ShantanuT01/DACTYL-Pretraining huggingface dataset:
We present a theory of the Raman scattering from the orbital wave excitations in manganese oxides. Two excitation processes of the Raman scattering are proposed. The Raman scattering cross section is formulated by using the pseudospin operator for orbital degree of freedom in a Mn ion. The Raman spectra from the orbital wave excitations are calculated and their implications in the recent experimental results reported in LaMnO$_3$ are discussed.
The combination of high frequency vibrations and metallic transport in graphene makes it a unique material for nano-electromechanical devices. In this letter, we show that graphene-based nano-electromechanical devices are extremely well suited for charge pumping, due to the sensitivity of its transport coefficients to perturbations in electrostatic potential and mechanical deformations, with the potential for novel small scale devices with useful applications.
For k greater than 1 and r different from 0, let pi^k_{2r}(x) denote the number of prime pairs (p,p^k+2r) with p not exceeding (large) x. By the Bateman-Horn conjecture, the function pi^k_{2r}(x) should be asymptotic to (2/k)C^k_{2r}li_2(x), with certain specific constants C^k_{2r}. Heuristic arguments lead to the conjecture that these constants have mean value one, just like the Hardy-Littlewood constants C_{2r} for prime pairs (p,p+2r). The conjecture is supported by extensive numerical work.
We describe a functional framework suitable to the analysis of the Cahn-Hilliard equation on an evolving surface whose evolution is assumed to be given \textit{a priori}. The model is derived from balance laws for an order parameter with an associated Cahn-Hilliard energy functional and we establish well-posedness for general regular potentials, satisfying some prescribed growth conditions, and for two singular nonlinearities -- the thermodynamically relevant logarithmic potential and a double obstacle potential. We identify, for the singular potentials, necessary conditions on the initial data and the evolution of the surfaces for global-in-time existence of solutions, which arise from the fact that integrals of solutions are preserved over time, and prove well-posedness for initial data on a suitable set of admissible initial conditions. We then briefly describe an alternative derivation leading to a model that instead preserves a weighted integral of the solution, and explain how our arguments can be adapted in order to obtain global-in-time existence without restrictions on the initial conditions. Some illustrative examples and further research directions are given in the final sections.
Excitons are electron-hole (e-h) pair quasiparticles, which may form a Bose-Einstein condensate (BEC) and collapse into the phase coherent state at low temperature. However, because of ephemeral strength of pairing, a clear evidence for BEC in electron-hole system has not yet been observed. Here, we report electron-hole pair condensation in graphene (Gr)/MoS2 heterointerface at 10K without magnetic field. As a direct indication of e-h pair condensation, we demonstrate a vanished Hall drag voltage and the resultant divergence of drag resistance. While strong excitons are formed at Gr/MoS2 heterointerface without insulating layer, carrier recombination via interlayer tunneling of carriers is suppressed by the vertical p-Gr/n-MoS2 junction barrier, consequently yielding high BEC temperature of 10K, ~1000 times higher than that of two-dimensional electron gas in III-V quantum wells. The observed excitonic transport is mainly governed by the interfacial properties of the Gr/MoS2 heterostructure, rather than the intrinsic properties of each layer. Our approach with available large-area monolayer graphene and MoS2 provides a high feasibility for quantum dissipationless electronics towards integration.
The problem of faces detection in images or video streams is a classical problem of computer vision. The multiple solutions of this problem have been proposed, but the question of their optimality is still open. Many algorithms achieve a high quality face detection, but at the cost of high computational complexity. This restricts their application in the real-time systems. This paper presents a new solution of the frontal face detection problem based on compact convolutional neural networks cascade. The test results on FDDB dataset show that it is competitive with state-of-the-art algorithms. This proposed detector is implemented using three technologies: SSE/AVX/AVX2 instruction sets for Intel CPUs, Nvidia CUDA, OpenCL. The detection speed of our approach considerably exceeds all the existing CPU-based and GPU-based algorithms. Because of high computational efficiency, our detector can processing 4K Ultra HD video stream in real time (up to 27 fps) on mobile platforms (Intel Ivy Bridge CPUs and Nvidia Kepler GPUs) in searching objects with the dimension 60x60 pixels or higher. At the same time its performance weakly dependent on the background and number of objects in scene. This is achieved by the asynchronous computation of stages in the cascade.
From a sample of 12 well-observed Type Ia supernovae, we find clear evidence of correlations between early phase (U-B), (V-R), and (V-I) colors and the velocity shifts of the [Fe II] \lambda 7155 and [Ni II] \lambda 7378 nebular lines measured from late-phase spectra. As these lines are thought to trace the ashes of the initial deflagration process, our findings provide additional support to the new paradigm of off-center explosions in Type Ia supernovae, and we interpret these correlations as viewing angle effects in the observed colors. We also show that the nebular velocity shifts are related to the strength and width of the Ca II H&K and IR-triplet lines near-maximum light. The evidence presented here implies that the viewing angle must be taken into account when deriving extinction values and distances in future cosmological studies based on Type Ia supernovae.
Gene regulatory networks, i.e. DNA segments in a cell which interact with each other indirectly through their RNA and protein products, lie at the heart of many important intracellular signal transduction processes. In this paper we analyse a mathematical model of a canonical gene regulatory network consisting of a single negative feedback loop between a protein and its mRNA (e.g. the Hes1 transcription factor system). The model consists of two partial differential equations describing the spatio-temporal interactions between the protein and its mRNA in a 1-dimensional domain. Such intracellular negative feedback systems are known to exhibit oscillatory behaviour and this is the case for our model, shown initially via computational simulations. In order to investigate this behaviour more deeply, we next solve our system using Green's functions and then undertake a linearized stability analysis of the steady states of the model. Our results show that the diffusion coefficient of the protein/mRNA acts as a bifurcation parameter and gives rise to a Hopf bifurcation. This shows that the spatial movement of the mRNA and protein molecules alone is sufficient to cause the oscillations. This has implications for transcription factors such as p53, NF-$\kappa$B and heat shock proteins which are involved in regulating important cellular processes such as inflammation, meiosis, apoptosis and the heat shock response, and are linked to diseases such as arthritis and cancer.
Accurately predicting and detecting interstitial lung disease (ILD) patterns given any computed tomography (CT) slice without any pre-processing prerequisites, such as manually delineated regions of interest (ROIs), is a clinically desirable, yet challenging goal. The majority of existing work relies on manually-provided ILD ROIs to extract sampled 2D image patches from CT slices and, from there, performs patch-based ILD categorization. Acquiring manual ROIs is labor intensive and serves as a bottleneck towards fully-automated CT imaging ILD screening over large-scale populations. Furthermore, despite the considerable high frequency of more than one ILD pattern on a single CT slice, previous works are only designed to detect one ILD pattern per slice or patch.   To tackle these two critical challenges, we present multi-label deep convolutional neural networks (CNNs) for detecting ILDs from holistic CT slices (instead of ROIs or sub-images). Conventional single-labeled CNN models can be augmented to cope with the possible presence of multiple ILD pattern labels, via 1) continuous-valued deep regression based robust norm loss functions or 2) a categorical objective as the sum of element-wise binary logistic losses. Our methods are evaluated and validated using a publicly available database of 658 patient CT scans under five-fold cross-validation, achieving promising performance on detecting four major ILD patterns: Ground Glass, Reticular, Honeycomb, and Emphysema. We also investigate the effectiveness of a CNN activation-based deep-feature encoding scheme using Fisher vector encoding, which treats ILD detection as spatially-unordered deep texture classification.
The main result of the paper is that assuming that the level $\theta$ of distribution of primes exceeds 1/2, then there exists a positive $d\leq C(\theta)$ such that there are arbitrarily long arithmetic progressions with the property that $p'=p+d$ is the next prime for each element of the progression. If $\theta>0.971$, then the above holds for some $d\leq 16$.
We investigate the transfer between carrier and Mn spins due to the s-d-exchange interaction in a Mn doped bulk semiconductor within a microscopic quantum kinetic theory. We demonstrate that the spin transfer dynamics is qualitatively different for components of the carrier spin parallel and perpendicular to the Mn magnetization. From our quantum kinetic equations we have worked out the corresponding Markov limit which is equivalent to rate equations based on Fermi's golden rule. The resulting equations resemble the widely used Landau-Lifshitz-Gilbert-equations, but also describe genuine spin transfer due to quantum corrections. Although it is known that the Markovian rate description works well for bulk systems when the initial Mn magnetization is zero, we find large qualitative deviations from the full quantum kinetic theory for finite initial Mn magnetizations. These deviations mainly reflect corrections of higher than leading order in the interaction which are not accounted for in golden rule-type rates.
This note is concerned with an important for modelling question of existence of solutions of stochastic partial differential equations as proper stochastic processes, rather than processes in the generalized sense. We consider a first order stochastic partial differential equations of the form $\pd Ut = DW$, and $\pd Ut-\pd Ux= DW$, where $D$ is a differential operator and $W(t,x)$ is a continuous but non-differentiable function (field).   We give a necessary and sufficient condition for stochastic equations to have solutions as functions. The result is then applied to the equation for a yield curve. Proofs are based on probability arguments.
Starting from the overdamped Langevin dynamics in $\mathbb{R}^n$, $$ dX_t = -\nabla V(X_t) dt + \sqrt{2 \beta^{-1}} dW_t, $$ we consider a scalar Markov process $\xi_t$ which approximates the dynamics of the first component $X^1_t$. In the previous work [F. Legoll, T. Lelievre, Nonlinearity 2010], the fact that $(\xi_t)_{t \ge 0}$ is a good approximation of $(X^1_t)_{t \ge 0}$ is proven in terms of time marginals, under assumptions quantifying the timescale separation between the first component and the other components of $X_t$. Here, we prove an upper bound on the trajectorial error $\mathbb{E} \left( \sup_{0 \leq t \leq T} \left| X^1_t - \xi_t \right| \right)$, for any $T > 0$, under a similar set of assumptions. We also show that the technique of proof can be used to obtain quantitative averaging results.
Thermodynamic properties of cubic Heisenberg ferromagnets with competing exchange interactions are considered near the frustration point where the coefficient $D$ in the spin-wave spectrum $E_{\mathbf{k}}\sim D k^{2}$ vanishes. Within the Dyson-Maleev formalism it is found that at low temperatures thermal fluctuations stabilize ferromagnetism by increasing the value of $D$. For not too strong frustration this leads to an unusual "concave" shape of the temperature dependence of magnetization, which is in agreement with experimental data on the europium chalcogenides. Anomalous temperature behavior of magnetization is confirmed by Monte Carlo simulation. Strong field dependence of magnetization (paraprocess) at finite temperature is found near the frustration point.
Recently the Schur index of ${\cal N}=4$ SYM was evaluated in closed form to all orders including exponential corrections in the large $N$ expansion and for fixed finite $N$. This was achieved by identifying the matrix model which calculates the index with the partition function of a system of free fermions on a circle. The index can be enriched by the inclusion of loop operators and the case of Wilson loops is particularly easy, as it amounts to inserting extra characters into the matrix model. The Fermi-gas approach is applied here to this problem, the formalism is explored and explicit results at large $N$ are found for the fundamental as well as a few other symmetric and antisymmetric representations.
For stochastic processes leading to condensation, the condensate, once it is formed, performs an ergodic stationary-state motion over the system. We analyse this motion, and especially its characteristic time, for zero-range processes. The characteristic time is found to grow with the system size much faster than the diffusive timescale, but not exponentially fast. This holds both in the mean-field geometry and on finite-dimensional lattices. In the generic situation where the critical mass distribution follows a power law, the characteristic time grows as a power of the system size.
Given a smooth projective complex curve $X$ with an involution $\sigma$, we study the Hitchin systems for the locus of anti-invariant (resp. invariant) stable vector bundles over $X$ under $\sigma$. Using these integrable systems and the theory of the nilpotent cone, we study the irreducibility of these loci. The anti-invariant locus can be thought of as a generalisation of Prym varieties to higher rank.
We present a new non-existence proof for the strongly regular graph $G$ with parameters $(76,21,2,7)$, using the unit vector representation of the graph.
We study time-dependent coupled-cluster theory in the framework of nuclear physics. Based on Kvaal's bi-variational formulation of this method [S. Kvaal, arXiv:1201.5548], we explicitly demonstrate that observables that commute with the Hamiltonian are conserved under time evolution. We explore the role of the energy and of the similarity-transformed Hamiltonian under real and imaginary time evolution and relate the latter to similarity renormalization group transformations. Proof-of-principle computations of He-4 and O-16 in small model spaces, and computations of the Lipkin model illustrate the capabilities of the method.
We have examined 426 {\it Voyager} fields distributed across the sky for \ion{O}{6} ($\lambda \lambda$ 1032/1038 \AA) emission from the Galactic diffuse interstellar medium. No such emission was detected in any of our observed fields. Our most constraining limit was a 90% confidence upper limit of 2600 \phunit on the doublet emission in the direction (l, b) = (117\fdegree3, 50\fdegree6). Combining this with an absorption line measurement in nearly the same direction allows us to place an upper limit of 0.01 cm$^{-3}$ on the electron density of the hot gas in this direction. We have placed 90% confidence upper limits of less than or equal to 10,000 \phunit on the \ion{O}{6} emission in 16 of our 426 observations.
We propose a method of calculation of the power spectrum of cosmological perturbations by means of a direct numerical integration of hydrodynamic equations in the Fourier space for a random ensemble of initial conditions with subsequent averaging procedure. This method can be an alternative to the cosmological N-body simulations. We test realizability of this method in case of one-dimensional motion of gravitating matter pressureless shells. In order to test the numerical simulations, we found an analytical solution which describes one-dimensional collapse of plane shells. The results are used to study a nonlinear interaction of different Fourier modes.
We determine the $3$-class groups of $\mathbb{Q}(\sqrt[3]{p})$ and $K=\mathbb{Q}(\sqrt[3]{p},\sqrt{-3})$ when $p\equiv 4,7\bmod 9$ is a prime and $3$ is a cubic modulo $p$. This confirms a conjecture made by Barrucand-Cohn, and proves the last remaining case of a conjecture of Lemmermeyer on the $3$-class group of $K$.
We calculate the hyperelliptic Hodge integral lambda_g lambda_{g-1} / (1 - psi) for use in arXiv:math/0702219. The proof uses the WDVV equations for the genus zero Gromov--Witten invariants of P(1,1,2).
Investigating the non-linear transport regime in a quantum dot heat engine described by the Anderson-Holstein model, it is shown that a finite electron-phonon interaction leads to a charge induced phonon generation that stimulates a phonon current even in the absence of a thermal gradient. This gives rise to the non-linear phonon Peltier effect which shows a non-trivial dependence on varying the electron-phonon interaction. Utilizing the reversal of phonon currents via charge induced phonon accumulation, we demonstrate that the heat engine surprisingly can be cooled when coupled to a hot reservoir. In further exploring possibilities that can arise from this effect, we propose a charge-induced phonon switching mechanism.
In this paper, we study the existence and (H\"older) regularity of local times of stochastic differential equations driven by fractional Brownian motions. In particular, we show that in one dimension and in the rough case H<1/2, the H\"older exponent (in t) of the local time is 1-H, where H is the Hurst parameter of the driving fractional Brownian motion.
We investigate the effects of dichotomous noise added to a classical harmonic oscillator in the form of stochastic time-dependent gain and loss states, whose durations are sampled from two distinct exponential waiting time distributions. Despite the stochasticity, stability criteria can be formulated when averaging over many realizations in the asymptotic time limit and serve to determine the boundary line in parameter space that separates regions of growing amplitudes from those of decaying ones. Furthermore, the concept of $\mathcal{PT}$ symmetry remains applicable for such a stochastic oscillator and we use it to distinguish between an underdamped symmetric phase and an overdamped asymmetric phase. In the former case, the limit of stability is marked by the same average duration for the gain and loss states, whilst in the the latter case, a higher duration of the loss state is necessary to keep the system stable. The overdamped phase has an ordered structure imposing a position-velocity ratio locking and is viewed as a phase transition from the underdamped phase, which instead displays a broad and more disordered, but nevertheless, $\mathcal{PT}$ symmetric structure. We also address the short time limit and the dynamics of the moments of the position and the velocity with the aim of revealing the extremely rich dynamics offered by this apparently quite simple mechanical system. The notions established so far may be extended and applied in the stabilization of light propagation in metamaterials and optical fibres with randomly distributed regions of asymmetric active and passive media.
Let L/F be a dihedral extension of degree 2p, where p is an odd prime. Let K/F and k/F be subextensions of L/F with degrees p and 2, respectively. Then we will study relations between the p-ranks of the class groups Cl(K) and Cl(k).
Target mass corrections to the twist-4 terms $\tilde f_2^{p,n,d}$ as well as to the leading-twist $\tilde a_2$ are discussed.
The probabilistic Glauber formula for nuclear absorption used in the literature is only valid at low energies and $x_+ \simeq 0$. Due to energy conservation, $\sigma_{abs}$ is replaced by an effective cross-section $\sigma_{abs} + x_+^{\gamma}$ ($\sigma_{c\bar{c}-N} - \sigma_{abs})$ which increases with $x_+$ and tends to the total $c\bar{c}-N$ cross-section $\sigma_{c\bar{c}-N}$. Experimental data can be described with $\sigma_{abs} \sim 4 \div 5$mb and $\sigma_{c\bar{c}-N} \sim 15 \div 20$mb. At high energies, due to the increase of the coherence length, this formula changes. The main change is the replacement of $\sigma_{abs}$ by $\sigma_{c\bar{c}-N}$ -- for all values of $x_+$, as $s \to \infty$. Thus, if $\sigma_{c\bar{c}-N} > \sigma_{abs}$ the $J/\psi$ suppression due to nuclear interaction will increase with energy.
We study by Montecarlo simulation the non-equilibrium stationary behavior of a three-dimensional stochastic lattice gas with reversible kinetic constraints and in diffusive contact with two particle reservoirs at different chemical potential. When one of the boundaries is placed in the glassy phase, the statistics of entropy production fluctuations driven by the chemical potential gradient satisfy the Gallavotti-Cohen fluctuation theorem provided that an effective entropy production is introduced.
This paper concerns a generalization of nowhere-zero modular q-flows from graphs to simplicial complexes of dimension d greater than 1. A modular q-flow of a simplicial complex is an element of the kernel of the d-th boundary map with coefficients in Z/qZ; it is called nowhere-zero if it is not zero restricted to any of the facets of the complex. Briefly noting connections to other invariants of simplicial complexes, this paper provides a generalization of Tutte's 5-flow conjecture, which claims the universal existence of a 5-flow for all bridgeless graphs. Once phrased, this paper concludes with bounds on what "5" ought to be for simplicial complexes of dimension d: proving a lower bound linear in d and a partial upper bound exponential in d.
A straightforward calculation reveals the essentially nonlocal character of the leading heavy $Q\bar{Q}$ interaction arising from nonperturbative gluon field correlations in the model of a fluctuating QCD vacuum. In light of this quarkonium spin splitting ratio predictions which have supported the scalar confinement ansatz are reconsidered as a specific example of possible consequences for spectroscopy.
The halo model is a theoretically and empirically well-motivated framework for predicting the statistics of the nonlinear matter distribution in the Universe. However, current incarnations of the halo model suffer from two major deficiencies: $(i)$ they do not enforce the stress-energy conservation of matter; $(ii)$ they are not guaranteed to recover exact perturbation theory results on large scales. Here, we provide a formulation of the halo model ("EHM") that remedies both drawbacks in a consistent way, while attempting to maintain the predictivity of the approach. In the formulation presented here, mass and momentum conservation are guaranteed on large scales, and results of perturbation theory and the effective field theory can in principle be matched to any desired order on large scales. We find that a key ingredient in the halo model power spectrum is the halo stochasticity covariance, which has been studied to a much lesser extent than other ingredients such as mass function, bias, and profiles of halos. As written here, this approach still does not describe the transition regime between perturbation theory and halo scales realistically, which is left as an open problem. We also show explicitly that, when implemented consistently, halo model predictions do not depend on any properties of low-mass halos that are smaller than the scales of interest.
These notes reproduce the content of a short, 50-minutes, survey talk given at the Nice University in September, 2004. We added a few topics that have not been touched on in the lecture by lack of time.