The basic reproduction number $R_0$ is a fundamental quantity in epidemiological modeling, reflecting the typical number of secondary infections that arise from a single infected individual. While $R_0$ is widely known to scientists, policymakers, an
d the general public, it has received comparatively little attention in the controls community. This note provides two novel characterizations of $R_0$: a stability characterization and a geometric program characterization. The geometric program characterization allows us to write $R_0$-constrained and budget-constrained optimal resource allocation problems as geometric programs, which are easily transformed into convex optimization problems. We apply these programs to a case study of allocating vaccines and antidotes, finding that targeting $R_0$ instead of the spectral abscissa of the Jacobian matrix (a common target in the controls literature) leads to qualitatively different solutions.
We present the discovery and characterisation of an eclipsing binary identified by the Next Generation Transit Survey in the $sim$115 Myr old Blanco 1 open cluster. NGTS J0002-29 comprises three M dwarfs: a short-period binary and a companion in a wi
der orbit. This system is the first well-characterised, low-mass eclipsing binary in Blanco 1. With a low mass ratio, a tertiary companion and binary components that straddle the fully convective boundary, it is an important benchmark system, and one of only two well-characterised, low-mass eclipsing binaries at this age. We simultaneously model light curves from NGTS, TESS, SPECULOOS and SAAO, radial velocities from VLT/UVES and Keck/HIRES, and the systems spectral energy distribution. We find that the binary components travel on circular orbits around their common centre of mass in $P_{rm orb} = 1.09800524 pm 0.00000038$ days, and have masses $M_{rm pri}=0.3978pm 0.0033$ M$_{odot}$ and $M_{rm sec}=0.2245pm 0.0018$ M$_{odot}$, radii $R_{rm pri}=0.4037pm 0.0048$ R$_{odot}$ and $R_{rm sec}=0.2759pm 0.0055$ R$_{odot}$, and effective temperatures $T_{rm pri}=3372,^{+44}_{-37}$ K and $T_{rm sec}=3231,^{+38}_{-31}$ K. We compare these properties to the predictions of seven stellar evolution models, which typically imply an inflated primary. The system joins a list of 19 well-characterised, low-mass, sub-Gyr, stellar-mass eclipsing binaries, which constitute some of the strongest observational tests of stellar evolution theory at low masses and young ages.
We experimentally investigate the nature of 2D phase transitions in a quasi-2D granular fluid. Using a surface decorated with periodically spaced dimples we observe interfacial tension between coexisting liquid and crystal phases. Measurements of the
orientational and translational order parameters and associated susceptibilities indicate that the surface topography alters the order of the phase transition from a two-step continuous one to a first-order liquid-crystal one. The interplay of boundary inelasticity and geometry, either order-promoting or inhibiting, controls the wetting of the granular crystal / fluid. This order induced wetting has important consequences, determining how coexisting phases separate spatially.
The Drake Equation has proven fertile ground for speculation about the abundance, or lack thereof, of communicating extraterrestrial intelligences (CETIs) for decades. It has been augmented by subsequent authors to include random variables in order t
o understand its probabilistic behavior. In this paper, the first model for the number of CETIs with stochastic processes governing both their emergence and quiescence is developed using the Skellam Distribution. Results from this include the possibility that there can still be substantial times multiple CETIs exist even if the Drake Equation terms are approximately zero. In addition, it can give us a basic estimate of the average CETI age gap based on their broadcast time. Finally, we will introduce a definition of how the interaction between CETIs, where possible, can be measured by statistical dependence between the terms N and L in the Drake Equation by indicating how the number of co-existing CETIs affect their relative individual lifetimes.
Supermassive black hole (SMBH) masses can be measured by resolving the dynamical influences of the SMBHs on spatially-resolved tracers of the central potentials. Modern long-baseline interferometers have enabled the use of molecular gas as such a tra
cer. We present here Atacama Large Millimeter/submillimeter Array observations of the elliptical galaxy NGC 7052 at 0.11 arcseconds (37 pc) resolution in the 12CO(2-1) line and 1.3mm continuum emission. This resolution is sufficient to resolve the region in which the potential is dominated by the SMBH. We forward model these observations, using a multi-Gaussian expansion of a Hubble Space Telescope F814W image and spatially-constant mass-to-light ratio to model the stellar mass distribution. We infer a SMBH mass of $2.5pm0.3times10^9,mathrm{M_odot}$ and a stellar I-band mass-to-light ratio of $4.6pm 0.2,mathrm{M_odot/L_{odot,I}}$ ($3sigma$ confidence intervals). This SMBH mass is significantly larger than that derived using ionised gas kinematics, which however appear significantly more kinematically disturbed than the molecular gas. We also show that a central molecular gas deficit is likely to be the result of tidal disruption of molecular gas clouds due to the strong gradient in the central gravitational potential.
Vast cavities in the intergalactic medium are excavated by radio galaxies. The cavities appear as such in X-ray images because the external medium has been swept up, leaving a hot but low density bubble surrounding the radio lobes. We explore here th
e predicted thermal X-ray emission from a large set of high-resolution three dimensional simulations of radio galaxies driven by supersonic jets. We assume adiabatic non-relativistic hydrodynamics with injected straight and precessing jets of supersonic gas emitted from nozzles. Images of X-ray Bremsstrahlung emission tend to generate oval cavities in the soft keV bands and leading arcuate structures in hard X-rays. However, the cavity shape is sensitive to the jet-ambient density contrast, varying from concave-shaped at $eta = 0.1$ to convex for $eta = 0.0001$ where $eta$ is the jet/ambient density ratio. We find lateral ribs in the soft X-rays in certain cases and propose this as an explanation for those detected in the vicinity of Cygnus,A. In bi-lobed or X-shaped sources and in curved or deflected jets, the strongest X-ray emission is not associated with the hotspot but with the relic lobe or deflection location. This is because the hot high-pressure and dense high-compression regions do not coincide. Directed toward the observer, the cavity becomes a deep round hole surrounded by circular ripples. With short radio-mode outbursts with a duty cycle of 10% , the intracluster medium simmers with low Mach number shocks widely dissipating the jet energy in between active jet episodes.
Empirical correlations between the masses of supermassive black holes (SMBHs) and properties of their host galaxies are well-established. Among these is the correlation with the flat rotation velocity of each galaxy measured either at a large radius
in its rotation curve or via a spatially-integrated emission line width. We propose here the use of the de-projected integrated CO emission line width as an alternative tracer of this rotation velocity, that has already been shown useful for the Tully-Fisher (luminosity-rotation velocity) relation. We investigate the correlation between CO line widths and SMBH masses for two samples of galaxies with dynamical SMBH mass measurements, with respectively spatially-resolved and unresolved CO observations. The tightest correlation is found using the resolved sample of 24 galaxies as $log (M_mathrm{BH}/mathrm{M_odot})=(7.5pm0.1)+(8.5pm0.9)[log(W_mathrm{50}/sin i ,mathrm{km,s}^{-1})-2.7]$, where $M_mathrm{BH}$ is the central SMBH mass, $W_{50}$ the full-width at half-maximum of a double-horned emission line profile, and $i$ the inclination of the CO disc. This relation has a total scatter of $0.6,$dex, comparable to those of other SMBH mass correlations, and dominated by the intrinsic scatter of $0.5,$dex. A tight correlation is also found between the de-projected CO line widths and the stellar velocity dispersions averaged within one effective radius. We apply our correlation to the COLD GASS sample to estimate the local SMBH mass function.
The balloon-borne ANITA experiment is designed to detect ultra-high energy neutrinos via radio emissions produced by an in-ice shower. Although initially purposed for interactions within the Antarctic ice sheet, ANITA also demonstrated the ability to
self-trigger on radio emissions from ultra-high energy charged cosmic rays interacting in the Earths atmosphere. For showers produced above the Antarctic ice sheet, reflection of the down-coming radio signals at the Antarctic surface should result in a polarity inversion prior to subsequent observation at the $sim$35-40 km altitude ANITA gondola. ANITA has published two anomalous instances of upcoming cosmic-rays with measured polarity opposite the remaining sample of $sim$50 UHECR signals. The steep observed upwards incidence angles (25--30 degrees relative to the horizontal) require non-Standard Model physics if these events are due to in-ice neutrino interactions, as the Standard Model cross-section would otherwise prohibit neutrinos from penetrating the long required chord of Earth. Shoemaker et al. posit that glaciological effects may explain the steep observed anomalous events. We herein consider the scenarios offered by Shoemaker et al. and find them to be disfavored by extant ANITA and HiCal experimental data. We note that the recent report of four additional near-horizon anomalous ANITA-4 events, at $>3sigma$ significance, are incompatible with their model, which requires significant signal transmission into the ice.
The concordance signature of a multivariate continuous distribution is the vector of concordance probabilities for margins of all orders; it underlies the bivariate and multivariate Kendalls tau measure of concordance. It is shown that every attainab
le concordance signature is equal to the concordance signature of a unique mixture of the extremal copulas, that is the copulas with extremal correlation matrices consisting exclusively of 1s and -1s. This result establishes that the set of attainable Kendall rank correlation matrices of multivariate continuous distributions in arbitrary dimension is the set of convex combinations of extremal correlation matrices, a set known as the cut polytope. A methodology for testing the attainability of concordance signatures using linear optimization and convex analysis is provided. The elliptical copulas are shown to yield a strict subset of the attainable concordance signatures as well as a strict subset of the attainable Kendall rank correlation matrices; the Student t copula is seen to converge to a mixture of extremal copulas sharing its concordance signature with all elliptical distributions that have the same correlation matrix. A method of estimating an attainable concordance signature from data is derived and shown to correspond to using standard estimates of Kendalls tau in the absence of ties. The methodology has application to Monte Carlo simulations of dependent random variables as well as expert elicitation of consistent systems of Kendalls tau dependence measures.
Two estimates for the inverse binary entropy function are derived using the property of information entropy to estimate combinatorics of sequences as well as related formulas from population genetics for the effective number of alleles. The second es
timate shows close correspondence to the actual value of the inverse binary entropy function and can be seen as a close approximation away from low values of binary entropy where $p$ or $1-p$ are small.
