ShantanuT01/DACTYL-Pretraining huggingface dataset:
In this paper we study a 2-type linear-fractional branching process in varying environment with asymptotically constant mean matrices. Let $\nu$ be the extinction time and for $k\ge1$ let $M_k$ be the mean matrix of offspring distribution of individuals of the $(k-1)$-th generation. Under certain conditions, we show that $P(\nu=n)$ and $P(\nu>n)$ are asymptotically equivalent to some functions of products of spectral radii of the mean matrices. This paper complements a former result [arXiv: 2007.07840] which requires in addition a condition $\forall k\ge1,\rm{det}(M_k)<-\varepsilon$ for some $\varepsilon>0.$ Such a condition excludes a large class of mean matrices. As byproducts, we also get some results on asymptotics of products of nonhomogeneous matrices which have their own interests.
For a probability measure $\mu$ on $[0,1]$ without discrete component, the best possible order of approximation by a finite point set in terms of the star-discrepancy is $\frac{1}{2N}$ as has been proven relatively recently. However, if $\mu$ contains a discrete component no non-trivial lower bound holds in general because it is straightforward to construct examples without any approximation error in this case. This might explain, why the approximation of discrete measures on $[0,1]$ by finite point sets has so far not been completely covered in the existing literature. In this note, we close this gap by giving a complete description of the discrete case. Most importantly, we prove that for any discrete measure the best possible order of approximation is for infinitely many $N$ bounded from below by $\frac{1}{cN}$ for some constant $c \geq 2$ which depends on the measure. This implies, that for a finitely supported discrete measure on $[0,1]^d$ the known possible order of approximation $\frac{1}{N}$ is indeed the optimal one.
We analyze an example of a photon in superposition of different modes, and ask what is the degree of their entanglement with vacuum. The problem turns out to be ill-posed since we do not know which representation of the algebra of canonical commutation relations (CCR) to choose for field quantization. Once we make a choice, we can solve the question of entanglement unambiguously. So the difficulty is not with mathematics, but with physics of the problem. In order to make the discussion explicit we analyze from this perspective a popular argument based on a photon leaving a beam splitter and interacting with two two-level atoms. We first solve the problem algebraically in Heisenberg picture, without any assumption about the form of representation of CCR. Then we take the $\infty$-representation and show in two ways that in two-mode states the modes are maximally entangled with vacuum, but single-mode states are not entangled. Next we repeat the analysis in terms of the representation of CCR taken from Berezin's book and show that two-mode states do not involve the mode-vacuum entanglement. Finally, we switch to a family of reducible representations of CCR recently investigated in the context of field quantization, and show that the entanglement with vacuum is present even for single-mode states. Still, the degree of entanglement is here difficult to estimate, mainly because there are $N+2$ subsystems, with $N$ unspecified and large.
We introduce a monoid structure on a certain set of labelled binary trees, by a process similar to the construction of the plactic monoid. This leads to a new interpretation of the algebra of planar binary trees of Loday-Ronco.
When a charged particle encircles around an Alice string, it changes the sign of the electric charge. In this paper we find a BPS-saturated Alice string in $U(1)\times SO(3)$ gauge theory with charged complex scalar fields belonging to the vector representation. After performing BPS completion we solve the BPS equations numerically. We further embed the Alice string into an ${\cal N}=1$ supersymmetric gauge theory to show that it is half BPS.
In this paper, we calculate neutron and proton decay rates and branching ratios in a predictive SO(10) SUSY GUT which agrees well with low energy data. We show that the nucleon lifetimes are consistent with the experimental bounds. The nucleon decay rates are calculated using all one-loop chargino and gluino dressed diagrams regardless of their chiral structure. We show that the four-fermion operator $C_{jk} (u_R {d_j}_R)({d_k}_L {\nu_\tau}_L)$, commonly neglected in previous nucleon decay calculations, not only contributes significantly to nucleon decay, but, for many values of the initial GUT parameters and for large $\tan\beta$, actually dominates the decay rate. As a consequence, we find that $\tau_p/\tau_n$ is often substantially larger than the prediction obtained in small $\tan\beta$ models. We also find that gluino-dressed diagrams, often neglected in nucleon decay calculations, contribute significantly to nucleon decay. In addition we find that the branching ratios obtained from this realistic SO(10) SUSY GUT differ significantly from the predictions obtained from ``generic" SU(5) SUSY GUTS. Thus nucleon decay branching ratios, when observed, can be used to test theories of fermion masses.
Previous observations of the middle-aged pulsar Geminga with XMM-Newton and Chandra have shown an unusual pulsar wind nebula (PWN), with a 20" long central (axial) tail directed opposite to the pulsar's proper motion and two 2' long, bent lateral (outer) tails. Here we report on a deeper (78 ks) Chandra observation and a few additional XMM-Newton observations of the Geminga PWN. The new Chandra observation has shown that the axial tail, which includes up to three brighter blobs, extends at least 50" (i.e., 0.06 d_{250} pc) from the pulsar. It also allowed us to image the patchy outer tails and the emission in the immediate vicinity of the pulsar with high resolution. The PWN luminosity, L_{0.3-8 keV} ~ 3\times 10^{29} d_{250}^2 erg/s, is lower than the pulsar's magnetospheric luminosity by a factor of 10. The spectra of the PWN elements are rather hard (photon index ~ 1). Comparing the two Chandra images, we found evidence of PWN variability, including possible motion of the blobs along the axial tail. The X-ray PWN is the synchrotron radiation from relativistic particles of the pulsar wind; its morphology is connected with the supersonic motion of Geminga. We speculate that the outer tails are either (1) a sky projection of the limb-brightened boundary of a shell formed in the region of contact discontinuity, where the wind bulk flow is decelerated by shear instability, or (2) polar outflows from the pulsar bent by the ram pressure from the ISM. In the former case, the axial tail may be a jet emanating along the pulsar's spin axis, perhaps aligned with the direction of motion. In the latter case, the axial tail may be the shocked pulsar wind collimated by the ram pressure.
In the recent years, a spin-valve was developed with a current-confined-path structure consisting of a non-oxide-layer (NOL). We analyze magnetic structures of the current-confinedpath in the nano-oxide layer sandwiched between ferromagnetic electrodes and clarify the dependency of the magnetic structure on the shape and size of the current-confined-path. Our results of stiffness energy density and thermal stability shows that we should fabricate a CPP spin-valve with narrow current-confinedpaths with large aspect ratio and strong constriction in order to enhance the MR ratio.
We present the first results obtained at CFHT with the TRIDENT infrared camera, dedicated to the detection of faint companions close to bright nearby stars. Its main feature is the acquisition of three simultaneous images in three wavelengths (simultaneous differential imaging) across the methane absorption bandhead at 1.6 micron, that enables a precise subtraction of the primary star PSF while keeping the companion signal. Gl229 and 55Cnc observations are presented to demonstrate TRIDENT subtraction performances. It is shown that a faint companion with a DeltaH of 10 magnitudes would be detected at 0.5 arcsec from the primary.
We show that the Okounkov body of a big divisor with finitely generated section ring is a rational simplex, for an appropriate choice of flag; furthermore, when the ambient variety is a surface, the same holds for every big divisor. Under somewhat more restrictive hypotheses, we also show that the corresponding semigroup is finitely generated.
The optical medium analogy of a given spacetime was developed decades ago and has since then been widely applied to different gravitational contexts. Here we consider the case of a colliding gravitational wave spacetime, generalizing previous results concerning single gravitational pulses. Given the complexity of the nonlinear interaction of two gravitational waves in the framework of general relativity, typically leading to the formation of either horizons or singularities, the optical medium analogy proves helpful to simply capture some interesting effects of photon propagation.
We have made a systematic numerical study of the 16 Wilf classes of length-5 classical pattern-avoiding permutations from their generating function coefficients. We have extended the number of known coefficients in fourteen of the sixteen classes. Careful analysis, including sequence extension, has allowed us to estimate the growth constant of all classes, and in some cases to estimate the sub-dominant power-law term associated with the exponential growth.   In six of the sixteen classes we find the familiar power-law behaviour, so that the coefficients behave like $s_n \sim C \cdot \mu^n \cdot n^g,$ while in the remaining ten cases we find a stretched exponential as the most likely sub-dominant term, so that the coefficients behave like $s_n \sim C \cdot \mu^n \cdot \mu_1^{n^\sigma} \cdot n^g,$ where $0 < \sigma < 1.$ We have also classified the 120 possible permutations into the 16 distinct classes.   We give compelling numerical evidence, and in one case a proof, that all 16 Wilf-class generating function coefficients can be represented as moments of a non-negative measure on $[0,\infty).$ Such sequences are known as {\em Stieltjes moment sequences}. They have a number of nice properties, such as log-convexity, which can be used to provide quite strong rigorous lower bounds.   Stronger bounds still can be established under plausible monotonicity assumptions about the terms in the continued-fraction expansion of the generating functions implied by the Stieltjes property. In this way we provide strong (non-rigorous) lower bounds to the growth constants, which are sometimes within a few percent of the exact value.
We construct a DGP-inspired braneworld model where induced gravity on the brane is modified in the spirit of $f(R)$ gravity and stringy effects are taken into account by incorporation of the Gauss-Bonnet term in the bulk action. We explore cosmological dynamics of this model and we show that this scenario is a successful alternative for dark energy proposal. Interestingly, it realizes the phantom-like behavior without introduction of any phantom field on the brane and the effective equation of state parameter crosses the cosmological constant line naturally in the same way as observational data suggest.
Vlasov kinetic theory is extended by adopting an extra one particle distribution function as an additional state variable characterizing the micro-turbulence internal structure. The extended Vlasov equation keeps the reversibility, the Hamiltonian structure, and the entropy conservation of the original Vlasov equation. In the setting of the extended Vlasov theory we then argue that the Fokker-Planck type damping in the velocity dependence of the extra distribution function induces the Landau damping. The same type of extension is made also in the setting of fluid mechanics.
A code, Epic5, has been developed which computes, in the two-dimensional case, the initially circular orbits of guiding centra in an arbitrary axisymmetric potential with an arbitrary, weak perturbing potential in solid body rotation. This perturbing potential is given by its Fourier expansion. The analytic solution solves the linear epicyclic approximation of the equations of motion. To simulate the motion of interstellar matter and to damp the Lindblad resonances, we have in these equations introduced a friction which is proportional to the deviation from circular velocity. The corotation resonance is also damped by a special parameter. The program produces, in just a few seconds, orbital and density maps, as well as line of sight velocity maps for a chosen orientation of the galaxy.   We test Epic5 by comparing its results with previous simulations and observations from the literature, which gives satisfactory agreement. The aim is that this program should be a useful complement to elaborate numerical simulations. Particularly so are its abilities to quickly explore the parameter space, to construct artificial galaxies, and to isolate various single agents important for developing structure of interstellar matter in disc galaxies.
Multimodal prediction results are essential for trajectory prediction task as there is no single correct answer for the future. Previous frameworks can be divided into three categories: regression, generation and classification frameworks. However, these frameworks have weaknesses in different aspects so that they cannot model the multimodal prediction task comprehensively. In this paper, we present a novel insight along with a brand-new prediction framework by formulating multimodal prediction into three steps: modality clustering, classification and synthesis, and address the shortcomings of earlier frameworks. Exhaustive experiments on popular benchmarks have demonstrated that our proposed method surpasses state-of-the-art works even without introducing social and map information. Specifically, we achieve 19.2% and 20.8% improvement on ADE and FDE respectively on ETH/UCY dataset. Our code will be made publicly availabe.
We study the perturbative renormalizability of chiral two pion exchange in nucleon-nucleon scattering for p- and d-waves within the effective field theory approach. The one pion exchange potential is fully iterated at the leading order in the expansion, a choice generating a consistent and well-defined power counting that we explore in detail. The results show that perturbative chiral two pion exchange reproduces the data up to a center-of-mass momentum of k_cm ~300 MeV at NNLO and that the effective field theory expansion convergences up to k_cm ~ 350 MeV.
We discuss a method to select the velocities of ultra-cold atoms with a modified Fabry-Perot type of device made of two effective barriers and a well created, respectively, by blue and red detuned lasers. The laser parameters may be used to select the peak and width of the transmitted velocity window. In particular, lowering the central well provides a peak arbitrarily close to zero velocity having a minimum but finite width. The low-energy atomic scattering off this laser device is parameterized and approximate formulae are found to describe and explain its behaviour.
We propose a very simple physical mechanism responsible for the formation of the Low Ionization Line part of the Broad Line Region in Active Galactic Nuclei. It explains the scaling of the Broad Line Region size with the monochromatic luminosity, including the exact slope and the proportionality constant, seen in the reverberation studies of nearby sources. The scaling is independent from the mass and accretion rate of an active nucleus. The mechanism predicts the formation of a dust-driven wind in the disk region where the local effective temperature of a non-illuminated accretion disk drops below 1000 K and allows for dust formation. We explore now the predictive power of the model with the aim to differentiate between this model and the previously proposed mechanisms of the formation of the Broad Line Region. We discuss the expected departures from the universal scaling at long wavelength, and the role of the inclination angle of the accretion disk in the source. We compare the expected line profiles with Mg II line profiles in the quasars observed by us with the SALT telescope. We also discuss the tests based on the presence or absence of the broad emission lines in low luminosity active galaxies. Finally, we discuss the future tests of the model to be done with expected ground-based observations and satellite missions.
Observations show that luminous blue variables (LBVs) are far more dispersed than massive O-type stars, and Smith & Tombleson suggested that these large separations are inconsistent with a single-star evolution model of LBVs. Instead, they suggested that the large distances are most consistent with binary evolution scenarios. To test these suggestions, we modelled young stellar clusters and their passive dissolution, and we find that, indeed, the standard single-star evolution model is mostly inconsistent with the observed LBV environments. If LBVs are single stars, then the lifetimes inferred from their luminosity and mass are far too short to be consistent with their extreme isolation. This implies that there is either an inconsistency in the luminosity- to-mass mapping or the mass-to-age mapping. In this paper, we explore binary solutions that modify the mass-to-age mapping and are consistent with the isolation of LBVs. For the binary scenarios, our crude models suggest that LBVs are rejuvenated stars. They are either the result of mergers or they are mass gainers and received a kick when the primary star exploded. In the merger scenario, if the primary is about 19 solar masses, then the binary has enough time to wander far afield, merge and form a rejuvenated star. In the mass-gainer and kick scenario, we find that LBV isolation is consistent with a wide range of kick velocities, anywhere from 0 to ~ 105 km/s. In either scenario, binarity seems to play a major role in the isolation of LBVs.
The goal of this note is to provide an analysis of the positive integers that are represented everywhere locally, but not globally, by each of the 29 spinor regular positive definite integral ternary quadratic forms that are not regular.
The many body quantum dynamics of dipolar coupled nuclear spins I = 1/2 on an otherwise isolated cubic lattice are studied with nuclear magnetic resonance (NMR). By increasing the signal-to-noise ratio by two orders of magnitude compared with previous reports for the free induction decay (FID) of 19F in CaF2 we obtain new insight into its long-time behavior. We confirm that the tail of the FID is an exponentially decaying cosine, but our measurements reveal a second universal decay mode with comparable frequency but twice the decay constant. This result is in agreement with a recent theoretical prediction for the FID in terms of eigenvalues for the time evolution of chaotic many-body quantum systems.
This paper is centered on the random graph generated by a Doeblin-type coupling of discrete time processes on a countable state space whereby when two paths meet, they merge. This random graph is studied through a novel subgraph, called a bridge graph, generated by paths started in a fixed state at any time. The bridge graph is made into a unimodular network by marking it and selecting a root in a specified fashion. The unimodularity of this network is leveraged to discern global properties of the larger Doeblin graph. Bi-recurrence, i.e., recurrence both forwards and backwards in time, is introduced and shown to be a key property in uniquely distinguishing paths in the Doeblin graph, and also a decisive property for Markov chains indexed by $\mathbb{Z}$. Properties related to simulating the bridge graph are also studied.
Let $f(m,c)=\sum_{k=0}^{\infty} (km+1)^{k-1} c^k e^{-c(km+1)/m} / (m^kk!)$. For any positive integer $m$ and positive real $c$, the identity $f(m,c)=f(1,c)^{1/m}$ arises in the random graph theory. In this paper, we present two elementary proofs of this identity: a pure combinatorial proof and a power-serial proof. We also proved that this identity holds for any positive reals $m$ and $c$.
We show that vacuum string field theory with the singular kinetic operator conjectured by Gaiotto, Rastelli, Sen and Zwiebach can be obtained by field redefinition from a regular theory constructed by Takahashi and Tanimoto. We solve the equation of motion both by level truncation and by a series expansion using the regulated butterfly state, and we find evidence that the energy density of a D25-brane is well defined and finite. Although the equation of motion naively factorizes into the matter and ghost sectors in the singular limit, subleading terms in the kinetic operator are relevant and the factorization does not strictly hold. Nevertheless, solutions corresponding to different D-branes can be constructed by changing the boundary condition in the boundary conformal field theory formulation of string field theory, and ratios of D-brane tensions are shown to be reproduced correctly.
We discuss the peculiar nature of the nucleus of M94 (NGC 4736) in the context of new measurements of the broad H_alpha emission from HST-STIS observations. We show that this component is unambiguously associated with the high-resolution X-ray, radio, and variable UV sources detected at the optical nucleus of this galaxy. These multi-wavelength observations suggest that NGC 4736 is one of the least luminous broad-line (type 1) LINERs, with Lbol = 2.5 \times 10^40 erg/s. This LINER galaxy has also possibly the least luminous broad line region known (LH_alpha =2.2\times10^37 erg/s). We compare black hole mass estimates of this system to the recently measured ~7 \times 10^6 M_sun dynamical black hole mass measurement. The fundamental plane and M-sigma relationship roughly agree with the measured black hole mass, while other accretion based estimates (the M-FWHM(H_alpha) relation, empirical correlation of BH mass with high-ionization mid IR emission lines, and the X-ray excess variance) provide much lower estimates (~10^5 M_sun). An energy budget test shows that the AGN in this system may be deficient in ionizing radiation relative to the observed emission-line activity. This deficiency may result from source variability or the superposition of multiple sources including supernovae.
We develop a semi-analytic model to explore different prescriptions of supermassive black hole (SMBH) fuelling. This model utilises a merger-triggered burst mode in concert with two possible implementations of a long-lived steady mode for assembling the mass of the black hole in a galactic nucleus. We improve modelling of the galaxy-halo connection in order to more realistically determine the evolution of a halo's velocity dispersion. We use four model variants to explore a suite of observables: the M-sigma relation, mass functions of both the overall and broad-line quasar population, and luminosity functions as a function of redshift. We find that "downsizing" is a natural consequence of our improved velocity dispersion mappings, and that high-mass SMBHs assemble earlier than low-mass SMBHs. The burst mode of fuelling is sufficient to explain the assembly of SMBHs to z=2, but an additional steady mode is required to both assemble low-mass SMBHs and reproduce the low-redshift luminosity function. We discuss in detail the trade-offs in matching various observables and the interconnected modelling components that govern them. As a result, we demonstrate the utility as well as the limitations of these semi-analytic techniques.