Constrained Dynamics of Universally Coupled Massive Spin 2-spin 0 Gravities

The 2-parameter family of massive variants of Einstein's gravity (on a Minkowski background) found by Ogievetsky and Polubarinov by excluding lower spins can also be derived using universal coupling. A Dirac-Bergmann constrained dynamics analysis seems not to have been presented for these theories, the Freund-Maheshwari-Schonberg special case, or any other massive gravity beyond the linear level treated by Marzban, Whiting and van Dam. Here the Dirac-Bergmann apparatus is applied to these theories. A few remarks are made on the question of positive energy. Being bimetric, massive gravities have a causality puzzle, but it appears soluble by the introduction and judicious use of gauge freedom.Comment: 6 pages; Talk given at QG05, Cala Gonone (Italy), September 200

A Semi-Blind Source Separation Method for Differential Optical Absorption Spectroscopy of Atmospheric Gas Mixtures

Differential optical absorption spectroscopy (DOAS) is a powerful tool for detecting and quantifying trace gases in atmospheric chemistry \cite{Platt_Stutz08}. DOAS spectra consist of a linear combination of complex multi-peak multi-scale structures. Most DOAS analysis routines in use today are based on least squares techniques, for example, the approach developed in the 1970s uses polynomial fits to remove a slowly varying background, and known reference spectra to retrieve the identity and concentrations of reference gases. An open problem is to identify unknown gases in the fitting residuals for complex atmospheric mixtures. In this work, we develop a novel three step semi-blind source separation method. The first step uses a multi-resolution analysis to remove the slow-varying and fast-varying components in the DOAS spectral data matrix $X$. The second step decomposes the preprocessed data $\hat{X}$ in the first step into a linear combination of the reference spectra plus a remainder, or $\hat{X} = A\,S + R$, where columns of matrix $A$ are known reference spectra, and the matrix $S$ contains the unknown non-negative coefficients that are proportional to concentration. The second step is realized by a convex minimization problem $S = \mathrm{arg} \min \mathrm{norm}\,(\hat{X} - A\,S)$, where the norm is a hybrid $\ell_1/\ell_2$ norm (Huber estimator) that helps to maintain the non-negativity of $S$. The third step performs a blind independent component analysis of the remainder matrix $R$ to extract remnant gas components. We first illustrate the proposed method in processing a set of DOAS experimental data by a satisfactory blind extraction of an a-priori unknown trace gas (ozone) from the remainder matrix. Numerical results also show that the method can identify multiple trace gases from the residuals.Comment: submitted to Journal of Scientific Computin

Exposure of bald eagle nestlings to contaminants on National Park Service lands within the Chesapeake Bay

We examined breeding performance (N=921) and nestling exposure (N=25 nests) to heavy metals (cadmium, lead, mercury), polychlorinated biphenyls (PCBs - 91 congeners) and organochlorine pesticides (OCPs - 11 compounds) for bald eagles nesting on National Park Service (NPS) and associated lands within the Chesapeake Bay (2016-2018). Nesting pairs on NPS lands were consistently more successful and had higher reproductive rates compared to other pairs along the James/York River study area but these differences were not statistically significant. Mean reproductive rates were above the level believed to be required for population maintenance for all areas examined. Blood concentrations of heavy metals were generally low and varied between metals examined. Cadmium did not exceed the level-of-detection (LOD) for any sample. Detection frequencies for Lead and Mercury were 86 and 100% respectively. Lead concentrations (range = 0.21-0.88, geometric mean = 0.49 ?g/g ww) were low and no sample exceeded the level (?g/dL) believed to represent background for raptors. Blood concentrations (range = 0.106-0.903, geometric mean = 0.335 ?g/g ww) of mercury were toward the lower to middle range of values reported from other studies of nestlings. Broods reared around lakes or tidal-fresh reaches had higher concentrations than broods reared around high-saline waters. No samples approached the general threshold (\u3e3.0 ?g/g ww) believed to result in possible reproductive impacts. Total PCB concentrations estimated during this study (range = 1.35-23.51, geometric mean = 6.34 ng/g ww) were on the low end of values reported from other regions. A cluster of the highest values were found within the lower James River. However, the highest values represented approximately 10% of the threshold (190 ng/g ww) suggested for reproductive impairment and 50% of the threshold (36 µg/kg) suggested for no-observed-adverse-effect-level (NOEL). Total OCP concentrations (range = 0.87-8.78, geometric mean = 2.68 ng/g ww) were lower than those reported from most other populations. p,p\u27-DDE was the most widespread pesticide compound and accounted for 93% of the total OCP values. Concentrations of p,p\u27-DDE (range = 0.6-8.78, geometric mean of 2.41 ng/g ww) were all below the level suggested for reproductive impairment (28 ng/g ww) and below the NOEL (11.4 ng/g ww) for productivity. Total concentrations of PCBs and OCPs were positively correlated (r=0.62,

State Differentiation by Transient Truncation in Coupled Threshold Dynamics

Dynamics with a threshold input--output relation commonly exist in gene, signal-transduction, and neural networks. Coupled dynamical systems of such threshold elements are investigated, in an effort to find differentiation of elements induced by the interaction. Through global diffusive coupling, novel states are found to be generated that are not the original attractor of single-element threshold dynamics, but are sustained through the interaction with the elements located at the original attractor. This stabilization of the novel state(s) is not related to symmetry breaking, but is explained as the truncation of transient trajectories to the original attractor due to the coupling. Single-element dynamics with winding transient trajectories located at a low-dimensional manifold and having turning points are shown to be essential to the generation of such novel state(s) in a coupled system. Universality of this mechanism for the novel state generation and its relevance to biological cell differentiation are briefly discussed.Comment: 8 pages. Phys. Rev. E. in pres

Universally Coupled Massive Gravity

We derive Einstein's equations from a linear theory in flat space-time using free-field gauge invariance and universal coupling. The gravitational potential can be either covariant or contravariant and of almost any density weight. We adapt these results to yield universally coupled massive variants of Einstein's equations, yielding two one-parameter families of distinct theories with spin 2 and spin 0. The Freund-Maheshwari-Schonberg theory is therefore not the unique universally coupled massive generalization of Einstein's theory, although it is privileged in some respects. The theories we derive are a subset of those found by Ogievetsky and Polubarinov by other means. The question of positive energy, which continues to be discussed, might be addressed numerically in spherical symmetry. We briefly comment on the issue of causality with two observable metrics and the need for gauge freedom and address some criticisms by Padmanabhan of field derivations of Einstein-like equations along the way.Comment: Introduction notes resemblance between Einstein's discovery process and later field/spin 2 project; matches journal versio

Magic number 7 ±\pm 2 in networks of threshold dynamics

Information processing by random feed-forward networks consisting of units with sigmoidal input-output response is studied by focusing on the dependence of its outputs on the number of parallel paths M. It is found that the system leads to a combination of on/off outputs when $M \lesssim 7$, while for $M \gtrsim 7$, chaotic dynamics arises, resulting in a continuous distribution of outputs. This universality of the critical number $M \sim 7$ is explained by combinatorial explosion, i.e., dominance of factorial over exponential increase. Relevance of the result to the psychological magic number $7 \pm 2$ is briefly discussed.Comment: 6 pages, 5 figure

The Field Theory of Gravitation and The Rest Mass of Particles

It is shown in this work that all free physical fields should have a nonzero rest mass according to the field theory of gravitation.Comment: 4 page