ShantanuT01/DACTYL-Pretraining huggingface dataset:
In classifying the ensemble of powerful extragalactic radio sources, considerable evidence has accumulated that radio galaxies and quasars are orientation-dependent manifestations of the same parent population: massive spheroidal galaxies containing correspondingly massive black holes. [...] In this study, we exploit the opportunity to eliminate the quasar glare by performing sensitive spectropolarimetry with the Keck II telescope of a sample of radio galaxies with redshifts around 2.5. [...] We show that dust-reflected quasar light generally dominates the restframe ultraviolet continuum of these sources and that a highly clumped scattering medium results in almost grey scattering of the active galactic nucleus photons. The observations, however, do not exclude a substantial star formation rate averaged over a Gyr of evolution. The sub-mm reradiation from the scattering dust is likely to represent only a small fraction (~10%) of the total far infrared luminosity. An analysis of the emission lines excited in the interstellar medium of the host galaxy by the hard quasar radiation field reveals evidence of a dramatic chemical evolution within the spheroid during this epoch. Secondary nitrogen production in intermediate mass stars produces a characteristic signature in the NV/CIV and NV/HeII line ratios which has been seen previously in the broad line region of quasars at similar redshifts. We find intriguing correlations between the strengths of the Ly alpha and NV emission lines and the degree of ultraviolet continuum polarization which may represent the dispersal of dust associated with the chemical enrichment of the spheroid.
In this work, trions in two-dimensional (2D) space are studied by variational method with trial wavefunctions being constructed by linear combinations of 2D slater-type orbitals (STOs). Via this method, trion energy levels and wavefunctions can be calculated efficiently with fairly good accuracy. We first apply this method to study trion energy levels in a 2D hydrogen-like system with respect to a wide range of mass ratios and screening lengths. We find that the ground-state trion is bound for the whole parameter range, and an excited-state trion with antisymmetric permutation of electrons with finite angular momentum is bound for large electron-hole mass ratios or long screening lengths. The binding energies of ground-state trions calculated by the present method agree well with those calculated by more sophisticated but computationally-demanding methods. We then calculate trion states in various monolayer transition metal dichalcogenides (TMDCs) by using this method with the inclusion of electron-hole exchange (EHX) interaction. For TMDCs, we found that the effect of EHX can be significant in determining the trion binding energy and the possible existence of stable excited-state trions.
We discuss the length $\vec{L}_{c,n}$ of the longest directed cycle in the sparse random digraph $D_{n,p},p=c/n$, $c$ constant. We show that for large $c$ there exists a function $\vec{f}(c)$ such that $\vec{L}_{c,n}/n\to \vec{f}(c)$ a.s. The function $\vec{f}(c)=1-\sum_{k=1}^\infty p_k(c)e^{-kc}$ where $p_k$ is a polynomial in $c$. We are only able to explicitly give the values $p_1,p_2$, although we could in principle compute any $p_k$.
Contrary to the longtime and widely conceived belief, we proved that the specific heat coefficient $\gamma$ --also called Sommerfeld coefficient -- of the interacting Fermion system is not renormalized by the wave-function renormalization factor $Z$ as far as the system remains a Fermi liquid state.
Using angle-resolved photoelectron spectroscopy and ab-initio GW calculations, we unambiguously show that the widely investigated three-dimensional topological insulator Bi2Se3 has a direct band gap at the Gamma point. Experimentally, this is shown by a three-dimensional band mapping in large fractions of the Brillouin zone. Theoretically, we demonstrate that the valence band maximum is located at the Brillouin center only if many-body effects are included in the calculation. Otherwise, it is found in a high-symmetry mirror plane away from the zone center.
Enhancement of omega and antiomega baryon production in Pb+Pb collisions at a c.m. energy of 17 A GeV can be explained by the formation of many small disoriented chiral condensate regions. This explanation implies that neutral and charged kaons as well as pions must exhibit novel isospin fluctuations. We compute the distribution of the fraction of neutral pions and kaons from such regions. We then propose robust statistical observables that can be used to extract the novel fluctuations from background contributions in pion and kaon measurements at RHIC and LHC.
Four propositions are considered concerning the relationship between the zeros of two combinations of the Riemann zeta function and the function itself. The first is the Riemann hypothesis, while the second relates to the zeros of a derivative function. It is proved that these are equivalent, and that, if the Riemann hypothesis holds, then all zeros of the zeta function on the critical line are simple. The Riemann hypothesis is then shown to imply the third proposition holds, this being a new necessary condition for the Riemann hypothesis. The third proposition is shown to be equivalent to the fourth, and either is shown to yield the result that the distribution of zeros on the critical line of $\zeta (s)$ is that given by the Riemann hypothesis. The results given are obtained from a combination of analytic arguments, experimental mathematical techniques and graphical reasoning.
The analytic properties of the eikonal and U-matrix unitarization schemes are examined. It is shown that the basic properties of these schemes are identical. Both can fill the full circle of unitarity, and both can lead to standard and non-standard asymptotic relations for the ratio of the elastic cross section to the total cross section. The relation between the phases of the unitarized amplitudes in each scheme is examined, and it is shown that demanding equivalence of the two schemes leads to a bound on the phase in the U-matrix scheme.
The rigid registration of two 3D point sets is a fundamental problem in computer vision. The current trend is to solve this problem globally using the BnB optimization framework. However, the existing global methods are slow for two main reasons: the computational complexity of BnB is exponential to the problem dimensionality (which is six for 3D rigid registration), and the bound evaluation used in BnB is inefficient. In this paper, we propose two techniques to address these problems. First, we introduce the idea of translation invariant vectors, which allows us to decompose the search of a 6D rigid transformation into a search of 3D rotation followed by a search of 3D translation, each of which is solved by a separate BnB algorithm. This transformation decomposition reduces the problem dimensionality of BnB algorithms and substantially improves its efficiency. Then, we propose a new data structure, named 3D Integral Volume, to accelerate the bound evaluation in both BnB algorithms. By combining these two techniques, we implement an efficient algorithm for rigid registration of 3D point sets. Extensive experiments on both synthetic and real data show that the proposed algorithm is three orders of magnitude faster than the existing state-of-the-art global methods.
For decades, a lot of work has been devoted to the problem of constructing a non-trivial quantum field theory in four-dimensional space time. This letter addresses the attempts to construct an algebraic quantum field theory in the framework of non-standard theories like hyperfunction or ultra-hyperfunction quantum field theory. For this purpose model theories of formally interacting neutral scalar fields are constructed and some of their characteristic properties like two-point functions are discussed. The formal self-couplings are obtained from local normally-ordered analytic redefinitions of the free scalar quantum field, mimicking a non-trivial structure of the resulting Lagrangians and equations of motion.
We discuss the expected properties of pair echo emission from gamma-ray bursts (GRBs) at high redshifts ($z \gtrsim 5$), their detectability, and the consequent implications for probing intergalactic magnetic fields (IGMFs) at early epochs. Pair echos comprise inverse Compton emission by secondary electron-positron pairs produced via interactions between primary gamma-rays from the GRB and low-energy photons of the diffuse intergalactic radiation, arriving with a time delay that depends on the nature of the intervening IGMFs. At sufficiently high $z$, the IGMFs are unlikely to have been significantly contaminated by astrophysical outflows, and the relevant intergalactic radiation may be dominated by the well-understood cosmic microwave background (CMB). Pair echoes from luminous GRBs at $z \sim 5-10$ may be detectable by future facilities such as the Cherenkov Telescope Array or the Advanced Gamma-ray Imaging System, as long as the GRB primary emission extends to multi-TeV energies, the comoving IGMFs at these redshifts are $B \sim 10^{-16}-10^{-15}~{\rm Gauss}$, and the non-CMB component of the diffuse intergalactic radiation is relatively low. Observations of pair echos from high-$z$ GRBs can provide a unique, in-situ probe of weak IGMFs during the epochs of early structure formation and cosmic reionization.
The question of what ontological message (if any) is encoded in the formalism of contemporary physics is, to say the least, controversial. The reasons for this state of affairs are psychological and neurobiological. The processes by which the visual world is constructed by our minds, predispose us towards concepts of space, time, and substance that are inconsistent with the spatiotemporal and substantial aspects of the quantum world. In the first part of this chapter, the latter are extracted from the quantum formalism. The nature of a world that is fundamentally and irreducibly described by a probability algorithm is determined. The neurobiological processes responsible for the mismatch between our "natural" concepts of space, time, and substance and the corresponding aspects of the quantum world are discussed in the second part. These natural concepts give rise to pseudoproblems that foil our attempts to make ontological sense of quantum mechanics. If certain psychologically motivated but physically unwarranted assumptions are discarded (in particular our dogged insistence on obtruding upon the quantum world the intrinsically and completely differentiated spatiotemporal background of classical physics), we are in a position to see why our fundamental physical theory is a probability algorithm, and to solve the remaining interpretational problems.
The availability of large magnetic fields at international facilities and of simulated magnetic fields that can reach the flux-quantum-per-unit-area level in cold atoms, calls for systematic studies of orbital effects of the magnetic field on the self-energy of interacting systems. Here we demonstrate theoretically that orbital effects of magnetic fields can be treated within single-site dynamical mean-field theory with a translationally invariant quantum impurity problem. As an example, we study the one-band Hubbard model on the square lattice using iterated perturbation theory as an impurity solver. We recover the expected quantum oscillations in the scattering rate and we show that the magnetic fields allow the interaction-induced effective mass to be measured through the single-particle density of states accessible in tunneling experiments. The orbital effect of magnetic fields on scattering becomes particularly important in the Hofstadter butterfly regime.
Junctions play an important role in the characterization of local geometric structures in images, the detection of which is a longstanding and challenging task. Existing junction detectors usually focus on identifying the junction locations and the orientations of the junction branches while ignoring their scales; however, these scales also contain rich geometric information. This paper presents a novel approach to junction detection and characterization that exploits the locally anisotropic geometries of a junction and estimates the scales of these geometries using an \emph{a contrario} model. The output junctions have anisotropic scales --- i.e., each branch of a junction is associated with an independent scale parameter --- and are thus termed anisotropic-scale junctions (ASJs). We then apply the newly detected ASJs for the matching of indoor images, in which there may be dramatic changes in viewpoint and the detected local visual features, e.g., key-points, are usually insufficiently distinctive. We propose to use the anisotropic geometries of our junctions to improve the matching precision for indoor images. Matching results obtained on sets of indoor images demonstrate that our approach achieves state-of-the-art performance in indoor image matching.
Content-based image retrieval (CBIR) of medical images is a crucial task that can contribute to a more reliable diagnosis if applied to big data. Recent advances in feature extraction and classification have enormously improved CBIR results for digital images. However, considering the increasing accessibility of big data in medical imaging, we are still in need of reducing both memory requirements and computational expenses of image retrieval systems. This work proposes to exclude the features of image blocks that exhibit a low encoding error when learned by a $n/p/n$ autoencoder ($p\!<\!n$). We examine the histogram of autoendcoding errors of image blocks for each image class to facilitate the decision which image regions, or roughly what percentage of an image perhaps, shall be declared relevant for the retrieval task. This leads to reduction of feature dimensionality and speeds up the retrieval process. To validate the proposed scheme, we employ local binary patterns (LBP) and support vector machines (SVM) which are both well-established approaches in CBIR research community. As well, we use IRMA dataset with 14,410 x-ray images as test data. The results show that the dimensionality of annotated feature vectors can be reduced by up to 50% resulting in speedups greater than 27% at expense of less than 1% decrease in the accuracy of retrieval when validating the precision and recall of the top 20 hits.
We clarify and strengthen our demonstration that arrows of time necessarily arise in unconfined systems. Contrary to a recent claim, this does not require an improbable selection principle.
We show that the class of finite rooted binary plane trees is a Ramsey class (with respect to topological embeddings that map leaves to leaves). That is, for all such trees P,H and every natural number k there exists a tree T such that for every k-coloring of the (topological) copies of P in T there exists a (topological) copy H' of H in T such that all copies of P in H' have the same color. When the trees are represented by the so-called rooted triple relation, the result gives rise to a Ramsey class of relational structures with respect to induced substructures.
This article is a survey of two subjects: the first part is devoted to field generators in two variables, and the second to birational endomorphisms of the affine plane. Each one of these subjects originated in Abhyankar's seminar in Purdue University in the 1970s. Note that the part on field generators is more than a survey, since it contains a considerable amount of new material.
Random Matrix theory has become a field on its own with a breadth of new results, techniques, and ideas in the last thirty years. In these proceedings of the 8ECM 2021, I illustrate some of these advances by describing what is known about the spectrum and the eigenvectors of Bernoulli matrices.
We consider the N=1 supersymmetric QCD with SU(N_c) gauge group involving   N_f = N_c - 1 pairs of chiral matter multiplets in fundamental and antifundamental color representations. For this theory in the framework of the effective lagrangian approach, we solve the BPS equations for the domain walls interpolating between different vacua. The equations always have a unique solution for the walls interpolating between the chirally symmetric and a chirally asymmetric vacua. For the walls interpolating between different chirally asymmetric vacua, the equations admit two different solutions which exist when the mass of the matter field is below some critical value m*. At m = m*, two branches join together and, at m > m*, no BPS - saturated complex domain walls exist.
We solve analytically master equations that describe a cavity filled with a kerr medium, taking into account the dissipation induced by the environment, and parametric down conversion processes. We use superoperator techniques.
In this paper we consider $j$-tuple-connected components in random $k$-uniform hypergraphs (the $j$-tuple-connectedness relation can be defined by letting two $j$-sets be connected if they lie in a common edge and consider the transitive closure; the case $j=1$ corresponds to the common notion of vertex-connectedness). We determine that the existence of a $j$-tuple-connected component containing $\Theta (n^j)$ $j$-sets in random $k$-uniform hypergraphs undergoes a phase transition and show that the threshold occurs at edge probability $\tfrac{(k-j)!}{\binom{k}{j}-1}n^{j-k}$. Our proof extends the recent short proof for the graph case by Krivelevich and Sudakov which makes use of a depth-first search to reveal the edges of a random graph.   Our main original contribution is a "bounded degree lemma" which controls the structure of the component grown in the search process.
There has been considerable interest in recent years in cosmological models in which we inhabit a very large, underdense void as an alternative to dark energy. A longstanding objection to this proposal is that observations limit our position to be very close to the void centre. By selecting from a family of void profiles that fit supernova luminosity data, we carefully determine how far from the centre we could be. To do so, we use the observed dipole component of the cosmic microwave background, as well as an additional stochastic peculiar velocity arising from primordial perturbations. We find that we are constrained to live within 80 Mpc of the centre of a void--a somewhat weaker constraint than found in previous studies, but nevertheless a strong violation of the Copernican principle. By considering how such a Gpc-scale void would appear on the microwave sky, we also show that there can be a maximum of one of these voids within our Hubble radius. Hence, the constraint on our position corresponds to a fraction of the Hubble volume of order 10^{-8}. Finally, we use the fact that void models only look temporarily similar to a cosmological-constant-dominated universe to argue that these models are not free of temporal fine-tuning.
H. Furstenberg introduced the notion of central set in terms of topological dynamics and established the central set theorem. The essence of central set theorem is that it is the simultaneous extension of van der Waerden's theorem and Hindman's theorem. Later V. Bergelson and N. Hindman established a connection between central sets and the algebra of Stone-cech compactification and proved that the central sets are the member of minimal idempotent ultrafilter of discrete semigroup. In some subsequent papers the central set theorem has been studied more deeply and some generalizations has been established. Those works use the techniques of Stone-Cech compactification of discrete semigroup. In this work we will prove central set theorem via combinatorial approach using the combinatorial characterization of central set established by N. Hindman, A. Malkeki and D. Strauss. Though we will use the combinatorial approach but the technique of the proof is similar to the proof of D. De, N. Hindman, D. Strauss.
We discuss the rest-frame optical emission line spectra of a large (~50) sample of z=3.1 Lyman alpha emitters (LAEs) whose physical properties suggest such sources are promising analogs of galaxies in the reionization era. Reliable Lyman continuum escape fractions have now been determined for a large sample of such LAEs from the Lyman Continuum Escape Survey (LACES) undertaken via deep HST imaging in the SSA22 survey area reported in Fletcher et al. (2019). Using new measures of [OII] emission secured from Keck MOSFIRE spectra we re-examine, for a larger sample, earlier claims that Lyman continuum leakages may correlate with the nebular emission line ratio [OIII]/[OII] as expected for density-bound HII regions. We find that a large [OIII]/[OII] line ratio is indeed a necessary condition for Lyman continuum leakage, strengthening earlier claims made using smaller samples at various redshifts. However, not all LAEs with large [OIII]/[OII] line ratios are leakers and leaking radiation appears not to be associated with differences in other spectral diagnostics. This suggests the detection of leaking radiation is modulated by an additional property, possibly the viewing angle for porous HII regions. We discuss our new results in the context of the striking bimodality of LAE leakers and non-leakers found in the LACES program and the implications for the sources of cosmic reionization.
The production of heavy-flavored hadron at the hadronic colliders provides a challenging opportunity to test the validity of pQCD predictions. There are two mechanisms for the $B^{(*)}_s$ hadroproduction, i.e. the gluon-gluon fusion mechanism via the subprocess $g+g\rightarrow B^{(*)}_s+b+\bar{s}$ and the extrinsic heavy quark mechanism via the subprocesses $g+\bar{b}\to B^{(*)}_s +\bar{s}$ and $g+s\to B^{(*)}_s +b$, both of which shall have sizable contributions in proper kinematic region. Different from the fixed-flavor-number scheme (FFNS) previously adopted in the literature, we study the $B^{(*)}_s$ hadroproduction under the general-mass variable-flavor-number scheme (GM-VFNS), in which we can consistently deal with the double counting problem from the above two mechanisms. Properties for the $B^{(*)}_s$ hadroproduction are discussed. To be useful reference, a comparative study of FFNS and GM-VFNS is presented. Both of which can provide reasonable estimations for the $B^{(*)}_s$ hadroproduction. At the Tevatron, the difference between these two schemes is small, however such difference is obvious at the LHC. The forthcoming more precise data on LHC shall provide a good chance to check which scheme is more appropriate to deal with the $B^{(*)}_s$-meson production and to further study the heavy quark components in hadrons.
Suppose that $\{S_n,\ n\geq0\}$ is an asymptotically stable random walk. Let $g$ be a positive function and $T_g$ be the first time when $S_n$ leaves $[-g(n),\infty)$. In this paper we study asymptotic behaviour of $T_g$. We provide integral tests for function $g$ that guarantee $P(T_g>n)\sim V(g)P(T_0>n)$ where $T_0$ is the first strict descending ladder epoch of $\{S_n\}$
We discuss possible D-brane configurations on SU(2) group manifolds in the sigma model approach. When we turn the boundary conditions of the spacetime fields into the boundary gluing conditions of chiral currents, we find that for all D-branes except the spherical D2-branes, the gluing matrices R^a_{b} depend on the fields, so the chiral Kac-Moody symmetry is broken, but conformal symmetry is maintained. Matching the spherical D2-branes derived from the sigma model with those from the boundary state approach we obtain a U(1) field strength that is consistent with flux quantization.