ShantanuT01/DACTYL-Pretraining huggingface dataset:
Superstring perturbation theory is traditionally carried out by using picture-changing operators (PCO's) to integrate over odd moduli. Naively the PCO's can be inserted anywhere on a string worldsheet, but actually a constraint must be placed on PCO insertions to avoid spurious singularities. Accordingly, it has been long known that the simplest version of the PCO procedure is valid only locally on the moduli space of Riemann surfaces, and that a correct PCO-based algorithm to compute scattering amplitudes must be based on piecing together local descriptions. Recently, "vertical integration" was proposed as a relatively simple method to do this. Here, we spell out in detail what vertical integration means if carried out systematically. This involves a hierarchical procedure with corrections of high order. One might anticipate such a structure from the viewpoint of super Riemann surfaces.
We present a comprehensive model of the global properties of Alfven waves in the solar atmosphere and fast solar wind. Linear non-WKB wave transport equations are solved from the photosphere to 4 AU, and for wave periods ranging from 3 seconds to 3 days. We derive a radially varying power spectrum of kinetic and magnetic energy fluctuations for waves propagating in both directions along a superradially expanding magnetic flux tube. This work differs from previous models in 3 major ways. (1) In the chromosphere and low corona, the successive merging of flux tubes on granular and supergranular scales is described using a 2D magnetostatic model of a network element. Below a critical merging height the waves are modeled as thin-tube kink modes, and we assume that all of the kink-mode wave energy is transformed into volume-filling Alfven waves above the merging height. (2) The frequency spectrum of horizontal motions is specified only at the photosphere based on prior analyses of G-band bright point kinematics. Everywhere else the amplitudes of outward and inward propagating waves are computed with no free parameters. We find that the wave amplitudes in the corona agree well with off-limb nonthermal line widths. (3) Nonlinear turbulent damping is applied to the results of the linear model using a phenomenological loss term. A single choice for the normalization of the turbulent outer-scale length produces both the right amount of damping at large distances (to agree with in situ measurements) and the right amount of heating in the extended corona (to agree with empirical wind acceleration models). In the corona, the modeled heating rate differs by more than an order of magnitude from a rate based on isotropic Kolmogorov turbulence.
The behavior of the dc-component of the current along a quantum loop of tight-binding electrons threaded by a magnetic flux that varies linearly in time Phi_M(t)= Phi t is investigated. We analize the electron transport in different kinds of one-dimensional structures bended into a ring geometry: a clean one-dimensional metal, a chain with a two-band structure and a disordered chain. Inelastic scattering events are introduced through the coupling to a particle reservoir. We use a theoretical treatment based in Baym-Kadanoff-Keldysh non-equilibrium Green functions, which allows us to solve the problem exactly.
The phenomenological gravitational waveform models, which we refer to as PhenomA, PhenomB and PhenomC, generate full inspiral-merger-ringdown waveforms of coalescing binary back holes (BBHs). These models are defined in the Fourier domain, thus can be used for fast matched filtering in the gravitational wave search. PhenomA has been developed for nonspinning BBH waveforms, while PhenomB and PhenomC were designed to model the waveforms of BBH systems with nonprecessing (aligned) spins, but can also be used for nonspinning systems. In this work, we study the validity of the phenomenological models for nonspinning BBH searches at low masses, $m_{1,2}\geq 4 Msun$ and $m_1+m_2\equiv M \leq 30 Msun$, with Advanced LIGO. As our complete signal waveform model, we adopt EOBNRv2 that is a time-domain inspiral-merger-ringdown waveform model. To investigate the search efficiency of the phenomenological template models, we calculate fitting factors by exploring overlap surfaces. We find that only PhenomC is valid to obtain the fitting factors better than 0.97 in the mass range of $M<15 Msun$. Above $15 Msun$, PhenomA is most efficient in symmetric mass region, PhenomB is most efficient in highly asymmetric mass region, and PhenomC is most efficient in the intermediate region. Specifically, we propose an effective phenomenological template family that can be constructed by employing the phenomenological models in four subregions individually. We find that fitting factors of the effective templates are better than 0.97 in our entire mass region and mostly greater than 0.99.
A diagram is introduced for visualizing matrix product states which makes transparent a connection between matrix product factorizations of states and operators, and complex weighted finite state automata. It is then shown how one can proceed in the opposite direction: writing an automaton that ``generates'' an operator gives one an immediate matrix product factorization of it. Matrix product factorizations have the advantage of reducing the cost of computing expectation values by facilitating caching of intermediate calculations. Thus our connection to complex weighted finite state automata yields insight into what allows for efficient caching in matrix product algorithms. Finally, these techniques are generalized to the case of multiple dimensions.
We discuss the field theory interpretation (via holographic duality) of some recently-discovered string theory solutions with varying flux, focusing on four dimensional theories with N=2 supersymmetry and with N=1 supersymmetry which arise as the near-horizon limits of "fractional D3-branes". We argue that in the N=2 case the best interpretation of the varying flux in field theory is via a Higgs mechanism reducing the rank of the gauge group, and that there is no need to invoke a duality to explain the varying flux in this case. We discuss why a similar interpretation does not seem to apply to the N=1 case of Klebanov and Strassler, which was interpreted as a "duality cascade". However, we suggest that it might apply to different vacua of the same theory, such as the one constructed by Pando Zayas and Tseytlin.
The material presented here is supplementary to the article entitled: "Density-functional investigation of the rhombohedral to simple cubic phase transition of arsenic"; it deals with the convergence issues involved in studying a semi-metal to metal structural phase transition such as the A7 to sc transition of arsenic.
NGC 7129 is a bright reflection nebula located in the molecular cloud complex near l=105.4, b=+9.9, about 1.15 kpc distant. Embedded within the reflection nebula is a young cluster dominated by a compact grouping of four early-type stars: BD+65 1638 (B3V), BD+65 1637 (B3e), SVS 13 (B5e), and LkH-alpha 234 (B8e). About 80 H-alpha emission sources brighter than V~23 are identified in the region, many of which are presumably T Tauri star members of the cluster. We also present deep (V~23), optical (VRI) photometry of a field centered on the reflection nebula and spectral types for more than 130 sources determined from low dispersion, optical spectroscopy. The narrow pre-main sequence evident in the color-magnitude diagram suggests that star formation was rapid and coeval. A median age of about 1.8 Myr is inferred for the H-alpha and literature-identified X-ray emission sources having established spectral types, using pre-main sequence evolutionary models. Our interpretation of the structure of the molecular cloud and the distribution of young stellar objects is that BD+65 1638 is primarily responsible for evacuating the blister-like cavity within the molecular cloud. LkH-alpha 234 and several embedded sources evident in near infrared adaptive optics imaging have formed recently within the ridge of compressed molecular gas. The compact cluster of low-mass stars formed concurrently with the early-type members, concentrated within a central radius of ~0.7 pc. Star formation is simultaneously occurring in a semi-circular arc some ~3 pc in radius that outlines remaining dense regions of molecular gas. High dispersion, optical spectra are presented for BD+65 1638, BD+65 1637, SVS 13, LkH-alpha 234, and V350 Cep. These spectra are discussed in the context of the circumstellar environments inferred for these stars.
We introduce a model for rectification in three-terminal ballistic conductors, where the central connecting node is modeled as a chaotic cavity. For bias voltages comparable to the Fermi energy, a strong nonlinearity is created by the opening of a gap in the transport window. Both noninteracting cavity electrons at arbitrary temperature as well as the hot electron regime are considered. Charging effects are treated within the transmission formalism using a self-consistent analysis. The conductance of the third lead in a voltage probe configuration is varied to also model inelastic effects. We find that the basic transport features are insensitive to all of these changes, indicating that the nonlinearity is robust and well suited to applications such as current rectification in ballistic systems. Our findings are in broad agreement with several recent experiments.
The cross-resonant gate is an entangling gate for fixed frequency superconducting qubits introduced for untunable qubits. While being simple and extensible, it suffers from long duration and limited fidelity. Using two different optimal control algorithms, we probe the quantum speed limit for a CNOT gate in this system. We show that the ability to approach this limit depends strongly on the ansatz used to describe the optimal control pulse. A piecewise constant ansatz with a single carrier leads to an experimentally feasible pulse shape, shorter than the one currently used in experiments, but that remains relatively far from the speed limit. On the other hand, an ansatz based on the two dominant frequencies involved in the optimal control problem allows to generate an optimal solution more than twice as fast, in under $30$ns. This comes close to the theoretical quantum speed limit, which we estimate at $15$ns for typical circuit-QED parameters, which is more than an order of magnitude faster than current experimental microwave-driven realizations, and more than twice as fast as tunable direct-coupling experimental realizations.
The application in cryptography of quantum algorithms for prime factorization fostered the interest in quantum computing. However, quantum computers, and particularly quantum annealers, can also be helpful to construct secure cryptographic keys. Indeed, finding robust Boolean functions for cryptography is an important problem in sequence ciphers, block ciphers, and hash functions, among others. Due to the super-exponential size $\mathcal{O}(2^{2^n})$ of the associated space, finding $n$-variable Boolean functions with global cryptographic constraints is computationally hard. This problem has already been addressed employing generic low-connected incoherent D-Wave quantum annealers. However, the limited connectivity of the Chimera graph, together with the exponential growth in the complexity of the Boolean function design problem, limit the problem scalability. Here, we propose a special-purpose coherent quantum annealing architecture with three couplers per qubit, designed to optimally encode the bent function design problem. A coherent quantum annealer with this tree-type architecture has the potential to solve the $8$-variable bent function design problem, which is classically unsolved, with only $127$ physical qubits and $126$ couplers. This paves the way to reach useful quantum supremacy within the framework of quantum annealing for cryptographic purposes.
We present spectroscopic follow-up observations on two bright Ly$\alpha$ emitter (LAE) candidates originally found by Krug et al. (2012) at a redshift of z~7.7 using the Multi-Object Spectrometer for Infra-Red Exploration (MOSFIRE) at Keck. We rule out any line emission at the >5$\sigma$ level for both objects, putting on solid ground a previous null result for one of the objects. The limits inferred from the non-detections rule out the previous claim of no or even reversed evolution between 5.7 < z < 7.7 in the Ly$\alpha$ luminosity function (LF) and suggest a drop in the Ly$\alpha$ luminosity function consistent with that seen in Lyman Break galaxy (LBG) samples. We model the redshift evolution of the LAE LF using the LBG UV continuum LF and the observed rest-frame equivalent width distribution. From the comparison of our empirical model with the observed LAE distribution, we estimate lower limits of the neutral hydrogen fraction to be 50-70% at z~7.7. Together with this, we find a strong evolution in the Ly$\alpha$ optical depth characterized by (1+z)^(2.2 $\pm$ 0.5) beyond z=6 indicative of a strong evolution of the IGM. Finally, we extrapolate the LAE LF to z~9 using our model and show that it is unlikely that large area surveys like UltraVISTA or Euclid pick up LAEs at this redshift assuming the current depths and area.
We provide a decomposition that is sufficient in showing when a symmetric tridiagonal matrix $A$ is completely positive. Our decomposition can be applied to a wide range of matrices. We give alternate proofs for a number of related results found in the literature in a simple, straightforward manner. We show that the cp-rank of any irreducible tridiagonal doubly stochastic matrix is equal to its rank. We then consider symmetric pentadiagonal matrices, proving some analogous results, and providing two different decompositions sufficient for complete positivity. We illustrate our constructions with a number of examples.
A dominating set of a graph $G$ is a set $D$ of vertices of $G$ such that every vertex outside $D$ is adjacent to a vertex in $D$. A locating-dominating set of $G$ is a dominating set $D$ of $G$ with the additional property that every two distinct vertices outside $D$ have distinct neighbors in $D$; that is, for distinct vertices $u$ and $v$ outside $D$, $N(u) \cap D \neq N(v) \cap D$ where $N(u)$ denotes the open neighborhood of $u$. A graph is twin-free if every two distinct vertices have distinct open and closed neighborhoods. The location-domination number of $G$, denoted $\gamma_L(G)$, is the minimum cardinality of a locating-dominating set in $G$. Garijo, Gonzalez and Marquez [Applied Math. Computation 249 (2014), 487--501] posed the conjecture that for $n$ sufficiently large, the maximum value of the location-domination number of a twin-free, connected graph on $n$ vertices is equal to $\lfloor \frac{n}{2} \rfloor$. We propose the related (stronger) conjecture that if $G$ is a twin-free graph of order $n$ without isolated vertices, then $\gamma_L(G)\leq \frac{n}{2}$. We prove the conjecture for cubic graphs. We rely heavily on proof techniques from matching theory to prove our result.
We extend the recent rigorous convergence result of Abels and the second author (arXiv preprint 2105.08434) concerning convergence rates for solutions of the Allen-Cahn equation with a nonlinear Robin boundary condition towards evolution by mean curvature flow with constant contact angle. More precisely, in the present work we manage to remove the perturbative assumption on the contact angle being close to ninety degree. We establish under usual double-well type assumptions on the potential and for a certain class of boundary energy densities the sub-optimal convergence rate of order $\smash{\varepsilon^{\frac{1}{2}}}$ for general contact angles $\alpha \in (0,\pi)$. For a very specific form of the boundary energy density, we even obtain from our methods a sharp convergence rate of order $\varepsilon$; again for general contact angles $\alpha \in (0,\pi)$.   Our proof deviates from the popular strategy based on rigorous asymptotic expansions and stability estimates for the linearized Allen-Cahn operator. Instead, we follow the recent approach by Fischer, Laux and Simon (SIAM J. Math. Anal. 52, 2020), thus relying on a relative entropy technique. We develop a careful adaptation of their approach in order to encode the constant contact angle condition. In fact, we perform this task at the level of the notion of gradient flow calibrations. This concept was recently introduced in the context of weak-strong uniqueness for multiphase mean curvature flow by Fischer, Laux, Simon and the first author (arXiv preprint 2003.05478).
Recent advances in deep learning led to novel generative modeling techniques that achieve unprecedented quality in generated samples and performance in learning complex distributions in imaging data. These new models in medical image computing have important applications that form clinically relevant and very challenging unsupervised learning problems. In this paper, we explore the feasibility of using state-of-the-art auto-encoder-based deep generative models, such as variational and adversarial auto-encoders, for one such task: abnormality detection in medical imaging. We utilize typical, publicly available datasets with brain scans from healthy subjects and patients with stroke lesions and brain tumors. We use the data from healthy subjects to train different auto-encoder based models to learn the distribution of healthy images and detect pathologies as outliers. Models that can better learn the data distribution should be able to detect outliers more accurately. We evaluate the detection performance of deep generative models and compare them with non-deep learning based approaches to provide a benchmark of the current state of research. We conclude that abnormality detection is a challenging task for deep generative models and large room exists for improvement. In order to facilitate further research, we aim to provide carefully pre-processed imaging data available to the research community.
Recent weak and strong lensing data of the galaxy cluster A1689 are modelled by dark fermions that are quantum degenerate within some core. The gas density, deduced from X-ray observations up to 1 Mpc and obeying a cored power law, is taken as input, while the galaxy mass density is modelled. An additional dark matter tail may arise from cold or warm dark matter, axions or non-degenerate neutrinos. The fit yields that the fermions are degenerate within a 430 kpc radius. The fermion mass is a few eV and the best case involves 3 active plus 3 sterile neutrinos of equal mass, for which we deduce $1.51 \pm 0.04$ eV. The eV mass range will be tested in the KATRIN experiment.
We prove an orbifold Riemann--Roch formula for a polarized 3--fold (X,D). As an application, we construct new families of projective Calabi--Yau threefolds.
Geometric $\sigma$-models have been defined as purely geometric theories of scalar fields coupled to gravity. By construction, these theories possess arbitrarily chosen vacuum solutions. Using this fact, one can build a Kaluza--Klein geometric $\sigma$-model by specifying the vacuum metric of the form $M^4\times B^d$. The obtained higher dimensional theory has vanishing cosmological constant but fails to give massless gauge fields after the dimensional reduction. In this paper, a modified geometric $\sigma$-model is suggested, which solves the above problem.
In this paper, we formulate a new \emph{multiple-correction method}. The goal is to accelerate the rate of convergence. In particular, we construct some sequences to approximate the Euler-Mascheroni and Landau constants, which are faster than the classical approximations in literature.
The watchman's walk problem in a digraph calls for finding a minimum length closed dominating walk, where direction of arcs is respected. The watchman's walk of a de Bruijn graph of order $k$ is described by a de Bruijn sequence of order $k-1$. This idea is extended to certain subdigraphs of de Bruijn graphs.
The contribution of the Unresolved Extragalactic Radio Sources to the diffuse brightness of the sky was evaluated using the source number - flux measurements available in literature. We first optimized the fitting function of the data based on number counts distribution. We then computed the brightness temperature at various frequencies from 151 MHz to 8440 MHz and derived its spectral dependence. As expected the frequency dependence can be described by a power law with a spectral index $\gamma \simeq -2.7$, in agreement with the flux emitted by the {\it steep spectrum} sources. The contribution of {\it flat spectrum} sources becomes relevant at frequencies above several GHz. Using the data available in literature we improved our knowledge of the brightness of the unresolved extragalactic radio sources. The results obtained have general validity and they can be used to disentangle the various contributions of the sky brightness and to evaluate the CMB temperature.
Coulomb energy differences between mirror nuclei with $A \le 70$ are calculated within the framework of the nuclear shell model using an effective Coulomb plus isovector and isotensor interaction. Absolute binding energies for proton-rich nuclei are predicted by adding the calculated Coulomb shifts to experimentally measured binding energies for the neutron-rich mirror. The location of the proton drip-line is investigated, as well as candidates for the exotic decay mode known as di-proton emission. Taking into account the lifetimes of competing decay modes and limits imposed by experimental setups, it is concluded that the best candidates for the observation of correlated di-proton emission are $^{45}$Fe, $^{48}$Ni, and $^{63}$Se.
We study the invariant measures of infinite systems of stochastic differential equations (SDEs) indexed by the vertices of a regular tree. These invariant measures correspond to Gibbs measures associated with certain continuous specifications, and we focus specifically on those measures which are homogeneous Markov random fields. We characterize the joint law at any two adjacent vertices in terms of a new two-dimensional SDE system, called the "local equation", which exhibits an unusual dependence on a conditional law. Exploiting an alternative characterization in terms of an eigenfunction-type fixed point problem, we derive existence and uniqueness results for invariant measures of the local equation and infinite SDE system. This machinery is put to use in two examples. First, we give a detailed analysis of the surprisingly subtle case of linear coefficients, which yields a new way to derive the famous Kesten-McKay law for the spectral measure of the regular tree. Second, we construct solutions of tree-indexed SDE systems with nearest-neighbor repulsion effects, similar to Dyson's Brownian motion.
We present the results of simultaneous analysis of the S-wave pi pi-spectra in the reactions pi^- p -> (pi^0 pi^0)_S n at p_{lab}=38 GeV/c (GAMS) and pi^- p -> (pi^+ pi^-)_S n at p_{lab}=18 GeV/c (E852 Collaboration) at moderate momenta transferred to the nucleon, |t| < 1.5 (GeV/c)^2. The t-distributions are described by the reggeized pi- and a_1-exchanges provided by the leading and daughter trajectories, while the M_{pi pi}-spectra are determined by a set of scalar-isoscalar resonances. With M_{pi pi}-distributions averaged over t-intervals, we have found several solutions given by different t-channel exchange mechanisms at |t| ~ (0.5-1.5) (GeV/c)^2, with resonance parameters close to each other. We conclude that despite a poor knowledge of the structure of the t-exchange, the characteristics of resonances such as masses and widths can be reliably determined using the processes under discussion. As to pole positions, we have found (1031 +/- 10) - i(35 +/- 6) MeV for f_0(980) and (1315 +/- 20) - i(150 +/- 30) MeV for f_0(1300).