Detecting bifurcation values at infinity of real polynomials

We present a new approach for estimating the set of bifurcation values at infinity. This yields a significant shrinking of the number of coefficients in the recent algorithm introduced by Jelonek and Kurdyka for reaching critical values at infinity by rational arcs

Angular Momentum Projected Configuration Interaction with Realistic Hamiltonians

The Projected Configuration Interaction (PCI) method starts from a collection of mean-field wave functions, and builds up correlated wave functions of good symmetry. It relies on the Generator Coordinator Method (GCM) techniques, but it improves the past approaches by a very efficient method of selecting the basis states. We use the same realistic Hamiltonians and model spaces as the Configuration Interaction (CI) method, and compare the results with the full CI calculations in the sd and pf shell. Examples of 24Mg, 28Si, 48Cr, 52Fe and 56Ni are discussed.Comment: 10 pages, 10 figures. Revised version. To be published in Physical Review

Single-cycle gap soliton in a subwavelength structure

We demonstrate that a single sub-cycle optical pulse can be generated when a pulse with a few optical cycles penetrates through resonant two-level dense media with a subwavelength structure. The single-cycle gap soliton phenomenon in the full Maxwell-Bloch equations without the frame of slowly varying envelope and rotating wave approximations is observed. Our study shows that the subwavelength structure can be used to suppress the frequency shift caused by intrapulse four-wave mixing in continuous media and supports the formation of single-cycle gap solitons even in the case when the structure period breaks the Bragg condition. This suggests a way toward shortening high-intensity laser fields to few- and even single-cycle pulse durations.Comment: 4 pages, 6 figure

Positivity and optimization for semi-algebraic functions

We describe algebraic certificates of positivity for functions belonging to a finitely generated algebra of Borel measurable functions, with particular emphasis to algebras generated by semi-algebraic functions. In which case the standard global optimization problem with constraints given by elements of the same algebra is reduced via a natural change of variables to the better understood case of polynomial optimization. A collection of simple examples and numerical experiments complement the theoretical parts of the article.Comment: 20 page

Photon scattering from strongly driven atomic ensembles

The second order correlation function for light emitted from a strongly and near-resonantly driven dilute cloud of atoms is discussed. Because of the strong driving, the fluorescence spectrum separates into distinct peaks, for which the spectral properties can be defined individually. It is shown that the second-order correlations for various combinations of photons from different spectral lines exhibit bunching together with super- or sub-Poissonian photon statistics, tunable by the choice of the detector positions. Additionally, a Cauchy-Schwarz inequality is violated for photons emitted from particular spectral bands. The emitted light intensity is proportional to the square of the number of particles, and thus can potentially be intense. Three different averaging procedures to model ensemble disorder are compared.Comment: 7 pages, 4 figure

Innate immune memory: implications for development of pediatric immunomodulatory agents and adjuvanted vaccines

Unique features of immunity early in life include a distinct immune system particularly reliant on innate immunity, with weak T helper (Th)1-polarizing immune responses, and impaired responses to certain vaccines leading to a heightened susceptibility to infection. To these important aspects, we now add an increasingly appreciated concept that the innate immune system displays epigenetic memory of an earlier infection or vaccination, a phenomenon that has been named “trained immunity”. Exposure of neonatal leukocytes in vitro or neonatal animals or humans in vivo to specific innate immune stimuli results in an altered innate immune set point. Given the particular importance of innate immunity early in life, trained immunity to early life infection and/or immunization may play an important role in modulating both acute and chronic diseases