Star Cluster Formation from Turbulent Clumps. I. The Fast Formation Limit

We investigate the formation and early evolution of star clusters assuming that they form from a turbulent starless clump of given mass bounded inside a parent self-gravitating molecular cloud characterized by a particular mass surface density. As a first step we assume instantaneous star cluster formation and gas expulsion. We draw our initial conditions from observed properties of starless clumps. We follow the early evolution of the clusters up to 20 Myr, investigating effects of different star formation efficiencies, primordial binary fractions and eccentricities and primordial mass segregation levels. We investigate clumps with initial masses of $M_{\rm cl}=3000\:{\rm M}_\odot$ embedded in ambient cloud environments with mass surface densities, $\Sigma_{\rm cloud}=0.1$ and $1\:{\rm g\:cm^{-2}}$. We show that these models of fast star cluster formation result, in the fiducial case, in clusters that expand rapidly, even considering only the bound members. Clusters formed from higher $\Sigma_{\rm cloud}$ environments tend to expand more quickly, so are soon larger than clusters born from lower $\Sigma_{\rm cloud}$ conditions. To form a young cluster of a given age, stellar mass and mass surface density, these models need to assume a parent molecular clump that is many times denser, which is unrealistic compared to observed systems. We also show that in these models the initial binary properties are only slightly modified by interactions, meaning that binary properties, e.g., at 20 Myr, are very similar to those at birth. With this study we set up the basis of future work where we will investigate more realistic models of star formation compared to this instantaneous, baseline case.Comment: 25 pages, 19 figures. Accepted by Ap

A full quantal theory of one-neutron halo breakup reactions

We present a theory of one-neutron halo breakup reactions within the framework of post-form distorted wave Born approximation wherein pure Coulomb, pure nuclear and their interference terms are treated consistently in a single setup. This formalism is used to study the breakup of one-neutron halo nucleus 11Be on several targets of different masses. We investigate the role played by the pure Coulomb, pure nuclear and the Coulomb-nuclear interference terms by calculating several reaction observables. The Coulomb-nuclear interference terms are found to be important for more exclusive observables.Comment: 22 pages latex, 9 figures, submitted to Phy. Rev.

κ\kappa-Minkowski and Snyder algebra from reparametrisation symmetry

Following our earlier work \cite{sunandan1, sunandan2}, we derive noncommuting phase-space structures which are combinations of both the $\kappa$-Minkowski and Snyder algebra by exploiting the reparametrisation symmetry of the recently proposed Lagrangian for a point particle \cite{subir} satisfying the exact Doubly Special Relativity dispersion relation in the Magueijo-Smolin framework.Comment: Accepted in Euro Physics Letter

New approximations, and policy implications, from a delayed dynamic model of a fast pandemic

We study an SEIQR (Susceptible-Exposed-Infectious-Quarantined-Recovered) model for an infectious disease, with time delays for latency and an asymptomatic phase. For fast pandemics where nobody has prior immunity and everyone has immunity after recovery, the SEIQR model decouples into two nonlinear delay differential equations (DDEs) with five parameters. One parameter is set to unity by scaling time. The subcase of perfect quarantining and zero self-recovery before quarantine, with two free parameters, is examined first. The method of multiple scales yields a hyperbolic tangent solution; and a long-wave approximation yields a first order ordinary differential equation (ODE). With imperfect quarantining and nonzero self-recovery, the long-wave approximation is a second order ODE. These three approximations each capture the full outbreak, from infinitesimal initiation to final saturation. Low-dimensional dynamics in the DDEs is demonstrated using a six state non-delayed reduced order model obtained by Galerkin projection. Numerical solutions from the reduced order model match the DDE over a range of parameter choices and initial conditions. Finally, stability analysis and numerics show how correctly executed time-varying social distancing, within the present model, can cut the number of affected people by almost half. Alternatively, faster detection followed by near-certain quarantining can potentially be even more effective

Complete dimensional collapse in the continuum limit of a delayed SEIQR network model with separable distributed infectivity

We take up a recently proposed compartmental SEIQR model with delays, ignore loss of immunity in the context of a fast pandemic, extend the model to a network structured on infectivity, and consider the continuum limit of the same with a simple separable interaction model for the infectivities $\beta$. Numerical simulations show that the evolving dynamics of the network is effectively captured by a single scalar function of time, regardless of the distribution of $\beta$ in the population. The continuum limit of the network model allows a simple derivation of the simpler model, which is a single scalar delay differential equation (DDE), wherein the variation in $\beta$ appears through an integral closely related to the moment generating function of $u=\sqrt{\beta}$. If the first few moments of $u$ exist, the governing DDE can be expanded in a series that shows a direct correspondence with the original compartmental DDE with a single $\beta$. Even otherwise, the new scalar DDE can be solved using either numerical integration over $u$ at each time step, or with the analytical integral if available in some useful form. Our work provides a new academic example of complete dimensional collapse, ties up an underlying continuum model for a pandemic with a simpler-seeming compartmental model, and will hopefully lead to new analysis of continuum models for epidemics

Non-Zero Sum Games for Reactive Synthesis

In this invited contribution, we summarize new solution concepts useful for the synthesis of reactive systems that we have introduced in several recent publications. These solution concepts are developed in the context of non-zero sum games played on graphs. They are part of the contributions obtained in the inVEST project funded by the European Research Council.Comment: LATA'16 invited pape

Knowledge graphs for covid-19: An exploratory review of the current landscape

Background: Searching through the COVID-19 research literature to gain actionable clinical insight is a formidable task, even for experts. The usefulness of this corpus in terms of improving patient care is tied to the ability to see the big picture that emerges when the studies are seen in conjunction rather than in isolation. When the answer to a search query requires linking together multiple pieces of information across documents, simple keyword searches are insufficient. To answer such complex information needs, an innovative artificial intelligence (AI) technology named a knowledge graph (KG) could prove to be effective. Methods: We conducted an exploratory literature review of KG applications in the context of COVID-19. The search term used was "covid-19 knowledge graph". In addition to PubMed, the first five pages of search results for Google Scholar and Google were considered for inclusion. Google Scholar was used to include non-peer-reviewed or non-indexed articles such as pre-prints and conference proceedings. Google was used to identify companies or consortiums active in this domain that have not published any literature, peer-reviewed or otherwise. Results: Our search yielded 34 results on PubMed and 50 results each on Google and Google Scholar. We found KGs being used for facilitating literature search, drug repurposing, clinical trial mapping, and risk factor analysis. Conclusions: Our synopses of these works make a compelling case for the utility of this nascent field of research