We develop the basic theory of projective modules and splitting in the more general setting of systems. This enables us to prove analogues of classical theorems for tropical and hyperfield theory. In this context we prove a Dual Basis Lemma and deve…

We develop the basic theory of projective modules and splitting in the more general setting of systems. This enables us to prove analogues of classic…

The classical admissible cover space ¯¯¯¯¯Hg,d(→μ) admits a branch map, recording the base curve, marked at its branch points:

We study the relationship between tropical and classical Hurwitz moduli spaces. Following recent work of Abramovich, Caporaso and Payne, we outline a…

With the preliminaries out of the way, we are now ready to prove Theorem 1.

In 1989, Thomassen asked whether there is an integer-valued function f(k) such that every f(k)-connected graph admits a spanning, bipartite $k$-conne…

In the last 25 years a new understanding has evolved of the role of information in quantum mechanics. At the same time there has been tremendous prog…

We study the problem of testing for community structure in networks using relations between the observed frequencies of small subgraphs. We propose a…

Most results in nonparametric regression theory are developed only for the case of additive noise. In such a setting many smoothing techniques includ…

We exploit a key result from visual psychophysics -- that individuals perceive shape qualitatively -- to develop a geometrical/topological invariant …

An important task of human genetics studies is to accurately predict disease risks in individuals based on genetic markers, which allows for identify…

We construct a density functional theory (DFT) for the sticky hard sphere (SHS) fluid which, like Rosenfeld's fundamental measure theory (FMT) for th…

We propose a novel framework for combining datasets via alignment of their intrinsic geometry. This alignment can be used to fuse data originating fr…

Many large-scale machine learning problems--clustering, non-parametric learning, kernel machines, etc.--require selecting a small yet representative …

This paper studies the performance of sparse regression codes for lossy compression with the squared-error distortion criterion. In a sparse regressi…

We present SED modeling of a sample of 34 K-selected galaxies at z ~ 2.3. These galaxies have NIR spectroscopy that samples the rest-frame Balmer/400…

We address the problem of motion planning for a robotic manipulator with the task to place a grasped object in a cluttered environment. In this task,…

We derive and test a generalization of Steady-State Ab Initio Laser Theory (SALT) to treat complex gain media. The generalized theory (C-SALT) is abl…

Scanning tunneling microscopy (STM) provides real-space electronic state information at the atomic scale that is most commonly used to study material…

With a sample of 406 Kepler planet host stars taken from Buchhave et al. (2014), we compared the stellar properties from the KIC and those from the SPC analysis. From the comparison, we derived a method to convert the KIC values for stellar properti…

The metallicity of exoplanet systems serves as a critical diagnostic of planet formation mechanisms. Previous studies have demonstrated the planet-me…

Linear parametric amplification is a key operation in information processing. Our interest here is quantum-limited parametric amplification, $i.e.$, …

A number of authors have proposed that the statistically significant orbital alignment of the most distant Kuiper Belt Objects (KBOs) is evidence of …

NASA's Kepler mission is providing basic asteroseismic data for hundreds of stars. One of the more common ways of determining stellar characteristics…

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