ShantanuT01/DACTYL-Pretraining huggingface dataset:
We obtain new upper tail probabilities of $m$-times integrated Brownian motions under the uniform norm and the $L^p$ norm. For the uniform norm, Talagrand's approach is used, while for the $L^p$ norm, Zolotare's approach together with suitable metric entropy and the associated small ball probabilities are used. This proposed method leads to an interesting and concrete connection between small ball probabilities and upper tail probabilities (large ball probabilities) for general Gaussian random variable in Banach spaces. As applications, explicit bounds are given for the largest eigenvalue of the covariance operator, and appropriate limiting behaviors of the Laplace transforms of $m$-times integrated Brownian motions are presented as well.
We consider the non-Fermi liquid quantum critical state of the spin-S two-impurity Kondo model, and its potential realization in a quantum dot device. Using conformal field theory (CFT) and the numerical renormalization group (NRG), we show the critical point to be identical to that of the two-channel Kondo model with additional potential scattering, for any spin-S. Distinct conductance signatures are shown to arise as a function of device asymmetry; with the `smoking gun' square-root behavior, commonly believed to arise at low-energies, dominant only in certain regimes.
For a non-local semilinear eigenvalue problem, we prove simplicity and isolation of the first eigenvalue with homogeneous Dirichlet boundary conditions on open sets supporting a suitable compact Sobolev embedding.
This is a contribution to the forthcoming book "Canonical Gravity: {}From Classical to Quantum" edited by J. Ehlers and H. Friedrich. Ashtekar's criterion for choosing an inner product in the quantisation of constrained systems is discussed. An erroneous claim in a previous paper is corrected and a cautionary example is presented.
Physical consistency of quantum fields in anti-de Sitter space time requires that the space must be compactified by the inclusion of a boundary where appropriate conditions are imposed. An interpretation for the presence of this boundary is found taking AdS as a limiting case of the space generated by a large number of coincident branes. The compactification of AdS leads to a discretization of the spectrum of bulk fields. As a consequence, we find a one to one mapping between the quantum states of scalar fields in AdS bulk and boundary. Using this mapping as an approximation for the dual relation between string dilaton field and scalar QCD glueballs the high energy QCD scaling is reproduced. We also use this map to estimate the ratio of scalar glueball masses.
A metric with signature (-+++) can be constructed from a metric with signature (++++) and a double-sided vector field called the line element field. Some of the classical and quantum properties of this vector field are studied.
In this paper, we introduce VeriQBench -- an open source benchmark for quantum circuits. It offers high-level quantum circuit abstractions of various circuit types, including 1) combinational, 2) dynamic, 3) sequential, and 4) variational quantum circuits, which cover almost all existing types of quantum circuits in the literature. Meanwhile, VeriQBench is a versatile benchmark which can be used in verifying quantum software for different applications, as is evidenced by the existing works including quantum circuit verification (e.g., equivalence checking [Hon+21a; WLY21] and model checking [Yin21]), simulation (e.g., fault simulation), testing (e.g., test pattern generation [CY22]) and debugging (e.g., runtime assertions [Li+20b]). All the circuits are described in OpenQASM and are validated on Qiskit and QCOR simulators. With the hope that it can be used by other researchers, VeriQBench is released at: https://github.com/Veri-Q/Benchmark.
One of the factors limiting electron mobility in supported graphene is remote phonon scattering. We formulate the theory of the coupling between graphene plasmon and substrate surface polar phonon (SPP) modes, and find that it leads to the formation of interfacial plasmon-phonon (IPP) modes, from which the phenomena of dynamic anti-screening and screening of remote phonons emerge. The remote phonon-limited mobilities for SiO$_{2}$, HfO$_{2}$, h-BN and Al$_{2}$O$_{3}$ substrates are computed using our theory. We find that h-BN yields the highest peak mobility, but in the practically useful high-density range the mobility in HfO$_{2}$-supported graphene is high, despite the fact that HfO$_{2}$ is a high-$\kappa$ dielectric with low-frequency modes. Our theory predicts that the strong temperature dependence of the total mobility effectively vanishes at very high carrier concentrations. The effects of polycrystallinity on IPP scattering are also discussed.
We propose a new iterative segmentation model which can be accurately learned from a small dataset. A common approach is to train a model to directly segment an image, requiring a large collection of manually annotated images to capture the anatomical variability in a cohort. In contrast, we develop a segmentation model that recursively evolves a segmentation in several steps, and implement it as a recurrent neural network. We learn model parameters by optimizing the interme- diate steps of the evolution in addition to the final segmentation. To this end, we train our segmentation propagation model by presenting incom- plete and/or inaccurate input segmentations paired with a recommended next step. Our work aims to alleviate challenges in segmenting heart structures from cardiac MRI for patients with congenital heart disease (CHD), which encompasses a range of morphological deformations and topological changes. We demonstrate the advantages of this approach on a dataset of 20 images from CHD patients, learning a model that accurately segments individual heart chambers and great vessels. Com- pared to direct segmentation, the iterative method yields more accurate segmentation for patients with the most severe CHD malformations.
As a test of the standard inflationary cosmology, which generically predicts nearly scale-invariant spectrum of primordial curvature fluctuations, we perform Markov-Chain Monte-Carlo analysis to search for possible modulations in the power spectrum and determine its shape together with the cosmological parameters using cosmic microwave background radiation data. By incorporating various three-parameter features on the simple power-law spectrum, we find an oscillatory modulation localized around the comoving wavenumber $k\simeq 0.009\mathrm{Mpc}^{-1}$ at 99.995% confidence level which improves the log-likelihood as much as $-\Delta 2\ln {\cal L}\equiv \Delta \chi^2_{\rm eff}=-22$. This feature can be detected even if we use only the cross correlation between the temperature and the E-mode polarization anisotropies.
We develop a new class of path transformations for one-dimensional diffusions that are tailored to alter their long-run behaviour from transient to recurrent or vice versa. This immediately leads to a formula for the distribution of the first exit times of diffusions, which is recently characterised by Karatzas and Ruf \cite{KR} as the minimal solution of an appropriate Cauchy problem under more stringent conditions. A particular limit of these transformations also turn out to be instrumental in characterising the stochastic solutions of Cauchy problems defined by the generators of strict local martingales, which are well-known for not having unique solutions even when one restricts solutions to have linear growth. Using an appropriate diffusion transformation we show that the aforementioned stochastic solution can be written in terms of the unique classical solution of an {\em alternative} Cauchy problem with suitable boundary conditions. This in particular resolves the long-standing issue of non-uniqueness with the Black-Scholes equations in derivative pricing in the presence of {\em bubbles}. Finally, we use these path transformations to propose a unified framework for solving explicitly the optimal stopping problem for one-dimensional diffusions with discounting, which in particular is relevant for the pricing and the computation of optimal exercise boundaries of perpetual American options.
We present BEAMER: a new spatially exploitative approach to learning object detectors which shows excellent results when applied to the task of detecting objects in greyscale aerial imagery in the presence of ambiguous and noisy data. There are four main contributions used to produce these results. First, we introduce a grammar-guided feature extraction system, enabling the exploration of a richer feature space while constraining the features to a useful subset. This is specified with a rule-based generative grammar crafted by a human expert. Second, we learn a classifier on this data using a newly proposed variant of AdaBoost which takes into account the spatially correlated nature of the data. Third, we perform another round of training to optimize the method of converting the pixel classifications generated by boosting into a high quality set of (x, y) locations. Lastly, we carefully define three common problems in object detection and define two evaluation criteria that are tightly matched to these problems. Major strengths of this approach are: (1) a way of randomly searching a broad feature space, (2) its performance when evaluated on well-matched evaluation criteria, and (3) its use of the location prediction domain to learn object detectors as well as to generate detections that perform well on several tasks: object counting, tracking, and target detection. We demonstrate the efficacy of BEAMER with a comprehensive experimental evaluation on a challenging data set.
We prove that the Gibbs measures $\rho$ for a class of Hamiltonian equations written $\partial_t u = J (-\triangle u + V'(|u|^2)u)$ on the real line are invariant under the flow of this equation in the sense that there exist random variables $X(t)$ whose laws are $\rho$ (thus independent from $t$) and such that $t\mapsto X(t)$ is a solution to the above equation. Besides, for all $t$, $X(t)$ is almost surely not in $L^2$ which provides as a direct consequence the existence of weak solutions for initial data not in $L^2$. The proof uses Prokhorov's theorem, Skorohod's theorem, as in the strategy in \cite{burqtzv} and Feynman-Kac's integrals.
The Large Area Telescope on board the Fermi satellite observed a gamma-ray flare in the Crab nebula lasting for approximately nine days in April of 2011. The source, which at optical wavelengths has a size of ~11 ly across, doubled its gamma-ray flux within eight hours. The peak photon flux was (186 +- 6) 10-7 cm-2 s-1 above 100 MeV, which corresponds to a 30-fold increase compared to the average value. During the flare, a new component emerged in the spectral energy distribution, which peaked at an energy of (375 +- 26) MeV at flare maximum. The observations imply that the emission region was likely relativistically beamed toward us and that variations in its motion are responsible for the observed spectral variability.
We compute the cone of effective divisors on the Hilbert scheme of points in the projective plane. We show the sections of many stable vector bundles satisfy a natural interpolation condition, and that these bundles always give rise to the edge of the effective cone of the Hilbert scheme. To do this, we give a generalization of Gaeta's theorem on the resolution of the ideal sheaf of a general collection of points in the plane. This resolution has a natural interpretation in terms of Bridgeland stability, and we observe that ideal sheaves of collections of points are destabilized by exceptional bundles. By studying the Bridgeland stability of exceptional bundles, we also show that our computation of the effective cone of the Hilbert scheme is consistent with a conjecture which predicts a correspondence between Mori and Bridgeland walls for the Hilbert scheme.
Around 10% of white dwarfs exhibit global magnetic structures with fields ranging from 1 kG to hundreds of MG. Recently, the first radiation magnetohydrodynamics simulations of the atmosphere of white dwarfs showed that convection should be suppressed in their photospheres for magnetic fields with strengths B $\gtrsim$ 50 kG. These predictions are in agreement with our knowledge of stellar physics (e.g. energy transfer in strong magnetic field regions of the solar photosphere), but have yet to be directly confirmed from white dwarf observations. We obtained COS far-UV spectroscopy of the weakly magnetic, hydrogen-atmosphere, white dwarf WD2105-820 and of three additional non-magnetic, convective remnants (all in the $T_{\mathrm{eff}}$ range 9000-11,000 K). We fitted both the COS and the already available optical spectra with convective and radiative atmospheric models. As expected, we find that for two of the non-magnetic comparison stars only convective model fits predict consistent $T_{\mathrm{eff}}$ values from both the optical and the FUV spectra. In contrast, for WD2105-820 only the best fitting radiative model produced consistent results.
A new formalism for generation of solutions in the consistently truncated low-energy bosonic string theory is developed. This formalism gives a correspondence of the projection type between the theories toroidally compactified from the diverse to three dimensions. Taking the stationary Einstein-dilaton gravity as the theory with a lower dimension, we generate its bosonic string theory extension and calculate the bosonic string theory solution corresponding to the Kerr-NUT one modified by the presence of the charged dilaton field.
We prove in this paper a classicality result for overconvergent modular forms on PEL Shimura varieties of type (A) or (C) associated to an unramified reductive group on $\mathbb{Q}_p$. To get this result, we use the analytic continuation method, first used by Buzzard and Kassaei.
We present a comprehensive examination of optical pumping of spins in individual GaAs quantum dots as we change the charge from positive to neutral to negative using a Schottky diode. We observe that photoluminescence polarization memory has the same sign as the net charge of the dot. Optical pumping of ground state electron spins enhances this effect, as demonstrated through the first measurements of the Hanle effect on an individual quantum dot. With the Overhauser effect in a high longitudinal magnetic field, we demonstrate efficient optical pumping of the quantum dot's nuclear spins for all three charge states.
We present late-time optical spectroscopy taken with the Large Binocular Telescope's Multi-Object Double Spectrograph, an improved ASAS-SN pre-discovery non-detection, and late-time SWIFT observations of the nearby ($d=193$ Mpc, $z=0.0436$) tidal disruption event (TDE) ASASSN-14ae. Our observations span from $\sim$20 days before to $\sim$750 days after discovery. The proximity of ASASSN-14ae allows us to study the optical evolution of the flare and the transition to a host dominated state with exceptionally high precision. We measure very weak H$\alpha$ emission 300 days after discovery ($L_{\rm H\alpha} \simeq 4\times 10^{39}$ ergs s$^{-1}$) and the most stringent upper limit to date on the H$\alpha$ luminosity $\sim$750 days after discovery ($L_{\rm H\alpha} \lesssim 10^{39}$ ergs s$^{-1}$), suggesting that the optical emission arising from a TDE can vanish on a timescale as short as 1 year. Our results have important implications for both spectroscopic detection of TDE candidates at late times, as well as the nature of TDE host galaxies themselves.
We define and study a variant of the \emph{Stanley depth} which we call \emph{total depth} for partially ordered sets (posets). This total depth is the most natural variant of Stanley depth from $\llbracket S_k\rrbracket$ -- the poset of nonempty subsets of $\{1,2,\dots,k\}$ ordered by inclusion -- to any finite poset. In particular, the total depth can be defined for the poset of nonempty submultisets of a multiset ordered by inclusion, which corresponds to a product of chains with the bottom element deleted. We show that the total depth agrees with Stanley depth for $\llbracket S_k\rrbracket$ but not for such posets in general. We also prove that the total depth of the product of chains $\bm{n}^k$ with the bottom element deleted is $(n-1)\lceil{k/2}\rceil$, which generalizes a result of Bir{\'{o}}, Howard, Keller, Trotter, and Young (2010). Further, we provide upper and lower bounds for a general multiset and find the total depth for any multiset with at most five distinct elements. In addition, we can determine the total depth for any multiset with $k$ distinct elements if we know all the interval partitions of $\llbracket S_k\rrbracket$.
Possible nonlinear completion of massive gravity is presented. An additional scalar ghost contained in linear theory condensates to give rise to positive-energy excitations.
${\rm SrRuO_3}$ is a 4d itinerant ferromagnet (T$_{c}$ $\sim $150 K) with stripe domain structure. Using high-quality thin films of SrRuO$_{3}$ we study the resistivity induced by its very narrow ($\sim 3$ nm) Bloch domain walls, $\rho_{DW}$ (DWR), at temperatures between 2 K and T$_{c}$ as a function of the angle, $\theta $, between the electric current and the ferromagnetic domains walls. We find that $\rho_{DW}(T,\theta)=\sin^2\theta \rho_{DW}(T,90)+B(\theta)\rho_{DW}(T,0)$ which provides the first experimental indication that the angular dependence of spin accumulation contribution to DWR is $\sin^2\theta$. We expect magnetic multilayers to exhibit a similar behavior.
We investigate the cosmic thermal evolution with a vacuum energy which decays into photon at the low-redshift. We assume that the vacuum energy is a function of the scale factor that increases toward the early universe. We put on the constraints using recent observations of both type Ia supernovae (SNIa) by Union-2 compilation and the cosmic microwave background (CMB) temperature at the range of the redshift 0.01 < z < 3. From SNIa, we find that the effects of a decaying vacuum energy on the cosmic expansion rate should be very small but could be possible for z < 1.5. On the other hand, we obtain the severe constraints for parameters from the CMB temperature observations. Although the temperature can be still lower than the case of the standard cosmological model, it should only affect the thermal evolution at the early epoch.
Electric field-controlled, two-dimensional (2D) exciton dynamics in transition metal dichalcogenide monolayers is a current research focus in condensed matter physics. We have experimentally investigated the spectral and temporal properties of the A-exciton in a molybdenum diselenide (MoSe2) monolayer under controlled variation of a vertical, electric dc field at room temperature. By using steady-state and time-resolved photoluminescence spectroscopies, we have observed dc field-induced spectral shifts and linewidth broadenings that are consistent with the shortening of the exciton's non-radiative lifetime due to field-induced dissociation. We discuss the implications of the results for future developments in nanoscale metrology and exploratory, optoelectronics technologies based on layered, 2D semiconductors.
Using the concept of the Boolean derivative we study damage spreading for one dimensional elementary cellular automata and define their maximal Lyapunov exponent. A random matrix approximation describes quite well the behavior of ``chaotic'' rules and predicts a directed percolation-type phase transition. After the introduction of a small noise elementary cellular automata reveal the same type of transition.
Based on the recent understanding of the role of the densitized lapse function in Einstein's equations and of the proper way to pose the thin sandwich problem, a slight readjustment of the minimal distortion shift gauge in the 3+1 approach to the dynamics of general relativity allows this shift vector to serve as the vector potential for the longitudinal part of the extrinsic curvature tensor in the new approach to the initial value problem, thus extending the initial value decomposition of gravitational variables to play a role in the evolution as well. The new shift vector globally minimizes the changes in the conformal 3-metric with respect to the spacetime measure rather than the spatial measure on the time coordinate hypersurfaces, as the old shift vector did.
We test the predictive power of first-oder reversal curve (FORC) diagrams using simulations of random magnets. In particular, we compute a histogram of the switching fields of the underlying microscopic switching units along the major hysteresis loop, and compare to the corresponding FORC diagram. We find qualitative agreement between the switching-field histogram and the FORC diagram, yet differences are noticeable. We discuss possible sources for these differences and present results for frustrated systems where the discrepancies are more pronounced.
We have investigated the relaxation of a hydrostatic hot plasma column containing toroidal magnetic field by the Current-Driven (CD) kink instability as a model of pulsar wind nebulae. In our simulations the CD kink instability is excited by a small initial velocity perturbation and develops turbulent structure inside the hot plasma column. We demonstrate that, as envisioned by Begelman, the hoop stress declines and the initial gas pressure excess near the axis decreases. The magnetization parameter \sigma, the ratio of the Poynting to the kinetic energy flux, declines from an initial value of 0.3 to about 0.01 when the CD kink instability saturates. Our simulations demonstrate that axisymmetric models strongly overestimate the elongation of the pulsar wind nebulae. Therefore, the previous requirement for an extremely low pulsar wind magnetization can be abandoned. The observed structure of the pulsar wind nebulae do not contradict the natural assumption that the magnetic energy flux still remains a good fraction of the total energy flux after dissipation of alternating fields.
Super-symmetric tensors - a higher-order extension of scatter matrices - are becoming increasingly popular in machine learning and computer vision for modelling data statistics, co-occurrences, or even as visual descriptors. However, the size of these tensors are exponential in the data dimensionality, which is a significant concern. In this paper, we study third-order super-symmetric tensor descriptors in the context of dictionary learning and sparse coding. Our goal is to approximate these tensors as sparse conic combinations of atoms from a learned dictionary, where each atom is a symmetric positive semi-definite matrix. Apart from the significant benefits to tensor compression that this framework provides, our experiments demonstrate that the sparse coefficients produced by the scheme lead to better aggregation of high-dimensional data, and showcases superior performance on two common computer vision tasks compared to the state-of-the-art.
We obtain estimates near the boundary for the critical dissipative SQG equation in bounded domains, with the square root of the Dirichlet Laplacian dissipation. We prove that global regularity up to the boundary holds if and only if a certain quantitative vanishing of the scalar at the boundary is maintained.
The extragalactic analogs of the microquasars, the quasars, are strong gamma-ray emitters at GeV energies. It is expected that microquasars are also gamma-ray sources, because of the analogy with quasars and because theoretical models predict the high-energy emission. There are two microquasars that appear as the possible counterparts for two unidentified high-energy gamma-ray sources.