ShantanuT01/DACTYL-Pretraining huggingface dataset:
We consider the first-passage percolation problem on the random graph with vertex set N\times{0,1}, edges joining vertices at Euclidean distance equal to unity and independent exponential edge weights. We provide a central limit theorem for the first-passage times l_n between the vertices (0,0) and (n,0), thus extending earlier results about the almost sure convergence of l_n/n as n goes to infinity. We use generating function techniques to compute the n-step transition kernels of a closely related Markov chain which can be used to calculate explicitly the asymptotic variance in the central limit theorem.
This thesis presents the study of four aspects of high energy astronomy. The first part of the thesis is dedicated to an aspect of instrument development for imaging atmospheric Cherenkov telescopes, namely the Level 2 trigger system of the High Energy Stereoscopic System (H.E.S.S.). I am providing the motivation and principle of the operation of the Level 2 trigger, I am describing hardware implementation of the system and then I am evaluating expected performances. The second part of my thesis deals with the data analysis and modeling of broad-band emission of particular blazar PKS 1510-089. I am presenting the analysis of the H.E.S.S. data, together with the FERMI data and a collection of multi-wavelength data obtained with various instruments. I am presenting the model of PKS 1510-089 observations carried out during a flare recorded by H.E.S.S.. The third part of my thesis deals with blazars observed by the FERMI-LAT, but from the point of view of other phenomena: a strong gravitational lensing. This part of my thesis shows the first evidence for gravitational lensing phenomena in high energy gamma-rays. This evidence comes from the observation of a gravitational lens system induced echo in the light curve of the distant blazar PKS 1830-211. The last part concentrates on another lensing phenomena called femtolensing. The search for femtolensing effects has been used to derive limits on the primordial black holes abundance. I have used gamma-ray bursts with known redshifts detected by the FERMI Gamma-ray Burst Monitor (GBM) to search for the femtolensing effects caused by compact objects.
Ti substituting Ru in Sr$_2$RuO$_4$ in small concentrations induces incommensurate spin density wave order with a wave vector $\boldsymbol{Q} \simeq (2 \pi /3, 2 \pi /3)$ corresponding to the nesting vector of two out of three Fermi surface sheets. We consider a microscopic model for these two bands and analyze the correlation effects leading to magnetic order through non-magnetic Ti-doping. For this purpose we use a position dependent mean field approximation for the microscopic model and a phenomenological Ginzburg-Landau approach, which both deliver consistent results and allow us to examine the inhomogeneous magnetic order. Spin-orbit coupling additionally leads to spin currents around each impurity, which in combination with the magnetic polarization produce a charge current pattern. This is also discussed within a gauge field theory in both charge and spin channel. This spin-orbit coupling effect causes an interesting modification of the magnetic structure, if currents run through the system. Our findings allow a more detailed analysis of the experimental data for Sr$_{2}$Ru$_{1-x}$Ti$_{x}$O$_{4}$. In particular, we find that the available measurements are consistent with our theoretical predictions.
The calculations in the temporal axial gauge (TAG) are revised and a new prescription is introduced to avoid the well-known TAG-singularity. With this prescription we use the TAG-formalism to calculate the one-loop dispersion equation for the longitudinal plasma oscillations in the high temperature limit and find the complete selfconsistency of TAG for pragmatic aims. Our result reproduces the earlier known dispersion equation obtained in covariant gauges and this equality explicitly demonstrates the gauge independence of the dispersion law in the high temperature limit and its reliability.
In this paper we consider a large class of fully nonlinear integro-differential equations. The class of our nonlocal operators we consider is not spatial homogeneous and we put mild assumptions on its kernel near zero. We prove the H\"older regularity for such equation. In particular, our result covers the case that the kernel $K(x,y)$ is comparable to $|x-y|^{-d-\alpha} \ln (|x-y|^{-1})$ for $|x-y|<c$ where $0<\alpha<2$.
In this work, we show that for the martingale problem for a class of degenerate diffusions with bounded continuous drift and diffusion coefficients, the small noise limit of non-degenerate approximations leads to a unique Feller limit. The proof uses the theory of viscosity solutions applied to the associated backward Kolmogorov equations. Under appropriate conditions on drift and diffusion coefficients, we will establish a comparison principle and a one-one correspondence between Feller solutions to the martingale problem and continuous viscosity solutions of the associated Kolmogorov equation. This work can be considered as an extension to the work of V. S. Borkar and K. S. Kumar (2010).
We study a doubly parabolic Keller-Segel system in one spatial dimension, with diffusions given by fractional laplacians. We obtain several local and global well-posedness results for the subcritical and critical cases (for the latter we need certain smallness assumptions). We also study dynamical properties of the system with added logistic term. Then, this model exhibits a spatio-temporal chaotic behavior, where a number of peaks emerge. In particular, we prove the existence of an attractor and provide an upper bound on the number of peaks that the solution may develop. Finally, we perform a numerical analysis suggesting that there is a finite time blow up if the diffusion is weak enough, even in presence of a damping logistic term. Our results generalize on one hand the results for local diffusions, on the other the results for the parabolic-elliptic fractional case.
Optical model potentials for elastic nucleon nucleus scattering are calculated for a number of target nuclides from a full-folding integral of two different realistic target density matrices together with full off-shell nucleon-nucleon t-matrices derived from two different Bonn meson exchange models. Elastic proton and neutron scattering observables calculated from these full-folding optical potentials are compared to those obtained from `optimum factorized' approximations in the energy regime between 65 and 400 MeV projectile energy. The optimum factorized form is found to provide a good approximation to elastic scattering observables obtained from the full-folding optical potentials, although the potentials differ somewhat in the structure of their nonlocality.
We present a tight-binding model study of a two-terminal graphene nanopore device for sequential determination of DNA bases. Using Green's function technique we investigate the changes in electronic transport properties of the device due to insertion of different nucleotides into the nanopore created within a zigzag graphene nanoribbon. First we try to characterise the device in static condition and then go for sequencing application by setting the bias across it to a specific voltage and then recording the characteristic current signals corresponding to each nucleotides of a translocating DNA. Our investigations show that graphene nanopores can certainly become very efficient and reliable for sequencing applications in future.
Herein, we report the appearance of a large exchange bias (EB) effect in a moderate cooling field (cooling field, H$_{FC}$ = 1 kOe) for the 314-Sr3YCo4O10.5 material. The exchange bias has started to appear near room temperature and reaches a maximum value of 5.5 kOe at 4 K. The existence of ferrimagnetic clusters in the compensated host in this layered structure originates the large exchange anisotropy. Remarkably, the observed value of moderate magnetic field induced exchange bias field is extremely large in comparison with material systems which are recognized to exhibit giant exchange bias effect. In combination with the feasibility of room temperature application, the appearance of large exchange bias in a moderate cooling field exemplifying the present material system as a promising class of compounds for designing coherent magnetic materials with huge exchange bias in low/moderate magnetic field.
In this note, we investigate, under what circumstances, a warm standby system (formed by n active components and m warm standby components) has more number of surviving warm standby components than another similar system at the time of $k$th failure of the active component of the respective system. The number of such components being random, the comparison has been done with respect to different stochastic orders, viz. usual stochastic order, hazard rate and reversed hazard rate orders, and likelihood ratio order.
Motivated by the detection of a recent outburst of the massive luminous blue variable LMC-R71, which reached an absolute magnitude M_V = -9.3 mag, we undertook a systematic study of the optical variability of 1268 massive stars in the Large Magellanic Cloud, using a recent catalog by Bonanos et al. (2009) as the input. The ASAS All Star Catalog (Pojmanski 2002) provided well-sampled light curves of these bright stars spanning 10 years. Combining the two catalogs resulted in 599 matches, on which we performed a variability search. We identified 117 variable stars, 38 of which were not known before, despite their brightness and large amplitude of variation. We found 13 periodic stars that we classify as eclipsing binary (EB) stars, eight of which are newly discovered bright, massive eclipsing binaries composed of OB type stars. The remaining 104 variables are either semi- or non-periodic, the majority (85) being red supergiants. Most (26) of the newly discovered variables in this category are also red supergiants with only three B and four O stars.
We consider a chiral cosmological model in the framework of Einstein-Gauss-Bonnet cosmology. Using a decomposition of the latter equations in such a way that the first chiral field is responsible for the Einstein part of the model, while the second field together with the kinetic interaction is connected with the Gauss--Bonnet part of the theory, we find new exact solutions for the 2-component chiral cosmological model with and without the kinetic interaction between fields.
Relying only on first principles, we derive a master equation of Lindblad form generally applicable for adiabatically time dependent systems. Our analysis shows that the much debated secular approximation can be valid for slowly time dependent Hamiltonians when performed in an appropriate basis. We apply our approach to the well known Landau-Zener problem where we find that adiabaticity is improved by coupling to a low temperature environment.
The analysis of spontaneous gauge symmetry breaking of N=1 supersymmetric SU(N_c) Yang-Mills theory with matter is performed. The supersymmetric $R_\xi$-gauge is used and its non-local effects investigated. Superpropagators and vertices are computed, and it is shown that the non-local terms introduced by the $R_\xi$-gauge-fixing are well-behaved in general gauge at one-loop. It is argued that this feature generalizes to multiple loops.
We propose a concept for a graphene tunnel field-effect transistor. The main idea is based on the use of two graphene electrodes with zigzag termination divided by a narrow gap under the influence of the common gate. Our analysis shows that such device will have a pronounced switching effect at low gate voltage and high on/off current ratio at room temperature.
All possible transformations from the Robertson-Walker metric to those conformal to the Lorentz-Minkowski form are derived. It is demonstrated that the commonly known family of transformations and associated conformal factors are not exhaustive and that there exists another relatively less well known family of transformations with a different conformal factor in the particular case that K = -1. Simplified conformal factors are derived for the special case of maximally-symmetric spacetimes. The full set of all possible cosmologically-compatible conformal forms is presented as a comprehensive table. A product of the analysis is the determination of the set-theoretical relationships between the maximally symmetric spacetimes, the Robertson-Walker spacetimes, and functionally more general spacetimes. The analysis is preceded by a short historical review of the application of conformal metrics to Cosmology.
The Boltzmann type kinetic equation for solitons in Nonlinear Schr\"{o}dinger equation has been constructed on the base of analysis of two soliton collision. Possible applications for Langmuir solitons in plasma and solitons in optic fiber are discussed.
A relativistic extension of the particle-particle hole-hole ring-diagram many-body formalism is developed by using the Dirac equation for single-particle motion in the medium. Applying this new formalism, calculations are performed for nuclear matter. The results show that the saturation density is improved and the equation of state becomes softer as compared to corresponding Dirac-Brueckner-Hartree-Fock calculations. Using the Bonn A potential, nuclear matter is predicted to saturate at an energy per nucleon of --15.30 MeV and a density equivalent to a Fermi momentum of 1.38 fm$^{-1}$, in excellent agreement with empirical information. The compression modulus is 152 MeV at the saturation point.
We present the analytic calculation of two-loop master integrals that are relevant for $tW$ production at hadron colliders. We focus on the integral families with only one massive propagator. After choosing a canonical basis, the differential equations for the master integrals can be transformed into the $d$ln form. The boundaries are determined by simple direct integrations or regularity conditions at kinematic points without physical singularities. The analytical results in this work are expressed in terms of multiple polylogarithms, and have been checked with numerical computations.
The asymptotics of the SU(2) 15j symbol are obtained using coherent states for the boundary data. The geometry of all non-suppressed boundary data is given. For some boundary data, the resulting formula is interpreted in terms of the Regge action of the geometry of a 4-simplex in 4-dimensional Euclidean space. This asymptotic formula can be used to derive and extend the asymptotics of the spin foam amplitudes for quantum gravity models. The relation of the SU(2) Ooguri model to these quantum gravity models and their continuum Lagrangians is discussed.
Most of the recent Deep Semantic Segmentation algorithms suffer from large generalization errors, even when powerful hierarchical representation models based on convolutional neural networks have been employed. This could be attributed to limited training data and large distribution gap in train and test domain datasets. In this paper, we propose a multi-level self-supervised learning model for domain adaptation of semantic segmentation. Exploiting the idea that an object (and most of the stuff given context) should be labeled consistently regardless of its location, we generate spatially independent and semantically consistent (SISC) pseudo-labels by segmenting multiple sub-images using base model and designing an aggregation strategy. Image level pseudo weak-labels, PWL, are computed to guide domain adaptation by capturing global context similarity in source and domain at latent space level. Thus helping latent space learn the representation even when there are very few pixels belonging to the domain category (small object for example) compared to rest of the image. Our multi-level Self-supervised learning (MLSL) outperforms existing state-of art (self or adversarial learning) algorithms. Specifically, keeping all setting similar and employing MLSL we obtain an mIoU gain of 5:1% on GTA-V to Cityscapes adaptation and 4:3% on SYNTHIA to Cityscapes adaptation compared to existing state-of-art method.
We study large time behaviour of solutions of the Cauchy problem for equations of the form $\partial_tu-L u+\lambda u=f(x,u)+g(x,u)\cdot\mu$, where $L$ is the operator associated with a regular lower bounded semi-Dirichlet form ${\mathcal{E}}$ and $\mu$ is a nonnegative bounded smooth measure with respect to the capacity determined by ${\mathcal{E}}$. We show that under the monotonicity and some integrability assumptions on $f,g$ as well as some assumptions on the form ${\mathcal{E}}$, $u(t,x)\rightarrow v(x)$ as $t\rightarrow\infty$ for quasi-every $x$, where $v$ is a solution of some elliptic equation associated with our parabolic equation. We also provide the rate convergence. Some examples illustrating the utility of our general results are given.
I report on a sample of new type I X-ray bursters, firstly detected with the Wide Field Cameras on board BeppoSAX and then studied with the Narrow Field Instruments on a broad spectral range (0.1-200 keV). Properties of the transient/persistent emission are summarized and the broad band X-ray spectra discussed in detail for a few sources.
In 1981 Unruh proposed that fluid mechanical experiments could be used to probe key aspects of the quantum phenomenology of black holes. In particular, he claimed that an analogue to Hawking radiation could be created within a fluid mechanical `dumb hole', with the event horizon replaced by a sonic horizon. Since then an entire sub-field of `analogue gravity' has been created. In 2016 Steinhauer reported the experimental observation of quantum Hawking radiation and its entanglement in a Bose-Einstein condensate analogue black hole. What can we learn from such analogue experiments? In particular, in what sense can they provide evidence of novel phenomena such as black hole Hawking radiation?
X-ray observations of EXO 0748-676 during thermonuclear bursts revealed a set of narrow absorption lines that potentially originate from the stellar photosphere. The identification of these lines with particular atomic transitions led to the measurement of the surface gravitational redshift of the neutron star and to constraints on its mass and radius. However, the recent detection of 552 Hz oscillations at 15% rms amplitude revealed the spin frequency of the neutron star and brought into question the consistency of such a rapid spin with the narrow width of the absorption lines. Here, we calculate the amplitudes of burst oscillations and the width of absorption lines emerging from the surface of a rapidly rotating neutron star for a wide range of model parameters. We show that no combination of neutron-star and geometric parameters can simultaneously reproduce the narrowness of the absorption lines, the high amplitude of the oscillations, and the observed flux at the time the oscillations were detected. We, therefore, conclude that the observed absorption lines are unlikely to originate from the surface of this neutron star.
Let $\|\cdot\|$ denote the minimum distance to an integer. For $0<\gamma< 1$, $\theta>0$ and $(\alpha, \beta) \in \mathbb{R} \setminus \{0\} \times \mathbb{R}$ we study when \begin{equation*} \|\alpha p^{\gamma}+\beta \|<p^{-\theta}, \end{equation*} holds for infinitely many primes $p$ of a special type. In particular, we consider when this inequality holds for primes $p$ such that $p+2$ has few prime factors counted with multiplicity. This is done using an exponential sum estimate of the author and the linear sieve of Iwaniec with bilinear error term. This is related to recent work of Tolev, Todorova, Mat\"{o}maki and Cai.
Recent advances in experimental techniques emphasize the usefulness of multiple scanning probe techniques when analyzing nanoscale samples. Here, we analyze theoretically dual-probe setups with probe separations in the nanometer range, i.e., in a regime where quantum coherence effects can be observed at low temperatures. In a dual-probe setup the electrons are injected at one probe and collected at the other. The measured conductance reflects the local transport properties on the nanoscale, thereby yielding information complementary to that obtained with a standard one-probe setup (the local density-of-states). In this work we develop a real space Green's function method to compute the conductance. This requires an extension of the standard calculation schemes, which typically address a finite sample between the probes. In contrast, the developed method makes no assumption on the sample size (e.g., an extended graphene sheet). Applying this method, we study the transport anisotropies in pristine graphene sheets, and analyze the spectroscopic fingerprints arising from quantum interference around single-site defects, such as vacancies and adatoms. Furthermore, we demonstrate that the dual-probe setup is a useful tool for characterizing the electronic transport properties of extended defects or designed nanostructures. In particular, we show that nanoscale perforations, or antidots, in a graphene sheet display Fano-type resonances with a strong dependence on the edge geometry of the perforation.
Continuum effects in the weakly bound nuclei close to the drip-line are investigated using the analytically soluble Poschl-Teller-Ginocchio potential. Pairing correlations are studied within the Hartree-Fock-Bogoliubov method. We show that both resonant and non-resonant continuum phase space is active in creating the pairing field. The influence of positive-energy phase space is quantified in terms of localizations of states within the nuclear volume.
A simple modification of the ``Wang-Landau sampling'' algorithm removes the systematic error that occurs at the boundary of the range of energy over which the random walk takes place in the original algorithm.
Ludwig Boltzmann had a hunch that irreversibility exhibited by a macroscopic system arises from the reversible dynamics of its microscopic constituents. He derived a nonlinear integro-differential equation - now called the Boltzmann equation - for the phase space density of the molecules of a dilute fluid. He showed that the Second law of thermodynamics emerges from Newton's equations of motion. However Boltzmann realized that stosszahlansatz, employed in the derivation, smuggles in an element of stochasticity into the transport equation. He then proposed a fully stochastic description of entropy which laid the foundation for statistical mechanics. Recent developments, embodied in different fluctuation theorems, have shown that Boltzmann's hunch was, in essence, correct.
We introduce an invertible operation on finite sequences of positive integers and call it "kneading". Kneading preserves three invariants of sequences -- the parity of the length, the sum of the entries, and one we call the "alternant". We provide a bijection between the set of sequences with alternant $a$ and parity $s$ and the set of Zagier-reduced indefinite binary quadratic forms with discriminant $a^2 + (-1)^s \cdot 4$, and show that kneading corresponds to Zagier reduction of the corresponding forms. It follows that the sum of a sequence is a class invariant of the corresponding form. We conclude with some observations and conjectures concerning this new invariant.
We investigate the scattering matrix in mass-deformed N>=4 Chern-Simons models including as special cases the BLG and ABJM theories of multiple M2 branes. Curiously the structure of this scattering matrix in three spacetime dimensions is equivalent to (a) the two-dimensional worldsheet matrix found in the context of AdS/CFT integrability and (b) the R-matrix of the one-dimensional Hubbard model. The underlying reason is that all three models are based on an extension of the psu(2|2) superalgebra which constrains the matrix completely. We also compute scattering amplitudes in one-loop field theory and find perfect agreement with scattering unitarity.