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Recently, heatmap regression methods based on 1D landmark representations have shown prominent performance on locating facial landmarks. However, previous methods ignored to make deep explorations on the good potentials of 1D landmark representations for sequential and structural modeling of multiple landmarks to track facial landmarks. To address this limitation, we propose a Transformer architecture, namely 1DFormer, which learns informative 1D landmark representations by capturing the dynamic and the geometric patterns of landmarks via token communications in both temporal and spatial dimensions for facial landmark tracking. For temporal modeling, we propose a recurrent token mixing mechanism, an axis-landmark-positional embedding mechanism, as well as a confidence-enhanced multi-head attention mechanism to adaptively and robustly embed long-term landmark dynamics into their 1D representations; for structure modeling, we design intra-group and inter-group structure modeling mechanisms to encode the component-level as well as global-level facial structure patterns as a refinement for the 1D representations of landmarks through token communications in the spatial dimension via 1D convolutional layers. Experimental results on the 300VW and the TF databases show that 1DFormer successfully models the long-range sequential patterns as well as the inherent facial structures to learn informative 1D representations of landmark sequences, and achieves state-of-the-art performance on facial landmark tracking.
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https://arxiv.org/abs/2311.00241v2
|
In the absence of a sufficient amount of plasma injection into the black hole (BH) magnetosphere, the force-free state of the magnetosphere cannot be maintained, leading to the emergence of strong, time-dependent, longitudinal electric field (spark gap). Recent studies of supermassive BH magnetospheres by using analytical methods and particle-in-cell (PIC) simulations propose the possibility of the efficient particle acceleration and consequent gamma-ray emissions in the spark gap. In this work, we perform one-dimensional general relativistic PIC simulations to examine the gamma-ray emission from stellar-mass BH magnetospheres. We find that intermittent spark gaps emerge and particles are efficiently accelerated, in a similar manner to the supermassive BH case. We build a semi-analytic model of the plasma dynamics and radiative processes which reproduces the maximum electron energies and peak gamma-ray luminosities in the simulation results. Based on this model, we show that gamma-ray signals from stellar-mass BHs wandering through the interstellar medium could be detected by gamma-ray telescopes such as the Fermi Large Area Telescope, or the Cherenkov Telescope Array.
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https://arxiv.org/abs/2310.12532v2
|
We investigate the finite time stability property of one-dimensional nonautonomous initial boundary value problems for linear decoupled hyperbolic systems with nonlinear boundary conditions. We establish sufficient and necessary conditions under which continuous or $L^2$-generalized solutions stabilize to zero in a finite time. Our criteria are expressed in terms of a propagation operator along characteristic curves.
|
https://arxiv.org/abs/2208.00858v1
|
The study of privacy-preserving Natural Language Processing (NLP) has gained rising attention in recent years. One promising avenue studies the integration of Differential Privacy in NLP, which has brought about innovative methods in a variety of application settings. Of particular note are $\textit{word-level Metric Local Differential Privacy (MLDP)}$ mechanisms, which work to obfuscate potentially sensitive input text by performing word-by-word $\textit{perturbations}$. Although these methods have shown promising results in empirical tests, there are two major drawbacks: (1) the inevitable loss of utility due to addition of noise, and (2) the computational expensiveness of running these mechanisms on high-dimensional word embeddings. In this work, we aim to address these challenges by proposing $\texttt{1-Diffractor}$, a new mechanism that boasts high speedups in comparison to previous mechanisms, while still demonstrating strong utility- and privacy-preserving capabilities. We evaluate $\texttt{1-Diffractor}$ for utility on several NLP tasks, for theoretical and task-based privacy, and for efficiency in terms of speed and memory. $\texttt{1-Diffractor}$ shows significant improvements in efficiency, while still maintaining competitive utility and privacy scores across all conducted comparative tests against previous MLDP mechanisms. Our code is made available at: https://github.com/sjmeis/Diffractor.
|
https://arxiv.org/abs/2405.01678v1
|
Let $u$ be a non-negative super-solution to a $1$-dimensional singular
parabolic equation of $p$-Laplacian type ($1<p<2$). If $u$ is bounded below on
a time-segment $\{y\}\times(0,T]$ by a positive number $M$, then it has a
power-like decay of order $\frac p{2-p}$ with respect to the space variable $x$
in $\mathbb R\times[T/2,T]$. This fact, stated quantitatively in Proposition
1.1, is a "sidewise spreading of positivity" of solutions to such singular
equations, and can be considered as a form of Harnack inequality. The proof of
such an effect is based on geometrical ideas.
|
http://arxiv.org/abs/1503.07448v1
|
Given a compact geodesic space $X$ we apply the fundamental group and alternatively the first homology group functor to the corresponding Rips or \v{C}ech filtration of $X$ to obtain what we call a persistence. This paper contains the theory describing such persistence: properties of the set of critical points, their precise relationship to the size of holes, the structure of persistence and the relationship between open and close, Rips and \v{C}ech induced persistences. Amongst other results we prove that a Rips critical point $c$ corresponds to an isometrically embedded circle of length $3c$, that a homology persistence of a locally contractible space with coefficients in a field encodes the lengths of the lexicographically smallest base and that Rips and \v{C}ech induced persistences are isomorphic up to a factor $3/4$. The theory describes geometric properties of the underlying space encoded and extractable from persistence.
|
https://arxiv.org/abs/1709.05164v4
|
We introduce a new microeconomics foundation of a specific type of competitive market equilibrium that can be used to study several markets with information asymmetry such as commodity market, credit market, and insurance market.
|
https://arxiv.org/abs/2505.08425v1
|
In addition to being extremely non-linear, modern problems require millions if not billions of parameters to solve or at least to get a good approximation of the solution, and neural networks are known to assimilate that complexity by deepening and widening their topology in order to increase the level of non-linearity needed for a better approximation. However, compact topologies are always preferred to deeper ones as they offer the advantage of using less computational units and less parameters. This compacity comes at the price of reduced non-linearity and thus, of limited solution search space. We propose the 1-Dimensional Polynomial Neural Network (1DPNN) model that uses automatic polynomial kernel estimation for 1-Dimensional Convolutional Neural Networks (1DCNNs) and that introduces a high degree of non-linearity from the first layer which can compensate the need for deep and/or wide topologies. We show that this non-linearity enables the model to yield better results with less computational and spatial complexity than a regular 1DCNN on various classification and regression problems related to audio signals, even though it introduces more computational and spatial complexity on a neuronal level. The experiments were conducted on three publicly available datasets and demonstrate that, on the problems that were tackled, the proposed model can extract more relevant information from the data than a 1DCNN in less time and with less memory.
|
https://arxiv.org/abs/2009.04077v2
|
We consider one-dimensional self-similar solutions to the isentropic Euler system when the initial data are at vacuum to the left of the origin. For $x>0$ the initial velocity and sound speed are of form $u_0(x)=u_+x^{1-\lambda}$ and $c_0(x)=c_+x^{1-\lambda}$, for constants $u_+\in\RR$, $c_+>0$, $\lambda\in\RR$. We analyze the resulting solutions in terms of the similarity parameter $\lambda$, the adiabatic exponent $\gamma$, and the initial (signed) Mach number $\text{Ma}=u_+/c_+$. Restricting attention to locally bounded data, we find that when the sound speed initially decays to zero in a H\"older manner ($0<\lambda<1$), the resulting flow is always defined globally. Furthermore, there are three regimes depending on $\text{Ma}$: for sufficiently large positive $\text{Ma}$-values, the solution is continuous and the initial H\"older decay is immediately replaced by $C^1$-decay to vacuum along a stationary vacuum interface; for moderate values of $\text{Ma}$, the solution is again continuous and with an accelerating vacuum interface along which $c^2$ decays linearly to zero (i.e., a "physical singularity''); for sufficiently large negative $\text{Ma}$-values, the solution contains a shock wave emanating from the initial vacuum interface and propagating into the fluid, together with a physical singularity along an accelerating vacuum interface. In contrast, when the sound speed initially decays to zero in a $C^1$ manner ($\lambda<0$), a global flow exists only for sufficiently large positive values of $\text{Ma}$. Non-existence of global solutions for smaller $\text{Ma}$-values is due to rapid growth of the data at infinity and is unrelated to the presence of a vacuum.
|
https://arxiv.org/abs/2312.07689v1
|
Calculations in Ising model can be cumbersome and non-intuitive. Here we provide a formulation that addresses these issues for 1-D scenario. We represent the microstates of spin interactions as a diagonal matrix. This is done using two operations: Kronecker sum and Kronecker product. The calculations thus become simple matter of manipulating diagonal matrices. We address the following problems in this work: spins in the magnetic field, open-chain 1-D Ising model, closed-chain 1-D Ising model, 1-D Ising model in an external magnetic field. We believe that this representation will help provide students as well as experts with a simple yet powerful technique to carry out calculations in this model.
|
https://arxiv.org/abs/2011.00760v2
|
We study the 1d Ising model with long-range interactions decaying as $1/r^{1+s}$. The critical model corresponds to a family of 1d conformal field theories (CFTs) whose data depends nontrivially on $s$ in the range $1/2\leq s\leq 1$. The model is known to be described by a generalized free field with quartic interaction, which is weakly coupled near $s=1/2$ but strongly coupled near the short-range crossover at $s=1$. We propose a dual description which becomes weakly coupled at $s=1$. At $s=1$, our model becomes an exactly solvable conformal boundary condition for the 2d free scalar. We perform a number of consistency checks of our proposal and calculate the perturbative CFT data around $s=1$ analytically using both 1) our proposed field theory and 2) the analytic conformal bootstrap. Our results show complete agreement between the two methods.
|
https://arxiv.org/abs/2412.12243v2
|
We present a comparison of the observed, spatially integrated stellar and
ionized gas velocity dispersions of $\sim1000$ massive ($\log
M_{\star}/M_{\odot}\gtrsim\,10.3$) galaxies in the Large Early Galaxy
Astrophysics Census (LEGA-C) survey at $0.6\lesssim\,z\lesssim1.0$. The high
$S/N\sim20{\rm\AA^{-1}}$ afforded by 20 hour VLT/VIMOS spectra allows for joint
modeling of the stellar continuum and emission lines in all galaxies, spanning
the full range of galaxy colors and morphologies. These observed integrated
velocity dispersions (denoted as $\sigma'_{g, int}$ and $\sigma'_{\star, int}$)
are related to the intrinsic velocity dispersions of ionized gas or stars, but
also include rotational motions through beam smearing and spectral extraction.
We find good average agreement between observed velocity dispersions, with
$\langle\log(\sigma'_{g, int}/\sigma'_{\star, int})\rangle=-0.003$. This result
does not depend strongly on stellar population, structural properties, or
alignment with respect to the slit. However, in all regimes we find significant
scatter between $\sigma'_{g, int}$ and $\sigma'_{\star, int}$, with an overall
scatter of 0.13 dex of which 0.05 dex is due to observational uncertainties.
For an individual galaxy, the scatter between $\sigma'_{g, int}$ and
$\sigma'_{\star, int}$ translates to an additional uncertainty of
$\sim0.24\rm{dex}$ on dynamical mass derived from $\sigma'_{g, int}$, on top of
measurement errors and uncertainties from Virial constant or size estimates. We
measure the $z\sim0.8$ stellar mass Faber-Jackson relation and demonstrate that
emission line widths can be used to measure scaling relations. However, these
relations will exhibit increased scatter and slopes that are artificially
steepened by selecting on subsets of galaxies with progressively brighter
emission lines.
|
http://arxiv.org/abs/1811.07900v1
|
Orbital-free density functional theory promises to deliver linear-scaling electronic structure calculations. This requires the knowledge of the non-interacting kinetic-energy density functional (KEDF), which should be accurate and must admit accurate functional derivatives, so that a minimization procedure can be designed. In this work, symbolic regression is explored as an alternative means to machine-learn the KEDF, which results into analytical expressions, whose functional derivatives are easy to compute. The so-determined semi-local functional forms are investigated as a function of the electron number, and we are able to track the transition from the von Weizs\"acker functional, exact for the one-electron case, to the Thomas-Fermi functional, exact in the homogeneous electron gas limit. A number of separate searches are performed, ranging from totally unconstrained to constrained in the form of an enhancement factor. This work highlights the complexity in constructing semi-local approximations of the KEDF and the potential of symbolic regression to advance the search.
|
https://arxiv.org/abs/2412.08143v1
|
Using the inverse period map of the Gauss-Manin connection associated with $QH^{*}(\mathbb{CP}^2)$ and the Dubrovin construction of Landau-Ginzburg superpotential for Dubrovin Frobenius manifolds, we construct a one-dimensional Landau-Ginzburg superpotential for the quantum cohomology of $\mathbb{CP}^2$. In the case of small quantum cohomology, the Landau-Ginzburg superpotential is expressed in terms of the cubic root of the j-invariant function. For big quantum cohomology, the one-dimensional Landau-Ginzburg superpotential is given by Taylor series expansions whose coefficients are expressed in terms of quasi-modular forms. Furthermore, we express the Landau-Ginzburg superpotential for both small and big quantum cohomology of $QH^{*}(\mathbb{CP}^2)$ in closed form as the composition of the Weierstrass $\wp$-function and the universal coverings of $\mathbb{C} \setminus (\mathbb{Z} \oplus e^{\frac{\pi i}{3}}\mathbb{Z})$ and $\mathbb{C} \setminus (\mathbb{Z} \oplus z\mathbb{Z})$ respectively.
|
https://arxiv.org/abs/2402.09574v1
|
It is well known that symmetry protected topological (SPT) phases host
non-trivial boundaries that cannot be mimicked in a lower-dimensional system
with a conventional realization of symmetry. However, for SPT phases of bosons
(fermions) within the cohomology (supercohomology) classification the boundary
can be recreated without the bulk at the cost of a non-onsite symmetry action.
This raises the question: can one also mimic the boundaries of SPT phases which
lie outside the (super)cohomology classification? In this paper, we study this
question in the context of 2+1D fermion SPTs. We focus on the root SPT phase
for the symmetry group $G =Z_2 \times Z^f_2$. Starting with an exactly solvable
model for the bulk of this phase constructed by Tarantino and Fidkowski, we
derive an effective 1d lattice model for the boundary. Crucially, the Hilbert
space of this 1d model does not have a local tensor product structure, but
rather is obtained by placing a local constraint on a local tensor product
Hilbert space. We derive the action of the $Z_2$ symmetry on this Hilbert space
and find a simple 3-site Hamiltonian that respects this symmetry. We study this
Hamiltonian numerically using exact diagonalization and DMRG and find strong
evidence that it realizes an Ising CFT where the $Z_2$ symmetry acts as the
Kramers-Wannier duality; this is the expected stable gapless boundary state of
the present SPT. A simple modification of our construction realizes the
boundary of the 2+1D topological superconductor protected by time-reversal
symmetry ${\cal T}$ with ${\cal T}^2 = (-1)^{\cal F}$.
|
http://arxiv.org/abs/1902.05957v1
|
We demonstrate a 1D magneto-optical trap of the polar free radical calcium
monohydroxide (CaOH). A quasi-closed cycling transition is established to
scatter $\sim 10^3$ photons per molecule, predominantly limited by interaction
time. This enables radiative laser cooling of CaOH while compressing the
molecular beam, leading to a significant increase in on-axis beam brightness
and reduction in temperature from 8.4 mK to 1.4 mK.
|
http://arxiv.org/abs/2001.10525v2
|
Realizing Majorana modes in topological superconductors, i.e., the condensed-matter counterpart of Majorana fermions in particle physics, may lead to a major advance in the field of topologically-protected quantum computation. Here, we introduce one-dimensional, counterpropagating, and dispersive Majorana modes as bulk excitations of a periodic chain of partially-overlapping, zero-dimensional Majorana modes in proximitized nanowires via periodically-modulated fields. This system realizes centrally-extended quantum-mechanical supersymmetry with spontaneous partial supersymmetry breaking. The massless Majorana modes are the Nambu-Goldstone fermions (Goldstinos) associated with the spontaneously broken supersymmetry. Their experimental fingerprint is a dip-to-peak transition in the zero-bias conductance, which is generally not expected for Majorana modes overlapping at a finite distance. Moreover, the Majorana modes can slide along the wire by applying a rotating magnetic field, realizing a "Majorana pump". This may suggest new braiding protocols and implementations of topological qubits.
|
https://arxiv.org/abs/2106.09039v4
|
Recent work suggests that a sharp definition of `phase of matter' can be
given for periodically driven `Floquet' quantum systems exhibiting many-body
localization. In this work we propose a classification of the phases of
interacting Floquet localized systems with (completely) spontaneously broken
symmetries -- we focus on the one dimensional case, but our results appear to
generalize to higher dimensions. We find that the different Floquet phases
correspond to elements of $Z(G)$, the centre of the symmetry group in question.
In a previous paper we offered a companion classification of unbroken, i.e.,
paramagnetic phases.
|
http://arxiv.org/abs/1602.06949v2
|
Two-dimensional (2D) lateral heterojunctions of transition metal
dichalcogenides (TMDCs) have become a reality in recent years. Semiconducting
TMDC layers in their common H -structure have a nonzero in-plane electric
polarization, which is a topological invariant. We show by means of
first-principles calculations that lateral 2D heterojunctions between TMDCs
with a different polarization generate one-dimensional (1D) metallic states at
the junction, even in cases where the different materials are joined
epitaxially. The metallicity does not depend upon structural details, and is
explained from the change in topological invariant at the junction.
Nevertheless, these 1D metals are susceptible to 1D instabilities, such as
charge- and spin-density waves, making 2D TMDC heterojunctions ideal systems
for studying 1D physics.
|
http://arxiv.org/abs/2008.06758v1
|
We propose a one-dimensional (1D) model for the three-dimensional(3D) incompressible ideal magnetohydrodynamics. We establish a regularity criterion of the Beale-Kato-Majda type for this 1D model. Without the stretching effect, the model with only transport effect equipped with a proper sign is shown to have global in time strong solution. Some numerical simulations suggest that solutions of this model with smooth periodic initial data do not tend to develop singularities at finite time.
|
https://arxiv.org/abs/2107.02920v2
|
In this paper, we first remodel the line coverage as a 1D discrete problem
with co-linear targets. Then, an order-based greedy algorithm, called OGA, is
proposed to solve the problem optimally. It will be shown that the existing
order in the 1D modeling, and especially the resulted Markov property of the
selected sensors can help design greedy algorithms such as OGA. These
algorithms demonstrate optimal/efficient performance and have lower complexity
compared to the state-of-the-art. Furthermore, it is demonstrated that the
conventional continuous line coverage problem can be converted to an equivalent
discrete problem and solved optimally by OGA. Next, we formulate the well-known
weak barrier coverage problem as an instance of the continuous line coverage
problem (i.e. a 1D problem) as opposed to the conventional 2D graph-based
models. We demonstrate that the equivalent discrete version of this problem can
be solved optimally and faster than the state-of-the-art methods using an
extended version of OGA, called K-OGA. Moreover, an efficient local algorithm,
called LOGM, is proposed to mend barrier gaps due to sensor failure. In the
case of m gaps, LOGM is proved to select at most 2m-1 sensors more than the
optimal while being local and implementable in distributed fashion. We
demonstrate the optimal/efficient performance of the proposed algorithms via
extensive simulations.
|
http://arxiv.org/abs/1704.05576v1
|
A Coupled Natural Circulation Loop (CNCL) consists of two Natural Circulation
Loops (NCL) coupled thermally via a common heat exchanger. The transient
modelling of such systems that have practical relevance has not been reported
in the literature to the best of the author's knowledge. The present work aims
to bridge this gap and investigate the dynamic characteristics of a CNCL system
using a 1-D mathematical model. The validation of the model is accomplished by
comparison of the results obtained via 3-D CFD simulation. Both horizontal and
vertical CNCL systems have been considered for this study and behaviour of the
system for parallel and counter flow configurations in the heat exchanger
section is elaborated. Transient and steady state CFD analysis has been
conducted to analyse CNCL system for different heater and cooler orientations
and flow initialisation. The behaviour of the CNCL system is then examined by
carrying a thorough parametric study employing the validated 1-D single phase
CNCL model with liquid sodium as the operating fluid. The CNCL orientation
(vertical or horizontal) coupled with the heater and cooler configuration
determines the system dynamics and behaviour. The CNCL system also exhibits
chaotic flow oscillations at high heat loads.
|
http://arxiv.org/abs/1804.10051v1
|
Mott variable-range hopping is a fundamental mechanism for electron transport
in disordered solids in the regime of strong Anderson localization. We give a
brief description of this mechanism, recall some results concerning the
behavior of the conductivity at low temperature and describe in more detail
recent results (obtained in collaboration with N. Gantert and M. Salvi)
concerning the one-dimensional Mott variable-range hopping under an external
field.
|
http://arxiv.org/abs/1803.05166v2
|
Detailed chemical abundances of very metal-poor (VMP, [Fe/H] < -2) stars are important for better understanding the First Stars, early star formation and chemical enrichment of galaxies. Big on-going and coming high-resolution spectroscopic surveys provide a wealth of material that needs to be carefully analysed. For VMP stars, their elemental abundances should be derived based on the non-local thermodynamic equilibrium (non-LTE = NLTE) line formation because low metal abundances and low electron number density in the atmosphere produce the physical conditions favorable for the departures from LTE. The galactic archaeology research requires homogeneous determinations of chemical abundances. For this purpose, we present grids of the 1D-NLTE abundance corrections for the Na I, Mg I, Ca I, Ca II, Ti II, Fe I, Zn I, Zn II, Sr II, and Ba II lines, which are used in the galactic archaeology research. The range of atmospheric parameters represents VMP stars on various evolutionary stages and covers effective temperatures from 4000 to 6500~K, surface gravities from log g = 0.5 to log g = 5.0, and metallicities $-5.0 \le$ [Fe/H] $\le -2.0$. The data is publicly available, and we provide the tools for interpolating in the grids online.
|
https://arxiv.org/abs/2307.04523v1
|
We say that a knot $k_1$ in the $3$-sphere {\it $1$-dominates} another $k_2$
if there is a proper degree 1 map $E(k_1) \to E(k_2)$ between their exteriors,
and write $k_1 \ge k_2$. When $k_1 \ge k_2$ but $k_1 \ne k_2$ we write $k_1 >
k_2$. One expects in the latter eventuality that $k_1$ is more {\it
complicated}. In this paper we produce various sorts of evidence to support
this philosophy.
|
http://arxiv.org/abs/1511.07073v1
|
Neptune remains a mysterious world that deserves further exploration and is a
high-priority objective for a future planetary mission in order to better
understand the formation and evolution of ice giant planets. We have developed
a coupled ion-neutral 1D photochemical model of Neptune's atmosphere to study
the origin and evolution of the hydrocarbons and the oxygen species. The
up-to-date chemical scheme is derived from one used for Titan's atmosphere,
which led to good agreements with the Cassini-CIRS observations for oxygen
species and the main hydrocarbons. The main results we obtain are the
following: The ion-neutral chemistry coupling produces aromatics (and benzene
in particular) in the atmosphere of Neptune with relatively high abundances.
Our model results are in good agreement with observations (taking model
uncertainties into account). Two ionospheric peaks are present in the
atmosphere located above the pressure level of 10$^{-5}$ mbar and around
10$^{-3}$ mbar. The influx of oxygen species in the upper atmosphere of Neptune
has an effect on the concentration of many ions. We show that in situ
exploration of Neptune's atmosphere would provide very interesting constraints
for photochemical models concerning in particular the origin of oxygen species
and the contribution of ion chemistry. A precise description of upper
atmospheric chemistry is crucial for a better understanding of the internal
composition and the formation processes of this planet.
|
http://arxiv.org/abs/2011.07984v1
|
The design and development of new photonic devices for technological applications requires a deep understanding of the effect of structural properties on the resulting band gap size and its position. Here, we perform a theoretical study of behavior of the photonic band gap sizes, positions and percentages under variations of the parameters characterizing binary (two materials), ternary (three materials) and linear dielectric grating multilayer structures. The resulting band gap atlas show that binary systems may suffice for most applications but ternary systems may add additional flexibility in design if needed. Linear gratings show a regular pattern for all gaps studied, this regularity was able to be reproduced with only few materials involved. The position of the gaps showed a very monotonous behavior for all calculations performed. Finally, additional extensions of formulas commonly used in the design of Bragg mirrors/reflectors using binary materials were proposed with their corresponding limitations discussed. These results can be seen as a technological horizon for photonic device development.
|
https://arxiv.org/abs/2405.13633v1
|
GeSn alloys have been regarded as a potential lasing material for a complementary metal-oxide-semiconductor (CMOS)-compatible light source. Despite their remarkable progress, all GeSn lasers reported to date have large device footprints and active areas, which prevent the realization of densely integrated on-chip lasers operating at low power consumption. Here, we present a 1D photonic crystal (PC) nanobeam with a very small device footprint of 7 ${\mu}m^2$ and a compact active area of ~1.2 ${\mu}m^2$ on a high-quality GeSn-on-insulator (GeSnOI) substrate. We also report that the improved directness in our strain-free nanobeam lasers leads to a lower threshold density and a higher operating temperature compared to the compressive strained counterparts. The threshold density of the strain-free nanobeam laser is ~18.2 kW cm$^{ -2}$ at 4 K, which is significantly lower than that of the unreleased nanobeam laser (~38.4 kW cm$^{ -2}$ at 4 K). Lasing in the strain-free nanobeam device persists up to 90 K, whereas the unreleased nanobeam shows a quenching of the lasing at a temperature of 70 K. Our demonstration offers a new avenue towards developing practical group-IV light sources with high-density integration and low power consumption.
|
https://arxiv.org/abs/2108.06142v2
|
The space electron-ion-positive dust plasma system containing isothermal
inertialess electron species, cold inertial ion species, and stationary
positive (positivively charged) dust species is considered. The basic features
of one dimensional (1D) planar and nonplanar subsonic solitary waves are
investigated by the pseudo-potential and reductive perturbation methods,
respectively. It is observed that the presence of the positive dust species
reduces the phase speed of the ion-acoustic waves, and consequently supports
the subsonic solitary waves with the positive wave potential in such a space
dusty plasma system. It is observed that the cylindrical and spherical subsonic
solitary waves significantly evolve with time, and that the time evolution of
the spherical solitary waves is faster than that of the cylindrical ones. The
applications of the work in many space dusty plasma systems, particularly in
Earth's mesosphere, cometary tails, Jupiter's magnetosphere, etc. are
addressed.
|
http://arxiv.org/abs/2009.09131v1
|
With increasing miniaturization of diagnostic devices for more effective detection of blood-borne pathogens for example, Poiseuille molecular flow in micro channels has become increasingly relevant. Since continuum mechanics no longer applies for Poiseuille flow when the Knudson number is near or larger than unity, kinetic theory is required to capture the microscopic molecular scattering responsible for channel molecular flow and the velocity profile across a channel. Here, we apply a response matrix solution to the 1D Poiseuille flow with a BGK approximation featuring simplicity with precision by following a consistent numerical formulation leading to high precision, 8-place benchmarks.
|
https://arxiv.org/abs/2406.16954v1
|
We construct explicit measure-valued solutions to the one-dimensional pressureless gas dynamics system in a strip-like domain by introducing a new boundary potential. The constructed solutions satisfy an entropy condition, and depending on the boundary data and the behavior of the potentials, mass accumulation can occur at the boundaries. The approach relies on a systematic treatment of boundary potentials and their interactions with the initial data, providing a more precise understanding of the formation and propagation of singularities in measure-valued solutions.
|
https://arxiv.org/abs/2502.15927v2
|
Magnetic resonance imaging (MRI) is mainly limited by long scanning time and vulnerable to human tissue motion artifacts, in 3D clinical scenarios. Thus, k-space undersampling is used to accelerate the acquisition of MRI while leading to visually poor MR images. Recently, some studies 1) use effective undersampling patterns, or 2) design deep neural networks to improve the quality of resulting images. However, they are considered as two separate optimization strategies. In this paper, we propose a cross-domain network for MR image reconstruction, in a retrospective data-driven manner, under limited sampling rates. Our method can simultaneously obtain the optimal undersampling pattern (in k-space) and the reconstruction model, which are customized to the type of training data, by using an end-to-end learning strategy. We propose a 1D probabilistic undersampling layer, to obtain the optimal undersampling pattern and its probability distribution in a differentiable way. We propose a 1D inverse Fourier transform layer, which connects the Fourier domain and the image domain during the forward pass and the backpropagation. In addition, by training 3D fully-sampled k-space data and MR images with the traditional Euclidean loss, we discover the universal relationship between the probability distribution of the optimal undersampling pattern and its corresponding sampling rate. Experiments show that the quantitative and qualitative results of recovered MR images by our 1D probabilistic undersampling pattern obviously outperform those of several existing sampling strategies.
|
https://arxiv.org/abs/2003.03797v3
|
In this paper we prove an infinite dimensional KAM theorem, in which the
assumptions on the derivatives of perturbation in \cite{GT} are weakened from
polynomial decay to logarithmic decay. As a consequence, we apply it to 1d
quantum harmonic oscillators and prove the reducibility of a linear harmonic
oscillator, $T=- \frac{d^2}{dx^2}+x^2$, on $L^2(\R)$ perturbed by a
quasi-periodic in time potential $V(x,\omega t; \omega)$ with logarithmic
decay. This entails the pure-point nature of the spectrum of the Floquet
operator $K$, where K:=-{\rm i}\sum_{k=1}^n\omega_k\frac{\partial}{\partial
\theta_k}- \frac{d^2}{dx^2}+x^2+\varepsilon V(x,\theta;\omega), is defined on
$L^2(\R) \otimes L^2(\T^n)$ and the potential $V(x,\theta;\omega)$ has
logarithmic decay as well as its gradient in $\omega$.
|
http://arxiv.org/abs/1605.05480v1
|
For a family of 1-d quantum harmonic oscillator with a perturbation which is $C^2$ parametrized by $E\in{\mathcal I}\subset{\Bbb R}$ and quadratic on $x$ and $-{\rm i}\partial_x$ with coefficients quasi-periodically depending on time $t$, we show the reducibility (i.e., conjugation to time-independent) for a.e. $E$. As an application of reducibility, we describe the behaviors of solution in Sobolev space: -- Boundedness w.r.t. $t$ is always true for "most" $E\in{\mathcal I}$. -- For "generic" time-dependent perturbation, polynomial growth and exponential growth to infinity w.r.t. $t$ occur for $E$ in a "small" part of ${\mathcal I}$. Concrete examples are given for which the growths of Sobolev norm do occur.
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https://arxiv.org/abs/2003.13034v2
|
Local topological markers are effective tools for determining the topological properties of both homogeneous and inhomogeneous systems. The Chern marker is an established topological marker that has previously been shown to effectively reveal the topological properties of 2D systems. In an earlier work, the present authors have developed a marker that can be applied to 1D time-dependent systems which can be used to explore their topological properties, like charge pumping under the presence of disorder. In this paper, we show how to alter the 1D marker so that it can be applied to quasiperiodic and aperiodic systems. We then verify its effectiveness against different quasicrystal Hamiltonians, some which have been addressed in previous studies using existing methods, and others which possess topological structures that have been largely unexplored. We also demonstrate that the altered 1D marker can be productively applied to systems that are fully aperiodic.
|
https://arxiv.org/abs/2201.09741v2
|
Filaments are ubiquitous in astronomical data sets. Be it in particle simulations or observations, filaments are always tracers of a perturbation in the equilibrium of the studied system and hold essential information on its history and future evolution. However, the recovery of such structures is often complicated by the presence of a large amount of background and transverse noise in the observation space. While the former is generally detrimental to the analysis, the latter can be attributed to measurement errors and it can hold essential information about the structure. To further complicate the scenario, 1D manifolds (filaments) are generally non-linear and their geometry difficult to extract and model. In order to study hidden manifolds within the dataset, particular care has to be devoted to background noise removal and transverse noise modelling, while still maintaining accuracy in the recovery of their geometrical structure. We propose 1-DREAM: a toolbox composed of five main Machine Learning methodologies whose aim is to facilitate manifold extraction in such cases. Each methodology has been designed to address issues when dealing with complicated low-dimensional structures convoluted with noise and it has been extensively tested in previously published works. In this work all methodologies are presented in detail, joint within a cohesive framework and demonstrated for three interesting astronomical cases: a simulated jellyfish galaxy, a filament extracted from a simulated cosmic web and the stellar stream of Omega-Centauri as observed with the GAIA DR2. Two newly developed visualization techniques are also proposed, that take full advantage of the results obtained with 1-DREAM. The code is made publicly available to benefit the community. The controlled experiments on a purposefully built data set prove the accuracy of the pipeline in recovering the hidden structures.
|
https://arxiv.org/abs/2503.21584v1
|
In this article, we present our contribution to the ICPHM 2023 Data Challenge on Industrial Systems' Health Monitoring using Vibration Analysis. For the task of classifying sun gear faults in a gearbox, we propose a residual Convolutional Neural Network that operates on raw three-channel time-domain vibration signals. In conjunction with data augmentation and regularization techniques, the proposed model yields very good results in a multi-class classification scenario with real-world data despite its relatively small size, i.e., with less than 30,000 trainable parameters. Even when presented with data obtained from multiple operating conditions, the network is still capable to accurately predict the condition of the gearbox under inspection.
|
https://arxiv.org/abs/2304.07305v2
|
The influence of surface constraints on the self-assembly of liquid droplets
is investigated. A semi-quantitative explanation for large scale pattern
formation consisting of small scale closely arranged droplets inside the large
scale distorted ring of droplets is presented in this paper. The scale at which
the influence of constraints become dominant is also determined in this study.
It is seen that the underlying roughness has a larger impact than the nature of
polymer on pore size. Comparative studies of pore patterns formed on smooth and
constrained substrates are reported. The simulated energy minimized shape of
the droplets on smooth and constrained substrates are obtained using
\textit{Surface Evolver}.
|
http://arxiv.org/abs/1605.02942v2
|
On a star graph $G$ with $n = n_+ + n_-$ edges of unit length, we study the operator $-\frac{\mathrm{d}^2}{\mathrm{d} x^2}$ on $n_+$ and $\frac{\mathrm{d}^2}{\mathrm{d} x^2}$ on $n_-$ edges equipped with Dirichlet boundary conditions at the outer vertices and a Kirchhoff condition at the central vertex. We study the spectral properties of the corresponding indefinite Kirchhoff Laplacian on $G$ and we show that it is similar to a selfadjoint operator in the Hilbert space $L^2(G)$ and that its eigenfunctions form a Riesz basis. Furthermore, we give a complete description of the point spectrum.
|
https://arxiv.org/abs/2505.22901v1
|
We consider a Schr\"odinger operator with complex-valued potentials on the
line. The operator has essential spectrum on the half-line plus eigenvalues
(counted with algebraic multiplicity) in the complex plane without the positive
half-line. We determine series of trace formulas. Here we have the new term: a
singular measure, which is absent for real potentials. Moreover, we estimate of
sum of Im part of eigenvalues plus singular measure in terms of the norm of
potentials. The proof is based on classical results about the Hardy spaces.
|
http://arxiv.org/abs/1909.08454v1
|
Since the first experimental observation of optical Airy beams, various applications ranging from particle and cell micromanipulation to laser micromachining have exploited their non-diffracting and accelerating properties. The later discovery that Airy beams can self-heal after being blocked by an obstacle further proved their robustness to propagate under scattering and disordered environment. Here, we report the generation of Airy beams on an integrated silicon photonic chip and demonstrate that the on-chip 1D Airy beams preserve the same properties as the 2D beams. The 1D meta-optics used to create the Airy beam has the size of only 3 by 16 microns, at least three orders of magnitude smaller than the conventional optic. The on-chip self-healing beams demonstrated here could potentially enable diffraction-free light routing for on-chip optical networks and high-precision micromanipulation of bio-molecules on an integrated photonic chip.
|
https://arxiv.org/abs/2103.12254v1
|
We establish asymptotics of growing one dimensional self-similar fractal graphs, they are networks that allow multiple weighted edges between nodes, in terms of quantum central limit theorems for algebraic probability spaces in pure state. An additional structure is endowed with the repeating units of centro-symmetric Jacobians in the adjacency of a linear graph creating a self-similar fractal. The family of fractals induced by centro-symmetric Jacobians formulated as orthogonal polynomials that satisfy three term recurrence relations support such limits. The construction proceeds with the interacting fock spaces, T-algebras endowed with a quantum probability space, corresponding to the Jacobi coefficients of the recurrence relations and when some elements of the centro-symmetric matrix are constrained in a specific way we obtain, as the same Jacobian structure is repeated, the central limits. The generic formulation of Leonard pairs that form bases of conformal blocks and probablistic laplacians used in physics provide choice of centro-symmetric Jacobians widening the applicability of the result. We establish that the T-algebras of these 1D fractals, as they form a special class of distance-regular graphs, are thin and the induced association schemes are self-duals that lead to anyon systems with modular invariance.
|
https://arxiv.org/abs/2401.15515v1
|
The study of heat exchangers with both the hot and cold fluid sides driven by
buoyancy forces is an area of considerable interest due to their inherent
passivity and non-existence of moving parts. The current study aims to study
such heat exchange devices employing the basic Coupled Natural Circulation Loop
(CNCL) systems. A 1-D Fourier series based semi-analytical model of the basic
CNCL system is proposed. A 3-D CFD validation is performed to validate the
developed 1-D model. The non-dimensional numbers such as Grashof number,
Fourier number, Stanton number and Reynolds number, which determine the system
behavior are identified and a detailed parametric study is performed. Both
vertical and horizontal CNCL systems are considered along with the parallel and
counter flow configurations. The heater-cooler location greatly influences the
behavior of CNCL system. The vertical CNCL always exhibits counter flow
configuration whereas the horizontal CNCL system may exhibit parallel or
counter flow arrangement depending on the heater-cooler location and initial
flow conditions.
|
http://arxiv.org/abs/1811.08074v1
|
Analytical/quasi-analytical solutions are proposed for a steady, compressible, two-phase flow in mechanical equilibrium in a rectilinear duct subjected to heating followed by cooling. The flow is driven by the pressure ratio between a variable outlet pressure and an upstream tank. A critical pressure ratio distinguishes subsonic and supersonic outlet regimes: the article proposes a methodology to determine the full flow behaviour, as a function of pressure ratio and heat-flux distribution. Going forward, these analytical reference solutions will help validate numerical codes for more complex industrial applications. Specific results are studied for a mixture of liquid water and water vapour.
|
https://arxiv.org/abs/2404.10345v1
|
A study of the one-dimensional molecular chain (MC) with two single-particle degenerate states is presented. We establish connection of the MC with the Ising model with phononic interactions and investigate properties of the model using a transfer matrix method. The transfer matrix method offers a promising pathway for simulating such materials properties. The role of degeneracy of states and phononic interaction being made explicit. We analyze regimes of the system and parameters of the occurring crossover. Here, we present exact results for the magnetization per spin, the correlation function and the effective volume of the system. We demonstrate possibility of existence of two peaks in the specific heat capacity thermal behavior.
|
https://arxiv.org/abs/2102.13627v2
|
Spontaneous symmetry breaking generally circumvents one-dimensional systems with local interactions in thermal equilibrium. Here, we analyze a category of one-dimensional Hermitian models via local non-Hermitian constructions. Notably, spontaneous symmetry breaking and long-range order may emerge at finite temperatures in such systems under periodic boundary conditions, in sharp contrast to Hermitian constructions. We demonstrate clear numerical evidence, such as order parameters and specific heat, supporting phase diagrams with robust ordered phases. Non-Hermitian physics plays a vital role in prohibiting domain-wall proliferation and promoting spontaneous symmetry breaking. The fermions exhibit an exotic topological nature in their path-integral windings, which uphold nonzero integers -- commonly a non-Hermitian signature -- in the ordered phases, thus offering a novel and spontaneous origin for both symmetry breaking and non-Hermiticity.
|
https://arxiv.org/abs/2410.19052v1
|
Airborne electromagnetic surveys may consist of hundreds of thousands of soundings. In most cases, this makes 3D inversions unfeasible even when the subsurface is characterized by a high level of heterogeneity. Instead, approaches based on 1D forwards are routinely used because of their computational efficiency. However, it is relatively easy to fit 3D responses with 1D forward modelling and retrieve apparently well-resolved conductivity models. However, those detailed features may simply be caused by fitting the modelling error connected to the approximate forward. In addition, it is, in practice, difficult to identify this kind of artifacts as the modeling error is correlated. The present study demonstrates how to assess the modelling error introduced by the 1D approximation and how to include this additional piece of information into a probabilistic inversion. Not surprisingly, it turns out that this simple modification provides not only much better reconstructions of the targets but, maybe, more importantly, guarantees a correct estimation of the corresponding reliability.
|
https://arxiv.org/abs/2109.13780v1
|
We study unique solvability for one dimensional stochastic pressure equation with diffusion coefficient given by the Wick exponential of log-correlated Gaussian fields. We prove well-posedness for Dirichlet, Neumann and periodic boundary data, and the initial value problem, covering the cases of both the Wick renormalization of the diffusion and of point-wise multiplication. We provide explicit representations for the solutions in both cases, characterized by the $S$-transform and the Gaussian multiplicative chaos measure.
|
https://arxiv.org/abs/2402.09127v1
|
We study two homogeneous supersymmetric extensions for the $f(R)$ modified gravity model of Starobinsky with the FLRW metric. The actions are defined in terms of a superfield $\mathcal{R}$ that contains the FLRW scalar curvature. One model has N=1 local supersymmetry, and its bosonic sector is the Starobinsky action; the other action has N=2, its bosonic sector contains, in additional to Starobinsky, a massive scalar field without self-interaction. As expected, the bosonic sectors of these models are consistent with cosmic inflation, as we show by solving numerically the classical dynamics. Inflation is driven by the $R^2$ term during the large curvature regime. In the N=2 case, the additional scalar field remains in a low energy state during inflation. Further, by means of an additional superfield, we write equivalent tensor-scalar-like actions from which we can give the Hamiltonian formulation.
|
https://arxiv.org/abs/2110.00556v2
|
Objective: Innovative therapies such as thermoembolization are expected to play an important role in improvising care for patients with diseases such as hepatocellular carcinoma. Thermoembolization is a minimally invasive strategy that combines thermal ablation and embolization in a single procedure. This approach exploits an exothermic chemical reaction that occurs when an acid chloride is delivered via an endovascular route. However, comprehension of the complexities of the biophysics of thermoembolization is challenging. Mathematical models can aid in understanding such complex processes and assisting clinicians in making informed decisions. In this study, we used a Hagen Poiseuille 1D blood flow model to predict the mass transport and possible embolization locations in a porcine hepatic artery. Method: The 1D flow model was used on in vivo embolization imaging data of three pigs. The hydrolysis time constant of acid chloride chemical reaction was optimized for each pig, and LOOCV method was used to test the model's predictive ability. Conclusion: This basic model provided a balanced accuracy rate of 66.8% for identifying the possible locations of embolization in the hepatic artery. Use of the model provides an initial understanding of the vascular transport phenomena that are predicted to occur as a result of thermoembolization.
|
https://arxiv.org/abs/2409.06811v1
|
In this work, we propose a meta algorithm that can solve a multivariate global optimization problem using univariate global optimizers. Although the univariate global optimization does not receive much attention compared to the multivariate case, which is more emphasized in academia and industry; we show that it is still relevant and can be directly used to solve problems of multivariate optimization. We also provide the corresponding regret bounds in terms of the time horizon $T$ and the average regret of the univariate optimizer, when it is robust against nonnegative noises with robust regret guarantees.
|
https://arxiv.org/abs/2209.03246v1
|
Existing text selection techniques on touchscreen focus on improving the control for moving the carets. Coarse-grained text selection on word and phrase levels has not received much support beyond word-snapping and entity recognition. We introduce 1D-Touch, a novel text selection method that complements the carets-based sub-word selection by facilitating the selection of semantic units of words and above. This method employs a simple vertical slide gesture to expand and contract a selection area from a word. The expansion can be by words or by semantic chunks ranging from sub-phrases to sentences. This technique shifts the concept of text selection, from defining a range by locating the first and last words, towards a dynamic process of expanding and contracting a textual semantic entity. To understand the effects of our approach, we prototyped and tested two variants: WordTouch, which offers a straightforward word-by-word expansion, and ChunkTouch, which leverages NLP to chunk text into syntactic units, allowing the selection to grow by semantically meaningful units in response to the sliding gesture. Our evaluation, focused on the coarse-grained selection tasks handled by 1D-Touch, shows a 20% improvement over the default word-snapping selection method on Android.
|
https://arxiv.org/abs/2310.17576v1
|
We prove that for a symmetric, strictly log-convex density on the real line,
there are four possible types of perimeter-minimizing triple bubbles. This
extends the work of Bongiovanni et al., which shows that there are two possible
types of perimeter-minimizing double bubbles.
|
http://arxiv.org/abs/1805.08377v2
|
A Valence bond solid (VBS) is a nonmagnetic, long-range ordered state of a
quantum spin system where local spin singlets are formed in some regular
pattern. We here study the competition between VBS order and a fully polarized
ferromagnetic state as function of an external magnetic field in a
one-dimensional extended Heisenberg model---the J-Q$_2$ model---using
stochastic series expansion quantum Monte Carlo simulations with directed loop
updates. We discuss the ground state phase diagram.
|
http://arxiv.org/abs/1510.07680v1
|
Experimental demonstrations of 1D van der Waals material tellurium have been
presented by Raman spectroscopy under strain and magneto-transport. Raman
spectroscopy measurements have been performed under strains along different
principle axes. Pronounced strain response along c-axis is observed due to the
strong intra-chain covalent bonds, while no strain response is obtained along
a-axis due to the weak inter-chain van der Waals interaction. Magneto-transport
results further verify its anisotropic property, resulting in dramatically
distinct magneto-resistance behaviors in terms of three different magnetic
field directions. Specifically, phase coherence length extracted from weak
antilocalization effect, L$_{\Phi}$ ~ T$^{-0.5}$, claims its 2D transport
characteristics when an applied magnetic field is perpendicular to the thin
film. In contrast, L$_{\Phi}$ ~ T$^{-0.33}$ is obtained from universal
conductance fluctuations once the magnetic field is along c-axis of Te,
indicating its nature of 1D transport along the helical atomic chains. Our
studies, which are obtained on high quality single crystal tellurium thin film,
appear to serve as strong evidences of its 1D van der Waals structure from
experimental perspectives. It is the aim of this paper to address this special
concept that differs from the previous well-studied 1D nanowires or 2D van der
Waals materials.
|
http://arxiv.org/abs/1704.07020v1
|
We present a computational assessment system that promotes the learning of basic rhythmic patterns. The system is capable of generating multiple rhythmic patterns with increasing complexity within various cycle lengths. For a generated rhythm pattern the performance assessment of the learner is carried out through the statistical deviations calculated from the onset detection and temporal assessment of a learner's performance. This is compared with the generated pattern, and their performance accuracy forms the feedback to the learner. The system proceeds to generate a new pattern of increased complexity when performance assessment results are within certain error bounds. The system thus mimics a learner-teacher relationship as the learner progresses in their feedback-based learning. The choice of progression within a cycle for each pattern is determined by a predefined complexity metric. This metric is based on a coded element model for the perceptual processing of sequential stimuli. The model earlier proposed for a sequence of tones and non-tones, is now used for onsets and silences. This system is developed into a web-based application and provides accessibility for learning purposes. Analysis of the performance assessments shows that the complexity metric is indicative of the perceptual processing of rhythm patterns and can be used for rhythm learning.
|
https://arxiv.org/abs/2109.04440v1
|
Arrowed Gelfand-Tsetlin patterns have recently been introduced to study alternating sign matrices. In this paper, we show that a $(-1)$-enumeration of arrowed Gelfand-Tsetlin patterns can be expressed by a simple product formula. The numbers are a one-parameter generalization of the numbers $2^{n(n-1)/2} \prod_{j=0}^{n-1} \frac{(4j+2)!}{(n+2j+1)!}$ that appear in recent work of Di Francesco. A second result concerns the (-1)-enumeration of arrowed Gelfand-Tsetlin patterns when excluding double-arrows as decoration in which case we also obtain a simple product formula. We are also able to provide signless interpretations of our results. The proofs of the enumeration formulas are based on a recent Littlewood-type identity, which allows us to reduce the problem to the evaluations of two determinants. The evaluations are accomplished by means of the LU-decompositions of the underlying matrices, and an extension of Sister Celine's algorithm as well as creative telescoping to evaluate certain triple sums. In particular, we use implementations of such algorithms by Koutschan, and by Wegschaider and Riese.
|
https://arxiv.org/abs/2302.04164v2
|
This paper considers the $1/\epsilon$ problem, which is the divergent
behavior of the ground state energy of asymmetric potential in quantum
mechanics, which is calculated with semi-classical expansion and resurgence
technique. Using resolvent method, It is shown that including not only one
complex bion but multi-complex bion and multi-bounce contributions solves this
problem. This result indicates the importance of summing all possible saddle
points contribution and also the relationship between exact WKB and path
integral formalism.
|
http://arxiv.org/abs/1912.03518v3
|
In the 70s, Berge introduced 1-extendable graphs (also called B-graphs), which are graphs where every vertex belongs to a maximum independent set. Motivated by an application in the design of wireless networks, we study the computational complexity of 1-extendability, the problem of deciding whether a graph is 1-extendable. We show that, in general, 1-extendability cannot be solved in $2^{o(n)}$ time assuming the Exponential Time Hypothesis, where $n$ is the number of vertices of the input graph, and that it remains NP-hard in subcubic planar graphs and in unit disk graphs (which is a natural model for wireless networks). Although 1-extendability seems to be very close to the problem of finding an independent set of maximum size (a.k.a. Maximum Independent Set), we show that, interestingly, there exist 1-extendable graphs for which Maximum Independent Set is NP-hard. Finally, we investigate a parameterized version of 1-extendability.
|
https://arxiv.org/abs/2204.05809v1
|
To identify the decoherence origin, frequency spectra using multiple
{\pi}-pulses have been extensively studied. However, little has been discussed
on how to define the spectral intensities from multiple-echo decays and how to
incorporate the Hahn-echo T_2 in the noise spectra. Here, we show that
experiments based on two theories solve these issues. With the previous theory
clarifying that the spectral intensity should be given as the decay in the
long-time limit, the intensity can be deduced without experimental artifacts
usually entailed in the initial process. The other is the
fluctuation-dissipation theory, with which the Hahn-echo T_2 is utilized as the
zero-frequency limit of the noise spectrum and as an answer to the divergent
issue on the 1/f^n noises. As a result, arsenic nuclear spins are found to
exhibit 1/f2 dependences over two orders of magnitude in all the substrates of
un-doped, Cr-doped semi-insulating and Si-doped metallic GaAs at 297 K. The
1/f^2 dependence indicates single noise source that is characterized by the
characteristic frequency f_c_^un^=170 Hz, f_c_^Cr^=210 Hz and f_c_^Si^ =460 Hz.
These f_c values are explained by a model that the decoherence is caused by the
fluctuations of next-nearest-neighboring nuclear spins.
|
http://arxiv.org/abs/1905.12906v1
|
We study the power spectral density of continuous time Markov chains and explicit its relationship with the eigenstructure of the infinitesimal generator. This result helps us understand the dynamics of the number of customers for a M/M/1 queuing process in the heavy traffic regime.Closed-form relations for the power law scalings associated to the eigenspectrum of the M/M/1 queue generator are obtained, providing a detailed description of the power spectral density structure, which is shown to exhibit a $1/f^{3/2}$ noise.We confirm this result by numerical simulation.We also show that a continuous time random walk on a ring exhibits very similar behavior.It is remarkable than a complex behavior such as $1/f$ noise can emerge from the M/M/1 queue, which is the ''simplest'' queuing model.
|
https://arxiv.org/abs/2302.03467v2
|
Let $G$ be a bridgeless cubic graph. Consider a list of $k$ 1-factors of $G$.
Let $E_i$ be the set of edges contained in precisely $i$ members of the $k$
1-factors. Let $\mu_k(G)$ be the smallest $|E_0|$ over all lists of $k$
1-factors of $G$.
Any list of three 1-factors induces a core of a cubic graph. We use results
on the structure of cores to prove sufficient conditions for Berge-covers and
for the existence of three 1-factors with empty intersection. Furthermore, if
$\mu_3(G) \not = 0$, then $2 \mu_3(G)$ is an upper bound for the girth of $G$.
We also prove some new upper bounds for the length of shortest cycle covers of
bridgeless cubic graphs.
Cubic graphs with $\mu_4(G) = 0$ have a 4-cycle cover of length $\frac{4}{3}
|E(G)|$ and a 5-cycle double cover. These graphs also satisfy two conjectures
of Zhang. We also give a negative answer to a problem of Zhang.
|
http://arxiv.org/abs/1209.4510v3
|
A $1$-factorization of a graph $G$ is a collection of edge-disjoint perfect
matchings whose union is $E(G)$. A trivial necessary condition for $G$ to admit
a $1$-factorization is that $|V(G)|$ is even and $G$ is regular; the converse
is easily seen to be false. In this paper, we consider the problem of finding
$1$-factorizations of regular, pseudorandom graphs. Specifically, we prove that
an $(n,d,\lambda)$-graph $G$ (that is, a $d$-regular graph on $n$ vertices
whose second largest eigenvalue in absolute value is at most $\lambda$) admits
a $1$-factorization provided that $n$ is even, $C_0\leq d\leq n-1$ (where $C_0$
is a universal constant), and $\lambda\leq d^{1-o(1)}$. In particular, since
(as is well known) a typical random $d$-regular graph $G_{n,d}$ is such a
graph, we obtain the existence of a $1$-factorization in a typical $G_{n,d}$
for all $C_0\leq d\leq n-1$, thereby extending to all possible values of $d$
results obtained by Janson, and independently by Molloy, Robalewska, Robinson,
and Wormald for fixed $d$. Moreover, we also obtain a lower bound for the
number of distinct $1$-factorizations of such graphs $G$ which is off by a
factor of $2$ in the base of the exponent from the known upper bound. This
lower bound is better by a factor of $2^{nd/2}$ than the previously best known
lower bounds, even in the simplest case where $G$ is the complete graph. Our
proofs are probabilistic and can be easily turned into polynomial time
(randomized) algorithms.
|
http://arxiv.org/abs/1803.10361v1
|
Single-layer Graphene (SLG) is a promising material for sensing applications. High performance graphene sensors can be achieved when Interdigitated Electrodes (IDE) are used. In this research work, we fabricated SLG micro-ribbon (GMR) devices with IDE having different geometric parameters. 1/f noise behavior was observed in all of the examined devices, and in some cases random telegraph noise (RTN) signals suggesting that carrier trapping/de-trapping is taking place. Our experimental results indicate that the geometrical characteristics can have a crucial impact on device performance, due to the direct area dependence of the noise level.
|
https://arxiv.org/abs/2502.01348v1
|
Short ballistic graphene Josephson junctions sustain superconducting current
with a non-sinusoidal current-phase relation up to a critical current
threshold. The current-phase relation, arising from proximitized
superconductivity, is gate-voltage tunable and exhibits peculiar skewness
observed in high quality graphene superconductors heterostructures with clean
interfaces. These properties make graphene Josephson junctions promising
sensitive quantum probes of microscopic fluctuations underlying transport in
two-dimensions. We show that the power spectrum of the critical current
fluctuations has a characteristic $1/f$ dependence on frequency, $f$, probing
two points and higher correlations of carrier density fluctuations of the
graphene channel induced by carrier traps in the nearby substrate. Tunability
with the Fermi level, close to and far from the charge neutrality point, and
temperature dependence of the noise amplitude are clear fingerprints of the
underlying material-inherent processes. Our results suggest a roadmap for the
analysis of decoherence sources in the implementation of coherent devices by
hybrid nanostructures.
|
http://arxiv.org/abs/1909.06246v1
|
It is shown here that $1/f^\alpha$ flux noise in conventional low-T$_c$
SQUIDs is a result of low temperature superparamagnetic phase transitions in
small clusters of strongly correlated color center defects. The spins in each
cluster interact via long-range ferromagnetic interactions. Due to its small
size, the cluster behaves like a 'random-telegraphic' macro-spin when
transitioning to the superparamagnetic phase. This results in $1/f^{\alpha}$
noise when ensemble averaged over a random distribution of clusters. This model
is self-consistent and explains all related experimental results which includes
$\alpha\sim 0.8$ independent of system-size. The experimental
flux-inductance-noise spectrum is explained through three-point correlation
calculations and time reversal symmetry breaking arguments. Also, unlike the
flux noise, it is shown why the second-spectrum inductance noise is inherently
temperature dependent due to the fluctuation-dissipation theorem. A
correlation-function calculation methodology using Ising-Glauber dynamics was
key for obtaining these results.
|
http://arxiv.org/abs/1710.09114v3
|
Cobalt disilicide provides a promising nearly-epitaxial superconducting material on silicon, which is compatible with high-density integrated circuit technology. We have characterized CoSi$_{2}$ superconducting microwave cavities around 5.5 GHz for resonance frequency fluctuations at temperatures 10 - 200 mK. We found relatively weak fluctuations $(\delta f/f)^2$ following the spectral density $A/f^{\gamma} $, with $A \simeq 6 \times 10^{-16}$ and $\gamma$ slightly below 1 at an average number of photons of $10^4$; the noise decreased with measurement power as $1/P^{1/2}$. We identify the noise as arising from kinetic inductance fluctuations and discuss possible origins of such fluctuations.
|
https://arxiv.org/abs/2403.08347v1
|
We investigate the 1/f noise of the Five-hundred-meter Aperture Spherical Telescope (FAST) receiver system using drift-scan data from an intensity mapping pilot survey. All the 19 beams have 1/f fluctuations with similar structures. Both the temporal and the 2D power spectrum densities are estimated. The correlations directly seen in the time series data at low frequency $f$ are associated with the sky signal, perhaps due to a coupling between the foreground and the system response. We use Singular Value Decomposition (SVD) to subtract the foreground. By removing the strongest components, the measured 1/f noise power can be reduced significantly. With 20 modes subtraction, the knee frequency of the 1/f noise in a 10 MHz band is reduced to $1.8 \times 10^{-3}\Hz$, well below the thermal noise over 500-seconds time scale. The 2D power spectra show that the 1/f-type variations are restricted to a small region in the time-frequency space and the correlations in frequency can be suppressed with SVD modes subtraction. The residual 1/f noise after the SVD mode subtraction is uncorrelated in frequency, and a simple noise diode frequency-independent calibration of the receiver gain at 8s interval does not affect the results. The 1/f noise can be important for HI intensity mapping, we estimate that the 1/f noise has a knee frequency $(f_{k}) \sim$ 6 $\times$ 10$^{-4}$Hz, and time and frequency correlation spectral indices $(\alpha) \sim 0.65$, $(\beta) \sim 0.8$ after the SVD subtraction of 30 modes. This can bias the HI power spectrum measurement by 10 percent.
|
https://arxiv.org/abs/2109.06447v1
|
On-off intermittency occurs in nonequilibrium physical systems close to bifurcation points and is characterised by an aperiodic switching between a large-amplitude "on" state and a small-amplitude "off" state. L\'evy on-off intermittency is a recently introduced generalisation of on-off intermittency to multiplicative L\'evy noise, which depends on a stability parameter $\alpha$ and a skewness parameter $\beta$. Here, we derive two novel results on L\'evy on-off intermittency by leveraging known exact results on the first-passage time statistics of L\'evy flights. First, we compute anomalous critical exponents explicitly as a function of arbitrary L\'evy noise parameters $(\alpha,\beta)$ for the first time, by a heuristic method, complementing previous results. The predictions are verified using numerical solutions of the fractional Fokker-Planck equation. Second, we derive the power spectrum $S(f)$ of L\'evy on-off intermittency and show that it displays a power law $S(f)\propto f^\kappa$ at low frequencies $f$, where $\kappa\in (-1,0)$ depends on the noise parameters $\alpha,\beta$. An explicit expression for $\kappa$ is obtained in terms of $(\alpha,\beta)$. The predictions are verified using long time series realisations of L\'evy on-off intermittency. Our findings help shed light on instabilities subject to non-equilibrium, power-law-distributed fluctuations, emphasizing that their properties can differ starkly from the case of Gaussian fluctuations.
|
https://arxiv.org/abs/2210.10197v2
|
An approach to the problem of 1/f voltage noise in conductors is developed
based on an uncertainty relation for the Fourier-transformed signal. The
quantum indeterminacy caused by non-commutativity of the observables at
different times makes the voltage autocovariance ambiguous, but the power
spectrum of fluctuations remains well-defined. It is shown that a lower bound
on the power spectrum exists, which is related to the antisymmetric part of the
voltage correlation function. Using the Schwinger-Keldysh method, this bound is
calculated explicitly in the case of unpolarized charge carriers with a
parabolic dispersion, and is found to have a 1/f low-frequency asymptotic. A
comparison with the 1/f-noise measurements in InGaAs quantum wells is made
which shows that the observed noise levels are only a few times higher than the
bound established.
|
http://arxiv.org/abs/2006.12412v1
|
Internal mechanism leading to the emergence of the widely occurring 1/f noise
still remains an open issue. In this paper we investigate the distinction
between internal time of the system and the physical time as a source of 1/f
noise. After demonstrating the appearance of 1/f noise in the earlier proposed
point process model, we generalize it starting from a stochastic differential
equation which describes a Brownian-like motion in the internal (operational)
time. We consider this equation together with an additional equation relating
the internal time to the external (physical) time. We show that the relation
between the internal time and the physical time that depends on the intensity
of the signal can lead to 1/f noise in a wide interval of frequencies. The
present model can be useful for the explanation of the appearance of 1/f noise
in different systems.
|
http://arxiv.org/abs/1512.03910v1
|
The origin of the low-frequency noise with power spectrum $1/f^\beta$ (also
known as $1/f$ fluctuations or flicker noise) remains a challenge. Recently,
the nonlinear stochastic differential equations for modeling $1/f^\beta$ noise
have been proposed and analyzed. Here we use the self-similarity properties of
this model with respect to the nonlinear transformations of the variable of
these equations and show that $1/f^\beta$ noise of the observable may yield
from the power-law transformations of well-known standard processes, like the
Brownian motion, Bessel and similar stochastic processes. Analytical and
numerical investigations of such techniques for modeling processes with
$1/f^\beta$ fluctuations is presented.
|
http://arxiv.org/abs/1512.04298v1
|
We analyze the power spectral density of a signal composed of nonoverlapping rectangular pulses. First, we derive a general formula for the power spectral density of a signal constructed from the sequence of nonoverlapping pulses. Then we perform a detailed analysis of the rectangular pulse case. We show that pure $1/f$ noise can be observed until extremely low frequencies when the characteristic pulse (or gap) duration is long in comparison to the characteristic gap (or pulse) duration, and gap (or pulse) durations are power-law distributed. The obtained results hold for the ergodic and weakly nonergodic processes.
|
https://arxiv.org/abs/2210.11792v5
|
Fundamental issues of 1/f noise in quantum nanoscience are reviewed starting from basic statistical noise processes. Fundamental noise models based on two-level systems (TLS) are described. We emphasize the importance of TLSs in materials parameter fluctuations, such as dielectric constant. The present understanding of 1/f noise in superconducting quantum interferometers and in single electron devices is summarized. For coherent quantum nanoscience, we introduce superconducting qubits and the relation between decoherence and 1/f noise using the filter function formulation. We also clarify the qubit noise spectroscopy and emphasize the importance of materials with reduced 1/f noise for future quantum coherent nanodevices.
|
https://arxiv.org/abs/2401.11989v1
|
We propose a model of $1/f$ noise in semiconductors based on the drift of individual charge carriers and their interaction with the trapping centers. We assume that the trapping centers are homogeneously distributed in the material. The trapping centers are assumed to be heterogeneous and have unique detrapping rates. We show that uniform detrapping rate distribution emerges as a natural consequence of the vacant trap depths following the Boltzmann distribution, and the detrapping process obeying Arrhenius law. When these laws apply, and if the trapping rate is low in comparison to the maximum detrapping rate, $1/f$ noise in the form of Hooge's relation is recovered. Hooge's parameter, $\alpha_{H}$, is shown to be a ratio between the characteristic trapping rate and the maximum detrapping rate. The proposed model implies that $1/f$ noise arises from the temporal charge carrier number fluctuations, not from the spatial mobility fluctuations.
|
https://arxiv.org/abs/2306.07009v5
|
We present a broad review of 1/f noise observations in the heliosphere, and discuss and complement the theoretical background of generic 1/f models as relevant to NASA's PUNCH mission. First observed in the voltage fluctuations of vacuum tubes, the scale-invariant 1/f spectrum has since been identified across a wide array of natural and artificial systems, including heart rate fluctuations and loudness patterns in musical compositions. In the solar wind, the interplanetary magnetic field trace spectrum exhibits 1/f scaling within the frequency range from around 2e-6 Hz to around 1e-3 Hz at 1 au. One compelling mechanism for the generation of 1/f noise is the superposition principle, where a composite 1/f spectrum arises from the superposition of a collection of individual power-law spectra characterized by a scale-invariant distribution of correlation times. In the context of the solar wind, such a superposition could originate from scale-invariant reconnection processes in the corona. Further observations have detected 1/f signatures in the photosphere and corona at frequency ranges compatible with those observed at 1 au, suggesting an even lower altitude origin of 1/f spectrum in the solar dynamo itself. This hypothesis is bolstered by dynamo experiments and simulations that indicate inverse cascade activities, which can be linked to successive flux tube reconnections beneath the corona, and are known to generate 1/f noise possibly through nonlocal interactions at the largest scales. Conversely, models positing in situ generation of $1/f$ signals face causality issues in explaining the low-frequency portion of the 1/f spectrum. Understanding 1/f noise in the solar wind may inform central problems in heliospheric physics, such as the solar dynamo, coronal heating, the origin of the solar wind, and the nature of interplanetary turbulence.
|
https://arxiv.org/abs/2409.02255v2
|
We simulate the $N$-spin critical Ising model on a square lattice using Glauber dynamics and consider the typical one-unit time equal to $N$ single-spin-flip attempts. The divergence of correlation time with the linear extent of the system results in critical slowing down, a challenge to equilibration because the spin configurations generated in such a way are temporally correlated. We examine temporal correlations in the number of accepted spin flips and show a signature of non-trivial long-time correlation of a logarithmically decaying form or the corresponding power spectral density follows canonical $1/f$ noise.
|
https://arxiv.org/abs/2503.04105v1
|
We report the experimental observation of $1/f$ fluctuations in three
different turbulent flow configurations: the large scale velocity driven by a
two-dimensional turbulent flow, the magnetic field generated by a turbulent
swirling flow of liquid sodium and the pressure fluctuations due to vorticity
filaments in a swirling flow. For these three systems, $1/f$ noise is shown to
result from the dynamics of coherent structures that display transitions
between a small number of states. The interevent duration is distributed as a
power-law. The exponent of this power-law and the nature of the dynamics
(transition between symmetric states or asymmetric ones) select the exponent of
the $1/f$ fluctuations.
|
http://arxiv.org/abs/1605.09666v1
|
Tunnel magnetoresistance (TMR) sensor is a highly sensitive magnetic field sensor and is expected to be applied in various fields, such as magnetic recording, industrial sensing, and bio-medical sensing. To improve the detection capability of TMR sensors in low frequency regime it is necessary to suppress the 1/f noise. We theoretically study 1/f noise of a tiny TMR sensor using the macrospin model. Starting from the generalized Langevin equation, 1/f noise power spectrum and the Hooge parameter are derived. The calculated Hooge parameter of a tiny TMR sensor is much smaller than that of a conventional TMR sensor with large junction area. The results provide a new perspective on magnetic 1/f noise and will be useful for improvement of TMR sensors.
|
https://arxiv.org/abs/2406.18811v1
|
The collective behavior of a two-dimensional wet granular cluster under
horizontal swirling motions is investigated experimentally. Depending on the
balance between the energy injection and dissipation, the cluster evolves into
various nonequilibrium stationary states with strong internal structure
fluctuations with time. Quantitative characterizations of the fluctuations with
the bond orientational order parameter $q_{\rm 6}$ reveal power spectra of the
form $f^{\alpha}$ with the exponent $\alpha$ closely related to the stationary
states of the system. In particular, $1/f$ type of noise with $\alpha\approx-1$
emerges as melting starts from the free surface of the cluster, suggesting the
possibility of using $1/f$ noise as an indicator for phase transitions in
systems driven far from thermodynamic equilibrium.
|
http://arxiv.org/abs/1502.04921v2
|
In this paper, an in-pixel chopping technique to reduce the low-frequency or
1/f noise of the source follower (SF) transistor in an active pixel sensor
(APS) is presented. The SF low-frequency noise is modulated at higher
frequencies through chopping, implemented inside the pixel, and in later stage
eliminated using low-pass filtering. To implement the chopping, the
conventional 3T APS architecture is modified, with only one additional
transistor of minimum size per pixel. Reduction in the noise also enhances the
dynamic range (DR) of the image sensor. The test circuit is fabricated in UMC
0.18 um standard CMOS technology. The measured results show a reduction of 1/f
noise by approximately 22 dB for 50 MHz chopping frequency.
|
http://arxiv.org/abs/1807.11577v1
|
In this paper, we review the 1/f-type noise properties of nanoelectronic devices focusing on three demonstrative platforms: resistive switching memories, graphene nanogaps and single-molecule nanowires. The functionality of such ultrasmall devices is confined to an extremely small volume, where bulk considerations on the noise loose their validity: the relative contribution of a fluctuator heavily depends on its distance from the device bottleneck, and the noise characteristics are sensitive to the nanometer-scale device geometry and the details of the mostly non-classical transport mechanism. All these are reflected by a highly system-specific dependence of the noise properties on the active device volume (and the related device resitance), the frequency, or the applied voltage. Accordingly, 1/f-type noise measurements serve as a rich fingerprint of the relevant transport and noise-generating mechanisms in the studied nanoelectronic systems. Finally, we demonstrate that not only the fundamental understanding and the targeted noise suppression is fueled by the 1/f-type noise analysis, but novel probabilistic computing hardware platforms heavily seek well tailorable nanoelectric noise sources.
|
https://arxiv.org/abs/2106.02683v1
|
Voss and Clarke observed 1/f noise in the square of Johnson noise across samples in thermal equilibrium without applying a current. We refer to this phenomenon as thermal 1/f noise. Voss and Clarke suggested spatially correlated temperature fluctuations as an origin of thermal 1/f noise; they also showed that thermal 1/f noise closely matches the 1/f spectrum obtained by passing a current through the sample. An intermittent generation-recombination (g-r) process has recently been introduced to interpret 1/f noise in semiconductors. The square of this intermittent g-r process generates a 1/f noise component which correlates with Voss and Clarke's empirical findings. Traps which intermittently rather than continuously generate g-r pulses are suggested as the origin of 1/f noise under drift and thermal agitation. We see no need to introduce correlated temperature fluctuations or oxide traps with a large distribution of time constants to explain 1/f noise.
|
https://arxiv.org/abs/2202.05390v1
|
The 1-form symmetry, manifesting as loop-like symmetries, has gained prominence in the study of quantum phases, deepening our understanding of symmetry. However, the role of 1-form symmetries in Projected Entangled-Pair States (PEPS), two-dimensional tensor network states, remains largely underexplored. We present a novel framework for understanding 1-form symmetries within tensor networks, specifically focusing on the derivation of algebraic relations for symmetry matrices on the PEPS virtual legs. Our results reveal that 1-form symmetries impose stringent constraints on tensor network representations, leading to distinct anomalous braiding phases carried by symmetry matrices. We demonstrate how these symmetries influence the ground state and tangent space in PEPS, providing new insights into their physical implications for enhancing ground state optimization efficiency and characterizing the 1-form symmetry structure in excited states.
|
https://arxiv.org/abs/2407.16531v2
|
We investigate (-1)-form symmetries using the framework of symmetry topological field theories. Previous studies of (-1)-form symmetries have primarily focused on SymTFTs with topological point operators. Here we examine SymTFTs devoid of point operators, constructed to realize zero-form symmetries of some physical theory. In this context we identify codimension-one defects within the bulk of SymTFT constructed via higher gauging which can be interpreted as the generators of the (-1)-form symmetry of the absolute theory. In addition, we present examples where (-1)-form symmetries exhibit the novel ability to shift the 't Hooft anomalies of the theory.
|
https://arxiv.org/abs/2505.14807v1
|
We explore $(-1)$-form symmetries within the framework of geometric engineering in M-theory. By constructing the Symmetry Topological Field Theory (SymTFT) for selected 5d $\mathcal{N}=1$, 4d $\mathcal{N}=2$ and 4d $\mathcal{N}=1$ theories, we formalize the geometric origin of these symmetries and compute the mixed anomaly polynomials involving $(-1)$-form and higher-form symmetries. Our findings consistently reveal both discrete and continuous $(-1)$-form symmetries, aligning with established field theory results, while also uncovering new $(-1)$-form symmetry factors and structural insights. In particular, we study the SymTFT of 4d $\mathcal{N}=1$ theories from M-theory on a class of spaces with $G_2$ holonomy, and obtain properties such as modified instanton sums and 4-group structures observed in other 4d gauge theories. Additionally, we systematically construct symmetry operators for continuous abelian symmetries, refining existing proposals, and providing an M-theory origin for them.
|
https://arxiv.org/abs/2411.19683v3
|
We determine the 1-form symmetry group for any 4d N = 2 class S theory constructed by compactifying a 6d N=(2,0) SCFT on a Riemann surface with arbitrary regular untwisted and twisted punctures. The 6d theory has a group of mutually non-local dimension-2 surface operators, modulo screening. Compactifying these surface operators leads to a group of mutually non-local line operators in 4d, modulo screening and flavor charges. Complete specification of a 4d theory arising from such a compactification requires a choice of a maximal subgroup of mutually local line operators, and the 1-form symmetry group of the chosen 4d theory is identified as the Pontryagin dual of this maximal subgroup. We also comment on how to generalize our results to compactifications involving irregular punctures. Finally, to complement the analysis from 6d, we derive the 1-form symmetry from a Type IIB realization of class S theories.
|
https://arxiv.org/abs/2102.01693v2
|
We study the plaquette valence bond solid phase in a XXZ type spin-1/2 model in the kagome lattice. The low energy theory for this phase is a U(1) lattice gauge theory on the honeycomb lattice. We find that there is an emergent 1-form U(1) symmetry in low energy, and there is a mixed anomaly. We also show that this 1-form symmetry constraints the longitudinal dynamical structure factor and leads to the selection rule relating to the vanishing intensity along some high symmetry momentum paths (e.g. $\Gamma-M$ path). We point out that this emergent 1-form symmetry is robust against the translation symmetry preserving UV perturbation, thus the selection rule will also apply to the model which is obtained by perturbing the classical limit of our model.
|
https://arxiv.org/abs/2306.03348v1
|
We systematically study 4D $\mathcal{N}=2$ superconformal field theories (SCFTs) that can be constructed via type IIB string theory on isolated hypersurface singularities (IHSs) embedded in $\mathbb{C}^4$. We show that if a theory in this class has no $\mathcal{N}=2$-preserving exactly marginal deformation (i.e., the theory is isolated as an $\mathcal{N}=2$ SCFT), then it has no 1-form symmetry. This situation is somewhat reminiscent of 1-form symmetry and decomposition in 2D quantum field theory. Moreover, our result suggests that, for theories arising from IHSs, 1-form symmetries originate from gauge groups (with vanishing beta functions). One corollary of our discussion is that there is no 1-form symmetry in IHS theories that have all Coulomb branch chiral ring generators of scaling dimension less than two. In terms of the $a$ and $c$ central charges, this condition implies that IHS theories satisfying $a<{1\over24}(15r+2f)$ and $c<{1\over6}(3r+f)$ (where $r$ is the complex dimension of the Coulomb branch, and $f$ is the rank of the continuous 0-form flavor symmetry) have no 1-form symmetry. After reviewing the 1-form symmetries of other classes of theories, we are motivated to conjecture that general interacting 4D $\mathcal{N}=2$ SCFTs with all Coulomb branch chiral ring generators of dimension less than two have no 1-form symmetry.
|
https://arxiv.org/abs/2106.09807v2
|
We show that large N QCD does not have an emergent $\mathbb{Z}_N$ 1-form symmetry. Our results suggest that a symmetry-based understanding of (approximate) confinement in QCD would require some further generalization of the notion of generalized global symmetries.
|
https://arxiv.org/abs/2209.00027v2
|
AI faces a trifecta of grand challenges: the Energy Wall, the Alignment Problem and the Leap from Narrow AI to AGI. Contemporary AI solutions consume unsustainable amounts of energy during model training and daily operations. Making things worse, the amount of computation required to train each new AI model has been doubling every 2 months since 2020, directly translating to unprecedented increases in energy consumption. The leap from AI to AGI requires multiple functional subsystems operating in a balanced manner, which requires a system architecture. However, the current approach to artificial intelligence lacks system design; even though system characteristics play a key role in the human brain; from the way it processes information to how it makes decisions. System design is the key to alignment, one of the most challenging goals in AI. This difficulty stems from the fact that the complexity of human moral system requires a similarly sophisticated system for alignment. Without accurately reflecting the complexity of these core moral subsystems and systems, aligning AI with human values becomes significantly more challenging. In this paper, we posit that system design is the missing piece in overcoming the grand challenges. We present a Systematic Approach to AGI that utilizes system design principles to AGI, while providing ways to overcome the energy wall and the alignment challenges. This paper asserts that artificial intelligence can be realized through a multiplicity of design-specific pathways, rather than a singular, overarching AGI architecture. AGI systems may exhibit diverse architectural configurations and capabilities, contingent upon their intended use cases. It advocates for a focus on employing system design principles as a guiding framework, rather than solely concentrating on a universal AGI architecture.
|
https://arxiv.org/abs/2310.15274v2
|
We consider the Robin Hood dynamics, a one-dimensional extremal self-organized critical model that describes the evolution of low-temperature creep. One of the key quantities is the time evolution of the state variable (force noise). To understand the temporal correlations, we compute the power spectra of the local force fluctuations and apply finite-size scaling to get scaling functions and critical exponents. We find a signature of the $1/f^{\alpha}$ noise for the local force with a nontrivial value of the spectral exponent $0< \alpha < 2$. We also examine temporal fluctuations in the position of the extremal site and a local activity signal. We present results for different local interaction rules of the model.
|
https://arxiv.org/abs/2405.00443v1
|
Quantum networks are essential for realising distributed quantum computation and quantum communication. Entangled photons are a key resource, with applications such as quantum key distribution, quantum relays, and quantum repeaters. All components integrated in a quantum network must be synchronised and therefore comply with a certain clock frequency. In quantum key distribution, the most mature technology, clock rates have reached and exceeded 1GHz. Here we show the first electrically pulsed sub-Poissonian entangled photon source compatible with existing fiber networks operating at this clock rate. The entangled LED is based on InAs/InP quantum dots emitting in the main telecom window, with a multi-photon probability of less than 10% per emission cycle and a maximum entanglement fidelity of 89%. We use this device to demonstrate GHz clocked distribution of entangled qubits over an installed fiber network between two points 4.6km apart.
|
https://arxiv.org/abs/2004.14880v2
|
Dual-frequency comb spectroscopy permits broadband precision spectroscopic measurements with short acquisition time. A dramatic improvement of the maximal spectral bandwidth and the minimal measurement time can be expected when the lasers' pulse repetition rate is increased, owing to a quadratic dependence (Nyquist criterion). Here, we demonstrate a dual-comb system operating at a high repetition rate of 1 GHz based on mature, digitally-controlled, low-noise mode-locked lasers. Compared to conventional lower repetition rate ($\sim$100 MHz) oscillators, this represents a 100-fold improvement in terms of the Nyquist criterion, while still providing adequate spectral sampling even for trace gas absorption fingerprints. Two spectroscopy experiments are performed with acquisition parameters not attainable in a 100 MHz system: detection of water vapor absorption around 1375 nm, demonstrating the potential for fast and ambiguity-free broadband operation, and real-time acquisition of narrow gas absorption features across a spectral span of 0.6 THz (600 comb lines) in only 5 $\mu$s. Additionally, we show high mutual coherence of the lasers below the Hz-level, generating opportunities for broadband spectroscopy even with low-bandwidth detectors such as mid-infrared, imaging or photo-acoustic detectors.
|
https://arxiv.org/abs/2111.08599v1
|
Mid-infrared (MIR) spectrometers are invaluable tools for molecular fingerprinting and hyper-spectral imaging. Among the available spectroscopic approaches, GHz MIR dual-comb absorption spectrometers have the potential to simultaneously combine the high-speed, high spectral resolution, and broad optical bandwidth needed to accurately study complex, transient events in chemistry, combustion, and microscopy. However, such a spectrometer has not yet been demonstrated due to the lack of GHz MIR frequency combs with broad and full spectral coverage. Here, we introduce the first broadband MIR frequency comb laser platform at 1 GHz repetition rate that achieves spectral coverage from 3 to 13 {\mu}m. This frequency comb is based on a commercially available 1.56 {\mu}m mode-locked laser, robust all-fiber Er amplifiers and intra-pulse difference frequency generation (IP-DFG) of few-cycle pulses in \c{hi}(2) nonlinear crystals. When used in a dual comb spectroscopy (DCS) configuration, this source will simultaneously enable measurements with {\mu}s time resolution, 1 GHz (0.03 cm-1) spectral point spacing and a full bandwidth of >5 THz (>166 cm-1) anywhere within the MIR atmospheric windows. This represents a unique spectroscopic resource for characterizing fast and non-repetitive events that are currently inaccessible with other sources.
|
https://arxiv.org/abs/2201.07134v1
|
Garling sequence spaces admit a renorming with respect to which their
standard unit vector basis is 1-greedy. We also discuss some additional
properties of these Banach spaces related to uniform convexity and
superreflexivity. In particular, our approach to the study of the
superreflexivity of Garling sequence space provides an example of how
essentially non-linear tools from greedy approximation can be used to shed
light into the linear structure of the spaces.
|
http://arxiv.org/abs/1705.03924v1
|
The Imagenet Large Scale Visual Recognition Challenge (ILSVRC) is the one of
the most important big data challenges to date. We participated in the object
detection track of ILSVRC 2014 and received the fourth place among the 38
teams. We introduce in our object detection system a number of novel techniques
in localization and recognition. For localization, initial candidate proposals
are generated using selective search, and a novel bounding boxes regression
method is used for better object localization. For recognition, to represent a
candidate proposal, we adopt three features, namely, RCNN feature, IFV feature,
and DPM feature. Given these features, category-specific combination functions
are learned to improve the object recognition rate. In addition, object context
in the form of background priors and object interaction priors are learned and
applied in our system. Our ILSVRC 2014 results are reported alongside with the
results of other participating teams.
|
http://arxiv.org/abs/1409.6155v3
|
We provide a quantitative description of a method to measure neutron-induced
fission cross sections in ratio to elastic hydrogen scattering in a
white-source neutron beam with the fission Time Projection Chamber. This
detector has measured precision fission cross section ratios using actinide
references such as $^{235}$U(n,f) and $^{238}$U(n,f). However, by employing a
more precise reference such as the H(n,el) cross section there is the potential
to further reduce the evaluation uncertainties of the measured cross sections.
In principle the fissionTPC could provide a unique measurement by
simultaneously measuring both fission fragments and proton recoils over a large
solid angle. We investigate one method with a hydrogenous gas target and with
the neutron energy determined by the proton recoil kinematics. This method
enables the measurement to be performed in a white-source neutron beam and with
the current configuration of the fissionTPC. We show that while such a
measurement is feasible in the energy range of 0.5 MeV to $\sim$10 MeV,
uncertainties on the proton detection efficiency and the neutron energy
resolution do not allow us to preform a fission ratio measurement to the
desired precision. Utilizing either a direct measurement of the neutron
time-of-flight for the recoil proton or a mono-energetic neutron source or some
combination of both would provide a path to a sub-percent precision
measurement.
|
http://arxiv.org/abs/1904.10558v1
|
The intra-molecular $^1$H-NMR dipole-dipole relaxation of molecular fluids
has traditionally been interpreted within the Bloembergen-Purcell-Pound (BPP)
theory of NMR intra-molecular relaxation. The BPP theory draws upon Debye's
theory for describing the rotational diffusion of the $^1$H-$^1$H pair and
predicts a mono-exponential decay of the $^1$H-$^1$H dipole-dipole
autocorrelation function between distinct spin pairs. Using molecular dynamics
(MD) simulations, we show that for both $n$-heptane and water this is not the
case. In particular, the autocorrelation function of individual $^1$H-$^1$H
intra-molecular pairs itself evinces a rich stretched-exponential behavior,
implying a distribution in rotational correlation times. However for the
high-symmetry molecule neopentane, the individual $^1$H-$^1$H intra-molecular
pairs do conform to the BPP description, suggesting an important role of
molecular symmetry in aiding agreement with the BPP model. The inter-molecular
autocorrelation functions for $n$-heptane, water, and neopentane also do not
admit a mono-exponential behavior of individual $^1$H-$^1$H inter-molecular
pairs at distinct initial separations. We suggest expanding the
auto-correlation function in terms of molecular modes, where the molecular
modes do have an exponential relaxation behavior. With care, the resulting
Fredholm integral equation of the first kind can be inverted to recover the
probability distribution of the molecular modes. The advantages and limitations
of this approach are noted.
|
http://arxiv.org/abs/2006.06055v3
|
We present the first theoretical prediction of the production rate of $1^{-+}$ light hybrid meson $\eta_1$ in $J/\psi$ radiative decays. In the $N_f=2$ lattice QCD formalism with the pion mass $m_\pi\approx 350$ MeV, the related electromagnetic multipole form factors are extracted from the three-point functions that involve necessarily quark annihilation diagrams, which are calculated through the distillation method. The partial width of $J/\psi\to \gamma \eta_1$ is determined to be $2.29(77)~\mathrm{eV}$ at the $\eta_1$ mass $m_{\eta_1}=2.23(4)$ GeV. If $\eta_1$ corresponds to the recently observed $\eta_1(1855)$ in the process $J/\psi\to \gamma\eta_1(1855)\to \gamma \eta\eta'$ by BESIII, then the branching fraction $\mathrm{Br}(J/\psi\to \gamma\eta_1(1855))$ is estimated to be $6.2(2.2)\times 10^{-5}$, which implies $\mathrm{Br}(\eta_1(1855)\to \eta\eta')\sim 4.3\%$.
|
https://arxiv.org/abs/2207.04694v3
|
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