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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.
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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
|
We present the first Open Gravitational-wave Catalog (1-OGC), obtained by
using the public data from Advanced LIGO's first observing run to search for
compact-object binary mergers. Our analysis is based on new methods that
improve the separation between signals and noise in matched-filter searches for
gravitational waves from the merger of compact objects. The three most
significant signals in our catalog correspond to the binary black hole mergers
GW150914, GW151226, and LVT151012. We observe these signals at a true discovery
rate of $99.92\%$. We find that LVT151012 alone has a 97.6$\%$ probability of
being astrophysical in origin. No other significant binary black hole
candidates are found, nor did we observe any significant binary neutron star or
neutron star--black hole candidates. We make available our complete catalog of
events, including the sub-threshold population of candidates.
|
http://arxiv.org/abs/1811.01921v2
|
A temperature controlled 1 {\Omega}-10 k{\Omega} standard Resistors
transportable setup was developed at National Institute of Metrological
Research, (INRIM) for the calibration and adjustment of multifunction
electrical instruments. The two Standards consist respectively of two 10
{\Omega} and 100 k{\Omega} parallel connected resistors nets inserted in a
temperature controlled aluminium box. Novelty of the realization is the oil
insertion of the 1 {\Omega} net with its internal connectors lowering the
thermo-electromotive forces (emfs) effects. Short and mid-term stabilities of
the setup Standards resulted on the order and in some cases better than other
top level 1 {\Omega} and 10 k{\Omega} commercial Standards. The transport
effect turning off the setup temperature control did not cause appreciable
measurement deviations on the two Standards. The Standards uncertainties meet
those requested by DMMs and MFCs manufacturers to calibrate and adjust these
instruments. A test to adjust a multifunction calibrator gave satisfactory
results.
|
http://arxiv.org/abs/1505.04398v1
|
Oblivious transfer (OT) is an important tool in cryptography. It serves as a
subroutine to other complex procedures of both theoretical and practical
significance. Common attribute of OT protocols is that one party (Alice) has to
send a message to another party (Bob) and has to stay oblivious on whether Bob
did receive the message. Specific (OT) protocols vary by exact definition of
the task - in the all-or-nothing protocol Alice sends a single bit-string
message, which Bob is able to read only with 50% probability, whereas in
1-out-of-2 OT protocol Bob reads one out of two messages sent by Alice. These
two flavours of protocol are known to be equivalent. Recently a computationally
secure all-or-nothing OT protocol based on quantum states was developed in [A.
Souto et. al., PRA 91, 042306], which however cannot be reduced to 1-out-of-2
OT protocol by standard means. Here we present an elaborated reduction of this
protocol which retains the security of the original.
|
http://arxiv.org/abs/1611.10087v1
|
1-out-of-n oblivious signature by Chen (ESORIC 1994) is a protocol between the user and the signer. In this scheme, the user makes a list of n messages and chooses the message that the user wants to obtain a signature from the list. The user interacts with the signer by providing this message list and obtains the signature for only the chosen message without letting the signer identify which messages the user chooses. Tso et al. (ISPEC 2008) presented a formal treatment of 1-out-of-n oblivious signatures. They defined unforgeability and ambiguity for 1-out-of-n oblivious signatures as a security requirement. In this work, first, we revisit the unforgeability security definition by Tso et al. and point out that their security definition has problems. We address these problems by modifying their security model and redefining unforgeable security. Second, we improve the generic construction of a 1-out-of-n oblivious signature scheme by Zhou et al. (IEICE Trans 2022). We reduce the communication cost by modifying their scheme with a Merkle tree. Then we prove the security of our modified scheme.
|
https://arxiv.org/abs/2404.00602v1
|
We present 1-Pager the first system that answers a question and retrieves evidence using a single Transformer-based model and decoding process. 1-Pager incrementally partitions the retrieval corpus using constrained decoding to select a document and answer string, and we show that this is competitive with comparable retrieve-and-read alternatives according to both retrieval and answer accuracy metrics. 1-Pager also outperforms the equivalent closed-book question answering model, by grounding predictions in an evidence corpus. While 1-Pager is not yet on-par with more expensive systems that read many more documents before generating an answer, we argue that it provides an important step toward attributed generation by folding retrieval into the sequence-to-sequence paradigm that is currently dominant in NLP. We also show that the search paths used to partition the corpus are easy to read and understand, paving a way forward for interpretable neural retrieval.
|
https://arxiv.org/abs/2310.16568v1
|
We introduce 1P1Q, a novel quantum data encoding scheme for high-energy physics (HEP), where each particle is assigned to an individual qubit, enabling direct representation of collision events without classical compression. We demonstrate the effectiveness of 1P1Q in quantum machine learning (QML) through two applications: a Quantum Autoencoder (QAE) for unsupervised anomaly detection and a Variational Quantum Circuit (VQC) for supervised classification of top quark jets. Our results show that the QAE successfully distinguishes signal jets from background QCD jets, achieving superior performance compared to a classical autoencoder while utilizing significantly fewer trainable parameters. Similarly, the VQC achieves competitive classification performance, approaching state-of-the-art classical models despite its minimal computational complexity. Furthermore, we validate the QAE on real experimental data from the CMS detector, establishing the robustness of quantum algorithms in practical HEP applications. These results demonstrate that 1P1Q provides an effective and scalable quantum encoding strategy, offering new opportunities for applying quantum computing algorithms in collider data analysis.
|
https://arxiv.org/abs/2502.17301v1
|
A graph G is said to be 1-perfectly orientable (1-p.o. for short) if it
admits an orientation such that the out-neighborhood of every vertex is a
clique in G. The class of 1-p.o. graphs forms a common generalization of the
classes of chordal and circular arc graphs. Even though 1-p.o. graphs can be
recognized in polynomial time, no structural characterization of 1-p.o. graphs
is known. In this paper we consider the four standard graph products: the
Cartesian product, the strong product, the direct product, and the
lexicographic product. For each of them, we characterize when a nontrivial
product of two graphs is 1-p.o.
|
http://arxiv.org/abs/1511.07314v2
|
A graph $G$ is said to be $1$-perfectly orientable if it has an orientation
such that for every vertex $v\in V(G)$, the out-neighborhood of $v$ in $D$ is a
clique in $G$. In $1982$, Skrien posed the problem of characterizing the class
of $1$-perfectly orientable graphs. This graph class forms a common
generalization of the classes of chordal and circular arc graphs; however,
while polynomially recognizable via a reduction to $2$-SAT, no structural
characterization of this intriguing class of graphs is known. Based on a
reduction of the study of $1$-perfectly orientable graphs to the biconnected
case, we characterize, both in terms of forbidden induced minors and in terms
of composition theorems, the classes of $1$-perfectly orientable
$K_4$-minor-free graphs and of $1$-perfectly orientable outerplanar graphs. As
part of our approach, we introduce a class of graphs defined similarly as the
class of $2$-trees and relate the classes of graphs under consideration to two
other graph classes closed under induced minors studied in the literature:
cyclically orientable graphs and graphs of separability at most~$2$.
|
http://arxiv.org/abs/1604.04598v2
|
An odd coloring of a graph $G$ is a proper coloring such that any non-isolated vertex in $G$ has a coloring appears odd times on its neighbors. The odd chromatic number, denoted by $\chi_o(G)$, is the minimum number of colors that admits an odd coloring of $G$. Petru\v{s}evski and \v{S}krekovski in 2021 introduced this notion and proved that if $G$ is planar, then $\chi_o(G)\le9$ and conjectured that $\chi_o(G)\le5$. More recently, Petr and Portier improved $9$ to $8$. A graph is $1$-planar if it can be drawn in the plane so that each edge is crossed by at most one other edge. Cranston, Lafferty and Song showed that every $1$-planar graph is odd $23$-colorable. In this paper, we improved this result and showed that every $1$-planar graph is odd $13$-colorable.
|
https://arxiv.org/abs/2206.13967v1
|
We show that every 1-planar graph with minimum degree at least 4 has girth at
most $8$, and every 1-planar graph with minimum degree at least 3 has girth at
most $198$.
|
http://arxiv.org/abs/2001.05402v2
|
A matchstick graph is a plane graph with edges drawn as unit distance line segments. This class of graphs was introduced by Harborth who conjectured that a matchstick graph on $n$ vertices can have at most $\lfloor 3n - \sqrt{12n - 3}\rfloor$ edges. Recently his conjecture was settled by Lavoll\'ee and Swanepoel. In this paper we consider $1$-planar unit distance graphs. We say that a graph is a $1$-planar unit distance graph if it can be drawn in the plane such that all edges are drawn as unit distance line segments while each of them are involved in at most one crossing. We show that such graphs on $n$ vertices can have at most $3n-\sqrt[4]{n}/10$ edges.
|
https://arxiv.org/abs/2310.00940v1
|
Within the framework of string theory, a number of new fields are possible correcting the Einstein-Hilbert action, including a Kalb-Ramond two-form field. In this work we derive explicitly first order relativistic corrections to conservative dynamics with a Kalb-Ramond field, using the effective field theory approach. The resulting additional terms in the Lagrangian governing conservative binary dynamics are presented explicitly.
|
https://arxiv.org/abs/2312.11322v1
|
In this paper, we compute the 1-point correlation functions of all states for the $\mathbb{Z}_2$-orbifolds of lattice vertex operator algebras.
|
https://arxiv.org/abs/2505.02954v1
|
We obtain explicit formulas for the $1$-point functions of all states in the symmetrized Heisenberg algebra $M^+$ and symmetrized lattice VOAs $V_L^+$. For this we employ a new $\mathbf Z_2$-twisted variant of so-called Zhu recursion.
|
https://arxiv.org/abs/2204.08318v1
|
Solving Perspective-n-Point (PnP) problems is a traditional way of estimating object poses. Given outlier-contaminated data, a pose of an object is calculated with PnP algorithms of n = {3, 4} in the RANSAC-based scheme. However, the computational complexity considerably increases along with n and the high complexity imposes a severe strain on devices which should estimate multiple object poses in real time. In this paper, we propose an efficient method based on 1-point RANSAC for estimating a pose of an object on the ground. In the proposed method, a pose is calculated with 1-DoF parameterization by using a ground object assumption and a 2D object bounding box as an additional observation, thereby achieving the fastest performance among the RANSAC-based methods. In addition, since the method suffers from the errors of the additional information, we propose a hierarchical robust estimation method for polishing a rough pose estimate and discovering more inliers in a coarse-to-fine manner. The experiments in synthetic and real-world datasets demonstrate the superiority of the proposed method.
|
https://arxiv.org/abs/2008.03718v2
|
This paper proposes a RANSAC-based algorithm for determining the axial rotation angle of an object from a pair of its tomographic projections. An equation is derived for calculating the rotation angle using one correct keypoints correspondence of two tomographic projections. The proposed algorithm consists of the following steps: keypoints detection and matching, rotation angle estimation for each correspondence, outliers filtering with the RANSAC algorithm, finally, calculation of the desired angle by minimizing the re-projection error from the remaining correspondences. To validate the proposed method an experimental comparison against methods based on analysis of the distribution of the angles computed from all correspondences is conducted.
|
https://arxiv.org/abs/1910.01681v1
|
Let $G$ be a finite group and $D_{2n}$ be the dihedral group of $2n$
elements. For a positive integer $d$, let $\mathsf{s}_{d\mathbb{N}}(G)$ denote
the smallest integer $\ell\in \mathbb{N}_0\cup \{+\infty\}$ such that every
sequence $S$ over $G$ of length $|S|\geq \ell$ has a nonempty $1$-product
subsequence $T$ with $|T|\equiv 0$ (mod $d$). In this paper, we mainly study
the problem for dihedral groups $D_{2n}$ and determine their exact values:
$\mathsf{s}_{d\mathbb{N}}(D_{2n})=2d+\lfloor log_2n\rfloor$, if $d$ is odd with
$n|d$; $\mathsf{s}_{d\mathbb{N}}(D_{2n})=nd+1$, if $gcd(n,d)=1$. Furthermore,
we also analysis the problem for metacyclic groups $C_p\ltimes_s C_q$ and
obtain a result: $\mathsf{s}_{kp\mathbb{N}}(C_p\ltimes_s
C_q)=lcm(kp,q)+p-2+gcd(kp,q)$, where $p\geq 3$ and $p|q-1$.
|
http://arxiv.org/abs/2003.14007v1
|
In the framework of quasi-regular strongly local Dirichlet form $(\mathscr{E},D(\mathscr{E}))$ on $L^2(X;\mathfrak{m})$ admitting minimal $\mathscr{E}$-dominant measure $\mu$, we construct a natural $p$-energy functional $(\mathscr{E}^{\,p},D(\mathscr{E}^{\,p}))$ on $L^p(X;\mathfrak{m})$ and $(1,p)$-Sobolev space $(H^{1,p}(X),\|\cdot\|_{H^{1,p}})$ for $p\in]1,+\infty[$. In this paper, we establish the Clarkson type inequality for $(H^{1,p}(X),\|\cdot\|_{H^{1,p}})$. As a consequence, $(H^{1,p}(X),\|\cdot\|_{H^{1,p}})$ is a uniformly convex Banach space, hence it is reflexive. Based on the reflexivity of $(H^{1,p}(X),\|\cdot\|_{H^{1,p}})$, we prove that (generalized) normal contraction operates on $(\mathscr{E}^{\,p},D(\mathscr{E}^{\,p}))$, which has been shown in the case of various concrete settings, but has not been proved for such general framework. Moreover, we prove that $(1,p)$-capacity ${\rm Cap}_{1,p}(A)<\infty$ for open set $A$ admits an equilibrium potential $e_A\in D(\mathscr{E}^{\,p})$ with $0\leq e_A\leq 1$ $\mathfrak{m}$-a.e. and $e_A=1$ $\mathfrak{m})$-a.e.~on $A$.
|
https://arxiv.org/abs/2310.11652v2
|
I calculate ${1\over Q^2}$ power corrections to unpolarized Drell-Yan hadronic tensor for electromagnetic (EM) current at large $N_c$ and demonstrate the EM gauge invariance at this level.
|
https://arxiv.org/abs/2404.15116v3
|
We report the discovery of 1RXH J082623.6-505741, a 10.4 hr orbital period compact binary. Modeling extensive optical photometry and spectroscopy reveals a $\sim 0.4 M_{\odot}$ K-type secondary transferring mass through a low-state accretion disk to a non-magnetic $\sim 0.8 M_{\odot}$ white dwarf. The secondary is overluminous for its mass and dominates the optical spectra at all epochs, and must be evolved to fill its Roche Lobe at this orbital period. The X-ray luminosity $L_X \sim 1$-$2 \times 10^{32}$ erg s$^{-1}$ derived from both new XMM-Newton and archival observations, although high compared to most CVs, still only requires a modest accretion rate onto the white dwarf of $\dot{M} \sim 3 \times 10^{-11}$ to $3 \times 10^{-10} M_{\odot}$ yr$^{-1}$, lower than expected for a cataclysmic variable with an evolved secondary. No dwarf nova outbursts have yet been observed from the system, consistent with the low derived mass transfer rate. Several other cataclysmic variables with similar orbital periods also show unexpectedly low mass transfer rates, even though selection effects disfavor the discovery of binaries with these properties. This suggests the abundance and evolutionary state of long-period, low mass transfer rate cataclysmic variables is worthy of additional attention.
|
https://arxiv.org/abs/2206.10625v1
|
We report the discovery of a new cataclysmic variable DDE 32 identified with
the ROSAT X-ray source 1RXS J161935.7+524630 in Draco. The variability was
originally found by D. Denisenko on the digitized Palomar plates centered at
the position of X-ray source. The photometric observations by F. Martinelli at
Lajatico Astronomical Center in June 2015 have shown the large amplitude
(nearly 2 magnitudes) variability with a period about 100.5 minutes. Using the
publicly available Catalina Sky Survey data from 2005 to 2013 we have improved
the value of period to 0.0697944 days. Comparison of the archival CRTS data
with more recent observations from Lajatico shows the dramatic changes in the
light curve shape. Instead of a single peak present in Catalina data before
2014, there were two peaks of nearly the same height during 2015. SDSS spectrum
taken in June 2009 shows prominent Helium emission lines between the bright
Balmer series. He II 4686 AA line has more than 30% effective width compared to
H_beta line. All those features allow us to interpret 1RXS J161935.7+524630 as
a magnetic cataclysmic variable (polar) with the accretion mode changing from
one pole before 2014 to two poles in 2015.
|
http://arxiv.org/abs/1609.08511v1
|
We present a detailed NIR/optical/UV study of the transient low mass X-ray
binary 1RXS J180408.9-342058 performed during its 2015 outburst, aimed at
determining the nature of its companion star. We obtained three optical spectra
at the 2.1 m San Pedro Martir Observatory telescope (Mexico). We performed
optical and NIR photometric observations with both the REM telescope and the
New Technology Telescope (NTT) in La Silla. We obtained optical and UV
observations from the Swift archive. Finally, we performed optical polarimetry
of the source by using the EFOSC2 instrument mounted on the NTT. The optical
spectrum of the source is almost featureless since the hydrogen and He I
emissions lines, typically observed in LMXBs, are not detected. Similarly,
carbon and oxygen lines are neither observed. We marginally detect the He II
4686 AA emission line, suggesting the presence of helium in the accretion disc.
No significant optical polarisation level was observed. The lack of hydrogen
and He I emission lines in the spectrum implies that the companion is likely
not a main sequence star. Driven by the tentative detection of the He II 4686
AA emission line, we suggest that the system could harbour a helium white
dwarf. If this is the case, 1RXS J180408.9-342058 would be an ultra-compact
X-ray binary. By combining an estimate of the mass accretion rate together with
evolutionary tracks for a He white dwarf, we obtain a tentative orbital period
of ~ 40 min. On the other hand, we also built the NIR-optical-UV spectral
energy distribution (SED) of the source at two different epochs. One SED was
gathered when the source was in the soft X-ray state, and it is consistent with
the presence of a single thermal component. The second SED, obtained when the
source was in the hard X-ray state, shows a thermal component together with a
tail in the NIR, likely indicating the presence of a (transient) jet.
|
http://arxiv.org/abs/1601.05091v1
|
The possibility of neutron pairing in the $^1S_0$ channel is studied for
dense neutron matter in a vicinity of the $\pi^0$ condensation point. The
$^1S_0$ pairing gap $\Delta$ is shown to occur in a model with a pairing force
induced by the exchange of a soft neutral pionic mode. The soft pion induced
potential $V_{\pi}(r)$ is characterized by an attenuating oscillatory behavior
in coordinate space, while in momentum space all $S$-wave matrix elements
$V_{\pi}(p,p')$ are positive. The solution of the gap equation reveals strong
momentum dependence.
|
http://arxiv.org/abs/1409.7225v2
|
Temperature and velocity-dependent $^1$S$_0$ pairing gaps, chemical potentials and entrainment matrix in dense homogeneous neutron-proton superfluid mixtures constituting the outer core of neutron stars, are determined fully self-consistently by solving numerically the time-dependent Hartree-Fock-Bogoliubov equations over the whole range of temperatures and flow velocities for which superfluidity can exist. Calculations have been made for $npe\mu$ in beta-equilibrium using the Brussels-Montreal functional BSk24. The accuracy of various approximations is assessed and the physical meaning of the different velocities and momentum densities appearing in the theory is clarified. Together with the unified equation of state published earlier, the present results provide consistent microscopic inputs for modeling superfluid neutron-star cores.
|
https://arxiv.org/abs/2203.08778v1
|
We report calculations of the superfluid pairing gap in neutron matter for
the $^1S_0$ components of the Reid soft-core $V_6$ and the Argonne $V_{4}'$
two-nucleon interactions. Ground-state calculations have been carried out using
the central part of the operator-basis representation of these interactions to
determine optimal Jastrow-Feenberg correlations and corresponding effective
pairing interactions within the correlated-basis formalism (CBF), the required
matrix elements in the correlated basis being evaluated by Fermi
hypernetted-chain techniques. Different implementations of the
Fermi-Hypernetted Chain Euler-Lagrange method (FHNC-EL) agree at the percent
level up to nuclear matter saturation density. For the assumed interactions,
which are realistic within the low density range involved in $^1S_0$ neutron
pairing, we did not find a dimerization instability arising from divergence of
the in-medium scattering length, as was reported recently for simple
square-well and Lennard-Jones potential models (Phys. Rev. A {\bf 92}, 023640
(2015)).
|
http://arxiv.org/abs/1707.07268v1
|
We study the 1S-3S two-photon transition of hydrogen in a thermal atomic beam, using a homemade cw laser source at 205 nm. The experimental method is described, leading in 2017 to the measurement of the 1S-3S transition frequency in hydrogen atom with a relative uncertainty of $9 \times 10^{-13}$. This result contributes to the "proton puzzle" resolution but is in disagreement with the ones of some others experiments. We have recently improved our setup with the aim of carrying out the same measurement in deuterium. With the improved detection system, we have observed a broadened fluorescence signal, superimposed on the narrow signal studied so far, and due to the stray accumulation of atoms in the vacuum chamber. The possible resulting systematic effect is discussed.
|
https://arxiv.org/abs/2302.07537v1
|
Nielsen, Plotkin, and Winskel (1981) proved that every 1-safe Petri net $N$
unfolds into an event structure $\mathcal{E}_N$. By a result of Thiagarajan
(1996 and 2002), these unfoldings are exactly the trace regular event
structures. Thiagarajan (1996 and 2002) conjectured that regular event
structures correspond exactly to trace regular event structures. In a recent
paper (Chalopin and Chepoi, 2017, 2018), we disproved this conjecture, based on
the striking bijection between domains of event structures, median graphs, and
CAT(0) cube complexes. On the other hand, in Chalopin and Chepoi (2018) we
proved that Thiagarajan's conjecture is true for regular event structures whose
domains are principal filters of universal covers of (virtually) finite special
cube complexes.
In the current paper, we prove the converse: to any finite 1-safe Petri net
$N$ one can associate a finite special cube complex ${X}_N$ such that the
domain of the event structure $\mathcal{E}_N$ (obtained as the unfolding of
$N$) is a principal filter of the universal cover $\widetilde{X}_N$ of $X_N$.
This establishes a bijection between 1-safe Petri nets and finite special cube
complexes and provides a combinatorial characterization of trace regular event
structures.
Using this bijection and techniques from graph theory and geometry (MSO
theory of graphs, bounded treewidth, and bounded hyperbolicity) we disprove yet
another conjecture by Thiagarajan (from the paper with S. Yang from 2014) that
the monadic second order logic of a 1-safe Petri net is decidable if and only
if its unfolding is grid-free.
Our counterexample is the trace regular event structure $\mathcal{\dot E}_Z$
which arises from a virtually special square complex $\dot Z$. The domain of
$\mathcal{\dot E}_Z$ is grid-free (because it is hyperbolic), but the MSO
theory of the event structure $\mathcal{\dot E}_Z$ is undecidable.
|
http://arxiv.org/abs/1810.03395v2
|
Let $s(n)$ be the number of 1-shell totally symmetric plane partitions
(TSPPs) of $n$. In this paper, an infinite family of congruences modulo powers
of $5$ for $s(n)$ will be deduced through an elementary approach. Namely,
$$s\left(2\cdot 5^{2\alpha-1}n+5^{2\alpha-1}\right)\equiv 0
\pmod{5^{\alpha}}.$$
|
http://arxiv.org/abs/1802.04344v2
|
In this paper, we define (cohomologically) 1-shifted Manin triples and 1-shifted Lie bialgebras, and study their properties. We derive many results that are parallel to those found in ordinary Lie bialgebras, including the double construction and the existence of a 1-shifted $r$-matrix satisfying the classical Yang-Baxter equation. Turning to quantization, we first construct a canonical quantization for each 1-shifted metric Lie algebra $\mathfrak{g}$, producing a deformation to the symmetric monoidal category of $\mathfrak{g}$ modules over a formal variable $\hbar$. This quantization is in terms of a curved differential graded algebra. Under a further technical assumption, we construct quantizations of transverse Lagrangian subalgebras of $\mathfrak{g}$, which is a pair of DG algebras connected by Koszul duality, and give rise to monoidal module categories of the quantized double. Finally, we apply this to Manin triples arising from Lie algebras of loop groups, and construct 1-shifted meromorphic $r$-matrices. The resulting quantizations are the cohomologically-shifted analogue of Yangians.
|
https://arxiv.org/abs/2503.08770v1
|
Few primitives are as intertwined with the foundations of cryptography as Oblivious Transfer (OT). Not surprisingly, with the advent of the use of quantum resources in information processing, OT played a central role in establishing new possibilities (and defining impossibilities) pertaining to the use of these novel assets. A major research path is minimizing the required assumptions to achieve OT, and studying their consequences. Regarding its computation, it is impossible to construct unconditionally-secure OT without extra assumptions; and, regarding communication complexity, achieving 1-shot (and even non-interactive) OT has proved to be an elusive task, widely known to be impossible classically. Moreover, this has strong consequencesfor realizing round-optimal secure computation, in particular 1-shot 2-Party Computation (2PC). In this work, three main contributions are evidenced by leveraging quantum resources: 1. Unconditionally-secure 2-message non-interactive OT protocol constructed in the Noisy-Quantum-Storage Model. 2. 1-shot OT in the Noisy-Quantum-Storage Model -- proving that this construction is possible assuming the existence of one-way functions and sequential functions. 3. 1-shot 2PC protocol compiled from a semi-honest 1-shot OT to semi-honest 1-shot Yao's Garbled Circuits protocol.
|
https://arxiv.org/abs/2410.08367v1
|
We consider the polyhedral properties of two spanning tree problems with
additional constraints. In the first problem, it is required to find a tree
with a minimum sum of edge weights among all spanning trees with the number of
leaves less or equal a given value. In the second problem, an additional
constraint is the assumption that the degree of all vertices of the spanning
tree does not exceed a given value. The decision versions of both problems are
NP-complete.
We consider the polytopes of these problems and their 1-skeletons. We prove
that in both cases it is a NP-complete problem to determine whether the
vertices of 1-skeleton are adjacent. Although it is possible to obtain a
superpolynomial lower bounds on the clique numbers of these graphs. These
values characterize the time complexity in a broad class of algorithms based on
linear comparisons. The results indicate a fundamental difference in
combinatorial and geometric properties between the considered problems and the
classical minimum spanning tree problem.
|
http://arxiv.org/abs/1710.09672v1
|
Let $p$ be a prime. A pro-$p$ group $G$ is said to be 1-smooth if it can be endowed with a homomorphism of pro-$p$ groups $G\to1+p\mathbb{Z}_p$ satisfying a formal version of Hilbert 90. By Kummer theory, maximal pro-$p$ Galois groups of fields containing a root of 1 of order $p$, together with the cyclotomic character, are 1-smooth. We prove that a finitely generated $p$-adic analytic pro-$p$ group is 1-smooth if, and only if, it occurs as the maximal pro-$p$ Galois group of a field containing a root of 1 of order $p$. This gives a positive answer to De Clerq-Florence's "Smoothness Conjecture" - which states that the Rost-Voevodsky Theorem (a.k.a. Bloch-Kato Conjecture) follows from 1-smoothness - for the class of finitely generated $p$-adic analytic pro-$p$ groups.
|
https://arxiv.org/abs/1904.00667v7
|
Recent studies have made some progress in refining end-to-end (E2E) speech recognition encoders by applying Connectionist Temporal Classification (CTC) loss to enhance named entity recognition within transcriptions. However, these methods have been constrained by their exclusive use of the ASCII character set, allowing only a limited array of semantic labels. We propose 1SPU, a 1-step Speech Processing Unit which can recognize speech events (e.g: speaker change) or an NL event (Intent, Emotion) while also transcribing vocal content. It extends the E2E automatic speech recognition (ASR) system's vocabulary by adding a set of unused placeholder symbols, conceptually akin to the <pad> tokens used in sequence modeling. These placeholders are then assigned to represent semantic events (in form of tags) and are integrated into the transcription process as distinct tokens. We demonstrate notable improvements on the SLUE benchmark and yields results that are on par with those for the SLURP dataset. Additionally, we provide a visual analysis of the system's proficiency in accurately pinpointing meaningful tokens over time, illustrating the enhancement in transcription quality through the utilization of supplementary semantic tags.
|
https://arxiv.org/abs/2311.04753v3
|
In this paper, we study the functional convergence in law of the fluctuations of the derivative martingale of branching random walk on the real line. Our main result strengthens the results of Buraczewski et. al. [Ann. Probab., 2021] and is the branching random walk counterpart of the main result of Maillard and Pain [Ann. Probab., 2019] for branching Brownian motion.
|
https://arxiv.org/abs/2311.16407v1
|
Let $\mu_t$ denote the critical derivative Gibbs measure of branching Brownian motion at time $t$. It has been proved by Madaule [Stochastic Process. Appl., 126(2):470--502, 2016] and Maillard and Zeitouni [Ann. Inst. Henri Poincar\'e Probab. Stat., 52(3):1144--1160, 2016] that $\mu_t$ converges weakly to the random measure $Z_\infty \sqrt{2/\pi} x^2 e^{-x^2/2} \mathbb{1}_{x >0} \,\mathrm{d} x$, where $Z_\infty$ is the limit of the derivative martingale. In this paper, we are interested in the fluctuations that occur in this convergence and prove for a large class of functions $F$ that \[ \sqrt{t} \left( \int_{\mathbb{R}} F \,\mathrm{d} \mu_t - Z_\infty \int_0^\infty F(x) \sqrt{\frac{2}{\pi}} x^2 e^{-x^2/2} \,\mathrm{d} x - \frac{c(F) \log t}{\sqrt{t}} Z_\infty \right) \xrightarrow[t\to\infty]{} S^F_{Z_\infty}, \quad \text{in law}, \] where $c(F)$ is a constant depending on $F$ and $(S^F_r)_{r\geq0}$ is a 1-stable L\'evy process independent of $Z_\infty$. Moreover, we extend this result to a functional convergence, and we identify precisely the particles responsible for the fluctuations. In particular, this proves the following result for the critical additive martingale $(W_t)_{t\geq 0}$: \[ \sqrt{t} \left( \sqrt{t} W_t - \sqrt{\frac{2}{\pi}} Z_\infty \right) \xrightarrow[t\to\infty]{} S_{Z_\infty}, \quad \text{in law}, \] where here $(S_r)_{r\geq0}$ is a Cauchy process independent of $Z_\infty$, confirming a conjecture by Mueller and Munier [Phys. Rev. E, 90:042143, 2014] in the physics literature.
|
https://arxiv.org/abs/2103.10412v1
|
Let $(Z_t)_{t\geq 0}$ denote the derivative martingale of branching Brownian
motion, i.e.\@ the derivative with respect to the inverse temperature of the
normalized partition function at critical temperature. A well-known result by
Lalley and Sellke [\textit{Ann. Probab.}, 15(3):1052--1061, 1987] says that
this martingale converges almost surely to a limit $Z_\infty$, positive on the
event of survival. In this paper, our concern is the fluctuations of the
derivative martingale around its limit. A corollary of our results is the
following convergence, confirming and strengthening a conjecture by Mueller and
Munier [\textit{Phys. Rev. E}, 90:042143, 2014]: \[ \sqrt{t} \left( Z_\infty -
Z_t + \frac{\log t}{\sqrt{2\pi t}} Z_\infty \right) \xrightarrow[t\to\infty]{}
S_{Z_\infty}, \quad \text{in law}, \] where $S$ is a spectrally positive
1-stable L\'evy process independent of $Z_\infty$.
In a first part of the paper, a relatively short proof of (a slightly
stronger form of) this convergence is given based on the functional equation
satisfied by the characteristic function of $Z_\infty$ together with tail
asymptotics of this random variable. We then set up more elaborate arguments
which yield a more thorough understanding of the trajectories of the particles
contributing to the fluctuations. In this way, we can upgrade our convergence
result to functional convergence. This approach also sets the ground for a
follow-up paper, where we study the fluctuations of more general functionals
including the renormalized critical additive martingale.
All proofs in this paper are given under the hypothesis $E[L(\log L)^3] <
\infty$, where the random variable $L$ follows the offspring distribution of
the branching Brownian motion. We believe this hypothesis to be optimal.
|
http://arxiv.org/abs/1806.05152v2
|
Proceedings of the 1st AfricaNLP Workshop held on 26th April alongside ICLR 2020, Virtual Conference, Formerly Addis Ababa Ethiopia.
|
https://arxiv.org/abs/2011.10361v1
|
Let $M^n$ be a closed convex hypersurface lying in a convex ball $B(p,R)$ of
the ambient $(n+1)$-manifold $N^{n+1}$. We prove that, by pinching
Heintze-Reilly's inequality via sectional curvature upper bound of $B(p,R)$,
1st eigenvalue and mean curvature of $M$, not only $M$ is Hausdorff close and
almost isometric to a geodesic sphere $S(p_0,R_0)$ in $N$, but also its
enclosed domain is $C^{1,\alpha}$-close to a geodesic ball of constant
curvature.
|
http://arxiv.org/abs/1905.05572v1
|
Recent years have seen advances on principles and guidance relating to accountable and ethical use of artificial intelligence (AI) spring up around the globe. Specifically, Data Privacy, Accountability, Interpretability, Robustness, and Reasoning have been broadly recognized as fundamental principles of using machine learning (ML) technologies on decision-critical and/or privacy-sensitive applications. On the other hand, in tremendous real-world applications, data itself can be well represented as various structured formalisms, such as graph-structured data (e.g., networks), grid-structured data (e.g., images), sequential data (e.g., text), etc. By exploiting the inherently structured knowledge, one can design plausible approaches to identify and use more relevant variables to make reliable decisions, thereby facilitating real-world deployments.
|
https://arxiv.org/abs/2210.03612v1
|
A general nonlinear $1$st-order consensus-based solution for distributed constrained convex optimization is proposed with network resource allocation applications. The solution is used to optimize continuously-differentiable strictly convex cost functions over weakly-connected undirected networks, while it is anytime feasible and models various nonlinearities to account for imperfections and constraints on the (physical model of) agents in terms of limited actuation capabilities, e.g., quantization and saturation. Due to such inherent nonlinearities, the existing linear solutions considering ideal agent models may not necessarily converge with guaranteed optimality and anytime feasibility. Some applications also impose specific nonlinearities, e.g., convergence in fixed/finite-time or sign-based robust disturbance-tolerant dynamics. Our proposed distributed protocol generalizes such nonlinear models. Putting convex set analysis together with nonsmooth Lyapunov analysis, we prove convergence, (i) regardless of the particular type of nonlinearity, and (ii) with weak network-connectivity requirements (uniform-connectivity).
|
https://arxiv.org/abs/2109.04822v2
|
Sharpness-Aware Minimization (SAM) is an optimization technique designed to improve generalization by favoring flatter loss minima. To achieve this, SAM optimizes a modified objective that penalizes sharpness, using computationally efficient approximations. Interestingly, we find that more precise approximations of the proposed SAM objective degrade generalization performance, suggesting that the generalization benefits of SAM are rooted in these approximations rather than in the original intended mechanism. This highlights a gap in our understanding of SAM's effectiveness and calls for further investigation into the role of approximations in optimization.
|
https://arxiv.org/abs/2411.01714v1
|
The budgeted model training challenge aims to train an efficient classification model under resource limitations. To tackle this task in ImageNet-100, we describe a simple yet effective resource-aware backbone search framework composed of profile and instantiation phases. In addition, we employ multi-resolution ensembles to boost inference accuracy on limited resources. The profile phase obeys time and memory constraints to determine the models' optimal batch-size, max epochs, and automatic mixed precision (AMP). And the instantiation phase trains models with the determined parameters from the profile phase. For improving intra-domain generalizations, the multi-resolution ensembles are formed by two-resolution images with randomly applied flips. We present a comprehensive analysis with expensive experiments. Based on our approach, we win first place in International Conference on Computer Vision (ICCV) 2023 Workshop Challenge Track 1 on Resource Efficient Deep Learning for Computer Vision (RCV).
|
https://arxiv.org/abs/2311.11470v1
|
The recent transformer-based models have dominated the Referring Video Object Segmentation (RVOS) task due to the superior performance. Most prior works adopt unified DETR framework to generate segmentation masks in query-to-instance manner. In this work, we integrate strengths of that leading RVOS models to build up an effective paradigm. We first obtain binary mask sequences from the RVOS models. To improve the consistency and quality of masks, we propose Two-Stage Multi-Model Fusion strategy. Each stage rationally ensembles RVOS models based on framework design as well as training strategy, and leverages different video object segmentation (VOS) models to enhance mask coherence by object propagation mechanism. Our method achieves 75.7% J&F on Ref-Youtube-VOS validation set and 70% J&F on test set, which ranks 1st place on 5th Large-scale Video Object Segmentation Challenge (ICCV 2023) track 3. Code is available at https://github.com/RobertLuo1/iccv2023_RVOS_Challenge.
|
https://arxiv.org/abs/2401.00663v1
|
This technical report introduces our winning solution to the spatio-temporal action localization track, AVA-Kinetics Crossover, in ActivityNet Challenge 2020. Our entry is mainly based on Actor-Context-Actor Relation Network. We describe technical details for the new AVA-Kinetics dataset, together with some experimental results. Without any bells and whistles, we achieved 39.62 mAP on the test set of AVA-Kinetics, which outperforms other entries by a large margin. Code will be available at: https://github.com/Siyu-C/ACAR-Net.
|
https://arxiv.org/abs/2006.09116v1
|
Currently, Video Instance Segmentation (VIS) aims at segmenting and categorizing objects in videos from a closed set of training categories that contain only a few dozen of categories, lacking the ability to handle diverse objects in real-world videos. As TAO and BURST datasets release, we have the opportunity to research VIS in long-tailed and open-world scenarios. Traditional VIS methods are evaluated on benchmarks limited to a small number of common classes, But practical applications require trackers that go beyond these common classes, detecting and tracking rare and even never-before-seen objects. Inspired by the latest MOT paper for the long tail task (Tracking Every Thing in the Wild, Siyuan Li et), for the BURST long tail challenge, we train our model on a combination of LVISv0.5 and the COCO dataset using repeat factor sampling. First, train the detector with segmentation and CEM on LVISv0.5 + COCO dataset. And then, train the instance appearance similarity head on the TAO dataset. at last, our method (LeTracker) gets 14.9 HOTAall in the BURST test set, ranking 1st in the benchmark. for the open-world challenges, we only use 64 classes (Intersection classes of BURST Train subset and COCO dataset, without LVIS dataset) annotations data training, and testing on BURST test set data and get 61.4 OWTAall, ranking 1st in the benchmark. Our code will be released to facilitate future research.
|
https://arxiv.org/abs/2308.04598v1
|
OOD-CV challenge is an out-of-distribution generalization task. In this challenge, our core solution can be summarized as that Noisy Label Learning Is A Strong Test-Time Domain Adaptation Optimizer. Briefly speaking, our main pipeline can be divided into two stages, a pre-training stage for domain generalization and a test-time training stage for domain adaptation. We only exploit labeled source data in the pre-training stage and only exploit unlabeled target data in the test-time training stage. In the pre-training stage, we propose a simple yet effective Mask-Level Copy-Paste data augmentation strategy to enhance out-of-distribution generalization ability so as to resist shape, pose, context, texture, occlusion, and weather domain shifts in this challenge. In the test-time training stage, we use the pre-trained model to assign noisy label for the unlabeled target data, and propose a Label-Periodically-Updated DivideMix method for noisy label learning. After integrating Test-Time Augmentation and Model Ensemble strategies, our solution ranks the first place on the Image Classification Leaderboard of the OOD-CV Challenge. Code will be released in https://github.com/hikvision-research/OOD-CV.
|
https://arxiv.org/abs/2301.04795v1
|
OOD-CV challenge is an out-of-distribution generalization task. To solve this problem in object detection track, we propose a simple yet effective Generalize-then-Adapt (G&A) framework, which is composed of a two-stage domain generalization part and a one-stage domain adaptation part. The domain generalization part is implemented by a Supervised Model Pretraining stage using source data for model warm-up and a Weakly Semi-Supervised Model Pretraining stage using both source data with box-level label and auxiliary data (ImageNet-1K) with image-level label for performance boosting. The domain adaptation part is implemented as a Source-Free Domain Adaptation paradigm, which only uses the pre-trained model and the unlabeled target data to further optimize in a self-supervised training manner. The proposed G&A framework help us achieve the first place on the object detection leaderboard of the OOD-CV challenge. Code will be released in https://github.com/hikvision-research/OOD-CV.
|
https://arxiv.org/abs/2301.04796v1
|
In this report, we present the 1st place solution for ICCV 2023 OmniObject3D Challenge: Sparse-View Reconstruction. The challenge aims to evaluate approaches for novel view synthesis and surface reconstruction using only a few posed images of each object. We utilize Pixel-NeRF as the basic model, and apply depth supervision as well as coarse-to-fine positional encoding. The experiments demonstrate the effectiveness of our approach in improving sparse-view reconstruction quality. We ranked first in the final test with a PSNR of 25.44614.
|
https://arxiv.org/abs/2404.10441v1
|
In this technical report, we present our 1st place solution for the ICDAR 2021 competition on mathematical formula detection (MFD). The MFD task has three key challenges including a large scale span, large variation of the ratio between height and width, and rich character set and mathematical expressions. Considering these challenges, we used Generalized Focal Loss (GFL), an anchor-free method, instead of the anchor-based method, and prove the Adaptive Training Sampling Strategy (ATSS) and proper Feature Pyramid Network (FPN) can well solve the important issue of scale variation. Meanwhile, we also found some tricks, e.g., Deformable Convolution Network (DCN), SyncBN, and Weighted Box Fusion (WBF), were effective in MFD task. Our proposed method ranked 1st in the final 15 teams.
|
https://arxiv.org/abs/2107.05534v1
|
Motion Expression guided Video Segmentation (MeViS), as an emerging task, poses many new challenges to the field of referring video object segmentation (RVOS). In this technical report, we investigated and validated the effectiveness of static-dominant data and frame sampling on this challenging setting. Our solution achieves a J&F score of 0.5447 in the competition phase and ranks 1st in the MeViS track of the PVUW Challenge. The code is available at: https://github.com/Tapall-AI/MeViS_Track_Solution_2024.
|
https://arxiv.org/abs/2406.07043v1
|
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