Anosov diffeomorphismIn mathematics, more particularly in the fields of dynamical systems and geometric topology, an Anosov map on a manifold M is a certain type of mapping, from M to itself, with rather clearly marked local directions of "expansion" and "contraction". Anosov systems are a special case of Axiom A systems. Anosov diffeomorphisms were introduced by Dmitri Victorovich Anosov, who proved that their behaviour was in an appropriate sense generic (when they exist at all).
Vector (mathematics and physics)In mathematics and physics, vector is a term that refers colloquially to some quantities that cannot be expressed by a single number (a scalar), or to elements of some vector spaces. Historically, vectors were introduced in geometry and physics (typically in mechanics) for quantities that have both a magnitude and a direction, such as displacements, forces and velocity. Such quantities are represented by geometric vectors in the same way as distances, masses and time are represented by real numbers.
Transcranial DopplerTranscranial Doppler (TCD) and transcranial color Doppler (TCCD) are types of Doppler ultrasonography that measure the velocity of blood flow through the brain's blood vessels by measuring the echoes of ultrasound waves moving transcranially (through the cranium). These modes of medical imaging conduct a spectral analysis of the acoustic signals they receive and can therefore be classified as methods of active acoustocerebrography.
Directional derivativeA directional derivative is a concept in multivariable calculus that measures the rate at which a function changes in a particular direction at a given point. The directional derivative of a multivariable differentiable (scalar) function along a given vector v at a given point x intuitively represents the instantaneous rate of change of the function, moving through x with a velocity specified by v. The directional derivative of a scalar function f with respect to a vector v at a point (e.g.
Carotid ultrasonographyCarotid ultrasonography is an ultrasound-based diagnostic imaging technique to evaluate structural details of the carotid arteries. Carotid ultrasound is used to diagnose carotid artery stenosis (CAS) and can assess atherosclerotic plaque morphology and characteristics. Carotid duplex and contrast-enhanced ultrasound are two of the most common imaging techniques used to evaluate carotid artery disease. Carotid ultrasound is a low-cost, noninvasive, and accurate diagnostic imaging modality used to evaluate diseases of the carotid arteries.
Long-range dependenceLong-range dependence (LRD), also called long memory or long-range persistence, is a phenomenon that may arise in the analysis of spatial or time series data. It relates to the rate of decay of statistical dependence of two points with increasing time interval or spatial distance between the points. A phenomenon is usually considered to have long-range dependence if the dependence decays more slowly than an exponential decay, typically a power-like decay. LRD is often related to self-similar processes or fields.
