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.
Soft roboticsSoft robotics is a subfield of robotics that concerns the design, control, and fabrication of robots composed of compliant materials, instead of rigid links. In contrast to rigid-bodied robots built from metals, ceramics and hard plastics, the compliance of soft robots can improve their safety when working in close contact with humans. The goal of soft robotics is the design and construction of robots with physically flexible bodies and electronics. Sometimes softness is limited to part of the machine.
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.
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.
RoboticsRobotics is an interdisciplinary branch of electronics and communication, computer science and engineering. Robotics involves the design, construction, operation, and use of robots. The goal of robotics is to design machines that can help and assist humans. Robotics integrates fields of mechanical engineering, electrical engineering, information engineering, mechatronics engineering, electronics, biomedical engineering, computer engineering, control systems engineering, software engineering, mathematics, etc.
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.
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.
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.
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.
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.
Scalar curvatureIn the mathematical field of Riemannian geometry, the scalar curvature (or the Ricci scalar) is a measure of the curvature of a Riemannian manifold. To each point on a Riemannian manifold, it assigns a single real number determined by the geometry of the metric near that point. It is defined by a complicated explicit formula in terms of partial derivatives of the metric components, although it is also characterized by the volume of infinitesimally small geodesic balls.
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.
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.
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.
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.
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.
Ricci curvatureIn differential geometry, the Ricci curvature tensor, named after Gregorio Ricci-Curbastro, is a geometric object which is determined by a choice of Riemannian or pseudo-Riemannian metric on a manifold. It can be considered, broadly, as a measure of the degree to which the geometry of a given metric tensor differs locally from that of ordinary Euclidean space or pseudo-Euclidean space. The Ricci tensor can be characterized by measurement of how a shape is deformed as one moves along geodesics in the space.
CephalopodA cephalopod ˈsɛfələpɒd is any member of the molluscan class Cephalopoda sɛfəˈlɒpədə (Greek plural κεφαλόποδες, kephalópodes; "head-feet") such as a squid, octopus, cuttlefish, or nautilus. These exclusively marine animals are characterized by bilateral body symmetry, a prominent head, and a set of arms or tentacles (muscular hydrostats) modified from the primitive molluscan foot. Fishers sometimes call cephalopods "inkfish", referring to their common ability to squirt ink.
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.
