How else can we detect Fast Radio Bursts?

We discuss possible electromagnetic signals accompanying Fast Radio Bursts (FRBs) that are expected in the scenario where FRBs originate in neutron star magnetospheres. For models involving Crab-like giant pulses, no appreciable contemporaneous emission is expected at other wavelengths. Magnetar giant flares, driven by the reconfiguration of the magnetosphere, however, can produce both contemporaneous bursts at other wavelengths as well as afterglow-like emission. We conclude that the best chances are: (i) prompt short GRB-like emission; (ii) a contemporaneous optical flash that can reach naked eye peak luminosity (but only for a few milliseconds); (iii) a high energy afterglow emission. Case (i) could be tested by coordinated radio and high-energy experiments. Case (ii) could be seen in a coordinated radio-optical surveys, \eg\ by the Palomar Transient Factory in a 60-second frame as a transient object of $m=15-20$ magnitude with an expected optical detection rate of about 0.1~hr$^{-1}$, an order of magnitude higher than in radio. Shallow, but large-area sky surveys such as ASAS-SN and EVRYSCOPE could also detect prompt optical flashes from the more powerful Lorimer-burst clones. The best constraints on the optical-to-radio power for this kind of emission could be provided by future observations with facilities like LSST. Case (iii) might be seen in relatively rare cases that the relativistically ejected magnetic blob is moving along the line of sight

Survival Probabilities at Spherical Frontiers

Motivated by tumor growth and spatial population genetics, we study the interplay between evolutionary and spatial dynamics at the surfaces of three-dimensional, spherical range expansions. We consider range expansion radii that grow with an arbitrary power-law in time: $R(t)=R_0(1+t/t^*)^{\Theta}$, where $\Theta$ is a growth exponent, $R_0$ is the initial radius, and $t^*$ is a characteristic time for the growth, to be affected by the inflating geometry. We vary the parameters $t^*$ and $\Theta$ to capture a variety of possible growth regimes. Guided by recent results for two-dimensional inflating range expansions, we identify key dimensionless parameters that describe the survival probability of a mutant cell with a small selective advantage arising at the population frontier. Using analytical techniques, we calculate this probability for arbitrary $\Theta$. We compare our results to simulations of linearly inflating expansions ($\Theta=1$ spherical Fisher-Kolmogorov-Petrovsky-Piscunov waves) and treadmilling populations ($\Theta=0$, with cells in the interior removed by apoptosis or a similar process). We find that mutations at linearly inflating fronts have survival probabilities enhanced by factors of 100 or more relative to mutations at treadmilling population frontiers. We also discuss the special properties of "marginally inflating" $(\Theta=1/2)$ expansions.Comment: 35 pages, 11 figures, revised versio

Pcf theory and cardinal invariants of the reals

The additivity spectrum ADD(I) of an ideal I is the set of all regular cardinals kappa such that there is an increasing chain {A_alpha:alpha<kappa\} in the ideal I such that the union of the chain is not in I. We investigate which set A of regular cardinals can be the additivity spectrum of certain ideals. Assume that I=B or I=N, where B denotes the sigma-ideal generated by the compact subsets of the Baire space omega^omega, and N is the ideal of the null sets. For countable sets we give a full characterization of the additivity spectrum of I: a non-empty countable set A of uncountable regular cardinals can be ADD(I) in some c.c.c generic extension iff A=pcf(A).Comment: 9 page

Electrostatic Point Charge Fitting as an Inverse Problem: Revealing the Underlying Ill-Conditioning

Atom-centered point charge model of the molecular electrostatics---a major workhorse of the atomistic biomolecular simulations---is usually parameterized by least-squares (LS) fitting of the point charge values to a reference electrostatic potential, a procedure that suffers from numerical instabilities due to the ill-conditioned nature of the LS problem. Here, to reveal the origins of this ill-conditioning, we start with a general treatment of the point charge fitting problem as an inverse problem, and construct an analytically soluble model with the point charges spherically arranged according to Lebedev quadrature naturally suited for the inverse electrostatic problem. This analytical model is contrasted to the atom-centered point-charge model that can be viewed as an irregular quadrature poorly suited for the problem. This analysis shows that the numerical problems of the point charge fitting are due to the decay of the curvatures corresponding to the eigenvectors of LS sum Hessian matrix. In part, this ill-conditioning is intrinsic to the problem and related to decreasing electrostatic contribution of the higher multipole moments, that are, in the case of Lebedev grid model, directly associated with the Hessian eigenvectors. For the atom-centered model, this association breaks down beyond the first few eigenvectors related to the high-curvature monopole and dipole terms; this leads to even wider spread-out of the Hessian curvature values. Using these insights, it is possible to alleviate the ill-conditioning of the LS point-charge fitting without introducing external restraints and/or constraints. Also, as the analytical Lebedev grid PC model proposed here can reproduce multipole moments up to a given rank, it may provide a promising alternative to including explicit multipole terms in a force field

Probing a Secluded U(1) at B-factories

A secluded U(1) gauge field, kinetically mixed with Standard Model hypercharge, provides a `portal' mediating interactions with a hidden sector at the renormalizable level, as recently exploited in the context of WIMP dark matter. The secluded U(1) symmetry-breaking scale may naturally be suppressed relative to the weak scale, and so this sector is efficiently probed by medium energy electron-positron colliders. We study the collider signatures of the minimal secluded U(1) model, focusing on the reach of B-factory experiments such as BaBar and BELLE. In particular, we show that Higgs-strahlung in the secluded sector can lead to multi-lepton signatures which probe the natural range for the kinetic mixing angle of 10^(-2)-10^(-3) over a large portion of the kinematically accessible parameter space.Comment: 14 pages, 3 figure

Genetic Algorithm Optimization of Point Charges in Force Field Development: Challenges and Insights

Evolutionary methods, such as genetic algorithms (GAs), provide powerful tools for optimization of the force field parameters, especially in the case of simultaneous fitting of the force field terms against extensive reference data. However, GA fitting of the nonbonded interaction parameters that includes point charges has not been explored in the literature, likely due to numerous difficulties with even a simpler problem of the least-squares fitting of the atomic point charges against a reference molecular electrostatic potential (MEP), which often demonstrates an unusually high variation of the fitted charges on buried atoms. Here, we examine the performance of the GA approach for the least-squares MEP point charge fitting, and show that the GA optimizations suffer from a magnified version of the classical buried atom effect, producing highly scattered yet correlated solutions. This effect can be understood in terms of the linearly independent, natural coordinates of the MEP fitting problem defined by the eigenvectors of the least-squares sum Hessian matrix, which are also equivalent to the eigenvectors of the covariance matrix evaluated for the scattered GA solutions. GAs quickly converge with respect to the high-curvature coordinates defined by the eigenvectors related to the leading terms of the multipole expansion, but have difficulty converging with respect to the low-curvature coordinates that mostly depend on the buried atom charges. The performance of the evolutionary techniques dramatically improves when the point charge optimization is performed using the Hessian or covariance matrix eigenvectors, an approach with a significant potential for the evolutionary optimization of the fixed-charge biomolecular force fields