This paper presents algorithms for performing data-driven reachability analysis under temporal logic side information. In certain scenarios, the data-driven reachable sets of a robot can be prohibitively conservative due to the inherent noise in the
robots historical measurement data. In the same scenarios, we often have side information about the robots expected motion (e.g., limits on how much a robot can move in a one-time step) that could be useful for further specifying the reachability analysis. In this work, we show that if we can model this side information using a signal temporal logic (STL) fragment, we can constrain the data-driven reachability analysis and safely limit the conservatism of the computed reachable sets. Moreover, we provide formal guarantees that, even after incorporating side information, the computed reachable sets still properly over-approximate the robots future states. Lastly, we empirically validate the practicality of the over-approximation by computing constrained, data-driven reachable sets for the Small-Vehicles-for-Autonomy (SVEA) hardware platform in two driving scenarios.
We present an analysis of all the archival high resolution spectra of the Narrow-line Seyfert 1 galaxy Mrk~335 obtained with Reflection Grating Spectrometer (RGS) on board textit{XMM-Newton}. The spectra show rich emission and absorption features in
low and intermediate flux intervals. We model the emission lines with the textsc{pion_xs} grid and try to find any possible correlation between the properties of the emitting gas and the source flux. Current data does not allow detailed trace of the response of the line emitting gas to the X-ray flux of Mrk~335, but the flux of the X-ray lines is significantly less variable than the X-ray continuum. We also find that the warm absorbers properties are not correlated with the flux variability. From the latest textit{XMM-Newton} observation in 2019 December, we find that the photoionized emission and distant reflection components have not responded to the flux drop of Mrk~335 from 2018 July. However, the possible existence of partial covering absorber in the 2018--2019 low state of Mrk~335 makes it difficult to constrain the scale of the emitting gas using this lack of response.
The $U(1)$ quantum link model on the triangular lattice has two rotation-symmetry-breaking nematic confined phases. Static external charges are connected by confining strings consisting of individual strands with fractionalized electric flux. The two
phases are separated by a weak first order phase transition with an emergent almost exact $SO(2)$ symmetry. We construct a quantum circuit on a chip to facilitate near-term quantum computations of the non-trivial string dynamics.
A unified description of finite nuclei and equation of state of neutron stars present a major challenge as well as opportunities for understandings of nuclear interactions.Inspired by the Lee-Huang-Yang formula of hard-sphere gases, we developed effe
ctive nuclear interactions with an additional high-order density dependent term.The original Skyrme force SLy4 is widely used in studies of neutron stars but is not satisfied for global descriptions of finite nuclei. The refitted SLy4${}$ force can improve descriptions of finite nuclei but slightly reduces the radius of neutron star of 1.4 solar mass.We found that the extended SLy4 force with a higher-order density dependence can properly describe properties of both finite nuclei and GW170817 binary neutron stars, including the mass-radius relation and the tidal deformability. This demonstrated the essential role of high-order density dependence at ultrahigh densities. Our work provides a unified and predictive model for neutron stars, as well as new insights for the future development of effective interactions.
We propose algorithms for performing model checking and control synthesis for discrete-time uncertain systems under linear temporal logic (LTL) specifications. We construct temporal logic trees (TLT) from LTL formulae via reachability analysis. In co
ntrast to automaton-based methods, the construction of the TLT is abstraction-free for infinite systems, that is, we do not construct discrete abstractions of the infinite systems. Moreover, for a given transition system and an LTL formula, we prove that there exist both a universal TLT and an existential TLT via minimal and maximal reachability analysis, respectively. We show that the universal TLT is an underapproximation for the LTL formula and the existential TLT is an overapproximation. We provide sufficient conditions and necessary conditions to verify whether a transition system satisfies an LTL formula by using the TLT approximations. As a major contribution of this work, for a controlled transition system and an LTL formula, we prove that a controlled TLT can be constructed from the LTL formula via control-dependent reachability analysis. Based on the controlled TLT, we design an online control synthesis algorithm, under which a set of feasible control inputs can be generated at each time step. We also prove that this algorithm is recursively feasible. We illustrate the proposed methods for both finite and infinite systems and highlight the generality and online scalability with two simulated examples.
We explore a disc origin for the highly-blueshifted, variable absorption lines seen in the X-ray spectrum of the Narrow Line Seyfert 1 galaxy IRAS13224-3809. The blueshift corresponds to a velocity of about 0.25c. Such features in other Active Galact
ic Nuclei are often interpreted as UltraFast Outflows (UFOs). The velocity is of course present in the orbital motions of the inner disk. The absorption lines in IRAS13224-3809 are best seen when the flux is low and the reflection component of the disk is strong relative to the power-law continuum. The spectra are consistent with a model in which the reflection component passes through a thin, highly-ionized absorbing layer at the surface of the inner disc, the blue-shifted side of which dominates the flux due to relativistic aberration (the disc inclination is about 70 deg). No fast outflow need occur beyond the disc.
Natural rubber vucanizates containing 0-50 phr of a fine carbon black (N115,d=27nm) were prepared and tensile strengths of normal (no pre-cut) and edge pre-cut specimens were determined. Normal tensile strengths of all vulcanizates were similar. At t
he relatively slow strain rate experienced wholesale by normal uncut specimens, all vulcanizates, prior to crack initiation, strain-crystallized sufficiently to be strong. However, pre-cut specimens experience increased strain rate at a cut tip. Magnification of the strain rate increases as cut depth c increases. Fracture in the gum NR and vulcanizates with up to 14 phr of black occurred by simple forward crack growth from a cut tip, and all exhibited a critical cut size, above which strength dropped abruptly. Furthermore, for these lightly filled samples, strength and critical cut size decreased with increased black content. This indicates less strain-crystalliation before rupture of pre-cut specimens, when levels of black are low. This effect is attributerd to rapid straining at a cut tip and hindering of the chain mobility necessary for crystallization. When black content was increased to 15 phr, with 1 mm<c<2 mm, about 50% of specimens retained simple lateral fracture and were weak, but the other 50% developed deviated cracks (knotty tearing) and were significantly stronger than corresponding pre-cut gum specimens, especially at large c. High strength with sufficient black levels are attributed to increased strain-crystallization and super-blunting (multiple cracks) at a cut tip. These inhibit forward crack growth. For carbon black to enhance strain-crystallization relative to the gum, it appears there must be enough of it to form a bound rubber/black network. If the black concentration is less than this percolation threshold, strain-crystallization is hindered at a cut tip.
We collate active galactic nuclei (AGN) with reported detections of both relativistic reflection and ultra-fast outflows. By comparing the inclination of the inner disc from reflection with the line-of-sight velocity of the outflow, we show that it i
s possible to meaningfully constrain the geometry of the absorbing material. We find a clear relation between the velocity and inclination, and demonstrate that it can potentially be explained either by simple wind geometries or by absorption from the disc surface. Due to systematic errors and a shortage of high- quality simultaneous measurements our conclusions are tentative, but this study represents a proof-of-concept that has great potential.
We present a detailed spectral analysis of the recent 1.5,Ms XMM-Newton observing campaign on the narrow line Seyfert 1 galaxy IRAS~13224$-$3809, taken simultaneously with 500,ks of NuSTAR data. The X-ray lightcurve shows three flux peaks, registerin
g at about 100 times the minimum flux seen during the campaign, and rapid variability with a time scale of kiloseconds. The spectra are well fit with a primary powerlaw continuum, two relativistic-blurred reflection components from the inner accretion disk with very high iron abundance, and a simple blackbody-shaped model for the remaining soft excess. The spectral variability is dominated by the power law continuum from a corona region within a few gravitational radii from the black hole. Additionally, blueshifted Ne textsc{x}, Mg textsc{xii}, Si textsc{xiv} and S textsc{xvi} absorption lines are identified in the stacked low-flux spectrum, confirming the presence of a highly ionized outflow with velocity up to $v= 0.267$ and $0.225$,c. We fit the absorption features with texttt{xstar} models and find a relatively constant velocity outflow through the whole observation. Finally, we replace the texttt{bbody} and supersolar abundance reflection models by fitting the soft excess successfully with the extended reflection model texttt{relxillD}, which allows for higher densities than the standard texttt{relxill} model. This returns a disk electron density $n_{rm e}>10^{18.7}$,cm$^{-3}$ and lowers the iron abundance from $Z_{rm Fe}=24^{+3}_{-4}Z_odot$ with $n_{rm e}equiv10^{15}$,cm$^{-3}$ to $Z_{rm Fe}=6.6^{+0.8}_{-2.1}Z_odot$.
We consider the $(2+1)$-d $SU(2)$ quantum link model on the honeycomb lattice and show that it is equivalent to a quantum dimer model on the Kagome lattice. The model has crystalline confined phases with spontaneously broken translation invariance as
sociated with pinwheel order, which is investigated with either a Metropolis or an efficient cluster algorithm. External half-integer non-Abelian charges (which transform non-trivially under the $mathbb{Z}(2)$ center of the $SU(2)$ gauge group) are confined to each other by fractionalized strings with a delocalized $mathbb{Z}(2)$ flux. The strands of the fractionalized flux strings are domain walls that separate distinct pinwheel phases. A second-order phase transition in the 3-d Ising universality class separates two confining phases; one with correlated pinwheel orientations, and the other with uncorrelated pinwheel orientations.
