ShantanuT01/DACTYL-Pretraining huggingface dataset:
In this paper, we investigate the combination of voxel-based methods and point-based methods, and propose a novel end-to-end two-stage 3D object detector named SGNet for point clouds scenes. The voxel-based methods voxelize the scene to regular grids, which can be processed with the current advanced feature learning frameworks based on convolutional layers for semantic feature learning. Whereas the point-based methods can better extract the geometric feature of the point due to the coordinate reservations. The combination of the two is an effective solution for 3D object detection from point clouds. However, most current methods use a voxel-based detection head with anchors for final classification and localization. Although the preset anchors cover the entire scene, it is not suitable for point clouds detection tasks with larger scenes and multiple categories due to the limitation of voxel size. In this paper, we propose a voxel-to-point module (VTPM) that captures semantic and geometric features. The VTPM is a Voxel-Point-Based Module that finally implements 3D object detection in point space, which is more conducive to the detection of small-size objects and avoids the presets of anchors in inference stage. In addition, a Confidence Adjustment Module (CAM) with the center-boundary-aware confidence attention is proposed to solve the misalignment between the predicted confidence and proposals in the regions of the interest (RoI) selection. The SGNet proposed in this paper has achieved state-of-the-art results for 3D object detection in the KITTI dataset, especially in the detection of small-size objects such as cyclists. Actually, as of September 19, 2021, for KITTI dataset, SGNet ranked 1st in 3D and BEV detection on cyclists with easy difficulty level, and 2nd in the 3D detection of moderate cyclists.
We propose a model based on Regge theory to describe photoproduction of light vector mesons. We fit the SLAC data and make predictions for the energy and momentum transfer dependence of the spin-density matrix elements in photoproduction of $\omega$, $\rho^0$ and $\phi$ mesons at $E_\gamma \sim 8.5$ GeV, which are soon to be measured at Jefferson Lab.
We study for rationally connected varieties $X$ the group of degree 2 integral homology classes on $X$ modulo those which are algebraic. We show that the Tate conjecture for divisor classes on surfaces defined over finite fields implies that this group is trivial for any rationally connected variety.
We study time scheduling problems with allowed absences as a new kind of graph coloring problem. One may think of a sport tournament where each player (each team) is permitted a certain number $t$ of absences. We then examine how many rounds are needed to schedule the whole tournament in the worst case. This upper limit depends on $t$ and on the structure of the graph $G$ whose edges represent the games that have to be played, but also on whether or not the absences are announced before the tournament starts. Therefore, we actually have two upper limits for the number of required rounds. We have $\chi^t(G)$ for pre-scheduling if all absences are pre-fixed, and we have $\chi_{\textit{OL}}^t(G)$ for on-line scheduling if we have to stay flexible and deal with absences when they occur. We conjecture that $\chi^t(G)=\Delta(G)+2t$ and that $\chi_{\textit{OL}}^t(G)=\chi'(G)+2t.$ The first conjecture is stronger than the Total Coloring Conjecture while the second is weaker than the On-Line List Edge Coloring Conjecture. Our conjectures hold for all bipartite graphs. For complete graphs, we prove them partially. Lower and upper bounds to $\chi^t(G)$ and $\chi_{\textit{OL}}^t(G)$ for general multigraphs $G$ are established, too.
We establish multiplicity results for the following class of quasilinear problems $$ \left\{ \begin{array}{l} -\Delta_{\Phi}u=f(x,u) \quad \mbox{in} \quad \Omega, \\ u=0 \quad \mbox{on} \quad \partial \Omega, \end{array} \right. \leqno{(P)} $$ where $\Delta_{\Phi}u=\text{div}(\varphi(x,|\nabla u|)\nabla u)$ for a generalized N-function $\Phi(x,t)=\int_{0}^{|t|}\varphi(x,s)s\,ds$. We consider $\Omega\subset\mathbb{R}^N$ to be a smooth bounded domain that contains two disjoint open regions $\Omega_N$ and $\Omega_p$ such that $\overline{\Omega_N}\cap\overline{\Omega_p}=\emptyset$. The main feature of the problem $(P)$ is that the operator $-\Delta_{\Phi}$ behaves like $-\Delta_N$ on $\Omega_N$ and $-\Delta_p$ on $\Omega_p$. We assume the nonlinearity $f:\Omega\times\mathbb{R}\to\mathbb{R}$ of two different types, but both behaves like $e^{\alpha|t|^\frac{N}{N-1}}$ on $\Omega_N$ and $|t|^{p^*-2}t$ on $\Omega_p$ as $|t|$ is large enough, for some $\alpha>0$ and $p^*=\frac{Np}{N-p}$ being the critical Sobolev exponent for $1<p<N$. In this context, for one type of nonlinearity $f$, we provide multiplicity of solutions in a general smooth bounded domain and for another type of nonlinearity $f$, in an annular domain $\Omega$, we establish existence of multiple solutions for the problem $(P)$ that are nonradial and rotationally nonequivalent.
We briefly summarise the basic properties of spacetimes representing rotating, charged black holes in strong axisymmetric magnetic fields. We concentrate on extremal cases, for which the horizon surface gravity vanishes. We investigate their properties by finding simpler spacetimes that exhibit their geometries near degenerate horizons. Employing the simpler geometries obtained by near-horizon limiting description we analyse the Meissner effect of magnetic field expulsion from extremal black holes.
We have investigated the valley degeneracy of MoS2 multilayers and its effect on thermoelectric properties. By modulating the layer thickness and external electric field, the hole valleys at {\Gamma} and K points in the highest energy valence band and the electron valleys at K and {\Sigma}min points in the lowest energy conduction band are shifted differently. The hole valley degeneracy is observed in MoS2 monolayer, while that of electron valley is in MoS2 bilayer and monolayer under the external electric field. By tuning the valley degeneracy, the Seebeck coefficient and electrical conductivity can be separately controlled, and the maximum power factor can be obtained in n-type (p-type) MoS2 monolayer with (without) the external electric field. We suggest that the transition metal dichalcogenides are good example to investigate the role of valley degeneracy in the thermoelectric and optical properties with the control of interlayer interaction and external electric field strength.
The purpose of this article is to give an explicit description, in terms of hypergeometric functions over finite fields, of zeta function of a certain type of smooth hypersurfaces that generalizes Dwork family. The point here is that we count the number of rational points employing both character sums and the theory of weights, which enables us to enlighten the calculation of the zeta function.
The ground state and magnetization process of the mixed spin-(1,1/2) Ising diamond chain is exactly solved by employing the generalized decoration-iteration mapping transformation and the transfer-matrix method. The decoration-iteration transformation is first used in order to establish a rigorous mapping equivalence with the corresponding spin-1 Blume-Emery-Griffiths chain in a non-zero magnetic field, which is subsequently exactly treated within the framework of the transfer-matrix technique. It is shown that the ground-state phase diagram includes just four different ground states and the low-temperature magnetization curve may exhibit an intermediate plateau precisely at one half of the saturation magnetization. Our rigorous results disprove recent Monte Carlo simulations of Zihua Xin et al. [Z. Xin, S. Chen, C. Zhang, J. Magn. Magn. Mater. 324 (2012) 3704], which imply an existence of the other magnetization plateaus at 0.283 and 0.426 of the saturation magnetization.
Let $K$ be an imaginary quadratic field and $\mathcal{O}_K$ be its ring of integers. Let $h_E$ be the Weber function on certain elliptic curve $E$ with complex multiplication by $\mathcal{O}_K$. We show that if $N$ ($>1$) is an integer prime to $6$, then the function $h_E$ alone generates the ray class field modulo $N\mathcal{O}_K$ over $K$ when evaluated at some $N$-torsion point of $E$.
The high pressure structural and electronic evolution of bulk MoS$_2$, an important transition metal layered dichalchogenide, is currently under active investigation. Recent theoretical and experimental work predicted and verified a 2H$_c \to$ 2H$_a$ layer sliding structural transition at 20 GPa and a band overlap semiconductor-semimetal transition in the same pressure range. The 2H$_a$ structure is known to persist up to pressure of 81 GPa but properties at higher pressures remain experimentally unknown. Here we predict, with a reliable first-principles evolutionary search, that major structural transformations should take place in equilibrium at higher pressures near 130-140 GPa. The main motif is a decomposition into MoS + S, also heralded in a small bimolecular cell by the appearance of a metastable non-layered metallic MoS$_2$ structure with space group \textit{P4/mmm}. Unlike semimetallic 2H$_a$-MoS$_2$, both this phase and sulphur in the fully phase separated system are fully metallic and superconducting with higher critical temperatures than alkali-intercalated MoS$_2$.
Deep learning generates state-of-the-art semantic segmentation provided that a large number of images together with pixel-wise annotations are available. To alleviate the expensive data collection process, we propose a semi-supervised domain adaptation method for the specific case of images with similar semantic content but different pixel distributions. A network trained with supervision on a past dataset is finetuned on the new dataset to conserve its features maps. The domain adaptation becomes a simple regression between feature maps and does not require annotations on the new dataset. This method reaches performances similar to classic transfer learning on the PASCAL VOC dataset with synthetic transformations.
We introduce a class of two-dimensional non-resonant single-phase phononic materials and investigate its peculiar dispersion characteristics. The material consists of a thin plate-like structure with an embedded periodic lattice of Acoustic Black Holes. The use of these periodic tapers allows achieving remarkable dispersion properties such as Zero Group Velocity in the fundamental modes, negative group refraction index, bi-refraction, and mode anisotropy. The dispersion properties are numerically investigated using a three-dimensional supercell plane wave expansion method. The effect on the dispersion characteristics of key geometric parameters of the black hole, such as the taper profile and the residual thickness, are also explored.
We combine the results of perturbative continuous unitary transformations with a mean-field calculation to determine the evolution of the single-mode, i.e., one-triplon, contribution to the dynamic structure factor of a two-leg $S=1/2$ ladder on increasing temperature from zero to a finite value. The temperature dependence is induced by two effects: (i) no triplon can be excited on a rung where a thermally activated triplon is present; (ii) conditional excitation processes take place if a thermally activated triplon is present. Both effects diminish the one-triplon spectral weight upon heating. It is shown that the second effect is the dominant vertex correction in the calculation of the dynamic structure factor. The matrix elements describing the conditional triplon excitation in the two-leg Heisenberg ladder with additional four-spin ring exchange are calculated perturbatively up to order 9. The calculated results are compared to those of an inelastic neutron scattering experiment on the cuprate-ladder compound La$_{4}$Sr$_{10}$Cu$_{24}$O$_{41}$ showing convincing agreement for established values of the exchange constants.
This paper deals with the homogenization of fully nonlinear second order equation with an oscillating Dirichlet boundary data when the operator and boundary data are $\e$-periodic. We will show that the solution $u_\e$ converges to some function $\bar u(x)$ uniformly on every compact subset $K$ of the domain $D$. Moreover, $\bar u$ is a solution to some boundary value problem. For this result, we assume that the boundary of the domain has no (rational) flat spots and the ratio of elliptic constants $\Lambda / \lambda$ is sufficiently large.
We propose a new model for naturally light Dirac neutrinos and explain the baryon asymmetry of the universe through neutrinogenesis. We extend the standard model with a real singlet scalar, a heavy singlet Dirac fermion and a heavy doublet scalar besides three right-handed neutrinos, respecting lepton number conservation and a Z_2 symmetry. The neutrinos acquire small Dirac masses due to the suppression of the weak scale over the heavy mass scale. As a key feature of our construction, once the heavy Dirac fermion and doublet scalar go out of equilibrium, their decays induce the CP asymmetry from the interference of tree-level processes with the \textit{radiative vertex corrections} (rather than the self-energy corrections). Although there is no lepton number violation, an equal and opposite amount of CP asymmetry is generated in the left-handed and the right-handed neutrinos. The left-handed lepton asymmetry would then be converted to the baryon asymmetry in the presence of the sphalerons, while the right-handed lepton asymmetry remains unaffected.
We establish the canonical class inequality for families of higher dimensional projective manifolds. As an application, we get a new inequality between the Chern numbers of 3-folds with smooth families of minimal surfaces of general type over a curve, $c_1^3<18c_3$.
We regularized the 3D Navier-Stokes equations by adding a fourth-order viscosity term. We study the upper semicontinuity, of the global attractors of the Leray-Hopf weak solutions of the regularized 3D Navier-Stokes equations, as the artificial dissipation goes to 0. We also consider applications of obtained results to the regularized problem by allowing the family of forcing functions to vary with epsilon, for epsilon >0.
High time resolution observations of a white--light flare on the active star EQ PegB show evidence of intensity variations with a period of approximately 10 s. The period drifts to longer values during the decay phase of the flare. If the oscillation is interpreted as an impulsively--excited, standing--acoustic wave in a flare loop, the period implies a loop length of 1.7 Mm and 3.4 Mm for the case of the fundamental mode and the second harmonic, respectively. However, the small loop lengths imply a very high modulation depth making the acoustic interpretation unlikely. A more realistic interpretation may be that of a fast--MHD wave, with the modulation of the emission being due to the magnetic field. Alternatively, the variations could be due to a series of reconnection events. The periodic signature may then arise as a result of the lateral separation of individual flare loops or current sheets with oscillatory dynamics (i.e. periodic reconnection).
We adapt the well known "displace, cut and reflect" method to construct exact solutions of the Einstein-Maxwell equations corresponding to infinitesimally thin disks of matter endowed with dipole magnetic fields, which are entirely supported by surface polar currents on the disk. Our starting point is the Gutsunaev-Manko axisymmetric solution describing massive magnetic dipoles in General Relativity, from which we obtain a continuous three-parameter family of asymptotically flat static magnetized disks with finite mass and energy. For strong magnetic fields, the disk surface density profile resembles some well known self-gravitating ring-like structures.   We show that many of these solutions can be indeed stable and, hence, they could be in principle useful for the study of the abundant astrophysical situations involving disks of matter and magnetic fields.
The primary goal of this document is to record the asymptotic effects that preimage constraints impose upon the sizes of the iterated images of a random function. Specifically, given a subset $\mathcal{P}\subseteq \mathbb{Z}_{\geq 0}$ and a finite set $S$ of size $n$, choose a function uniformly from the set of functions $f:S\rightarrow S$ that satisfy the condition that $|f^{-1}(x)|\in\mathcal{P}$ for each $x\in S$, and ask what $|f^k(S)|$ looks like as $n$ goes to infinity. The robust theory of singularity analysis allows one to completely answer this question if one accepts that $0\in\mathcal{P}$, that $\mathcal{P}$ contains an element bigger than 1, and that $\gcd(\mathcal{P})=1$; only the third of these conditions is a meaningful restriction. The secondary goal of this paper is to record much of the background necessary to achieve the primary goal.
This article develops a new sieve method which by adding an additional axiom to the classical formulation breaks the well-known parity problem and allows one to detect primes in thin, interesting integer sequences. In the accompanying paper [math.NT/9811184] the practicality of the axiom is demonstrated by verifying it (and the other axioms) to produce primes in the sequence a^2+b^4 with the relevant asymptotics.
Monte Carlo approaches are a powerful tool in collider physics as they allow to make theory-data comparison on complex multi-particle observables, otherwise difficult for perturbative calculations. In heavy-ion collisions, there is a multitude of Monte Carlo approaches that try to address jet quenching phenomena, name given to the collection of medium-induced modifications that high momentum particles and jets undergo when traversing the hot and dense medium that is produced in such collisions. These models are being continuous developed alongside the theoretical efforts to understand and accurately describe experimental results provided by both RHIC and the LHC. In this manuscript, it is given a general overview about the fundamental building blocks that these tools have to address to describe jets in heavy-ion collisions. It follows a comparison on the latest results provided by some of the jet quenching Monte Carlo models to jet and intra-jet observables. A final personal outlook is presented at the end of the manuscript.
We carry out the molecular statics simulations of depinning of an edge dislocation at voids of diameters of the order of ~1 nm. We show that the dislocation-void interactions are non-trivial as the applied shear load is found to enhance the pinning strength of the nanovoid itself. This leads to the surprising observation of multiple CRSS values for a given nanovoid.
We report two different types of backflow from jets by performing 2D special relativistic hydrodynamical simulations. One is anti-parallel and quasi-straight to the main jet (quasi-straight backflow), and the other is bent path of the backflow (bent backflow). We find that the former appears when the head advance speed is comparable to or higher than the local sound speed at the hotspot while the latter appears when the head advance speed is slower than the sound speed bat the hotspot. Bent backflow collides with the unshocked jet and laterally squeezes the jet. At the same time, a pair of new oblique shocks are formed at the tip of the jet and new bent fast backflows are generated via these oblique shocks. The hysteresis of backflow collisions is thus imprinted in the jet as a node and anti-node structure. This process also promotes broadening of the jet cross sectional area and it also causes a decrease in the head advance velocity. This hydrodynamic process may be tested by observations of compact young jets.
We present two new methods for performing ab initio calculations of excited states for closed-shell systems within the in-medium similarity renormalization group (IMSRG) framework. Both are based on combining the IMSRG with simple many-body methods commonly used to target excited states, such as the Tamm-Dancoff approximation (TDA) and equations-of-motion (EOM) techniques. In the first approach, a two-step sequential IMSRG transformation is used to drive the Hamiltonian to a form where a simple TDA calculation (i.e., diagonalization in the space of $1$p$1$h excitations) becomes exact for a subset of eigenvalues. In the second approach, equations-of-motion (EOM) techniques are applied to the ground-state-decoupled IMSRG Hamiltonian to access excited states. We perform proof-of-principle calculations for parabolic quantum dots in two-dimensions and the closed shell nuclei $^{16}$O and $^{22}$O. We find that the TDA-IMSRG approach gives better accuracy than the EOM-IMSRG when calculations converge, but is otherwise lacking the versatility and numerical stability of the latter. Our calculated spectra are in reasonable agreement with analogous EOM-coupled-cluster (EOM-CC) calculations, which paves the way for more interesting applications of the EOM-IMSRG to calculations of consistently evolved observables such as electromagnetic strength functions and nuclear matrix elements, and extensions to nuclei within 1-2 nucleons of a closed shell by generalizing the EOM ladder operator to include particle-number nonconserving terms.
Quantum key distribution (QKD) is a cryptographic protocol to enable two parties to share a secure key string, which can be used in one-time pad cryptosystem. There has been an ongoing surge of interest in implementing long-haul photonic-implementation of QKD protocols. However, the endeavour is challenging in many aspects. In particular, one of the major challenges is the polarization degree of freedom of single-photons getting affected while transmission through optical fibres, or atmospheric turbulence. Conventionally, an active feedback-based mechanism is employed to achieve real-time polarization tracking. In this work, we propose an alternative approach where we first perform a state tomography to reconstruct the output density matrix. We then evaluate the optimal measurement bases at Bob's end that leads to the maximum (anti-)correlation in the measurement outcomes of both parties. As a proof-of-principle demonstration, we implement an in-lab BBM92 protocol -- a particular variant of a QKD protocol using quantum entanglement as a resource -- to exemplify the performance of our technique. We experimentally generate polarization-entangled photon pairs having $94\%$ fidelity with $\ket{\psi}_1 = 1/\sqrt{2}\,(\ket{HV}+\ket{VH})$ state and a concurrence of $0.92$. By considering a representative 1 ns coincidence window span, we are able to achieve a quantum-bit-error-rate (QBER) of $\approx 5\%$, and a key rate of $\approx 35$ Kbps. The protocol performance is independent of local polarization rotations through optical fibres. We also develop an algorithmic approach to optimize the trade-off between the key rate and QBER. Our approach obviates the need for active polarization tracking. Our method is also applicable to entanglement-based QKD demonstrations using partially mixed as well as non-maximally entangled states, and extends to single-photon implementations over fibre channels.
By using Oprea's Bialynicki-Birula decomposition for the stack of genus zero stable maps to flag manifolds. We calculate the Poincar\'e polynomial of the moduli space in degree one and degree two.