ShantanuT01/DACTYL-Pretraining huggingface dataset:
Given a morphism between complex projective varieties, we make several conjectures on the relations between the set of pseudo-effective (co)homology classes which are annihilated by pushforward and the set of classes of varieties contracted by the morphism. We prove these conjectures for classes of curves or divisors. We also prove that one of these conjectures implies Grothendieck's generalized Hodge conjecture for varieties with Hodge coniveau at least 1.
In this paper we establish some relations between percolation on a given graph G and its geometry. Our main result shows that, if G has polynomial growth and satisfies what we call the local isoperimetric inequality of dimension d > 1, then p_c(G) < 1. This gives a partial answer to a question of Benjamini and Schramm. As a consequence of this result we derive, under the additional condition of bounded degree, that these graphs also undergo a non-trivial phase transition for the Ising-Model, the Widom-Rowlinson model and the beach model. Our techniques are also applied to dependent percolation processes with long range correlations. We provide results on the uniqueness of the infinite percolation cluster and quantitative estimates on the size of finite components. Finally we leave some remarks and questions that arise naturally from this work.
In d+1 dimensions we solve the equations of motion for the case of gravity minimally or conformally coupled to a scalar field. For the minimally coupled system the equations can either be solved directly or by transforming vacuum solutions, as shown before in 3+1 dimensions by Buchdahl. In d+1 dimensions the solutions have been previously found directly by Xanthopoulos and Zannias. Here we first rederive these earlier results, and then extend Buchdahl's method of transforming vacuum solutions to d+1 dimensions. We also review the conformal coupling case, in which d+1 dimensional solutions can be found by extending Bekenstein's method of conformal transformation of the minimal coupling solution. Combining the extended versions of Buchdahl transformations and Bekenstein transformations we can in arbitrary dimensions always generate solutions of both the minimal and the conformal equations from known vacuum solutions.
We have developed an efficient method for quantum number projection from most general HFB type mean-field states, where all the symmetries like axial symmetry, number conservation, parity and time-reversal invariance are broken. Applying the method, we have microscopically calculated, for the first time, the energy spectra based on the exotic tetrahedral deformation in $^{108,110}$Zr. The nice low-lying rotational spectra, which have all characteristic features of the molecular tetrahedral rotor, are obtained for large tetrahedral deformation, $\alpha_{32} \gtsim 0.25$, while the spectra are of transitional nature between vibrational and rotational with rather high excitation energies for $\alpha_{32}\approx 0.1-0.2$
We analyze the impact of electron and positron beam polarization on radiative neutralino production at the International Linear Collider (ILC). We focus on three different mSUGRA scenarios in turn at the Higgs strahlung threshold, the top pair production threshold, and at $\sqrt{s} =500\GeV$. In these scenarios at the corresponding $\sqrt{s}$, radiative neutralino production is the only supersymmetric production mechanism which is kinematically allowed. The heavier neutralinos, and charginos as well as the sleptons, squarks and gluinos are too heavy to be pair produced. We calculate the signal cross section and also the Standard Model background from radiative neutrino production. For our scenarios, we obtain significances larger than 10 and signal to background ratios between 2% and 5%, if we have electron beam polarization $P_{e^-} = 0.0- 0.8$ and positron beam polarization $P_{e^+} = 0.0 - 0.3$. If we have electron beam polarization of $P_{e^-} = 0.9$, then the signal is observable with $P_{e^+} = 0.0$ but both the significance and the signal to background ratio are significantly improved for $P_{e^+} = 0.3$.
Previous studies have demonstrated that gravitational radiation reliably encodes information about the natural emission direction of the source (e.g., the orbital plane). In this paper, we demonstrate that these orientations can be efficiently estimated by the principal axes of <L_a L_b>, an average of the action of rotation group generators on the Weyl tensor at asymptotic infinity. Evaluating this average at each time provides the instantaneous emission direction. Further averaging across the entire signal yields an average orientation, closely connected to the angular components of the Fisher matrix. The latter direction is well-suited to data analysis and parameter estimation when the instantaneous emission direction evolves significantly. Finally, in the time domain, the average <L_a L_b> provides fast, invariant diagnostics of waveform quality.
We prove the existence of a class of plane symmetric perfect-fluid cosmologies with a (-1/3, 2/3, 2/3) Kasner-like singularity. These solutions of the Einstein equations depend on two smooth functions of one space coordinate. They are constructed by solving a symmetric hyperbolic system of Fuchsian equations.
We present a deep Chandra X-ray Observatory study of the peculiar binary radio millisecond pulsar PSR J1740--5340 and candidate millisecond pulsars (MSPs) in the globular cluster NGC 6397. The X-rays from PSR J1740--5340 appear to be non-thermal and exhibit variability at the binary period. These properties suggest the presence of a relativistic intrabinary shock formed due to interaction of a relativistic rotation-powered pulsar wind and outflow from the unusual "red-straggler/sub-subgiant" companion. We find the X-ray source U18 to show similar X-ray and optical properties to those of PSR J1740--5340, making it a strong MSP candidate. It exhibits variability on timescales from hours to years, also consistent with an intrabinary shock origin of its X-ray emission. The unprecedented depth of the X-ray data allows us to conduct a complete census of MSPs in NGC 6397. Based on the properties of the present sample of X-ray--detected MSPs in the Galaxy we find that NGC 6397 probably hosts no more than 6 MSPs.
This paper deals with numerical methods for reconstruction of inhomogeneous conductivities. We use the concept of Generalized Polarization Tensors, which were introduced in [3], to do reconstruction. Basic resolution and stability analysis are presented. Least square norm methods with respect to Generalized Polarization Tensors are used for reconstruction of conductivities. Finally, reconstruction of three different types of conductivities in the plane is demonstrated.
Let $A$ be an Azumaya algebra over a field. If $G$ is the group of automorphisms of $A$ and $X$ denotes a projective homogeneous variety under $G$, we construct in a very explicit way and under suitable hypotheses a bundle $\mathcal{V}$ on $S$, where $S$ is a (generalized) Severi-Brauer variety associated to $A$, and a canonical isomorphism between $X$ and a flag bundle on $\mathcal{V}$. This allows to explicitely compute Chow groups of $X$ in terms of the Chow groups of $S$.
We study properties of (D$(p-2)$, D$p$) nonthreshold bound states ($2 \le p \le 6 $) in the dual gravity description. These bound states can be viewed as D$p$-branes with a nonzero NS $B$ field of rank two. We find that in the decoupling limit, the thermodynamics of the $N_p$ coincident D$p$-branes with $B$ field is the same not only as that of $N_p$ coincident D$p$-branes without $B$ field, but also as that of the $N_{p-2}$ coincident D$(p-2)$-branes with two smeared coordinates and no $B$ field, for $N_{p-2}/N_p= \tilde{V}_2/[(2\pi)^2 \tilde{b}]$ with $\tilde{V}_2$ being the area of the two smeared directions and $\tilde{b}$ a noncommutativity parameter. We also obtain the same relation from the thermodynamics and dynamics by probe methods. This suggests that the noncommutative super Yang-Mills with gauge group $U(N_p)$ in ($p+1$) dimensions is equivalent to an ordinary one with gauge group $U(\infty)$ in ($p-1$) dimensions in the limit $\tilde{V}_2 \to \infty$. We also find that the free energy of a D$p$-brane probe with $B$ field in the background of D$p$-branes with $B$ field coincides with that of a D$p$-brane probe in the background of D$p$-branes without $B$ field.
In this paper we study the mean of the first exit time from a bounded interval of various L\'evy processes. We establish sharp two-sided estimates of the mean for L\'evy processes under certain condition on their characteristic exponents. We also study the cumulative distribution function of the supremum and infimum processes. Finally, we establish integral conditions that assure that the renewal function of the ladder height process is comparable with the linear one.
Gaussian linking of a semiclassical path of a charged particle with a magnetic flux tube is responsible for the Aharonov-Bohm effect, where one observes interference proportional to the magnitude of the enclosed flux. We construct quantum mechanical wave functions where semiclassical paths can have second order linking to two magnetic flux tubes, and show there is interference proportional to the product of the two fluxes.
The Milky Way has been estabished to emit gamma rays. These gamma rays are presumably dominated by decays of neutral pions, although inverse Compton scatterings and bremsstrahlung also contribute. It is plausible that other galaxies can be diffuse sources of gamma rays in a similar manner. Starburst galaxies are particularly interesting to study as they are expected to have much higher cosmic-ray fluxes and interstellar matter densities. The neutral pions are created in cosmic-ray interactions with interstellar matter. Presented here is an overview of the recent work by Karlsson and co-workers on proton-proton interactions and the resulting secondary particle inclusive cross sections and angular distributions. This model can be used to calculated the $\pi^{0}$ component of the gamma-ray yield and spectrum from a starburst galaxy. The yield is expected to increase significantly (30% to 50%) and the spectrum to be harder than the incident proton spectrum.
It is currently impossible to determine the abundances and ages of the stellar populations of distant, dense stellar systems star by star. Therefore, methods to analyze the composite light of stellar systems are required. I review the modelling and analysis of integrated spectra of the stellar populations of individual globular clusters, globular cluster systems, early-type galaxies, and the bulges of spiral galaxies, with a focus on their abundances and abundance ratios. I conclude with a list of continuing difficulties in the modelling that complicate the interpretation of integrated spectra as well as a look ahead to new methods and new observations.
Ternary real-valued quartics in $\mathbb{R}^3$ being invariant under octahedral symmetry are considered. The geometric classification of these surfaces is given. A new type of surfaces emerge from this classification.
Feedback by active galactic nuclei (AGNs) is essential for regulating the fast radiative cooling of low-entropy gas at the centers of galaxy clusters and for reducing star formation rates of central ellipticals. The details of self-regulation depend critically on the unknown contents of AGN-inflated bubbles. Observations of the Sunyaev-Zeldovich (SZ) signal of AGN bubbles provide us with the ability to directly measure the lobe electron pressure given a bubble morphology. Here we compute the SZ signal of jet-inflated bubbles in three-dimensional magnetohydrodynamical simulations of the galaxy cluster MS0735.6+7421 with the Arepo code, and compare our synthetic SZ results to inferences obtained with popular modelling approaches. We find that cutting out ellipsoidal bubbles from a double-beta pressure profile only matches the inner bubble edges in the simulations and fails to account for the emission of the shock-enhanced pressure cocoon outside the bubbles. This additional contribution significantly worsens the accuracy of the cut-out method for jets with small inclinations with respect to the line of sight. Also, the kinetic SZ effect of the bubbles, a previously neglected contribution, becomes relevant at these smaller inclinations due to entrainment and mixing of the intracluster medium with low-density jet material. Fortunately, the different signs of the kinetic SZ signal in opposite lobes allow modelling this effect. We present an approximate method to determine the jet inclination, which combines jet power and lifetime estimates, the stand-off distance between jet head and bow shock, and the kinetic SZ effect, thereby helping to correctly infer the bubble contents.
Since 1999 we carried out seven trial VLBI radar experiments under LFVN project. The aim of this work is to adjust new research technique for investigating the Solar system bodies (planets, asteroids, space debris). It is planned to obtain the information on their movement parameters, proper rotation and structure of surface. The transmitter of Evpatoria RT-70 sounded the space objects. Array of Bear Lakes RT-64, Noto RT-32, Urumqi RT-25, Simeiz RT-22 received the echo-signals. The data were processed with NIRFI-3 Mk-2 correlator in N. Novgorod, Russia and NRTV processor in Noto, Italy. The first results of these experiments are presented.
We study nonlinear sigma model, especially Skyrme model with twist: twisted Skyrmion string where twist term, $mkz$, is indicated in vortex solution. To add gravity, we replace $\eta^{\mu\nu}$ in Lagrangian system with a space-time metric tensor, $g^{\mu\nu}$, which in view of the time-independence and cylindrical symmetry of the assumed vortex solution is taken to be a function of $r$ alone. We use ode45 for numerical calculation, i.e. a tool box in Matlab to solve coupled Einstein field equations which have ordinary differential equations (ODE) form.
We study the following coupled Schr\"{o}dinger equations which have appeared as several models from mathematical physics: {displaymath} {cases}-\Delta u_1 +\la_1 u_1 = \mu_1 u_1^3+\beta u_1 u_2^2, \quad x\in \Omega, -\Delta u_2 +\la_2 u_2 =\mu_2 u_2^3+\beta u_1^2 u_2, \quad x\in \Om, u_1=u_2=0 \,\,\,\hbox{on \,$\partial\Om$}.{cases}{displaymath} Here $\Om$ is a smooth bounded domain in $\R^N (N=2, 3)$ or $\Om=\RN$, $\la_1,\, \la_2$, $\mu_1,\,\mu_2$ are all positive constants and the coupling constant $\bb<0$. We show that this system has infinitely many sign-changing solutions. We also obtain infinitely many semi-nodal solutions in the following sense: one component changes sign and the other one is positive. The crucial idea of our proof, which has never been used for this system before, is turning to study a new problem with two constraints. Finally, when $\Om$ is a bounded domain, we show that this system has a least energy sign-changing solution, both two components of which have exactly two nodal domains, and we also study the asymptotic behavior of solutions as $\beta\to -\infty$ and phase separation is expected.
In this paper we use the dynamical methods to establish the existence of nontrivial solution for a class of nonlocal problem of the type $$ \left\{\begin{array}{l} -a\left(x,\int_{\Omega}g(u)\,dx \right)\Delta u =f(u), \quad x \in \Omega \\ u=0, \hspace{2 cm} x \in \partial \Omega, \end{array}\right. \leqno{(P)} $$ where $\Omega \subset \mathbb{R}^N \, ( N \geq 2)$ is a smooth bounded domain and $a:\overline{\Omega} \times \mathbb{R} \to \mathbb{R}$ and $g,f: \mathbb{R} \to \mathbb{R}$ are $C^1$-functions that satisfy some technical conditions.
Multidimensional model describing the "cosmological" and/or spherically symmetric configuration with n+1 Einstein spaces in the theory with several scalar fields and forms is considered. When electro-magnetic composite p-brane ansatz is adopted, n "internal" spaces are Ricci-flat, one space M_0 has a non-zero curvature, and all p-branes do not "live" in M_0, a class of exact solutions is obtained if certain block-orthogonality relations on p-brane vectors are imposed. A subclass of spherically-symmetric solutions containing non-extremal p-brane black holes is considered. Post-Newtonian parameters are calculated and some examples are considered.
We investigate some probabilistic aspects of the unique global strong solution of a two dimensional system of stochastic differential equations describing a prey-predator model perturbed by Gaussian noise. We first establish, for any fixed $t> 0$, almost sure upper and lower bounds for the components $X(t)$ and $Y(t)$ of the solution vector: these explicit estimates emphasize the interplay between the various parameters of the model and agree with the asymptotic results found in the literature. Then, standing on the aforementioned bounds, we derive upper and lower estimates for the joint moments and distribution function of $(X(t),Y(t))$. Our analysis is based on a careful use of comparison theorems for stochastic differential equations and exploits several peculiar features of the noise driving the equation.
Magnetic field emerges at the surface of the Sun as sunspots and active regions. This process generates a poloidal magnetic field from a rising toroidal flux tube, it is a crucial but poorly understood aspect of the solar dynamo. The emergence of magnetic field is also important because it is a key driver of solar activity. We show that measurements of horizontal flows at the solar surface around emerging active regions, in combination with numerical simulations of solar magnetoconvection, can constrain the subsurface rise speed of emerging magnetic flux. The observed flows imply that the rise speed of the magnetic field is no larger than 150 m/s at a depth of 20 Mm, that is, well below the prediction of the (standard) thin flux tube model but in the range expected for convective velocities at this depth. We conclude that convective flows control the dynamics of rising flux tubes in the upper layers of the Sun and cannot be neglected in models of flux emergence.
From the random matrix theory all the energy levels should be strongly correlated due to the presence of all off-diagonal entries.In this work we introduce two new statistics to more accurately characterize these long-distance interactions in the disordered many-body systems with only short-range interaction. In the $(p, q)$ statistics, we directly measure the long distance energy level spacings, while in the second approach, we randomly eliminate some of the energy levels, and then measure the reserved $\eta\%$ energy levels using nearest-neighbor level spacings. We benchmark these results using the results in standard Gaussian ensembles. Some analytical distribution functions with extremely high accuracy are derived, which automatically satisfy the inverse relation and duality relation. These two measurements satisfy the same universal scaling law during the transition from the Gaussian ensembles to the Poisson ensemble, with critical disorder strength and corresponding exponent are independent of these measurements. These results shade new insight into the stability of many-body localized phase and their universal properties in the disordered many-body systems.
In this note, we use crystalline methods and the Tate-conjecture to give a short proof that the Picard rank of an Enriques surface is equal to its second Betti number.
According to the Bloch-Beilinson conjectures, an automorphism of a K3 surface X that acts as the identity on the transcendental lattice should act trivially on CH^2(X). We discuss this conjecture for symplectic involutions and prove it in one third of all cases. The main point is to use special elliptic K3 surfaces and stable maps to produce covering families of elliptic curves on the generic K3 surface that are invariant under the involution.
Despite significant advances in clustering methods in recent years, the outcome of clustering of a natural image dataset is still unsatisfactory due to two important drawbacks. Firstly, clustering of images needs a good feature representation of an image and secondly, we need a robust method which can discriminate these features for making them belonging to different clusters such that intra-class variance is less and inter-class variance is high. Often these two aspects are dealt with independently and thus the features are not sufficient enough to partition the data meaningfully. In this paper, we propose a method where we discover these features required for the separation of the images using deep autoencoder. Our method learns the image representation features automatically for the purpose of clustering and also select a coherent image and an incoherent image simultaneously for a given image so that the feature representation learning can learn better discriminative features for grouping the similar images in a cluster and at the same time separating the dissimilar images across clusters. Experiment results show that our method produces significantly better result than the state-of-the-art methods and we also show that our method is more generalized across different dataset without using any pre-trained model like other existing methods.
Let $u$ be a weak solution of the free boundary problem $$\mathcal L u=\lambda_0 \mathcal H^1\lfloor\partial\{u>0\}, u\ge 0,$$ where $\mathcal L u={\text{div}}(g(\nabla u)\nabla u)$ is a quasilinear elliptic operator and $g(\xi)$ is a given function of $\xi$ satisfying some structural conditions. We prove that the free boundary $\partial\{ u>0\}$ is continuously differentiable in $\mathbb R^2$, provided that $\partial\{ u>0\}$ has locally finite connectivity. Moreover, we show that the free boundaries of weak solutions with finite $\it{Morse \ index}$ must have finite connectivity. The weak solutions are locally Lipschitz continuous and non-degenerate stationary points of the Alt-Caffarelli type functional $J[u]=\int_{\Omega}F(\nabla u)+Q^2\chi_{\{ u>0\}}$.   The full regularity of the free boundary is not fully understood even for the {\it minimizers} of $J[u]$ in the simplest case $g(\xi)=|\xi|^{p-2}, p>1$, partly because the methods from the classical case $p=2$ cannot be generalized to the full range of $p$. Our method, however, is very geometric and works even for the $ stationary\ points$ of the functional $J[u]$ for a large class of nonlinearities $F$.
An attempt is made to promote an analogy between quantized vortex in condensed matter and black hole: both compact objects have fermion zero modes which induce the finite temperature of these objects. The motion of the quantized vortex lines in Fermi superfluids and superconductors leads to the spectral flow of fermion zero mode. This results in finite temperature and entropy of the moving vortex. The tunneling transition rate between the fermionic levels under the influence of the vortex motion suggests the effective temperature of the vortex core $T_{\rm eff}=(2/\pi) p_Fv_L$, where $v_L$ is the velocity of the vortex with respect to the heat bath reference frame and $p_F$ the Fermi momentum. This is an analogue of the Unruh temperature of the accelerating object in the relativistic system. For the vortex ring with the radius $R$ this leads to the Hawking type temperature $T_{\rm vortex~ring}=(\hbar v_F / 2\pi R) \ln (R/r_c)$, where $v_F$ is the Fermi velocity and $r_c$ is the radius of the vortex core. The corresponding "Hawking" entropy of the vortex ring of radius $R$ and area $A=\pi R^2$ appears to be ${\cal S}_{\rm vortex ~ring}=(1/6) A p_F^2$. Similar expression but with different numerical factor is obtained for the instanton action for the quantum nucleation of the vortex loop from the homogeneous vacuum, and also for the "Bekenstein" entropy obtained by counting the number of fermionic bound states which appear when the vortex loop is created. For the superfluid $^3$He-A, where some components of the order parameter play the part of the gravitational field, the Fermi momentum $p_F$ corresponds to the Planck scale for this effective gravity. The effective action for the gravity field is obtained after integration over the fermion fields in correspondence with the Sakharov