ShantanuT01/DACTYL-Pretraining huggingface dataset:
We formulate matrix string models on a class of exact string backgrounds with non constant RR-flux parameterized by a holomorphic prepotential function and with manifest (2,2) supersymmetry. This lifts these string theories to M-theory exposing the non perturbative string interaction which is studied by generalizing the instanton asymptotic expansion, well established in the flat background case, to this more general case. We obtain also a companion matrix model with four manifest supersymmetries in eleven dimensions.
We study Bernoulli bond percolation on a random recursive tree of size $n$ with percolation parameter $p(n)$ converging to $1$ as $n$ tends to infinity. The sizes of the percolation clusters are naturally stored in a tree. We prove convergence in distribution of this tree to the genealogical tree of a continuous-state branching process in discrete time. As a corollary we obtain the asymptotic sizes of the largest and next largest percolation clusters, extending thereby a recent work of Bertoin (2014) which deals with cluster sizes in the supercritical regime. In a second part, we show that the same limit tree appears in the study of the tree components which emerge from a continuous-time destruction of a random recursive tree. We comment on the connection to our first result on Bernoulli bond percolation.
We study the advantage of the co-existence of future ground and space based gravitational wave detectors, in estimating the parameters of a binary coalescence. Using the post-Newtonian waveform for the inspiral of non-spinning neutron star-black hole pairs in circular orbits, we study how the estimates for chirp mass, symmetric mass ratio, and time and phase at coalescence are improved by combining the data from different space-ground detector pairs. Since the gravitational waves produced by binary coalescence also provide a suitable domain where we can study strong field gravity, we also study the deviations from general relativity using the parameterized post-Einsteinian framework. As an example, focusing on the Einstein telescope and DECIGO pair, we demonstrate that there exists a sweet spot range of sensitivity in the pre-DECIGO phase where the best enhancement due to the synergy effect can be obtained for the estimates of the post-Newtonian waveform parameters as well as the modification parameters to general relativity.
Large optical nonlinearities can have numerous applications, ranging from the generation of cat-states for optical quantum computation, through to quantum sensing where the sensitivity exceeds Heisenberg scaling in the resources. However, the generation of ultra-large optical nonlinearities has proved immensely challenging experimentally. We describe a novel protocol where one can effectively generate large optical nonlinearities via the conditional application of a linear operation on an optical mode by an ancilla mode, followed by a measurement of the ancilla and corrective operation on the probe mode. Our protocol can generate high quality optical Schr{\"{o}}dinger cat states useful for optical quantum computing and can be used to perform sensing of an unknown rotation or displacement in phase space, with super-Heisenberg scaling in the resources. We finally describe a potential experimental implementation using atomic ensembles interacting with optical modes via the Faraday effect.
It is now well established that Kepler's supernova remnant is the result of a Type Ia explosion. With an age of 407 years, and an angular diameter of ~ 4', Kepler is estimated to be between 3.0 and 7.0 kpc distant. Unlike other Galactic Type Ia supernova remnants such as Tycho and SN 1006, and SNR 0509-67.5 in the Large Magellanic Cloud, Kepler shows evidence for a strong circumstellar interaction. A bowshock structure in the north is thought to originate from the motion of a mass-losing system through the interstellar medium prior to the supernova. We present results of hydrodynamical and spectral modeling aimed at constraining the circumstellar environment of the system and the amount of 56Ni produced in the explosion. Using models that contain either 0.3 M_sun (subenergetic) or 1 M_sun (energetic) of 56Ni, we simulate the interaction between supernova Ia ejecta and various circumstellar density models. Based on dynamical considerations alone, we find that the subenergetic models favor a distance to the SNR of < 6.4 kpc, while the model that produces 1 M_sun of 56Ni requires a distance to the SNR of > 7 kpc. The X-ray spectrum is consistent with an explosion that produced ~ 1 M_sun of 56Ni, ruling out the subenergetic models, and suggesting that Kepler's SNR was a SN 1991T-like event. Additionally, the X-ray spectrum rules out a pure 1/r^2 wind profile expected from isotropic mass loss up to the time of the supernova. Introducing a small cavity around the progenitor system results in modeled X-ray spectra that are consistent with the observed spectrum. If a wind shaped circumstellar environment is necessary to explain the dynamics and X-ray emission from the shocked ejecta in Kepler's SNR, then we require that the distance to the remnant be greater than 7 kpc.
We report our Keck/MOSFIRE and Magellan/LDSS3 spectroscopy for an [OII] Blob, OIIB10, that is a high-$z$ galaxy with spatially extended [OII]$\lambda\lambda3726,3729$ emission over 30 kpc recently identified by a Subaru large-area narrowband survey. The systemic redshift of OIIB10 is $z=1.18$ securely determined with [OIII]$\lambda\lambda4959,5007$ and H$\beta$ emission lines. We identify FeII$\lambda$2587 and MgII$\lambda\lambda$2796,2804 absorption lines blueshifted from the systemic redshift by $80\pm50$ and $260\pm40$ km s$^{-1}$, respectively, which indicate gas outflow from OIIB10 with the velocity of $\sim 80-260$ km s$^{-1}$. This outflow velocity is comparable with the escape velocity, $250\pm140$ km s$^{-1}$, estimated under the assumption of a singular isothermal halo potential profile. Some fraction of the outflowing gas could escape from the halo of OIIB10, suppressing OIIB10's star-formation activity. We estimate a mass loading factor, $\eta$, that is a ratio of mass outflow rate to star-formation rate, and obtain $\eta>0.8\pm 0.1$ which is relatively high compared with low-$z$ starbursts including U/LIRGs and AGNs. The major energy source of the outflow is unclear with the available data. Although no signature of AGN is found in the X-ray data, OIIB10 falls in the AGN/star-forming composite region in the line diagnostic diagrams. It is possible that the outflow is powered by star formation and a type-2 AGN with narrow FWHM emission line widths of $70-130$ km s$^{-1}$. This is the first detailed spectroscopic study of oxygen-line blobs, which includes the analyses of the escape velocity, the mass loading factor, and the presence of an AGN, and a significant step to understanding the nature of oxygen-line blobs and the relation with gas outflow and star-formation quenching at high redshift.
This paper is concerned with Darcy's law for an incompressible viscous fluid flowing in a porous medium. We establish the sharp $O(\sqrt{\e})$ convergence rate in a periodically perforated and bounded domain in $R^d$ for $d\ge 2$, where $\e$ represents the size of solid obstacles. This is achieved by constructing two boundary correctors to control the boundary layers created by the incompressibility condition and the discrepancy of boundary values between the solution and the leading term in its asymptotic expansion. One of the correctors deals with the tangential boundary data, while the other handles the normal boundary data.
While the research on convolutional neural networks (CNNs) is progressing quickly, the real-world deployment of these models is often limited by computing resources and memory constraints. In this paper, we address this issue by proposing a novel filter pruning method to compress and accelerate CNNs. Our work is based on the linear relationship identified in different feature map subspaces via visualization of feature maps. Such linear relationship implies that the information in CNNs is redundant. Our method eliminates the redundancy in convolutional filters by applying subspace clustering to feature maps. In this way, most of the representative information in the network can be retained in each cluster. Therefore, our method provides an effective solution to filter pruning for which most existing methods directly remove filters based on simple heuristics. The proposed method is independent of the network structure, thus it can be adopted by any off-the-shelf deep learning libraries. Experiments on different networks and tasks show that our method outperforms existing techniques before fine-tuning, and achieves the state-of-the-art results after fine-tuning.
Accuracy of depth estimation from static images has been significantly improved recently, by exploiting hierarchical features from deep convolutional neural networks (CNNs). Compared with static images, vast information exists among video frames and can be exploited to improve the depth estimation performance. In this work, we focus on exploring temporal information from monocular videos for depth estimation. Specifically, we take the advantage of convolutional long short-term memory (CLSTM) and propose a novel spatial-temporal CSLTM (ST-CLSTM) structure. Our ST-CLSTM structure can capture not only the spatial features but also the temporal correlations/consistency among consecutive video frames with negligible increase in computational cost. Additionally, in order to maintain the temporal consistency among the estimated depth frames, we apply the generative adversarial learning scheme and design a temporal consistency loss. The temporal consistency loss is combined with the spatial loss to update the model in an end-to-end fashion. By taking advantage of the temporal information, we build a video depth estimation framework that runs in real-time and generates visually pleasant results. Moreover, our approach is flexible and can be generalized to most existing depth estimation frameworks. Code is available at: https://tinyurl.com/STCLSTM
We investigate lepton flavor violating decays in a SUSY SO(10) model with symmetric textures recently constructed by us. Unlike the models with lop-sided textures which give rise to a large decay rate for mu -> e gamma, the decay rate we get is much suppressed and yet it is large enough to be accessible to the next generation of experiments. We have also investigated the possibility of baryogenesis resulting from soft leptogenesis. We find that with the soft SUSY masses assuming their natural values, B^\prime \equiv \sqrt{BM_{1}} ~ 1.4 TeV and Im(A) ~ 1 TeV, the observed baryon asymmetry in the Universe can be accommodated in our model. We have also updated the predictions of our model for the masses, mixing angles and CP violating measures in both charged fermion and neutrino sectors, using the most up-to-date experimental data as input.
Phonon-induced orbital and spin relaxation rates of single electron states in lateral single and double quantum dots are obtained numerically for realistic materials parameters. The rates are calculated as a function of magnetic field and interdot coupling, at various field and quantum dot orientations. It is found that orbital relaxation is due to deformation potential phonons at low magnetic fields, while piezoelectric phonons dominate the relaxation at high fields. Spin relaxation, which is dominated by piezoelectric phonons, in single quantum dots is highly anisotropic due to the interplay of the Bychkov-Rashba and Dresselhaus spin-orbit couplings. Orbital relaxation in double dots varies strongly with the interdot coupling due to the cyclotron effects on the tunneling energy. Spin relaxation in double dots has an additional anisotropy due to anisotropic spin hot spots which otherwise cause giant enhancement of the rate at useful magnetic fields and interdot couplings. Conditions for the absence of the spin hot spots in in-plane magnetic fields (easy passages) and perpendicular magnetic fields (weak passages) are formulated analytically for different growth directions of the underlying heterostructure. It is shown that easy passages disappear (spin hot spots reappear) if the double dot system loses symmetry by an xy-like perturbation.
Various choices of the geometry degrees of freedom as the emergent time are tested on the model of an isotropic universe with a scalar field of $\phi^2$ potential. Potential problems with each choices as well as possible applications in loop quantization are discussed.
Observations reveal massive amounts of OVI around star-forming $L_*$ galaxies, with covering fractions of near unity extending to the host halo's virial radius. This OVI absorption is typically kinematically centered upon photoionized gas, with line widths that are suprathermal and kinematically offset from the galaxy. We discuss various scenarios and whether they could result in the observed phenomenology (cooling gas flows, boundary layers, shocks, virialized gas, photoionized clouds in thermal equilibrium). If predominantly collisionally ionized, as we argue is most probable, the OVI observations require that the circumgalactic medium (CGM) of $L_*$ galaxies holds nearly all the associated baryons within a virial radius ($\sim 10^{11}M_\odot$) and hosts massive flows of cooling gas with $\approx30[nT/30{\rm~cm^{-3}K}]~M_\odot~$yr$^{-1}$, which must be largely prevented from accreting onto the host galaxy. Cooling and feedback energetics considerations require $10 <\langle nT\rangle<100{\rm~cm^{-3}K}$ for the warm and hot halo gases. We argue that virialized gas, boundary layers, hot winds, and shocks are unlikely to directly account for the bulk of the OVI. Furthermore, we show that there is a robust constraint on the number density of many of the photoionized $\sim10^4$K absorption systems that yields upper bounds in the range $n<(0.1-3)\times10^{-3}(Z/0.3)$cm$^{-3}$, where $Z$ is the metallicity, suggestive that the dominant pressure in some photoionized clouds is nonthermal. This constraint, which requires minimal ionization modeling, is in accord with the low densities inferred from more complex photoionization modeling. The large amount of cooling gas that is inferred could re-form these clouds in a fraction of the halo dynamical time, as some arguments require, and it requires much of the feedback energy available from supernovae and stellar winds to be dissipated in the CGM.
In this work we study $k$-type uniform Steiner bundles, being $k$ the lowest degree of the splitting. We prove sharp upper and lower bounds for the rank in the case $k=1$ and moreover we give families of examples for every allowed possible rank and explain which relation exists between the families. After dealing with the case $k$ in general, we conjecture that every $k$-type uniform Steiner bundle is obtained through the proposed construction technique.
Oscillating phases in Bianchi type IX anisotropic universes are obtained as linearized solutions of Einstein-Cartan theory of gravity.Instead of making use of Weyssenhoff spinning fluids we addopt axionic torsion matter where the torsion tensor is totally skew-symmetric as in Kalb-Rammond type theories.Spin-torsion,metric and matter density oscillate at different phases.
We demonstate the existence of a large $N$ phase transition with respect to the 't Hooft coupling in q-deformed Yang-Mills theory on $S^2$. The strong coupling phase is characterized by the formation of a clump of eigenvalues in the associated matrix model of Douglas-Kazakov (DK) type (hep-th/9305047). By understanding this in terms of instanton contributions to the q-deformed Yang-Mills theory, we gain some insight into the strong coupling phase as well as probe the phase diagram at nonzero values of the $\theta$ angle. The Ooguri-Strominger-Vafa relation (hep-th/0405146) of this theory to topological strings on the local Calabi-Yau $\mathcal{O}(-p) \oplus \mathcal{O}(p-2) \to \mathbb{P}^1$ via a chiral decompostion at large $N$ hep-th/0411280, motivates us to investigate the phase structure of the trivial chiral block, which corresponds to the topological string partition function, for $p>2$. We find a phase transition at a different value of the coupling than in the full theory, indicating the likely presence of a rich phase structure in the sum over chiral blocks.
Stacking-dependent interlayer interactions are important for understanding the structural and electronic properties in incommensurable two dimensional material assemblies where long-range moir\'e patterns arise due to small lattice constant mismatch or twist angles. Here, we study the stacking-dependent interlayer coupling energies between graphene (G) and hexagonal boron nitride (BN) homo- and hetero-structures using high-level random-phase approximation (RPA) ab initio calculations. Our results show that although total binding energies within LDA and RPA differ substantially between a factor of 200%-400%, the energy differences as a function of stacking configuration yield nearly constant values with variations smaller than 20% meaning that LDA estimates are quite reliable. We produce phenomenological fits to these energy differences, which allows us to calculate various properties of interest including interlayer spacing, sliding energetics, pressure gradients and elastic coefficients to high accuracy. The importance of long-range interactions (captured by RPA but not LDA) on various properties is also discussed. Parameterisations for all fits are provided.
We investigate theoretically the spatial dependence of the linear absorption spectra of single and coupled semiconductor quantum dots, where the strong three-dimensional quantum confinement leads to an overall enhancement of Coulomb interaction and, in turn, to a pronounced renormalization of the excitonic properties. We show that -because of such Coulomb correlations and the spatial interference of the exciton wavefunctions- unexpected spectral features appear whose intensity depends on spatial resolution in a highly non-monotonic way when the spatial resolution is comparable with the excitonic Bohr radius. We finally discuss how the optical near-field properties of double quantum dots are affected by their coupling.
The dimension of spaces of global sections for line bundles on semistable curves parametrized by the compactified Picard scheme is studied. The theorem of Riemann is shown to hold. The theorem of Clifford is shown to hold in the following cases: the curve has two components; the curve is any semistable curve and the degree is either 0 or 2g-2; the curve is stable, free from separating nodes, and the degree is at most 4. These results are all shown to be sharp. Applications to the Clifford index, to the combinatorial description of hyperelliptic curves, and to plane quintics are given.
We consider the KPZ equation in space dimension 2 driven by space-time white noise. We showed in previous work that if the noise is mollified in space on scale $\epsilon$ and its strength is scaled as $\hat\beta / \sqrt{|\log \epsilon|}$, then a transition occurs with explicit critical point $\hat\beta_c = \sqrt{2\pi}$. Recently Chatterjee and Dunlap showed that the solution admits subsequential scaling limits as $\epsilon \downarrow 0$, for sufficiently small $\hat\beta$. We prove here that the limit exists in the entire subcritical regime $\hat\beta \in (0, \hat\beta_c)$ and we identify it as the solution of an additive Stochastic Heat Equation, establishing so-called Edwards-Wilkinson fluctuations. The same result holds for the directed polymer model in random environment in space dimension 2.
Person re-identification is the task of matching pedestrian images across non-overlapping cameras. In this paper, we propose a non-linear cross-view similarity metric learning for handling small size training data in practical re-ID systems. The method employs non-linear mappings combined with cross-view discriminative subspace learning and cross-view distance metric learning based on pairwise similarity constraints. It is a natural extension of XQDA from linear to non-linear mappings using kernels, and learns non-linear transformations for efficiently handling complex non-linearity of person appearance across camera views. Importantly, the proposed method is very computationally efficient. Extensive experiments on four challenging datasets shows that our method attains competitive performance against state-of-the-art methods.
By a commutative action on a smooth quadric $Q_n$ in $P^{n+1}$ we mean an effective action of a commutative connected algebraic group on $Q_n$ with an open orbit. We show that for $n \geq 3$ all commutative actions on $Q_n$ are additive actions described by Sharoiko in 2009. So there is a unique commutative action on $Q_n$ up to equivalence. For $n = 2$ there are three commutative actions on $Q_2$ up to equivalence, for $n = 1$ there are two commutative actions on $Q_1$ up to equivalence.
We checked consistency between the copper abundance derived in six metal-poor stars using UV Cu II lines (which are assumed to form in LTE) and UV Cu I lines (treated in NLTE). Our program stars cover the atmosphere parameters which are typical for intermediate temperature dwarfs (effective temperature is in the range from approximately 5800 to 6100 K, surface garvity is from 3.6 to 4.5, metallicity is from about -1 to -2.6 dex). We obtained a good agreement between abundance from these two sets of the lines, and this testifies about reliability of our NLTE copper atomic model. We confirmed that no underabundace of this element is seen at low metallicities (the mean [Cu/Fe] value is about -0.2 dex, while as it follows from the previous LTE studies copper behaves as a secondary element and [Cu/Fe] ratio in the range of [Fe/H from -2 to -3 dex should be about -1 dex). According to our NLTE data the copper behaves as a primary element at low metallicity regime. We also conclude that our new NLTE copper abundance in metal-poor stars requires significant reconsideration of this element yields in the explosive nucleosynthesis.
It is a classical result that any permutation in the symmetric group can be generated by a sequence of adjacent transpositions. The sequences of minimal length are called reduced words, and in this paper we study the graphs of these reduced words, with edges determined by relations in the underlying Coxeter group. Recently, the diameter has been calculated for the longest permutation $n\ldots 21$ by Reiner and Roichman as well as Assaf. In this paper we find inductive formulas for the diameter of the graphs of 12-inflations and many 21-inflations. These results extend to the associated graphs on commutation and long braid classes. Also, these results give a recursive formula for the diameter of the longest permutation, which matches that of Reiner, Roichman and Assaf. Lastly, We make progress on conjectured bounds of the diameter by Reiner and Roichman, which are based on the underlying hyperplane arrangement, and find families of permutations that achieve the upper bound and lower bound of the conjecture. In particular permutations that avoid 312 or 231 have graphs that achieve the upper bound.
Catalan numbers arise in many enumerative contexts as the counting sequence of combinatorial structures. In this work, we consider natural Markov chains on some of the realizations of the Catalan sequence. While our main result is in deriving an $O(n^2 \log n)$ bound on the mixing time in $L_2$ (and hence total variation) distance for the random transposition chain on Dyck paths, we raise several open questions, including the optimality of the above bound. The novelty in our proof is in establishing a certain negative correlation property among random bases of lattice path matroids, including the so-called Catalan matroid which can be defined using Dyck paths.
Let $(u_n)_{n \geq 0}$ be a nondegenerate linear recurrence of integers, and let $\mathcal{A}$ be the set of positive integers $n$ such that $u_n$ and $n$ are relatively prime. We prove that $\mathcal{A}$ has an asymptotic density, and that this density is positive unless $(u_n / n)_{n \geq 1}$ is a linear recurrence.