ShantanuT01/DACTYL-Pretraining huggingface dataset:
We study measurements of the unitary generalization of Pauli operators. First, an analytical (constructive) solution to the eigenproblem of these operators is presented. Next, in the case of two subsystems, the Schmidt form of the eigenvectors is derived to identify measurements which are easy to implement. These results are utilized to show that quantum cryptography with two bases, when operating on a two-component qudit, can be realized with measurements on individual subsystems, assisted with classical communication. We also discuss feasible devices which perform tomography of polarisation-path qudits.
We performed a systematic search for stellar tidal disruption events (TDE) by looking for X-ray sources that were detected during the ROSAT All Sky Survey and faded by more than an order of magnitude over the next two decades according to XMM-Newton serendipitous observations. Besides a number of highly variable persistent X-ray sources (like active galactic nuclei and cataclysmic variables), we found three sources that are broadly consistent with the TDE scenario: 1RXS J114727.1+494302, 1RXS J130547.2+641252, and 1RXS J235424.5-102053. A TDE association is also acceptable for the fourth source, 1RXS J112312.7+012858, but an AGN origin cannot be ruled out either. This statistics implies a TDE rate of $ \sim 3\times 10^{-5} $ yr$ ^{-1} $ per galaxy in the Universe within $z\sim 0.18$, which is broadly consistent with the estimates of the TDE rate in the more local Universe obtained previously.
It is still a challenge to experimentally realize shortcuts to adiabaticity (STA) for a non-Hermitian quantum system since a non-Hermitian quantum system's counterdiabatic driving Hamiltonian contains some unrealizable auxiliary control fields. In this paper, we relax the strict condition in constructing STA and propose a method to redesign a realizable supplementary Hamiltonian to construct non-Hermitian STA. The redesigned supplementary Hamiltonian can be eithersymmetric or asymmetric. For the sake of clearness, we apply this method to an Allen-Eberly model as an example to verify the validity of the optimized non-Hermitian STA. The numerical simulation demonstrates that a ultrafast population inversion could be realized in a two-level non-Hermitian system.
A connected digraph in which the in-degree of any vertex equals its out-degree is Eulerian; this baseline result is used as the basis of existence proofs for universal cycles (also known as ucycles or generalized deBruijn cycles or U-cycles) of several combinatorial objects. The existence of ucycles is often dependent on the specific representation that we use for the combinatorial objects. For example, should we represent the subset $\{2,5\}$ of $\{1,2,3,4,5\}$ as "25" in a linear string? Is the representation "52" acceptable? Or it it tactically advantageous (and acceptable) to go with $\{0,1,0,0,1\}$? In this paper, we represent combinatorial objects as graphs, as in \cite{bks}, and exhibit the flexibility and power of this representation to produce {\it graph universal cycles}, or {\it Gucycles}, for $k$-subsets of an $n$-set; permutations (and classes of permutations) of $[n]=\{1,2,\ldots,n\}$, and partitions of an $n$-set, thus revisiting the classes first studied in \cite{cdg}. Under this graphical scheme, we will represent $\{2,5\}$ as the subgraph $A$ of $C_5$ with edge set consisting of $\{2,3\}$ and $\{5,1\}$, namely the "second" and "fifth" edges in $C_5$. Permutations are represented via their permutation graphs, and set partitions through disjoint unions of complete graphs.
This review provides an overview of the literature on the edge detection methods for pattern recognition that inspire from the understanding of human vision. We note that edge detection is one of the most fundamental process within the low level vision and provides the basis for the higher level visual intelligence in primates. The recognition of the patterns within the images relate closely to the spatiotemporal processes of edge formations, and its implementation needs a crossdisciplanry approach in neuroscience, computing and pattern recognition. In this review, the edge detectors are grouped in as edge features, gradients and sketch models, and some example applications are provided for reference. We note a significant increase in the amount of published research in the last decade that utilizes edge features in a wide range of problems in computer vision and image understanding having a direct implication to pattern recognition with images.
We are interested in the structure of the positive radial solutions of the supercritical Neumann problem $\varepsilon^2\Delta u-u+u^p=0$ on a unit ball in $\mathbb{R}^N$ , where $N$ is the spatial dimension and $p>p_S:=(N+2)/(N-2)$, $N\ge 3$. We show that there exists a sequence $\{\varepsilon_n^*\}_{n=1}^{\infty}$ ($\varepsilon_1^*>\varepsilon_2^*>\cdots\rightarrow 0$) such that this problem has infinitely many singular solutions $\{(\varepsilon_n^*,U_n^*)\}_{n=1}^{\infty}\subset\mathbb{R}\times (C^2(0,1)\cap C^1(0,1])$ and that the nonconstant regular solutions consist of infinitely many smooth curves in the $(\varepsilon,U(0))$-plane. It is shown that each curve blows up at $\varepsilon_n^*$ and if $p_{\rm{S}}<p<p_{\rm{JL}}$, then each curve has infinitely many turning points around $\varepsilon_n^*$. Here, $p_{\rm{JL}}$ stands for the Joseph-Lundgren exponent. In particular, the problem has infinitely many solutions if $\varepsilon\in\{\varepsilon_n^*\}_{n=1}^{\infty}$. We also show that there exists $\bar{\varepsilon}>0$ such that the problem has no nonconstant regular solution if $\varepsilon>\bar{\varepsilon}$. The main technical tool is the intersection number between the regular and singular solutions.
CMB polarization data is usually analyzed using $E$ and $B$ modes because they are scalars quantities under rotations along the lines of sight and have distinct physical origins. We explore the possibility of using the Stokes parameters $Q$ and $U$ for complementary analysis and consistency checks in the context of searches for non-Gaussianity. We show that the Minkowski Functionals (MFs) of $Q,U$ are invariant under local rotations along the lines of sight even though $Q,U$ are spin-2 variables, for full sky analysis. The invariance does not hold for incomplete sky. For local type primordial non-Gaussianity, when we compare the non-Gaussian deviations of MFs for $Q,U$ to what is obtained for $E$ mode or temperature fluctuations, we find that the amplitude is about an order of magnitude lower and the shapes of the deviations are different. This finding can be useful in distinguishing local type non-Gaussianity from other origins of non-Gaussianity in the observed data. Lastly, we analyze the sensitivity of the amplitudes of the MFs for $Q$, $U$ and the number density of singularities of the total polarization intensity to the tensor-to-scalar ratio, $r$, and find that all of them decrease as $r$ increases.
Both, X-ray and radio observations, are beginning to probe regions in galaxy clusters close to the virial radius. These are particularly interesting regions as they are (i) crucial for the thermal evolution of the intra-cluster medium and (ii) they host plasmas under conditions that are poorly understood. Recently discovered giant radio relics in the galaxy cluster CIZA J2242.8+5301 provide unprecedented evidence for particle acceleration in cluster outskirts. We will discuss some of the intriguing puzzles that surround these relics. The polarisation of the radio emission yields information about the topology of magnetic fields in these shock waves. Here we report on MHD simulations that highlight some problems about the origin of these magnetic fields.
The study of the Higgs boson properties is one of the most relevant activities in current particle physics. In particular, the Higgs boson couplings to third generation fermions is an important test of the mechanism of mass generation. In spite of their impact on the production and decay properties of the Higgs boson, the values of these couplings are still uncertain and, in models of new physics, they can differ in magnitude as well as in sign with respect to the Standard Model case. In this article, we study the possibility of a wrong sign bottom-quark Yukawa coupling within the framework of the Minimal and Next-to-Minimal Supersymmetric Standard Model. Possible experimental tests are also discussed, including novel decays of the heavy CP-even and CP-odd Higgs fields that may be probed in the near future and that may lead to an explanation of some intriguing di-boson signatures observed at the ATLAS experiment.
We give an extension of Hoeffding's inequality to the case of supermartingales with differences bounded from above. Our inequality strengthens or extends the inequalities of Freedman, Bernstein, Prohorov, Bennett and Nagaev.
The light curve diversity of hydrogen-poor superluminous supernovae (SLSNe) has kept open the possibility that multiple power sources account for the population. Specifically, pair-instability explosions (PISNe), which produce large masses of $^{56}$Ni, have been argued as the origin of some slowly-evolving SLSNe. Here we present detailed observations of SN 2016inl (=PS16fgt), a slowly-evolving SLSN at $z=0.3057$, whose unusually red spectrum matches PS1-14bj, a SLSN with an exceptionally long rise time consistent with a PISN. Ground-based and Hubble Space Telescope data, spanning about 800 rest-frame days, reveal a significant light curve flattening, similar to that seen in SN 2015bn, and much slower than the decline rate expected from radioactive decay of $^{56}$Co. We therefore conclude that despite its slow evolution, SN 2016inl is inconsistent with a PISN. Instead, the light curve evolution matches the expected power-law spin-down of a magnetar central engine, but with a shallower power law ($L\propto t^{-2.8}$) compared to that in SN 2015bn, indicating a possible difference in the $\gamma$-ray opacity between the two events. Analytical modeling indicates typical magnetar engine parameters, but one of the highest ejecta masses ($\approx 20$ M$_{\odot}$) inferred for a SLSN. Our results indicate that monitoring the late-time light curve evolution of SLSNe provides a powerful diagnostic of their energy source.
Previous studies of type IIP supernovae have inferred that progenitor masses recovered from hydrodynamic models are higher than 15 Msun. To verify the progenitor mass of this supernova category, we attempt a parameter determination of the well-observed luminous type IIP supernova 2004et. We model the bolometric light curve and the photospheric velocities of SN 2004et by means of hydrodynamic simulations in an extended parameter space. From hydrodynamic simulations and observational data, we infer a presupernova radius of 1500 Rsun, an ejecta mass of 24.5 Msun, an explosion energy of 2.3x10^{51} erg, and a radioactive Ni-56 mass of 0.068 Msun. The estimated progenitor mass on the main sequence is in the range of 25-29 Msun. In addition, we find clear signatures of the explosion asymmetry in the nebular spectra of SN 2004et. The measured progenitor mass of SN 2004et is significantly higher than the progenitor mass suggested by the pre-explosion images. We speculate that the mass inferred from hydrodynamic modeling is overestimated and crucial missing factors are multi-dimensional effects.
The present work is based on the holographic dark energy model with Hubble horizon as the infrared cut-off. The interaction rate between dark energy and dark matter has been reconstructed for three different parameterizations of the deceleration parameter. Observational constraints on the model parameters have been obtained by maximum likelihood analysis using the observational Hubble parameter data (OHD), type Ia supernovab data (SNe), baryon acoustic oscillation data (BAO) and the distance prior of cosmic microwave background (CMB) namely the CMB shift parameter data (CMBShift). The interaction rate obtained in the present work remains always positive and increases with expansion. It is very similar to the result obtained in previous findings where the interaction rate has been reconstructed for a parametrization of the dark energy equation of state. Tighter constraints on the interaction rate have been obtained in the present work as it is based on larger data sets. The nature of the dark energy equation of state parameter has also been studied for the present models. Though the reconstruction is done from different parametrizations, the overall nature of the interaction rate is very similar in all the cases. Different information criteria and the Bayesian evidence, which have been invoked in the context of model selection, show that the these models are at close proximity of each other.
We prove the existence of global, smooth solutions to the 2D Muskat problem in the stable regime whenever the product of the maximal and minimal slopes is strictly less than 1. The curvature of these solutions solutions decays to 0 as $t$ goes to infinity, and they are unique when the initial data is $C^{1,\epsilon}$. We do this by constructing a modulus of continuity generated by the equation, just as Kiselev, Nazarov, and Volberg did in their proof of the global well-posedness for the quasi-geostraphic equation.
Local cubic vertex functions of three higher even spin fields on AdS_D are constructed from the Green function of three conserved currents that are dual to the higher spin fields. Conservation of the currents implies lowest order gauge invariance. These vertex functions appear by the UV divergence as the residue of the highest order pole in the dimensional regularization parameter \epsilon. The method works for even D and maintains covariance at any step. The resulting formula is quite concise.
Medical Mixed Reality helps surgeons to contextualize intraoperative data with video of the surgical scene. Nonetheless, the surgical scene and anatomical target are often occluded by surgical instruments and surgeon hands. In this paper and to our knowledge, we propose a multi-layer visualization in Medical Mixed Reality solution which subtly improves a surgeon's visualization by making transparent the occluding objects. As an example scenario, we use an augmented reality C-arm fluoroscope device. A video image is created using a volumetric-based image synthesization technique and stereo-RGBD cameras mounted on the C-arm. From this synthesized view, the background which is occluded by the surgical instruments and surgeon hands is recovered by modifying the volumetric-based image synthesization technique. The occluding objects can, therefore, become transparent over the surgical scene. Experimentation with different augmented reality scenarios yield results demonstrating that the background of the surgical scenes can be recovered with accuracy between 45%-99%. In conclusion, we presented a solution that a Mixed Reality solution for medicine, providing transparency to objects occluding the surgical scene. This work is also the first application of volumetric field for Diminished Reality/ Mixed Reality.
We consider the Stokes equations on a bounded perforated domaincompleted with non-zero constant boundary conditions on the holes. We investigate configurations forwhich the holes are identical spheres and their number N goes to infinity while their radius1/N tends to zero. We prove that, under the assumption that there is no concentrationin the distribution of holes, the solution is well approximated asymptotically by solving aStokes-Brinkman problem.
Using x-ray diffraction Ghose et al. [Surf. Sci. {\bf 581} (2005) 199] have recently produced a structural model for the quantum-wire surface Si(553)-Au. This model presents two parallel gold wires located at the step edge. Thus, the structure and the gold coverage are quite different from previous proposals. We present here an ab initio study using density functional theory of the stability, electronic band structure and scanning tunneling microscopy images of this model.
We consider the closed locus of $r$-tuples of hypersurfaces in $\mathbb{P}^r$ with positive dimensional intersection, and show in a large range of degrees that its largest component is the locus of $r$-tuples of hypersurfaces whose intersection contains a line. We then apply our methods to obtain new results on the largest components of the locus of hypersurfaces with positive dimensional singular loci and the locus of smooth hypersurfaces with a higher dimensional family of lines through a point than expected.
The purpose of this article is to discuss cluster expansions in dense quantum systems as well as their interconnection with exchange cycles. We show in general how the Ursell operators of order 3 or more contribute to an exponential which corresponds to a mean-field energy involving the second operator U2, instead of the potential itself as usual. In a first part, we consider classical statistical mechanics and recall the relation between the reducible part of the classical cluster integrals and the mean-field; we introduce an alternative method to obtain the linear density contribution to the mean-field, which is based on the notion of tree-diagrams and provides a preview of the subsequent quantum calculations. We then proceed to study quantum particles with Boltzmann statistics (distinguishable particles) and show that each Ursell operator Un with n greater or equal to 3 contains a ``tree-reducible part'', which groups naturally with U2 through a linear chain of binary interactions; this part contributes to the associated mean-field experienced by particles in the fluid. The irreducible part, on the other hand, corresponds to the effects associated with three (or more) particles interacting all together at the same time. We then show that the same algebra holds in the case of Fermi or Bose particles, and discuss physically the role of the exchange cycles, combined with interactions. Bose condensed systems are not considered at this stage. The similarities and differences between Boltzmann and quantum statistics are illustrated by this approach, in contrast with field theoretical or Green's functions methods, which do not allow a separate study of the role of quantum statistics and dynamics.
We denote by $\mathcal{H}_{d,g,r}$ the Hilbert scheme of smooth curves, which is the union of components whose general point corresponds to a smooth irreducible and non-degenerate curve of degree $d$ and genus $g$ in $\PP^r$. In this article, we show that for low genus $g$ outside the Brill-Noether range, the Hilbert scheme $\mathcal{H}_{g+1,g,4}$ is non-empty whenever $g\ge 9$ and irreducible whose only component generically consists of linearly normal curves unless $g=9$ or $g=12$. This complements the validity of the original assertion of Severi regarding the irreducibility of $\mathcal{H}_{d,g,r}$ outside the Brill-Nother range for $d=g+1$ and $r=4$.
We employed accurate full potential density-functional theory and linearized augmented plane wave method to investigate the electronic properties and possible phase transitions of Cu3N under high pressure. The anti perovskite structure Cu3N is a semiconductor with a small indirect band gap at ambient pressure. The band gap becomes narrower with increasing pressure, and the semi-conducting anti ReO3 structure undergoes a semiconductor to semimetal transition at pressure around 8.0 GPa. At higher pressure, a subsequent semimetal to metal transition could take place above 15GPa with a structural transition from anti ReO3 to Cu3Au structure.
The paper consists of two sections. The first section provides a new definition of mirror symmetry of abelian varieties making sense also over $p$-adic fields. The second section introduces and studies quantized theta-functions with two-sided multipliers, which are functions on non-commutative tori. This is an extension of an earlier work by the author. In the Introduction and in the Appendix the constructions of this paper are put into a wider context.
We examine the leptophilic two Higgs doublet model with fermionic dark matter, considering the range of experimental constraints on the Higgs sector. The measurements of the 125 GeV Higgs from the LHC Run-I allow us to focus on those remaining processes that may play an important role at colliders. We find that the leptophilic model allows for a much lighter Higgs than in other two-Higgs models, although discovery at the LHC will be difficult. Adding a dark matter sector motivated by supersymmetric extensions of the leptophilic model, we find the existing parameter space can accommodate constraints from direct detection and the invisible widths of the Higgs and $Z$, while also fitting the Galactic Center gamma ray excess reported by analyses of Fermi-LAT data. We also discuss the status of the fully supersymmetric version of such models, which include four Higgs doublets and a natural dark matter candidate.
This review summarizes more than 100 years of research on spinel compounds, mainly focusing on the progress in understanding their magnetic, electronic, and polar properties during the last two decades. Many spinel compounds are magnetic insulators or semiconductors; however, a number of spinel-type metals exists including superconductors and some rare examples of d-derived heavy-fermion compounds. In the early days, they gained importance as ferrimagnetic or even ferromagnetic insulators with relatively high saturation magnetization and high ordering temperatures, with magnetite being the first magnetic mineral known to mankind. However, spinels played an outstanding role in the development of concepts of magnetism, in testing and verifying the fundamentals of magnetic exchange, in understanding orbital-ordering and charge-ordering phenomena. In addition, the A- site as well as the B-site cations in the spinel structure form lattices prone to strong frustration effects resulting in exotic ground-state properties. In case the A-site cation is Jahn-Teller active, additional entanglements of spin and orbital degrees of freedom appear, which can give rise to a spin-orbital liquid or an orbital glass state. The B-site cations form a pyrochlore lattice, one of the strongest contenders of frustration in three dimensions. In addition, in spinels with both cation lattices carrying magnetic moments, competing magnetic exchange interactions become important, yielding ground states like the time-honoured triangular Yafet-Kittel structure. Finally, yet importantly, there exists a long-standing dispute about the possibility of a polar ground state in spinels, despite their reported overall cubic symmetry. Indeed, over the years number of multiferroic spinels were identified.
We give canonical resolutions of singularities of several cone varieties arising from invariant theory. We establish a connection between our resolutions and resolutions of singularities of closure of conjugacy classes in classical Lie algebras.