ShantanuT01/DACTYL-Pretraining huggingface dataset:
In relation to Hall's conjecture, a new algorithm is presented to search for small k = |x^3 -y^2| values. Thirteen new values of k < x^(1/2) are reported.
We suggest a particular procedure of derivation of the beta-stability line and isotopic symmetry energy. The behavior of the symmetry energy coefficient $b(A,N-Z)$ is analyzed. We redefine the surface tension coefficient and the surface symmetry energy for an asymmetric nuclear Fermi-liquid drop with a finite diffuse layer. Following Gibbs-Tolman concept, we introduce the equimolar radius at which the surface tension is applied. The relation of the nuclear macroscopic characteristics like surface and symmetry energies, Tolman length, etc. to the bulk properties of nuclear matter is considered. The surface-to-volume symmetry energy ratio for several Skyrme-force parametrizations is obtained.
The peripheral heavy-ion collisions of $^{112, 124}Sn+ ^{86}Kr$ at $E_{b}= 25AMeV$ are studied by means of the Improved Quantum Molecular Dynamics Model(ImQMD). It is shown that the slope of the average N/Z ratio of emitted nucleons vs impact parameters for these reactions is very sensitive to the density dependence of the symmetry energy. Our study also shows that the yields of $^{3}H$ and $^{3}He$ decrease with impact parameters and slope of the yield of $^{3}H$ vs impact parameters as well as the ratio of Y($^{3}H$)/Y($^{3}He$) depend on the symmetry potential strongly for peripheral heavy-ion collisions.
We present the observations of the reflection nebulae IC4954 and IC4955 region with the Infrared Camera (IRC) and the Far-Infrared Surveyor (FIS) on board the infrared astronomical satellite AKARI during its performance verification phase. We obtained 7 band images from 7 to 160um with higher spatial resolution and higher sensitivities than previous observations. The mid-infrared color of the S9W (9um) and L18W (18um) bands shows a systematic variation around the exciting sources. The spatial variation in the mid-infrared color suggests that the star-formation in IC4954/4955 is progressing from south-west to north-east. The FIS data also clearly resolve two nebulae for the first time in the far-infrared. The FIS 4-band data from 65um to 160um allow us to correctly estimate the total infrared luminosity from the region, which is about one sixth of the energy emitted from the existing stellar sources. Five candidates for young stellar objects have been detected as point sources for the first time in the 11um image. They are located in the red S9W to L18W color regions, suggesting that current star-formation has been triggered by previous star-formation activities. A wide area map of the size of about 1 x 1 (deg^2) around the IC4954/4955 region was created from the AKARI mid-infrared all-sky survey data. Together with the HI 21cm data, it suggests a large hollow structure of a degree scale, on whose edge the IC4954/4955 region has been created, indicating star formation over three generations in largely different spatial scales.
In his doctoral thesis, Snover proved that any binary $(m,256,\delta)$ code is equivalent to the Nordstrom-Robinson code or the punctured Nordstrom-Robinson code for $(m,\delta)=(16,6)$ or $(15,5)$ respectively. We prove that these codes are also characterised as \emph{completely regular} binary codes with $(m,\delta)=(16,6)$ or $(15,5)$, and moreover, that they are \emph{completely transitive}. Also, it is known that completely transitive codes are necessarily completely regular, but whether the converse holds has up to now been an open question. We answer this by proving that certain completely regular codes are not completely transitive, namely, the (Punctured) Preparata codes other than the (Punctured) Nordstrom-Robinson code.
Ru 3d core-level x-ray photoemission spectra of various ruthenates are examined. They show in general two-peak structures, which can be assigned as the screened and unscreened peaks. The screened peak is absent in a Mott insulator, but develops into a main peak in the metallic regime. This spectral behavior is well explained by the dynamical mean-field theory calculation for the single-band Hubbard model with on-site core-hole potential using the exact diagonalization method. The new mechanism of the core-level photoemission satellite can be utilized to reveal the Mott transition phenomenon in various strongly correlated electron systems, especially in nano-scale devices and phase-separated materials.
We propose and experimentally demonstrate an optimal non-unity gain Gaussian scheme for partial measurement of an unknown coherent state that causes minimal disturbance of the state. The information gain and the state disturbance are quantified by the noise added to the measurement outcomes and to the output state, respectively. We derive the optimal trade-off relation between the two noises and we show that the trade-off is saturated by non-unity gain teleportation. Optimal partial measurement is demonstrated experimentally using a linear optics scheme with feed-forward.
It is shown that the addition of a single chiral symmetry breaking term to the standard omega meson variant of the nuclear Skyrme model can reproduce the proton-neutron mass difference.
Multimessenger observations may hold the key to learn about the most energetic sources in the universe. The recent construction of large scale observatories opened new possibilities in testing non thermal cosmic processes with alternative probes, such as high energy neutrinos and gravitational waves. We propose to combine information from gravitational wave detections, neutrino observations and electromagnetic signals to obtain a comprehensive picture of some of the most extreme cosmic processes. Gravitational waves are indicative of source dynamics, such as the formation, evolution and interaction of compact objects. These compact objects can play an important role in astrophysical particle acceleration, and are interesting candidates for neutrino and in general high-energy astroparticle studies. In particular we will concentrate on the most promising gravitational wave emitter sources: compact stellar remnants. The merger of binary black holes, binary neutron stars or black hole-neutron star binaries are abundant gravitational wave sources and will likely make up the majority of detections. However, stellar core collapse with rapidly rotating core may also be significant gravitational wave emitter, while slower rotating cores may be detectable only at closer distances. The joint detection of gravitational waves and neutrinos from these sources will probe the physics of the sources and will be a smoking gun of the presence of hadrons in these objects which is still an open question. Conversely, the non-detection of neutrinos or gravitational waves from these sources will be fundamental to constrain the hadronic content.
A superconducting transmon qubit resilient to strong magnetic fields is an important component for proposed topological and hybrid quantum computing (QC) schemes. Transmon qubits consist of a Josephson junction (JJ) shunted by a large capacitance, coupled to a high quality factor superconducting resonator. In conventional transmon devices, the JJ is made from an Al/AlO$_x$/Al tunnel junction which ceases operation above the critical magnetic field of Al, 10 mT. Alternative junction technologies are therefore required to push the operation of these qubits into strong magnetic fields. Graphene JJs are one such candidate due to their high quality, ballistic transport and electrically tunable critical current densities. Importantly the monolayer structure of graphene protects the JJ from orbital interference effects that would otherwise inhibit operation at high magnetic field. Here we report the integration of ballistic graphene JJs into microwave frequency superconducting circuits to create the first graphene transmons. The electric tunability allows the characteristic band dispersion of graphene to be resolved via dispersive microwave spectroscopy. We demonstrate that the device is insensitive to the applied field and perform energy level spectroscopy of the transmon at 1 T, more than an order of magnitude higher than previous studies.
High momentum jets and hadrons are important probes for the quark gluon plasma (QGP) formed in nuclear collisions at high energies. We investigate how fluctuations in the background density of the QGP and fluctuations in the spatial distribution of the hard process create azimuthal asymmetries of the high momentum hadron spectrum, described by the Fourier coefficients $v_n$, $n > 0$ . We estimate the coefficients up to $v_6$ in a simple energy loss model tuned to single inclusive hadron suppression.
In this paper we study the tightness of solutions for a family of recursion equations. These equations arise naturally in the study of random walks on tree-like structures. Examples include the maximal displacement of a branching random walk in one dimension and the cover time of a symmetric simple random walk on regular binary trees. Recursion equations associated with the distribution functions of these quantities have been used to establish weak laws of large numbers. Here, we use these recursion equations to establish the tightness of the corresponding sequences of distribution functions after appropriate centering. We phrase our results in a fairly general context, which we hope will facilitate their application in other settings.
We propose a scheme for the determination of the coupling parameters in a chain of interacting spins. This requires only time-resolved measurements over a single particle, simple data post-processing and no state initialization or prior knowledge of the state of the chain. The protocol fits well into the context of quantum-dynamics characterization and is efficient even when the spin-chain is affected by general dissipative and dephasing channels. We illustrate the performance of the scheme by analyzing explicit examples and discuss possible extensions.
Single-source domain generalization (SDG) in medical image segmentation is a challenging yet essential task as domain shifts are quite common among clinical image datasets. Previous attempts most conduct global-only/random augmentation. Their augmented samples are usually insufficient in diversity and informativeness, thus failing to cover the possible target domain distribution. In this paper, we rethink the data augmentation strategy for SDG in medical image segmentation. Motivated by the class-level representation invariance and style mutability of medical images, we hypothesize that unseen target data can be sampled from a linear combination of $C$ (the class number) random variables, where each variable follows a location-scale distribution at the class level. Accordingly, data augmented can be readily made by sampling the random variables through a general form. On the empirical front, we implement such strategy with constrained B$\acute{\rm e}$zier transformation on both global and local (i.e. class-level) regions, which can largely increase the augmentation diversity. A Saliency-balancing Fusion mechanism is further proposed to enrich the informativeness by engaging the gradient information, guiding augmentation with proper orientation and magnitude. As an important contribution, we prove theoretically that our proposed augmentation can lead to an upper bound of the generalization risk on the unseen target domain, thus confirming our hypothesis. Combining the two strategies, our Saliency-balancing Location-scale Augmentation (SLAug) exceeds the state-of-the-art works by a large margin in two challenging SDG tasks. Code is available at https://github.com/Kaiseem/SLAug .
In this note we consider algebraic exponential sums over the values of homogeneous nonsingular polynomials $F(x_1, \cdots, x_n) \in \mathbb{Z}[x_1, \cdots, x_n]$ in the quotient ring $\mathbb{Z}/p^2\mathbb{Z}$. We provide an estimate of this exponential sum and a corresponding stratification of the space $\mathbb{A}_{\mathbb{F}_p}^n$, which in particular illustrates a general stratification theorem of Fouvry and Katz.
We investigate the critical behavior of three-dimensional antiferromagnetic CP(N-1) [ACP(N-1)] models in cubic lattices, which are characterized by a global U(N) symmetry and a local U(1) gauge symmetry. Assuming that critical fluctuations are associated with a staggered gauge-invariant (hermitian traceless matrix) order parameter, we determine the corresponding Landau-Ginzburg-Wilson (LGW) model. For N=3 this mapping allows us to conclude that the three-component ACP(2) model undergoes a continuous transition that belongs to the O(8) vector universality class, with an effective enlargement of the symmetry at the critical point. This prediction is confirmed by a detailed numerical comparison of finite-size data for the ACP(2) and the O(8) vector models. We also present a renormalization-group (RG) analysis of the LGW theories for N>3. We compute perturbative series in two different renormalization schemes and analyze the corresponding RG flow. We do not find stable fixed points that can be associated with continuous transitions.
The partition crank is a statistic on partitions introduced by Freeman Dyson to explain Ramanujan's congruences. In this paper, we prove that the crank is asymptotically equidistributed modulo Q, for any odd number Q. To prove this, we obtain effective bounds on the error term from Zapata Rolon's asymptotic estimate for the crank function. We then use those bounds to prove the surjectivity and strict log-subadditivity of the crank function.
Sparse depth measurements are widely available in many applications such as augmented reality, visual inertial odometry and robots equipped with low cost depth sensors. Although such sparse depth samples work well for certain applications like motion tracking, a complete depth map is usually preferred for broader applications, such as 3D object recognition, 3D reconstruction and autonomous driving. Despite the recent advancements in depth prediction from single RGB images with deeper neural networks, the existing approaches do not yield reliable results for practical use. In this work, we propose a neural network with post-optimization, which takes an RGB image and sparse depth samples as input and predicts the complete depth map. We make three major contributions to advance the state-of-the-art: an improved backbone network architecture named EDNet, a semantic edge-weighted loss function and a semantic mesh deformation optimization method. Our evaluation results outperform the existing work consistently on both indoor and outdoor datasets, and it significantly reduces the mean average error by up to 19.5% under the same settings of 200 sparse samples on NYU-Depth-V2 dataset.
We provide a systematic construction of string junctions in curved backgrounds which are relevant in computing, within the gauge/gravity correspondence, the interaction energy of heavy dyons, notably of quark-monopole pairs, in strongly coupled SYM theories. To isolate the configurations of physical interest we examine their stability under small fluctuations and prove several general statements. We present all details, in several examples, involving non-extremal and multicenter D3-brane backgrounds as well as the Rindler space. We show that a string junction could be perturbatively stable even in branches that are not energetically the most favorable ones. We present a mechanical analog of this phenomenon.
One of the fundamental challenges in video object segmentation is to find an effective representation of the target and background appearance. The best performing approaches resort to extensive fine-tuning of a convolutional neural network for this purpose. Besides being prohibitively expensive, this strategy cannot be truly trained end-to-end since the online fine-tuning procedure is not integrated into the offline training of the network.   To address these issues, we propose a network architecture that learns a powerful representation of the target and background appearance in a single forward pass. The introduced appearance module learns a probabilistic generative model of target and background feature distributions. Given a new image, it predicts the posterior class probabilities, providing a highly discriminative cue, which is processed in later network modules. Both the learning and prediction stages of our appearance module are fully differentiable, enabling true end-to-end training of the entire segmentation pipeline. Comprehensive experiments demonstrate the effectiveness of the proposed approach on three video object segmentation benchmarks. We close the gap to approaches based on online fine-tuning on DAVIS17, while operating at 15 FPS on a single GPU. Furthermore, our method outperforms all published approaches on the large-scale YouTube-VOS dataset.
We compute the motive of the variety of representations of the torus knot of type (m,n) into the affine groups $AGL_1$ and $AGL_2$ for an arbitrary field $k$. In the case that $k = F_q$ is a finite field this gives rise to the count of the number of points of the representation variety, while for $k = C$ this calculation returns the E-polynomial of the representation variety. We discuss the interplay between these two results in sight of Katz theorem that relates the point count polynomial with the E-polynomial. In particular, we shall show that several point count polynomials exist for these representation varieties, depending on the arithmetic between m,n and the characteristic of the field, whereas only one of them agrees with the actual E-polynomial.
Experimental and theoretical studies of manganese deposition on graphene/Ni(111) shows that a thin ferromagnetic Ni3Mn layer, which is protected by the graphene overlayer, is formed upon Mn intercalation. The electronic bands of graphene are affected by Ni3Mn interlayer formation through a slight reduction of n-type doping compared to graphene/Ni(111) and a suppression of the interface states characteristic of graphene/Ni(111). Our DFT-based theoretical analysis of interface geometric, electronic, and magnetic structure gives strong support to our interpretation of the experimental scanning tunneling microscopy, low energy electron diffraction, and photoemission results, and shows that the magnetic structure of graphene is strongly influenced by Ni3Mn formation.
Motivated by recent developments in the computation of periods for string compactifications with $c=9$, we develop a complementary method which also produces a convenient basis for related calculations. The models are realized as Calabi--Yau hypersurfaces in weighted projective spaces of dimension four or as Landau-Ginzburg vacua. The calculation reproduces known results and also allows a treatment of Landau--Ginzburg orbifolds with more than five fields.
On the basis of the C-metric, we investigate the conformal Schwarzschild - deSitter spacetime and compute the source stress tensor and study its properties, including the energy conditions. Then we study its extremal version ($b^{2} = 27m^{2}$, where $b$ is the deS radius and $m$ is the source mass), when the metric is nonstatic. The weak-field version is analyzed in several frames, and the metric becomes flat with the special choice $b = 1/a$, $a$ being the constant acceleration of the Schwarzschild-like mass or black hole. This form is Rindler's geometry in disguise and is also conformal to a de Sitter metric where the acceleration plays the role of the Hubble constant. In its time dependent version, one finds that the proper acceleration of a static observer is constant everywhere, in contrast with the standard Rindler case. The timelike geodesics along the z-direction are calculated and proves to be hyperbolae.
In the present paper we obtain a new correlation inequality and use it for the purpose of extending the theory of the Almost Sure Local Limit Theorem to the case of lattice random sequences in the domain of attraction of a stable law. In particular, we prove ASLLT in the case of the normal domain of attraction of $\alpha$--stable law, $\alpha\in(1,2)$.
The analysis of a physical problem simplifies considerably when one uses a suitable coordinate system. We apply this approach to the discrete-time quantum walks with coins given by $2j+1$-dimensional Wigner rotation matrices (Wigner walks), a model which was introduced in T. Miyazaki et al., Phys. Rev. A 76, 012332 (2007). First, we show that from the three parameters of the coin operator only one is physically relevant for the limit density of the Wigner walk. Next, we construct a suitable basis of the coin space in which the limit density of the Wigner walk acquires a much simpler form. This allows us to identify various dynamical regimes which are otherwise hidden in the standard basis description. As an example, we show that it is possible to find an initial state which reduces the number of peaks in the probability distribution from generic $2j+1$ to a single one. Moreover, the models with integer $j$ lead to the trapping effect. The derived formula for the trapping probability reveals that it can be highly asymmetric and it deviates from purely exponential decay. Explicit results are given up to the dimension five.
We investigate the four dimensional gravitational theories which admit homogeneous but anisotropic black brane solutions in asymptotically AdS space-time. The gravitational theories we consider are 1) Einstein-Maxwell-dilaton theory, and 2) Einstein-Maxwell-dilaton-axion theory with SL(2,R) symmetry. We obtain the solutions both analytically and numerically. Analytical solutions are obtained by perturbation from the isotropic solutions. Our solutions approach singular behavior at the horizon in the extremal limit but in non-extremal case, they are smooth everywhere. We also discuss how the third law of thermodynamics holds in our set-up.
We propose a method based on the process of extracting gravitational wave (GW) parameters from GW signals to simulate the binary neutron-star (BNS) merging events. We simulate 1000 GW standard sirens based on the observation of the Einstein Telescope (ET). Almost all the simulated GW data are in the redshift range of $[0,3]$. The role of the GW standard siren in the inference of the cosmological parameters is investigated. We find that the GW data can help improve the accuracy of cosmological parameters. Moreover, the degeneracy of cosmological parameters is broken by the GW data. The GW standard siren is helpful for the constraint of the cosmological parameters.
A nonlinear transformation of the dispersive long wave equations in (2+1) dimensions is derived by using the homogeneous balance method. With the aid of the transformation given here, exact solutions of the equations are obtained.