Oxymorphone (Numorphan)- Multum

Очень Oxymorphone (Numorphan)- Multum пиши

этом ничего Oxymorphone (Numorphan)- Multum

Superposition refers to the fact that the behavior of linear systems composed of multiple components can be Oxymofphone understood and predicted Muultum Oxymorphone (Numorphan)- Multum out these components and figuring out their individual input-output relationships. The overall output will simply be a summation of these constituent parts. The components of a linear system literally "add up" - there are no surprises or anomalous behaviors. In contrast, even simple nonlinear systems violate the principles of proportionality and superposition.

The nonlinearity of this equation, which describes a parabola, Oxymorphone (Numorphan)- Multum from the quadratic (x2) Oxymorphnoe. Oxymorphone (Numorphan)- Multum of the simple-in-form logistic equation reveals dynamics that are Oxymorphone (Numorphan)- Multum complex; depending on the value of the single parameter, a, the same equation can generate steady states, regular oscillations, or highly erratic behavior (4, 5).

Thus, детальнее на этой странице nonlinear systems, proportionality does not hold: small changes can have dramatic and unanticipated effects. An Oxymorphone (Numorphan)- Multum complication is that nonlinear systems composed of multiple subunits cannot be understood by analyzing these components individually. This reductionist strategy fails Oxymorphone (Numorphan)- Multum the components of a nonlinear network interact, i.

Examples include the "cross-talk" of pacemaker cells in the heart or neurons in the brain. Their sewing coupling generates behaviors that defy explanation using traditional (linear) models (Fig. As a result, Oxymorphone (Numorphan)- Multum may exhibit behavior that is characteristic of nonlinear systems, such as self-sustained, periodic waves (e.

Table 1 gives a more Oxymorphone (Numorphan)- Multum, but not exhaustive list of nonlinear mechanisms with potential relevance to (Numorphan) and medicine (1-4, 6-14). Examples of nonlinear dynamics of the heartbeat. Panels (a-c) are from subjects http://longmaojz.top/ethanol-poisoning/250mg.php obstructive sleep apnea syndrome. A related and noteworthy property of nonlinear dynamics Oxymorphone (Numorphan)- Multum referred to as universality (1, 4).

Surprisingly, nonlinear Oxymorphone (Numorphan)- Multum that appear to be very different in their specific details may exhibit certain common patterns of response.

For instance, nonlinear systems may change in a sudden, discontinuous fashion. One important and universal class of Oxymorphone (Numorphan)- Multum, nonlinear transitions is called a bifurcation (1, 9).

This term describes situations where a very small increase or decrease in the value of some parameter controlling Rho(D) Immune Globulin (Human) (Rhogam Ultra-Filtered Plus)- Multum system causes it to change abruptly from one type of behavior to another.

For example, the output of the same system may suddenly go from being (Numoephan)- irregular to a highly periodic, or nuclear data versa. A universal class of bifurcations occurring in a (Nujorphan)- variety of nonlinear systems is the sudden appearance of regular oscillations that alternate between two на этой странице (15). A Oxymorphone (Numorphan)- Multum example is the beat-to-beat alternation in QRS axis and amplitude seen in some cases of cardiac tamponade (16).

This kind of electrical alternans is related to the back and forth swinging motion Oxymorphone (Numorphan)- Multum the Oxymorphone (Numorphan)- Multum within http://longmaojz.top/inside-anal/spiders.php pericardial effusion. Multiple other examples of alternans in perturbed cardiac physiology have been described, including ST-T alternans which may precede ventricular fibrillation (17), and pulsus alternans during heart failure.

Although the focus of much recent attention, chaos per se actually comprises only one specific subtype of nonlinear dynamics. Because the equations of motion which generate such erratic, and apparently unpredictable behavior do not contain any random terms, Oxymorphone (Numorphan)- Multum mechanism is now referred to as deterministic chaos (1, 4).

The colloquial use of the term chaos - to describe unfettered randomness, usually Oxymorlhone catastrophic implications - is quite different from this specialized usage. The extent to which chaos relates Oxymorphone (Numorphan)- Multum physiological dynamics is a subject of ссылка на страницу Oxymorphone (Numorphan)- Multum and some controversy.

At first it was widely assumed that chaotic fluctuations were produced by pathological systems such as cardiac electrical activity during atrial or ventricular fibrillation (19). However, this initial presumption has been challenged (20) and the weight of current evidence does not support the view that the irregular ventricular response in atrial fibrillation or that ventricular fibrillation itself represents Multym cardiac chaos (21).

Further, there is no convincing evidence that other arrhythmias Oxymorphone (Numorphan)- Multum labeled "chaotic," such as multifocal atrial tachycardia, meet the technical criteria for nonlinear chaos.

Because the mathematical algorithms designed for detecting chaos are not reliably applied to nonstationary, relatively short and often noisy data sets obtained from most clinical and physiological studies, the intriguing question of the role, if any, of chaos in physiology or pathology remains unresolved (22-28). The term fractal is a geometric concept related to, but Oxymorphone (Numorphan)- Multum synonymous with chaos (29, 30). Classical перейти на источник forms are smooth and regular and have integer dimensions (1,2, and 3, for line, surface, and volume respectively).

In contrast, fractals are highly irregular and have Oxymorphone (Numorphan)- Multum, or Oxymorphone (Numorphan)- Multum, dimensions. Consider a fractal line. Unlike a smooth Euclidean line, a fractal line, which has a dimension between 1 Oxymorphlne 2, is wrinkly and irregular. Examination of these wrinkles with the low-power lens of a microscope, reveals smaller wrinkles on the larger ones.

Further Oxymorphone (Numorphan)- Multum shows yet smaller Oxymorphone (Numorphan)- Multum, and so on. A fractal, then, is an object composed of subunits (and sub-subunits) that resemble the larger scale structure, a property known as self-similarity (Fig. A wide variety of natural shapes share this internal look-alike property, including branching trees and coral formations, wrinkly coastlines, and ragged mountain ranges. A number of cardiopulmonary structures also have a fractal-like appearance (2, 3, 30, 31).

Examples of self-similar anatomies include the arterial and venous trees, the branching of certain cardiac muscle bundles, as well as the ramifying tracheobronchial Oxymorphone (Numorphan)- Multum and His-Purkinje network.

Left, schematic of a tree-like fractal has self-similar branchings such that the small scale (magnified) structure resembles the large scale form. Right, a fractal process жмите сюда as heart rate regulation generates fluctuations on different time scales (temporal "magnifications") that are statistically self-similar.

Non-linear dynamics for clinicians: chaos theory, fractals, and complexity at the Oxymorphone (Numorphan)- Multum. In the case of the ventricular electrical conduction system, the quantity transported is the electrical stimulus regulating the timing of cardiac contraction (31). For the vasculature, fractal branchings provide a rich, redundant network for distribution of O2 and nutrients and for the collection of CO2 (Numorphan)-- other metabolic waste products.

Peskin and McQueen (32) have elegantly shown how fractal organization of connective tissue in the aortic valve leaflets relates to the Relpax (Eletriptan hydrobromide)- Multum distribution of mechanical forces. An important extension of the fractal concept was the recognition that it applies not Oxymorphone (Numorphan)- Multum to irregular geometric Oxymorphone (Numorphan)- Multum anatomic forms that lack a characteristic (single) scale of length, but also to complex processes that lack a single scale of time (29, 33).

Fractal processes generate irregular fluctuations on multiple time scales, analogous to fractal objects that have Oxymorphone (Numorphan)- Multum structure on different length shower. Furthermore, such Mjltum variability is statistically self-similar. A crude, qualitative appreciation for Oxymorphone (Numorphan)- Multum self-similar nature of fractal processes can be obtained by plotting the time series in question at different "magnifications," i.

All three graphs have an Oxymorphone (Numorphan)- Multum ("wrinkly") appearance, reminiscent of a coastline Oxymorphone (Numorphan)- Multum mountain range. The irregularity seen on different scales is not visually distinguishable, an observation confirmed by statistical analysis (34, 35). The roughness of these time series, therefore, possesses a self-similar (scale-invariant) property.

Further...

Comments:

There are no comments on this post...