Trophic classification of selected Colorado lakes

Multispectral scanner data, acquired over several Colorado lakes using LANDSAT-1 and aircraft, were used in conjunction with contact-sensed water quality data to determine the feasibility of assessing lacustrine trophic levels. A trophic state index was developed using contact-sensed data for several trophic indicators. Relationships between the digitally processed multispectral scanner data, several trophic indicators, and the trophic index were examined using a supervised multispectral classification technique and regression techniques. Statistically significant correlations exist between spectral bands, several of the trophic indicators and the trophic state index. Color-coded photomaps were generated which depict the spectral aspects of trophic state

Mathematical Foundations of Complex Tonality

Equal temperament, in which semitones are tuned in the irrational ratio of $2^{1/12} : 1$, is best seen as a serviceable compromise, sacrificing purity for flexibility. Just intonation, in which intervals given by products of powers of $2$, $3$, and $5$, is more natural, but of limited flexibility. We propose a new scheme in which ratios of Gaussian integers form the basis of an abstract tonal system. The tritone, so problematic in just temperament, given ambiguously by the ratios $\tfrac{45}{32}$, $\tfrac{64}{45}$, $\tfrac{36}{25}$, $\tfrac{25}{18}$, none satisfactory, is in our scheme represented by the complex ratio $1 + \rm{i} : 1$. The major and minor whole tones, given by intervals of $\tfrac{9}{8}$ and $\tfrac{10}{9}$, can each be factorized into products of complex semitones, giving us a major complex semitone $\tfrac{3}{4}(1 + \rm{i})$ and a minor complex semitone $\tfrac{1}{3}(3 + \rm{i})$. The perfect third, given by the interval $\tfrac{5}{4}$, factorizes into the product of a complex whole tone $\tfrac{1}{2}(1 + 2\rm{i})$ and its complex conjugate. Augmented with these supplementary tones, the resulting scheme of complex intervals based on products of powers of Gaussian primes leads very naturally to the construction of a complete system of major and minor scales in all keys.Comment: 35 pages, revise

Mathematical Foundations of Complex Tonality

Equal temperament, in which semitones are tuned in irrational ratios, is best seen as a serviceable compromise, sacrificing purity for flexibility. Just intonation, in which intervals are given by products of powers of 2, 3, and 5, is more natural, but of limited flexibility. We propose a new scheme in which ratios of Gaussian integers form the basis of an abstract tonal system. The tritone, so problematic in just temperament, given ambiguously by the ratios 45:32, 64:45, 36:25, 25:18, none satisfactory, is in our scheme represented by the complex ratio 1 + i : 1. The major and minor whole tones, given by intervals of 9/8 and 10/9, can each be factorized into products of complex semitones, giving us a major complex semitone 3/4 (1 + i) and a minor complex semitone 1/3 (3 + i). The perfect third, given by the interval 5/4 , factorizes into the product of a complex whole tone 1/2 (1 + 2i) and its complex conjugate. Augmented with these supplementary tones, the resulting scheme of complex intervals based on products of low powers of Gaussian primes leads naturally to the construction of a complete system of major and minor scales in all keys

Conditional value-at-risk for water management in Lake Burley Griffin

Copyright © Australian Mathematical SocietyAs the centrepiece of Canberra, Lake Burley Griffin provides the setting for buildings of national importance and a venue for aquatic recreation while, as part of the Molonglo River, the lake has a role in the ecological processes of its broader setting. For the purposes of recreation and landscape a constant water level is preferred: the management plan requires the lake to be maintained at a prescribed normal level. In years of low rainfall this requirement could conflict with the water demands of other users. Episodes of high rainfall may also require compromise between competing objectives. For example, drawdown of lake levels for flood mitigation could impact on the lake's recreational and amenity values and the spill may not be a good use of water. Conditional Value at Risk, a risk measure developed by the financial industry for portfolio management, is defined as the expected loss given that some loss threshold is exceeded. Here, Conditional Value at Risk is applied as decision support for strategic planning and day-to-day operational problems in the hydraulic management of Lake Burley Griffin.R. B. Webby, J. Boland, P. G. Howlett, A. V. Metcalfe, T. Srithara

An exactly solvable coarse-grained model for species diversity

We present novel analytical results about ecosystem species diversity that stem from a proposed coarse grained neutral model based on birth-death processes. The relevance of the problem lies in the urgency for understanding and synthesizing both theoretical results of ecological neutral theory and empirical evidence on species diversity preservation. Neutral model of biodiversity deals with ecosystems in the same trophic level where per-capita vital rates are assumed to be species-independent. Close-form analytical solutions for neutral theory are obtained within a coarse-grained model, where the only input is the species persistence time distribution. Our results pertain: the probability distribution function of the number of species in the ecosystem both in transient and stationary states; the n-points connected time correlation function; and the survival probability, definned as the distribution of time-spans to local extinction for a species randomly sampled from the community. Analytical predictions are also tested on empirical data from a estuarine fish ecosystem. We find that emerging properties of the ecosystem are very robust and do not depend on specific details of the model, with implications on biodiversity and conservation biology.Comment: 20 pages, 4 figures. To appear in Journal of Statistichal Mechanic

Observation of twin beam correlations and quadrature entanglement by frequency doubling in a two-port resonator

We demonstrate production of quantum correlated and entangled beams by second harmonic generation in a nonlinear resonator with two output ports. The output beams at wavelength 428.5 nm exhibit 0.9 dB of nonclassical intensity correlations and 0.3 dB of entanglement.Comment: 5 pages, 7 figure

APEX-CHAMP+ high-J CO observations of low-mass young stellar objects: II. Distribution and origin of warm molecular gas

The origin and heating mechanisms of warm (50<T<200 K) molecular gas in low-mass young stellar objects (YSOs) are strongly debated. Both passive heating of the inner collapsing envelope by the protostellar luminosity as well as active heating by shocks and by UV associated with the outflows or accretion have been proposed. We aim to characterize the warm gas within protosteller objects, and disentangle contributions from the (inner) envelope, bipolar outflows and the quiescent cloud. High-J CO maps (12CO J=6--5 and 7--6) of the immediate surroundings (up to 10,000 AU) of eight low-mass YSOs are obtained with the CHAMP+ 650/850 GHz array receiver mounted on the APEX telescope. In addition, isotopologue observations of the 13CO J=6--5 transition and [C I] 3P_2-3P_1 line were taken. Strong quiescent narrow-line 12CO 6--5 and 7--6 emission is seen toward all protostars. In the case of HH~46 and Ced 110 IRS 4, the on-source emission originates in material heated by UV photons scattered in the outflow cavity and not just by passive heating in the inner envelope. Warm quiescent gas is also present along the outflows, heated by UV photons from shocks. Shock-heated warm gas is only detected for Class 0 flows and the more massive Class I sources such as HH~46. Outflow temperatures, estimated from the CO 6--5 and 3--2 line wings, are ~100 K, close to model predictions, with the exception of the L~1551 IRS 5 and IRAS 12496-7650, for which temperatures <50 K are found. APEX-CHAMP+ is uniquely suited to directly probe a protostar's feedback on its accreting envelope gas in terms of heating, photodissociation, and outflow dispersal by mapping 1'x1' regions in high-J CO and [C I] lines.Comment: 18 pages, accepted by A&A, A version with the figures in higher quality can be found on my website: http://www.cfa.harvard.edu/~tvankemp

Exploring music with a probabilistic projection interface

We present the design and evaluation of an in- teractive tool for music exploration, with musi- cal mood and genre inferred directly from tracks. It uses probabilistic representations of multivari- able predictions of subjective characteristics of the music to give users subtle, nuanced visuali- sations of the 2D map. These explicitly repre- sent the uncertainty and overlap among features and support music exploration and casual playlist generation. A longitudinal trial in users’ homes showed that probabilistic highlighting of subjec- tive features led to more focused exploration in mouse activity logs, and 6 of 8 users preferred the probabilistic highlighting

Anion dual mode fluoro-chromogenic chemosensor based on a BODIPY core

Herein, we report the synthesis and chromo-fluorogenic behaviour of a BODIPY derivative. The BODIPY core was functionalized with a phenyl group at meso-position and a formyl group at 2-postion introduced through the Vilsmeier Haack reaction. The compound showed an absorption band at 492 nm and an emission band at 508 nm, with a ФF = 0.84. The evaluation of the chemosensing ability of the BODIPY was investigated in the presence of several anions with environmental and biomedical relevance and a simultaneous colorimetric and fluorimetric response was observed for cyanide and fluoride anions.The authors acknowledge Fundação para a Ciência e Tecnologia—FCT (Portugal) for funding through CQUM (UID/QUI/00686/2020) and a Ph.D. grant to. R. C. R. Gonçalves (SFRH/BD/05278/2020). The NMR spectrometer Bruker Avance III 400 is part of the National NMR Network and was purchased within the framework of the National Program for Scientific Re-equipment, contract REDE/1517/RMN/2005 with funds from POCI 2010 (FEDER) and FCT