We prove that any pair of bivariate trinomials has at most 5 isolated roots in the positive quadrant. The best previous upper bounds independent of the polynomial degrees were much larger, e.g., 248832 (for just the non-degenerate roots) via a famous general result of Khovanski. Our bound is sharp, allows real exponents, allows degeneracies, and extends to certain systems of n-variate fewnomial...

Type Ia supernova data have recently become strong enough to enable, for the first time, constraints on the time variation of the dark energy density and its equation of state. Most analyses, however, are using simple two or three-parameter descriptions of the dark energy evolution, since it is well known that allowing more degrees of freedom introduces serious degeneracies. Here we present a m...

Counterfactual learning is a natural scenario to improve web-based machine translation services by offline learning from feedback logged during user interactions. In order to avoid the risk of showing inferior translations to users, in such scenarios mostly exploration-free deterministic logging policies are in place. We analyze possible degeneracies of inverse and reweighted propensity scoring...

Large-N volume independence in circle-compactified QCD with adjoint Weyl fermions implies the absence of any phase transitions as the radius is dialed to arbitrarily small values. This class of theories are believed to possess a Hagedorn density of hadronic states. It turns out that these properties are in apparent tension with each other, because a Hagedorn density of states typically implies ...

We use closed geodesics to construct and compute Botttype Morse homology groups for the energy functional on the loop space of flat n-dimensional tori, n ≥ 1, and Bott-type Floer cohomology groups for their cotangent bundles equipped with the natural symplectic structure. Both objects are isomorpic to the singular homology of the loop space. In an appendix we perturb the equations in order to e...

Determination of the neutrino mass hierarchy using a reactor neutrino experiment at ∼60 km is analyzed. Such a measurement is challenging due to the finite detector resolution, the absolute energy scale calibration, as well as the degeneracies caused by current experimental uncertainty of |∆m232|. The standard χ 2 method is compared with a proposed Fourier transformation method. In addition, we...

We investigate the potential of a flavor pure high gamma electron capture electron neutrino beam directed towards a large Water Cherenkov detector with 500 kt fiducial mass. The energy of the neutrinos is reconstructed by the position measurement within the detector and superb energy resolution capabilities could be achieved. We estimate the requirements for such a scenario to be competitive to...

A planetary microlensing event occurs when a planet perturbs one of the two images created in a point-mass microlensing event, causing a deviation from the standard Paczyński curve. Determination of the two physical parameters that can be extracted from a planetary microlensing event, the planet/star mass ratio q, and the planet/star separation in units of the stellar Einstein ring, yp, is hamp...

We show how the topological string partition function, which is known to capture the degeneracies of a gas of BPS spinning M2-branes in M-theory compactified to 5 dimensions, is related to a 4-dimensional D-brane system that consists of single D6-brane bound to lower-dimensional branes. This system is described by a topologically twisted U(1) gauge theory, that has been conjecturally identified...

The variation of the expansion rate of the Universe with time produces an evolution in the cosmological redshift of distant sources (for example quasar Lyman-α absorption lines), that might be directly observed by future ultra stable, high-resolution spectrographs (such as CODEX) coupled to extremely large telescopes (such as European Southern Observatory’s Extremely Large Telescope, ELT). This...