ShantanuT01/DACTYL-Pretraining huggingface dataset:
In this paper, we regard dilaton in Weyl-scaled induced gravitational theory as coupled Quintessence, which is called DCQ model by us. Parametrization of the dark energy model is a good method by which we can construct the scalar potential directly from the effective equation of state function $\omega_\sigma(z)$ describing the properties of the dark energy. Applying this method to the DCQ model, we consider four parametrizations of $\omega(z)$ and investigate the features of the constructed DCQ potentials, which possess two different evolutive behaviors called "O" mode and "E" mode. Lastly, we comprise the results of the constructed DCQ model with those of quintessence model numerically.
We consider the branching ratio of $b \to s\gamma$ in gauge mediated supersymmetry breaking theories. Useful bounds on the parameter space of these models are derived from the experimental bounds on $b \to s\gamma$. Constraints on masses of NLSP are presented as a function of $tan\beta$ and $M/\Lambda$ for $\mu<0$ and $\mu>0$.
In this note we consider stochastic heat equation with general additive Gaussian noise. Our aim is to derive some necessary and sufficient conditions on the Gaussian noise in order to solve the corresponding heat equation. We investigate this problem invoking two different methods, respectively based on variance computations and on path-wise considerations in Besov spaces. We are going to see that, as anticipated, both approaches lead to the same necessary and sufficient condition on the noise. In addition, the path-wise approach brings out regularity results for the solution.
We prove low regularity local well-posedness results in Bourgain-Klainerman-Machedon spaces for the Chern-Simons-Dirac system in the temporal gauge and the Coulomb gauge. Under slightly stronger assumptions on the data we also obtain "unconditional" uniqueness in the natural solution spaces.
We test the integrated galactic initial mass function (IGIMF) on the chemical evolution of 16 ultra-faint dwarf (UFD) galaxies discussing in detail the results obtained for three of them: Bo\"otes I, Bo\"otes II and Canes Venatici I, taken as prototypes of the smallest and the largest UFDs. These objects have very small stellar masses ($\sim 10^3-10^4 \mathrm{M_{\odot}}$) and quite low metallicities ([Fe/H]$<-1.0$ dex). We consider four observational constraints: the present-day stellar mass, the [$\alpha$/Fe] vs. [Fe/H] relation, the stellar metallicity distribution function and the cumulative star formation history. Our model follows in detail the evolution of several chemical species (H, He, $\alpha$-elements and Fe). We take into account detailed nucleosynthesis and gas flows (in and out). Our results show that the IGIMF, coupled with the very low star formation rate predicted by the model for these galaxies ($\sim 10^{-4}-10^{-6}\ \mathrm{M_{\odot}yr^{-1}}$), cannot reproduce the main chemical properties, because it implies a negligible number of core-collapse SNe and even Type Ia SNe, the most important polluters of galaxies. On the other hand, a constant classical Salpeter IMF gives the best agreement with data, but we cannot exclude that other formulations of the IGIMF could reproduce the properties of these galaxies. Comparing with Galaxy data we suggest that UFDs could not be the building blocks of the entire Galactic halo, although more data are necessary to draw firmer conclusions.
We use nominally forbidden electron-nuclear spin transitions in nitrogen-vacancy (NV) centers in diamond to demonstrate coherent manipulation of a nuclear spin ensemble using microwave fields at room temperature. We show that employing an off-axis magnetic field with a modest amplitude($\approx$ 0.01 T) at an angle with respect to the NV natural quantization axes is enough to tilt the direction of the electronic spins, and enable efficient spin exchange with the nitrogen nuclei of the NV center. We could then demonstrate fast Rabi oscillations on electron-nuclear spin exchanging transitions, coherent population trapping and polarization of nuclear spin ensembles in the microwave regime. Coupling many electronic spins of NV centers to their intrinsic nuclei offers full scalability with respect to the number of controllable spins and provides prospects for transduction. In particular, the technique could be applied to long-lived storage of microwave photons and to the coupling of nuclear spins to mechanical oscillators in the resolved sideband regime.
We study a $SU(2)$-symmetric spin-${3}/{2}$ system on a bipartite lattice close to the antiferromagnetic $SU(4)$-symmetric point, which can be described by the $CP^{3}$ model with a perturbation breaking the symmetry from $SU(4)$ down to $SU(2)$ and favoring the N\'eel ordering. We show that the effective theory of the perturbed model is not the usual $O(3)$ nonlinear sigma model (NLSM), but rather the $O(3)\times O(2)$ NLSM. We show that in the presence of perturbation, the topological charge $q$ of the $CP^{3}$ field is connected to the $O(3)$-NLSM type topological charge of the spin texture $Q$ (defined in a usual way via the unit N\'eel vector) by the relation $q=3Q$, thus under the influence of the perturbation unit-charge skyrmions of $CP^{3}$ model bind into triplets. We also show that in the general spin-$S$ case, symmetry breaking from $SU(2S+1)$ to $SU(2)$ results in the general relation $2S Q_{O(3)}=q_{CP^{2S}}$ between $CP^{2S}$ and $O(3)$ charges, so one can expect $2S$-multiplet binding of skyrmions.
The analysis of statistical and systematic uncertainties and their propogation to nuclear extremes has been performed. Two extremes of nuclear landscape (neutron-rich nuclei and superheavy nuclei) have been investigated. For the first extreme, we focus on the ground state properties. For the second extreme, we pay a particular attention to theoretical uncertainties in the description of fission barriers of superheavy nuclei and their evolution on going to neutron-rich nuclei.
We compute the effective coupling of the Majoron to W bosons at $\cO(\hbar)$ by evaluating the matrix element of the (B-L) current between the vacuum and a $W^+W^-$ state. The (B-L) anomaly vanishes, but the amplitude does not vanish as a result of a UV finite and non-local contribution which is entirely due to the mixing between left-chiral and right-chiral neutrinos. The result shows how anomaly-like couplings may arise in spite of the fact that the (B-L) current remains exactly conserved to all orders in $\hbar$, lending additional support to our previous proposal to identify the Majoron with the axion.
The ionization fraction plays a key role in the chemistry and dynamics of molecular clouds. We study the H13CO+, DCO+ and HOC+ line emission towards the Horsehead, from the shielded core to the UV irradiated cloud edge, i.e., the Photodissociation Region (PDR), as a template to investigate the ionization fraction gradient in molecular clouds. We analyze a PdBI map of the H13CO+ J=1-0 line, complemented with IRAM-30m H13CO+ and DCO+ higher-J line maps and new HOC+ and CO+ observations. We compare self-consistently the observed spatial distribution and line intensities with detailed depth-dependent predictions of a PDR model coupled with a nonlocal radiative transfer calculation. The chemical network includes deuterated species, 13C fractionation reactions and HCO+/HOC+ isomerization reactions. The role of neutral and charged PAHs in the cloud chemistry and ionization balance is investigated. The detection of HOC+ reactive ion towards the Horsehead PDR proves the high ionization fraction of the outer UV irradiated regions, where we derive a low [HCO+]/[HOC+]~75-200 abundance ratio. In the absence of PAHs, we reproduce the observations with gas-phase metal abundances, [Fe+Mg+...], lower than 4x10(-9) (with respect to H) and a cosmic-rays ionization rate of zeta=(5+/-3)x10(-17) s(-1). The inclusion of PAHs modifies the ionization fraction gradient and increases the required metal abundance. The ionization fraction in the Horsehead edge follows a steep gradient, with a scale length of ~0.05 pc (or ~25''), from [e-]~10(-4) (or n_e ~ 1-5 cm(-3)) in the PDR to a few times ~10(-9) in the core. PAH^- anions play a role in the charge balance of the cold and neutral gas if substantial amounts of free PAHs are present ([PAH] >10(-8)).
This paper describes a systematic approach towards building a new family of neural networks based on a delay-loop version of a reservoir neural network. The resulting architecture, called Scaled-Time-Attention Robust Edge (STARE) network, exploits hyper dimensional space and non-multiply-and-add computation to achieve a simpler architecture, which has shallow layers, is simple to train, and is better suited for Edge applications, such as Internet of Things (IoT), over traditional deep neural networks. STARE incorporates new AI concepts such as Attention and Context, and is best suited for temporal feature extraction and classification. We demonstrate that STARE is applicable to a variety of applications with improved performance and lower implementation complexity. In particular, we showed a novel way of applying a dual-loop configuration to detection and identification of drone vs bird in a counter Unmanned Air Systems (UAS) detection application by exploiting both spatial (video frame) and temporal (trajectory) information. We also demonstrated that the STARE performance approaches that of a State-of-the-Art deep neural network in classifying RF modulations, and outperforms Long Short-term Memory (LSTM) in a special case of Mackey Glass time series prediction. To demonstrate hardware efficiency, we designed and developed an FPGA implementation of the STARE algorithm to demonstrate its low-power and high-throughput operations. In addition, we illustrate an efficient structure for integrating a massively parallel implementation of the STARE algorithm for ASIC implementation.
The high-temperature superconducting state in cuprates appears if charge carriers are doped into a Mott insulating parent compound. An unresolved puzzle is the unconventional nature of the normal state above the superconducting dome, and its connection to the superconducting instability. At weak hole-doping, a "pseudo-gap" metal state with signatures of time-reversal symmetry breaking is observed, which near optimal doping changes into a "strange metal" with non-Fermi liquid properties. Qualitatively similar phase diagrams are found in multi-orbital systems, such as pnictides, where the unconventional metal states arise from a Hund coupling induced spin-freezing. Here, we show that the relevant model for cuprates, the single-orbital Hubbard model on the square lattice, can be mapped onto an effective multi-orbital problem with strong ferromagnetic Hund coupling. The spin-freezing physics of this multi-orbital system explains the phenomenology of cuprates, including the pseudo-gap, the strange metal, and the d-wave superconducting instability. Our analysis suggests that spin-freezing is the universal mechanism which controls the properties of unconventional superconductors.
We provide results relating to the integrability, uniform integrability and local integrability of exponential MAPs, which are natural extensions of exponential Levy models. Then, we use Mellin transform and partial integro-differential equation methods to value European options under a such a model. Finally, a comparison is made between the price of a European call option and that of an Asian call option.
We consider a percolation model on square lattices with sites weighted by beta-distributed random variables $S\sim \mathrm{Beta}(a,b)$ with a positive real parameters $a>0$ and $b>0$. Using the Monte Carlo method, we estimate the percolation probability $P_\infty$ as a relative frequency $P^*_\infty$ averaged over the target subset of sites on a square lattice. As a result of the comparative analysis, we formulate two empirical hypotheses: the first on the correspondence of percolation thresholds $p_c$ to $p_0$-quantiles (where $p_0=0.592746\ldots$) of random variables $S_i$ weighing sites of the square lattice with $(1,0)$-neighborhood, and the second on the convergence of statistical estimates of percolation probability functions $P^*_\infty(p)$ to cumulative distribution functions $F_{S_i}(p)$ of these variables $S_i$ for the supercritical values of the occupation probability $p\geq p_c$.
6-d polyhedral models give a periodic description of aperiodic quasicrystals. There are powerful tools to describe their structural surface properties. Basis of the model for icosahedral quasicrystals are given. This description is further used to interpret high resolution STM images of the surface of i-AlPdMn which surface preparation was followed by He diffraction. It is found that both terrace structure and step-terrace height profiles in STM images can be consistently interpreted by the described model.
For a proper local embedding between two Deligne--Mumford stacks Y and X, we find, under certain mild conditions, a new (possibly non-separated) Deligne--Mumford stack X', with an etale, surjective and universally closed map to the target X, and whose fiber product with the image of the local embedding is a finite union of stacks with corresponding etale, surjective and universally closed maps to Y. Moreover, a natural set of weights on the substacks of X' allows the construction of a universally closed push-forward, and thus a comparison between the Chow groups of X' and X. We apply the construction above to the computation of the Chern classes of a weighted blow-up along a regular local embedding via deformation to a weighted normal cone and localization. We describe the stack X' in the case when X is the moduli space of stable maps with local embeddings at the boundary. We apply the methods above to find the Chern classes of the stable map spaces.
What if normal baryonic matter is compressed so tightly that atomic nuclei come into close contact? This question has been asked since 1930s. The fist answer was presented by Lev Landau whose speculation has been developed, and the concept of neutron star is then popularized. However, another answer is related to strange star, which becomes worthy of attention especially after the establishment of the standard model of particle physics in 1960s. The basic ideas of this study are introduced pedagogically. We must point out emphatically that flavour symmetry of and strong coupling between quarks would be essential in seeking true answer to the question. The final answer is expected to appear in the era of multimessenger astronomy. It is emphasized too that, besides the differences of global properties (e.g., mass-radius relation, maximum mass, tidal deformability), the strong-bound surface of strange star (rather than the gravity-bound one for conventional neutron star) could play an important role in identifying a strange star by astronomical observations.
We used the database of eclipsing binaries detected by the OGLE microlensing project in the pencil-beam search volume toward Baade's Window to define a sample of 74 detached, equal-mass, main-sequence binary stars with short orbital periods in the range 0.19<P<8 days. The logarithmic slope of the period distribution, logN propto (-0.8 pm 0.2) logP, was used to infer the angular-momentum-loss (AML) efficiency for the late, rapidly-rotating members of close binaries. It is very likely that the main cause of the negative slope is a discovery selection bias that progressively increases with the orbital period length. Assuming a power-law dependence for the correction for the bias: bias propto -C logP (with C ge 0), the AML braking-efficiency exponent alpha in dH/dt = P^-alpha can take any value alpha = (-1.1 pm 0.2) + C. Very simple considerations of discovery biases suggest C simeq 4/3, which would give an AML braking law very close to the "saturated" one, with no dependence on the period. However, except for plausibility arguments, we have no firm data to support this estimate of C, so that alpha remains poorly constrained. The results signal the utmost importance of the detection bias evaluation for variable star databases used in analyses similar to the one presented in this study.
The paper describes a solution to the problem of quantum measurement that has been proposed recently. The literal understanding of the basic rule of quantum mechanics on identical particles violates the cluster separation principle and so leads to difficulties. A proposal due to Peres of how such difficulties could be removed is reformulated and extended. Cluster separability leads to a locality requirement on observables and to the key notion of separation status. Separation status of a microsystem is shown to change in preparation and registration processes. The indispensability of detectors plays an important role. Changes of separation status are alterations of kinematic description rather than some parts of dynamical trajectories and so more radical than 'collapse of the wave function'. Textbook quantum mechanics does not provide any information of how separation status changes run, hence new rules must be formulated. This enables to satisfy the objectification requirement for registrations. To show how the ideas work, a simplified model of registration apparatus is constructed.
Minimal conductivity of a single undoped graphene layer is known to be of the order of the conductance quantum, independent of the electron velocity. We show that this universality does not survive electron-electron interaction which results in the non-trivial frequency dependence. We begin with analyzing the perturbation theory in the interaction parameter 'g' for the electron self-energy and observe the failure of the random-phase approximation. The optical conductivity is then derived from the quantum kinetic equation and the exact result is obtained in the limit when g << 1 << g ln\omega.
Given a local gapped Hamiltonian with a global symmetry on a one dimensional lattice we describe a method to identify if the Hamiltonian belongs to a quantum phase in which the symmetry is spontaneously broken in the ground states or to a specific symmetry protected phase, without using local or string order parameters. We obtain different matrix product state (MPS) descriptions of the symmetric ground state(s) of the Hamiltonian by restricting the MPS matrices to transform under different projective representations of the symmetry. The phase of the Hamiltonian is identified by examining which MPS descriptions, if any, are injective, namely, whether the largest eigenvalue of the "transfer matrix" obtained from the MPS is unique. We demonstrate the method for translation invariant Hamiltonians with a global SO(3), Z_2 and Z_2 x Z_2 symmetry on an infinite chain.
Starting from Israel equations for the spherically symmetric thin shells we introduce the effective potential and show how it can be used in constructing, without further thorough investigation, the corresponding Carter-Penrose diagrams describing clearly the global geometry of the composite space-time manifolds. We demonstrate, how this new method works, by considering all possible configurations for the neutral thin dust shell immersed into different types of Reissner-Nordstr\"om electro-vacuum manifolds.
We attempt to understand the driving mechanism of a macrospicule and its relationship with a coronal jet. We study the dynamics of a macrospicule and an associated coronal jet captured by multi-spacecraft observations. Doppler velocities both in the macrospicule and the coronal jet are determined by EIS and SUMER spectra. Their temporal evolution is studied using X-ray and He II 304 images. A blueshift of -120+/-15 km/s is detected on one side of the macrospicule, while a redshift of 50+/-6 km/s is found at the base of the other side. The inclination angle of the macrospicule inferred from a stereoscopic analysis with STEREO suggests that the measured Doppler velocities can be attributed to a rotating motion of the macrospicule rather than a radial flow or an expansion. The macrospicule is driven by the unfolding motion of a twisted magnetic flux rope, while the associated X-ray jet is a radial outflow.
In Gert Almkvist's beautiful article, entitled "Invariants, mostly old ones", (that appeared in the Pacific Journal of Mathematics, vol. 86 (1980), pp. 1-13) he talked about a sequence of generating functions that came up in his work, that turned out to be the same as generating functions for the number of covariants of binary quadratic forms studied by Faa de Bruno, Cayley, Sylvester, and other 19th century savantes. Using a very simple-minded Maple program (that uses the partial-fraction decomposition of a rational function), we recompute them, and go all the way to degree 18. It turns out that the same method can be used to answer many other enumeration questions, including the one in the title.
Crystal symmetry governs the nature of electronic Bloch states. For example, in the presence of time reversal symmetry, the orbital magnetic moment and Berry curvature of the Bloch states must vanish unless inversion symmetry is broken. In certain 2D electron systems such as bilayer graphene, the intrinsic inversion symmetry can be broken simply by applying a perpendicular electric field. In principle, this offers the remarkable possibility of switching on/off and continuously tuning the magnetic moment and Berry curvature near the Dirac valleys by reversible electrical control. Here we demonstrate this principle for the first time using bilayer MoS2, which has the same symmetry as bilayer graphene but has a bandgap in the visible that allows direct optical probing of these Berry-phase related properties. We show that the optical circular dichroism, which reflects the orbital magnetic moment in the valleys, can be continuously tuned from -15% to 15% as a function of gate voltage in bilayer MoS2 field-effect transistors. In contrast, the dichroism is gate-independent in monolayer MoS2, which is structurally non-centrosymmetric. Our work demonstrates the ability to continuously vary orbital magnetic moments between positive and negative values via symmetry control. This represents a new approach to manipulating Berry-phase effects for applications in quantum electronics associated with 2D electronic materials.
Motivated by the fact that a polarized ${}^3$He nucleus behaves as an `effective' neutron target, we examine manifestations of neutron electromagnetic polarizabilities in elastic Compton scattering from the Helium-3 nucleus. We calculate both unpolarized and double-polarization observables using chiral perturbation theory to next-to-leading order (${\mathcal O}(e^2 Q)$) at energies, $\omega \leq m_{\pi}$, where $m_{\pi}$ is the pion mass. Our results show that the unpolarized differential cross section can be used to measure neutron electric and magnetic polarizabilities, while two double-polarization observables are sensitive to different linear combinations of the four neutron spin polarizabilities.   [Note added in 2018] The qualitative conclusions and analytic formulae presented in this paper are correct, but several of the numerical results are wrong: see the erratum posted as arXiv:1804.01206 for further details. A full suite of corrected numerical results for cross sections and asymmetries can be found in Margaryan et al., arXiv:1804.00956. They can also be obtained as an interactive Mathematica notebook by emailing hgrie@gwu.edu.