ShantanuT01/DACTYL-Pretraining huggingface dataset:
Let $S$ be the first degeneracy locus of a morphism of vector bundles corresponding to a general matrix of linear forms in $\mathbb{P}^s$. We prove that, under certain positivity conditions, its Hilbert square $\mathrm{Hilb}^2(S)$ is isomorphic to the zero locus of a global section of an irreducible homogeneous vector bundle on a product of Grassmannians. Our construction involves a naturally associated Fano variety, and an explicit description of the isomorphism.
Charge transport through single molecules can be influenced by the charge and spin states of redox-active metal centres placed in the transport pathway. These molecular intrinsic properties are usually addressed by varying the molecules electrochemical and magnetic environment, a procedure that requires complex setups with multiple terminals. Here we show that oxidation and reduction of organometallic compounds containing either Fe, Ru or Mo centres can solely be triggered by the electric field applied to a two-terminal molecular junction. Whereas all compounds exhibit bias-dependent hysteresis, the Mo-containing compound additionally shows an abrupt voltage-induced conductance switching, yielding high to low current ratios exceeding 1000 at voltage stimuli of less than 1.0 V. DFT calculations identify a localized, redox active molecular orbital that is weakly coupled to the electrodes and closely aligned with the Fermi energy of the leads because of the spin-polarised ground state unique to the Mo centre. This situation opens an additional slow and incoherent hopping channel for transport, triggering a transient charging effect of the entire molecule and a strong hysteresis with unprecedented high low-to-high current ratios.
The stellar population models dramatically progressed with the arrival of large and complete libraries, ELODIE, CFLIB (=Indo-US) and MILES at a relatively high resolution. We show that the quality of the fits is not anymore limited by the size of the stellar libraries in a large range of ages (0.1 to 10 Gyrs) and metallicities (-2 to +0.4 dex). The main limitations of the empirical stellar libraries are (i) the coverage of the parameters space (lack of hot stars of low metallicity), (ii) the precision and homogeneity of the atmospheric parameters and (iii) the non-resolution of individual element abundances (in particular [$\alpha$/Fe]). Detailed abundance measurements in the large libraries, and usage of theoretical libraries are probably the next steps, and we show that a combination between an empirical (ELODIE) and a theoretical library (Coelho et al. 2005) immediately improves the modeling of ($\alpha$-enhanced) globular clusters.
Intrinsic transverse parton momenta pT play an important role in the understanding of azimuthal/spin asymmetries in semi-inclusive deep-inelastic scattering (SIDIS) and the Drell-Yan process (DY). We review and update what is presently known about pT from these processes. In particular, we address the question to which extent data support the popular Gauss model for the pT-distributions. We find that the Gauss model works very well, and observe that the intrinsic transverse momenta in SIDIS and DY are compatible, which is a support for the factorization approach. As a byproduct we recover a simple but practical way of taking into account the energy dependence of pT-distributions.
We have extended the range of the high-pressure optical spectroscopy to the far-infrared region keeping the accuracy of ambient-pressure experiments. The newly-developed method offers a powerful tool for the study of pressure-induced phase transitions and electronic-structural changes in correlated electron systems. The novel-type optical pressure cell, equipped with large free-aperture diamond window, allows the measurement of optical reflectivity down to $\omega\approx20-30$ cm$^{-1}$ for hydrostatic pressures up to $p\approx26$ kbar. The efficiency of the technique is demonstrated by the investigation of the 2-dimensional charge-density-wave 1$T$-TaS$_2$ whose electronic structure shows high sensitivity to external pressure. The room-temperature semi-metallic phase of 1$T$-TaS$_2$ is effectively extended by application of pressure and stabilized as the ground state above $p=14$ kbar. The corresponding fully incoherent low-energy optical conductivity is almost temperature independent below T=300 K. For intermediate pressures, the onset of the low-temperature insulating phase is reflected by the sudden drop of the reflectivity and by the emergence of sharp phonon resonances.
A collection of unlabelled tournaments P is called a hereditary property if it is closed under isomorphism and under taking induced sub-tournaments. The speed of P is the function n -> |P_n|, where P_n = {T \in P : |V(T)| = n}. In this paper, we prove that there is a jump in the possible speeds of a hereditary property of tournaments, from polynomial to exponential speed. Moreover, we determine the minimal exponential speed, |P_n| = c^(n + o(n)), where c = 1.47... is the largest real root of the polynomial x^3 = x^2 + 1, and the unique hereditary property with this speed.
Given a pair of n-dimensional complex Galois representations over Q, we define their matching density to be the density, if it exists, of the set of places at which the traces of Frobenius of the two Galois representations are equal. We will show that the set of matching densities of such pairs of irreducible Galois representations (for all n) is dense in the interval [0, 1]. Under the strong Artin conjecture, this also implies the corresponding statement for cuspidal automorphic representations.
We consider a homogenous fragmentation process with killing at an exponential barrier. With the help of two families of martingales we analyse the growth of the largest fragment for parameter values that allow for survival. In this respect the present paper is also concerned with the probability of extinction of the killed process.
This is an English translation of the paper M.B.Mensky, in: K.P.Stanyukovich (ed.), "Problems of Theory of Gravity and Elementary Particles", issue 6, Moscow, Atomizdat, 1975, p.181-190 (in Russian). This paper elaborates further the idea (formulated in 1971 by Braginsky and Mensky) of detecting high-frequency gravitational waves by observing resonance action of a gravitational wave on the electromagnetic wave in a closed resonator (waveguide). The phenomenon underlying such a detector was called gravitational-electromagnetic resonance (GER). In the present paper both closed (for example circular) resonator or waveguide and long (for example in the shape of a spiral) waveguide are considered as possible gravitational-wave detectors. High-frequency gravitational-wave detectors are now again actual (see A.M.Cruise and R.M.J.Ingley, Class. Quant. Grav. 22, S479, 2005), but the current literature on this topic does not cover all the issues discussed in the present paper.
The insulating magnetic material Fe3PO4O3 features a non-centrosymmetric lattice composed of Fe^{3+} triangular units. Frustration, due to competing near neighbor ($J_1$) and next nearest neighbor ($J_2$) antiferromagnetic interactions, was recently suggested to be the origin of an antiferromagnetic helical ground state with unusual needle-like nanoscale magnetic domains in Fe3PO4O3. Magnetic dilution is shown here to tune the ratio of these magnetic interactions, thus providing deeper insight into this unconventional antiferromagnet. Dilution of the Fe^{3+} lattice in Fe3PO4O3 was accomplished by substituting non-magnetic Ga^{3+} to form the solid solution series Fe_{3-x}Ga_xPO4O3 with $x = 0.012, 0.06, 0.25, 0.5, 1.0, 1.5$. Magnetic susceptibility and neutron powder diffraction data from this series are presented. A continuous decrease of the both the helical pitch length and the domain size is observed with increasing dilution up to at least $x = 0.25$, while for $x \ge 0.5$, the compounds lack long range magnetic order entirely. The decrease in the helical pitch length with increasing $x$ can be qualitatively understood by reduction of the ratio of $J_2/J_1$ in the Heisenberg model, consistent with mean field considerations. Intriguingly, the magnetic correlation length in the $ab$ plane remains nearly equal to the pitch length for each value of $x \le 0.25$, showing that the two quantities are intrinsically connected in this unusual antiferromagnet.
The concentrations of dark matter haloes provide crucial information about their internal structure and how it depends on mass and redshift -- the so-called concentration-mass-redshift relation, denoted $c(M,z)$. We present here an extensive study of the cosmology-dependence of $c(M,z)$ that is based on a suite of 72 gravity-only, full N-body simulations in which the following cosmological parameters were varied: $\sigma_{8}$, $\Omega_{\mathrm{M}}$, $\Omega_{\mathrm{b}}$, $n_{\mathrm{s}}$, $h$, $M_{\nu}$, $w_{0}$ and $w_{\mathrm{a}}$. We characterize the impact of these parameters on concentrations for different halo masses and redshifts. In agreement with previous works, and for all cosmologies studied, we find that there exists a tight correlation between the characteristic densities of dark matter haloes within their scale radii, $r_{-2}$, and the critical density of the Universe at a suitably defined formation time. This finding, when combined with excursion set modelling of halo formation histories, allows us to accurately predict the concentrations of dark matter haloes as a function of mass, redshift, and cosmology. We use our simulations to test the reliability of a number of published models for predicting halo concentration and highlight when they succeed or fail to reproduce the cosmological $c(M,z)$ relation.
We report transport measurements of electrons on helium in a microchannel device where the channels are 200 nm deep and 3 $\mu$m wide. The channels are fabricated above amorphous metallic Ta$_{40}$W$_{40}$Si$_{20}$, which has surface roughness below 1 nm and minimal variations in work function across the surface due to the absence of polycrystalline grains. We are able to set the electron density in the channels using a ground plane. We estimate a mobility of 300 cm$^2$/V$\cdot$s and electron densities as high as 2.56$\times$10$^9$ cm$^{-2}$. We demonstrate control of the transport using a barrier which enables pinchoff at a central microchannel connecting two reservoirs. The conductance through the central microchannel is measured to be 10 nS for an electron density of 1.58$\times$10$^9$ cm$^{-2}$. Our work extends transport measurements of surface electrons to thin helium films in microchannel devices above metallic substrates.
We study and compare fitting methods for the Lyman-$\alpha$ (Ly$\alpha$) forest 3D correlation function. We use the nested sampler PolyChord and the community code picca to perform a Bayesian analysis which we compare with previous frequentist analyses. By studying synthetic correlation functions, we find that the frequentist profile likelihood produces results in good agreement with a full Bayesian analysis. On the other hand, Maximum Likelihood Estimation with the Gaussian approximation for the uncertainties is inadequate for current data sets. We compute for the first time the full posterior distribution from the Ly$\alpha$ forest correlation functions measured by the extended Baryon Oscillation Spectroscopic Survey (eBOSS). We highlight the benefits of sampling the full posterior distribution by expanding the baseline analysis to better understand the contamination by Damped Ly$\alpha$ systems (DLAs). We make our improvements and results publicly available as part of the picca package.
Robust and accurate planar tracking over a whole video sequence is vitally important for many vision applications. The key to planar object tracking is to find object correspondences, modeled by homography, between the reference image and the tracked image. Existing methods tend to obtain wrong correspondences with changing appearance variations, camera-object relative motions and occlusions. To alleviate this problem, we present a unified convolutional neural network (CNN) model that jointly considers homography, visibility, and confidence. First, we introduce correlation blocks that explicitly account for the local appearance changes and camera-object relative motions as the base of our model. Second, we jointly learn the homography and visibility that links camera-object relative motions with occlusions. Third, we propose a confidence module that actively monitors the estimation quality from the pixel correlation distributions obtained in correlation blocks. All these modules are plugged into a Lucas-Kanade (LK) tracking pipeline to obtain both accurate and robust planar object tracking. Our approach outperforms the state-of-the-art methods on public POT and TMT datasets. Its superior performance is also verified on a real-world application, synthesizing high-quality in-video advertisements.
The glass transition temperature (Tg) is the temperature, after which the supercooled liquid undergoes a dynamical arrest. Usually, the glass network modifiers (e.g., Na2O) affect the behavior of Tg. However, in aluminosilicate glasses, the effect of different modifiers on Tg is still unclear and show an anomalous behavior. Here, based on molecular dynamics simulations, we show that the glass transition temperature decreases with increasing charge balancing cations field strength (FS) in the aluminosilicate glasses, which is an anomalous behavior as compared to other oxide glasses. The results show that the origins of this anomaly come from the dynamics of the supercooled liquid above Tg, which in turn is correlated to pair excess entropy. Our results deepen our understanding of the effect of different modifiers on the properties of the aluminosilicate glasses.
A Platonic surface is a Riemann surface that underlies a regular map and so we can consider its vertices, edge-centres and face-centres. A symmetry (anticonformal involution) of the surface will fix a number of simple closed curves which we call mirrors. These mirrors must pass through the vertices, edge-centres and face-centres in some sequence which we call the pattern of the mirror. Here we investigate these patterns for various well-known families of Platonic surfaces, including genus 1 regular maps, and regular maps on Hurwitz surfaces and Fermat curves. The genesis of this paper is classical. Klein in Section 13 of his famous 1878 paper [11], worked out the pattern of the mirrors on the Klein quartic and Coxeter in his book on regular polytopes worked out the patterns for mirrors on the regular solids. We believe that this topic has not been pursued since then.
We formulate an equivalence between the 2-dim $\sigma$-model spectrum expanded on a non-trivial massive vacuum and a classical particle Hamiltonian with variable mass and potential. By considering methods of analytic Galoisian non-integrability on appropriate geodesics of the Hamiltonian system we algebraically constrain the particle masses at fixed time, such that integrability is allowed. Through our equivalence this explicitly constrains the masses of the excited spectrum of the dual 2-dim theory in such a way to imply the S-matrix factorization and no particle production. In particular, the integrability of the classical particle system, implies the factorization of the S-matrix in the dual quantum 2-dim theory. Our proposal provides also non-trivial evidence without any assumptions, on the connection between integrability and S-matrix factorization for large class of theories with interactions that break Lorentz invariance.
A major challenge in brain tumor treatment planning and quantitative evaluation is determination of the tumor extent. The noninvasive magnetic resonance imaging (MRI) technique has emerged as a front-line diagnostic tool for brain tumors without ionizing radiation. Manual segmentation of brain tumor extent from 3D MRI volumes is a very time-consuming task and the performance is highly relied on operator's experience. In this context, a reliable fully automatic segmentation method for the brain tumor segmentation is necessary for an efficient measurement of the tumor extent. In this study, we propose a fully automatic method for brain tumor segmentation, which is developed using U-Net based deep convolutional networks. Our method was evaluated on Multimodal Brain Tumor Image Segmentation (BRATS 2015) datasets, which contain 220 high-grade brain tumor and 54 low-grade tumor cases. Cross-validation has shown that our method can obtain promising segmentation efficiently.
We make use of micro-magneto Raman scattering spectroscopy to probe magneto-phonon resonances (MPR) in suspended mono- to penta-layer graphene. MPR correspond to avoided crossings between zone-center optical phonons (G-mode) and optically-active inter Landau level (LL) transitions and provide a tool to perform LL spectroscopy at a fixed energy ($\approx 197~\rm{meV}$) set by the G-mode phonon. Using a single-particle effective bilayer model, we readily extract the velocity parameter associated with each MPR. A single velocity parameter slightly above the bulk graphite value suffices to fit all MPR for $N\geq2$ layer systems. In contrast, in monolayer graphene, we find that the velocity parameter increases significantly from $(1.23\pm 0.01) \times 10^6~\mathrm{m.s^{-1}}$ up to $(1.45\pm0.02) \times 10^6~\mathrm{m.s^{-1}}$ as the first to third optically-active inter LL transition couple to the G-mode phonon. This result is understood as a signature of enhanced many-body effects in unscreened graphene.
We consider a model of quantum computation in which the set of elementary operations is limited to Clifford unitaries, the creation of the state $|0\rangle$ computational basis. In addition, we allow the creation of a one-qubit ancilla in a mixed state $\rho$, which should be regarded as a parameter of the model. Our goal is to determine for which $\rho$ universal quantum computation (UQC) can be efficiently simulated. To answer this question, we construct purification protocols that consume several copies of $\rho$ and produce a single output qubit with higher polarization. The protocols allow one to increase the polarization only along certain "magic" directions. If the polarization of $\rho$ along a magic direction exceeds a threshold value (about 65%), the purification asymptotically yields a pure state, which we call a magic state. We show that the Clifford group operations combined with magic states preparation are sufficient for UQC. The connection of our results with the Gottesman-Knill theorem is discussed.
We present an experimental study of the non-classical correlations of a pair of spatial qubits formed by passing two down-converted photons through a pair of double slits. After confirming the entanglement generated in our setup by quantum tomography using separate measurements of the slit images and the interference patterns, we show that the complete Hilbert space of the spatial qubits can be accessed by measurements performed in a single plane between the image plane and the focal plane of a lens. Specifically, it is possible to obtain both the which-path and the interference information needed for quantum tomography in a single scan of the transversal distribution of photon coincidences. Since this method can easily be extended to multi-dimensional systems, it may be a valuable tool in the application of spatial qudits to quantum information processes.
We provide a simple, unified approach to describing the impact of super-sample covariance, or beat coupling, on power spectrum estimation in a finite-volume survey. For a wide range of survey volumes, the sample variance that arises from modes that are larger than the survey dominates the covariance of power spectrum estimators for modes much smaller than the survey. The deeply nonlinear version of this effect is known as halo sample variance. We show that all variants are unified by the matter trispectrum of squeezed configurations and that such configurations obey a consistency relation which relates them to the response of the power spectrum to a change in the background density. Our method also applies to statistics that are based on radial projections of the density field such as weak lensing shear. While we use the halo model for an analytic description to expose the nature of the effect, the consistency description enables an accurate calibration of the full effect directly from simulations. It also suggests that super-sample covariance may be viewed as an additional interesting signal rather than excess noise.
Modeling the long-term facial aging process is extremely challenging due to the presence of large and non-linear variations during the face development stages. In order to efficiently address the problem, this work first decomposes the aging process into multiple short-term stages. Then, a novel generative probabilistic model, named Temporal Non-Volume Preserving (TNVP) transformation, is presented to model the facial aging process at each stage. Unlike Generative Adversarial Networks (GANs), which requires an empirical balance threshold, and Restricted Boltzmann Machines (RBM), an intractable model, our proposed TNVP approach guarantees a tractable density function, exact inference and evaluation for embedding the feature transformations between faces in consecutive stages. Our model shows its advantages not only in capturing the non-linear age related variance in each stage but also producing a smooth synthesis in age progression across faces. Our approach can model any face in the wild provided with only four basic landmark points. Moreover, the structure can be transformed into a deep convolutional network while keeping the advantages of probabilistic models with tractable log-likelihood density estimation. Our method is evaluated in both terms of synthesizing age-progressed faces and cross-age face verification and consistently shows the state-of-the-art results in various face aging databases, i.e. FG-NET, MORPH, AginG Faces in the Wild (AGFW), and Cross-Age Celebrity Dataset (CACD). A large-scale face verification on Megaface challenge 1 is also performed to further show the advantages of our proposed approach.
This paper is a natural continuation of a joint paper with Bajpai, Harder and Moya Giusti \cite{BHHM}, even though it began as an answer to Goncharov's question. It that paper, we had complete description for all representations except for odd symmetric powers and their dual ones. For those representations we were left with two options: certain one dimensional module is a ghost space or not. Here we find the $H^2(SL_3(\Z),V_3)$ has ghost classes. It means that it is generated by a class from the cohomology of the Borel subgroup.   With the techniques developed here, we show that the $d_2$ map of the spectral sequence for the boundary cohomology of $GL_4(\Z)$ is non-trivial if and only if there is a ghost class in $GL_3(\Z)$ (see Propositions 11 and 12.) We use a result of Elbaz-Vincent, Gangl and Soule to show that a spectral sequence related to $GL_4(\Z)$ does not degenerate at $E_2$-level. Then $d_2$ is non-trivial. Therefore, we obtain that $H^2(SL_3(\Z),V_3))$ is a ghost space, where $V_3$ is the standard representation.
The method of maximum entropy is used to model curved physical space in terms of points defined with a finite resolution. Such a blurred space is automatically endowed with a metric given by information geometry. The corresponding space-time is such that the geometry of any embedded spacelike surface is given by its information geometry. The dynamics of blurred space, its geometrodynamics, is constructed by requiring that as space undergoes the deformations associated with evolution in local time, it sweeps a four-dimensional space-time. This reproduces Einstein's equations for vacuum gravity. We conclude with brief comments on some of the peculiar properties of blurred space: There is a minimum length and blurred points have a finite volume. There is a relativistic "blur dilation". The volume of space is a measure of its entropy.