ShantanuT01/DACTYL-Pretraining huggingface dataset:
We $q$-enumerate lozenge tilings of a hexagon with three bowtie-shaped regions have been removed from three non-consecutive sides. The unweighted version of the result generalizes a problem posed by James Propp on enumeration of lozenge tilings of a hexagon of side-lengths $2n,2n+3,2n,2n+3,2n,2n+3$ (in cyclic order) with the central unit triangles on the $(2n+3)$-sides removed.
Scattering of particles in the gravitational field of rotating black holes is considered. It is shown that scattering energy of particles in the centre of mass system can obtain very large values not only for extremal black holes but also for nonextremal ones. Extraction of energy after the collision is investigated. It is shown that due to the Penrose process the energy of the particle escaping the hole at infinity can be large. Contradictions in the problem of getting high energetic particles escaping the black hole are resolved.
The structure function of the nucleus in the cumulative region $x>1$ is studied in terms of nucleon degrees of freedom. At high $Q^2$ the resulting expressions are presented as a sum of contributions from few-nucleon correlations. Two-nucleon correlations are studied in some detail. Spin variables are averaged out. In the region $1<x<2$ the structure functions are calculated for the relativistic interaction proposed by F.Gross {\it et al}. They are found to fall with $x$ faster than the exponential. For Carbon at $x=1.05$, where the method is not rigorously applicable, they turn out to be rougly twice larger than the experimental data.
The standard solar model was so reliable that it could predict the existence of the massive neutrino. Helioseismology measurements were so precise that they could determine the depth of the convection zone. This agreement between theory and observation was the envy of all astrophysics -- until recently when sophisticated three-dimensional hydrodynamic calculations of the solar atmosphere reduced the metal content by a factor of almost two. Antia & Basu (2005) suggested that a higher value of the solar neon abundance, Ne/O = 0.52, would resolve this controversy. Drake & Testa (2005) presented strong evidence in favor of this idea from a sample of 21 Chandra stars with enhanced values of the neon abundance, Ne/O = 0.41. In this paper, we have analyzed solar active region spectra from the archive of the Flat Crystal Spectrometer on Solar Maximum Mission, a NASA mission from the 1980s, as well as full-Sun spectra from the pioneering days of X-ray astronomy in the 1960s. These data seem consistent with the standard neon-to-oxygen abundance value, Ne/O = 0.15 (Grevesse & Sauval 1998). If these results prove to be correct, than the enhanced-neon hypothesis will not resolve the current controversy.
Several methods proposed to measure the angle $\gamma$ in the KM unitarity triangle assumed that the tree contribution to $B^-\to \pi^-\bar K^0 $ is purely due to annihilation contributions and is negligibly small. This assumption has to be tested in order to have a correct interpretation of the experimental data. In this paper we show that using SU(3) symmetry, the smallness of the tree contribution can be tested in a dynamic model independent way. We also derive several relations between CP violating rate differences for $B\to P P$ decays without assuming the smallness of the annihilation contributions. These relations provide important tests for the Standard Model of CP violation.
The electronic structure of the three-particle donor bound exciton (D$^0$X) in silicon is computed using a large-scale atomic orbital tight-binding method within the Hartree approximation. The calculations yield a transition energy close to the experimentally measured value of 1150 meV in bulk, and show how the transition energy and transition probability can change with applied fields and proximity to surfaces, mimicking the conditions of realistic devices. The spin-resolved transition energy from a neutral donor state (D$^0$) to D$^0$X depends on the three-particle Coulomb energy, and the interface and electric field induced hyperfine splitting and heavy-hole-light-hole splitting. Although the Coulomb energy decreases as a result of Stark shift, the spatial separation of the electron and hole wavefunctions by the field also reduces the transition dipole. A bulk-like D$^0$X dissociates abruptly at a modest electric field, while a D$^0$X at a donor close to an interface undergoes a gradual ionization process. Our calculations take into account the full bandstructure of silicon and the full energy spectrum of the donor including spin directly in the atomic orbital basis and treat the three-particle Coulomb interaction self-consistently to provide quantitative guidance to experiments aiming to realize hybrid opto-electric techniques for addressing donor qubits.
In this paper, we consider infinite Galois extensions of number fields and study the relation between their local degrees and the structure of their Galois groups. It is known that, if $K$ is a number field and $L/K$ is an infinite Galois extension of group $G$, then the local degrees of $L$ are uniformly bounded at all rational primes if and only if $G$ has finite exponent. In this note we show that the non uniform boundedness of the local degrees is not equivalent to any group theoretical property. More precisely, we exhibit several groups that admit two different realisations over a given number field, one with bounded local degrees at a given set of primes and one with infinite local degrees at the same primes.
A new approach to quantum gravity is presented based on a nonlinear quantization scheme for canonical field theories with an implicitly defined Hamiltonian. The constant mean curvature foliation is employed to eliminate the momentum constraints in canonical general relativity. It is, however, argued that the Hamiltonian constraint may be advantageously retained in the reduced classical system to be quantized. This permits the Hamiltonian constraint equation to be consistently turned into an expectation value equation on quantization that describes the scale factor on each spatial hypersurface characterized by a constant mean exterior curvature. This expectation value equation augments the dynamical quantum evolution of the unconstrained conformal three-geometry with a transverse traceless momentum tensor density. The resulting quantum theory is inherently nonlinear. Nonetheless, it is unitary and free from a nonlocal and implicit description of the Hamiltonian operator. Finally, by imposing additional homogeneity symmetries, a broad class of Bianchi cosmological models are analyzed as nonlinear quantum minisuperspaces in the context of the proposed theory.
This article deals with the existence and non-existence of positive solutions for the eigenvalue problem driven by nonhomogeneous fractional $p\& q$ Laplacian operator with indefinite weights $$\left(-\Delta_p\right)^{\alpha}u + \left(-\Delta_q\right)^{\beta}u \,= \lambda\left[a(x) \left|u\right|^{p-2}u + b(x) \left|u\right|^{q-2}u \right]\quad\quad\textrm{in $\O$},$$ where $\O$ is a smooth bounded domain in $\R^N$ extended by zero outside. When $\O=\R^N$ and $b\equiv0$, we further show that there exists a continuous family of the eigenvalue if $1<q<p<q^*_\beta=\frac{Nq}{N-q\beta}$ and $0\leq a\in L^{\left(\frac{q_{\beta}^*}{s}\right)'}\left(\R^N\right)\bigcap L^{\infty}\left(\R^N\right)$ with $s$ satisfies $\dfrac{p-t}{p_{\alpha}^*}+ \dfrac{p\left(1-t\right)}{s} =1$, for some $t\in \left(0, \sqrt{\dfrac{p-q}{p}}\right).$ Our approach replies strongly on variational analysis, in which the Mountain pass theorem plays the key role. The main difficulty in this study is that how to establish the Palais-Smale conditions. In particular, in $\R^N$, due to the lack of spatial compactness and the embedding $W^{\alpha, p}\left(\R^N\right) \hookrightarrow W^{\beta, q}\left(\R^N\right)$, we must employ the concentration-compactness principle of P.L. Lions \cite{PLL} to overcome the difficulty.
Clusters in the three-dimensional Ising model rigorously obey reducibility and thermal scaling up to the critical temperature. The barriers extracted from Arrhenius plots depend on the cluster size as $B \propto A^{\sigma}$ where $\sigma$ is a critical exponent relating the cluster size to the cluster surface. All the Arrhenius plots collapse into a single Fisher-like scaling function indicating liquid-vapor-like phase coexistence and the univariant equilibrium between percolating clusters and finite clusters. The compelling similarity with nuclear multifragmentation is discussed.
We show theoretically that two atomic dipoles in a resonator constitute a non-linear medium, whose properties can be controlled through the relative position of the atoms inside the cavity and the detuning and intensity of the driving laser. We identify the parameter regime where the system operates as a parametric amplifier, based on the cascade emission of the collective dipole of the atoms, and determine the corresponding spectrum of squeezing of the field at the cavity output. This dynamics could be observed as a result of self-organization of laser-cooled atoms in resonators.
We discuss the spectral properties of a sample of type-2 Seyfert galaxies based upon the analysis of \asca data. In this paper we consider the sources for which the X-ray spectra appear to be dominated by the nuclear continuum, transmitted through a large column of absorbing material. We find that both Seyfert-2 galaxies and NELGs show iron K$\alpha$ line profiles indicative of reprocessing of nuclear X-rays in a face-on accretion disk. Such line profiles are also observed in Seyfert-1 galaxies. This result is contrary to unification models, which would predict the inner regions of Seyfert-2 galaxies to be observed edge-on. This raises some questions as to the orientation of the circumnuclear absorber. If the observed differences between Seyfert type-1 and type-2 galaxies, and NELGs are not due to differences in the orientation of the absorbing material, then we suggest that differences in dust composition and grain size, and in the density of the circumnuclear gas could be of primary importance.
Singularity-free cosmological solutions may be obtained from the string action at tree level if the dimension of the space-time is greater than 10 and if brane configurations are taken into account. The behaviour of the dilaton field in this case is also regular. Asymptotically a radiative phase is attained indicating a smooth transition to the standard cosmological model.
This note is a survey of results on the function $F_{\mathbf{k}}(z)$ introduced by G. Kawashima, and its applications to the study of multiple zeta values. We stress the viewpoint that the Kawashima function is a generalization of the digamma function $\psi(z)$, and explain how various formulas for $\psi(z)$ are generalized. We also discuss briefly the relationship of the results on the Kawashima functions with a recent work on Kawashima's MZV relation by M. Kaneko and the author.
We define a sample designed to select low-mass T Tauri stars and young brown dwarfs using DENIS data in the Chamaeleon II molecular cloud. We use a star count method to construct an extinction map of the Chamaeleon II cloud. We select our low-mass T Tauri star and young brown dwarf candidates by their strong infrared colour excess in the I-J/J-K_s colour-colour dereddened diagram. We retain only objects with colours I-J>2, and spatially distributed in groups around the cloud cores. This provides a sample of 70 stars of which 4 are previously known T Tauri stars. We have carefully checked the reliability of all these objects by visual inspection on the DENIS images. Thanks to the association of the optical I-band to the infra-red J and K_s bands in DENIS, we can apply this selection method to all star formation regions observed in the southern hemisphere. We also identify six DENIS sources with X-ray sources detected by ROSAT. Assuming that they are reliable low-mass candidates and using the evolutionary models for low-mass stars, we estimate the age of these sources between 1 Myr and < 10 Myr.
We investigate the rate of superradiant emission for a number of artificial atoms (qubits) embedded in a one-dimensional open waveguide. More specifically, we study the 1D (N+1)- qubit chain where N qubits are identical in respect to their excitation frequency $\Omega$ but have different rates of spontaneous emission $\Gamma_n$, and a single impurity qubit which is different from N qubits by its excitation frequency $\Omega_P$ and rate of spontaneous emission $\Gamma_P$. This system is shown to have two hybridized collective states which accumulates the widths of all qubits. The energy spectrum of these states and corresponding probabilities are investigated as the function of the frequency detuning between the impurity and other qubits in a chain. It is shown that the inclusion of impurity qubit alter the resonance widths of the system only in a narrow range of the frequency detuning between qubits and impurity, where the resonance widths experience a significant repulsion. The photon transmission through disordered N- qubit chain with impurity qubit is also considered. It is shown that a single photon transport through this system is described by a simple expression which predicts for specific photon frequency the existence of a complete transmission peak and transparency window between frequencies $\Omega$ and $\Omega_P$.
Multiple zeta values are real numbers defined by an infinite series generalizing values of the Riemann zeta function at positive integers. Finite truncations of this series are called multiple harmonic sums and are known to have interesting arithmetic properties. When the truncation point is one less than a prime $p$, the mod $p$ values of multiple harmonic sums are called finite multiple zeta values. The present work introduces a new class of congruence for multiple harmonic sums, which we call weighted congruences. These congruences can hold modulo arbitrarily large powers of $p$. Unlike results for finite multiple zeta values, weighted congruences typically involve harmonic sums of multiple weights, which are multiplied by explicit powers of $p$ depending on weight. We also introduce certain formal weighted congruences inolving an infinite number of terms, which we call asymptotic relations. We define a weighted analogue of the finite multiple zeta function, and give an algebraic framework for classifying weighted congruences and asymptotic relations.
Many high dimensional vector distances tend to a constant. This is typically considered a negative "contrast-loss" phenomenon that hinders clustering and other machine learning techniques. We reinterpret "contrast-loss" as a blessing. Re-deriving "contrast-loss" using the law of large numbers, we show it results in a distribution's instances concentrating on a thin "hyper-shell". The hollow center means apparently chaotically overlapping distributions are actually intrinsically separable. We use this to develop distribution-clustering, an elegant algorithm for grouping of data points by their (unknown) underlying distribution. Distribution-clustering, creates notably clean clusters from raw unlabeled data, estimates the number of clusters for itself and is inherently robust to "outliers" which form their own clusters. This enables trawling for patterns in unorganized data and may be the key to enabling machine intelligence.
Two- and three- particles photodisintegration of the triton is investigated in a three-dimensional (3D) Faddeev approach. For this purpose the Jacobi momentum vectors for three particles system and spin-isospin quantum numbers of the individual nucleons are considered. Based on this picture the three-nucleon Faddeev integral equations with the two-nucleon interaction are formulated without employing the partial wave decomposition. The single nucleon current as well as $\pi-$ and $\rho-$ like exchange currents are used in an appropriate form to be employed in 3D approach. The exchange currents are derived from AV18 NN force. The two-body t-matrix, Deuteron and Triton wave functions are calculated in the 3D approach by using AV18 potential. Benchmarks are presented to compare the total cross section for the two- and three- particles photodisintegration in the range of $E_{\gamma}<30 MeV$. The 3D Faddeev approach shows promising results.
Using a localization procedure and the result of Holley-Kusuoka-Stroock [7] in the torus, we widely weaken the usual growth assumptions concerning the success of the continuous-time simulated annealing in $\mathbf{R}^d$. Our only assumption is the existence of an invariant probability measure for a sufficiently low temperature. We also prove, in an appendix, a non-explosion criterion for a class of time-inhomogeneous diffusions.
The many unusual properties of the enigmatic AT2018cow suggested that at least some subset of the empirical class of fast blue optical transients (FBOTs) represents a genuinely new astrophysical phenomenon. Unfortunately, the intrinsic rarity and fleeting nature of these events have made it difficult to identify additional examples early enough to acquire the observations necessary to constrain theoretical models. We present here the Zwicky Transient Facility discovery of AT2020xnd (ZTF20acigmel, the "Camel") at z=0.243, the first unambiguous AT2018cow analog to be found and confirmed in real time. AT2018cow and AT2020xnd share all key observational properties: a fast optical rise, sustained high photospheric temperature, absence of a second peak attributable to ejection of a radioactively-heated stellar envelope, extremely luminous radio, millimetre, and X-ray emission, and a dwarf-galaxy host. This supports the argument that AT2018cow-like events represent a distinct phenomenon from slower-evolving radio-quiet supernovae, likely requiring a different progenitor or a different central engine. The sample properties of the four known members of this class to date disfavour tidal disruption models but are consistent with the alternative model of an accretion powered jet following the direct collapse of a massive star to a black hole. Contextual filtering of alert streams combined with rapid photometric verification using multi-band imaging provides an efficient way to identify future members of this class, even at high redshift.
K2, the two-wheel mission of the Kepler space telescope, observed the pulsating subdwarf B star EQ Psc during engineering tests in 2014 February. In addition to a rich spectrum of g-mode pulsation frequencies, the observations demonstrate a light variation with a period of 19.2 h and a full amplitude of 2%. We suggest that this is due to reflection from a cool companion, making EQ\,Psc the longest-period member of some 30 binaries comprising a hot subdwarf and a cool dwarf companion (sdB+dM), and hence useful for exploring the common-envelope ejection mechanism in low-mass binaries.
Rastall's theory is a generalization of Einstein's equations in which the energy-momentum tensor is not a conserved quantity, its covariant derivative is proportional to the gradient of the Ricci scalar and this fact can be associated with quantum effects in curved space-time. In this work we will go study the Rastall's gravity in the context of the G\"odel-type universe.
Aquaculture industries rely on the availability of accurate fish body measurements, e.g., length, width and mass. Manual methods that rely on physical tools like rulers are time and labour intensive. Leading automatic approaches rely on fully-supervised segmentation models to acquire these measurements but these require collecting per-pixel labels -- also time consuming and laborious: i.e., it can take up to two minutes per fish to generate accurate segmentation labels, almost always requiring at least some manual intervention. We propose an automatic segmentation model efficiently trained on images labeled with only point-level supervision, where each fish is annotated with a single click. This labeling process requires significantly less manual intervention, averaging roughly one second per fish. Our approach uses a fully convolutional neural network with one branch that outputs per-pixel scores and another that outputs an affinity matrix. We aggregate these two outputs using a random walk to obtain the final, refined per-pixel segmentation output. We train the entire model end-to-end with an LCFCN loss, resulting in our A-LCFCN method. We validate our model on the DeepFish dataset, which contains many fish habitats from the north-eastern Australian region. Our experimental results confirm that A-LCFCN outperforms a fully-supervised segmentation model at fixed annotation budget. Moreover, we show that A-LCFCN achieves better segmentation results than LCFCN and a standard baseline. We have released the code at \url{https://github.com/IssamLaradji/affinity_lcfcn}.
One of the unique features of graphene is that the Fermi wavelength of its charge carriers can be tuned electrostatically over a wide range. This allows in principle to tune the transparency of a pn-junction electrostatically, as this depends on the ratio between the physical extension of the junction and the electron wavelength, i.e. on the effective width of the junction itself. However, this simple idea - which would allow to switch smoothly between a Veselago lens and a Klein-collimator - has proved to be difficult to demonstrate experimentally because of the limited amount of independently-tunable parameters available in most setups. In this work, we present transport measurements in a quasi-ballistic Aharonov-Bohm graphene ring with gate tunable pn-junctions in one arm, and show that the interference patterns provide unambiguous information on the Klein tunneling efficiency and on the junctions effective width. We find a gate-controlled transparency of the pn-junctions ranging from 35-100%. Our results are in excellent agreement with a semiclassical description.
Pulsations and binarity are both common features of massive stars. The study of pulsating massive stars in eclipsing binary systems hold great potential for constraining stellar structure and evolution theory. However, prior to the all-sky Transiting Exoplanet Survey Satellite (TESS) mission, few such systems had been discovered or studied in detail. We have inspected the TESS light curves of a large number of eclipsing binaries known to contain high-mass stars, and compiled a list of 18 objects which show intrinsic variability. The light curves were modelled both to determine the physical properties of the systems, and to remove the effects of binarity in order to leave residual light curves suitable for asteroseismic analysis. Precise mass and radius measurements were obtained for delta Cir, CC Cas, SZ Cam, V436 Per and V539 Ara. We searched the residual light curves for pulsation signatures and, within our sample of 18 objects, we find six definite and eight possible cases of beta Cephei pulsation, seven cases of stochastic low-frequency (SLF) variability, and eight instances of possible slowly pulsating B (SPB) star pulsation. The large number of pulsating eclipsing systems we have identified makes asteroseismology of high-mass stars in eclipsing binaries a feasible avenue to constrain the interior physics of a large sample of massive stars for the first time.
Muon spin rotation and resonant soft X-ray scattering experiments on prototype multiferroics RMn2O5 (R = Y, Sm) are used to demonstrate that the local electric displacements are driven by the spin-current (SC) mechanism. Small local electric displacements were evaluated by observing spin polarization at ligand O ions, for which implanted muons served as an extremely sensitive probe. Our results for YMn2O5 provide evidence that the spin polarization of O ions forming a spin cycloid chain with Mn spins increases in proportion to the vector spin chirality (Si x Sj ) of the Mn ions. This relationship strongly indicates that the charge transfer between O and Mn ions is driven by the SC mechanism, which leads to the ferroelectricity accompanying O spin polarization.