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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.
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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.
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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.
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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.
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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.
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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.
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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
|
Discovery of the first interstellar asteroid (ISA) - 1I/2017 'Oumuamua -
raised a number of questions regarding its origin. Many of them relate to its
lack of cometary activity, suggesting refractory composition of 'Oumuamua. Here
we explore the possibility that 'Oumuamua-like ISAs are produced in tidal
disruption events (TDEs) of refractory planetoids (asteroids, dwarf planets,
etc.) by the white dwarfs (WDs). This idea is supported by existing
spectroscopic observations of metal-polluted WDs, hinting at predominantly
volatile-poor composition of accreted material. We show that such TDEs sourced
by realistic planetary systems (including a population of >1000 km planetoids
and massive perturbers - Neptune-to-Saturn mass planets) can eject to
interstellar space up to 30% of planetary mass involved in them. Collisional
fragmentation, caused by convergent vertical motion of the disrupted
planetoid's debris inside the Roche sphere of the WD, channels most of the
original mass into 0.1-1 km fragments, similar to 'Oumuamua. Such size spectrum
of ISAs (very different from the top-heavy distributions expected in other
scenarios) implies that planetary TDEs can account for a significant fraction
(up to ~30% under optimistic assumptions) of the ISAs. This figure is based on
existing observations of WD metal pollution and accounts for observational
biases by using realistic models of circum-WD planetary systems. ISAs should
exhibit kinematic characteristics similar to old, dynamically hot Galactic
populations; we interpret 'Oumuamua's slow Galactic motion as a statistical
fluctuation. ISA ejection in individual planetary TDEs is highly anisotropic,
resulting in large fluctuations of their space density. We also show that other
ISA production mechanisms involving stellar remnants - direct ejection by
massive planets around WDs and SN explosions - have difficulty explaining
'Oumuamua-like ISAs.
|
http://arxiv.org/abs/1801.02658v3
|
1I/2017 U1 (`Oumuamua), a recently discovered asteroid in a hyperbolic orbit,
is likely the first macroscopic object of extrasolar origin identified in the
solar system. Here, we present imaging and spectroscopic observations of
\textquoteleft Oumuamua using the Palomar Hale Telescope as well as a search of
meteor activity potentially linked to this object using the Canadian Meteor
Orbit Radar. We find that \textquoteleft Oumuamua exhibits a moderate spectral
gradient of $10\%\pm6\%~(100~\mathrm{nm})^{-1}$, a value significantly lower
than that of outer solar system bodies, indicative of a formation and/or
previous residence in a warmer environment. Imaging observation and spectral
line analysis show no evidence that \textquoteleft Oumuamua is presently
active. Negative meteor observation is as expected, since ejection driven by
sublimation of commonly-known cometary species such as CO requires an extreme
ejection speed of $\sim40$ m s$^{-1}$ at $\sim100$ au in order to reach the
Earth. No obvious candidate stars are proposed as the point of origin for
\textquoteleft Oumuamua. Given a mean free path of $\sim10^9$ ly in the solar
neighborhood, \textquoteleft Oumuamua has likely spent a very long time in the
interstellar space before encountering the solar system.
|
http://arxiv.org/abs/1711.02320v2
|
In this work we find evidence that the object is of cometary origin.
|
http://arxiv.org/abs/1711.07535v1
|
The 1-in-3 and Not-All-Equal satisfiability problems for Boolean CNF formulas are two well-known NP-hard problems. In contrast, the promise 1-in-3 vs. Not-All-Equal problem can be solved in polynomial time. In the present work, we investigate this constraint satisfaction problem in a regime where the promise is weakened from either side by a rainbow-free structure, and establish a complexity dichotomy for the resulting class of computational problems.
|
https://arxiv.org/abs/2302.03456v3
|
A random graph model on a host graph H is said to be 1-independent if for every pair of vertex-disjoint subsets A,B of E(H), the state of edges (absent or present) in A is independent of the state of edges in B. For an infinite connected graph H, the 1-independent critical percolation probability $p_{1,c}(H)$ is the infimum of the p in [0,1] such that every 1-independent random graph model on H in which each edge is present with probability at least p almost surely contains an infinite connected component. Balister and Bollob\'as observed in 2012 that $p_{1,c}(\mathbb{Z}^d)$ is nonincreasing and tends to a limit in [1/2, 1] as d tends to infinity. They asked for the value of this limit. We make progress towards this question by showing that \[\lim_{n\rightarrow \infty}p_{1,c}(\mathbb{Z}^2\times K_n)=4-2\sqrt{3}=0.5358\ldots \ .\] In fact, we show that the equality above remains true if the sequence of complete graphs $K_n$ is replaced by a sequence of weakly pseudorandom graphs on n vertices with average degree $\omega(\log n)$. We conjecture that the equality also remains true if $K_n$ is replaced instead by the n-dimensional hypercube $Q_n$. This latter conjecture would imply the answer to Balister and Bollob\'as's question is $4-2\sqrt{3}$. Using our results, we are also able to resolve a problem of Day, Hancock and the first author on the emergence of long paths in 1-independent random graph models on $\mathbb{Z}\times K_n$. Finally, we prove some results on component evolution in 1-independent random graphs, and discuss a number of open problems arising from our work that may pave the way for further progress on the question of Balister and Bollob\'as.
|
https://arxiv.org/abs/2106.08674v2
|
The origin of the interstellar object 1I/'Oumuamua, has defied explanation. In a companion paper (Jackson & Desch, 2021), we show that a body of N2 ice with axes 45 m x 44 m x 7.5 m at the time of observation would be consistent with its albedo, non-gravitational acceleration, and lack of observed CO or CO2 or dust. Here we demonstrate that impacts on the surfaces of Pluto-like Kuiper belt objects (KBOs) would have generated and ejected ~10^14 collisional fragments--roughly half of them H2O ice fragments and half of them N2 ice fragments--due to the dynamical instability that depleted the primordial Kuiper belt. We show consistency between these numbers and the frequency with which we would observe interstellar objects like 1I/'Oumuamua, and more comet-like objects like 2I/Borisov, if other stellar systems eject such objects with efficiency like that of the Sun; we infer that differentiated KBOs and dynamical instabilities that eject impact-generated fragments may be near-universal among extrasolar systems. Galactic cosmic rays would erode such fragments over 4.5 Gyr, so that fragments are a small fraction (~0.1%) of long-period Oort comets, but C/2016 R2 may be an example. We estimate 'Oumuamua was ejected about 0.4-0.5 Gyr ago, from a young (~10^8 yr) stellar system, which we speculate was in the Perseus arm. Objects like 'Oumuamua may directly probe the surface compositions of a hitherto-unobserved type of exoplanet: "exo-plutos". 'Oumuamua may be the first sample of an exoplanet brought to us.
|
https://arxiv.org/abs/2103.08812v1
|
The origin of the interstellar object 1I/'Oumuamua has defied explanation. We perform calculations of the non-gravitational acceleration that would be experienced by bodies composed of a range of different ices and demonstrate that a body composed of N2 ice would satisfy the available constraints on the non-gravitational acceleration, size and albedo, and lack of detectable emission of CO or CO2 or dust. We find that 'Oumuamua was small, with dimensions 45 m x 44 m x 7.5 m at the time of observation at 1.42 au from the Sun, with a high albedo of 0.64. This albedo is consistent with the N2 surfaces of bodies like Pluto and Triton. We estimate 'Oumuamua was ejected about 0.4-0.5 Gyr ago from a young stellar system, possibly in the Perseus arm. Objects like 'Oumuamua may directly probe the surface compositions of a hitherto-unobserved type of exoplanet: "exo-plutos". In a companion paper (Desch & Jackson, 2021) we demonstrate that dynamical instabilities like the one experienced by the Kuiper belt, in other stellar systems, plausibly could generate and eject large numbers of N2 ice fragments. 'Oumuamua may be the first sample of an exoplanet brought to us.
|
https://arxiv.org/abs/2103.08788v1
|
1I/`Oumuamua is the first known interstellar small body, probably being only
about 100~m in size. Against expectations based on comets, `Oumuamua does not
show any activity and has a very elongated figure, and also exhibits undamped
rotational tumbling. In contrast, `Oumuamua's trajectory indicates that it was
moving with the local stars, as expected from a low-velocity ejection from a
relatively nearby system. Here I assume that `Oumuamua is typical of 100-m
interstellar objects, and speculate on its origins. I find that giant planets
are relatively inefficient at ejecting small bodies from inner solar systems of
main-sequence stars, and that binary systems offer a much better opportunity
for ejections of non-volatile bodies. I also conclude that `Oumuamua is not a
member of a collisional population, which could explain its dramatic difference
from small asteroids. I observe that 100-m small bodies are expected to carry
little mass in realistic collisional populations, and that occasional events
when whole planets are disrupted in catastrophic encounters may dominate
interstellar population of 100-m fragments. Unlike the Sun or Jupiter, red
dwarf stars are very dense and are capable of thoroughly tidally disrupting
terrestrial planets. I conclude that the origin of `Oumuamua as a fragment from
a planet that was tidally disrupted and then ejected by a dense member of a
binary system could explain its peculiarities.
|
http://arxiv.org/abs/1712.01823v2
|
Intrinsically faint comets in nearly-parabolic orbits with perihelion
distances much smaller than 1 AU exhibit strong propensity for suddenly
disintegrating at a time not long before perihelion, as shown by Bortle (1991).
Evidence from available observations of such comets suggests that the
disintegration event usually begins with an outburst and that the debris is
typically a massive cloud of dust grains that survives over a limited period of
time. Recent CCD observations revealed, however, that also surviving could be a
sizable fragment, resembling a devolatilized aggregate of loosely-bound dust
grains that may have exotic shape, peculiar rotational properties, and
extremely high porosity, all acquired in the course of the disintegration
event. Given that the brightness of 1I/`Oumuamua's parent could not possibly
equal or exceed the Bortle survival limit, there are reasons to believe that it
suffered the same fate as do the frail comets. The post-perihelion observations
then do not refer to the object that was entering the inner Solar System in
early 2017, as is tacitly assumed, but to its debris. Comparison with C/2017 S3
and C/2010 X1 suggests that, as a monstrous fluffy dust aggregate released in
the recent explosive event, `Oumuamua should be of strongly irregular shape,
tumbling, not outgassing, and subjected to effects of solar radiation pressure,
consistent with observation. The unknown timing of the disintegration event may
compromise studies of the parent's home stellar system. Limited search for
possible images of the object to constrain the time of the (probably minor)
outburst is recommended.
|
http://arxiv.org/abs/1901.08704v3
|
We present $O(\alpha_s)$ analytic predictions for event shape 1-jettiness $\tau_1$ distribution aiming measurements in deep inelastic scattering process at future Electron Ion Colliders. The result depends on conventional variables $x$ and $Q$ as well as on $\tau_1$ and is relatively compact and easy to implement for numerical calculation. Three different choices of axis, with respect to which $\tau_1$ is measured are considered in the Breit frame. The first is the one optimally adjusted to minimize $\tau_1$ and the second and third are taken from anti-$k_T$ and Centauro jet algorithms defined with a jet radius parameter $R$, respectively. We find that the first and second give the same result at this order and are independent of $R$, while the third depends on the radius. This fixed-order result provides a nonsingular contribution to be combined with a singular log-resummed contribution to give the full spectrum in $\tau_1$ space and also shows how fixed-order and resummation regions change as a function of $x$ and $Q$.
|
https://arxiv.org/abs/2202.08040v2
|
We study non-analytic behavior in the static charge susceptibility in finite
density states of the ABJM theory using its holographic dual. Emphasis is
placed on a particular state characterized by vanishing entropy density at zero
temperature, and Fermi surface-like singularities in various fermionic
correlation functions. The susceptibility exhibits branch points in the complex
momentum plane, with a real part quantitatively very similar to the location of
the Fermi surface singularities.
|
http://arxiv.org/abs/1612.06823v2
|
We study nonmetric analogues of Vietoris solenoids. Let $\Lambda$ be an
ordered continuum, and let $\vec{p}=\langle p_1,p_2,\dots\rangle$ be a sequence
of positive integers. We define a natural inverse limit space
$S(\Lambda,\vec{p})$, where the first factor space is the nonmetric "circle"
obtained by identifying the endpoints of $\Lambda$, and the $n$th factor space,
$n>1$, consists of $p_1p_2\cdot\dots \cdot p_{n-1}$ copies of $\Lambda$ laid
end to end in a circle. We prove that for every cardinal $\kappa\geq 1$, there
is an ordered continuum $\Lambda$ such that $S(\Lambda,\vec{p})$ is
$\frac{1}{\kappa}$-homogeneous; for $\kappa>1$, $\Lambda$ is built from copies
of the long line. Our example with $\kappa=2$ provides a nonmetric answer to a
question of Neumann-Lara, Pellicer-Covarrubias and Puga-Espinosa from 2005, and
with $\kappa=1$ provides an example of a nonmetric homogeneous circle-like
indecomposable continuum. Finally, we employ a cohomology argument to prove
that for each ordered continuum $\Lambda$, as $\vec{p}$ varies there are
$2^\omega$-many nonhomeomorphic spaces $S(\Lambda,\vec{p})$.
|
http://arxiv.org/abs/1412.8508v2
|
We study a family of orthogonal polynomials which satisfy (apart from a
3-term recurrence relation) an eigenvalue equation involving a third order
differential operator of Dunkl-type. The orthogonality measure of these
polynomials consists in the continuous measure of the little -1 Jacobi
polynomials to which is added an arbitrary mass located at the point $x=0$, the
middle of the orthogonality interval. This provides the first nontrivial
example of Krall-type polynomials with a point mass inside the orthogonality
interval. These polynomials can be obtained by a Geronimus transform of the
little $q$-Jacobi polynomials in the limit $q=-1$.
|
http://arxiv.org/abs/1205.7037v2
|
An ultrafast fiber chirped-pulse amplification laser system based on coherent combination of 16 ytterbium-doped rod-type amplifiers is presented. It generates 10 mJ pulse energy at 1 kW average power and 120 fs pulse duration. A partially helium-protected, two-staged chirped-pulse amplification grating compressor is implemented to maintain the close to diffraction-limited beam quality by avoiding nonlinear absorption in air.
|
https://arxiv.org/abs/2103.05614v1
|
An ultrafast fiber chirped-pulse amplifier comprising 8 coherently combined amplifier channels is presented. The laser delivers 1 kW average power at 1 mJ pulse energy and 260 fs pulse duration. Excellent beam quality and low noise performance are confirmed. The laser has proven suitable for demanding scientific applications. Further power scaling is possible right away using even more amplifier channels
|
https://arxiv.org/abs/2101.08498v1
|
Classical soft theorems applied to probe scattering processes on AdS$_4$ spacetimes predict the existence of $1/L^2$ corrections to the soft photon and soft graviton factors of asymptotically flat spacetimes. In this paper, we establish that the $1/L^2$ corrected soft photon theorem can be derived from a large $N$ CFT$_3$ Ward identity. We derive a perturbed soft photon mode operator on a flat spacetime patch in global AdS$_4$ in terms of an integrated expression of the boundary CFT current. Using the same in the CFT$_3$ Ward identity, we recover the $1/L^2$ corrected soft photon theorem derived from classical soft theorems.
|
https://arxiv.org/abs/2209.06802v1
|
We show optimal existence, nonexistence and regularity results for
nonnegative solutions to Dirichlet problems as $$ \begin{cases} \displaystyle
-\Delta_1 u = g(u)|D u|+h(u)f & \text{in}\;\Omega,\\ u=0 &
\text{on}\;\partial\Omega, \end{cases} $$ where $\Omega$ is an open bounded
subset of $\mathbb{R}^N$, $f\geq 0$ belongs to $L^N(\Omega)$, and $g$ and $h$
are continuous functions that may blow up at zero. As a noteworthy fact we show
how a non-trivial interaction mechanism between the two nonlinearities $g$ and
$h$ produces remarkable regularizing effects on the solutions. The sharpness of
our main results is discussed through the use of appropriate explicit examples.
|
http://arxiv.org/abs/1910.13311v1
|
In this paper, we will apply the Goldstone equivalence gauge to calculate the
$1 \leftrightarrow 2$ processes of a sterile neutrino in the thermal plasma
below the standard model (SM) critical temperature $T_c \approx 160 \text{
GeV}$. The sterile neutrino's mass is around the electroweak scale $50 \text{
GeV} \leq m_N \leq 200 \text{ GeV}$, and the acquired thermal averaged
effective width $\bar{\Gamma}_{\text{tot}}$ is continuous around the
cross-over. We will also apply our results to perform a preliminary calculation
of the leptogenesis.
|
http://arxiv.org/abs/2008.00642v2
|
The robustness of neural networks against input perturbations with bounded magnitude represents a serious concern in the deployment of deep learning models in safety-critical systems. Recently the scientific community has focused on enhancing certifiable robustness guarantees by crafting \ols neural networks that leverage Lipschitz bounded dense and convolutional layers. Different methods have been proposed in the literature to achieve this goal however comparing the performance of such methods is not straightforward since different metrics can be relevant (e.g. training time memory usage accuracy certifiable robustness) for different applications. Therefore this work provides a thorough comparison between different methods covering theoretical aspects such as computational complexity and memory requirements as well as empirical measurements of time per epoch required memory accuracy and certifiable robust accuracy. The paper also provides some guidelines and recommendations to support the user in selecting the methods that work best depending on the available resources. We provide code at github.com/berndprach/1LipschitzLayersCompared
|
http://openaccess.thecvf.com//content/CVPR2024/html/Prach_1-Lipschitz_Layers_Compared_Memory_Speed_and_Certifiable_Robustness_CVPR_2024_paper.html
|
The robustness of neural networks against input perturbations with bounded magnitude represents a serious concern in the deployment of deep learning models in safety-critical systems. Recently, the scientific community has focused on enhancing certifiable robustness guarantees by crafting 1-Lipschitz neural networks that leverage Lipschitz bounded dense and convolutional layers. Although different methods have been proposed in the literature to achieve this goal, understanding the performance of such methods is not straightforward, since different metrics can be relevant (e.g., training time, memory usage, accuracy, certifiable robustness) for different applications. For this reason, this work provides a thorough theoretical and empirical comparison between methods by evaluating them in terms of memory usage, speed, and certifiable robust accuracy. The paper also provides some guidelines and recommendations to support the user in selecting the methods that work best depending on the available resources. We provide code at https://github.com/berndprach/1LipschitzLayersCompared.
|
https://arxiv.org/abs/2311.16833v1
|
Neural implicit surfaces are a promising tool for geometry processing that represent a solid object as the zero level set of a neural network. Usually trained to approximate a signed distance function of the considered object, these methods exhibit great visual fidelity and quality near the surface, yet their properties tend to degrade with distance, making geometrical queries hard to perform without the help of complex range analysis techniques. Based on recent advancements in Lipschitz neural networks, we introduce a new method for approximating the signed distance function of a given object. As our neural function is made 1- Lipschitz by construction, it cannot overestimate the distance, which guarantees robustness even far from the surface. Moreover, the 1-Lipschitz constraint allows us to use a different loss function, called the hinge-Kantorovitch-Rubinstein loss, which pushes the gradient as close to unit-norm as possible, thus reducing computation costs in iterative queries. As this loss function only needs a rough estimate of occupancy to be optimized, this means that the true distance function need not to be known. We are therefore able to compute neural implicit representations of even bad quality geometry such as noisy point clouds or triangle soups. We demonstrate that our methods is able to approximate the distance function of any closed or open surfaces or curves in the plane or in space, while still allowing sphere tracing or closest point projections to be performed robustly.
|
https://arxiv.org/abs/2407.09505v1
|
A crucial property for achieving secure, trustworthy and interpretable deep learning systems is their robustness: small changes to a system's inputs should not result in large changes to its outputs. Mathematically, this means one strives for networks with a small Lipschitz constant. Several recent works have focused on how to construct such Lipschitz networks, typically by imposing constraints on the weight matrices. In this work, we study an orthogonal aspect, namely the role of the activation function. We show that commonly used activation functions, such as MaxMin, as well as all piece-wise linear ones with two segments unnecessarily restrict the class of representable functions, even in the simplest one-dimensional setting. We furthermore introduce the new N-activation function that is provably more expressive than currently popular activation functions. We provide code at https://github.com/berndprach/NActivation.
|
https://arxiv.org/abs/2311.06103v2
|
We recently proposed the Halohedron to be the 1-loop Amplituhedron for planar
$\phi^3$ theory. Here we prove this claim by showing how it is possible to
extract the integrand for the partial amplitude $m^1_n(1,\dots,n|1,\dots,n)$
from the canonical form of an Halohedron which lives in an abstract space. This
space is just a step away from ordinary kinematical space at 1-loop, because it
is composed by abstract variables associated to propagators of 1-loop Feynman
diagrams. Such variables, however, are unbound from momentum conservation
relations that would give problems such as double poles. As an application of
our construction, we exploit a well known recursion formula for the canonical
form of a polytope in order to produce an expression for the 1-loop integrand
which would not be evident starting from Feynman diagrams.
|
http://arxiv.org/abs/1806.01842v2
|
Recently the space of tree level color structures for gluon scattering was
determined in arXiv:1403.6837 together with its transformation properties under
permutations. Here we generalize the discussion to loops, demonstrating a
reduction of an arbitrary color diagram to its vacuum skeleton plus rays. For
1-loop there are no residual relations and we determine the space of color
structures both diagrammatically and algebraically in terms of certain sunny
diagrams. We present the generating function for the characteristic polynomials
and a list of irreducible representations for $3 \le n \le 9$ external legs.
Finally we present a new proof for the 1-loop shuffle relations based on the
cyclic shuffle and split operations.
|
http://arxiv.org/abs/1406.1504v2
|
In earlier work of two of the authors, two 1-loop polynomial invariants of cusped 3-manifolds were constructed using combinatorial data of ideal triangulations, and conjectured to be equal to the $\mathbb{C}^2$ and the $\mathbb{C}^3$-torsion polynomials. Here, we prove this conjecture for layered triangulations of fibered 3-manifolds with toroidal boundary, and we illustrate our theorems with exact computations of the 1-loop and the torsion polynomials. As further evidence for the conjecture, we confirm it for more than 6,600 nonfibered manifolds, and use this data to explore the extent to which the $\mathbb{C}^2$-torsion determines the Thurston norm.
|
https://arxiv.org/abs/2304.00469v3
|
Motivated by the conjectured asymptotics of the Kashaev invariant, Dimofte and the first author introduced a power series associated to a suitable ideal triangulation of a cusped hyperbolic 3-manifold, proved that its constant (1-loop) term is a topological invariant and conjectured that it equals to the adjoint Reidemeister torsion. We prove this conjecture for hyperbolic 2-bridge knots by combining the work of Ohtsuki--Takata with an explicit computation.
|
https://arxiv.org/abs/2411.03801v2
|
The 1-loop self-energy of a Dirac electron of mass m propagating in a thin
medium simulating graphene in an external magnetic field B is investigated in
Quantum Field Theory. Equivalence is shown with the so-called reduced QED_{3+1}
on a 2-brane. Schwinger-like methods are used to calculate the self-mass \delta
m_{LLL} of the electron when it lies in the lowest Landau level. Unlike in
standard QED_{3+1}, it does not vanish at the limit m -> 0 :\delta m_{LLL} ->
(\alpha/2)\sqrt{pi/2}sqrt{\hbar|e|B/c^2}; all Landau levels of the virtual
electron are taken into account and on mass-shell renormalization conditions
are implemented. Restricting to the sole lowest Landau level of the virtual
electron is explicitly shown to be inadequate. Resummations at higher orders
lie beyond the scope of this work.
|
http://arxiv.org/abs/1607.00838v2
|
Studying the diffusion and kinetic equilibration of heavy quarks within a hot QCD medium profits from the knowledge of a coloured Lorentz force that acts on them. Starting from the spatial components of the vector current, and carrying out two matching computations, one for the heavy quark mass scale ($M$) and another for thermal scales ($\sqrt{MT}$, $T$), we determine 1-loop matching coefficients for the electric and magnetic parts of a Lorentz force. The magnetic part has a non-zero anomalous dimension, which agrees with that extracted from two other considerations, one thermal and the other in vacuum. The matching coefficient could enable a lattice study of a colour-magnetic 2-point correlator.
|
https://arxiv.org/abs/2103.14270v2
|
The leading terms in the large-$R$ asymptotics of the functional of the one-electron reduced density matrix for the ground-state energy of the H$_2$ molecule with the internuclear separation $R$ is derived thanks to the solution of the phase dilemma at the $R \to \infty$ limit. At this limit, the respective natural orbitals (NOs) are given by symmetric and antisymmetric combinations of "half-space" orbitals with the corresponding natural amplitudes of the same amplitudes but opposite signs. Minimization of the resulting explicit functional yields the large-$R$ asymptotics for the occupation numbers of the weakly occupied NOs and the $C_6$ dispersion coefficient. The highly accurate approximates for the radial components of the $p$-type "half-space" orbitals and the corresponding occupation numbers (that decay like $R^{-6}$), which are available for the first time thanks to the development of the present formalism, have some unexpected properties.
|
https://arxiv.org/abs/2303.06400v1
|
The detection and localization of deepfake content, particularly when small fake segments are seamlessly mixed with real videos, remains a significant challenge in the field of digital media security. Based on the recently released AV-Deepfake1M dataset, which contains more than 1 million manipulated videos across more than 2,000 subjects, we introduce the 1M-Deepfakes Detection Challenge. This challenge is designed to engage the research community in developing advanced methods for detecting and localizing deepfake manipulations within the large-scale high-realistic audio-visual dataset. The participants can access the AV-Deepfake1M dataset and are required to submit their inference results for evaluation across the metrics for detection or localization tasks. The methodologies developed through the challenge will contribute to the development of next-generation deepfake detection and localization systems. Evaluation scripts, baseline models, and accompanying code will be available on https://github.com/ControlNet/AV-Deepfake1M.
|
https://arxiv.org/abs/2409.06991v1
|
We generated 1.7-cycle and 35-$\mu$J pulses at a 1-MHz repetition rate by using two-stage multiple plate continuum compression of Yb-laser pulses with 80-W average input power. By adjusting the plate positions with careful consideration of the thermal lensing effect due to the high average power, we compressed the output pulse with a 184-fs initial duration to 5.7 fs by using only group-delay-dispersion compensation. This pulse achieved a sufficient beam quality ($M^2$ < 1.5) reaching a focused intensity over 10$^{14}$ W/cm$^2$ and a high spatial-spectral homogeneity (98%). Our study holds promise for a MHz-isolated-attosecond-pulse source for advanced attosecond spectroscopic and imaging technologies with unprecedentedly high signal-to-noise ratios.
|
https://arxiv.org/abs/2210.12976v2
|
Images naturally appear alongside text in a wide variety of media, such as books, magazines, newspapers, and in online articles. This type of multi-modal data offers an interesting basis for vision and language research but most existing datasets use crowdsourced text, which removes the images from their original context. In this paper, we introduce the KBK-1M dataset of 1.6 million images in their original context, with co-occurring texts found in Dutch newspapers from 1922 - 1994. The images are digitally scanned photographs, cartoons, sketches, and weather forecasts; the text is generated from OCR scanned blocks. The dataset is suitable for experiments in automatic image captioning, image―article matching, object recognition, and data-to-text generation for weather forecasting. It can also be used by humanities scholars to analyse photographic style changes, the representation of people and societal issues, and new tools for exploring photograph reuse via image-similarity-based search.
|
https://aclanthology.org/L16-1488
|
The parity modulation of the ground state of a superconducting island is a
direct consequence of the presence of the Cooper pair condensate preferring an
even number of charge carriers. The addition energy of an odd, unpaired
quasiparticle equals to the superconducting gap, $\Delta$, suppressing single
electron hopping in the low temperature limit. Controlling the quasiparticle
occupation is of fundamental importance for superconducting qubits as single
electron tunneling results in decoherence. In particular, topological quantum
computation relies on the parity control and readout of Majorana bound states.
Here we present parity modulation for the first time of a niobium titanite
nitride (NbTiN) Cooper-pair transistor coupled to aluminium (Al) leads. We show
that this circuit is compatible with the magnetic field requirement in the
range of 100 mT of inducing topological superconductivity in spin-orbit coupled
nanowires. Our observed parity lifetime exceeding 1 minute is several orders of
magnitude higher than the required gate time of flux-controlled braiding of
Majorana states. Our findings readily demonstrate that a NbTiN island can be
parity-controlled and therefore provides a good platform for superconducting
coherent circuits operating in a magnetic field.
|
http://arxiv.org/abs/1501.03855v1
|
Performing long-term experimentation or large-scale data collection for machine learning in the field of soft robotics is challenging, due to the hardware robustness and experimental flexibility required. In this work, we propose a modular parallel robotic manipulation platform suitable for such large-scale data collection and compatible with various soft-robotic fabrication methods. Considering the computational and theoretical difficulty of replicating the high-fidelity, faster-than-real-time simulations that enable large-scale data collection in rigid robotic systems, a robust soft-robotic hardware platform becomes a high priority development task for the field. The platform's modules consist of a pair of off-the-shelf electrical motors which actuate a customizable finger consisting of a compliant parallel structure. The parallel mechanism of the finger can be as simple as a single 3D-printed urethane or molded silicone bulk structure, due to the motors being able to fully actuate a passive structure. This design flexibility allows experimentation with soft mechanism varied geometries, bulk properties and surface properties. Additionally, while the parallel mechanism does not require separate electronics or additional parts, these can be included, and it can be constructed using multi-functional soft materials to study compatible soft sensors and actuators in the learning process. In this work, we validate the platform's ability to be used for policy gradient reinforcement learning directly on hardware in a benchmark 2D manipulation task. We additionally demonstrate compatibility with multiple fingers and characterize the design constraints for compatible extensions.
|
https://arxiv.org/abs/2409.03614v1
|
In this article, we will give the Deligne 1-motives up to isogeny
corresponding to the $\mathbb{Q}$-limiting mixed Hodge structures of
semi-stable degenerations of curves, by using logarithmic structures and
Steenbrink's cohomological mixed Hodge complexes associated to semi-stable
degenerations of curves.
|
http://arxiv.org/abs/1707.08550v3
|
The classes of 1MP-inverses and MP1-inverses are recently introduced classes of generalized inverses of complex matrix. Actually, they coincide with the classes of $\{1,2,3\}$ and $\{1,2,4\}$ inverses, respectively. We consider these inverses in the context of a ring with involution and prove that their most important characterizations and properties remain true. We show that the binary relations based on these inverses are in fact the well known left-star and right-star partial orders. We extend these relations to the ring case, connect them with the unified theory of partial order relations based on generalized inverses and provide several properties. Finally, we indicate how these results can be applied to bounded Hilbert space operators.
|
https://arxiv.org/abs/2205.15132v1
|
Convolutional neural networks (CNNs) and Transformer-based models are being widely applied in medical image segmentation thanks to their ability to extract high-level features and capture important aspects of the image. However, there is often a trade-off between the need for high accuracy and the desire for low computational cost. A model with higher parameters can theoretically achieve better performance but also result in more computational complexity and higher memory usage, and thus is not practical to implement. In this paper, we look for a lightweight U-Net-based model which can remain the same or even achieve better performance, namely U-Lite. We design U-Lite based on the principle of Depthwise Separable Convolution so that the model can both leverage the strength of CNNs and reduce a remarkable number of computing parameters. Specifically, we propose Axial Depthwise Convolutions with kernels 7x7 in both the encoder and decoder to enlarge the model receptive field. To further improve the performance, we use several Axial Dilated Depthwise Convolutions with filters 3x3 for the bottleneck as one of our branches. Overall, U-Lite contains only 878K parameters, 35 times less than the traditional U-Net, and much more times less than other modern Transformer-based models. The proposed model cuts down a large amount of computational complexity while attaining an impressive performance on medical segmentation tasks compared to other state-of-the-art architectures. The code will be available at: https://github.com/duong-db/U-Lite.
|
https://arxiv.org/abs/2306.16103v2
|
We consider an expansion of the type-I seesaw mechanism by the inverse of the 3-3 matrix element $1/(M_{R})_{33}$ of the mass matrix of right-handed neutrinos $M_{R}$. Conditions of such a situation are obtained for $M_{R}$ and the Dirac mass matrix $m_{D}$. In this case, a partial $Z_{2}$ symmetry such as $S m_{D} P_{} = \pm m_{D} P_{}$ with a projection matrix $P_{} = {\rm diag} ( 1, 1, 0)$ leads to an approximate $Z_{2}$ symmetry by $S$ for the neutrino mass matrix $m_{\nu}$. Such a partial $Z_{2}$ symmetry is desirable in the context of unified theories because it allows hierarchical $m_{D}$ and the large mixing of $m_{\nu}$ simultaneously.
|
https://arxiv.org/abs/2208.10000v2
|
Lie symmetry method is applied to investigate symmetries of the combined
KdV-nKdV equation, that is a new integrable equation by combining the KdV
equation and negative order KdV equation. Symmetries which are obtained in this
article, are further helpful for reducing the combined KdV-nKdV equation into
ordinary differential equation. Moreover, a set of eight invariant solutions
for combined KdV-nKdV equation is obtained by using proposed method. Out of the
eight solutions so obtained in which two solutions generate progressive wave
solutions, five are singular solutions and one multisoliton solutions which is
in terms of WeierstrassZeta function.
|
http://arxiv.org/abs/1805.10983v1
|
In this work, we argue that the observed differences in the value of the vector coupling constant extracted from the decays $\rho\to \pi\pi$ ($g_{\rho} = 6.0$), $\rho\to l^+l^-$ ($g_{\rho} = 5.0 $) and $\omega\to l^+ l^-$ ($g_{\rho} = 5.7$), where $l=e,\mu $, are an indication of the important role played by the $1/N_c$ corrections in the description of these processes. We show that an emission of a photon by charged meson loops in the $\rho^0, \omega,\phi\to\gamma$ transitions is a key process that allows to describe above vector meson decays into two leptons with a single value $g_\rho = 6.0$. Our result supports the idea of universality of neutral vector mesons and clarifies the role of accounting of $1/N_c$ corrections to its fulfilment.
|
https://arxiv.org/abs/2105.02160v2
|
The mass formulas and decay constants of electrically charged and strange pseudoscalar mesons are analyzed within the combined framework of Nambu -- Jona-Lasinio model and the $1/N_c$ expansion up to $\mathcal O(1/N_c^2)$. The light quark masses explicitly violating $SU(3)_L\times SU(3)_R$ chiral symmetry of the strong interactions are taken to be of order $\mathcal O(1/N_c)$. The Fock-Schwinger proper-time method and the Volterra series are used to derive the effective action. A set of sum rules is obtained that relates the phenomenological values of the masses of pseudoscalar mesons to the mass ratios of light quarks. It is shown that combining the new sum rules with the experimental data on the decay width $\eta\to 3\pi$ allows to establish limits for the ratios: $0.47<m_u/m_d<0.59$ and $18.60<m_s/m_d<19.66$. A comparison with the results of similar calculations in $1/N_c$ chiral perturbation theory is made.
|
https://arxiv.org/abs/2302.14118v2
|
We continue to study the properties of the light pseudoscalar nonet within the combined framework of Nambu -- Jona-Lasinio model and $1/N_c$ expansion, assuming that current quark masses count of order $\mathcal O(1/N_c)$. The masses, mixing angles and decay constants of the $\pi^0$, $\eta$ and $\eta'$ are calculated. The role of the $U(1)_A$ anomaly is emphasized. It is shown that the gluon anomaly suppresses the leading order effects that might otherwise be substantial for the $\eta\to 3\pi$ amplitude. A detailed comparison with the known results of $1/N_c$ chiral perturbation theory is made.
|
https://arxiv.org/abs/2303.01865v2
|
In this paper we investigate $1/N$ corrections to mesonic spectrum in $1+1$-dimensional Quantum Chromodynamics ($\text{QCD}_2$) with fundamental quarks using effective Hamiltonian method. We express the corrections in terms of 't Hooft equation solutions. First, we consider 2-flavor model with a heavy and a light quark. We show that, in contrast to some claims in earlier literature, the $1/N$ correction to the mass of the heavy-light meson remains finite when the light quark mass is taken to zero. Nevertheless, the corrections become significantly larger in this limit; we attribute this to the presence of massless modes in the spectrum. We also study the corrections to the lightest meson mass in 1-flavor model and show that they are consistent with recent numerical data, but not with the prediction coming from bosonization. Then we study low energy effective theory for 2 flavors. We show that the 3-meson interaction vertex correctly reproduces Wess-Zumino-Witten (WZW) coupling when both quarks become massless. This coupling does not change even if one of the quarks is massive. We employ Discretized Light Cone Quatization (DLCQ) to check the continuum results and show that the improved version can be used for small quark mass. Finally, we study the states associated with $1\to 2$ meson thresholds. Using degenerate perturbation theory, we show that when the decay is allowed by parity, the infinite $N$ theory has near-threshold bound states that mix one- and two-meson parts. They are $1/3$ two-meson and $2/3$ one-meson and the corrections to their masses have unusual scaling $\sim 1/N^{2/3}$.
|
https://arxiv.org/abs/2405.04031v3
|
The structure functions $F_1$ and $F_2$ of the hadronic tensor of vector
mesons are obtained at order $1/N$ and strong coupling using the gauge/gravity
duality. We find that the large $N$ limit and the high energy one do not
commute. Thus, by considering the high energy limit first, our results of the
first moments of $F_1$ for the rho meson agree well with those from lattice
QCD, with an important improvement of the accuracy with respect to the
holographic dual calculation in the planar limit.
|
http://arxiv.org/abs/1809.10515v1
|
We study a class of four-fermion Gross-Neveu like models in four dimensions
with critical exponents $z=2$ and $z=3$. The models with $z=2$ are known to be
perturbatively nonrenormalizable but are shown to be renormalizable in the
context of the $1/N$ expansion. We calculate explicitly the effective potential
for these models.
|
http://arxiv.org/abs/2001.06467v1
|
We revised the large-$N$ expansion for a three-dimensional Bose system with
short-range repulsion in normal phase. Particularly, for the model potential
that is characterised only by the $s$-wave scattering length $a$ the full
numerical calculations of the critical temperature in the $1/N$-approximation
as a function of the gas parameter $an^{1/3}$ are performed. Additionally to
the well-known result in the dilute limit we estimated analytically the
leading-order strong-coupling behavior of the Bose-Einstein condensation
transition temperature. It is shown that the critical temperature shift of the
non-ideal Bose gas grows at small $an^{1/3}$, reaches some maximal value and
then falls down becoming negative.
|
http://arxiv.org/abs/1704.08968v1
|
Localization approach to $\mathcal N=2$ superconformal $SU(N) \times SU(N)$ quiver theory leads to a non-Gaussian two-matrix model representation for the expectation value of BPS circular $SU(N)$ Wilson loop $\langle\mathcal W\rangle$. We study the subleading $1/N^2$ term in the large $N$ expansion of $\langle\mathcal W\rangle$ at weak and strong coupling. We concentrate on the case of the symmetric quiver with equal gauge couplings which is equivalent to the $\mathbb Z_{2}$ orbifold of the $SU(2N)$ $\mathcal N=4$ SYM theory. This orbifold gauge theory should be dual to type IIB superstring in ${\rm AdS}_5\times (S^{5}/\mathbb Z_{2})$. We present a string theory argument suggesting that the $1/N^2$ term in $\langle\mathcal W\rangle$ in the orbifold theory should have the same strong-coupling asymptotics $ \lambda^{3/2}$ as in the $\mathcal N=4$ SYM case. We support this prediction by a numerical study of the localization matrix model on the gauge theory side. We also find a relation between the $1/N^2$ term in the Wilson loop expectation value and the derivative of the free energy of the orbifold gauge theory on 4-sphere.
|
https://arxiv.org/abs/2102.07696v3
|
We consider four dimensional $U(N)$ $\mathcal N=4$ SYM theory interacting with a 3d $\mathcal N=4$ theory living on a codimension-one interface and holographically dual to the D3-D5 system without flux. Localization captures several observables in this dCFT, including its free energy, related to the defect expectation value, and single trace $\frac{1}{2}$-BPS composite scalars. These quantities may be computed in a hermitian one-matrix model with non-polynomial single-trace potential. We exploit the integrable Volterra hierarchy underlying the matrix model and systematically study its $1/N$ expansion at any value of the 't Hooft coupling. In particular, the strong coupling regime is determined -- up to non-perturbative exponentially suppressed corrections -- by differential relations that constrain higher order terms in the $1/N$ expansion. The analysis is extended to the model with $SU(N)$ gauge symmetry by resorting to the more general Toda lattice equations.
|
https://arxiv.org/abs/2212.12415v2
|
Generalized inverses are important in statistics and other areas of applied
matrix algebra. A \emph{generalized inverse} of a real matrix $A$ is a matrix
$H$ that satisfies the Moore-Penrose (M-P) property $AHA=A$. If $H$ also
satisfies the M-P property $HAH=H$, then it is called \emph{reflexive}.
Reflexivity of a generalized inverse is equivalent to minimum rank, a highly
desirable property. We consider aspects of symmetry related to the calculation
of various \emph{sparse} reflexive generalized inverses of $A$. As is common,
we use (vector) 1-norm minimization for both inducing sparsity and for keeping
the magnitude of entries under control.
When $A$ is symmetric, a symmetric $H$ is highly desirable, but generally
such a restriction on $H$ will not lead to a 1-norm minimizing reflexive
generalized inverse. We investigate a block construction method to produce a
symmetric reflexive generalized inverse that is structured and has guaranteed
sparsity. Letting the rank of $A$ be $r$, we establish that the 1-norm
minimizing generalized inverse of this type is a 1-norm minimizing symmetric
generalized inverse when (i) $r=1$ and when (ii) $r=2$ and $A$ is nonnegative.
Another aspect of symmetry that we consider relates to another M-P property:
$H$ is \emph{ah-symmetric} if $AH$ is symmetric. The ah-symmetry property is
sufficient for a generalized inverse to be used to solve the least-squares
problem $\min\{\|Ax-b\|_2:~x\in\mathbb{R}^n\}$ using $H$, via $x:=Hb$. We
investigate a column block construction method to produce an ah-symmetric
reflexive generalized inverse that is structured and has guaranteed sparsity.
We establish that the 1-norm minimizing ah-symmetric generalized inverse of
this type is a 1-norm minimizing ah-symmetric generalized inverse when (i)
$r=1$ and when (ii) $r=2$ and $A$ satisfies a technical condition.
|
http://arxiv.org/abs/2010.11406v1
|
We develop the 1/N expansion for stable string bit models, focusing on a
model with bit creation operators carrying only transverse spinor indices
a=1,...,s. At leading order (1/N=0), this model produces a (discretized)
lightcone string with a "transverse space' of $s$ Grassmann worldsheet fields.
Higher orders in the 1/N expansion are shown to be determined by the overlap of
a single large closed chain (discretized string) with two smaller closed
chains. In the models studied here, the overlap is not accompanied with
operator insertions at the break/join point. Then the requirement that the
discretized overlap have a smooth continuum limit leads to the critical
Grassmann "dimension" of s=24. This "protostring", a Grassmann analog of the
bosonic string, is unusual, because it has no large transverse dimensions. It
is a string moving in one space dimension and there are neither tachyons nor
massless particles. The protostring, derived from our pure spinor string bit
model, has 24 Grassmann dimensions, 16 of which could be bosonized to form 8
compactified bosonic dimensions, leaving 8 Grassmann dimensions--the worldsheet
content of the superstring. If the transverse space of the protostring could be
"decompactified", string bit models might provide an appealing and solid
foundation for superstring theory.
|
http://arxiv.org/abs/1512.08439v1
|
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