Symmetry in Applied Mathematics

Applied mathematics and symmetry work together as a powerful tool for problem reduction and solving. We are communicating applications in probability theory and statistics (A Test Detecting the Outliers for Continuous Distributions Based on the Cumulative Distribution Function of the Data Being Tested, The Asymmetric Alpha-Power Skew-t Distribution), fractals - geometry and alike (Khovanov Homology of Three-Strand Braid Links, Volume Preserving Maps Between p-Balls, Generation of Julia and Mandelbrot Sets via Fixed Points), supersymmetry - physics, nanostructures -chemistry, taxonomy - biology and alike (A Continuous Coordinate System for the Plane by Triangular Symmetry, One-Dimensional Optimal System for 2D Rotating Ideal Gas, Minimal Energy Configurations of Finite Molecular Arrays, Noether-Like Operators and First Integrals for Generalized Systems of Lane-Emden Equations), algorithms, programs and software analysis (Algorithm for Neutrosophic Soft Sets in Stochastic Multi-Criteria Group Decision Making Based on Prospect Theory, On a Reduced Cost Higher Order Traub-Steffensen-Like Method for Nonlinear Systems, On a Class of Optimal Fourth Order Multiple Root Solvers without Using Derivatives) to specific subjects (Facility Location Problem Approach for Distributed Drones, Parametric Jensen-Shannon Statistical Complexity and Its Applications on Full-Scale Compartment Fire Data). Diverse topics are thus combined to map out the mathematical core of practical problems

Identifying outliers and influential observations in general linear regression models

Includes bibliographical references (leaves 140-149).Identifying outliers and/or influential observations is a fundamental step in any statistical analysis, since their presence is likely to lead to erroneous results. Numerous measures have been proposed for detecting outliers and assessing the influence of observations on least squares regression results. Since outliers can arise in different ways, the above mentioned measures are based on motivational arguments and they are designed to measure the influence of observations on different aspects of various regression results. In what follows, we investigate how one can combine different test statistics based on residuals and diagnostic plots to identify outliers and influential observations (both in the single and multiple case) in general linear regression models

Robust data analysis for factorial experimental designs: Improved methods and software

Factorial experimental designs are a large family of experimental designs. Robust statistics has been a subject of considerable research in recent decades. Therefore, robust analysis of factorial designs is applicable to many real problems. Seheult and Tukey (2001) suggested a method of robust analysis of variance for a full factorial design without replication. Their method is generalised for many other factorial designs without the restriction of one observation in each cell. Furthermore, a new algorithm to decompose data from a factorial design is introduced and programmed in the statistical computer package R. The whole procedure of robust data analysis is also programmed in R and it is intended to submit the library to the repository of R software, CRAN. In the procedure of robust data analysis, a cut-off value is needed to detect possible outliers. A set of optimum cut-off values for univariate data and some dimensions of two-way designs (complete and incomplete) has also been provided using an improved design of simulation study

Refining the ecological role of stingrays in coral reef ecosystems

Coral reefs are some of the most diverse and complex ecosystems in the world. They are known for their ability to support a high diversity of marine life. Unfortunately, coral reefs and their associated marine life are under intense anthropogenic pressures; climate change, habitat loss and overfishing are some of the main threats. These pressures also have negative effects on stingrays inhabiting coral reef areas. Management and conservation of stingrays is currently hindered by a lack of knowledge on essential aspects of their ecology. Therefore, this thesis aimed to refine the roles juvenile stingrays play in coral reef habitats and determine the importance of coral reef habitat to stingray populations in a nursery area in the Great Barrier Reef. To do so, this thesis addressed five specific aims: (1) review the current knowledge on batoid nursery areas; (2) identify movement patterns and determine habitat use of juvenile cowtail stingrays Pastinachus ater; (3) evaluate the accuracy of towed-float GPS tags to assess movement patterns and habitat use of stingrays; (4) identify diel movement patterns and habitat use of juvenile mangrove whiprays Urogymnus granulatus; and (5) investigate the relative trophic relationships of four juvenile elasmobranch species within a communal nursery area, with an emphasis on stingrays. Nursery areas are crucial for many elasmobranch species, providing advantages such as increased access to prey and reduced mortality. To date, batoid nurseries have been poorly studied in comparison with shark nurseries. The current decline of batoid populations worldwide, resulting in serious extinction threats, highlights the importance of better understanding these critical habitats. This dissertation presented a synthesis of the available knowledge on batoid nurseries and suggests the use of a combination of well-established criteria to standardize batoid nursery definition. Two telemetry approaches were used to examine movement patterns and habitat use of two stingray species commonly found in coral reef habitats: cowtail stingrays Pastinachus ater and mangrove whiprays Urogymnus granulatus. First, active acoustic telemetry was used to investigate cowtail stingray movements. Active acoustic telemetry provided fine-scale results, but had some limitations (e.g. potential human disturbance and difficulties in performing night tracks). Therefore, a new method was developed – towed-float GPS telemetry –- to investigate mangrove whipray activity patterns and habitat use. Lastly, stable isotope analysis was used to define the contribution of potential carbon sources in the food web and the trophic position and relationship of four juvenile elasmobranch species (mangrove whipray, cowtail stingray, blacktip reef shark Carcharhinus melanopterus and giant shovelnose ray Glaucostegus typus). Active acoustic telemetry results generated a total of 14 active tracks of cowtail stingrays ranging from 4.91 to 9 hours. Cowtail stingrays moved at an average speed of 2.44 m.min⁻¹ + 0.87 SE, with minimum distances travelled ranging from 546 to 1446 meters. Tracking data showed that juvenile cowtail stingrays move in response to tidal cycles, moving faster and with straighter pathways during incoming and outgoing tides, compared to low and high tides. Juvenile cowtail stingrays also showed a strong affinity to sand flat areas and mangrove edge areas, but were infrequently detected in mangrove root habitats. These areas provide food resources and potential refuges for juvenile rays to avoid potential predators. Reef crest habitats were identified as secondary refuge for juveniles during the lowest tides. Towed-float GPS tags were tested on juvenile stingrays with active tracking performed simultaneously for comparison. Individuals travelled 1332.15 ± 269.58 m SE across Pioneer Bay at an average speed of 6.87 m.min⁻¹ and average tracking time of 3.7 hours. Stationary tests demonstrated that the quality of the data obtained by towed-float GPS tags could not be matched by active, acoustic or ARGOS telemetry – on average reaching 99% of successful location recording and <15 meters accuracy. Location Error varied significantly based on the number of satellites detected, with error decreasing as satellite number increased. Towed-float GPS telemetry showed juvenile mangrove whiprays travelled distances from 394 to 2189 meters during tracks, moving at a mean rate of movement of 4.51 m.min⁻¹ ± 3.1 SE with track durations ranging from 1.5 to 9.0 hours. Juvenile mangrove whipray movements were strongly influenced by tidal cycles and rate of movement was significantly different between day and night. Individuals moved faster and chose more direct paths during the outgoing and incoming tide, and were significantly faster during the day than at night. Juvenile mangrove whiprays showed preference for mangrove root habitats during high tides. These areas are thought to reduce juvenile stingray predation risk. Stable isotope analysis showed all juvenile elasmobranchs in Pioneer Bay are at a trophic level of ~4. Isotopic niche size of blacktip reef sharks was smaller than both stingrays, and cowtail stingrays showed the largest niche size. Results showed strong evidence of niche partitioning between mangrove whiprays and cowtail stingrays with differences in feeding strategy. Nearshore pelagic and benthic prey items (e.g. crabs, annelid worms and small baitfishes) contributed most to juvenile elasmobranch diets, while mangrove or offshore prey and carbon sources appear to not have significant input. Results of telemetry and stable isotope analysis revealed juvenile stingrays were fully dependent on the Pioneer Bay system. This dissertation confirms juvenile stingrays play important roles as mesopredators and energetic links within the Pioneer Bay nursery area. By looking at fine scale movements and trophic relationships, this PhD provides important information to better understanding juvenile stingray's ecology, but also to support management and conservation policies

Synthetic Peptides and Peptidomimetics: From Basic Science to Biomedical Applications

This Special Issue, entitled "Synthetic Peptides and Peptidomimetics: From Basic Science to Biomedical Applications", has included both reviews and original research contributions focused on the chemical design and biomedical applications of structurally modified bioactive peptides. The papers collected show how successful this class of molecules still is, both as model molecules for studying the structure of proteins and as potential therapeutics and diagnostics, and also as laboratory tools for advanced basic and applied studies. The large scientific community working in this field is in fact very active and productive, and is making the most of the potential and versatility of these molecules to generate increasingly interesting and innovative molecules of therapeutic interest and to understand the fundamental molecular mechanisms of life