Photographic quantification of water quality in mixing zones

A method was developed to quantitatively delineate waste concentrations throughout waste effluent mixing zones on the basis of densitometric measurements extracted from aerial photography. A mixing zone is the extent of a receiving water body ultilized to dilute a waste discharge to a concentration characteristic of a totally mixed condition. Simultaneously-acquired color infrared photography and suspended solids water samples were used to quantitatively delineate the mixing zone resulting from the discharge of a paper mill effluent. Digital scanning microdensitometer data was used to estimate and delineate suspended solids concentrations on the basis of a semi-empirical model. Photographic photometry, when predicated on a limited amount of ground sampling, can measure and delineate mixing zone waste distributions in more detail then conventional surface measuring techniques. The method has direct application to: (1) the establishment of definite and rational water quality guidelines; (2) the development of sampling and surveillance programs for use by governmental and private agencies; and (3) the development of design and location criteria for industrial and municipal waste effluent outfalls

Dvoretzky type theorems for multivariate polynomials and sections of convex bodies

In this paper we prove the Gromov--Milman conjecture (the Dvoretzky type theorem) for homogeneous polynomials on $\mathbb R^n$, and improve bounds on the number $n(d,k)$ in the analogous conjecture for odd degrees $d$ (this case is known as the Birch theorem) and complex polynomials. We also consider a stronger conjecture on the homogeneous polynomial fields in the canonical bundle over real and complex Grassmannians. This conjecture is much stronger and false in general, but it is proved in the cases of $d=2$ (for $k$'s of certain type), odd $d$, and the complex Grassmannian (for odd and even $d$ and any $k$). Corollaries for the John ellipsoid of projections or sections of a convex body are deduced from the case $d=2$ of the polynomial field conjecture

Measurements of Anisotropy in the Cosmic Microwave Background Radiation at 0.5 Degree Angular Scales Near the Star Gamma Ursae Minoris

We present results from a four frequency observation of a 6 x 0.6 degree strip of the sky centered near the star Gamma Ursae Minoris during the fourth flight of the Millimeter-wave Anisotropy eXperiment (MAX). The observation was made with a 1.4 degree peak-to-peak sinusoidal chop in all bands. The FWHM beam sizes were 0.55 +/- 0.05 degrees at 3.5 cm-1 and 0.75 +/-0.05 degrees at 6, 9, and 14 cm-1. During this observation significant correlated structure was observed at 3.5, 6 and 9 cm-1 with amplitudes similar to those observed in the GUM region during the second and third flights of MAX. The frequency spectrum is consistent with CMB and inconsistent with thermal emission from interstellar dust. The extrapolated amplitudes of synchrotron and free-free emission are too small to account for the amplitude of the observed structure. If all of the structure is attributed to CMB anisotropy with a Gaussian autocorrelation function and a coherence angle of 25', then the most probable values of DeltaT/TCMB in the 3.5, 6, and 9 cm-1 bands are 4.3 (+2.7, -1.6) x 10-5, 2.8 (+4.3, -1.1) x 10-5, and 3.5 (+3.0, -1.6) x 10-5 (95% confidence upper and lower limits), respectively.Comment: 16 pages, postscrip

Measurements of Anisotropy in the Cosmic Microwave Background Radiation at Degree Angular Scales Near the Stars Sigma Hercules and Iota Draconis

We present results from two four-frequency observations centered near the stars Sigma Hercules and Iota Draconis during the fourth flight of the Millimeter-wave Anisotropy eXperiment (MAX). The observations were made of 6 x 0.6-degree strips of the sky with 1.4-degree peak to peak sinusoidal chop in all bands. The FWHM beam sizes were 0.55+/-0.05 degrees at 3.5 cm-1 and a 0.75+/-0.05 degrees at 6, 9, and 14 cm-1. Significant correlated structures were observed at 3.5, 6 and 9 cm-1. The spectra of these signals are inconsistent with thermal emission from known interstellar dust populations. The extrapolated amplitudes of synchrotron and free-free emission are too small to account for the amplitude of the observed structures. If the observed structures are attributed to CMB anisotropy with a Gaussian autocorrelation function and a coherence angle of 25', then the most probable values are DT/TCMB = (3.1 +1.7-1.3) x 10^-5 for the Sigma Hercules scan, and DT/TCMB = (3.3 +/- 1.1) x 10^-5 for the Iota Draconis scan (95% confidence upper and lower limits). Finally a comparison of all six MAX scans is presented.Comment: 13 pages, postscript file, 2 figure

The Ljapunov-Schmidt reduction for some critical problems

This is a survey about the application of the Ljapunov-Schmidt reduction for some critical problems

Detection of circulating tumour DNA is associated with inferior outcomes in Ewing sarcoma and osteosarcoma: a report from the Children's Oncology Group.

BackgroundNew prognostic markers are needed to identify patients with Ewing sarcoma (EWS) and osteosarcoma unlikely to benefit from standard therapy. We describe the incidence and association with outcome of circulating tumour DNA (ctDNA) using next-generation sequencing (NGS) assays.MethodsA NGS hybrid capture assay and an ultra-low-pass whole-genome sequencing assay were used to detect ctDNA in banked plasma from patients with EWS and osteosarcoma, respectively. Patients were coded as positive or negative for ctDNA and tested for association with clinical features and outcome.ResultsThe analytic cohort included 94 patients with EWS (82% from initial diagnosis) and 72 patients with primary localised osteosarcoma (100% from initial diagnosis). ctDNA was detectable in 53% and 57% of newly diagnosed patients with EWS and osteosarcoma, respectively. Among patients with newly diagnosed localised EWS, detectable ctDNA was associated with inferior 3-year event-free survival (48.6% vs. 82.1%; p = 0.006) and overall survival (79.8% vs. 92.6%; p = 0.01). In both EWS and osteosarcoma, risk of event and death increased with ctDNA levels.ConclusionsNGS assays agnostic of primary tumour sequencing results detect ctDNA in half of the plasma samples from patients with newly diagnosed EWS and osteosarcoma. Detectable ctDNA is associated with inferior outcomes

Nucleation in Systems with Elastic Forces

Systems with long-range interactions when quenced into a metastable state near the pseudo-spinodal exhibit nucleation processes that are quite different from the classical nucleation seen near the coexistence curve. In systems with long-range elastic forces the description of the nucleation process can be quite subtle due to the presence of bulk/interface elastic compatibility constraints. We analyze the nucleation process in a simple 2d model with elastic forces and show that the nucleation process generates critical droplets with a different structure than the stable phase. This has implications for nucleation in many crystal-crystal transitions and the structure of the final state

Determination of Inflationary Observables by Cosmic Microwave Background Anisotropy Experiments

Inflation produces nearly Harrison-Zel'dovich scalar and tensor perturbation spectra which lead to anisotropy in the cosmic microwave background (CMB). The amplitudes and shapes of these spectra can be parametrized by $Q_S^2$, $r\equiv Q_T^2/Q_S^2$, $n_S$ and $n_T$ where $Q_S^2$ and $Q_T^2$ are the scalar and tensor contributions to the square of the CMB quadrupole and $n_S$ and $n_T$ are the power-lawspectral indices. Even if we restrict ourselves to information from angles greater than one third of a degree, three of these observables can be measured with some precision. The combination $130^{1-n_S}Q_S^2$ can be known to better than $\pm 0.3\%$. The scalar index $n_S$ can be determined to better than $\pm 0.02$. The ratio $r$ can be known to about $\pm 0.1$ for $n_S \simeq 1$ and slightly better for smaller $n_S$. The precision with which $n_T$ can be measured depends weakly on $n_S$ and strongly on $r$. For $n_S \simeq 1$ $n_T$ can be determined with a precision of about $\pm 0.056(1.5+r)/r$. A full-sky experiment with a $20'$beam using technology available today, similar to those being planned by several groups, can achieve the above precision. Good angular resolution is more important than high signal-to-noise ratio; for a given detector sensitivity and observing time a smaller beam provides significantly more information than a larger beam. The uncertainties in $n_S$ and $r$ are roughly proportional to the beam size. We briefly discuss the effects of uncertainty in the Hubble constant, baryon density, cosmological constant and ionization history.Comment: 28 pages of uuencoded postscript with 8 included figures. A postscript version is also available by anonymous ftp at ftp://astro.uchicago.edu/pub/astro/knox/fullsim.p