ShantanuT01/DACTYL-Pretraining huggingface dataset:
This work is devoted to study the asymptotic behavior of critical points $\{(u_\varepsilon,v_\varepsilon)\}_{\varepsilon>0}$ of the Ambrosio-Tortorelli functional. Under a uniform energy bound assumption, the usual $\Gamma$-convergence theory ensures that $(u_\varepsilon,v_\varepsilon)$ converges in the $L^2$-sense to some $(u_*,1)$ as $\varepsilon\to 0$, where $u_*$ is a special function of bounded variation. Assuming further the Ambrosio-Tortorelli energy of $(u_\varepsilon,v_\varepsilon)$ to converge to the Mumford-Shah energy of $u_*$, the later is shown to be a critical point with respect to inner variations of the Mumford-Shah functional. As a byproduct, the second inner variation is also shown to pass to the limit. To establish these convergence results, interior ($\mathscr{C}^\infty$) regularity and boundary regularity for Dirichlet boundary conditions are first obtained for a fixed parameter $\varepsilon>0$. The asymptotic analysis is then performed by means of varifold theory in the spirit of scalar phase transition problems.
The dark energy issue is focusing the attention of an incresing number of physicists all over the world. Among the possible alternatives in order to explain what as been named the "Mystery of the Millennium" are the so-called Modified Theories of Gravity. A crucial test for such models is represented by the existence and (if this is the case) the properties of their black hole solutions. Nowadays, to our knowledge, only two non-trivial, spherically symmetric, solutions with vanishing cosmological constant are known by Barrow & Clifton (2005) and Deser, Sarioglu & Tekin (2008). Aim of the paper is to discuss some features of such solutions, with emphasis on their thermodynamic properties such as entropy and temperature, little progress being possible along the way which leads to a consistent definition of mass.
Estimating eye-gaze from images alone is a challenging task, in large parts due to un-observable person-specific factors. Achieving high accuracy typically requires labeled data from test users which may not be attainable in real applications. We observe that there exists a strong relationship between what users are looking at and the appearance of the user's eyes. In response to this understanding, we propose a novel dataset and accompanying method which aims to explicitly learn these semantic and temporal relationships. Our video dataset consists of time-synchronized screen recordings, user-facing camera views, and eye gaze data, which allows for new benchmarks in temporal gaze tracking as well as label-free refinement of gaze. Importantly, we demonstrate that the fusion of information from visual stimuli as well as eye images can lead towards achieving performance similar to literature-reported figures acquired through supervised personalization. Our final method yields significant performance improvements on our proposed EVE dataset, with up to a 28 percent improvement in Point-of-Gaze estimates (resulting in 2.49 degrees in angular error), paving the path towards high-accuracy screen-based eye tracking purely from webcam sensors. The dataset and reference source code are available at https://ait.ethz.ch/projects/2020/EVE
An unpolarized charge current passing through a chaotic quantum dot with spin-orbit coupling can produce a spin polarized exit current without magnetic fields or ferromagnets. We use random matrix theory to estimate the typical spin polarization as a function of the number of channels in each lead in the limit of large spin-orbit coupling. We find rms spin polarizations up to 45% with one input channel and two output channels. Finite temperature and dephasing both suppress the effect, and we include dephasing effects using a new variation of the third lead model. If there is only one channel in the output lead, no spin polarization can be produced, but we show that dephasing lifts this restriction.
In this note we investigate U(N) gauge theories with matter in the fundamental and adjoint representations of the gauge group, interacting via generalized Yukawa terms of the form Tr[Q \Phi^n {\tilde Q}]. We find agreement between the matrix model and the gauge theory descriptions of these theories. The analysis leads to a partial description of the Higgs branch of the gauge theory. We argue that the transition between phases with different unbroken flavor symmetry groups is related to the appearance of cuts in the matrix model computation.
Many models of new physics beyond the Standard Model are able to describe massive, long-lived particles with macroscopic decays, which can be reconstructed as displaced vertices inside the inner trackers of the LHC experiments. In addition, the lack of evidence of any new physics at the LHC motivates to perform more unconventional searches, such as looking for displaced vertices. I comment on the 13 TeV LHC reach with a proposed multitrack displaced vertex search strategy to probe light sterile neutrinos. Limits on active-sterile neutrino mixing are presented.
Recently, the problem of spin and orbital angular momentum (AM) separation has widely been discussed. Nowadays, all discussions about the possibility to separate the spin AM from the orbital AM in the gauge invariant manner are based on the ansatz that the gluon field can be presented in form of the decomposition where the physical gluon components are additive to the pure gauge gluon components, i.e. $A_\mu = A_\mu^{\text{phys}}+A_\mu^{\text{pure}}$. In the present paper, we show that in the non-Abelian gauge theory this gluon decomposition has a strong mathematical evidence in the frame of the contour gauge conception. In other words, we reformulate the gluon decomposition ansatz as a theorem on decomposition and, then, we use the contour gauge to prove this theorem. In the first time, we also demonstrate that the contour gauge possesses the special kind of residual gauge related to the boundary field configurations and expressed in terms of the pure gauge fields. As a result, the trivial boundary conditions lead to the inference that the decomposition includes the physical gluon configurations only provided the contour gauge condition.
Let $X$, $Y$ be Fano threefolds of Picard number one and such that the ample generators of Picard groups are very ample. Let $X$ be of index one and $Y$ be of index two. It is shown that the only morphisms from $X$ to $Y$ are double coverings. In fact nearly the whole paper is the analysis of the case where $Y$ is the linear section of the Grassmannian G(1,4), since the other cases were more or less solved in another article. This remaining case is treated with the help of Debarre's connectedness theorem for inverse images of Schubert cycles.
The baby Skyrme model is a (2+1)-dimensional analogue of the Skyrme model, in which baryons are described by topological solitons. In this paper we introduce a version of the baby Skyrme model in which the global O(3) symmetry is broken to the dihedral group D_N. It is found that the single soliton in this theory is composed of N partons, that are topologically confined. The case N=3 is studied in some detail and multi-soliton solutions are computed. These soliton solutions are related to polyiamonds, which are plane figures composed of equilateral triangles joined by common edges. It is shown that the solitons may be viewed as pieces of a doubly periodic soliton lattice. An alternative model with D_3 symmetry is also introduced, which has an exact explicit soliton lattice solution. Soliton solutions are computed and compared in the two D_3 theories. Some comments are made regarding the extension of these ideas to the Skyrme model.
We study the focusing mass-critical rough nonlinear Schroedinger equations, where the stochastic integration is taken in the sense of controlled rough path. We obtain the global well-posedness if the mass of initial data is below that of the ground state. Moreover, the existence of minimal mass blow-up solutions is also obtained in both dimensions one and two. In particular, these yield that the mass of ground state is exactly the threshold of global well-posedness and blow-up of solutions in the stochastic focusing mass-critical case. Similar results are also obtained for a class of nonlinear Schroedinger equations with lower order perturbations.
Let $G = (V, E)$ be a graph and $\sigma(G)$ the number of independent (vertex) sets in $G$. Then the Merrifield-Simmons conjecture states that the sign of the term $\sigma(G_{-u}) \cdot \sigma(G_{-v}) - \sigma(G) \cdot \sigma(G_{-u-v})$ only depends on the parity of the distance of the vertices $u, v \in V$ in $G$. We prove that the conjecture holds for bipartite graphs by considering a generalization of the term, where vertex subsets instead of vertices are deleted.
We study the system of nonisentropic thermoelasticity describing the motion of thermoelastic nonconductors of heat in two and three spatial dimensions, where the frame-indifferent constitutive relation generalizes that for compressible neo-Hookean materials. Thermoelastic contact discontinuities are characteristic discontinuities for which the velocity is continuous across the discontinuity interface. Mathematically, this renders a nonlinear multidimensional hyperbolic problem with a characteristic free boundary. We identify a stability condition on the piecewise constant background states and establish the linear stability of thermoelastic contact discontinuities in the sense that the variable coefficient linearized problem satisfies a priori tame estimates in the usual Sobolev spaces under small perturbations. Our tame estimates for the linearized problem do not break down when the strength of thermoelastic contact discontinuities tends to zero. The missing normal derivatives are recovered from the estimates of several quantities relating to physical involutions. In the estimate of tangential derivatives, there is a significant new difficulty, namely the presence of characteristic variables in the boundary conditions. To overcome this difficulty, we explore an intrinsic cancellation effect, which reduces the boundary terms to an instant integral. Then we can absorb the instant integral into the instant tangential energy by means of the interpolation argument and an explicit estimate for the traces on the hyperplane.
We study the angular power spectra of polarized Galactic synchrotron in the range 10<l<800, at several frequencies between 0.4 and 2.7 GHz and at several Galactic latitudes up to near the North Galactic Pole. Electric- and magnetic-parity polarization spectra are found to have slopes around alpha _{E,B} = 1.4 - 1.5 in the Parkes and Effelsberg Galactic-Plane surveys, but strong local fluctuations of alpha_{E,B} are found at | b | ~ 10 degree from the 1.4 GHz Effelsberg survey. The C_{PIl} spectrum, which is insensitive to the polarization direction, is somewhat steeper, being alpha_{PI} = 1.6 - 1.8 for the same surveys. The low-resolution multifrequency survey of Brouw and Spoelstra (1976) shows some flattening of the spectra below 1 GHz, more intense for C_{E,Bl} than for C_{PIl}. In no case we find evidence for really steep spectra. The extrapolation to the cosmological window shows that at 90 GHz the detection of E-mode harmonics in the cosmic background radiation should not be disturbed by synchrotron, even around l~10 for a reionization optical depth tau _{ri}>~0.05.
The nonlinear selfdual variational principle established in a preceeding paper [8] -- though good enough to be readily applicable in many stationary nonlinear partial differential equations -- did not however cover the case of nonlinear evolutions such as the Navier-Stokes equations. One of the reasons is the prohibitive coercivity condition that is not satisfied by the corresponding selfdual functional on the relevant path space. We show here that such a principle still hold for functionals of the form   I(u)= \int_0^T \Big [ L (t, u(t),\dot {u}(t)+\Lambda u(t)) +< \Lambda u(t), u(t) > \Big ] dt +\ell (u(0)- u(T), \frac {u(T)+ u(0)}{2})   where $L$ (resp., $\ell$) is an anti-selfdual Lagrangian on state space (resp., boundary space), and $\Lambda$ is an appropriate nonlinear operator on path space. As a consequence, we provide a variational formulation and resolution to evolution equations involving nonlinear operators such as the Navier-Stokes equation (in dimensions 2 and 3) with various boundary conditions. In dimension 2, we recover the well known solutions for the corresponding initial-value problem as well as periodic and anti-periodic ones, while in dimension 3 we get Leray solutions for the initial-value problems, but also solutions satisfying $u(0)=\alpha u(T)$ for any given $\alpha$ in $(-1,1)$. Our approach is quite general and does apply to many other situations.
GX 339--4 is a well-known microquasar. In this contribution we show the obtained results with the INTEGRAL and XMM-Newton observatories of the outburst undertaken on 2007. The observations cover spectral evolution from the hard, soft intermediate states to the high/soft state. Spectral hardening correlated with the appearance of an skewed Fe line is detected during one of the observations during the soft intermediate state. In all spectral states joint XMM/EPIC-pn, JEM-X, ISGRI and SPI data were fit with the hybrid thermal/non-thermal Comptonization model (EQPAIR). With this model a non-thermal component seems to be required by the data in all the observations. Our results imply evolution in the coronal properties, the most important one being the transition from a compact corona in the first observation to the disappearance of coronal material in the second and re-appearance in the third. We discuss the results obtained in the context of possible physical scenarios for the origin and geometry of the corona and its relation to black hole states.
Let $G$ be a simple graph with $n$ vertices and let $$C(G;x)=\sum_{k=0}^n(-1)^{n-k}c(G,k)x^k$$ denote the Laplacian characteristic polynomial of $G$. Then if the size $|E(G)|$ is large compared to the maximum degree $\Delta(G)$, Laplacian coefficients $c(G,k)$ are approximately normally distributed (by central and local limit theorems). We show that Laplacian coefficients of the paths, the cycles, the stars, the wheels and regular graphs of degree $d$ are approximately normally distributed respectively. We also point out that Laplacian coefficients of the complete graphs and the complete bipartite graphs are approximately Poisson distributed respectively.
Within the framework of the external shock model of gamma-ray bursts (GRBs) afterglows, we perform a morphological analysis of the early optical lightcurves to directly constrain model parameters. We define four morphological types, i.e. the reverse shock dominated cases with/without the emergence of the forward shock peak (Type I/ Type II), and the forward shock dominated cases without/with $\nu_m$ crossing the band (Type III/IV). We systematically investigate all the Swift GRBs that have optical detection earlier than 500 s and find 3/63 Type I bursts (4.8%), 12/63 Type II bursts (19.0%), 30/63 Type III bursts (47.6%), 8/63 Type IV bursts (12.7%) and 10/63 Type III/IV bursts (15.9%). We perform Monte Carlo simulations to constrain model parameters in order to reproduce the observations. We find that the favored value of the magnetic equipartition parameter in the forward shock ($\epsilon_B^f$) ranges from $10^{-6}$ to $10^{-2}$, and the reverse-to-forward ratio of $\epsilon_B$ ($R_B$) is about 100. The preferred electron equipartition parameter $\epsilon_e^{r,f}$ value is 0.01, which is smaller than the commonly assumed value, e.g., 0.1. This could mitigate the so- called "efficiency problem" for the internal shock model, if $\epsilon_e$ during the prompt emission phase (in the internal shocks) is large (say, $\sim 0.1$). The preferred $R_B$ value is in agreement with the results in previous works that indicates a moderately magnetized baryonic jet for GRBs.
We explore the persistence of the alignment of brightest cluster galaxies (BCGs) with their local environment. We find that a significant fraction of BCGs do not coincide with the centroid of the X-ray gas distribution and/or show peculiar velocities (they are not at rest with respect to the cluster mean). Despite this, we find that BCGs are generally aligned with the cluster mass distribution even when they have significant offsets from the X-ray centre and significant peculiar velocities. The large offsets are not consistent with simple theoretical models. To account for these observations BCGs must undergo mergers preferentially along their major axis, the main infall direction. Such BCGs may be oscillating within the cluster potential after having been displaced by mergers or collisions, or the dark matter halo itself may not yet be relaxed.
We report the observation of a fully developed fractional quantum Hall state at $\nu=5/2$ in GaAs/Al$_{x}$Ga$_{1-x}$As quantum wells with mobility well below $10^{7}$\thinspace cm$^{2}$/Vs. This is achieved either by strong illumination or reducing the barrier Al composition without illumination. We explain both results in terms of screening of the ionized remote impurity (RI) potential by nearby neutral shallow donors. Despite the dramatic improvement in the transport features, the energy gap $\Delta_{5/2}$ is limited to a rather small value ($\sim100$ mK), which indicates that once the RI potential is well screened and the $5/2$ state emerges, the size of $\Delta_{5/2}$ is limited by the mobility, i.e., by background impurities.
We investigate the properties of a set of solar flares originating from a single active region (AR) that exhibit QPPs, and look for signs of the QPP periods relating to AR properties. The AR studied, best known as NOAA 12192, was unusually long-lived and produced 181 flares. Data from the GOES, EVE, Fermi, Vernov and NoRH observatories were used to determine if QPPs were present in the flares. For the soft X-ray GOES and EVE data, the time derivative of the signal was used. Power spectra of the time series data (without any form of detrending) were inspected, and flares with a peak above the 95% confidence level in the spectrum were labelled as having candidate QPPs. The confidence levels were determined taking account of uncertainties and the possible presence of red noise. AR properties were determined using HMI line of sight magnetograms. A total of 37 flares (20% of the sample) show good evidence of having QPPs, and some of the pulsations can be seen in data from multiple instruments and in different wavebands. The QPP periods show a weak correlation with the flare amplitude and duration, but this may be due to an observational bias. A stronger correlation was found between the QPP period and duration of the QPP signal, which can be partially but not entirely explained by observational constraints. No correlations were found with the AR area, bipole separation, or average magnetic field strength. The fact that a substantial fraction of the flare sample showed evidence of QPPs using a strict detection method with minimal processing of the data demonstrates that these QPPs are a real phenomenon, which cannot be explained by the presence of red noise or the superposition of multiple unrelated flares. The lack of correlation between the QPP periods and AR properties implies that the small-scale structure of the AR is important, and/or that different QPP mechanisms act in different cases.
We propose a low energy effective theory of lightly doped two-leg t-J ladders with the help of slave fermion technique. The continuum limit of this model consists of two kinds of Dirac fermions which are coupled to the O(3) non-linear sigma model in terms of the gauge coupling with opposite sign of "charges". In addition to the gauge interaction, there is another kind of attractive force between these Dirac fermions, which arises from the short-ranged antiferromagnetic order. We show that the latter is essential to determine the low energy properties of lightly doped two-leg t-J ladders. The effective Hamiltonian we obtain is a bosonic Gaussian model and the boson field basically describes the particle density fluctuation. We also find two types of gapped spin excitations. Finally, we discuss the possible instabilities: charge density wave (CDW) and singlet superconductivity (SC). We find that the SC instability dominates in our approximation. Our results indicate that lightly doped ladders fall into the universality class of Luther-Emery model.
A new model of a Quantum Automaton (QA), working with qubits is proposed. The quantum states of the automaton can be pure or mixed and are represented by density operators. This is the appropriated approach to deal with measurements and dechorence. The linearity of a QA and of the partial trace super-operator, combined with the properties of invariant subspaces under unitary transformations, are used to minimize the dimension of the automaton and, consequently, the number of its working qubits. The results here developed are valid wether the state set of the QA is finite or not. There are two main results in this paper: 1) We show that the dimension reduction is possible whenever the unitary transformations, associated to each letter of the input alphabet, obey a set of conditions. 2) We develop an algorithm to find out the equivalent minimal QA and prove that its complexity is polynomial in its dimension and in the size of the input alphabet.
The recent experimental study of the far-infrared transmission spectroscopy of monolayer graphene has shown that the Drude peak width increases by more than $10\%$ per $1\%$ of applied mechanical strain, while the Drude weight remains unchanged. We study the influence of the strain on the resonant impurity scattering. We propose a mechanism of augmentation of the scattering rate due to the shift in the position of resonance. Using the Lifshitz model of substitutional impurities, we investigate changes in the Drude peak weight and width as functions of the Fermi energy, impurity concentration and magnitude of the impurity potential.
Lei and Lin have recently given a proof of a global mild solution of the three-dimensional Navier-Stokes equations in function spaces based on the Wiener algebra. An alternative proof of existence of these solutions was then developed by Bae, and this new proof allowed for an estimate of the radius of analyticity of the solutions at positive times. We adapt the Bae proof to prove existence of the Lei-Lin solution in the spatially periodic setting, finding an improved bound for the radius of analyticity in this case.
Self-consistent approach for interacting phonons description in lattice, which generalized Debye model, is proposed. Notion of "self-consistent" phonons is introduced, speed of which depends on temperature and is determined from non-linear equation. Debye energy is also a function of temperature in this approach. Thermodynamics of "self-consistent" phonon gas is constructed. It is shown, that at low temperatures there is a correction proportional to the seventh power of temperature to the cubic law of specific heat dependence on temperature. This may be one of the reasons why cubic law for specific heat is observed only at rather low temperatures. At high temperatures the theory predicts linear deviation from Dulong-Petit law, which is observed experimentally.