On Root Arrangements of Polynomial-Like Functions and their Derivatives

2000 Mathematics Subject Classification: 12D10.

Densities with Spherical Level Sets in the Gauss-exponential Domain

2000 Mathematics Subject Classification: 60F05, 60B10.

Generation of drifting optical pulses

The radiation in the form of Airy and Gaussian optical pulses is investigated. It is shown that the pulse envelope moves decelerating in the time-spatial coordinates on the surface of a parabolic cylinder for the Airy pulse and a hyperbolic cylinder for the Gaussian. © 2013 IEEE.

Resolvent and Scattering Matrix at the Maximum of the Potential

2000 Mathematics Subject Classification: 35P25, 81U20, 35S30, 47A10, 35B38.

A Harrod modell strukturális stabilitása (Structural stability of the Harrod model)

In this study it is shown that the nontrivial hyperbolic fixed point of a nonlinear dynamical system, which is formulated by means of the adaptive expectations, corresponds to the unstable equilibrium of Harrod. We prove that this nonlinear dynamical (in the sense of Harrod) model is structurally stable under suitable economic conditions. In the case of structural stability, small changes of the functions (C1-perturbations of the vector field) describing the expected and the true time variation of the capital coefficients do not influence the qualitative properties of the endogenous variables, that is, although the trajectories may slightly change, their structure is the same as that of the unperturbed one, and therefore these models are suitable for long-time predictions. In this situation the critique of Lucas or Engel is not valid. There is no topological conjugacy between the perturbed and unperturbed models; the change of the growth rate between two levels may require different times for the perturbed and unperturbed models.

Periphyton light transmission relationships in Florida Bay and the Florida Keys, USA

Light transmission was measured through intact, submerged periphyton communities on artificial seagrass leaves. The periphyton communities were representative of the communities on Thalassia testudinum in subtropical seagrass meadows. The periphyton communities sampled were adhered carbonate sediment, coralline algae, and mixed algal assemblages. Crustose or film-forming periphyton assemblages were best prepared for light transmission measurements using artificial leaves fouled on both sides, while measurements through three-dimensional filamentous algae required the periphyton to be removed from one side. For one-sided samples, light transmission could be measured as the difference between fouled and reference artificial leaf samples. For two-sided samples, the percent periphyton light transmission to the leaf surface was calculated as the square root of the fraction of incident light. Linear, exponential, and hyperbolic equations were evaluated as descriptors of the periphyton dry weight versus light transmission relationship. Hyperbolic and exponential decay models were superior to linear models and exhibited the best fits for the observed relationships. Differences between the coefficients of determination (r2) of hyperbolic and exponential decay models were statistically insignificant. Constraining these models for 100% light transmission at zero periphyton load did not result in any statistically significant loss in the explanatory capability of the models. In most all cases, increasing model complexity using three-parameter models rather than two-parameter models did not significantly increase the amount of variation explained. Constrained two-parameter hyperbolic or exponential decay models were judged best for describing the periphyton dry weight versus light transmission relationship. On T. testudinum in Florida Bay and the Florida Keys, significant differences were not observed in the light transmission characteristics of the varying periphyton communities at different study sites. Using pooled data from the study sites, the hyperbolic decay coefficient for periphyton light transmission was estimated to be 4.36 mg dry wt. cm−2. For exponential models, the exponential decay coefficient was estimated to be 0.16 cm2 mg dry wt.−1.

Using Image Processing Methods to Improve the Detection of Buried Explosive Threats in GPR Data

Current state of the art techniques for landmine detection in ground penetrating radar (GPR) utilize statistical methods to identify characteristics of a landmine response. This research makes use of 2-D slices of data in which subsurface landmine responses have hyperbolic shapes. Various methods from the field of visual image processing are adapted to the 2-D GPR data, producing superior landmine detection results. This research goes on to develop a physics-based GPR augmentation method motivated by current advances in visual object detection. This GPR specific augmentation is used to mitigate issues caused by insufficient training sets. This work shows that augmentation improves detection performance under training conditions that are normally very difficult. Finally, this work introduces the use of convolutional neural networks as a method to learn feature extraction parameters. These learned convolutional features outperform hand-designed features in GPR detection tasks. This work presents a number of methods, both borrowed from and motivated by the substantial work in visual image processing. The methods developed and presented in this work show an improvement in overall detection performance and introduce a method to improve the robustness of statistical classification.

n-alkane carbon isotope ratios in plants and recent lake sediments from Cameroon

Trees and shrubs in tropical Africa use the C3 cycle as a carbon fixation pathway during photosynthesis, while grasses and sedges mostly use the C4 cycle. Leaf-wax lipids from sedimentary archives such as the long-chain n-alkanes (e.g., n-C27 to n-C33) inherit carbon isotope ratios that are representative of the carbon fixation pathway. Therefore, n-alkane d13C values are often used to reconstruct past C3/C4 composition of vegetation, assuming that the relative proportions of C3 and C4 leaf waxes reflect the relative proportions of C3 and C4 plants. We have compared the d13C values of n-alkanes from modern C3 and C4 plants with previously published values from recent lake sediments and provide a framework for estimating the fractional contribution (areal-based) of C3 vegetation cover (fC3) represented by these sedimentary archives. Samples were collected in Cameroon, across a latitudinal transect that accommodates a wide range of climate zones and vegetation types, as reflected in the progressive northward replacement of C3-dominated rain forest by C4-dominated savanna. The C3 plants analysed were characterised by substantially higher abundances of n-C29 alkanes and by substantially lower abundances of n-C33 alkanes than the C4 plants. Furthermore, the sedimentary d13C values of n-C29 and n-C31 alkanes from recent lake sediments in Cameroon (-37.4 per mil to -26.5 per mil) were generally within the range of d13C values for C3 plants, even when from sites where C4 plants dominated the catchment vegetation. In such cases simple linear mixing models fail to accurately reconstruct the relative proportions of C3 and C4 vegetation cover when using the d13C values of sedimentary n-alkanes, overestimating the proportion of C3 vegetation, likely as a consequence of the differences in plant wax production, preservation, transport, and/or deposition between C3 and C4 plants. We therefore tested a set of non-linear binary mixing models using d13C values from both C3 and C4 vegetation as end-members. The non-linear models included a sigmoid function (sine-squared) that describes small variations in the fC3 values as the minimum and maximum d13C values are approached, and a hyperbolic function that takes into account the differences between C3 and C4 plants discussed above. Model fitting and the estimation of uncertainties were completed using the Monte Carlo algorithm and can be improved by future data addition. Models that provided the best fit with the observed d13C values of sedimentary n-alkanes were either hyperbolic functions or a combination of hyperbolic and sine-squared functions. Such non-linear models may be used to convert d13C measurements on sedimentary n-alkanes directly into reconstructions of C3 vegetation cover.

Arte, ciudad y creatividad. Los paisajes publicitarios de Nicolás Gless.

El presente artículo investiga la influencia del fenómeno publicitario como elemento configurador de la esencia urbana en la obra del dibujante y pintor Nicolás Gless. Una obra en la que la publicidad y el diseño gráfico sobrepasan el papel de ornamento para convertirse en rasgo hiperbólico de las sociedades posmodernas. Unos referentes decisivos que, unidos a un profundo conocimiento de los movimientos artísticos del siglo XX y un lenguaje visual cercano al comic, cristalizan en una serie de paisajes urbanos de estilo muy reconocible denominados “paisajes electrográficos”. Un caso paradigmático de las influencias recíprocas entre arte y publicidad vigentes desde mediados del siglo XIX.

Rationalizing spatial exploration patterns of wild animals and humans through a temporal discounting framework

Understanding the exploration patterns of foragers in the wild provides fundamental insight into animal behavior. Recent experimental evidence has demonstrated that path lengths (distances between consecutive turns) taken by foragers are well fitted by a power law distribution. Numerous theoretical contributions have posited that “Lévy random walks”—which can produce power law path length distributions—are optimal for memoryless agents searching a sparse reward landscape. It is unclear, however, whether such a strategy is efficient for cognitively complex agents, from wild animals to humans. Here, we developed a model to explain the emergence of apparent power law path length distributions in animals that can learn about their environments. In our model, the agent’s goal during search is to build an internal model of the distribution of rewards in space that takes into account the cost of time to reach distant locations (i.e., temporally discounting rewards). For an agent with such a goal, we find that an optimal model of exploration in fact produces hyperbolic path lengths, which are well approximated by power laws. We then provide support for our model by showing that humans in a laboratory spatial exploration task search space systematically and modify their search patterns under a cost of time. In addition, we find that path length distributions in a large dataset obtained from free-ranging marine vertebrates are well described by our hyperbolic model. Thus, we provide a general theoretical framework for understanding spatial exploration patterns of cognitively complex foragers.

Rationalizing spatial exploration patterns of wild animals and humans through a temporal discounting framework

Understanding the exploration patterns of foragers in the wild provides fundamental insight into animal behavior. Recent experimental evidence has demonstrated that path lengths (distances between consecutive turns) taken by foragers are well fitted by a power law distribution. Numerous theoretical contributions have posited that “Lévy random walks”—which can produce power law path length distributions—are optimal for memoryless agents searching a sparse reward landscape. It is unclear, however, whether such a strategy is efficient for cognitively complex agents, from wild animals to humans. Here, we developed a model to explain the emergence of apparent power law path length distributions in animals that can learn about their environments. In our model, the agent’s goal during search is to build an internal model of the distribution of rewards in space that takes into account the cost of time to reach distant locations (i.e., temporally discounting rewards). For an agent with such a goal, we find that an optimal model of exploration in fact produces hyperbolic path lengths, which are well approximated by power laws. We then provide support for our model by showing that humans in a laboratory spatial exploration task search space systematically and modify their search patterns under a cost of time. In addition, we find that path length distributions in a large dataset obtained from free-ranging marine vertebrates are well described by our hyperbolic model. Thus, we provide a general theoretical framework for understanding spatial exploration patterns of cognitively complex foragers.

A Scalable Design Framework for Variability Management in Large-Scale Software Product Lines

Variability management is one of the major challenges in software product line adoption, since it needs to be efficiently managed at various levels of the software product line development process (e.g., requirement analysis, design, implementation, etc.). One of the main challenges within variability management is the handling and effective visualization of large-scale (industry-size) models, which in many projects, can reach the order of thousands, along with the dependency relationships that exist among them. These have raised many concerns regarding the scalability of current variability management tools and techniques and their lack of industrial adoption. To address the scalability issues, this work employed a combination of quantitative and qualitative research methods to identify the reasons behind the limited scalability of existing variability management tools and techniques. In addition to producing a comprehensive catalogue of existing tools, the outcome form this stage helped understand the major limitations of existing tools. Based on the findings, a novel approach was created for managing variability that employed two main principles for supporting scalability. First, the separation-of-concerns principle was employed by creating multiple views of variability models to alleviate information overload. Second, hyperbolic trees were used to visualise models (compared to Euclidian space trees traditionally used). The result was an approach that can represent models encompassing hundreds of variability points and complex relationships. These concepts were demonstrated by implementing them in an existing variability management tool and using it to model a real-life product line with over a thousand variability points. Finally, in order to assess the work, an evaluation framework was designed based on various established usability assessment best practices and standards. The framework was then used with several case studies to benchmark the performance of this work against other existing tools.

Integrability for Relativistic Spin Networks

The evaluation of relativistic spin networks plays a fundamental role in the Barrett-Crane state sum model of Lorentzian quantum gravity in 4 dimensions. A relativistic spin network is a graph labelled by unitary irreducible representations of the Lorentz group appearing in the direct integral decomposition of the space of L^2 functions on three-dimensional hyperbolic space. To `evaluate' such a spin network we must do an integral; if this integral converges we say the spin network is `integrable'. Here we show that a large class of relativistic spin networks are integrable, including any whose underlying graph is the 4-simplex (the complete graph on 5 vertices). This proves a conjecture of Barrett and Crane, whose validity is required for the convergence of their state sum model.

Causal structure of the entanglement renormalization ansatz

We show that the multiscale entanglement renormalization ansatz (MERA) can be reformulated in terms of a causality constraint on discrete quantum dynamics. This causal structure is that of de Sitter space with a flat space-like boundary, where the volume of a spacetime region corresponds to the number of variational parameters it contains. This result clarifies the nature of the ansatz, and suggests a generalization to quantum field theory. It also constitutes an independent justification of the connection between MERA and hyperbolic geometry which was proposed as a concrete implementation of the AdS-CFT correspondence.

Fundamental domains for proper affine actions of Coxeter groups in three dimensions

We study proper actions of groups $G \cong \Z/2\Z \ast \Z/2\Z \ast \Z/2\Z$ on affine space of three real dimensions. Since $G$ is nonsolvable, work of Fried and Goldman implies that it preserves a Lorentzian metric. A subgroup $\Gamma < G$ of index two acts freely, and $\R^3/\Gamma$ is a Margulis spacetime associated to a hyperbolic surface $\Sigma$. When $\Sigma$ is convex cocompact, work of Danciger, Gu{\'e}ritaud, and Kassel shows that the action of $\Gamma$ admits a polyhedral fundamental domain bounded by crooked planes. We consider under what circumstances the action of $G$ also admits a crooked fundamental domain. We show that it is possible to construct actions of $G$ that fail to admit crooked fundamental domains exactly when the extended mapping class group of $\Sigma$ fails to act transitively on the top-dimensional simplices of the arc complex of $\Sigma$. We also provide explicit descriptions of the moduli space of $G$ actions that admit crooked fundamental domains.