Dynamical systemIn mathematics, a dynamical system is a system in which a function describes the time dependence of a point in an ambient space, such as in a parametric curve. Examples include the mathematical models that describe the swinging of a clock pendulum, the flow of water in a pipe, the random motion of particles in the air, and the number of fish each springtime in a lake. The most general definition unifies several concepts in mathematics such as ordinary differential equations and ergodic theory by allowing different choices of the space and how time is measured.
Dynamical systems theoryDynamical systems theory is an area of mathematics used to describe the behavior of complex dynamical systems, usually by employing differential equations or difference equations. When differential equations are employed, the theory is called continuous dynamical systems. From a physical point of view, continuous dynamical systems is a generalization of classical mechanics, a generalization where the equations of motion are postulated directly and are not constrained to be Euler–Lagrange equations of a least action principle.
Invertebrate zoologyInvertebrate zoology is the subdiscipline of zoology that consists of the study of invertebrates, animals without a backbone (a structure which is found only in fish, amphibians, reptiles, birds and mammals). Invertebrates are a vast and very diverse group of animals that includes sponges, echinoderms, tunicates, numerous different phyla of worms, molluscs, arthropods and many additional phyla. Single-celled organisms or protists are usually not included within the same group as invertebrates.
OctopusAn octopus (: octopuses or octopodes) is a soft-bodied, eight-limbed mollusc of the order Octopoda (ɒkˈtɒpədə, ). The order consists of some 300 species and is grouped within the class Cephalopoda with squids, cuttlefish, and nautiloids. Like other cephalopods, an octopus is bilaterally symmetric with two eyes and a beaked mouth at the center point of the eight limbs. The soft body can radically alter its shape, enabling octopuses to squeeze through small gaps. They trail their eight appendages behind them as they swim.
Bio-inspired roboticsBio-inspired robotic locomotion is a fairly new subcategory of bio-inspired design. It is about learning concepts from nature and applying them to the design of real-world engineered systems. More specifically, this field is about making robots that are inspired by biological systems, including Biomimicry. Biomimicry is copying from nature while bio-inspired design is learning from nature and making a mechanism that is simpler and more effective than the system observed in nature.
BionicsBionics or biologically inspired engineering is the application of biological methods and systems found in nature to the study and design engineering systems and modern technology. The word bionic, coined by Jack E. Steele in August 1958, is a portmanteau from biology and electronics which was popularized by the 1970s U.S. television series The Six Million Dollar Man and The Bionic Woman, both based on the novel Cyborg by Martin Caidin. All three stories feature humans given various superhuman powers by their electromechanical implants.
Marine invertebratesMarine invertebrates are the invertebrates that live in marine habitats. Invertebrate is a blanket term that includes all animals apart from the vertebrate members of the chordate phylum. Invertebrates lack a vertebral column, and some have evolved a shell or a hard exoskeleton. As on land and in the air, marine invertebrates have a large variety of body plans, and have been categorised into over 30 phyla. They make up most of the macroscopic life in the oceans.
InvertebrateInvertebrates are a paraphyletic group of animals that neither possess nor develop a vertebral column (commonly known as a backbone or spine), derived from the notochord. This is a grouping including all animals apart from the chordate subphylum Vertebrata. Familiar examples of invertebrates include arthropods, mollusks, annelids, echinoderms and cnidarians. The majority of animal species are invertebrates; one estimate puts the figure at 97%. Many invertebrate taxa have a greater number and variety of species than the entire subphylum of Vertebrata.
Motion planningMotion planning, also path planning (also known as the navigation problem or the piano mover's problem) is a computational problem to find a sequence of valid configurations that moves the object from the source to destination. The term is used in computational geometry, computer animation, robotics and computer games. For example, consider navigating a mobile robot inside a building to a distant waypoint. It should execute this task while avoiding walls and not falling down stairs.
BiomimeticsBiomimetics or biomimicry is the emulation of the models, systems, and elements of nature for the purpose of solving complex human problems. The terms "biomimetics" and "biomimicry" are derived from βίος (bios), life, and μίμησις (mīmēsis), imitation, from μιμεῖσθαι (mīmeisthai), to imitate, from μῖμος (mimos), actor. A closely related field is bionics. Nature has gone through evolution over the 3.8 billion years since life is estimated to have appeared on the Earth. It has evolved species with high performance using commonly found materials.
OrganismAn organism () is any biological living system that functions as an individual life form. All organisms are composed of cells (cell theory). The idea of organism is based on the concept of minimal functional unit of life. Three traits have been proposed to play the main role in qualification as an organism: noncompartmentability – structure that cannot be divided without its functionality loss, individuality – the entity has simultaneous holding of genetic uniqueness, genetic homogeneity and autonomy, distinctness – genetic information has to maintain open-system (a cell).
Biological processBiological processes are those processes that are vital for an organism to live, and that shape its capacities for interacting with its environment. Biological processes are made of many chemical reactions or other events that are involved in the persistence and transformation of life forms. Metabolism and homeostasis are examples. Biological processes within an organism can also work as bioindicators. Scientists are able to look at an individual's biological processes to monitor the effects of environmental changes.
Measure-preserving dynamical systemIn mathematics, a measure-preserving dynamical system is an object of study in the abstract formulation of dynamical systems, and ergodic theory in particular. Measure-preserving systems obey the Poincaré recurrence theorem, and are a special case of conservative systems. They provide the formal, mathematical basis for a broad range of physical systems, and, in particular, many systems from classical mechanics (in particular, most non-dissipative systems) as well as systems in thermodynamic equilibrium.
Gaussian curvatureIn differential geometry, the Gaussian curvature or Gauss curvature Κ of a smooth surface in three-dimensional space at a point is the product of the principal curvatures, κ1 and κ2, at the given point: The Gaussian radius of curvature is the reciprocal of Κ. For example, a sphere of radius r has Gaussian curvature 1/r2 everywhere, and a flat plane and a cylinder have Gaussian curvature zero everywhere. The Gaussian curvature can also be negative, as in the case of a hyperboloid or the inside of a torus.
Machine learningMachine learning (ML) is an umbrella term for solving problems for which development of algorithms by human programmers would be cost-prohibitive, and instead the problems are solved by helping machines 'discover' their 'own' algorithms, without needing to be explicitly told what to do by any human-developed algorithms. Recently, generative artificial neural networks have been able to surpass results of many previous approaches.
Stochastic optimizationStochastic optimization (SO) methods are optimization methods that generate and use random variables. For stochastic problems, the random variables appear in the formulation of the optimization problem itself, which involves random objective functions or random constraints. Stochastic optimization methods also include methods with random iterates. Some stochastic optimization methods use random iterates to solve stochastic problems, combining both meanings of stochastic optimization.
CurvatureIn mathematics, curvature is any of several strongly related concepts in geometry. Intuitively, the curvature is the amount by which a curve deviates from being a straight line, or a surface deviates from being a plane. For curves, the canonical example is that of a circle, which has a curvature equal to the reciprocal of its radius. Smaller circles bend more sharply, and hence have higher curvature. The curvature at a point of a differentiable curve is the curvature of its osculating circle, that is the circle that best approximates the curve near this point.
Blue-ringed octopusBlue-ringed octopuses, comprising the genus Hapalochlaena, are four extremely venomous species of octopus that are found in tide pools and coral reefs in the Pacific and Indian oceans, from Japan to Australia. They can be identified by their yellowish skin and characteristic blue and black rings that change color dramatically when the animal is threatened. They eat small crustaceans, including crabs, hermit crabs, shrimp and other small sea animals. They are one of the world's most venomous marine animals.
Mathematical optimizationMathematical optimization (alternatively spelled optimisation) or mathematical programming is the selection of a best element, with regard to some criterion, from some set of available alternatives. It is generally divided into two subfields: discrete optimization and continuous optimization. Optimization problems arise in all quantitative disciplines from computer science and engineering to operations research and economics, and the development of solution methods has been of interest in mathematics for centuries.
Biological organisationBiological organisation is the organisation of complex biological structures and systems that define life using a reductionistic approach. The traditional hierarchy, as detailed below, extends from atoms to biospheres. The higher levels of this scheme are often referred to as an ecological organisation concept, or as the field, hierarchical ecology. Each level in the hierarchy represents an increase in organisational complexity, with each "object" being primarily composed of the previous level's basic unit.
