Robust passive range estimation using the waveguide invariant

The waveguide invariant principle is used to estimate the range to a broadband acoustic source in a shallow-water waveguide using a single acoustic receiver towed along a path directly toward the acoustic source. A relationship between the signal processing parameters and the ocean-acoustic environmental parameters is used to increase the effective signal-to-noise ratio without requiring detailed knowledge of the environment. Heuristics are developed to estimate the minimum source bandwidth and minimum horizontal aperture required for range estimation. A range estimation algorithm is tested on experimental and simulated data for source ranges of 500-2200 m and frequencies from 350 to 700 Hz. The algorithm is accurate to within approximately 25% for the cases tested and requires only a minimal amount of a priori environmental knowledge.     

Measurement of ultraweak transitions in the visible region of molecular oxygen

A highly sensitive cavity-enhanced frequency modulation spectroscopy technique has been used to measure ultraweak transitions in molecular oxygen that had not previously been characterized. The self-broadened half-width and line intensity of the measured transitions are reported. We include 12 high J transitions in the band of ¹⁶O₂ (the so-called A band), 59 transitions in the hot band of ¹⁶O₂, and 17 high J transitions in the band of ¹⁶O¹⁸O. Our measurements of line positions of the ¹⁶O¹⁸O transitions are used to determine improved molecular constants for the excited state of ¹⁶O¹⁸O.     

Quantification of Structural Integrity and Stability Using Nanograms of Protein by Flow-Induced Dispersion Analysis

In the development of therapeutic proteins, analytical assessment of structural stability and integrity constitutes an important activity, as protein stability and integrity influence drug efficacy, and ultimately patient safety. Existing analytical methodologies solely rely on relative changes in optical properties such as fluorescence or scattering upon thermal or chemical perturbation. Here, we present an absolute analytical method for assessing protein stability, structure, and unfolding utilizing Taylor dispersion analysis (TDA) and LED-UV fluorescence detection. The developed TDA method measures the change in size (hydrodynamic radius) and intrinsic fluorescence of a protein during in-line denaturation with guanidinium hydrochloride (GuHCl). The conformational stability of the therapeutic antibody adalimumab and human serum albumin were characterized as a function of pH. The simple workflow and low sample consumption (40 ng protein per data point) of the methodology make it ideal for assessing protein characteristics related to stability in early drug development or when having a scarce amount of sample available.     

The primitive spectrum of a semigroup of Markov operators

Positivity - For a semigroup $$mathcal {S}$$ of Markov operators on a space of continuous functions, we use $$mathcal {S}$$-invariant ideals to describe qualitative properties of $$mathcal {S}$$...     

The algebra of generating functions for multiple divisor sums and applications to multiple zeta values

We study the algebra \({{\mathrm{{\mathcal {MD}}}}}\) of generating functions for multiple divisor sums and its connections to multiple zeta values. The generating functions for multiple divisor sums are formal power series in q with coefficients in \({\mathbb {Q}}\) arising from the calculation of the Fourier expansion of multiple Eisenstein series. We show that the algebra \({{\mathrm{{\mathcal {MD}}}}}\) is a filtered algebra equipped with a derivation and use this derivation to prove linear relations in \({{\mathrm{{\mathcal {MD}}}}}\). The (quasi-)modular forms for the full modular group \({{\mathrm{SL}}}_2({\mathbb {Z}})\) constitute a subalgebra of \({{\mathrm{{\mathcal {MD}}}}}\), and this also yields linear relations in \({{\mathrm{{\mathcal {MD}}}}}\). Generating functions of multiple divisor sums can be seen as a q-analogue of multiple zeta values. Studying a certain map from this algebra into the real numbers we will derive a new explanation for relations between multiple zeta values, including those of length 2, coming from modular forms.     

Cotorsion pairs associated with Auslander categories

Let N ≥ n + 1, and denote by K the convex hull of N independent standard gaussian random vectors in ℝⁿ. We prove that with high probability, the isotropic constant of K is bounded by a universal constant. Thus we verify the hyperplane conjecture for the class of gaussian random polytopes. Supported by the Clay Mathematics Institute and by NSF grant #DMS-0456590     

Statistics of Wave Functions for a Point Scatterer on the Torus

Quantum systems whose classical counterpart have ergodic dynamics are quantum ergodic in the sense that almost all eigenstates are uniformly distributed in phase space. In contrast, when the classical dynamics is integrable, there is concentration of eigenfunctions on invariant structures in phase space. In this paper we study eigenfunction statistics for the Laplacian perturbed by a delta-potential (also known as a point scatterer) on a flat torus, a popular model used to study the transition between integrability and chaos in quantum mechanics. The eigenfunctions of this operator consist of eigenfunctions of the Laplacian which vanish at the scatterer, and new, or perturbed, eigenfunctions. We show that almost all of the perturbed eigenfunctions are uniformly distributed in configuration space.