes in mathrmh_kmathcali_gmathbbz as multiplication by 1 provided that kg is even thus solving negatively a problem by hain for k2g3 we show that the group mathrmh_2g3mathcali_gmathbbz contains a free abelian subgroup of infinite rank generated by abelian cycles and we construct explicitly an infinite system of abelian cycles generating such subgroup as a consequence of our results we obtain that an eilenbergmaclane cw complex of type kmathcali_g1 cannot have a finite 2g3skeleton the proofs are based on the study of the spectral sequence for the action of mathcali_g on the complex of cycles constructed by bestvina bux and margalit
|
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|
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|
1,803.09312
|
Shot noise limited nanomechanical detection and radiation pressure
backaction from an electron beam
|
Detecting nanomechanical motion has become an important challenge in Science
and Technology. Recently, electromechanical coupling to focused electron beams
has emerged as a promising method adapted to ultra-low scale systems. However
the fundamental measurement processes associated with such complex interaction
remain to be explored. Here we report highly sensitive detection of the
Brownian motion of um-long semiconducting nanowires (InAs). The measurement
imprecision is found to be set by the shot noise of the secondary electrons
generated along the electromechanical interaction. By carefully analysing the
nano-electromechanical dynamics, we demonstrate the existence of a radial
backaction process which we identify as originating from the momentum exchange
between the electron beam and the nanomechanical device, which is also known as
radiation pressure.
|
cond-mat.mes-hall
|
detecting nanomechanical motion has become an important challenge in science and technology recently electromechanical coupling to focused electron beams has emerged as a promising method adapted to ultralow scale systems however the fundamental measurement processes associated with such complex interaction remain to be explored here we report highly sensitive detection of the brownian motion of umlong semiconducting nanowires inas the measurement imprecision is found to be set by the shot noise of the secondary electrons generated along the electromechanical interaction by carefully analysing the nanoelectromechanical dynamics we demonstrate the existence of a radial backaction process which we identify as originating from the momentum exchange between the electron beam and the nanomechanical device which is also known as radiation pressure
|
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|
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|
1,803.09313
|
The visualization of the space probability distribution for a particle
moving in a double ring-shaped Coulomb potential
|
The analytical solutions to a double ring-shaped Coulomb potential (RSCP) are
presented. The visualizations of the space probability distribution (SPD) are
illustrated for the two-(contour) and three-dimensional (isosurface) cases. The
quantum numbers (n, l, m) are mainly relevant for those quasi quantum numbers
(n' ,l' ,m' ) via the double RSCP parameter c. The SPDs are of circular ring
shape in spherical coordinates. The properties for the relative probability
values (RPVs) P are also discussed. For example, when we consider the special
case (n, l, m)=(6, 5, 0), the SPD moves towards two poles of axis z when the P
increases. Finally, we discuss the different cases for the potential parameter
b which is taken as negative and positive values for c>0 . Compared with the
particular case b=0 , the SPDs are shrunk for b=-0.5 while spread out for
b=0.5.
|
quant-ph
|
the analytical solutions to a double ringshaped coulomb potential rscp are presented the visualizations of the space probability distribution spd are illustrated for the twocontour and threedimensional isosurface cases the quantum numbers n l m are mainly relevant for those quasi quantum numbers n l m via the double rscp parameter c the spds are of circular ring shape in spherical coordinates the properties for the relative probability values rpvs p are also discussed for example when we consider the special case n l m6 5 0 the spd moves towards two poles of axis z when the p increases finally we discuss the different cases for the potential parameter b which is taken as negative and positive values for c0 compared with the particular case b0 the spds are shrunk for b05 while spread out for b05
|
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|
[-0.1586424617083086, 0.1302324364797267, 0.008056815532173085, 0.07470314079118372, -0.004828254120451782, -0.20805802793919986, 0.01916863746694563, 0.365057464579449, -0.22732464903417757, -0.2625602731234668, 0.06898307829798046, -0.3078435541503816, -0.09079441201345831, 0.200387094878619, 0.030211297153220372, 0.04507730297786218, 0.028141386786420995, 0.0678130314901115, -0.08560502516561161, -0.2323396555644542, 0.31094016448033096, 0.014840676077737418, 0.2138994361671126, -0.017841597604702282, 0.004137988982941298, 0.01690826179144685, -0.007333290475585005, 0.017746340921669743, -0.17528540782586788, 0.04430446057128446, 0.22369231242576942, 0.04772774486542296, 0.22822024417109787, -0.3365849460036877, -0.154098853117937, 0.10421252724892624, 0.1561135263832779, 0.04303378631747739, -0.03665850284810671, -0.25371656756204386, 0.10481581860050723, -0.12025377841885476, -0.19760332425015376, -0.038696782598408926, 0.13682972699205173, 0.06405745879430255, -0.2940116710960865, 0.04624315594157773, 0.04916433568022887, 0.03452424999148421, -0.02987005351785817, -0.22766284690313862, -0.052230195457334906, 0.09071460570532294, 0.016970556151457403, 0.01893007469291607, 0.10259467258241356, -0.09720458973007386, -0.05487442625385216, 0.3602711385225548, -0.024630909890487707, -0.2413407360230956, 0.1277482410916812, -0.1857518860933316, -0.09122401360967641, 0.13024543718903955, 0.10575409628355, 0.15003789354095182, -0.0329790928048811, 0.16079525008492912, -0.018133725255371675, 0.08302617370945346, 0.09723744418828145, -0.005230796893182046, 0.18787909884635798, 0.07285961283709827, 0.04164556747234789, 0.13089088295065962, -0.16138591706026895, -0.1085296930584317, -0.3518589067765895, -0.1740416189902188, -0.15708805466591216, 0.042720304829451966, -0.12637461702701436, -0.10991930151495206, 0.33100709636111036, 0.0304720361943028, 0.24713016360799564, 0.0462008630454554, 0.24392171531422613, 0.10543305677043356, 0.0027862105254077025, 0.0467460965121384, 0.19983284591067144, 0.1610898687161834, 0.07458372467012583, -0.20705159595030742, -0.0006297636085518581, 0.05002437961143989]
|
1,803.09314
|
A New Reconfigurable Antenna MIMO Architecture for mmWave Communication
|
The large spectrum available in the millimeter-Wave (mmWave) band has emerged
as a promising solution for meeting the huge capacity requirements of the 5th
generation (5G) wireless networks. However, to fully harness the potential of
mmWave communications, obstacles such as severe path loss, channel sparsity and
hardware complexity should be overcome. In this paper, we introduce a
generalized reconfigurable antenna multiple-input multiple-output (MIMO)
architecture that takes advantage of lens-based reconfigurable antennas. The
considered antennas can support multiple radiation patterns simultaneously by
using a single RF chain. The degrees of freedom provided by the reconfigurable
antennas are used to, first, combat channel sparsity in MIMO mmWave systems.
Further, to suppress high path loss and shadowing at mmWave frequencies, we use
a rate-one space-time block code. Our analysis and simulations show that the
proposed reconfigurable MIMO architecture achieves full-diversity gain by using
linear receivers and without requiring channel state information at the
transmitter. Moreover, simulations show that the proposed architecture
outperforms traditional MIMO transmission schemes in mmWave channel settings.
|
cs.IT math.IT
|
the large spectrum available in the millimeterwave mmwave band has emerged as a promising solution for meeting the huge capacity requirements of the 5th generation 5g wireless networks however to fully harness the potential of mmwave communications obstacles such as severe path loss channel sparsity and hardware complexity should be overcome in this paper we introduce a generalized reconfigurable antenna multipleinput multipleoutput mimo architecture that takes advantage of lensbased reconfigurable antennas the considered antennas can support multiple radiation patterns simultaneously by using a single rf chain the degrees of freedom provided by the reconfigurable antennas are used to first combat channel sparsity in mimo mmwave systems further to suppress high path loss and shadowing at mmwave frequencies we use a rateone spacetime block code our analysis and simulations show that the proposed reconfigurable mimo architecture achieves fulldiversity gain by using linear receivers and without requiring channel state information at the transmitter moreover simulations show that the proposed architecture outperforms traditional mimo transmission schemes in mmwave channel settings
|
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|
[-0.3078821607235217, 0.03177761062310484, 0.04153259041228382, -0.03797248398437594, -0.10701684339367924, -0.2621558943016086, 0.04216634465902932, 0.4264419684744256, -0.2451360321765442, -0.23837040793596806, 0.09007740727330218, -0.21715572638950215, -0.24795078518410063, 0.13400372398827604, -0.09539096939383064, 0.11375238758952406, 0.09483906205654323, -0.06227196434240082, -0.018406860200649206, -0.20540055169160673, 0.2662559513108593, 0.16501846511549914, 0.40598730641433933, 0.022845162017393613, 0.1295423458029187, 0.007631781764752315, 0.01639258400969274, -0.09631596928919682, -0.053445945620008053, 0.0814490063355756, 0.3963964715750587, 0.21452563038251982, 0.27549423458623495, -0.43662305842683524, -0.36145932177739765, 0.04409615542951548, 0.21792793997025262, 0.06422144283183633, -0.06504872178625383, -0.2921283145009576, 0.15527110991017992, -0.2869640449382655, -0.06703031687261146, 0.014306218773238137, -0.14846419961774487, 0.030844275245002422, -0.35417645261762387, -0.037278980072476195, -0.01618754567472476, 0.023770504547450357, 0.00499097005224335, -0.15084874523039574, 0.04226768298303251, 0.12538394811953568, -0.0390337592821769, -0.018302036436068307, 0.05348506415071814, -0.10673330385589269, -0.1278992698745367, 0.3685309729876253, -0.00039390323845346176, -0.2741008670610225, 0.16451235898090025, -0.09891714476338939, -0.09086735951184423, 0.18408208808542403, 0.3142994405690603, 0.009564896069556296, -0.1985989429424712, 0.034787862175450976, 0.03778732226447699, 0.2098075413217623, 0.11127502504390424, 0.21009454217287685, 0.17572358638038763, 0.22987277772344514, 0.1260791022740416, 0.14936410019823912, -0.17888024299890695, -0.08316289415460325, -0.17961617705341104, -0.11631626796819448, -0.279106098762574, 0.0027069858307420406, -0.11882696796764904, -0.038197017051725686, 0.32790928916144046, 0.1754655952606904, 0.03801931329991691, 0.1378544707249984, 0.4434986059180277, 0.07269153035033918, 0.16734443040018132, 0.14000216867596268, 0.2105458178696875, 0.11819091872563084, 0.16706024664405364, -0.2027116263895937, -0.00833679768284727, -0.09958810415565075]
|
1,803.09315
|
Analytical modeling of demagnetizing effect in magnetoelectric
ferrite/PZT/ferrite trilayers taking into account a mechanical coupling
|
In this paper, we investigate the demagnetizing effect in ferrite/PZT/ferrite
magnetoelectric (ME) trilayer composites consisting of commercial PZT discs
bonded by epoxy layers to Ni-Co-Zn ferrite discs made by a reactive Spark
Plasma Sintering (SPS) technique. ME voltage coefficients (transversal mode)
were measured on ferrite/PZT/ferrite trilayer ME samples with different
thicknesses or phase volume ratio in order to highlight the influence of the
magnetic field penetration governed by these geometrical parameters.
Experimental ME coefficients and voltages were compared to analytical
calculations using a quasi-static model. Theoretical demagnetizing factors of
two magnetic discs that interact together in parallel magnetic structures were
derived from an analytical calculation based on a superposition method. These
factors were introduced in ME voltage calculations which take account of the
demagnetizing effect. To fit the experimental results, a mechanical coupling
factor was also introduced in the theoretical formula. This reflects the
differential strain that exists in the ferrite and PZT layers due to shear
effects near the edge of the ME samples and within the bonding epoxy layers.
From this study, an optimization in magnitude of the ME voltage is obtained.
Lastly, an analytical calculation of demagnetizing effect was conducted for
layered ME composites containing higher numbers of alternated layers (). The
advantage of such a structure is then discussed.
|
cond-mat.mtrl-sci
|
in this paper we investigate the demagnetizing effect in ferritepztferrite magnetoelectric me trilayer composites consisting of commercial pzt discs bonded by epoxy layers to nicozn ferrite discs made by a reactive spark plasma sintering sps technique me voltage coefficients transversal mode were measured on ferritepztferrite trilayer me samples with different thicknesses or phase volume ratio in order to highlight the influence of the magnetic field penetration governed by these geometrical parameters experimental me coefficients and voltages were compared to analytical calculations using a quasistatic model theoretical demagnetizing factors of two magnetic discs that interact together in parallel magnetic structures were derived from an analytical calculation based on a superposition method these factors were introduced in me voltage calculations which take account of the demagnetizing effect to fit the experimental results a mechanical coupling factor was also introduced in the theoretical formula this reflects the differential strain that exists in the ferrite and pzt layers due to shear effects near the edge of the me samples and within the bonding epoxy layers from this study an optimization in magnitude of the me voltage is obtained lastly an analytical calculation of demagnetizing effect was conducted for layered me composites containing higher numbers of alternated layers the advantage of such a structure is then discussed
|
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|
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|
1,803.09316
|
$\mathbb{Z}_{q}(\mathbb{Z}_{q}+u\mathbb{Z}_{q})$-Linear Skew
Constacyclic Codes
|
In this paper, we study skew constacyclic codes over the ring
$\mathbb{Z}_{q}R$ where $R=\mathbb{Z}_{q}+u\mathbb{Z}_{q}$, $q=p^{s}$ for a
prime $p$ and $u^{2}=0$. We give the definition of these codes as subsets of
the ring $\mathbb{Z}_{q}^{\alpha}R^{\beta}$. Some structural properties of the
skew polynomial ring $ R[x,\theta]$ are discussed, where $ \theta$ is an
automorphism of $R$. We describe the generator polynomials of skew constacyclic
codes over $ R $ and $\mathbb{Z}_{q}R$. Using Gray images of skew constacyclic
codes over $\mathbb{Z}_{q}R$ we obtained some new linear codes over
$\mathbb{Z}_4$. Further, we have generalized these codes to double skew
constacyclic codes over $\mathbb{Z}_{q}R$.
|
cs.IT math.IT
|
in this paper we study skew constacyclic codes over the ring mathbbz_qr where rmathbbz_qumathbbz_q qps for a prime p and u20 we give the definition of these codes as subsets of the ring mathbbz_qalpharbeta some structural properties of the skew polynomial ring rxtheta are discussed where theta is an automorphism of r we describe the generator polynomials of skew constacyclic codes over r and mathbbz_qr using gray images of skew constacyclic codes over mathbbz_qr we obtained some new linear codes over mathbbz_4 further we have generalized these codes to double skew constacyclic codes over mathbbz_qr
|
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|
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|
1,803.09317
|
Diversity and Interdisciplinarity: How Can One Distinguish and Recombine
Disparity, Variety, and Balance?
|
The dilemma which remained unsolved using Rao-Stirling diversity, namely of
how variety and balance can be combined into "dual concept diversity"
(Stirling, 1998, pp. 48f.) can be clarified by using Nijssen et al.'s (1998)
argument that the Gini coefficient is a perfect indicator of balance. However,
the Gini coefficient is not an indicator of variety; this latter term can be
operationalized independently as relative variety. The three components of
diversity--variety, balance, and disparity--can thus be clearly distinguished
and independently operationalized as measures varying between zero and one. The
new diversity indicator ranges with more resolving power in the empirical case.
|
cs.DL
|
the dilemma which remained unsolved using raostirling diversity namely of how variety and balance can be combined into dual concept diversity stirling 1998 pp 48f can be clarified by using nijssen et als 1998 argument that the gini coefficient is a perfect indicator of balance however the gini coefficient is not an indicator of variety this latter term can be operationalized independently as relative variety the three components of diversityvariety balance and disparitycan thus be clearly distinguished and independently operationalized as measures varying between zero and one the new diversity indicator ranges with more resolving power in the empirical case
|
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|
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|
1,803.09318
|
Data-driven Discovery of Closure Models
|
Derivation of reduced order representations of dynamical systems requires the
modeling of the truncated dynamics on the retained dynamics. In its most
general form, this so-called closure model has to account for memory effects.
In this work, we present a framework of operator inference to extract the
governing dynamics of closure from data in a compact, non-Markovian form. We
employ sparse polynomial regression and artificial neural networks to extract
the underlying operator. For a special class of non-linear systems,
observability of the closure in terms of the resolved dynamics is analyzed and
theoretical results are presented on the compactness of the memory. The
proposed framework is evaluated on examples consisting of linear to nonlinear
systems with and without chaotic dynamics, with an emphasis on predictive
performance on unseen data.
|
math.DS nlin.CD stat.ML
|
derivation of reduced order representations of dynamical systems requires the modeling of the truncated dynamics on the retained dynamics in its most general form this socalled closure model has to account for memory effects in this work we present a framework of operator inference to extract the governing dynamics of closure from data in a compact nonmarkovian form we employ sparse polynomial regression and artificial neural networks to extract the underlying operator for a special class of nonlinear systems observability of the closure in terms of the resolved dynamics is analyzed and theoretical results are presented on the compactness of the memory the proposed framework is evaluated on examples consisting of linear to nonlinear systems with and without chaotic dynamics with an emphasis on predictive performance on unseen data
|
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|
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|
1,803.09319
|
SUNLayer: Stable denoising with generative networks
|
It has been experimentally established that deep neural networks can be used
to produce good generative models for real world data. It has also been
established that such generative models can be exploited to solve classical
inverse problems like compressed sensing and super resolution. In this work we
focus on the classical signal processing problem of image denoising. We propose
a theoretical setting that uses spherical harmonics to identify what
mathematical properties of the activation functions will allow signal denoising
with local methods.
|
cs.LG stat.ML
|
it has been experimentally established that deep neural networks can be used to produce good generative models for real world data it has also been established that such generative models can be exploited to solve classical inverse problems like compressed sensing and super resolution in this work we focus on the classical signal processing problem of image denoising we propose a theoretical setting that uses spherical harmonics to identify what mathematical properties of the activation functions will allow signal denoising with local methods
|
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|
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|
1,803.0932
|
Importance sampling for McKean-Vlasov SDEs
|
This paper deals with the Monte-Carlo methods for evaluating expectations of
functionals of solutions to McKean-Vlasov Stochastic Differential Equations
(MV-SDE) with drifts of super-linear growth. We assume that the MV-SDE is
approximated in the standard manner by means of an interacting particle system
and propose two importance sampling (IS) techniques to reduce the variance of
the resulting Monte Carlo estimator. In the \emph{complete measure change}
approach, the IS measure change is applied simultaneously in the coefficients
and in the expectation to be evaluated. In the \emph{decoupling} approach we
first estimate the law of the solution in a first set of simulations without
measure change and then perform a second set of simulations under the
importance sampling measure using the approximate solution law computed in the
first step.
For both approaches, we use large deviations techniques to identify an
optimisation problem for the candidate measure change. The decoupling approach
yields a far simpler optimisation problem than the complete measure change,
however, we can reduce the complexity of the complete measure change through
some symmetry arguments. We implement both algorithms for two examples coming
from the Kuramoto model from statistical physics and show that the variance of
the importance sampling schemes is up to 3 orders of magnitude smaller than
that of the standard Monte Carlo. The computational cost is approximately the
same as for standard Monte Carlo for the complete measure change and only
increases by a factor of 2--3 for the decoupled approach. We also estimate the
propagation of chaos error and find that this is dominated by the statistical
error by one order of magnitude.
|
math.PR
|
this paper deals with the montecarlo methods for evaluating expectations of functionals of solutions to mckeanvlasov stochastic differential equations mvsde with drifts of superlinear growth we assume that the mvsde is approximated in the standard manner by means of an interacting particle system and propose two importance sampling is techniques to reduce the variance of the resulting monte carlo estimator in the emphcomplete measure change approach the is measure change is applied simultaneously in the coefficients and in the expectation to be evaluated in the emphdecoupling approach we first estimate the law of the solution in a first set of simulations without measure change and then perform a second set of simulations under the importance sampling measure using the approximate solution law computed in the first step for both approaches we use large deviations techniques to identify an optimisation problem for the candidate measure change the decoupling approach yields a far simpler optimisation problem than the complete measure change however we can reduce the complexity of the complete measure change through some symmetry arguments we implement both algorithms for two examples coming from the kuramoto model from statistical physics and show that the variance of the importance sampling schemes is up to 3 orders of magnitude smaller than that of the standard monte carlo the computational cost is approximately the same as for standard monte carlo for the complete measure change and only increases by a factor of 23 for the decoupled approach we also estimate the propagation of chaos error and find that this is dominated by the statistical error by one order of magnitude
|
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|
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|
1,803.09321
|
Local Quadratic Estimation of the Curvature in a Functional Single Index
Model
|
The nonlinear effects of environmental variability on species abundance plays
an important role in the maintenance of ecological diversity. Nonetheless, many
common models use parametric nonlinear terms pre-determining ecological
conclusions. Motivated by this concern, we study the estimate of the second
derivative (curvature) of the link function g in a functional single index
model. Since the coefficient function and the link function are both unknown,
the estimate is expressed as a nested optimization. For a fixed and unknown
coefficient function, the link function and its second derivative are estimated
by local quadratic approximation, then the coefficient function is estimated by
minimizing the MSE of the model. In this paper, we derive the rate of
convergence of the estimation. In addition, we prove that the argument of g,
can be estimated root-n consistently. However, practical implementation of the
method requires solving a nonlinear optimization problem, and our results show
that the estimates of the link function and the coefficient function are quite
sensitive to the choices of starting values.
|
math.ST stat.ME stat.TH
|
the nonlinear effects of environmental variability on species abundance plays an important role in the maintenance of ecological diversity nonetheless many common models use parametric nonlinear terms predetermining ecological conclusions motivated by this concern we study the estimate of the second derivative curvature of the link function g in a functional single index model since the coefficient function and the link function are both unknown the estimate is expressed as a nested optimization for a fixed and unknown coefficient function the link function and its second derivative are estimated by local quadratic approximation then the coefficient function is estimated by minimizing the mse of the model in this paper we derive the rate of convergence of the estimation in addition we prove that the argument of g can be estimated rootn consistently however practical implementation of the method requires solving a nonlinear optimization problem and our results show that the estimates of the link function and the coefficient function are quite sensitive to the choices of starting values
|
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|
[-0.11979622434869054, 0.03529018888305776, -0.0693296174022613, 0.09148373959067699, -0.055594771025122704, -0.0925217258433501, 0.04642253330218539, 0.3442016511412692, -0.29033783534985214, -0.32315785863569807, 0.1269138944252128, -0.23991994389576748, -0.2211045149936884, 0.17647241595217825, -0.0557360995915674, 0.06487478672395464, 0.04256443837324956, 0.036822290226977895, -0.0719634536709193, -0.23563924109995632, 0.31184362024734064, 0.05299314635617304, 0.25698866736881126, 0.06420625524229504, 0.1360945055937572, 0.024006838705168947, -0.06578197238767254, -0.004397436255766522, -0.14670980474927223, 0.12838201744723068, 0.23708536031398625, 0.13002729343965516, 0.33383301164334017, -0.36181090752195033, -0.23779895539683776, 0.12571523019245692, 0.11403508317501594, 0.046247453190430644, -0.016000791314928348, -0.2043571649008386, 0.07022685393305783, -0.1534553620676022, -0.1333024242388395, -0.03989942255984282, -0.012582831822025279, 0.05085831947785448, -0.32052110508084297, 0.1344052085575337, 0.031498166329194124, 0.03948710662578898, -0.07119714448275599, -0.13561715724478876, -0.016094575336735164, 0.13126665354329384, 0.08361317515733563, 0.04447829598627452, 0.12528169485795798, -0.16676954120963014, -0.05551763719579737, 0.35374557947943686, -0.10202600206581078, -0.248382041254358, 0.1307964023158309, -0.1112416740257426, -0.12101838129317566, 0.08374159667651579, 0.1827844608785762, 0.13445413252893126, -0.15978507867839653, 0.07840998341998784, -0.027857822917645707, 0.15908087522534298, 0.024424687219184955, 0.017331085724955692, 0.14784968214475416, 0.1314075455995321, 0.09569445387647388, 0.13862916135154332, -0.05648182772815095, -0.0863403207400725, -0.307335283895511, -0.13485204987920865, -0.20542237576973138, 0.006980231360925938, -0.1615552596239078, -0.16639136975642205, 0.40905278291930225, 0.13601213946440976, 0.1961763954050617, 0.08574840407042454, 0.29443388308087987, 0.21978226104485138, 0.03223458277560504, 0.02769142993687031, 0.23228131554580095, 0.13585270404811517, 0.028822439997124354, -0.24301354688560378, 0.167894363622292, 0.07478242773712347]
|
1,803.09322
|
Algebras with two multiplications and their cumulants
|
Cumulants are a notion that comes from the classical probability theory, they
are an alternative to a notion of moments. We adapt the probabilistic concept
of cumulants to the setup of a linear space equipped with two multiplication
structures. We present an algebraic formula which involves those two
multiplications as a sum of products of cumulants. In our approach, beside
cumulants, we make use of standard combinatorial tools as forests and their
colourings. We also show that the resulting statement can be understood as an
analogue of Leonov--Shiraev's formula. This purely combinatorial presentation
leads to some conclusions about structure constant of Jack characters.
|
math.CO
|
cumulants are a notion that comes from the classical probability theory they are an alternative to a notion of moments we adapt the probabilistic concept of cumulants to the setup of a linear space equipped with two multiplication structures we present an algebraic formula which involves those two multiplications as a sum of products of cumulants in our approach beside cumulants we make use of standard combinatorial tools as forests and their colourings we also show that the resulting statement can be understood as an analogue of leonovshiraevs formula this purely combinatorial presentation leads to some conclusions about structure constant of jack characters
|
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|
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|
1,803.09323
|
ALOHA-NOMA for Massive Machine-to-Machine IoT Communication
|
This paper proposes a new medium access control (MAC) protocol for Internet
of Things (IoT) applications incorporating pure ALOHA with power domain
non-orthogonal multiple access (NOMA) in which the number of transmitters are
not known as a priori information and estimated with multi-hypothesis testing.
The proposed protocol referred to as ALOHA-NOMA is not only scalable, energy
efficient and matched to the low complexity requirements of IoT devices, but it
also significantly increases the throughput. Specifically, throughput is
increased to 1.27 with ALOHA-NOMA when 5 users can be separated via a SIC
(Successive Interference Cancellation) receiver in comparison to the classical
result of 0.18 in pure ALOHA. The results further show that there is a greater
than linear increase in throughput as the number of active IoT devices
increases.
|
eess.SP
|
this paper proposes a new medium access control mac protocol for internet of things iot applications incorporating pure aloha with power domain nonorthogonal multiple access noma in which the number of transmitters are not known as a priori information and estimated with multihypothesis testing the proposed protocol referred to as alohanoma is not only scalable energy efficient and matched to the low complexity requirements of iot devices but it also significantly increases the throughput specifically throughput is increased to 127 with alohanoma when 5 users can be separated via a sic successive interference cancellation receiver in comparison to the classical result of 018 in pure aloha the results further show that there is a greater than linear increase in throughput as the number of active iot devices increases
|
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|
[-0.21352627314445272, 0.06024198492013966, -0.018498608100344427, 0.007082497579176561, -0.07637947296461789, -0.2513357469520088, 0.11204007202195498, 0.3791596280934755, -0.2564488393836655, -0.33139561013376806, 0.07918252255421976, -0.2418001487130823, -0.14602064212476762, 0.17034133581182687, -0.14369601861289993, 0.026535343789873878, 0.02012409418966854, 0.027502424440172035, -0.027852023356899736, -0.27757988534358446, 0.23229736947905621, 0.12078974289033795, 0.38293209712719545, 0.048850631133973366, 0.03961329614685383, 0.00858748953532995, -0.009009731231344631, -0.006370717672325554, -0.056236406128221006, 0.06532029121626692, 0.349611384450327, 0.17542078563201358, 0.2981140075280564, -0.4071845349535579, -0.24898977695556823, 0.0790944353402665, 0.2136142277486215, 0.056570693491266866, -0.07165890425494581, -0.2561025137092656, 0.17939514235422394, -0.2584712100906472, -0.057866682956728255, 0.021789887781778816, -0.06200872283443459, 0.04595414410459853, -0.3277192285240744, 0.01894233962252656, -0.010287453865203133, 0.024993671284391894, -0.02658534898569087, -0.09991131971401046, 0.018017499958659755, 0.13614369045103558, 0.00843251451078686, 0.015641850167412485, 0.12190928911877563, -0.0859161208045407, -0.142912558630087, 0.3534618326375494, 0.0005210393422885318, -0.18938860094931442, 0.18556349759126078, -0.06690566275210585, -0.08447103384287402, 0.17093809742073063, 0.18958981640344064, 0.06991626508897753, -0.16905032452507385, -0.001296337972917172, 0.0060335711896186695, 0.21037720454478404, 0.10754364975946373, 0.17608998174546286, 0.10094432183905155, 0.2032798706804897, 0.16485422712867148, 0.111008612074329, -0.07260795461479574, -0.1051433799766528, -0.2039421866579687, -0.17257597190473462, -0.23118654510835768, 0.05255713644896787, -0.11244293392496729, -0.10125870711999596, 0.32821709127438226, 0.14194820866896407, 0.1246675100264838, 0.08364323101068294, 0.42548056959640235, 0.07540938082547655, 0.11973458272768767, 0.13798554134336882, 0.20860838415683247, 0.08994347201951314, 0.16363970041089715, -0.16775081803643843, 0.0706600760992444, -0.05624767161134514]
|
1,803.09324
|
Enhanced photon-phonon coupling via dimerization in one-dimensional
optomechanical crystals
|
We show that dimerization of an optomechanical crystal lattice, which leads
to folding of the band diagram, can couple flexural mechanical modes to optical
fields within the unit cell via radiation pressure. When compared to currently
realized crystals, a substantial improvement in the coupling between photons
and phonons is found. For experimental verification, we implement a dimerized
lattice in a silicon optomechanical nanobeam cavity and measure a vacuum
coupling rate of $g_0/2\pi=1.7MHz$ between an optical resonance at $\lambda_{c}
= 1545nm$ and a mechanical resonance at 1.14GHz.
|
cond-mat.mes-hall physics.optics
|
we show that dimerization of an optomechanical crystal lattice which leads to folding of the band diagram can couple flexural mechanical modes to optical fields within the unit cell via radiation pressure when compared to currently realized crystals a substantial improvement in the coupling between photons and phonons is found for experimental verification we implement a dimerized lattice in a silicon optomechanical nanobeam cavity and measure a vacuum coupling rate of g_02pi17mhz between an optical resonance at lambda_c 1545nm and a mechanical resonance at 114ghz
|
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|
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|
1,803.09325
|
Direct and indirect exciton mixture in double quantum wells
|
The exciton system in double quantum well is considered under condition when
the ground state is the spatially indirect exciton. At high pumping growth of
the exciton concentration can lead to so significant increase of the indirect
exciton energy that becomes equal to the direct exciton energy. Then further
increase of pumping leads to formation of mixed direct - indirect exciton
phase. A rough estimate of the exciton energy in the mixed phase explains
puzzling features of some recent exciton measurements. An experiment that would
reveal main characteristic features of the mixed phase is suggested.
|
cond-mat.mes-hall
|
the exciton system in double quantum well is considered under condition when the ground state is the spatially indirect exciton at high pumping growth of the exciton concentration can lead to so significant increase of the indirect exciton energy that becomes equal to the direct exciton energy then further increase of pumping leads to formation of mixed direct indirect exciton phase a rough estimate of the exciton energy in the mixed phase explains puzzling features of some recent exciton measurements an experiment that would reveal main characteristic features of the mixed phase is suggested
|
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|
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|
1,803.09326
|
Deep Depth Completion of a Single RGB-D Image
|
The goal of our work is to complete the depth channel of an RGB-D image.
Commodity-grade depth cameras often fail to sense depth for shiny, bright,
transparent, and distant surfaces. To address this problem, we train a deep
network that takes an RGB image as input and predicts dense surface normals and
occlusion boundaries. Those predictions are then combined with raw depth
observations provided by the RGB-D camera to solve for depths for all pixels,
including those missing in the original observation. This method was chosen
over others (e.g., inpainting depths directly) as the result of extensive
experiments with a new depth completion benchmark dataset, where holes are
filled in training data through the rendering of surface reconstructions
created from multiview RGB-D scans. Experiments with different network inputs,
depth representations, loss functions, optimization methods, inpainting
methods, and deep depth estimation networks show that our proposed approach
provides better depth completions than these alternatives.
|
cs.CV
|
the goal of our work is to complete the depth channel of an rgbd image commoditygrade depth cameras often fail to sense depth for shiny bright transparent and distant surfaces to address this problem we train a deep network that takes an rgb image as input and predicts dense surface normals and occlusion boundaries those predictions are then combined with raw depth observations provided by the rgbd camera to solve for depths for all pixels including those missing in the original observation this method was chosen over others eg inpainting depths directly as the result of extensive experiments with a new depth completion benchmark dataset where holes are filled in training data through the rendering of surface reconstructions created from multiview rgbd scans experiments with different network inputs depth representations loss functions optimization methods inpainting methods and deep depth estimation networks show that our proposed approach provides better depth completions than these alternatives
|
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|
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|
1,803.09327
|
Stabilizing Gradients for Deep Neural Networks via Efficient SVD
Parameterization
|
Vanishing and exploding gradients are two of the main obstacles in training
deep neural networks, especially in capturing long range dependencies in
recurrent neural networks~(RNNs). In this paper, we present an efficient
parametrization of the transition matrix of an RNN that allows us to stabilize
the gradients that arise in its training. Specifically, we parameterize the
transition matrix by its singular value decomposition(SVD), which allows us to
explicitly track and control its singular values. We attain efficiency by using
tools that are common in numerical linear algebra, namely Householder
reflectors for representing the orthogonal matrices that arise in the SVD. By
explicitly controlling the singular values, our proposed Spectral-RNN method
allows us to easily solve the exploding gradient problem and we observe that it
empirically solves the vanishing gradient issue to a large extent. We note that
the SVD parameterization can be used for any rectangular weight matrix, hence
it can be easily extended to any deep neural network, such as a multi-layer
perceptron. Theoretically, we demonstrate that our parameterization does not
lose any expressive power, and show how it controls generalization of RNN for
the classification task. %, and show how it potentially makes the optimization
process easier. Our extensive experimental results also demonstrate that the
proposed framework converges faster, and has good generalization, especially in
capturing long range dependencies, as shown on the synthetic addition and copy
tasks, as well as on MNIST and Penn Tree Bank data sets.
|
cs.LG stat.ML
|
vanishing and exploding gradients are two of the main obstacles in training deep neural networks especially in capturing long range dependencies in recurrent neural networksrnns in this paper we present an efficient parametrization of the transition matrix of an rnn that allows us to stabilize the gradients that arise in its training specifically we parameterize the transition matrix by its singular value decompositionsvd which allows us to explicitly track and control its singular values we attain efficiency by using tools that are common in numerical linear algebra namely householder reflectors for representing the orthogonal matrices that arise in the svd by explicitly controlling the singular values our proposed spectralrnn method allows us to easily solve the exploding gradient problem and we observe that it empirically solves the vanishing gradient issue to a large extent we note that the svd parameterization can be used for any rectangular weight matrix hence it can be easily extended to any deep neural network such as a multilayer perceptron theoretically we demonstrate that our parameterization does not lose any expressive power and show how it controls generalization of rnn for the classification task and show how it potentially makes the optimization process easier our extensive experimental results also demonstrate that the proposed framework converges faster and has good generalization especially in capturing long range dependencies as shown on the synthetic addition and copy tasks as well as on mnist and penn tree bank data sets
|
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|
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|
1,803.09328
|
Quasi-Harmonic Constraints for Toric B\'ezier Surfaces
|
Toric B\'ezier patches generalize the classical tensor-product triangular and
rectangular B\'ezier surfaces, extensively used in $CAGD$. The construction of
toric B\'ezier surfaces corresponding to multi-sided convex hulls for known
boundary mass-points with integer coordinates (in particular for trapezoidal
and hexagonal convex hulls) is given. For these toric B\'ezier surfaces, we
find approximate minimal surfaces obtained by extremizing the quasi-harmonic
energy functional. We call these approximate minimal surfaces as the
quasi-harmonic toric B\'ezier surfaces. This is achieved by imposing the
vanishing condition of gradient of the quasi-harmonic functional and obtaining
a set of linear constraints on the unknown inner mass-points of the toric
B\'ezier patch for the above mentioned convex hull domains, under which they
are quasi-harmonic toric B\'ezier patches. This gives us the solution of the
\textit{Plateau toric B\'ezier problem} for these illustrative instances for
known convex hull domains.
|
math.OC
|
toric bezier patches generalize the classical tensorproduct triangular and rectangular bezier surfaces extensively used in cagd the construction of toric bezier surfaces corresponding to multisided convex hulls for known boundary masspoints with integer coordinates in particular for trapezoidal and hexagonal convex hulls is given for these toric bezier surfaces we find approximate minimal surfaces obtained by extremizing the quasiharmonic energy functional we call these approximate minimal surfaces as the quasiharmonic toric bezier surfaces this is achieved by imposing the vanishing condition of gradient of the quasiharmonic functional and obtaining a set of linear constraints on the unknown inner masspoints of the toric bezier patch for the above mentioned convex hull domains under which they are quasiharmonic toric bezier patches this gives us the solution of the textitplateau toric bezier problem for these illustrative instances for known convex hull domains
|
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|
[-0.1053866810111356, -0.03337702827369524, -0.06213451874361414, 0.10448660411318575, -0.06515783924555434, -0.18820610303310273, 0.00433161659706114, 0.36522100306372496, -0.35134928247155756, -0.2066660885280673, 0.12405380780346341, -0.2547920542175247, -0.13417880635276652, 0.1903904433686124, -0.18247280069424407, 0.18368908362733066, 0.03266668958510137, -0.036394189132134554, -0.1670143289830657, -0.3627344991107458, 0.35905638800097117, -0.03995511152121859, 0.24654996434928497, 0.08344151288485221, 0.11119399572034246, 0.008392621282204662, 0.06767901479253087, 0.03747079410569985, -0.22742795074135874, 0.190889764109591, 0.312251810375871, 0.054681031162044084, 0.1044344275859117, -0.49317967139886343, -0.19236838097824965, 0.1373465702973603, 0.07924737806593918, 0.07594340844872827, -0.031061309910264623, -0.1981059346968929, 0.044805782327455454, -0.010944319187083107, -0.192109444591156, -0.12468369106046748, -0.027543761720205995, 0.08788547038600064, -0.23778604116776716, 0.0002452144871695318, 0.09736013120424974, 0.11563364853677542, -0.08560718855469664, -0.17587448018130616, -0.09755685579780814, -0.0004370228515640981, -0.044598923400516854, 0.08024343607299354, 0.12025325407233575, -0.042425410025685596, -0.09739477930765977, 0.3709961508360246, 0.005555207891713666, -0.3140388898740428, 0.11899505229666829, -0.06635068938055116, -0.07582450408211815, 0.1967221718505902, 0.14071596738463943, 0.19167545489103033, -0.12156256947091079, 0.18360264231054368, -0.10026080631296677, 0.05215027318943454, 0.18034813209247869, -0.0731185841191884, 0.17489875918524206, 0.0689666467141765, 0.11284308016394684, 0.21505226752977225, -0.06437652802897914, -0.12980154492433413, -0.3654334011649632, -0.15633213232407192, -0.218355902430156, 0.00034887354611756575, -0.19063828152950696, -0.27799675287003967, 0.40446546393028204, -0.03960985034253732, 0.13459282323205168, 0.13463927238616094, 0.24267829991067233, 0.01800128070992313, 0.048190714133417474, 0.10026092747010398, 0.17737229434314414, 0.12712805101688465, -0.046997884987765734, -0.17734547981830395, 0.00891565026688403, 0.2425162917866871]
|
1,803.09329
|
Julia operators and Halmos dilations
|
We offer a simple direct proof of the unitarity of the Julia operator
associated to a contraction $A$, from which follow the intertwining identity
$(I - A A^*)^{1/2} A = A (I - A^* A)^{1/2}$ and the unitarity of Halmos
dilations.
|
math.FA
|
we offer a simple direct proof of the unitarity of the julia operator associated to a contraction a from which follow the intertwining identity i a a12 a a i a a12 and the unitarity of halmos dilations
|
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|
[-0.15465634257385605, 0.10952169578032274, -0.17166900772013163, 0.06528295954003145, -0.15877869818359613, -0.17254702120676244, 0.11293435445373975, 0.26642726587229654, -0.3219112598974454, -0.08732485094744909, 0.13913154371670985, -0.3075095656278886, -0.13228165694071273, 0.10133468411176612, -0.025351203365349455, 0.026102820729934854, 0.03368892336852456, 0.0500780376728232, -0.1701155180650714, -0.141502042644118, 0.34268164183748395, 0.002126204830251242, 0.15265232380969743, 0.06301065201037809, 0.1421325421818581, -0.03895968071332103, -0.011186884765170123, -0.03164637233375719, -0.13198933997926743, 0.17874395120643863, 0.14583761708835433, 0.1816104984303054, 0.24951699434926636, -0.3479439552971407, -0.06582696390289225, 0.09941445442994959, 0.10859384272541654, 0.05556726364700712, -0.08517456066941745, -0.3071329132898858, -0.015877016685216835, -0.18893737641108027, -0.19035077477364162, -0.055667192993783636, 0.01617647006519531, -0.023231483260659797, -0.33806436352039637, 0.06478278250678589, 0.1711773284171757, 0.10955909350396771, -0.00403281249792168, -0.06772554029808625, -0.02841731327536859, 0.05471392864312388, -0.006531486091645141, 0.024720870399553525, 0.07335452448674723, -0.08993401760725599, -0.08184599671757926, 0.38822465125275285, -0.03446068452965272, -0.20355916260986737, 0.17662750767838015, -0.12899096565026985, -0.1883155292659802, 0.058824571731843446, 0.05173894841420023, 0.08814869056406774, -0.1295170791104044, 0.18160552141642639, -0.1107801666581317, 0.11629117883153652, 0.08915654876220383, -0.028755312883540204, 0.13824294632803158, 0.05194571986794472, 0.0911009969483865, 0.096739267807846, 0.035387723067910166, -0.04192385136296874, -0.45285561563153015, -0.2628979584888408, -0.155063531998741, 0.14870556397363544, -0.1149868680930874, -0.213581260587824, 0.40801219656867416, 0.11588348850215736, 0.26777667481158124, 0.11721824786294938, 0.22744460060800376, 0.12429050468888722, 0.13081122884575866, 0.037442389630565516, 0.20906263491825053, 0.18012378587828656, 0.05881914339567486, -0.20108610207190444, -0.05590842824772393, 0.17566761041158124]
|
1,803.0933
|
The top-degree part in the Matchings-Jack Conjecture
|
In 1996 Goulden and Jackson introduced a family of coefficients $( c_{\pi,
\sigma}^{\lambda} ) $ indexed by triples of partitions which arise in the power
sum expansion of some Cauchy sum for Jack symmetric functions $( J^{(\alpha
)}_\pi )$. The coefficients $ c_{\pi, \sigma}^{\lambda} $ can be viewed as an
interpolation between the structure constants of the class algebra and the
double coset algebra. Goulden and Jackson suggested that the coefficients $
c_{\pi, \sigma}^{\lambda} $ are polynomials in the variable $\beta := \alpha-1$
with non-negative integer coefficients and that there is a combinatorics of
matching hidden behind them. This \emph{Matchings-Jack Conjecture} remains
open. Do\l{}\oldk{e}ga and F\'eray showed the polynomiality of connection
coefficients $c^\lambda_{\pi,\sigma}$ and gave the upper bound on the degrees.
We give a necessary and sufficient condition for the polynomial $ c_{\pi,
\sigma}^{\lambda}$ to achieve this bound. We show that the leading coefficient
of $ c_{\pi, \sigma}^{\lambda}$ is a positive integer and we present it in the
context of Matchings-Jack Conjecture of Goulden and Jackson.
|
math.CO
|
in 1996 goulden and jackson introduced a family of coefficients c_pi sigmalambda indexed by triples of partitions which arise in the power sum expansion of some cauchy sum for jack symmetric functions jalpha _pi the coefficients c_pi sigmalambda can be viewed as an interpolation between the structure constants of the class algebra and the double coset algebra goulden and jackson suggested that the coefficients c_pi sigmalambda are polynomials in the variable beta alpha1 with nonnegative integer coefficients and that there is a combinatorics of matching hidden behind them this emphmatchingsjack conjecture remains open dololdkega and feray showed the polynomiality of connection coefficients clambda_pisigma and gave the upper bound on the degrees we give a necessary and sufficient condition for the polynomial c_pi sigmalambda to achieve this bound we show that the leading coefficient of c_pi sigmalambda is a positive integer and we present it in the context of matchingsjack conjecture of goulden and jackson
|
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|
[-0.1895009122773384, 0.11892313572044562, -0.07132407906465232, 0.04629342083819211, -0.10278988332177202, -0.14803748437358688, 0.032790844614307084, 0.2926093716515849, -0.30822804814359794, -0.22329099872149527, 0.1097717250805969, -0.25252668097304803, -0.20839002260938286, 0.1637046794158717, -0.06263044089078904, 0.0451749469867597, 0.012835832040097254, 0.041844628054726246, -0.05301713657720635, -0.29196161319036035, 0.31051227665971964, 0.008048287058869997, 0.16435250671890875, 0.10175308305459718, 0.10837909994026025, 0.0207408358498166, -0.05298257481190376, -0.06165083360858262, -0.18405138917805744, 0.12415636646406104, 0.2489114003876845, 0.10572301896618834, 0.20310375293251126, -0.3317368178954348, -0.09417116786818952, 0.1334943426772952, 0.12381893494166434, -0.022104619021993132, -0.00626125608648484, -0.22939482564417024, 0.08596804762259126, -0.18331555722281337, -0.15797151369042695, -0.08763712409728518, 0.06891515348417064, 0.0393847387303443, -0.3690943188891591, 0.10256052229553461, 0.1123396936233621, 0.03667073178861756, -0.03545181659826388, -0.20814818900932247, 8.120307543625434e-05, 0.07183345641940832, 0.0008827400859445333, 0.04055990552452082, -0.02280357158742845, -0.09589862192825725, -0.1382396344219645, 0.31986098528800844, -0.04462070976694425, -0.2456170700614651, 0.07548244932045539, -0.14918333138649661, -0.17484892678757508, 0.058317731528853375, 0.08043346780817956, 0.12596458138965924, -0.0682063732703682, 0.16615840528121528, -0.16975294394729037, 0.08950746045292665, 0.19996721267389755, 0.008232829812914132, 0.120212357196336, -0.019489411205674212, 0.021072121537290513, 0.16412005882943048, 0.0447646499950982, -0.0694706007000059, -0.3056819574596981, -0.18267706618411467, -0.1900677943105499, 0.0954375120314459, -0.1374709238894866, -0.18055167654451604, 0.34664115264934175, 0.03792798882039885, 0.19391037786379456, 0.10184433832842235, 0.15602307971722135, 0.1673499981845574, 0.052240949297944705, 0.09221058648079633, 0.1422963242646074, 0.2428981269352759, 0.047713593828181425, -0.18380120379539827, 0.0678586314463367, 0.204788985621805]
|
1,803.09331
|
StarMap for Category-Agnostic Keypoint and Viewpoint Estimation
|
Semantic keypoints provide concise abstractions for a variety of visual
understanding tasks. Existing methods define semantic keypoints separately for
each category with a fixed number of semantic labels in fixed indices. As a
result, this keypoint representation is in-feasible when objects have a varying
number of parts, e.g. chairs with varying number of legs. We propose a
category-agnostic keypoint representation, which combines a multi-peak heatmap
(StarMap) for all the keypoints and their corresponding features as 3D
locations in the canonical viewpoint (CanViewFeature) defined for each
instance. Our intuition is that the 3D locations of the keypoints in canonical
object views contain rich semantic and compositional information. Using our
flexible representation, we demonstrate competitive performance in keypoint
detection and localization compared to category-specific state-of-the-art
methods. Moreover, we show that when augmented with an additional depth channel
(DepthMap) to lift the 2D keypoints to 3D, our representation can achieve
state-of-the-art results in viewpoint estimation. Finally, we show that our
category-agnostic keypoint representation can be generalized to novel
categories.
|
cs.CV
|
semantic keypoints provide concise abstractions for a variety of visual understanding tasks existing methods define semantic keypoints separately for each category with a fixed number of semantic labels in fixed indices as a result this keypoint representation is infeasible when objects have a varying number of parts eg chairs with varying number of legs we propose a categoryagnostic keypoint representation which combines a multipeak heatmap starmap for all the keypoints and their corresponding features as 3d locations in the canonical viewpoint canviewfeature defined for each instance our intuition is that the 3d locations of the keypoints in canonical object views contain rich semantic and compositional information using our flexible representation we demonstrate competitive performance in keypoint detection and localization compared to categoryspecific stateoftheart methods moreover we show that when augmented with an additional depth channel depthmap to lift the 2d keypoints to 3d our representation can achieve stateoftheart results in viewpoint estimation finally we show that our categoryagnostic keypoint representation can be generalized to novel categories
|
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|
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|
1,803.09332
|
Exploring Core Regular Double Stone Algebras, CRDSA, III. Establishing
Duality
|
This is the last in a series of three notes on an investigation into core
regular double Stone algebras, CRDSA, which are meant to be read in order. This
note ends our initial investigation of duality for CRDSA through bi-topological
spaces. More succinctly, duality through refinement of a pre-established
duality of pairwise Stone spaces and bounded distributive lattices. In this
note we show that the pairwise Stone derived from a CRDSA L has a base that is
a CRDSA isomorphic to L. For the purposes of this note only we will call any
such pairwise zero-dimensional space a core regular double pairwise
zero-dimensional space and similarly for the corresponding pairwise Stone
spaces. Then we establish necessary and sufficient conditions for a
bi-continuous map to have an inverse that is a CRDSA homomorphism. These
results are topologically indactive of just how "nearly Boolean" CRDSA are,
these inverses must respect the appropriate conditions on the boundary of
non-clopen elements of the bases of the bi-topological space. From that result
we validate our earlier claim that the category of core regular double Stone
algebras is dually equivalent to the category of core regular double pairwise
Stone spaces. We note that the conditions for this duality should be able to be
easily relaxed to yield a duality for a less rigid subclass of bounded
distributive lattices than CRDSA, bounded distributive pseudo-complemented
lattices for example.
|
math.RA
|
this is the last in a series of three notes on an investigation into core regular double stone algebras crdsa which are meant to be read in order this note ends our initial investigation of duality for crdsa through bitopological spaces more succinctly duality through refinement of a preestablished duality of pairwise stone spaces and bounded distributive lattices in this note we show that the pairwise stone derived from a crdsa l has a base that is a crdsa isomorphic to l for the purposes of this note only we will call any such pairwise zerodimensional space a core regular double pairwise zerodimensional space and similarly for the corresponding pairwise stone spaces then we establish necessary and sufficient conditions for a bicontinuous map to have an inverse that is a crdsa homomorphism these results are topologically indactive of just how nearly boolean crdsa are these inverses must respect the appropriate conditions on the boundary of nonclopen elements of the bases of the bitopological space from that result we validate our earlier claim that the category of core regular double stone algebras is dually equivalent to the category of core regular double pairwise stone spaces we note that the conditions for this duality should be able to be easily relaxed to yield a duality for a less rigid subclass of bounded distributive lattices than crdsa bounded distributive pseudocomplemented lattices for example
|
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|
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|
1,803.09333
|
The effect of pulsation frequency on transition in pulsatile pipe flow
|
Pulsatile flows are common in nature and in applications, but their stability
and transition to turbulence are still poorly understood. Even in the simple
case of pipe flow subject to harmonic pulsation, there is no consensus among
experimental studies on whether pulsation delays or enhances transition. We
here report direct numerical simulations of pulsatile pipe flow at low
pulsation amplitude A<0.4. We use a spatially localized impulsive disturbance
to generate a single turbulent puff and track its dynamics as it travels
downstream. The computed relaminarization statistics are in quantitative
agreement with the experiments of Xu et al. (J. Fluid Mech., vol. 831, 2017,
pp. 418-432) and support the conclusion that increasing the pulsation amplitude
and lowering the frequency enhance the stability of the flow. In the
high-frequency regime, the behaviour of steady pipe flow is recovered. In
addition, we show that when the pipe length does not permit the observation of
a full cycle, a reduction of the transition threshold is observed. We obtain an
equation quantifying this effect and compare it favourably with the
measurements of Stettler & Hussain (J. Fluid Mech., vol. 170, 1986, pp.
169-197). Our results resolve previous discrepancies, which are due to
different pipe lengths, perturbation methods and criteria chosen to quantify
transition in experiments.
|
physics.flu-dyn
|
pulsatile flows are common in nature and in applications but their stability and transition to turbulence are still poorly understood even in the simple case of pipe flow subject to harmonic pulsation there is no consensus among experimental studies on whether pulsation delays or enhances transition we here report direct numerical simulations of pulsatile pipe flow at low pulsation amplitude a04 we use a spatially localized impulsive disturbance to generate a single turbulent puff and track its dynamics as it travels downstream the computed relaminarization statistics are in quantitative agreement with the experiments of xu et al j fluid mech vol 831 2017 pp 418432 and support the conclusion that increasing the pulsation amplitude and lowering the frequency enhance the stability of the flow in the highfrequency regime the behaviour of steady pipe flow is recovered in addition we show that when the pipe length does not permit the observation of a full cycle a reduction of the transition threshold is observed we obtain an equation quantifying this effect and compare it favourably with the measurements of stettler hussain j fluid mech vol 170 1986 pp 169197 our results resolve previous discrepancies which are due to different pipe lengths perturbation methods and criteria chosen to quantify transition in experiments
|
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|
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|
1,803.09334
|
The Coordinated Radio and Infrared Survey for High-Mass Star Formation
III. A catalogue of northern ultra-compact H II regions
|
A catalogue of 239 ultra-compact HII regions (UCHIIs) found in the CORNISH
survey at 5 GHz and 1.5" resolution in the region $10^{\circ} < l < 65^{\circ},
~|b| < 1^{\circ}$ is presented. This is the largest complete and well-selected
sample of UCHIIs to date and provides the opportunity to explore the global and
individual properties of this key state in massive star formation at multiple
wavelengths. The nature of the candidates was validated, based on observational
properties and calculated spectral indices, and the analysis is presented in
this work. The physical sizes, luminosities and other physical properties were
computed by utilising literature distances or calculating the distances
whenever a value was not available. The near- and mid-infrared extended source
fluxes were measured and the extinctions towards the UCHIIs were computed. The
new results were combined with available data at longer wavelengths and the
spectral energy distributions (SEDs) were reconstructed for 177 UCHIIs. The
bolometric luminosities obtained from SED fitting are presented. By comparing
the radio flux densities to previous observational epochs, we find about 5% of
the sources appear to be time variable. This first high-resolution area survey
of the Galactic plane shows that the total number of UCHIIs in the Galaxy is ~
750 - a factor of 3-4 fewer than found in previous large area radio surveys. It
will form the basis for future tests of models of massive star formation.
|
astro-ph.GA
|
a catalogue of 239 ultracompact hii regions uchiis found in the cornish survey at 5 ghz and 15 resolution in the region 10circ l 65circ b 1circ is presented this is the largest complete and wellselected sample of uchiis to date and provides the opportunity to explore the global and individual properties of this key state in massive star formation at multiple wavelengths the nature of the candidates was validated based on observational properties and calculated spectral indices and the analysis is presented in this work the physical sizes luminosities and other physical properties were computed by utilising literature distances or calculating the distances whenever a value was not available the near and midinfrared extended source fluxes were measured and the extinctions towards the uchiis were computed the new results were combined with available data at longer wavelengths and the spectral energy distributions seds were reconstructed for 177 uchiis the bolometric luminosities obtained from sed fitting are presented by comparing the radio flux densities to previous observational epochs we find about 5 of the sources appear to be time variable this first highresolution area survey of the galactic plane shows that the total number of uchiis in the galaxy is 750 a factor of 34 fewer than found in previous large area radio surveys it will form the basis for future tests of models of massive star formation
|
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|
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|
1,803.09335
|
The subcritical phase for a homopolymer model
|
We study a model of continuous-time nearest-neighbor random walk on
$\mathbb{Z}^d$ penalized by its occupation time at the origin, also known as a
homopolymer. For a fixed real parameter $\beta$ and time $t>0$, we consider the
probability measure on paths of the random walk starting from the origin whose
Radon-Nikodym derivative is proportional to the exponent of the product $\beta$
times the occupation time at the origin up to time $t$. The case $\beta>0$ was
studied previously by Cranston and Molchanov arXiv:1508.06915. We consider the
case $\beta<0$, which is intrinsically different only when the underlying walk
is recurrent, that is $d=1,2$. Our main result is a scaling limit for the
distribution of the homopolymer on the time interval $[0,t]$, as $t\to\infty$,
a result that coincides with the scaling limit for penalized Brownian motion
due to Roynette and Yor. In two dimensions, the penalizing effect is
asymptotically diminished, and the homopolymer scales to standard Brownian
motion. Our approach is based on potential analytic and martingale
approximation for the model. We also apply our main result to recover a scaling
limit for a wetting model. We study the model through analysis of resolvents.
|
math.PR
|
we study a model of continuoustime nearestneighbor random walk on mathbbzd penalized by its occupation time at the origin also known as a homopolymer for a fixed real parameter beta and time t0 we consider the probability measure on paths of the random walk starting from the origin whose radonnikodym derivative is proportional to the exponent of the product beta times the occupation time at the origin up to time t the case beta0 was studied previously by cranston and molchanov arxiv150806915 we consider the case beta0 which is intrinsically different only when the underlying walk is recurrent that is d12 our main result is a scaling limit for the distribution of the homopolymer on the time interval 0t as ttoinfty a result that coincides with the scaling limit for penalized brownian motion due to roynette and yor in two dimensions the penalizing effect is asymptotically diminished and the homopolymer scales to standard brownian motion our approach is based on potential analytic and martingale approximation for the model we also apply our main result to recover a scaling limit for a wetting model we study the model through analysis of resolvents
|
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|
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|
1,803.09336
|
On 2-Group Global Symmetries and Their Anomalies
|
In general quantum field theories (QFTs), ordinary (0-form) global symmetries
and 1-form symmetries can combine into 2-group global symmetries. We describe
this phenomenon in detail using the language of symmetry defects. We exhibit a
simple procedure to determine the (possible) 2-group global symmetry of a given
QFT, and provide a classification of the related 't Hooft anomalies (for
symmetries not acting on spacetime). We also describe how QFTs can be coupled
to extrinsic backgrounds for symmetry groups that differ from the intrinsic
symmetry acting faithfully on the theory. Finally, we provide a variety of
examples, ranging from TQFTs (gapped systems) to gapless QFTs. Along the way,
we stress that the "obstruction to symmetry fractionalization" discussed in
some condensed matter literature is really an instance of 2-group global
symmetry.
|
hep-th cond-mat.str-el
|
in general quantum field theories qfts ordinary 0form global symmetries and 1form symmetries can combine into 2group global symmetries we describe this phenomenon in detail using the language of symmetry defects we exhibit a simple procedure to determine the possible 2group global symmetry of a given qft and provide a classification of the related t hooft anomalies for symmetries not acting on spacetime we also describe how qfts can be coupled to extrinsic backgrounds for symmetry groups that differ from the intrinsic symmetry acting faithfully on the theory finally we provide a variety of examples ranging from tqfts gapped systems to gapless qfts along the way we stress that the obstruction to symmetry fractionalization discussed in some condensed matter literature is really an instance of 2group global symmetry
|
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|
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|
1,803.09337
|
Text Segmentation as a Supervised Learning Task
|
Text segmentation, the task of dividing a document into contiguous segments
based on its semantic structure, is a longstanding challenge in language
understanding. Previous work on text segmentation focused on unsupervised
methods such as clustering or graph search, due to the paucity in labeled data.
In this work, we formulate text segmentation as a supervised learning problem,
and present a large new dataset for text segmentation that is automatically
extracted and labeled from Wikipedia. Moreover, we develop a segmentation model
based on this dataset and show that it generalizes well to unseen natural text.
|
cs.CL
|
text segmentation the task of dividing a document into contiguous segments based on its semantic structure is a longstanding challenge in language understanding previous work on text segmentation focused on unsupervised methods such as clustering or graph search due to the paucity in labeled data in this work we formulate text segmentation as a supervised learning problem and present a large new dataset for text segmentation that is automatically extracted and labeled from wikipedia moreover we develop a segmentation model based on this dataset and show that it generalizes well to unseen natural text
|
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|
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|
1,803.09338
|
Exploring Core Regular Double Stone Algebras, CRDSA, II. Moving Towards
Duality
|
This is the second in a series of three notes on an investigation into core
regular double Stone algebras, CRDSA, which are meant to be read in order. This
note begins our investigation of duality for CRDSA through bi-topological
spaces. More succinctly, duality through refinement of a pre- established
duality of pairwise Stone spaces and bounded distributive lattices. In this
note we establish necessary and sufficient conditions on a pairwise
zero-dimensional space such that it will have a core regular double Stone
algebra base. We note that these conditions can easily be relaxed to that which
is necessary for a pairwise zero-dimensional space to have a base that is not
as rigid as a CRDSA such as bounded distributive-pseudo complemented lattices
for example. Furthermore, these conditions give a topological representation
indicative of just how "nearly Boolean" CRDSA are, the closure of
non-clopen/complemented base elements are clopen/complemented base elements.
For the purposes of this note only we will call any pairwise zero-dimensional
space with a core regular double Stone algebra base a core regular double
pairwise zero-dimensional space. From that result we gain confidence to claim
that the category of core regular double Stone algebras is dually equivalent to
what we refer to in this note as the category of core regular double pairwise
Stone spaces. We validate this claim in the next note, Exploring Core Regular
Double Stone Algebras, CRDSA, III. Establishing Duality.
|
math.RA
|
this is the second in a series of three notes on an investigation into core regular double stone algebras crdsa which are meant to be read in order this note begins our investigation of duality for crdsa through bitopological spaces more succinctly duality through refinement of a pre established duality of pairwise stone spaces and bounded distributive lattices in this note we establish necessary and sufficient conditions on a pairwise zerodimensional space such that it will have a core regular double stone algebra base we note that these conditions can easily be relaxed to that which is necessary for a pairwise zerodimensional space to have a base that is not as rigid as a crdsa such as bounded distributivepseudo complemented lattices for example furthermore these conditions give a topological representation indicative of just how nearly boolean crdsa are the closure of nonclopencomplemented base elements are clopencomplemented base elements for the purposes of this note only we will call any pairwise zerodimensional space with a core regular double stone algebra base a core regular double pairwise zerodimensional space from that result we gain confidence to claim that the category of core regular double stone algebras is dually equivalent to what we refer to in this note as the category of core regular double pairwise stone spaces we validate this claim in the next note exploring core regular double stone algebras crdsa iii establishing duality
|
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|
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|
1,803.09339
|
Triangle geometry of the qubit state in the probability representation
expressed in terms of the triada of Malevich's Squares
|
We map the density matrix of the qubit (spin-1/2) state associated with the
Bloch sphere and given in the tomographic probability representation onto
vertices of a triangle determining Triada of Malevich's squares. The three
triangle vertices are located on three sides of another equilateral triangle
with the sides equal to $\sqrt 2$. We demonstrate that the triangle vertices
are in one-to-one correspondence with the points inside the Bloch sphere and
show that the uncertainty relation for the three probabilities of spin
projections +1/2 onto three orthogonal directions has the bound determined by
the triangle area introduced. This bound is related to the sum of three
Malevich's square areas where the squares have sides coinciding with the sides
of the triangle. We express any evolution of the qubit state as the motion of
the three vertices of the triangle introduced and interpret the gates of qubit
states as the semigroup symmetry of the Triada of Malevich's squares. In view
of the dynamical semigroup of the qubit-state evolution, we constructed
nonlinear representation of the group U(2).
|
quant-ph
|
we map the density matrix of the qubit spin12 state associated with the bloch sphere and given in the tomographic probability representation onto vertices of a triangle determining triada of malevichs squares the three triangle vertices are located on three sides of another equilateral triangle with the sides equal to sqrt 2 we demonstrate that the triangle vertices are in onetoone correspondence with the points inside the bloch sphere and show that the uncertainty relation for the three probabilities of spin projections 12 onto three orthogonal directions has the bound determined by the triangle area introduced this bound is related to the sum of three malevichs square areas where the squares have sides coinciding with the sides of the triangle we express any evolution of the qubit state as the motion of the three vertices of the triangle introduced and interpret the gates of qubit states as the semigroup symmetry of the triada of malevichs squares in view of the dynamical semigroup of the qubitstate evolution we constructed nonlinear representation of the group u2
|
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|
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|
1,803.0934
|
DeepVesselNet: Vessel Segmentation, Centerline Prediction, and
Bifurcation Detection in 3-D Angiographic Volumes
|
We present DeepVesselNet, an architecture tailored to the challenges faced
when extracting vessel networks or trees and corresponding features in 3-D
angiographic volumes using deep learning. We discuss the problems of low
execution speed and high memory requirements associated with full 3-D
convolutional networks, high-class imbalance arising from the low percentage of
vessel voxels, and unavailability of accurately annotated training data - and
offer solutions as the building blocks of DeepVesselNet.
First, we formulate 2-D orthogonal cross-hair filters which make use of 3-D
context information at a reduced computational burden. Second, we introduce a
class balancing cross-entropy loss function with false positive rate correction
to handle the high-class imbalance and high false positive rate problems
associated with existing loss functions. Finally, we generate synthetic dataset
using a computational angiogenesis model capable of generating vascular trees
under physiological constraints on local network structure and topology and use
these data for transfer learning.
DeepVesselNet is optimized for segmenting and analyzing vessels, and we test
the performance on a range of angiographic volumes including clinical MRA data
of the human brain, as well as X-ray tomographic microscopy scans of the rat
brain. Our experiments show that, by replacing 3-D filters with cross-hair
filters in our network, we achieve over 23% improvement in speed, lower memory
footprint, lower network complexity which prevents overfitting and comparable
accuracy (with a Cox-Wilcoxon paired sample significance test p-value of 0.07
when compared to full 3-D filters). Our class balancing metric is crucial for
training the network and transfer learning with synthetic data is an efficient,
robust, and very generalizable approach leading to a network that excels in a
variety of angiography segmentation tasks.
|
cs.CV
|
we present deepvesselnet an architecture tailored to the challenges faced when extracting vessel networks or trees and corresponding features in 3d angiographic volumes using deep learning we discuss the problems of low execution speed and high memory requirements associated with full 3d convolutional networks highclass imbalance arising from the low percentage of vessel voxels and unavailability of accurately annotated training data and offer solutions as the building blocks of deepvesselnet first we formulate 2d orthogonal crosshair filters which make use of 3d context information at a reduced computational burden second we introduce a class balancing crossentropy loss function with false positive rate correction to handle the highclass imbalance and high false positive rate problems associated with existing loss functions finally we generate synthetic dataset using a computational angiogenesis model capable of generating vascular trees under physiological constraints on local network structure and topology and use these data for transfer learning deepvesselnet is optimized for segmenting and analyzing vessels and we test the performance on a range of angiographic volumes including clinical mra data of the human brain as well as xray tomographic microscopy scans of the rat brain our experiments show that by replacing 3d filters with crosshair filters in our network we achieve over 23 improvement in speed lower memory footprint lower network complexity which prevents overfitting and comparable accuracy with a coxwilcoxon paired sample significance test pvalue of 007 when compared to full 3d filters our class balancing metric is crucial for training the network and transfer learning with synthetic data is an efficient robust and very generalizable approach leading to a network that excels in a variety of angiography segmentation tasks
|
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|
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|
1,803.09341
|
Dissecting stellar chemical abundance space with t-SNE
|
In the era of industrial Galactic astronomy and multi-object spectroscopic
stellar surveys, the sample sizes and the number of available stellar chemical
abundances have reached dimensions in which it has become difficult to process
all the available information in an effective manner. In this paper we
demonstrate the use of a dimensionality-reduction technique (t-distributed
stochastic neighbour embedding; t-SNE) for analysing the stellar
abundance-space distribution. While the non-parametric non-linear behaviour of
this technique makes it difficult to estimate the significance of found
abundance-space substructure, we show that our results depend little on
parameter choices and are robust to abundance errors. By reanalysing the
high-resolution high-signal-to-noise solar-neighbourhood HARPS-GTO sample with
t-SNE, we find clearer chemical separations of the high- and low-[$\alpha$/Fe]
disc sequences, hints for multiple populations in the high-[$\alpha$/Fe]
population, and indications that the chemical evolution of the
high-[$\alpha$/Fe] metal-rich stars is connected with the super-metal-rich
stars. We also identify a number of chemically peculiar stars, among them a
high-confidence s-process-enhanced abundance-ratio pair (HD91345/HD126681) with
very similar ages and $v_X$ and $v_Y$ velocities, which we suggest to have a
common birth origin, possibly a dwarf galaxy. Our results demonstrate the
potential of abundance-space t-SNE and similar methods for chemical-tagging
studies with large spectroscopic surveys.
|
astro-ph.GA astro-ph.SR
|
in the era of industrial galactic astronomy and multiobject spectroscopic stellar surveys the sample sizes and the number of available stellar chemical abundances have reached dimensions in which it has become difficult to process all the available information in an effective manner in this paper we demonstrate the use of a dimensionalityreduction technique tdistributed stochastic neighbour embedding tsne for analysing the stellar abundancespace distribution while the nonparametric nonlinear behaviour of this technique makes it difficult to estimate the significance of found abundancespace substructure we show that our results depend little on parameter choices and are robust to abundance errors by reanalysing the highresolution highsignaltonoise solarneighbourhood harpsgto sample with tsne we find clearer chemical separations of the high and lowalphafe disc sequences hints for multiple populations in the highalphafe population and indications that the chemical evolution of the highalphafe metalrich stars is connected with the supermetalrich stars we also identify a number of chemically peculiar stars among them a highconfidence sprocessenhanced abundanceratio pair hd91345hd126681 with very similar ages and v_x and v_y velocities which we suggest to have a common birth origin possibly a dwarf galaxy our results demonstrate the potential of abundancespace tsne and similar methods for chemicaltagging studies with large spectroscopic surveys
|
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|
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|
1,803.09342
|
DMTCP Checkpoint/Restart of MPI Programs via Proxies
|
MPI accomplishes portable, standardized message-passing between processes by
exposing a standard API that hides the implementation of the underlying
mechanism for message passing. Until now, checkpointing an MPI program required
knowledge of these underlying mechanisms. Through the addition of a proxy, we
demonstrate that MPI programs can be checkpointed and restarted regardless of
the MPI implementation utilized. Further, proxies may enable MPI programs to be
checkpointed on one MPI implementation, and restarted on another.
|
cs.DC
|
mpi accomplishes portable standardized messagepassing between processes by exposing a standard api that hides the implementation of the underlying mechanism for message passing until now checkpointing an mpi program required knowledge of these underlying mechanisms through the addition of a proxy we demonstrate that mpi programs can be checkpointed and restarted regardless of the mpi implementation utilized further proxies may enable mpi programs to be checkpointed on one mpi implementation and restarted on another
|
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|
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|
1,803.09343
|
$\xi$-completely continuous operators and $\xi$-Schur Banach spaces
|
For each ordinal $0\leqslant \xi\leqslant \omega_1$, we introduce the notion
of a $\xi$-completely continuous operator and prove that for each ordinal $0<
\xi< \omega_1$, the class $\mathfrak{V}_\xi$ of $\xi$-completely continuous
operators is a closed, injective operator ideal which is not surjective,
symmetric, or idempotent. We prove that for distinct $0\leqslant \xi,
\zeta\leqslant \omega_1$, the classes of $\xi$-completely continuous operators
and $\zeta$-completely continuous operators are distinct. We also introduce an
ordinal rank $\textsf{v}$ for operators such that $\textsf{v}(A)=\omega_1$ if
and only if $A$ is completely continuous, and otherwise $\textsf{v}(A)$ is the
minimum countable ordinal such that $A$ fails to be $\xi$-completely
continuous. We show that there exists an operator $A$ such that
$\textsf{v}(A)=\xi$ if and only if $1\leqslant \xi\leqslant \omega_1$, and
there exists a Banach space $X$ such that $\textsf{v}(I_X)=\xi$ if and only if
there exists an ordinal $\gamma\leqslant \omega_1$ such that
$\xi=\omega^\gamma$. Finally, prove that for every $0<\xi<\omega_1$, the class
$\{A\in \mathcal{L}: \textsf{v}(A) \geqslant \xi\}$ is $\Pi_1^1$-complete in
$\mathcal{L}$, the coding of all operators between separable Banach spaces.
This is in contrast to the class $\mathfrak{V}\cap \mathcal{L}$, which is
$\Pi_2^1$-complete in $\mathcal{L}$.
|
math.FA
|
for each ordinal 0leqslant xileqslant omega_1 we introduce the notion of a xicompletely continuous operator and prove that for each ordinal 0 xi omega_1 the class mathfrakv_xi of xicompletely continuous operators is a closed injective operator ideal which is not surjective symmetric or idempotent we prove that for distinct 0leqslant xi zetaleqslant omega_1 the classes of xicompletely continuous operators and zetacompletely continuous operators are distinct we also introduce an ordinal rank textsfv for operators such that textsfvaomega_1 if and only if a is completely continuous and otherwise textsfva is the minimum countable ordinal such that a fails to be xicompletely continuous we show that there exists an operator a such that textsfvaxi if and only if 1leqslant xileqslant omega_1 and there exists a banach space x such that textsfvi_xxi if and only if there exists an ordinal gammaleqslant omega_1 such that xiomegagamma finally prove that for every 0xiomega_1 the class ain mathcall textsfva geqslant xi is pi_11complete in mathcall the coding of all operators between separable banach spaces this is in contrast to the class mathfrakvcap mathcall which is pi_21complete in mathcall
|
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|
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|
1,803.09344
|
Large Deviations from the Hydrodynamic Limit for a System with Nearest
Neighbor Interactions
|
We give a new proof of the large deviation principle from the hydrodynamic
limit for the Ginzberg-Landau model studied in Donsker and Varadhan (1989)
using techniques from the theory of stochastic control and weak convergence
methods. The proof is based on characterizing subsequential hydrodynamic limits
of controlled diffusions with nearest neighbor interaction that arise from a
variational representation of certain Laplace functionals. The approach taken
here does not require superexponential probability estimates, estimation of
exponential moments, or an analysis of eigenvalue problems, that are central
ingredients in previous proofs. Instead, proof techniques are very similar to
those used for the law of large number analysis, namely in the proof of
convergence to the hydrodynamic limit (cf. Guo, Papanicolaou and Varadhan
(1988)). Specifically, the key step in the proof is establishing suitable
bounds on relative entropies and Dirichlet forms associated with certain
controlled laws. This general approach has the promise to be applicable to
other interacting particle systems as well and to the case of non-equilibrium
starting configurations, and to infinite volume systems.
|
math.PR
|
we give a new proof of the large deviation principle from the hydrodynamic limit for the ginzberglandau model studied in donsker and varadhan 1989 using techniques from the theory of stochastic control and weak convergence methods the proof is based on characterizing subsequential hydrodynamic limits of controlled diffusions with nearest neighbor interaction that arise from a variational representation of certain laplace functionals the approach taken here does not require superexponential probability estimates estimation of exponential moments or an analysis of eigenvalue problems that are central ingredients in previous proofs instead proof techniques are very similar to those used for the law of large number analysis namely in the proof of convergence to the hydrodynamic limit cf guo papanicolaou and varadhan 1988 specifically the key step in the proof is establishing suitable bounds on relative entropies and dirichlet forms associated with certain controlled laws this general approach has the promise to be applicable to other interacting particle systems as well and to the case of nonequilibrium starting configurations and to infinite volume systems
|
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|
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|
1,803.09345
|
Semilinear elliptic equations in thin regions with terms concentrating
on oscillatory boundaries
|
In this work we study the behavior of a family of solutions of a semilinear
elliptic equation, with homogeneous Neumann boundary condition, posed in a
two-dimensional oscillating thin region with reaction terms concentrated in a
neighborhood of the oscillatory boundary. Our main result is concerned with the
upper and lower semicontinuity of the set of solutions. We show that the
solutions of our perturbed equation can be approximated with ones of a
one-dimensional equation, which also captures the effects of all relevant
physical processes that take place in the original problem.
|
math.AP
|
in this work we study the behavior of a family of solutions of a semilinear elliptic equation with homogeneous neumann boundary condition posed in a twodimensional oscillating thin region with reaction terms concentrated in a neighborhood of the oscillatory boundary our main result is concerned with the upper and lower semicontinuity of the set of solutions we show that the solutions of our perturbed equation can be approximated with ones of a onedimensional equation which also captures the effects of all relevant physical processes that take place in the original problem
|
[['in', 'this', 'work', 'we', 'study', 'the', 'behavior', 'of', 'a', 'family', 'of', 'solutions', 'of', 'a', 'semilinear', 'elliptic', 'equation', 'with', 'homogeneous', 'neumann', 'boundary', 'condition', 'posed', 'in', 'a', 'twodimensional', 'oscillating', 'thin', 'region', 'with', 'reaction', 'terms', 'concentrated', 'in', 'a', 'neighborhood', 'of', 'the', 'oscillatory', 'boundary', 'our', 'main', 'result', 'is', 'concerned', 'with', 'the', 'upper', 'and', 'lower', 'semicontinuity', 'of', 'the', 'set', 'of', 'solutions', 'we', 'show', 'that', 'the', 'solutions', 'of', 'our', 'perturbed', 'equation', 'can', 'be', 'approximated', 'with', 'ones', 'of', 'a', 'onedimensional', 'equation', 'which', 'also', 'captures', 'the', 'effects', 'of', 'all', 'relevant', 'physical', 'processes', 'that', 'take', 'place', 'in', 'the', 'original', 'problem']]
|
[-0.16249914320472342, 0.06743064209573217, -0.08496573856797653, 0.01745355167620621, -0.05705056983752401, -0.10156453930476046, 0.002792302160882033, 0.2491307811540357, -0.27771252127118656, -0.24817549224410737, 0.12463608650224549, -0.29939831088931596, -0.1547116577052153, 0.20956034422084524, -0.04783593952575197, 0.07861003870205892, 0.09195224720227359, 0.05175096343097451, -0.06480098672333982, -0.21608693383961589, 0.40587739155187713, -0.04654014815709421, 0.21209135268825097, 0.040857351794429536, 0.07545169790091177, -0.07593325503518457, 0.03300129470753146, 0.04781204521410413, -0.18653296297854247, 0.12953984827330275, 0.22768188515104926, 0.03540530440059828, 0.2741707912799749, -0.4342165554535913, -0.2517472736967298, 0.11140515298101601, 0.15119281782676558, 0.09078543337834692, -0.04636285361925979, -0.2873015596664378, 0.07822658918327191, -0.11516669578338554, -0.2118625010793599, 0.00505505249500377, -0.0012406871582453067, 0.06824711603266033, -0.28315735548788395, 0.11618789375195494, 0.13095898850012447, 0.005945992018646243, -0.17871731613854785, -0.06406661635264754, -0.025646581726435285, 0.08255190111103129, 0.04889930182157064, 0.003492354378577547, 0.044467795348552226, -0.13533233764970287, -0.05022299137979664, 0.3619553066788825, -0.09853358474652191, -0.2645343966413658, 0.15757840304829918, -0.18216179401337446, -0.11093973010205306, 0.11584950743017944, 0.1812455341639509, 0.18626571925623076, -0.16089469579734153, 0.13060301708014027, -0.09584916332112318, 0.12611269167142122, 0.07853606231971183, 0.005550702174122517, 0.11206082811139033, 0.19099149231448423, 0.10068936928963432, 0.19110962434206158, 0.009266150404013448, -0.131651231210556, -0.3477701617220601, -0.1462361503259412, -0.1275793476616145, 0.08967989768096052, -0.09073971852818172, -0.23653798709894724, 0.3942184856079601, 0.13905809642132985, 0.22847271911226785, 0.0383040777696706, 0.23408928317028088, 0.20276681462364848, -0.01175139058230363, 0.0950026980110004, 0.20143184445511836, 0.12321484817580862, 0.11029134012242539, -0.21875931551311534, 0.060933646597582235, 0.11394125499486268]
|
1,803.09346
|
Mechanism Deduction from Noisy Chemical Reaction Networks
|
We introduce KiNetX, a fully automated meta-algorithm for the kinetic
analysis of complex chemical reaction networks derived from semi-accurate but
efficient electronic structure calculations. It is designed to (i) accelerate
the automated exploration of such networks, and (ii) cope with model-inherent
errors in electronic structure calculations on elementary reaction steps. We
developed and implemented KiNetX to possess three features. First, KiNetX
evaluates the kinetic relevance of every species in a (yet incomplete) reaction
network to confine the search for new elementary reaction steps only to those
species that are considered possibly relevant. Second, KiNetX identifies and
eliminates all kinetically irrelevant species and elementary reactions to
reduce a complex network graph to a comprehensible mechanism. Third, KiNetX
estimates the sensitivity of species concentrations toward changes in
individual rate constants (derived from relative free energies), which allows
us to systematically select the most efficient electronic structure model for
each elementary reaction given a predefined accuracy. The novelty of KiNetX
consists in the rigorous propagation of correlated free-energy uncertainty
through all steps of our kinetic analyis. To examine the performance of KiNetX,
we developed AutoNetGen. It semirandomly generates chemistry-mimicking reaction
networks by encoding chemical logic into their underlying graph structure.
AutoNetGen allows us to consider a vast number of distinct chemistry-like
scenarios and, hence, to discuss assess the importance of rigorous uncertainty
propagation in a statistical context. Our results reveal that KiNetX reliably
supports the deduction of product ratios, dominant reaction pathways, and
possibly other network properties from semi-accurate electronic structure data.
|
physics.chem-ph physics.data-an q-bio.MN
|
we introduce kinetx a fully automated metaalgorithm for the kinetic analysis of complex chemical reaction networks derived from semiaccurate but efficient electronic structure calculations it is designed to i accelerate the automated exploration of such networks and ii cope with modelinherent errors in electronic structure calculations on elementary reaction steps we developed and implemented kinetx to possess three features first kinetx evaluates the kinetic relevance of every species in a yet incomplete reaction network to confine the search for new elementary reaction steps only to those species that are considered possibly relevant second kinetx identifies and eliminates all kinetically irrelevant species and elementary reactions to reduce a complex network graph to a comprehensible mechanism third kinetx estimates the sensitivity of species concentrations toward changes in individual rate constants derived from relative free energies which allows us to systematically select the most efficient electronic structure model for each elementary reaction given a predefined accuracy the novelty of kinetx consists in the rigorous propagation of correlated freeenergy uncertainty through all steps of our kinetic analyis to examine the performance of kinetx we developed autonetgen it semirandomly generates chemistrymimicking reaction networks by encoding chemical logic into their underlying graph structure autonetgen allows us to consider a vast number of distinct chemistrylike scenarios and hence to discuss assess the importance of rigorous uncertainty propagation in a statistical context our results reveal that kinetx reliably supports the deduction of product ratios dominant reaction pathways and possibly other network properties from semiaccurate electronic structure data
|
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|
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|
1,803.09347
|
Jarzynski's equality, fluctuation theorems, and variance reduction:
Mathematical analysis and numerical algorithms
|
In this paper, we study Jarzynski's equality and fluctuation theorems for
diffusion processes. While some of the results considered in the current work
are known in the (mainly physics) literature, we review and generalize these
nonequilibrium theorems using mathematical arguments, therefore enabling
further investigations in the mathematical community. On the numerical side,
variance reduction approaches such as importance sampling method are studied in
order to compute free energy differences based on Jarzynski's equality.
|
math-ph math.MP
|
in this paper we study jarzynskis equality and fluctuation theorems for diffusion processes while some of the results considered in the current work are known in the mainly physics literature we review and generalize these nonequilibrium theorems using mathematical arguments therefore enabling further investigations in the mathematical community on the numerical side variance reduction approaches such as importance sampling method are studied in order to compute free energy differences based on jarzynskis equality
|
[['in', 'this', 'paper', 'we', 'study', 'jarzynskis', 'equality', 'and', 'fluctuation', 'theorems', 'for', 'diffusion', 'processes', 'while', 'some', 'of', 'the', 'results', 'considered', 'in', 'the', 'current', 'work', 'are', 'known', 'in', 'the', 'mainly', 'physics', 'literature', 'we', 'review', 'and', 'generalize', 'these', 'nonequilibrium', 'theorems', 'using', 'mathematical', 'arguments', 'therefore', 'enabling', 'further', 'investigations', 'in', 'the', 'mathematical', 'community', 'on', 'the', 'numerical', 'side', 'variance', 'reduction', 'approaches', 'such', 'as', 'importance', 'sampling', 'method', 'are', 'studied', 'in', 'order', 'to', 'compute', 'free', 'energy', 'differences', 'based', 'on', 'jarzynskis', 'equality']]
|
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|
1,803.09348
|
Cosmic-ray ionisation in circumstellar discs
|
Galactic cosmic rays are a ubiquitous source of ionisation of the
interstellar gas, competing with UV and X-ray photons as well as natural
radioactivity in determining the fractional abundance of electrons, ions and
charged dust grains in molecular clouds and circumstellar discs. We model the
propagation of different components of Galactic cosmic rays versus the column
density of the gas. Our study is focussed on the propagation at high densities,
above a few g cm$^{-2}$, especially relevant for the inner regions of
collapsing clouds and circumstellar discs. The propagation of primary and
secondary CR particles (protons and heavier nuclei, electrons, positrons, and
photons) is computed in the continuous slowing down approximation, diffusion
approximation, or catastrophic approximation, by adopting a matching procedure
for the different transport regimes. A choice of the proper regime depends on
the nature of the dominant loss process, modelled as continuous or
catastrophic. The CR ionisation rate is determined by CR protons and their
secondary electrons below $\approx 130$ g cm$^{-2}$ and by electron/positron
pairs created by photon decay above $\approx600$ g cm$^{-2}$. We show that a
proper description of the particle transport is essential to compute the
ionisation rate in the latter case, since the electron/positron differential
fluxes depend sensitively on the fluxes of both protons and photons. Our
results show that the CR ionisation rate in high-density environments, like,
e.g., the inner parts of collapsing molecular clouds or the mid-plane of
circumstellar discs, is larger than previously assumed. It does not decline
exponentially with increasing column density, but follows a more complex
behaviour due to the interplay of different processes governing the generation
and propagation of secondary particles.
|
astro-ph.HE
|
galactic cosmic rays are a ubiquitous source of ionisation of the interstellar gas competing with uv and xray photons as well as natural radioactivity in determining the fractional abundance of electrons ions and charged dust grains in molecular clouds and circumstellar discs we model the propagation of different components of galactic cosmic rays versus the column density of the gas our study is focussed on the propagation at high densities above a few g cm2 especially relevant for the inner regions of collapsing clouds and circumstellar discs the propagation of primary and secondary cr particles protons and heavier nuclei electrons positrons and photons is computed in the continuous slowing down approximation diffusion approximation or catastrophic approximation by adopting a matching procedure for the different transport regimes a choice of the proper regime depends on the nature of the dominant loss process modelled as continuous or catastrophic the cr ionisation rate is determined by cr protons and their secondary electrons below approx 130 g cm2 and by electronpositron pairs created by photon decay above approx600 g cm2 we show that a proper description of the particle transport is essential to compute the ionisation rate in the latter case since the electronpositron differential fluxes depend sensitively on the fluxes of both protons and photons our results show that the cr ionisation rate in highdensity environments like eg the inner parts of collapsing molecular clouds or the midplane of circumstellar discs is larger than previously assumed it does not decline exponentially with increasing column density but follows a more complex behaviour due to the interplay of different processes governing the generation and propagation of secondary particles
|
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|
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|
1,803.09349
|
Logistic Regression: The Importance of Being Improper
|
Learning linear predictors with the logistic loss---both in stochastic and
online settings---is a fundamental task in machine learning and statistics,
with direct connections to classification and boosting. Existing "fast rates"
for this setting exhibit exponential dependence on the predictor norm, and
Hazan et al. (2014) showed that this is unfortunately unimprovable. Starting
with the simple observation that the logistic loss is $1$-mixable, we design a
new efficient improper learning algorithm for online logistic regression that
circumvents the aforementioned lower bound with a regret bound exhibiting a
doubly-exponential improvement in dependence on the predictor norm. This
provides a positive resolution to a variant of the COLT 2012 open problem of
McMahan and Streeter (2012) when improper learning is allowed. This improvement
is obtained both in the online setting and, with some extra work, in the batch
statistical setting with high probability. We also show that the improved
dependence on predictor norm is near-optimal.
Leveraging this improved dependency on the predictor norm yields the
following applications: (a) we give algorithms for online bandit multiclass
learning with the logistic loss with an $\tilde{O}(\sqrt{n})$ relative mistake
bound across essentially all parameter ranges, thus providing a solution to the
COLT 2009 open problem of Abernethy and Rakhlin (2009), and (b) we give an
adaptive algorithm for online multiclass boosting with optimal sample
complexity, thus partially resolving an open problem of Beygelzimer et al.
(2015) and Jung et al. (2017). Finally, we give information-theoretic bounds on
the optimal rates for improper logistic regression with general function
classes, thereby characterizing the extent to which our improvement for linear
classes extends to other parametric and even nonparametric settings.
|
cs.LG stat.ML
|
learning linear predictors with the logistic lossboth in stochastic and online settingsis a fundamental task in machine learning and statistics with direct connections to classification and boosting existing fast rates for this setting exhibit exponential dependence on the predictor norm and hazan et al 2014 showed that this is unfortunately unimprovable starting with the simple observation that the logistic loss is 1mixable we design a new efficient improper learning algorithm for online logistic regression that circumvents the aforementioned lower bound with a regret bound exhibiting a doublyexponential improvement in dependence on the predictor norm this provides a positive resolution to a variant of the colt 2012 open problem of mcmahan and streeter 2012 when improper learning is allowed this improvement is obtained both in the online setting and with some extra work in the batch statistical setting with high probability we also show that the improved dependence on predictor norm is nearoptimal leveraging this improved dependency on the predictor norm yields the following applications a we give algorithms for online bandit multiclass learning with the logistic loss with an tildeosqrtn relative mistake bound across essentially all parameter ranges thus providing a solution to the colt 2009 open problem of abernethy and rakhlin 2009 and b we give an adaptive algorithm for online multiclass boosting with optimal sample complexity thus partially resolving an open problem of beygelzimer et al 2015 and jung et al 2017 finally we give informationtheoretic bounds on the optimal rates for improper logistic regression with general function classes thereby characterizing the extent to which our improvement for linear classes extends to other parametric and even nonparametric settings
|
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|
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|
1,803.0935
|
Fusion of Correlated Decisions Using Regular Vine Copulas
|
In this paper, we propose a regular vine copula based methodology for the
fusion of correlated decisions. Regular vine copula is an extremely flexible
and powerful graphical model to characterize complex dependence among multiple
modalities. It can express a multivariate copula by using a cascade of
bivariate copulas, the so-called pair copulas. Assuming that local detectors
are single threshold binary quantizers and taking complex dependence among
sensor decisions into account, we design an optimal fusion rule using a regular
vine copula under the Neyman-Pearson framework. In order to reduce the
computational complexity resulting from the complex dependence, we propose an
efficient and computationally light regular vine copula based optimal fusion
algorithm. Numerical experiments are conducted to demonstrate the effectiveness
of our approach.
|
eess.SP
|
in this paper we propose a regular vine copula based methodology for the fusion of correlated decisions regular vine copula is an extremely flexible and powerful graphical model to characterize complex dependence among multiple modalities it can express a multivariate copula by using a cascade of bivariate copulas the socalled pair copulas assuming that local detectors are single threshold binary quantizers and taking complex dependence among sensor decisions into account we design an optimal fusion rule using a regular vine copula under the neymanpearson framework in order to reduce the computational complexity resulting from the complex dependence we propose an efficient and computationally light regular vine copula based optimal fusion algorithm numerical experiments are conducted to demonstrate the effectiveness of our approach
|
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|
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|
1,803.09351
|
Invariants and CP violation in the 2HDM
|
We discuss the importance of basis invariants in the general 2HDM and how
these relates to masses and couplings. We also present a simple, yet powerful
technique to translate parameters of the potential into combinations of masses
and couplings of the theory and apply this to CP odd invariants.
|
hep-ph
|
we discuss the importance of basis invariants in the general 2hdm and how these relates to masses and couplings we also present a simple yet powerful technique to translate parameters of the potential into combinations of masses and couplings of the theory and apply this to cp odd invariants
|
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|
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|
1,803.09352
|
A Convergence Analysis on URV Refinement
|
Recently, Stewart gave an algorithm for computing a rank revealing URV
decomposition of a rectangular matrix. His method makes use of a refinement
iteration to achieve an improved estimate of the smallest singular value and
its corresponding singular vectors of the matrix. Here, a new proof is given
for the convergence of the refinement iteration. This analysis is carried out
under slightly weaker assumptions than those of Mathias and Stewart.
|
math.NA
|
recently stewart gave an algorithm for computing a rank revealing urv decomposition of a rectangular matrix his method makes use of a refinement iteration to achieve an improved estimate of the smallest singular value and its corresponding singular vectors of the matrix here a new proof is given for the convergence of the refinement iteration this analysis is carried out under slightly weaker assumptions than those of mathias and stewart
|
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|
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|
1,803.09353
|
Stochastic bandits robust to adversarial corruptions
|
We introduce a new model of stochastic bandits with adversarial corruptions
which aims to capture settings where most of the input follows a stochastic
pattern but some fraction of it can be adversarially changed to trick the
algorithm, e.g., click fraud, fake reviews and email spam. The goal of this
model is to encourage the design of bandit algorithms that (i) work well in
mixed adversarial and stochastic models, and (ii) whose performance
deteriorates gracefully as we move from fully stochastic to fully adversarial
models.
In our model, the rewards for all arms are initially drawn from a
distribution and are then altered by an adaptive adversary. We provide a simple
algorithm whose performance gracefully degrades with the total corruption the
adversary injected in the data, measured by the sum across rounds of the
biggest alteration the adversary made in the data in that round; this total
corruption is denoted by $C$. Our algorithm provides a guarantee that retains
the optimal guarantee (up to a logarithmic term) if the input is stochastic and
whose performance degrades linearly to the amount of corruption $C$, while
crucially being agnostic to it. We also provide a lower bound showing that this
linear degradation is necessary if the algorithm achieves optimal performance
in the stochastic setting (the lower bound works even for a known amount of
corruption, a special case in which our algorithm achieves optimal performance
without the extra logarithm).
|
cs.LG cs.DS cs.GT stat.ML
|
we introduce a new model of stochastic bandits with adversarial corruptions which aims to capture settings where most of the input follows a stochastic pattern but some fraction of it can be adversarially changed to trick the algorithm eg click fraud fake reviews and email spam the goal of this model is to encourage the design of bandit algorithms that i work well in mixed adversarial and stochastic models and ii whose performance deteriorates gracefully as we move from fully stochastic to fully adversarial models in our model the rewards for all arms are initially drawn from a distribution and are then altered by an adaptive adversary we provide a simple algorithm whose performance gracefully degrades with the total corruption the adversary injected in the data measured by the sum across rounds of the biggest alteration the adversary made in the data in that round this total corruption is denoted by c our algorithm provides a guarantee that retains the optimal guarantee up to a logarithmic term if the input is stochastic and whose performance degrades linearly to the amount of corruption c while crucially being agnostic to it we also provide a lower bound showing that this linear degradation is necessary if the algorithm achieves optimal performance in the stochastic setting the lower bound works even for a known amount of corruption a special case in which our algorithm achieves optimal performance without the extra logarithm
|
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|
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|
1,803.09354
|
Learning-Based Quality Control for Cardiac MR Images
|
The effectiveness of a cardiovascular magnetic resonance (CMR) scan depends
on the ability of the operator to correctly tune the acquisition parameters to
the subject being scanned and on the potential occurrence of imaging artefacts
such as cardiac and respiratory motion. In the clinical practice, a quality
control step is performed by visual assessment of the acquired images: however,
this procedure is strongly operator-dependent, cumbersome and sometimes
incompatible with the time constraints in clinical settings and large-scale
studies. We propose a fast, fully-automated, learning-based quality control
pipeline for CMR images, specifically for short-axis image stacks. Our pipeline
performs three important quality checks: 1) heart coverage estimation, 2)
inter-slice motion detection, 3) image contrast estimation in the cardiac
region. The pipeline uses a hybrid decision forest method - integrating both
regression and structured classification models - to extract landmarks as well
as probabilistic segmentation maps from both long- and short-axis images as a
basis to perform the quality checks. The technique was tested on up to 3000
cases from the UK Biobank as well as on 100 cases from the UK Digital Heart
Project, and validated against manual annotations and visual inspections
performed by expert interpreters. The results show the capability of the
proposed pipeline to correctly detect incomplete or corrupted scans (e.g. on UK
Biobank, sensitivity and specificity respectively 88% and 99% for heart
coverage estimation, 85% and 95% for motion detection), allowing their
exclusion from the analysed dataset or the triggering of a new acquisition.
|
cs.CV
|
the effectiveness of a cardiovascular magnetic resonance cmr scan depends on the ability of the operator to correctly tune the acquisition parameters to the subject being scanned and on the potential occurrence of imaging artefacts such as cardiac and respiratory motion in the clinical practice a quality control step is performed by visual assessment of the acquired images however this procedure is strongly operatordependent cumbersome and sometimes incompatible with the time constraints in clinical settings and largescale studies we propose a fast fullyautomated learningbased quality control pipeline for cmr images specifically for shortaxis image stacks our pipeline performs three important quality checks 1 heart coverage estimation 2 interslice motion detection 3 image contrast estimation in the cardiac region the pipeline uses a hybrid decision forest method integrating both regression and structured classification models to extract landmarks as well as probabilistic segmentation maps from both long and shortaxis images as a basis to perform the quality checks the technique was tested on up to 3000 cases from the uk biobank as well as on 100 cases from the uk digital heart project and validated against manual annotations and visual inspections performed by expert interpreters the results show the capability of the proposed pipeline to correctly detect incomplete or corrupted scans eg on uk biobank sensitivity and specificity respectively 88 and 99 for heart coverage estimation 85 and 95 for motion detection allowing their exclusion from the analysed dataset or the triggering of a new acquisition
|
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|
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|
1,803.09355
|
From quantum to classical dipole plasmon resonances in highly-doped
nano-crystals
|
Dipole plasmon resonances are ubiquitous in nano-particles with delocalized
charge carriers. Doped semi-conductor colloidal nano-crystals constitute a
novel paradigm for plasmon excitations in a finite electron system and offer
the possibility to tune the carrier density and thus the dipole resonance from
visible to infra-red, which cannot be achieved with metallic clusters.
Restricting ourselves to highly n-doped ZnO nano-crystals, we explain the
observed smooth transition from small sizes dominated by quantum effects to
large sizes where the resonance reaches its classical value. A schematic two
interacting highly degenerate level quantum model, validated by a full Random
Phase Approximation calculation, yields nicely the experimentally observed
trends.
|
physics.atm-clus
|
dipole plasmon resonances are ubiquitous in nanoparticles with delocalized charge carriers doped semiconductor colloidal nanocrystals constitute a novel paradigm for plasmon excitations in a finite electron system and offer the possibility to tune the carrier density and thus the dipole resonance from visible to infrared which cannot be achieved with metallic clusters restricting ourselves to highly ndoped zno nanocrystals we explain the observed smooth transition from small sizes dominated by quantum effects to large sizes where the resonance reaches its classical value a schematic two interacting highly degenerate level quantum model validated by a full random phase approximation calculation yields nicely the experimentally observed trends
|
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|
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|
1,803.09356
|
Neural Nets via Forward State Transformation and Backward Loss
Transformation
|
This article studies (multilayer perceptron) neural networks with an emphasis
on the transformations involved --- both forward and backward --- in order to
develop a semantical/logical perspective that is in line with standard program
semantics. The common two-pass neural network training algorithms make this
viewpoint particularly fitting. In the forward direction, neural networks act
as state transformers. In the reverse direction, however, neural networks
change losses of outputs to losses of inputs, thereby acting like a
(real-valued) predicate transformer. In this way, backpropagation is functorial
by construction, as shown earlier in recent other work. We illustrate this
perspective by training a simple instance of a neural network.
|
cs.NE cs.LG
|
this article studies multilayer perceptron neural networks with an emphasis on the transformations involved both forward and backward in order to develop a semanticallogical perspective that is in line with standard program semantics the common twopass neural network training algorithms make this viewpoint particularly fitting in the forward direction neural networks act as state transformers in the reverse direction however neural networks change losses of outputs to losses of inputs thereby acting like a realvalued predicate transformer in this way backpropagation is functorial by construction as shown earlier in recent other work we illustrate this perspective by training a simple instance of a neural network
|
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|
[-0.07823918954706571, 0.027931246968224653, -0.041914977722066954, 0.06077346982783638, -0.1532481532328977, -0.19746905455115035, 0.05588154879828485, 0.4641808641787905, -0.3330676901610926, -0.25855046587709624, 0.0413740755242403, -0.2149621137023832, -0.2579178957838359, 0.18512953565312693, -0.1326279998756945, 0.10607932312772252, 0.11505221085658726, 0.02583766202084147, -0.05775919639115902, -0.2458936634580963, 0.32344284556053865, 0.0795091872748274, 0.3499978759520253, -0.03653770950264656, 0.09242633510327253, -0.0010365994754605568, -0.01669645213181726, -0.005256744724017783, -0.023434810369858148, 0.17209931029356085, 0.3115660940708879, 0.1540417439223697, 0.34865901628150964, -0.4925566374395902, -0.2619398691164791, 0.0897367372840213, 0.11297050815147276, 0.13754493091367365, -0.006443794289505324, -0.28959820312089646, 0.052542298212826535, -0.18383268758547133, -0.02957564908473824, -0.09245731671734785, -0.010143945051263122, 0.013602760704368567, -0.2516516170312221, -0.05195943908676362, 0.15459333919884208, 0.07134802063676314, 0.011109474441932084, -0.08933911332860589, 0.0015584169707905788, 0.09194908116702348, 0.026138097007508174, 0.1087502563246884, 0.1221493155328342, -0.1656936319307603, -0.19048172493393606, 0.31010670069820034, -0.07108624867284491, -0.21630301360542384, 0.13354607899404633, -0.005658857369920812, -0.16871371854750367, 0.055269890576780126, 0.2333933437923686, 0.09094862097453398, -0.1835997320102671, 0.02905265169941301, -0.04112694589779354, 0.12880218539122815, 0.0560007930572073, -0.009578904929535033, 0.1497188278903755, 0.2438034050506898, 0.048699018406645894, 0.17018606858115304, -0.07135741067647289, -0.0995286019192113, -0.26614673210916895, -0.11701281751587746, -0.13858690535506377, 0.02140288974624127, -0.06319816865890551, -0.1596425365073978, 0.39116027393342495, 0.18305702555853015, 0.25535636400141254, 0.15049346119093782, 0.36205738621692246, 0.08050626845663199, 0.11239610724330235, 0.07235034658963112, 0.19370405536476307, 0.12229062045942275, 0.19716079248778093, -0.12336318457248406, 0.13038010008816714, 0.08742770808748901]
|
1,803.09357
|
On the Local Minima of the Empirical Risk
|
Population risk is always of primary interest in machine learning; however,
learning algorithms only have access to the empirical risk. Even for
applications with nonconvex nonsmooth losses (such as modern deep networks),
the population risk is generally significantly more well-behaved from an
optimization point of view than the empirical risk. In particular, sampling can
create many spurious local minima. We consider a general framework which aims
to optimize a smooth nonconvex function $F$ (population risk) given only access
to an approximation $f$ (empirical risk) that is pointwise close to $F$ (i.e.,
$\|F-f\|_{\infty} \le \nu$). Our objective is to find the
$\epsilon$-approximate local minima of the underlying function $F$ while
avoiding the shallow local minima---arising because of the tolerance
$\nu$---which exist only in $f$. We propose a simple algorithm based on
stochastic gradient descent (SGD) on a smoothed version of $f$ that is
guaranteed to achieve our goal as long as $\nu \le O(\epsilon^{1.5}/d)$. We
also provide an almost matching lower bound showing that our algorithm achieves
optimal error tolerance $\nu$ among all algorithms making a polynomial number
of queries of $f$. As a concrete example, we show that our results can be
directly used to give sample complexities for learning a ReLU unit.
|
cs.LG math.OC stat.ML
|
population risk is always of primary interest in machine learning however learning algorithms only have access to the empirical risk even for applications with nonconvex nonsmooth losses such as modern deep networks the population risk is generally significantly more wellbehaved from an optimization point of view than the empirical risk in particular sampling can create many spurious local minima we consider a general framework which aims to optimize a smooth nonconvex function f population risk given only access to an approximation f empirical risk that is pointwise close to f ie ff_infty le nu our objective is to find the epsilonapproximate local minima of the underlying function f while avoiding the shallow local minimaarising because of the tolerance nuwhich exist only in f we propose a simple algorithm based on stochastic gradient descent sgd on a smoothed version of f that is guaranteed to achieve our goal as long as nu le oepsilon15d we also provide an almost matching lower bound showing that our algorithm achieves optimal error tolerance nu among all algorithms making a polynomial number of queries of f as a concrete example we show that our results can be directly used to give sample complexities for learning a relu unit
|
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|
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|
1,803.09358
|
Radiative enhancement of single quantum emitters in WSe2 monolayers
using site-controlled metallic nano-pillars
|
Plasmonic nano-structures provides an efficient way to control and enhance
the radiative properties of quantum emitters. Coupling these structures to
single defects in low-dimensional materials provides a particularly promising
material platform to study emitter-plasmon interactions because these emitters
are not embedded in a surrounding dielectric. They can therefore approach a
near-field plasmonic mode to nanoscale distances, potentially enabling strong
light-matter interactions. However, this coupling requires precise alignment of
the emitters to the plasmonic mode of the structures, which is particularly
difficult to achieve in a site-controlled structure. We present a technique to
generate quantum emitters in 2D tungsten diselenide (WSe2) coupled to
site-controlled plasmonic nano-pillars. The plasmonic nano-pillars induce
strain in the two dimensional material which generates quantum emitters near
the high-field region of the plasmonic mode. The electric field of the
nano-pillar mode lies close to parallel with the two-dimensional material, and
is therefore in the correct orientation to couple to quantum emitters.
Interactions between the emitter and plasmonic mode result in an enhanced
spontaneous emission and increased brightness. This approach may enable bright
site-controlled non-classical light sources for applications in quantum
communication and optical quantum computing.
|
cond-mat.mes-hall physics.app-ph quant-ph
|
plasmonic nanostructures provides an efficient way to control and enhance the radiative properties of quantum emitters coupling these structures to single defects in lowdimensional materials provides a particularly promising material platform to study emitterplasmon interactions because these emitters are not embedded in a surrounding dielectric they can therefore approach a nearfield plasmonic mode to nanoscale distances potentially enabling strong lightmatter interactions however this coupling requires precise alignment of the emitters to the plasmonic mode of the structures which is particularly difficult to achieve in a sitecontrolled structure we present a technique to generate quantum emitters in 2d tungsten diselenide wse2 coupled to sitecontrolled plasmonic nanopillars the plasmonic nanopillars induce strain in the two dimensional material which generates quantum emitters near the highfield region of the plasmonic mode the electric field of the nanopillar mode lies close to parallel with the twodimensional material and is therefore in the correct orientation to couple to quantum emitters interactions between the emitter and plasmonic mode result in an enhanced spontaneous emission and increased brightness this approach may enable bright sitecontrolled nonclassical light sources for applications in quantum communication and optical quantum computing
|
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|
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|
1,803.09359
|
A Face Recognition Signature Combining Patch-based Features with Soft
Facial Attributes
|
This paper focuses on improving face recognition performance with a new
signature combining implicit facial features with explicit soft facial
attributes. This signature has two components: the existing patch-based
features and the soft facial attributes. A deep convolutional neural network
adapted from state-of-the-art networks is used to learn the soft facial
attributes. Then, a signature matcher is introduced that merges the
contributions of both patch-based features and the facial attributes. In this
matcher, the matching scores computed from patch-based features and the facial
attributes are combined to obtain a final matching score. The matcher is also
extended so that different weights are assigned to different facial attributes.
The proposed signature and matcher have been evaluated with the UR2D system on
the UHDB31 and IJB-A datasets. The experimental results indicate that the
proposed signature achieve better performance than using only patch-based
features. The Rank-1 accuracy is improved significantly by 4% and 0.37% on the
two datasets when compared with the UR2D system.
|
cs.CV
|
this paper focuses on improving face recognition performance with a new signature combining implicit facial features with explicit soft facial attributes this signature has two components the existing patchbased features and the soft facial attributes a deep convolutional neural network adapted from stateoftheart networks is used to learn the soft facial attributes then a signature matcher is introduced that merges the contributions of both patchbased features and the facial attributes in this matcher the matching scores computed from patchbased features and the facial attributes are combined to obtain a final matching score the matcher is also extended so that different weights are assigned to different facial attributes the proposed signature and matcher have been evaluated with the ur2d system on the uhdb31 and ijba datasets the experimental results indicate that the proposed signature achieve better performance than using only patchbased features the rank1 accuracy is improved significantly by 4 and 037 on the two datasets when compared with the ur2d system
|
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|
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|
1,803.0936
|
Stochastic Model of Breakdown Nucleation under Intense Electric Fields
|
Plastic response due to dislocation activity under intense electric fields is
proposed as a source of breakdown. A model is formulated based on stochastic
multiplication and arrest under the stress generated by the field. A critical
transition in the dislocation population is suggested as the cause of
protrusion formation leading to subsequent arcing. The model is studied using
Monte Carlo simulations and theoretical analysis, yielding a simplified
dependence of the breakdown rates on the electric field. These agree with
experimental observations of field and temperature breakdown dependencies.
|
physics.plasm-ph
|
plastic response due to dislocation activity under intense electric fields is proposed as a source of breakdown a model is formulated based on stochastic multiplication and arrest under the stress generated by the field a critical transition in the dislocation population is suggested as the cause of protrusion formation leading to subsequent arcing the model is studied using monte carlo simulations and theoretical analysis yielding a simplified dependence of the breakdown rates on the electric field these agree with experimental observations of field and temperature breakdown dependencies
|
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|
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|
1,803.09361
|
Low energy process $e^{+}e^{-} \rightarrow K^{+} K^{-}$ in the extended
Nambu-Jona-Lasinio model
|
In the extended Nambu-Jona-Lasinio model, the process of production of
charged kaon pair on colliding electron-positron beams in the energy interval 1
- 1.7 GeV is described. In studying of this process, we take into account the
contact terms when the pairs $K^{+}$ $K^{-}$ are generated by an intermediate
photon, and processes with intermediate vector mesons $\rho$, $\omega$ and
$\phi$ in the ground and in the first radially excited states. The results
obtained here are compared with experimental data recently received in
Novosibirsk and in Stanford.
|
hep-ph
|
in the extended nambujonalasinio model the process of production of charged kaon pair on colliding electronpositron beams in the energy interval 1 17 gev is described in studying of this process we take into account the contact terms when the pairs k k are generated by an intermediate photon and processes with intermediate vector mesons rho omega and phi in the ground and in the first radially excited states the results obtained here are compared with experimental data recently received in novosibirsk and in stanford
|
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|
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|
1,803.09362
|
PI Consensus Error Transformation for Adaptive Cooperative Control of
Nonlinear Multi-Agent Systems
|
A solution is provided in this note for the adaptive consensus problem of
nonlinear multi-agent systems with unknown and non-identical control directions
assuming a strongly connected underlying graph topology. This is achieved with
the introduction of a novel variable transformation called PI consensus error
transformation. %that allows for decoupled consensus control design of
multi-agent systems. The new variables include the position error of each agent
from some arbitrary fixed point along with an integral term of the weighted
total displacement of the agent's position from all neighbor positions. It is
proven that if these new variables are bounded and regulated to zero, then
asymptotic consensus among all agents is ensured. The important feature of this
transformation is that it provides input decoupling in the dynamics of the new
error variables making the consensus control design a simple and direct task.
Using classical Nussbaum gain based techniques, distributed controllers are
designed to regulate the PI consensus error variables to zero and ultimately
solve the agreement problem. The proposed approach also allows for a specific
calculation of the final consensus point based on the controller parameter
selection and the associated graph topology. Simulation results verify our
theoretical derivations.
|
cs.SY math.OC
|
a solution is provided in this note for the adaptive consensus problem of nonlinear multiagent systems with unknown and nonidentical control directions assuming a strongly connected underlying graph topology this is achieved with the introduction of a novel variable transformation called pi consensus error transformation that allows for decoupled consensus control design of multiagent systems the new variables include the position error of each agent from some arbitrary fixed point along with an integral term of the weighted total displacement of the agents position from all neighbor positions it is proven that if these new variables are bounded and regulated to zero then asymptotic consensus among all agents is ensured the important feature of this transformation is that it provides input decoupling in the dynamics of the new error variables making the consensus control design a simple and direct task using classical nussbaum gain based techniques distributed controllers are designed to regulate the pi consensus error variables to zero and ultimately solve the agreement problem the proposed approach also allows for a specific calculation of the final consensus point based on the controller parameter selection and the associated graph topology simulation results verify our theoretical derivations
|
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|
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|
1,803.09363
|
Opinion dynamics in two dimensions: domain coarsening leads to stable
bi-polarization and anomalous scaling exponents
|
We study an opinion dynamics model that explores the competition between
persuasion and compromise in a population of agents with nearest-neighbor
interactions on a two-dimensional square lattice. Each agent can hold either a
positive or a negative opinion orientation, and can have two levels of
intensity --moderate and extremist. When two interacting agents have the same
orientation become extremists with persuasion probability $p$, while if they
have opposite orientations become moderate with compromise probability $q$.
These updating rules lead to the formation of same-opinion domains with a
coarsening dynamics that depends on the ratio $r=p/q$. The population initially
evolves to a centralized state for small $r$, where domains are composed by
moderate agents and coarsening is without surface tension, and to a
bi-polarized state for large $r$, where domains are formed by extremist agents
and coarsening is driven by curvature. Consensus in an extreme opinion is
finally reached in a time that scales with the population size $N$ and $r$ as
$\tau \simeq r^{-1} \ln N$ for small $r$ and as $\tau \sim r^2 N^{1.64}$ for
large $r$. Bi-polarization could be quite stable when the system falls into a
striped state where agents organize into single-opinion horizontal, vertical or
diagonal bands. An analysis of the stripes dynamics towards consensus allows to
obtain an approximate expression for $\tau$ which shows that the exponent
$1.64$ is a result of the diffusion of the stripe interfaces combined with
their roughness properties.
|
physics.soc-ph
|
we study an opinion dynamics model that explores the competition between persuasion and compromise in a population of agents with nearestneighbor interactions on a twodimensional square lattice each agent can hold either a positive or a negative opinion orientation and can have two levels of intensity moderate and extremist when two interacting agents have the same orientation become extremists with persuasion probability p while if they have opposite orientations become moderate with compromise probability q these updating rules lead to the formation of sameopinion domains with a coarsening dynamics that depends on the ratio rpq the population initially evolves to a centralized state for small r where domains are composed by moderate agents and coarsening is without surface tension and to a bipolarized state for large r where domains are formed by extremist agents and coarsening is driven by curvature consensus in an extreme opinion is finally reached in a time that scales with the population size n and r as tau simeq r1 ln n for small r and as tau sim r2 n164 for large r bipolarization could be quite stable when the system falls into a striped state where agents organize into singleopinion horizontal vertical or diagonal bands an analysis of the stripes dynamics towards consensus allows to obtain an approximate expression for tau which shows that the exponent 164 is a result of the diffusion of the stripe interfaces combined with their roughness properties
|
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|
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|
1,803.09364
|
Extinction debt repayment via timely habitat restoration
|
Habitat destruction threatens the viability of many populations, but its full
consequences can take considerable time to unfold. Much of the discourse
surrounding extinction debts--the number of species that persist transiently
following habitat loss, despite being headed for extinction--frames ultimate
population crashes as the means of settling the debt. However, slow population
decline also opens an opportunity to repay the debt by restoring habitat. The
timing necessary for such habitat restoration to rescue a population from
extinction has not been well studied. Here we determine habitat restoration
deadlines for a spatially implicit Levins/Tilman population model modified by
an Allee effect. We find that conditions that hinder detection of an extinction
debt also provide forgiving restoration timeframes. Our results highlight the
importance of transient dynamics in restoration and suggest the beginnings of
an analytic theory to understand outcomes of temporary press perturbations in a
broad class of ecological systems.
|
q-bio.PE math.DS
|
habitat destruction threatens the viability of many populations but its full consequences can take considerable time to unfold much of the discourse surrounding extinction debtsthe number of species that persist transiently following habitat loss despite being headed for extinctionframes ultimate population crashes as the means of settling the debt however slow population decline also opens an opportunity to repay the debt by restoring habitat the timing necessary for such habitat restoration to rescue a population from extinction has not been well studied here we determine habitat restoration deadlines for a spatially implicit levinstilman population model modified by an allee effect we find that conditions that hinder detection of an extinction debt also provide forgiving restoration timeframes our results highlight the importance of transient dynamics in restoration and suggest the beginnings of an analytic theory to understand outcomes of temporary press perturbations in a broad class of ecological systems
|
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|
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|
1,803.09365
|
Finite Sample Complexity of Sequential Monte Carlo Estimators
|
We present bounds for the finite sample error of sequential Monte Carlo
samplers on static spaces. Our approach explicitly relates the performance of
the algorithm to properties of the chosen sequence of distributions and mixing
properties of the associated Markov kernels. This allows us to give the first
finite sample comparison to other Monte Carlo schemes. We obtain bounds for the
complexity of sequential Monte Carlo approximations for a variety of target
distributions including finite spaces, product measures, and log-concave
distributions including Bayesian logistic regression. The bounds obtained are
within a logarithmic factor of similar bounds obtainable for Markov chain Monte
Carlo.
|
stat.CO math.PR stat.ME
|
we present bounds for the finite sample error of sequential monte carlo samplers on static spaces our approach explicitly relates the performance of the algorithm to properties of the chosen sequence of distributions and mixing properties of the associated markov kernels this allows us to give the first finite sample comparison to other monte carlo schemes we obtain bounds for the complexity of sequential monte carlo approximations for a variety of target distributions including finite spaces product measures and logconcave distributions including bayesian logistic regression the bounds obtained are within a logarithmic factor of similar bounds obtainable for markov chain monte carlo
|
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|
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|
1,803.09366
|
High temperature antiferromagnetism in Yb based heavy fermion systems
proximate to a Kondo insulator
|
Given the parallelism between the physical properties of Ce and Yb based
magnets and heavy fermions due to the electron-hole symmetry, it has been
rather odd that the transition temperature of the Yb based compounds is
normally very small, as low as $\sim$ 1 K or even lower, whereas Ce
counterparts may often have the transition temperature well exceeding 10 K.
Here, we report our experimental discovery of the transition temperature
reaching 20 K for the first time in a Yb based compound at ambient pressure.
The Mn substitution at the Al site in an intermediate valence state of
$\alpha$-YbAlB$_{4}$ not only induces antiferromagnetic transition at a record
high temperature of 20 K but also transforms the heavy fermion liquid state in
$\alpha$-YbAlB$_{4}$ into a highly resistive metallic state proximate to a
Kondo insulator.
|
cond-mat.str-el
|
given the parallelism between the physical properties of ce and yb based magnets and heavy fermions due to the electronhole symmetry it has been rather odd that the transition temperature of the yb based compounds is normally very small as low as sim 1 k or even lower whereas ce counterparts may often have the transition temperature well exceeding 10 k here we report our experimental discovery of the transition temperature reaching 20 k for the first time in a yb based compound at ambient pressure the mn substitution at the al site in an intermediate valence state of alphaybalb_4 not only induces antiferromagnetic transition at a record high temperature of 20 k but also transforms the heavy fermion liquid state in alphaybalb_4 into a highly resistive metallic state proximate to a kondo insulator
|
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|
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|
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