ShantanuT01/DACTYL-Pretraining huggingface dataset:
A frequency square is a square matrix in which each row and column is a permutation of the same multiset of symbols. A frequency square is of type $(n;\lambda)$ if it contains $n/\lambda$ symbols, each of which occurs $\lambda$ times per row and $\lambda$ times per column. In the case when $\lambda=n/2$ we refer to the frequency square as binary. A set of $k$-MOFS$(n;\lambda)$ is a set of $k$ frequency squares of type $(n;\lambda)$ such that when any two of the frequency squares are superimposed, each possible ordered pair occurs equally often.   A set of $k$-maxMOFS$(n;\lambda)$ is a set of $k$-MOFS$(n;\lambda)$ that is not contained in any set of $(k+1)$-MOFS$(n;\lambda)$. For even $n$, let $\mu(n)$ be the smallest $k$ such that there exists a set of $k$-maxMOFS$(n;n/2)$. It was shown in [Electron. J. Combin. 27(3) (2020), P3.7] that $\mu(n)=1$ if $n/2$ is odd and $\mu(n)>1$ if $n/2$ is even. Extending this result, we show that if $n/2$ is even, then $\mu(n)>2$. Also, we show that whenever $n$ is divisible by a particular function of $k$, there does not exist a set of $k'$-maxMOFS$(n;n/2)$ for any $k'\le k$. In particular, this means that $\limsup \mu(n)$ is unbounded. Nevertheless we can construct infinite families of maximal binary MOFS of fixed cardinality. More generally, let $q=p^u$ be a prime power and let $p^v$ be the highest power of $p$ that divides $n$. If $0\le v-uh<u/2$ for $h\ge1$ then we show that there exists a set of $(q^h-1)^2/(q-1)$-maxMOFS$(n;n/q)$.
We propose a fully quantum-mechanical method of treating four-body nuclear breakup processes in scattering of a projectile consisting of three constituents, by extending the continuum-discretized coupled-channels method. The three-body continuum states of the projectile are discretized by diagonalizing the internal   Hamiltonian of the projectile with the Gaussian basis functions. For   $^6$He+$^{12}$C scattering at 18 and 229.8 MeV, the validity of the method is tested by convergence of the elastic and breakup cross sections with respect to increasing the number of the basis functions. Effects of the four-body breakup and the Borromean structure of $^6$He on the elastic and total reaction cross sections are discussed.
Ab initio density functional theory calculations are carried out to predict the electronic properties and relative stability of gallium sulfide nanoribbons (Ga2S2-NRs) with either zigzag- or armchair-terminated edges. It is found that the electronic properties of the nanoribbons are very sensitive to the edge structure. The zigzag nanoribbons (Ga2S2-ZNRs) are metallic with spin-polarized edge states regardless of the H-passivation,whereas the bare armchair ones (Ga2S2-ANRs) are semiconducting with an indirect band gap. This band gap exhibits an oscillation behavior as the width increases and finally converges to a constant value. Similar behavior is also found in H-saturated Ga2S2-ANRs, although the band gap converges to a larger value. The relative stabilities of the bare ANRs and ZNRs are investigated by calculating their binding energies. It is found that for a similar width the ANRs are more stable than the ZNRs, and both are more stable than some Ga2S2 nanocluters with stable configurations.
We propose a novel approach for solving the scattering of light onto a two-level atom coupled to a one-dimensional waveguide. We first express the physical quantity of interest in terms of Feynman diagrams and treat the atom as a non-saturable linear beamsplitter. By using the atomic response to our advantage, a relevant substitution is then made that captures the nonlinearity of the atom, and the final result is obtained in terms of simple integrals over the initial incoming wavepackets. The procedure is not limited to post-scattering quantities and allows for instance to derive the atomic excitation during the scattering event.
We show that, over a field of characteristic 0, a normal, projective variety of dimension at least 4 is uniquely determined by its underlying topological space. The proof builds on previous work of Lieblich and Olsson. Version 2: many small changes and new references.
The CARMENES survey is searching for Earth-like planets orbiting M dwarfs using the radial velocity method. Studying the stellar activity of the target stars is important to avoid false planet detections and to improve our understanding of the atmospheres of late-type stars. In this work we present measurements of activity indicators at visible and near-infrared wavelengths for 331 M dwarfs observed with CARMENES. Our aim is to identify the activity indicators that are most sensitive and easiest to measure, and the correlations among these indicators. We also wish to characterise their variability. Using a spectral subtraction technique, we measured pseudo-equivalent widths of the He I D3, H$\alpha$, He I $\lambda$10833 {\AA}, and Pa$\beta$ lines, the Na I D doublet, and the Ca II infrared triplet, which have a chromospheric component in active M dwarfs. In addition, we measured an index of the strength of two TiO and two VO bands, which are formed in the photosphere. We also searched for periodicities in these activity indicators for all sample stars using generalised Lomb-Scargle periodograms. We find that the most slowly rotating stars of each spectral subtype have the strongest H$\alpha$ absorption. H$\alpha$ is correlated most strongly with He I D3, whereas Na I D and the Ca II infrared triplet are also correlated with H$\alpha$. He I $\lambda$10833 {\AA} and Pa$\beta$ show no clear correlations with the other indicators. The TiO bands show an activity effect that does not appear in the VO bands. We find that the relative variations of H$\alpha$ and He I D3 are smaller for stars with higher activity levels, while this anti-correlation is weaker for Na I D and the Ca II infrared triplet, and is absent for He I $\lambda$10833 {\AA} and Pa$\beta$. Periodic variation with the rotation period most commonly appears in the TiO bands, H$\alpha$, and in the Ca II infrared triplet.
A self-consistent calculation with variation after parity projection is proposed to study both ground and excited states of light nuclei. This procedure provides description of the ground state incorporating some correlation effects, and self-consistent solutions for the excited states of negative parity. For flexible description of nuclear shapes, single particle orbitals are represented on a uniform grid in the three-dimensional Cartesian coordinates. The angular momentum projection is performed after variation to calculate rotational spectra. To demonstrate the usefulness of the method, results are shown for two N=Z nuclei, 20Ne and 12C, for which clustering correlations are known to be important. In the 20Ne nucleus, both cluster-like and shell-model-like states are described simultaneously in the present framework. For 12C nucleus, the appearance of three-alpha clustering correlation in the ground state is investigated in relation to the strength of the two-body spin-orbit interaction.
The cross section for semi-inclusive deep inelastic charged current neutrino scattering on hydrogen and deuterium in which a slow proton is observed in coincidence with the muon is computed as a function of Bjorken x and light-cone momentum of the detected proton. In the Impulse Approximation contributions from hadronization and (in case of the deuteron) the emission of a spectator nucleon are considered. In addition the probability for rescattering is computed. The results are compared to a recent analysis of the data from the WA25 (BEBC) experiment at CERN. (KVI-1024)
We study magnetic vortex-like solutions lying on the spherical surface. The simplest cylindrically symmetric vortex presents two cores (instead of one, like in open surfaces) with same charge, so repealing each other. However, the net vorticity is computed to vanish in accordance with Gauss theorem. We also address the problem of a flat plane in which a conical, a pseudospherical and a hemispherical segments were incorporated. In this case, if we allow the vortex to move without appreciable deformation in this support, then it is attracted by the conical apex and by the pseudosphere as well, while it is repealed by the hemisphere. This suggests that such surfaces could be viewed as pinning and depinning geometries for those excitations. Spherical harmonics coreless solutions are discussed within some details.
Context. Recent observations of unexpected structures in the Galactic Cosmic Ray (GCR) spectrum and composition, as well as growing evidence for episodes of intense dynamical activity in the inner regions of the Galaxy, call for an evaluation of the high-energy particle acceleration associated with such activity and its potential impact on the global GCR phenomenology.   Aims. We investigate whether particles accelerated during high-power episodes around the Galactic center can account for a significant fraction of the observed GCRs, or conversely what constraints can be derived regarding their Galactic transport if their contributions are negligible.   Methods. We address these questions by studying the contribution of a continuous source of energetic particles at the Galactic center to the local GCRs. Particle transport in the Galaxy is described with a two-zone analytical model. We solve for the contribution of a Galactic Center Cosmic-Ray (GCCR) source using Green functions and Bessel expansion, and discuss the required injection power for these GCCRs to influence the global GCR phenomenology at Earth.   Results. We find that, with standard parameters for particle propagation in the galactic disk and halo, the GCCRs can make a significant or even dominant contribution to the total CR flux observed at Earth. Depending on the parameters, such a source can account for both the observed proton flux and B-to-C ratio (in the case of a Kraichnan-like scaling of the diffusion coefficient), or potentially produce spectral and composition features.   Conclusions. Our results show that the contribution of GCCRs cannot be neglected a priori, and that they can influence the global GCR phenomenology significantly, thereby calling for a reassessement of the standard inferences from a scenario where GCRs are entirely dominated by a single type of sources distributed throughout the Galactic disk.
The ratio of shear viscosity to entropy density, $\eta/s$, is computed in various holographic geometries that break translation invariance (but are isotropic). The shear viscosity does not have a hydrodynamic interpretation in such backgrounds, but does quantify the rate of entropy production due to a strain. Fluctuations of the metric components $\delta g_{xy}$ are massive about these backgrounds, leading to $\eta/s < 1/(4\pi)$ at all finite temperatures (even in Einstein gravity). As the temperature is taken to zero, different behaviors are possible. If translation symmetry breaking is irrelevant in the far IR, then $\eta/s$ tends to a constant at $T=0$. This constant can be parametrically small. If the translation symmetry is broken in the far IR (which nonetheless develops emergent scale invariance), then $\eta/s \sim T^{2 \nu}$ as $T \to 0$, with $\nu \leq 1$ in all cases we have considered. While these results violate simple bounds on $\eta/s$, we note that they are consistent with a possible bound on the rate of entropy production due to strain.
Increasing shape-bias in deep neural networks has been shown to improve robustness to common corruptions and noise. In this paper we analyze the adversarial robustness of texture and shape-biased models to Universal Adversarial Perturbations (UAPs). We use UAPs to evaluate the robustness of DNN models with varying degrees of shape-based training. We find that shape-biased models do not markedly improve adversarial robustness, and we show that ensembles of texture and shape-biased models can improve universal adversarial robustness while maintaining strong performance.
The measurement-device-independent quantum key distribution (MDI-QKD) protocol plays an important role in quantum communications due to its high level of security and practicability. It can be immune to all side-channel attacks directed on the detecting devices. However, the protocol still contains strict requirements during state preparation in most existing MDI-QKD schemes, e.g., perfect state preparation or perfectly characterized sources, which are very hard to realize in practice. In this letter, we investigate uncharacterized MDI-QKD by utilizing a three-state method, greatly reducing the finite-size effect. The only requirement for state preparation is that the state are prepared in a bidimensional Hilbert space. Furthermore, a proof-of-principle demonstration over a 170 km transmission distance is achieved, representing the longest transmission distance under the same security level on record.
Investigating the rigidly rotating disc of dust with constant specific charge, we find that it leads to an extreme Kerr-Newman black hole in the ultra-relativistic limit. A necessary and sufficient condition for a black hole limit is, that the electric potential in the co-rotating frame is constant on the disc. In that case certain other relations follow. These relations are reviewed with a highly accurate post-Newtonian expansion.   Remarkably it is possible to survey the leading order behaviour close to the black hole limit with the post-Newtonian expansion. We find that the disc solution close to that limit can be approximated very well by a "hyper\-extreme" Kerr-Newman solution with the same gravitational mass, angular momentum and charge.
Human emotions involve basic and compound facial expressions. However, current research on facial expression recognition (FER) mainly focuses on basic expressions, and thus fails to address the diversity of human emotions in practical scenarios. Meanwhile, existing work on compound FER relies heavily on abundant labeled compound expression training data, which are often laboriously collected under the professional instruction of psychology. In this paper, we study compound FER in the cross-domain few-shot learning setting, where only a few images of novel classes from the target domain are required as a reference. In particular, we aim to identify unseen compound expressions with the model trained on easily accessible basic expression datasets. To alleviate the problem of limited base classes in our FER task, we propose a novel Emotion Guided Similarity Network (EGS-Net), consisting of an emotion branch and a similarity branch, based on a two-stage learning framework. Specifically, in the first stage, the similarity branch is jointly trained with the emotion branch in a multi-task fashion. With the regularization of the emotion branch, we prevent the similarity branch from overfitting to sampled base classes that are highly overlapped across different episodes. In the second stage, the emotion branch and the similarity branch play a "two-student game" to alternately learn from each other, thereby further improving the inference ability of the similarity branch on unseen compound expressions. Experimental results on both in-the-lab and in-the-wild compound expression datasets demonstrate the superiority of our proposed method against several state-of-the-art methods.
We show that in certain theories with topologically trivial quotient space of spontaneously broken gauge symmetry there can exist topologically stable strings that carry nonabelian gauge flux. These objects result from the ``accidental'' global degeneracy of the vacuum which makes it topologically nontrivial.   In particular, some models contain the semiglobal analog of the Alice strings.
The Catalan numbers count many classes of combinatorial objects. The most emblematic such objects are probably the Dyck walks and the binary trees, and, whenever another class of combinatorial objects is counted by the Catalan numbers, it is natural to search for an explicit bijection between the latter objects and one of the former objects. In most cases, such a bijection happens to be relatively simple but it might sometimes be more intricate.   In this work, we focus on so-called \emph{basketball walks}, which are integer-valued walks with step-set $\{-2,-1,+1,+2\}$. The presence of $-2$ as an allowed step makes it impossible to use the classical {\L}ukasiewicz encoding of trees by integer-valued walks, and thus a different strategy is needed. We give an explicit bijection that maps, for each $n\ge 2$, $n$-step basketball walks from $0$ to $0$ that visit $1$ and are positive except at their extremities to $n$-leaf binary trees. Moreover, we can partition the steps of a walk into $\pm 1$-steps, odd $+2$-steps or even $-2$-steps, and odd $-2$-steps or even $+2$-steps, and these three types of steps are mapped through our bijection to double leaves, left leaves, and right leaves of the corresponding tree.   We also prove that basketball walks from $0$ to $1$ that are positive except at the origin are in bijection with increasing unary-binary trees with associated permutation avoiding $213$. We furthermore give the refined generating function of these objects with an extra variable accounting for the unary nodes.
Advanced LIGO's present baseline design uses arm cavities with Gaussian light beams supported by spherical mirrors. Because Gaussian beams have large intensity gradients in regions of high intensity, they average poorly over fluctuating bumps and valleys on the mirror surfaces, caused by random thermal fluctuations (thermoelastic noise). Flat-topped light beams (mesa beams) are being considered as an alternative because they average over the thermoelastic fluctuations much more effectively. However, the proposed mesa beams are supported by nearly flat mirrors, which experience a very serious tilt instability. In this paper we propose an alternative configuration in which mesa-shaped beams are supported by nearly concentric spheres, which experience only a weak tilt instability. The tilt instability is analyzed for these mirrors in a companion paper by Savov and Vyatchanin. We also propose a one-parameter family of light beams and mirrors in which, as the parameter alpha varies continuously from 0 to pi, the beams and supporting mirrors get deformed continuously from the nearly flat-mirrored mesa configuration ("FM") at alpha=0, to the nearly concentric-mirrored mesa configuration ("CM") at alpha=pi. The FM and CM configurations at the endpoints are close to optically unstable, and as alpha moves away from 0 or pi, the optical stability improves.
Solid-state thermoelectric cooling is expected to be widely used in various cryogenic applications such as local cooling of superconducting devices. At present, however, thermoelectric cooling using p- and n-type Bi2Te3-based materials has been put to practical use only at room temperature. Recently, M4SiTe4 (M = Ta, Nb) has been found to show excellent n-type thermoelectric properties down to 50 K. This paper reports on the synthesis of high-performance p-type M4SiTe4 by Ti doping, which can be combined with n-type M4SiTe4 in a cooling device at low temperatures. The thermoelectric power factor of p-type M4SiTe4 reaches a maximum value of approximately 60 uW cm-1 K-2 at 210 K and exceeds the practical level in a wide temperature range of 130-270 K. A finite temperature drop by Peltier cooling was also achieved in a cooling device made of p- and n-type Ta4SiTe4 whisker crystals. These results clearly indicate that M4SiTe4 is promising to realize a practical thermoelectric cooler for use at low temperatures, which are not covered by Bi2Te3-based materials.
We have completed the one-loop renormalisation of the Next-to-Minimal Supersymmetric Standard Model (NMSSM) allowing for and comparing between different renormalisation schemes. A special attention is paid to on-shell schemes. We study a variety of these schemes based on alternative choices of the physical input parameters. In this paper we present our approach to the renormalisation of the NMSSM and report on our results for the neutralino-chargino and sfermion sectors. We will borrow some results from our study of the Higgs sector whose full discussion is left for a separate publication. We have implemented the set up for all the sectors of the NMSSM within \sloops, a code for the automatic computation of one-loop corrections initially developed for the standard model and the MSSM. Among the many applications that allows the code, we present here the one-loop corrections to neutralino masses and to partial widths of neutralinos and charginos into final states with one gauge boson. One-loop electroweak and QCD corrections to the partial widths of third generation sfermions into a fermion and a chargino or a neutralino are also computed.
Quintessential inflation refers to scenarios in which a single scalar field is used to describe inflation and late-time acceleration. This review is dedicated to the framework of quintessential inflation, with a focus on the building blocks of formalism. Consistent unification of inflation and late time acceleration using a single scalar field asks for a shallow field potential initially followed by steep behaviour thereafter and shallow again around the present epoch. The requirement of non-interference of scalar field with thermal history dictates steep nature of potential in the post-inflationary era, with a further restriction that late time physics be independent of initial conditions. We describe, in detail the scaling and asymptotic scaling solutions and the mechanism of exit from the scaling regime to late time acceleration. Review includes a fresh look at scaling solutions which are central to the theme of unification of inflation and late time acceleration. As for the exit mechanism, special attention is paid to the coupling of massive neutrino matter to the scalar field, which builds up dynamically and can give rise to late time acceleration. We present a detailed analytical treatment of scalar field dynamics in the presence of coupling. We briefly discuss the distinguished feature of quintessential inflation, namely, the blue spectrum of gravity waves produced during the transition from inflation to the kinetic regime.
An analysis of the elastic and one-neutron removal channel for the reaction 8Li+208Pb reaction at energies around the Coulomb barrier is presented. For the elastic scattering, an optical model analysis of the experimental data is performed. The observed 7Li is interpreted as the superposition of the one-neutron transfer reaction, 208Pb(8Li,7Li)209Pb, and the breakup reaction. The separate contribution of each one of these processes has been calculated within the DWBA formalism. The sum of both contributions explains adequately the experimental angular distribution of 7Li.
The T-odd leptons are the typical particles predicted by the littlest Higgs model with T-parity (LHT model) and the observation of these particles might be regarded as the direct evidence of the LHT model. In this paper, we investigate the production of a pair of T-odd leptons associated with a gauge boson $V$($\gamma$ or $Z$) at the international linear $e^{+}e^{-}$ collider (ILC). The numerical results show that the possible signals of the T-odd leptons may be detected in the future ILC experiments.