ShantanuT01/DACTYL-Pretraining huggingface dataset:
The z=4.591 quasar PC 1415+3408 exhibits very strong associated metal-line absorption from the N V (1238,1242), Si IV (1393,1402), and C IV (1548,1550) doublets spanning the velocity interval -1700 < v < 0 km/s. Also present, are detached absorption troughs in N V and C IV spanning -5000 < v < -3000 km/s; this is characteristic of broad absorption line (BAL) quasars, but the small overall velocity spread suggests that PC 1415+3408 be classified as a Mini-BAL quasar. The N V doublet is consistent with black saturation over the velocity interval -1200 to -500 km/s; black N V absorption is extraordinary in all classes of quasars at all redshifts. Over this velocity interval, the C IV doublet is severely blended, but also consistent with black saturation. The material over this range of velocity appears to fully occult the continuum source, the broad emission line region, and any material that could give rise to scattered light. In view of a unified scenario for BAL and Mini-BAL absorption, these facts imply that the quasar is being viewed along a preferred direction. On the other hand, the black Mini-BALs in PC 1415+3408 could be explained if the BAL flow has an unusual geometry compared to the population of BAL quasars, and/or the spatial extent of a scattering region is small at the lower velocities (-1700 < v < 0 km/s).
This survey may be seen as an introduction to the use of toric and tropical geometry in the analysis of plane curve singularities, which are germs $(C,o)$ of complex analytic curves contained in a smooth complex analytic surface $S$. The embedded topological type of such a pair $(S, C)$ is usually defined to be that of the oriented link obtained by intersecting $C$ with a sufficiently small oriented Euclidean sphere centered at the point $o$, defined once a system of local coordinates $(x,y)$ was chosen on the germ $(S,o)$. If one works more generally over an arbitrary algebraically closed field of characteristic zero, one speaks instead of the combinatorial type of $(S, C)$. One may define it by looking either at the Newton-Puiseux series associated to $C$ relative to a generic local coordinate system $(x,y)$, or at the set of infinitely near points which have to be blown up in order to get the minimal embedded resolution of the germ $(C,o)$ or, thirdly, at the preimage of this germ by the resolution. Each point of view leads to a different encoding of the combinatorial type by a decorated tree: an Eggers-Wall tree, an Enriques diagram, or a weighted dual graph. The three trees contain the same information, which in the complex setting is equivalent to the knowledge of the embedded topological type. There are known algorithms for transforming one tree into another. In this paper we explain how a special type of two-dimensional simplicial complex called a lotus allows to think geometrically about the relations between the three types of trees. Namely, all of them embed in a natural lotus, their numerical decorations appearing as invariants of it. This lotus is constructed from the finite set of Newton polygons created during any process of resolution of $(C,o)$ by successive toric modifications.
Given a hilbertian field $k$ of characteristic zero and a finite Galois extension $E/k(T)$ with group $G$ such that $E/k$ is regular, we produce some specializations of $E/k(T)$ at points $t_0 \in \mathbb{P}^1(k)$ which have the same Galois group but also specified inertia groups at finitely many given primes. This result has two main applications. Firstly we conjoin it with previous works to obtain Galois extensions of $\mathbb{Q}$ of various finite groups with specified local behavior - ramified or unramified - at finitely many given primes. Secondly, in the case $k$ is a number field, we provide criteria for the extension $E/k(T)$ to satisfy this property: at least one Galois extension $F/k$ of group $G$ is not a specialization of $E/k(T)$.
We compute the energy per particle of infinite symmetric nuclear matter from chiral N3LO (next-to-next-to-next-to-leading order) two-body potentials plus N2LO three-body forces. The low-energy constants of the chiral three-nucleon force that cannot be constrained by two-body observables are fitted to reproduce the triton binding energy and the 3H-3He Gamow-Teller transition matrix element. In this way, the saturation properties of nuclear matter are reproduced in a parameter-free approach. The equation of state is computed up to third order in many-body perturbation theory, with special emphasis on the role of the third-order particle-hole diagram. The dependence of these results on the cutoff scale and regulator function is studied. We find that the inclusion of three-nucleon forces consistent with the applied two-nucleon interaction leads to a reduced dependence on the choice of the regulator only for lower values of the cutoff.
Polymers in confined spaces lose conformational entropy. This induces a net repulsive entropic force on the walls of the confining space. A model for this phenomenon is a lattice walk between confining walls, and in this paper a model of an adsorbing partially directed walk is used. The walk is placed in a half square lattice $L^2_+$ with boundary $\partial L^2_+$, and confined between two vertical parallel walls, which are vertical lines in the lattice, a distance $w$ apart. The free energy of the walk is determined, as a function of $w$, for walks with endpoints in the confining walls and adsorbing in $\partial L^2_+$. This gives the entropic force on the confining walls as a function of $w$. It is shown that there are zero force points in this model and the locations of these points are determined, in some cases exactly, and in other cases asymptotically.
The covariant form of the field equations for two--dimensional $R^2$--gravity with torsion as well as its Hamiltonian formulation are shown to suggest the choice of the light--cone gauge. Further a one--to--one correspondence between the Hamiltonian gauge symmetries and the diffeomorphisms and local Lorentz transformations is established, thus proving that there are no hidden local symmetries responsible for the complete integrability of the model. Finally the constraint algebra is shown to have no quantum anomalies so that Dirac's quantization should be applicable.
Recent applications of the M3Y-type semi-realistic interaction to the nuclear mean-field approaches are presented: (i) Prediction of magic numbers and (ii) isotope shifts of nuclei with magic proton numbers. The results exemplify that realistic interaction, which is derived from the base $2N$ and $3N$ interaction, furnish a new theoretical instrument for advancing nuclear mean-field approaches.
Shortcuts to adiabaticity is a general method for speeding up adiabatic quantum protocols, and has many potential applications in quantum information processing. Unfortunately, analytically constructing shortcuts to adiabaticity for systems having complex interactions and more than a few levels is a challenging task. This is usually overcome by assuming an idealized Hamiltonian [e.g., only a limited subset of energy levels are retained, and the rotating-wave approximation (RWA) is made]. Here we develop an $analytic$ approach that allows one to go beyond these limitations. Our method is general and results in analytically derived pulse shapes that correct both nonadiabatic errors as well as non-RWA errors. We also show that our approach can yield pulses requiring a smaller driving power than conventional nonadiabatic protocols. We show in detail how our ideas can be used to analytically design high-fidelity single-qubit "tripod" gates in a realistic superconducting fluxonium qubit.
Let F be a finite extension of Qp and G be GL(2,F). When V is the tensor product of three admissible, irreducible, finite dimensional representations of G, the space of G-invariant linear forms has dimension at most one. When a non zero linear form exists, one wants to find an element of V which is not in its kernel: this is a test vector. Gross and Prasad found explicit test vectors for some triple of representations. In this paper, others are found, and they almost complete the case when the conductor of each representation is at most 1.
In this paper, we study the amplification of weak frequency dependent signals in the CMB sky due to their cross correlation to intrinsic anisotropies. In particular, we center our attention on mechanisms generating some weak signal, of peculiar spectral behaviour, such as resonant scattering in ionic, atomic or molecular lines, thermal SZ effect or extragalactic foreground emissions, whose typical amplitude (denoted by $\epsilon$) is sufficiently smaller than the intrinsic CMB fluctuations. We find that all these effects involve either the autocorrelation of anisotropies generated during recombination ($z_{rec}$) or the cross-correlation of those anisotropies with fluctuations arising at some later redshift $z_i$. The degree of this correlation can be computed under the assumption that density fluctuations were generated as standard inflationary models dictate and that they evolved in time according to linear theory. In case that the weak signal is frequency dependent, we show that, by substracting power spectra at different frequencies, it is possible to avoid the limit associated to Cosmic Variance and unveil weaker terms linear in $\epsilon$. We find that the correlation term shows a different spectral dependence than the squared ($\propto \epsilon^2$) term considered usually, making its extraction particularly straightforward for the thermal SZ effect. Furthermore, we find that in most cases the correlation terms are particularly relevant at low multipoles and must be taken into account when characterising the power spectrum associated to weak signals in the large angular scales.
A quantum critical point arises at a continuous transformation between distinct phases of matter at zero temperature. Studies in antiferromagnetic heavy fermion materials have revealed that quantum criticality has several classes, with an unconventional type that involves a critical destruction of the Kondo entanglement. In order to understand such varieties, it is important to extend the materials basis beyond the usual setting of intermetallic compounds. Here we show that a nickel oxypnictide, CeNiAsO, displays a heavy-fermion antiferromagnetic quantum critical point as a function of either pressure or P/As substitution. At the quantum critical point, non-Fermi liquid behavior appears, which is accompanied by a divergent effective carrier mass. Across the quantum critical point, the low-temperature Hall coefficient undergoes a rapid sign change, suggesting a sudden jump of the Fermi surface and a destruction of the Kondo effect. Our results imply that the enormous materials basis for the oxypnictides, which has been so crucial to the search for high temperature superconductivity, will also play a vital role in the effort to establish the universality classes of quantum criticality in strongly correlated electron systems.
In this paper, we consider the problem of mean first-passage time (MFPT) in quantum mechanics; the MFPT is the average time of the transition from a given initial state, passing through some intermediate states, to a given final state for the first time. We apply the method developed in statistical mechanics for calculating the MFPT of random walks to calculate the MFPT of a transition process. As applications, we (1) calculate the MFPT for multiple-state systems, (2) discuss transition processes occurring in an environment background, (3) consider a roundabout transition in a hydrogen atom, and (4) apply the approach to laser theory.
We study the capture rate in the doublet hyperfine initial state for the muon capture reaction $\mu^- + \,^2{\rm H} \rightarrow \nu_\mu + n + n$ ($\Gamma^D$) and the total capture rate for the reaction $ \mu^- + \,^3{\rm He} \rightarrow \nu_\mu + \,^3{\rm H}$ ($\Gamma_0$). We investigate whether $\Gamma^D$ and $\Gamma_0$ could be sensitive to the $nn$ $S$-wave scattering length ($a_{nn}$). To this aim, we consider nuclear potentials and weak currents derived within $\chi$EFT. We employ the N3LO chiral potential with cutoff $\Lambda$=500 MeV, but the low-energy constant (LEC) determining $a_{nn}$ is varied so as to obtain $a_{nn}$=-18.95 (the present empirical value), -16.0, -22.0, and +18.22 fm. The last value leads to a $nn$ bound state with a binding energy of 139 keV. The LECs $c_D$ and $c_E$, present in the three-nucleon potential and axial-vector current, are fitted to reproduce the $A=3$ binding energies and the triton Gamow-Teller matrix element. The capture rate $\Gamma^D$ is found to be 399(3) s$^{-1}$ for $a_{nn}$=-18.95 and -16.0 fm; and 400(3) s$^{-1}$ for $a_{nn}$=-22.0 fm. For $a_{nn}$=+18.22 fm, we obtain 275(3) s$^{-1}$ (135(3) s$^{-1}$), when the final $nn$ system is unbound (bound). The rate $\Gamma_0$ is found to be 1494(15), 1491(16), 1488(18), and 1475(16) s$^{-1}$ for $a_{nn}$=-18.95, -16.0, -22.0, and +18.22 fm, respectively. The theoretical uncertainties are due to the fitting procedure and radiative corrections. Our results seem to exclude the possibility of constraining a negative $a_{nn}$ with an uncertainty of less than $\sim \pm$ 3 fm through an accurate determination of the muon capture rates, but the uncertainty on the present empirical value will not complicate the interpretation of the (forth-coming) experimental results for $\Gamma^D$. Finally, a comparison with the already available experimental data discourages the possibility of a bound $nn$ state.
Integrate and fire oscillators are widely used to model the generation of action potentials in neurons. In this paper, we discuss small noise asymptotic results for a class of stochastic integrate and fire oscillators (SIFs) in which the buildup of membrane potential in the neuron is governed by a Gaussian diffusion process. To analyze this model, we study the asymptotic behavior of the spectrum of the firing phase transition operator. We begin by proving strong versions of a law of large numbers and central limit theorem for the first passage-time of the underlying diffusion process across a general time dependent boundary. Using these results, we obtain asymptotic approximations of the transition operator's eigenvalues. We also discuss connections between our results and earlier numerical investigations of SIFs.
In this paper, structural and electronic properties and stability of (10, 0) born nitride nanotube (BNNT) are considered within density functional theory by doping group IV elements of the periodic table. The HOMO-LUMO gap has been strongly modified and treated a dual manner by choosing B or N sites for dopant atoms. Formation energy calculation shows that B site doping is more stable than N site doping. Results also show that all dopants turn the pristine BNNT into a p-type semiconductor except for carbon-doped BNNT at B site.
We study theoretically layered spin systems where long-range dipolar interactions play a relevant role. By choosing a specific sample shape, we are able to reduce the complex Hamiltonian of the system to that of a much simpler coupled rotator model with short-range and mean-field interactions. This latter model has been studied in the past because of its interesting dynamical and statistical properties related to exotic features of long-range interactions. It is suggested that experiments could be conducted such that within a specific temperature range the presence of long-range interactions crucially affect the behavior of the system.
The CHANG-ES (Continuum Halos in Nearby Galaxies) survey of 35 nearby edge-on galaxies is revealing new and sometimes unexpected and startling results in their radio continuum emission. The observations were in wide bandwidths centered at 1.6 and 6.0 GHz. Unique to this survey is full polarization data showing magnetic field structures in unprecedented detail, resolution and sensitivity for such a large sample. A wide range of new results are reported here, some never before seen in any galaxy. We see circular polarization and variability in active galactic nuclei (AGNs), in-disk discrete features, disk-halo structures sometimes only seen in polarization, and broad-scale halos with reversing magnetic fields, among others. This paper summarizes some of the CHANG-ES results seen thus far. Released images can be found at https://www.queensu.ca/changes.
We study the static and dynamical properties of a long-range Kitaev chain, i.e., a $p$-wave superconducting chain in which the superconducting pairing decays algebraically as $1/l^{\alpha}$, where $l$ is the distance between the two sites and $\alpha$ is a positive constant. Considering very large system sizes, we show that when $\alpha >1$, the system is topologically equivalent to the short-range Kitaev chain with massless Majorana modes at the ends of the system; on the contrary, for $\alpha <1$, there exist symmetry protected massive Dirac end modes. We further study the dynamical phase boundary of the model when periodic $\delta$-function kicks are applied to the chemical potential; we specially focus on the case $\alpha >1$ and analyze the corresponding Floquet quasienergies. Interestingly, we find that new topologically protected massless end modes are generated at the quasienergy $\pi/T$ (where $T$ is the time period of driving) in addition to the end modes at zero energies which exist in the static case. By varying the frequency of kicking, we can produce topological phase transitions between different dynamical phases. Finally, we propose some bulk topological invariants which correctly predict the number of massless end modes at quasienergies equal to 0 and $\pi/T$ for a periodically kicked system with $\alpha > 1$.
One of the main challenges of social interaction in virtual reality settings is that head-mounted displays occlude a large portion of the face, blocking facial expressions and thereby restricting social engagement cues among users. Hence, auxiliary means of sensing and conveying these expressions are needed. We present an algorithm to automatically infer expressions by analyzing only a partially occluded face while the user is engaged in a virtual reality experience. Specifically, we show that images of the user's eyes captured from an IR gaze-tracking camera within a VR headset are sufficient to infer a select subset of facial expressions without the use of any fixed external camera. Using these inferences, we can generate dynamic avatars in real-time which function as an expressive surrogate for the user. We propose a novel data collection pipeline as well as a novel approach for increasing CNN accuracy via personalization. Our results show a mean accuracy of 74% ($F1$ of 0.73) among 5 `emotive' expressions and a mean accuracy of 70% ($F1$ of 0.68) among 10 distinct facial action units, outperforming human raters.
For every polynomial f of degree n with no double roots, there is an associated family C(f) of harmonic algebraic curves, fibred over the circle, with at most n-1 singular fibres. We study the combinatorial topology of C(f) in the generic case when there are exactly n-1 singular fibres. In this case, the topology of C(f) is determined by the data of an n-tuple of noncrossing matchings on the set {0,1,...,2n-1} with certain extra properties. We prove that there are 2(2n)^{n-2} such n-tuples, and that all of them arise from the topology of C(f) for some polynomial f.
We investigate how well CLIP understands texture in natural images described by natural language. To this end, we analyze CLIP's ability to: (1) perform zero-shot learning on various texture and material classification datasets; (2) represent compositional properties of texture such as red dots or yellow stripes on the Describable Texture in Detail(DTDD) dataset; and (3) aid fine-grained categorization of birds in photographs described by color and texture of their body parts.
The latest measurement of the K_S to gamma gamma branching ratio clearly shows an enhancement over the current theoretical prediction. As in other K and B meson decays, this invites to consider the possibility of the contribution of new physics. We study a particular form of the latter, which may be referred to as manifest mirror symmetry. The experimental data are described using previously determined values for the mixing angles of the admixtures of mirror matter in ordinary hadrons and by assuming that for pi^0, eta, eta', the mirror decay amplitudes have the same magnitudes as their ordinary counterparts.
We look for positive solutions to the nonlinear Schrodinger equation with a potential, under the hypothesis of zero mass on the nonlinearity, in a particular situation. Existence and multiplicity results are provided.
Systems that exhibit topologically protected edge states are interesting both from a fundamental point of view as well as for potential applications, the latter because of the absence of back-scattering and robustness to perturbations. It is desirable to be able to control and manipulate such edge states. Here, we show that artificial square ices can incorporate both features: an interfacial Dzyaloshinksii-Moriya gives rise to topologically non-trivial magnon bands, and the equilibrium state of the spin ice is reconfigurable with different configurations having different magnon dispersions and topology. The topology is found to develop as odd-symmetry bulk and edge magnon bands approach each other, so that constructive band inversion occurs in reciprocal space. Our results show that topologically protected bands are supported in square spin ices.
The aim of this thesis is to derive new gradient estimates for parabolic equations. The gradient estimates found are independent of the regularity of the initial data. This allows us to prove the existence of solutions to problems that have non-smooth, continuous initial data. We include existence proofs for problems with both Neumann and Dirichlet boundary data. The class of equations studied is modelled on mean curvature flow for graphs. It includes anisotropic mean curvature flow, and other operators that have no uniform non-degeneracy bound. We arrive at similar estimates by three different paths: a 'double coordinate' approach, an approach examining the intersections of a solution and a given barrier, and a classical geometric approach.
We present a galaxy formation model to understand the evolution of stellar mass (M*) - UV luminosity relations, stellar mass functions and specific star formation rate (sSFR) of Lyman Break Galaxies (LBGs) along with their UV luminosity functions in the redshift range 3 < z < 8. Our models assume a physically motivated form for star formation in galaxies and model parameters are calibrated by fitting the observed UV luminosity functions (LFs) of LBGs. We find the fraction of baryons that gets converted into stars remains nearly constant for z < 4 but shows an increase for z < 4. However, the rate of converting baryons into stars does not evolve significantly in the redshift range 3 < z < 8. Our model further successfully explains the M* - UV luminosity (M_AB) correlations of LBGs. While our model predictions of stellar mass functions compare well with the inferred data from observations at the low mass end, we need to invoke the Eddington bias to fit the high mass end. At any given redshift, we find the sSFR to be constant over the stellar mass range 5 \times 10^8 -5 \times 10^9 M_\odot and the redshift evolution of sSFR is well approximated by a form (1+z)^2.4 for 3 < z < 8 which is consistent with observations. Thus we find that dark matter halo build up in the LCDM model is sufficient to explain the evolution of UV LFs of LBGs along with their M* - M_AB relations, the stellar mass functions and the sSFR for 3 < z < 8.