ShantanuT01/DACTYL-Pretraining huggingface dataset:
We present results referring to the Hadwiger-Nelson problem which asks for the minimum number of colours needed to colour the plane with no two points at distance $1$ having the same colour. Exoo considered a more general problem concerning graphs $G_{[a,b]}$ with $\mathbb{R}^2$ as the vertex set and two vertices adjacent if their distance is in the interval $[a,b]$. Exoo conjectured $\chi(G_{[a,b]}) = 7$ for sufficiently small but positive difference between $a$ and $b$. We partially answer this conjecture by proving that $\chi(G_{[a,b]}) \geq 5$ for $b > a$.   A $j$-fold colouring of graph $G = (V,E)$ is an assignment of $j$-elemental sets of colours to the vertices of $G$, in such a way that the sets assigned to any two adjacent vertices are disjoint. The fractional chromatic number $\chi_f(G)$ is the infimum of fractions $k/j$ for $j$-fold colouring of $G$ using $k$ colours. We generalize a method by Hochberg and O'Donnel (who proved that $G_{[1,1]} \leq 4.36$) for fractional colouring of graphs $G_{[a,b]}$, obtaining a bound dependant on $\frac{a}{b}$.   We also present few specific and two general methods for $j$-fold coloring of $G_{[a,b]}$ for small $j$, in particular for $G_{[1,1]}$ and $G_{[1,2]}$. The $j$-fold colouring for small $j$ has strong practical motivation especially in scheduling theory, while graph $G_{[1,2]}$ is often used to model hidden conflicts in radio networks.
We theoretically study the Coulomb drag resistivity in a double-layer electron system with highly anisotropic parabolic band structure using Boltzmann transport theory. As an example, we consider a double-layer phosphorene on which we apply our formalism. This approach, in principle, can be tuned for other double-layered systems with paraboloidal band structures. Our calculations show the rotation of one layer with respect to another layer can be considered a way of controlling the drag resistivity in such systems. As a result of rotation, the off-diagonal elements of drag resistivity tensor have non-zero values at any temperature. In addition, we show that the anisotropic drag resistivity is very sensitive to the direction of momentum transfer between two layers due to highly anisotropic inter-layer electron-electron interaction and also the plasmon modes. In particular, the drag anisotropy ratio, \r{ho}yy/\r{ho}xx, can reach up to ~ 3 by changing the temperature. Furthermore,our calculations suggest that including the local field correction in dielectric function changes the results significantly. Finally, We examine the dependence of drag resistivity and its anisotropy ratio on various parameters like inter-layer separation, electron density, short-range interaction and insulating substrate/spacer.
Over a smooth complex projective curve, we study an algebraic versal deformation space with fixed determinant of a coherent sheaf. The algebraic versal deformation space decomposes into a disjoint union of Shatz strata, namely locally closed subschemes which parametrize coherent sheaves with common Harder-Narasimhan types. We study the geometry and local topology of large unstable strata and their behavior along boundaries.
We show that any finite simple graph with minimum degree $d$ contains a spanning star forest in which every connected component is of size at least $\Omega((d/\log d)^{1/3})$. This settles a problem of J. Kratochvil.
Plenty of mid-eclipse timings of short-periodic eclipsing binaries derived from series of visual observations appear to be an acceptable source of information for orbital period analyses, namely if they were done in time-intervals not covered by other types of observations. However, our thorough period analysis of the nearly contact eclipsing binary BS Vulpeculae proves that visually determined timings done in 1979--2003 were undoubtedly biased to accommodate the existing linear ephemeris. The heavily subjective character of visual observations disqualifies them as a source of true phase information apt for fine eclipsing binary period analyses. Consequently we warn against the use of visual timings without a preceding careful verification.
In the recent work [DFM1, DFM2] G. David, J. Feneuil, and the first author have launched a program devoted to an analogue of harmonic measure for lower-dimensional sets. A relevant class of partial differential equations, analogous to the class of elliptic PDEs in the classical context, is given by linear degenerate equations with the degeneracy suitably depending on the distance to the boundary.   The present paper continues this line of research and focuses on the criteria of quantitative absolute continuity of the newly defined harmonic measure with respect to the Hausdorff measure, $\omega\in A_\infty(\sigma)$, in terms of solvability of boundary value problems. The authors establish, in particular, square function estimates and solvability of the Dirichlet problem in BMO for domains with lower-dimensional boundaries under the underlying assumption $\omega\in A_\infty(\sigma)$. More generally, it is proved that in all domains with Ahlfors regular boundaries the BMO solvability of the Dirichlet problem is necessary and sufficient for the absolute continuity of the harmonic measure.
We study the collective Raman cooling of a polarized trapped Fermi gas in the Festina Lente regime, when the heating effects associated with photon reabsorptions are suppressed. We predict that by adjusting the spontaneous Raman emission rates and using appropriately designed anharmonic traps, temperatures of the order of 2.7% of the Fermi temperature can be achieved in 3D.
It is known that solutions of nonlocal dispersal evolution equations do not become smoother in space as time elapses. This lack of space regularity would cause a lot of difficulties in studying transition fronts in nonlocal equations. In the present paper, we establish some general criteria concerning space regularity of transition fronts in nonlocal dispersal evolution equations with a large class of nonlinearities, which allows the applicability of various techniques for reaction-diffusion equations to nonlocal equation, and hence serves as an initial and fundamental step for further studying various qualitative properties of transition fronts such as stability and uniqueness. We also prove the existence of continuously differentiable and increasing interface location functions, which give a better characterization of the propagation of transition fronts and are of great technical importance.
We study statistical properties of synchrotron polarization emitted from media with magnetohydrodynamic (MHD) turbulence. We use both synthetic and MHD turbulence simulation data for our studies. We obtain the spatial spectrum and its derivative with respect to wavelength of synchrotron polarization arising from both synchrotron radiation and Faraday rotation fluctuations. In particular, we investigate how the spectrum changes with frequency. We find that our simulations agree with the theoretical predication in Lazarian \& Pogosyan (2016). We conclude that the spectrum of synchrotron polarization and it derivative can be very informative tools to get detailed information about the statistical properties of MHD turbulence from radio observations of diffuse synchrotron polarization. Especially, they are useful to recover the statistics of turbulent magnetic field as well as turbulent density of electrons. We also simulate interferometric observations that incorporate the effects of noise and finite telescope beam size, and demonstrate how we recover statistics of underlying MHD turbulence.
Interactive image segmentation aims at segmenting a target region through a way of human-computer interaction. Recent works based on deep learning have achieved excellent performance, while most of them focus on improving the accuracy of the training set and ignore potential improvement on the test set. In the inference phase, they tend to have a good performance on similar domains to the training set, and lack adaptability to domain shift, so they require more user efforts to obtain satisfactory results. In this work, we propose RAIS, a robust and accurate architecture for interactive segmentation with continuous learning, where the model can learn from both train and test data sets. For efficient learning on the test set, we propose a novel optimization strategy to update global and local parameters with a basic segmentation module and adaptation module, respectively. Moreover, we perform extensive experiments on several benchmarks that show our method can handle data distribution shifts and achieves SOTA performance compared with recent interactive segmentation methods. Besides, our method also shows its robustness in the datasets of remote sensing and medical imaging where the data domains are completely different between training and testing.
Capacitance-voltage (C-V) characteristics are important for understanding fundamental electronic structures and device applications of nanomaterials. The C-V characteristics of graphene nanoribbons (GNRs) are examined using self-consistent atomistic simulations. The results indicate strong dependence of the GNR C-V characteristics on the edge shape. For zigzag edge GNRs, highly non-uniform charge distribution in the transverse direction due to edge states lowers the gate capacitance considerably, and the self-consistent electrostatic potential significantly alters the band structure and carrier velocity. For an armchair edge GNR, the quantum capacitance is a factor of 2 smaller than its corresponding zigzag carbon nanotube, and a multiple gate geometry is less beneficial for transistor applications. Magnetic field results in pronounced oscillations on C-V characteristics.
The VRI passbands light curves of V344 Lac were presented and analyzed by using the latest version of the W-D code. The observed spectrum reveals that V344 Lac is not an A3 type but would be a later F type star according to the yielded temperature. The results of solution show that V344 Lac is an A-subtype contact binary, with a mediate photometric mass ratio of 0.387(0.003) and a mediate contact factor of 44.6(3.0)%. Based on the parallax given by Gaia, the parameters of the components are estimated as: M1 = 1.16 Ms, M2 = 0.45 Ms, R1 = 1.31 Rs, R2 = 0.88 Rs, L1 = 2.512 Ls, L2 = 1.057 Ls. The period investigation indicates that V344 Lac may have an eccentric orbital oscillation, with P3 = 12.4(0.5) yr, A3 = 0.0020(0.0002) d, and e = 0.38(0.16). Analysis shows such oscillation would be caused by a magnetic activity which can be explained by the Applegate mechanism. Meanwhile, according to the value of l3 and the estimated physical parameters of V344 Lac, the mass of the third companion may be 0.79 Ms. This third body could be a wide company.
We prove the unimodality of the Ehrhart $\delta$-polynomial of the chain polytope of the zig-zag poset, which was conjectured by Kirillov. First, based on a result due to Stanley, we show that this polynomial coincides with the $W$-polynomial for the zig-zag poset with some natural labeling. Then, its unimodality immediately follows from a result of Gasharov, which states that the $W$-polynomials of naturally labeled graded posets of rank $1$ or $2$ are unimodal.
We review the current state of our knowledge concerning the rotation and angular momentum evolution of young stellar objects and brown dwarfs from a primarily observational view point. Periods are typically accurate to 1% and available for about 1700 stars and 30 brown dwarfs in young clusters. Discussion of angular momentum evolution also requires knowledge of stellar radii, which are poorly known for pre-main sequence stars. It is clear that rotation rates at a given age depend strongly on mass; higher mass stars (0.4-1.2 M$_\odot$) have longer periods than lower mass stars and brown dwarfs. On the other hand, specific angular momentum is approximately independent of mass for low mass pre-main sequence stars and young brown dwarfs. A spread of about a factor of 30 is seen at any given mass and age. The evolution of rotation of solar-like stars during the first 100 Myr is discussed. A broad, bimodal distribution exists at the earliest observable phases ($\sim$1 Myr) for stars more massive than 0.4 M$_\odot$. The rapid rotators (50-60% of the sample) evolve to the ZAMS with little or no angular momentum loss. The slow rotators continue to lose substantial amounts of angular momentum for up to 5 Myr, creating the even broader bimodal distribution characteristic of 30-120 Myr old clusters. Accretion disk signatures are more prevalent among slowly rotating PMS stars, indicating a connection between accretion and rotation. Disks appear to influence rotation for, at most, $\sim$5 Myr, and considerably less than that for the majority of stars. If the dense clusters studied so far are an accurate guide, then the typical solar-like star may have only $\sim$1 Myr for this task. It appears that both disk interactions and stellar winds are less efficient at braking these objects.
We consider the Noether Problem for stable and retract rationality for the sequence of $d$-torsion subgroups $T[d]$ of a torus $T$, $d\geq 1$. We show that the answer to these questions only depends on $d\pmod{e(T)}$, where $e(T)$ is the period of the generic $T$-torsor. When $T$ is the norm one torus associated to a finite Galois extension, we find all $d$ such that the Noether Problem for retract rationality has a positive solution for $d$. We also give an application to the Grothendieck ring of stacks.
Resonant tunneling through a quantum dot weakly coupled to Tomonaga-Luttinger liquids is discussed. The linear conductance due to sequential tunneling is calculated by solving a master equation for temperatures below and above the average level spacing in the dot. When the parameter g characterizing the Tomonaga-Luttinger liquid is smaller than 1/2, the resonant tunneling process is incoherent down to zero temperature. At low temperature T the height and width of the conductance peaks in the Coulomb blockade oscillations are proportional to T^{(1/g)-2} and T, respectively. The contribution from tunneling via a virtual intermediate state (cotunneling) is also included. The resulting conductance formula can be applied for the resonant tunneling between edge states of fractional quantum Hall liquids with filling factor nu=1/(2m+1)=g.
We study Bell's inequality using the Bell states constructed from four component Dirac spinors. Spin operator is related to the Pauli-Lubanski pseudo vector which is relativistic invariant operator. By using Lorentz transformation, in both Bell states and spin operator, we obtain an observer independent Bell's inequality, so that it is maximally violated as long as it is violated maximally in the rest frame.
The gamma-ray binary system PSR B1259-63/LS 2883 went through periastron in May 2014. We report on the optical spectroscopic monitoring of the system from 33 d before to 78 d after periastron, undertaken with the Southern African Large Telescope (SALT). The H{\alpha} and He I ({\lambda}6678) lines exhibit an orbital variation around periastron, with the line strengths reaching a maximum ~13 d after periastron. The line strength is weaker than observed around the previous periastron in 2010. There is also a marked change in the line-strength and asymmetry around the first disc crossing. These observations are consistent with the disruption of the circumstellar disc around periastron due to the interaction with the pulsar.
Gamma-ray bursts (GRBs) of the long-duration class are the most luminous sources of electromagnetic radiation known in the Universe. They are generated by outflows of plasma ejected at near the speed of light by newly formed neutron stars or black holes of stellar mass at cosmological distances. Prompt flashes of MeV gamma rays are followed by longer-lasting afterglow emission from radio waves to GeV gamma rays, due to synchrotron radiation by energetic electrons in accompanying shock waves. Although emission of gamma rays at even higher, TeV energies by other radiation mechanisms had been theoretically predicted, it had never been detected previously. Here we report the clear detection of GRB 190114C in the TeV band, achieved after many years of dedicated searches for TeV emission from GRBs. Gamma rays in the energy range 0.2--1 TeV are observed from about 1 minute after the burst (at more than 50 standard deviations in the first 20 minutes). This unambiguously reveals a new emission component in the afterglow of a GRB, whose power is comparable to that of the synchrotron component. The observed similarity in the radiated power and temporal behaviour of the TeV and X-ray bands points to processes such as inverse Compton radiation as the mechanism of the TeV emission, while processes such as synchrotron emission by ultrahigh-energy protons are disfavoured due to their low radiative efficiency.
The dynamics of a quantum system driven by an external field is well described by a unitary transformation generated by a time dependent Hamiltonian. The inverse problem of finding the field that generates a specific unitary transformation is the subject of study. The unitary transformation which can represent an algorithm in a quantum computation is imposed on a subset of quantum states embedded in a larger Hilbert space. Optimal control theory (OCT) is used to solve the inversion problem irrespective of the initial input state. A unified formalism, based on the Krotov method is developed leading to a new scheme. The schemes are compared for the inversion of a two-qubit Fourier transform using as registers the vibrational levels of the $X^1\Sigma^+_g$ electronic state of Na$_2$. Raman-like transitions through the $A^1\Sigma^+_u$ electronic state induce the transitions. Light fields are found that are able to implement the Fourier transform within a picosecond time scale. Such fields can be obtained by pulse-shaping techniques of a femtosecond pulse. Out of the schemes studied the square modulus scheme converges fastest. A study of the implementation of the $Q$ qubit Fourier transform in the Na$_2$ molecule was carried out for up to 5 qubits. The classical computation effort required to obtain the algorithm with a given fidelity is estimated to scale exponentially with the number of levels. The observed moderate scaling of the pulse intensity with the number of qubits in the transformation is rationalized.
The exotic quantum double and its universal R-matrix for quantum Yang-Baxter equation are constructed in terms of Drinfeld's quantum double theory.As a new quasi-triangular Hopf algebra, it is much different from those standard quantum doubles that are the q-deformations for Lie algebras or Lie superalgebras. By studying its representation theory,many-parameter representations of the exotic quantum double are obtained with an explicit example associated with Lie algebra $A_2$ .The multi-parameter R-matrices for the quantum Yang-Baxter equation can result from the universal R-matrix of this exotic quantum double and these representattions.
Polariton lasing is demonstrated on the zero dimensional states of single GaAs/GaAlAs micropillar cavities. Under non resonant excitation, the measured polariton ground state occupancy is found to be as large as $10^{4}$. Changing the spatial excitation conditions, competition between several polariton lasing modes is observed, ruling out Bose-Einstein condensation. When the polariton state occupancy increases, the emission blueshift is the signature of self-interaction within the half-light half-matter polariton lasing mode.
In this first of several application papers, we investigate the mechanics of reionization from stellar sources in high-z galaxies, the utility of various clumping factors on estimating the recombination time in the IGM, and the photon budget required to achieve reionization. We test the accuracy of the static and time-dependent models of Madau et al. as predictors of reionization completion/maintenance. We simulate a WMAP7 LCDM cosmological model in a 20 Mpc comoving cube with 800^3 uniform fluid cells and dark matter particles. By tuning our star formation to approximately match the observed star formation rate density and luminosity function, we created a fully coupled radiation-hydro realization of H reionization which begins to ionize at z~10 and completes at z~5.8. We find that roughly 2 ionizing photons per H atom are required to convert the neutral IGM to a highly ionized state, which supports the "photon starved" scenario discussed by Bolton & Haehnelt. The events during reionization that lead to this number can generally be described as inside-out, but in reality the narrative depends on the level of ionization of the gas one attributes to as ionized. We find that the formula for the UV photon production rate dN/dt_ion(z) needed to maintain the IGM in an ionized state derived by Madau et al. should not be used to predict the epoch of reionization completion because it ignores history-dependent terms in the global ionization balance which are not ignorable. We find that the time-dependent model for the ionized volume fraction Q_HII is more predictive, but overestimates the redshift of reionization completion by delta_z~1. We propose a revised formulation of the time-dependent model which agrees with our simulation to O(1%). Finally, we use our simulation to estimate a global UV escape fraction due to circumgalactic gas resolved on our mesh to be <f_esc>~0.7.
In this paper, we present a fully fiber-based one-way Quantum Key Distribution (QKD) system implementing the Gaussian-Modulated Coherent States (GMCS) protocol. The system employs a double Mach-Zehnder Interferometer (MZI) configuration in which the weak quantum signal and the strong Local Oscillator (LO) go through the same fiber between Alice and Bob, and are separated into two paths inside Bob's terminal. To suppress the LO leakage into the signal path, which is an important contribution to the excess noise, we implemented a novel scheme combining polarization and frequency multiplexing, achieving an extinction ratio of 70dB. To further minimize the system excess noise due to phase drift of the double MZI, we propose that, instead of employing phase feedback control, one simply let Alice remap her data by performing a rotation operation. We further present noise analysis both theoretically and experimentally. Our calculation shows that the combined polarization and frequency multiplexing scheme can achieve better stability in practice than the time-multiplexing scheme, because it allows one to use matched fiber lengths for the signal and the LO paths on both sides of the double MZI, greatly reducing the phase instability caused by unmatched fiber lengths. Our experimental noise analysis quantifies the three main contributions to the excess noise, which will be instructive to future studies of the GMCS QKD systems. Finally, we demonstrate, under the "realistic model" in which Eve cannot control the system within Bob's terminal, a secure key rate of 0.3bit/pulse over a 5km fiber link. This key rate is about two orders of magnitude higher than that of a practical BB84 QKD system.