LpL^p-approximation of the integrated density of states for Schr\"odinger operators with finite local complexity

We study spectral properties of Schr\"odinger operators on \RR^d. The electromagnetic potential is assumed to be determined locally by a colouring of the lattice points in \ZZ^d, with the property that frequencies of finite patterns are well defined. We prove that the integrated density of states (spectral distribution function) is approximated by its finite volume analogues, i.e.the normalised eigenvalue counting functions. The convergence holds in the space $L^p(I)$ where $I$ is any finite energy interval and $1\leq p< \infty$ is arbitrary.Comment: 15 pages; v2 has minor fixe

Left ventricular remodelling post-myocardial infarction: pathophysiology, imaging, and novel therapies

Most patients survive acute myocardial infarction (MI). Yet this encouraging development has certain drawbacks: heart failure (HF) prevalence is increasing and patients affected tend to have more comorbidities worsening economic strain on healthcare systems and impeding effective medical management. The heart's pathological changes in structure and/or function, termed myocardial remodelling, significantly impact on patient outcomes. Risk factors like diabetes, chronic obstructive pulmonary disease, female sex, and others distinctly shape disease progression on the 'road to HF'. Despite the availability of HF drugs that interact with general pathways involved in myocardial remodelling, targeted drugs remain absent, and patient risk stratification is poor. Hence, in this review, we highlight the pathophysiological basis, current diagnostic methods and available treatments for cardiac remodelling following MI. We further aim to provide a roadmap for developing improved risk stratification and novel medical and interventional therapies

On non-local variational problems with lack of compactness related to non-linear optics

We give a simple proof of existence of solutions of the dispersion manage- ment and diffraction management equations for zero average dispersion, respectively diffraction. These solutions are found as maximizers of non-linear and non-local vari- ational problems which are invariant under a large non-compact group. Our proof of existence of maximizer is rather direct and avoids the use of Lions' concentration compactness argument or Ekeland's variational principle.Comment: 30 page

OGLE-2018-BLG-0022: A Nearby M-dwarf Binary

We report observations of the binary microlensing event OGLE-2018-BLG-0022, provided by the Robotic Observations of Microlensing Events (ROME)/Reactive Event Assessment (REA) Survey, which indicate that the lens is a low-mass binary star consisting of M3 (0.375 ± 0.020 M⊙) and M7 (0.098 ± 0.005 M⊙) components. The lens is unusually close, at 0.998 ± 0.047 kpc, compared with the majority of microlensing events, and despite its intrinsically low luminosity, it is likely that adaptive optics observations in the near future will be able to provide an independent confirmation of the lens masses

Spitzer Parallax Of Ogle-2015-blg-0966: A Cold Neptune In The Galactic Disk

We report the detection of a cold Neptune mplanet = 21 ± 2 M? orbiting a 0.38 M? M dwarf lying 2.5–3.3 kpc toward the Galactic center as part of a campaign combining ground-based and Spitzer observations to measure the Galactic distribution of planets. This is the first time that the complex real-time protocols described by Yee et al., which aim to maximize planet sensitivity while maintaining sample integrity, have been carried out in practice. Multiple survey and follow up teams successfully combined their efforts within the framework of these protocols to detect this planet. This is the second planet in the Spitzer Galactic distribution sample. Both are in the near to mid-disk and are clearly not in the Galactic bulge

The Spitzer Microlensing Program As A Probe For Globular Cluster Planets: Analysis Of Ogle-2015-BLG-0448

The microlensing event OGLE-2015-BLG-0448 was observed by Spitzer and lay within the tidal radius of the globular cluster NGC 6558. The event had moderate magnification and was intensively observed, hence it had the potential to probe the distribution of planets in globular clusters. We measure the proper motion of NGC 6558 (${{\boldsymbol{\mu }}}_{\mathrm{cl}}(N,E)=(+0.36\pm 0.10,+1.42\pm 0.10)\;{\rm{mas}}\;{{\rm{yr}}}^{-1}$) as well as the source and show that the lens is not a cluster member. Even though this particular event does not probe the distribution of planets in globular clusters, other potential cluster lens events can be verified using our methodology. Additionally, we find that microlens parallax measured using Optical Gravitational Lens Experiment (OGLE) photometry is consistent with the value found based on the light curve displacement between the Earth and Spitzer

Campaign 9 of the K2 Mission: Observational Parameters, Scientific Drivers, and Community Involvement for a Simultaneous Space- and Ground-based Microlensing Survey

K2's Campaign 9 (K2C9) will conduct a ~3.7 deg2 survey toward the Galactic bulge from 2016 April 22 through July 2 that will leverage the spatial separation between K2 and the Earth to facilitate measurement of the microlens parallax ${\pi }_{{\rm{E}}}$ for $\gtrsim 170$ microlensing events. These will include several that are planetary in nature as well as many short-timescale microlensing events, which are potentially indicative of free-floating planets (FFPs). These satellite parallax measurements will in turn allow for the direct measurement of the masses of and distances to the lensing systems. In this article we provide an overview of the K2C9 space- and ground-based microlensing survey. Specifically, we detail the demographic questions that can be addressed by this program, including the frequency of FFPs and the Galactic distribution of exoplanets, the observational parameters of K2C9, and the array of resources dedicated to concurrent observations. Finally, we outline the avenues through which the larger community can become involved, and generally encourage participation in K2C9, which constitutes an important pathfinding mission and community exercise in anticipation of WFIRST