On the average uncertainty for systems with nonlinear coupling

The increased uncertainty and complexity of nonlinear systems have motivated investigators to consider generalized approaches to defining an entropy function. New insights are achieved by defining the average uncertainty in the probability domain as a transformation of entropy functions. The Shannon entropy when transformed to the probability domain is the weighted geometric mean of the probabilities. For the exponential and Gaussian distributions, we show that the weighted geometric mean of the distribution is equal to the density of the distribution at the location plus the scale, i.e. at the width of the distribution. The average uncertainty is generalized via the weighted generalized mean, in which the moment is a function of the nonlinear source. Both the Renyi and Tsallis entropies transform to this definition of the generalized average uncertainty in the probability domain. For the generalized Pareto and Student's t-distributions, which are the maximum entropy distributions for these generalized entropies, the appropriate weighted generalized mean also equals the density of the distribution at the location plus scale. A coupled entropy function is proposed, which is equal to the normalized Tsallis entropy divided by one plus the coupling.Comment: 24 pages, including 4 figures and 1 tabl

Use of the geometric mean as a statistic for the scale of the coupled Gaussian distributions

The geometric mean is shown to be an appropriate statistic for the scale of a heavy-tailed coupled Gaussian distribution or equivalently the Student's t distribution. The coupled Gaussian is a member of a family of distributions parameterized by the nonlinear statistical coupling which is the reciprocal of the degree of freedom and is proportional to fluctuations in the inverse scale of the Gaussian. Existing estimators of the scale of the coupled Gaussian have relied on estimates of the full distribution, and they suffer from problems related to outliers in heavy-tailed distributions. In this paper, the scale of a coupled Gaussian is proven to be equal to the product of the generalized mean and the square root of the coupling. From our numerical computations of the scales of coupled Gaussians using the generalized mean of random samples, it is indicated that only samples from a Cauchy distribution (with coupling parameter one) form an unbiased estimate with diminishing variance for large samples. Nevertheless, we also prove that the scale is a function of the geometric mean, the coupling term and a harmonic number. Numerical experiments show that this estimator is unbiased with diminishing variance for large samples for a broad range of coupling values.Comment: 17 pages, 5 figure

Fifty years of Cook Inlet beluga whale ecology recorded as isotopes in bone and teeth

Thesis (M.S.) University of Alaska Fairbanks, 2017Beluga whales (Delphinapterus leucas) are found across the Arctic and Subarctic in seasonally ice covered waters. Five stocks of beluga whales are associated with the waters near Alaska for at least part of the year and four of those five stocks are abundant and commonly hunted by Alaskan Natives. The belugas resident in Cook Inlet are also an important cultural and subsistence resource to Alaskan Natives in the area, but a ~50% decline in abundance in the 1990's led to the stock being designated as depleted under the Marine Mammal Protection Act in 2000 and listed as endangered under the Endangered Species Act in 2008. Numerous studies of beluga whales in relation to stranding events, predation (killer whales), parasitism, disease, contaminants, and other potential population threats have not identified the reason for their inability to recover. Changes in diet have been considered, but are difficult to study because observations of feeding in muddy water and beluga stomachs are difficult to obtain. To investigate the past feeding ecology of beluga whales from Cook Inlet I sampled bone and teeth for isotopic analyses. I sampled bone from 20 individuals that died between 1964 and 2007 for stable carbon and nitrogen isotope analysis (values expressed as δ¹³C and δ¹⁵N values). I also micro-sampled annual growth layer groups in the teeth of 26 individuals representing the years from 1962 to 2007. Bone and tooth data showed a general decrease in δ¹³C and δ¹⁵N values over time. The δ¹³C values from analyses of growth layer groups declined from -13.4‰ to -16.2‰ and δ¹⁵N values declined from 17.2‰ to 15.4‰. Although these values are consistent with a change in feeding ecology over time, the magnitude of the decrease in δ¹⁵N values (~2‰) is insufficient for a full trophic level shift (~3‰).The relatively large decrease in the δ¹³C values over the same time period (~3‰), however, is much greater than a full trophic level shift (~1‰) and suggests an increase in prey associated with freshwater, which typically have lower δ¹³C values than prey associated with marine water. To test this hypothesis I analyzed the strontium isotope composition (⁸⁷Sr/⁸⁶Sr ratios) of growth layer groups in teeth from a sub-set of individuals. The resulting ⁸⁷Sr/⁸⁶Sr ratios trended away from the global marine signature (0.70918) over time and toward the more freshwater signatures measured in rivers flowing into the upper reaches of Cook Inlet. These results indicate that the diet of Cook Inlet beluga whales has changed over time. This could be from feeding on different, more freshwater derived prey species, or from feeding on the same species, but on individuals from locations with a more freshwater influence. Both of these interpretations are consistent with population survey data indicating a retraction in beluga range into the upper reaches of Cook Inlet. This study presents the first evidence of a long term (~50 years) change in Cook Inlet beluga whale feeding ecology. The consequences of this change toward more freshwater-influenced prey, and how this change relates to Cook Inlet beluga whales' decline or recovery remains unknown. However, to better examine this change in feeding ecology a follow-up study will; 1) develop a strontium isoscape for the Cook Inlet watershed; 2) analyze more teeth to better analyze changes in feeding ecology by demographic group (sex, age); and 3) analyze growth layer groups from Bristol Bay beluga teeth for a comparison with Cook Inlet belugas to determine if the changes represent an ecosystem change within Cook Inlet or a broader scale change affecting another region. This study builds towards a better understanding of the changes in Cook Inlet beluga feeding ecology and will help to determine if changes in diet could be a factor in their recovery

Thermodynamics and the Global Optimization of Lennard-Jones clusters

Theoretical design of global optimization algorithms can profitably utilize recent statistical mechanical treatments of potential energy surfaces (PES's). Here we analyze the basin-hopping algorithm to explain its success in locating the global minima of Lennard-Jones (LJ) clusters, even those such as \LJ{38} for which the PES has a multiple-funnel topography, where trapping in local minima with different morphologies is expected. We find that a key factor in overcoming trapping is the transformation applied to the PES which broadens the thermodynamic transitions. The global minimum then has a significant probability of occupation at temperatures where the free energy barriers between funnels are surmountable.Comment: 13 pages, 13 figures, revte

The double-funnel energy landscape of the 38-atom Lennard-Jones cluster

The 38-atom Lennard-Jones cluster has a paradigmatic double-funnel energy landscape. One funnel ends in the global minimum, a face-centred-cubic (fcc) truncated octahedron. At the bottom of the other funnel is the second lowest energy minimum which is an incomplete Mackay icosahedron. We characterize the energy landscape in two ways. Firstly, from a large sample of minima and transition states we construct a disconnectivity tree showing which minima are connected below certain energy thresholds. Secondly we compute the free energy as a function of a bond-order parameter. The free energy profile has two minima, one which corresponds to the fcc funnel and the other which at low temperature corresponds to the icosahedral funnel and at higher temperatures to the liquid-like state. These two approaches show that the greater width of the icosahedral funnel, and the greater structural similarity between the icosahedral structures and those associated with the liquid-like state, are the cause of the smaller free energy barrier for entering the icosahedral funnel from the liquid-like state and therefore of the cluster's preferential entry into this funnel on relaxation down the energy landscape. Furthermore, the large free energy barrier between the fcc and icosahedral funnels, which is energetic in origin, causes the cluster to be trapped in one of the funnels at low temperature. These results explain in detail the link between the double-funnel energy landscape and the difficulty of global optimization for this cluster.Comment: 12 pages, 11 figures, revte

Omnidirectional Sensory and Motor Volumes in Electric Fish

Active sensing organisms, such as bats, dolphins, and weakly electric fish, generate a 3-D space for active sensation by emitting self-generated energy into the environment. For a weakly electric fish, we demonstrate that the electrosensory space for prey detection has an unusual, omnidirectional shape. We compare this sensory volume with the animal's motor volume—the volume swept out by the body over selected time intervals and over the time it takes to come to a stop from typical hunting velocities. We find that the motor volume has a similar omnidirectional shape, which can be attributed to the fish's backward-swimming capabilities and body dynamics. We assessed the electrosensory space for prey detection by analyzing simulated changes in spiking activity of primary electrosensory afferents during empirically measured and synthetic prey capture trials. The animal's motor volume was reconstructed from video recordings of body motion during prey capture behavior. Our results suggest that in weakly electric fish, there is a close connection between the shape of the sensory and motor volumes. We consider three general spatial relationships between 3-D sensory and motor volumes in active and passive-sensing animals, and we examine hypotheses about these relationships in the context of the volumes we quantify for weakly electric fish. We propose that the ratio of the sensory volume to the motor volume provides insight into behavioral control strategies across all animals

Magnetic Wreaths and Cycles in Convective Dynamos

Solar-type stars exhibit a rich variety of magnetic activity. Seeking to explore the convective origins of this activity, we have carried out a series of global 3D magnetohydrodynamic (MHD) simulations with the anelastic spherical harmonic (ASH) code. Here we report on the dynamo mechanisms achieved as the effects of artificial diffusion are systematically decreased. The simulations are carried out at a nominal rotation rate of three times the solar value (3$\Omega_\odot$), but similar dynamics may also apply to the Sun. Our previous simulations demonstrated that convective dynamos can build persistent toroidal flux structures (magnetic wreaths) in the midst of a turbulent convection zone and that high rotation rates promote the cyclic reversal of these wreaths. Here we demonstrate that magnetic cycles can also be achieved by reducing the diffusion, thus increasing the Reynolds and magnetic Reynolds numbers. In these more turbulent models, diffusive processes no longer play a significant role in the key dynamical balances that establish and maintain the differential rotation and magnetic wreaths. Magnetic reversals are attributed to an imbalance in the poloidal magnetic induction by convective motions that is stabilized at higher diffusion levels. Additionally, the enhanced levels of turbulence lead to greater intermittency in the toroidal magnetic wreaths, promoting the generation of buoyant magnetic loops that rise from the deep interior to the upper regions of our simulated domain. The implications of such turbulence-induced magnetic buoyancy for solar and stellar flux emergence are also discussed.Comment: 21 pages, 16 figures, accepted for publication in Ap

Good aquaculture practices (GAqP): setting directions for harmonized regional standards - the Philippine experience

Abstract only.A milestone process on how Good Aquaculture Practices (GAqP) emanates in Philippine aquaculture and its integration to the ASEAN harmonized standardization efforts is discussed in the paper. The management model, value chain and draft Philippine National Standard of the GAqP code are presented and evaluated as to its impact to trade and marketing, socioeconomic considerations, food safety and technology

A Humanistic Approach to Understanding Child Consumer Socialization in US Homes

We present findings from a qualitative, multisite, multi-method, longitudinal study of parents and their preschool-aged children that explores the intersections of marketing influences in the home and in the larger outside world of children. Findings indicate that preschoolers represent complicated and nuanced “consumers in training” beyond predictions based on their “perceptual stage of development.” Specifically, our data revealed interesting ways in which marketing and consumer culture can foster a number of pro-social consumer outcomes (e.g., charity, gift-giving, financial literacy). We also noted an emerging understanding by preschoolers of the social meanings of goods for identity construction and product evaluation. Finally, through a presentation of an idiographic case, we show how consumer socialization cannot be attributed to one factor such as media but is based on multiple and concurrent factors—parents, siblings, peers, and home environment—that act to moderate, mediate, and provide meaning for marketing messages

Electronic properties of disclinated flexible membrane beyond the inextensional limit: Application to graphene

Gauge-theory approach to describe Dirac fermions on a disclinated flexible membrane beyond the inextensional limit is formulated. The elastic membrane is considered as an embedding of 2D surface into R^3. The disclination is incorporated through an SO(2) gauge vortex located at the origin, which results in a metric with a conical singularity. A smoothing of the conical singularity is accounted for by replacing a disclinated rigid plane membrane with a hyperboloid of near-zero curvature pierced at the tip by the SO(2) vortex. The embedding parameters are chosen to match the solution to the von Karman equations. A homogeneous part of that solution is shown to stabilize the theory. The modification of the Landau states and density of electronic states of the graphene membrane due to elasticity is discussed.Comment: 15 pages, Journal of Physics:Condensed Matter in pres