Search PubMed⌕ Search

SEARCH · Search PubMed

Results for “dynamics”

Search indexed PubMed citations on genomics, clinical trials, systematic reviews and public health. Explore titles, authors and supplied subject terms, then open the PubMed record.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 1,081 records · Page 60Linked to original sources
PubMed2001

The influence of static and dynamic loading on marginal bone reactions around osseointegrated implants: an animal experimental study.

Although it is generally accepted that adverse forces can impair osseointegration, the mechanism of this complication is unknown. In this study, static and dynamic loads were applied on 10 mm long implants (Brånemark System, Nobel Biocare, Sweden) installed bicortically in rabbit tibiae to investigate the bone response. Each of 10 adult New Zealand black rabbits had one statically loaded implant (with a transverse force of 29.4 N applied on a distance of 1.5 mm from the top of the implant, resulting in a bending moment of 4.4 Ncm), one dynamically loaded implant (with a transverse force of 14.7 N applied on a distance of 50 mm from the top of the implant, resulting in a bending moment of 73.5 Ncm, 2.520 cycles in total, applied with a frequency of 1 Hz), and one unloaded control implant. The loading was performed during 14 days. A numerical model was used as a guideline for the applied dynamic load. Histomorphometrical quantifications of the bone to metal contact area and bone density lateral to the implant were performed on undecalcified and toluidine blue stained sections. The histological picture was similar for statically loaded and control implants. Dense cortical lamellar bone was present around the marginal and apical part of the latter implants with no signs of bone loss. Crater-shaped bone defects and Howship's lacunae were explicit signs of bone resorption in the marginal bone area around the dynamically loaded implants. Despite those bone defects, bone islands were present in contact with the implant surface in this marginal area. This resulted in no significantly lower bone-to-implant contact around the dynamically loaded implants in comparison with the statically loaded and the control implants. However, when comparing the amount of bone in the immediate surroundings of the marginal part of the implants, significantly (P < 0.007) less bone volume (density) was present around the dynamically loaded in comparison with the statically loaded and the control implants. This study shows that excessive dynamic loads cause crater-like bone defects lateral to osseointegrated implants.

Animals↗
PubMed2026

Cell cycle-dependent protein dynamics in budding yeast resolved by deconvolution of bulk proteomics.

The cell division cycle is characterised by oscillatory dynamics in regulatory mechanisms and biosynthesis, coordinated with genome replication and segregation. To understand these dynamics, quantitative cell cycle-dependent protein concentration data are essential. Unfortunately, accurately resolving cell cycle-dependent protein dynamics is challenging because single-cell proteomics is currently infeasible and bulk proteomics requires - inherently imperfect - cell synchronisation. Here, we developed a computational method to deconvolve cell cycle-dependent protein concentration dynamics and applied it to new budding yeast bulk proteome data. Key to this method was a yeast population model, parameterised with experimental cell cycle progression and volume growth data, for quantifying the desynchronisation in sampled populations. We performed deconvolution on 3272 proteins, using cross-validation to determine regularisation parameters, and identified 539 proteins with cell cycle-dependent dynamics. Many of these dynamics were consistent with known yeast biology and dynamic proteins were enriched for several metabolic process, extending previous observations and supporting the emerging picture of metabolic activity as varying substantially over cell cycle phases. We consider the generated cell cycle-resolved budding yeast proteome data a key resource.

Journal Article↗
PubMed2003

The dynamic transition in proteins may have a simple explanation.

The transition that has been observed in the dynamics of hydrated proteins at low temperatures (180-230 K) is normally interpreted as a change from vibrational, harmonic motion at low temperatures to anharmonic motions as the temperature is raised. It is taken to be an intrinsic property of proteins and has been associated with the onset of protein functions. Examination of the dynamic behaviour of proteins in solution within a defined timescale window suggests that certain observations can be explained without the need to invoke a discontinuity in the dynamics of proteins with temperature, i.e. the existence of a dynamical transition is not required. This is discussed in the context of recent evidence that enzyme activity is independent of the activation of anharmonic picosecond dynamics and declines steadily with temperature through the apparent dynamic transition, in accordance with the Arrhenius relationship. That similar timescale dependent dynamical behaviour has been observed experimentally in chain polymers, and seen also in computer simulations of silica glasses, suggests that the phenomenon may be of wide general relevance in both simple glassy and more complex polymeric systems.

Enzymes↗
PubMed1975

Hepatic albumin and urea synthesis: The mathematical modelling of the dynamics of [14C]carbonate-derived guanidine-labelled arginine in the isolated perfused rat liver.

A mathematical model was constructed to define the dynamics of incorporation of radioactivity into urea carbon and the guanidine carbon of arginine in plasma albumin after the rapid intraportal-venous administration of Na214CO3 in the isolated perfused rat liver. 2. The model was formulated in terms of compartmental analysis and additional experiments were designed to provide further information on subsystem dynamics and to discriminate between alternative model structures. 3. Evidence for the rapid-time-constant of labelling of intracellular arginine was provided by precursor-product analysis of precursor [14C]carboante and product [14C]urea in the perfusate. 4. Compartmental analysis of the dynamics of newly synthesized urea was based on the fate of exogenous [13C]urea, endogenous [14C]urea and the accumulation of [12C]urea in perfusate water, confirming the early completion of urea carbon labelling, the absence of continuing synthesis of labelled urea, and the presence of a small intrahepatic urea-delay pool. 5. Analysis of the perfusate dynamics of endogenously synthesized and exogenously administered [6-14C]arginine indicated that although the capacity for extrahepatic formation of [14C]-urea exists, little or no arginine formed within the intrahepatic urea cycle was transported out of the liver. However, the presence of a rapidly turning-over intrahepatic arginine pool was confirmed. 6. On the basis of these subsystem analyses it was possible to offer feasible estimations for the parameters of the mathematical model. However, it was not possible to stimulate the form and magnitude of the dynamics of newly synthesized labelled urea and albumin which were simultaneously observed after administration of [14C]carbonate on the basis of a preliminary model which postulated that both products were derived from a single hepatic pool of [16-14C]arginine. On the other hand these observed dynamics could be satisfied to a two-compartment arginine model, which also provided an explanation for discrepancies observed between albumin synthesis measured radioisotopically and immunologically. This was based on a relative overestimation of [14C]urea specific radioactivity resulting from the rapid dynamics of [14C]carbonate and the [14C]urea subsystem relative to the labelled albumin subsystem. The effects of arginine compartmentalization could be minimized in the model by minor slowing of the rate of [14C]carbonate turnover or by constant infusion of [14C]carbonate, both of which permitted valid determination of albumin-synthesis rates.

Animals↗
PubMed1999

Diagnostic usefulness of endorectal magnetic resonance imaging with dynamic contrast-enhancement in patients with localized prostate cancer: mapping studies with biopsy specimens.

BACKGROUND: New diagnostic criteria for dynamic magnetic resonance (MR) imaging in prostate cancer are presented. The diagnostic usefulness of endorectal MR imaging with dynamic contrast-enhancement in localized prostate cancer and the validity of these criteria were evaluated. METHODS: Eighteen untreated patients who were suspected of localized prostate cancer were included in the study. They received endorectal dynamic MR imaging before systematic sextant needle biopsy. First. a mapping study with the findings of MR images and histopathology of biopsy specimens was performed in eight patients out of 18 to compare the difference in T2-weighted images with the endorectal coil and the body coil in the same individuals. Second, another mapping study was performed in all 18 patients by analyzing the findings of endorectal dynamic MR images. For the diagnosis of prostate cancer in MR imaging, we offered diagnostic criteria from our experience in addition to those in plain T2-weighted images from the literature. RESULTS: The overall diagnostic rates of endorectal dynamic MR imaging were 88.9% in accuracy, 100% in sensitivity, and 81.8% in specificity. In the comparison of the endorectal and body coils in T2-weighted images in eight patients, there was no difference in the diagnostic rates except for one more histopathologic false positive portion in endorectal MR imaging. In the second mapping study in 18 patients, the diagnostic rates were 92.6% in accuracy, 88.9% in sensitivity and 93.3% in specificity. Endorectal dynamic imaging raised the diagnostic sensitivity from 77.8 to 88.9%. CONCLUSION: The data demonstrated the validity of this diagnostic criteria and the diagnostic usefulness of endorectal dynamic MR imaging in localized prostate cancer.

Aged↗
PubMed2002

[Radiological assessment of small bowel obstructions: Value of conventional enteroclysis and dynamic MR-enteroclysis].

PURPOSE: To compare small bowel lesions, especially stenoses, with conventional enteroclysis, static MRI and dynamic MR-enteroclysis. MATERIALS AND METHODS: Forty-two patients with Crohn's disease or other suspected small bowel lesions were examined. MRI was performed in a static and a dynamic way either within one hour after conventional enteroclysis (n = 30) or a few days afterwards (n = 12). In order to monitor bowel filling and to characterize stenoses in a dynamic fashion, 4 series of coronal T2w HASTE breath hold sequences were used, first without additional bowel opacification and then during administration of 1,5 l methyl cellulose via a naso-intestinal tube in the MR unit. Intravenously applied Buscopan was used to reduce bowel movement. RESULTS: In 4 out of 42 Patients, application of methylcellulose was limited to 1000 ml because of gastrointestinal complaints or visible gastral reflux. All patients could be evaluated. Static MRI performed within one hour after conventional enteroclysis and no additional bowel opacification showed insufficient bowel distension. Distension was still better than in MRI without prior application of contrast medium. On the contrary, dynamic MR - enteroclysis lead to controlled and complete bowel distension which allowed for significantly better evaluation of normal bowel anatomy and pathological alterations of the gut. Because of a better bowel distension and dynamic evaluation, MR-enteroclysis revealed significantly more stenoses (n = 42) than MRI obtained with less distension (n = 27, p < 0.001), and characterization of lesions was comparable to conventional enteroclysis (p < 0.001). Fixed and non-fixed stenoses could be differentiated by dynamic MR-enteroclysis. Furthermore, extraluminal complication of Crohn's disease such as abscesses and fistulae or large bowel manifestation of disease were shown in 13 patients. CONCLUSIONS: Dynamic MR-enteroclysis is feasible in routine diagnostic work-up of the small bowel. It is superior in depicting intra- and extraluminal manifestation of small bowel lesions and enables characterization of stenoses comparable to conventional enteroclysis.

Adolescent↗
PubMed2001

Symbolic dynamics and computation in model gene networks.

We analyze a class of ordinary differential equations representing a simplified model of a genetic network. In this network, the model genes control the production rates of other genes by a logical function. The dynamics in these equations are represented by a directed graph on an n-dimensional hypercube (n-cube) in which each edge is directed in a unique orientation. The vertices of the n-cube correspond to orthants of state space, and the edges correspond to boundaries between adjacent orthants. The dynamics in these equations can be represented symbolically. Starting from a point on the boundary between neighboring orthants, the equation is integrated until the boundary is crossed for a second time. Each different cycle, corresponding to a different sequence of orthants that are traversed during the integration of the equation always starting on a boundary and ending the first time that same boundary is reached, generates a different letter of the alphabet. A word consists of a sequence of letters corresponding to a possible sequence of orthants that arise from integration of the equation starting and ending on the same boundary. The union of the words defines the language. Letters and words correspond to analytically computable Poincare maps of the equation. This formalism allows us to define bifurcations of chaotic dynamics of the differential equation that correspond to changes in the associated language. Qualitative knowledge about the dynamics found by integrating the equation can be used to help solve the inverse problem of determining the underlying network generating the dynamics. This work places the study of dynamics in genetic networks in a context comprising both nonlinear dynamics and the theory of computation. (c) 2001 American Institute of Physics.

Journal Article↗
PubMed2003

Can potentially useful dynamics to solve complex problems emerge from constrained chaos and/or chaotic itinerancy?

Complex dynamics including chaos in systems with large but finite degrees of freedom are considered from the viewpoint that they would play important roles in complex functioning and controlling of biological systems including the brain, also in complex structure formations in nature. As an example of them, the computer experiments of complex dynamics occurring in a recurrent neural network model are shown. Instabilities, itinerancies, or localization in state space are investigated by means of numerical analysis, for instance by calculating correlation functions between neurons, basin visiting measures of chaotic dynamics, etc. As an example of functional experiments with use of such complex dynamics, we show the results of executing a memory search task which is set in a typical ill-posed context. We call such useful dynamics "constrained chaos," which might be called "chaotic itinerancy" as well. These results indicate that constrained chaos could be potentially useful in complex functioning and controlling for systems with large but finite degrees of freedom typically observed in biological systems and may be such that working in a delicate balance between converging dynamics and diverging dynamics in high dimensional state space depending on given situation, environment and context to be controlled or to be processed.

Journal Article↗
PubMed1993

Implications of recording strategy for estimates of neocortical dynamics with electroencephalography.

Neocortical dynamics evidently involves very complex, nonlinear processes including top-down and bottom-up interactions across spatial scales. The dynamics may also be strongly influenced by global (periodic) boundary conditions. The primary experimental measure of human neocortical dynamics at short time scales ( approximately few ms) is the scalp electroencephalogram (EEG). It is shown that different recording and data analysis strategies are sensitive to different parts of the spatial spectrum. Thus experimental measures of system dynamics (e.g., correlation dimension estimates) can generally be expected to depend on experimental method. These ideas are illustrated in two ways: a large scale, quasilinear theory of neocortical dynamics in which standing wave phenomenon occur with predicted frequencies in the general range of EEG, and a relatively simple nonlinear physical system consisting of a linear string with attached nonlinear springs. The string/springs system is integrated numerically to illustrate transitions from periodic to chaotic behavior as mesoscopic nonlinear influences dominate macroscopic linear effects. The implications of these results for new theories of neocortical dynamics, experimental estimates of dynamic properties, and cognitive EEG studies are considered.

Journal Article↗
PubMed1997

Turning point properties as a method for the characterization of the ergodic dynamics of one-dimensional iterative maps.

Dynamical as well as statistical properties of the ergodic and fully developed chaotic dynamics of iterative maps are investigated by means of a turning point analysis. The turning points of a trajectory are hereby defined as the local maxima and minima of the trajectory. An examination of the turning point density directly provides us with the information of the position of the fixed point for the corresponding dynamical system. Dividing the ergodic dynamics into phases consisting of turning points and nonturning points, respectively, elucidates the understanding of the organization of the chaotic dynamics for maps. The turning point map contains information on any iteration of the dynamical law and is shown to possess an asymptotic scaling behaviour which is responsible for the assignment of dynamical structures to the environment of the two fixed points of the map. Universal statistical turning point properties are derived for doubly symmetric maps. Possible applications of the observed turning point properties for the analysis of time series are discussed in some detail. (c) 1997 American Institute of Physics.

Journal Article↗
PubMed2004

Feature activated molecular dynamics: an efficient approach for atomistic simulation of solid-state aggregation phenomena.

An efficient approach is presented for performing efficient molecular dynamics simulations of solute aggregation in crystalline solids. The method dynamically divides the total simulation space into "active" regions centered about each minority species, in which regular molecular dynamics is performed. The number, size, and shape of these regions is updated periodically based on the distribution of solute atoms within the overall simulation cell. The remainder of the system is essentially static except for periodic rescaling of the entire simulation cell in order to balance the pressure between the isolated molecular dynamics regions. The method is shown to be accurate and robust for the Environment-Dependant Interatomic Potential (EDIP) for silicon and an Embedded Atom Method potential (EAM) for copper. Several tests are performed beginning with the diffusion of a single vacancy all the way to large-scale simulations of vacancy clustering. In both material systems, the predicted evolutions agree closely with the results of standard molecular dynamics simulations. Computationally, the method is demonstrated to scale almost linearly with the concentration of solute atoms, but is essentially independent of the total system size. This scaling behavior allows for the full dynamical simulation of aggregation under conditions that are more experimentally realizable than would be possible with standard molecular dynamics.

Chemistry, Physical↗
PubMed2005

Quantum fluctuation of electronic wave-packet dynamics coupled with classical nuclear motions.

An ab initio electronic wave-packet dynamics coupled with the simultaneous classical dynamics of nuclear motions in a molecule is studied. We first survey the dynamical equations of motion for the individual components. Reflecting the nonadiabatic dynamics that electrons can respond to nuclear motions only with a finite speed, the equations of motion for nuclei include a force arising from the kinematic (nuclear momentum) coupling from electron cloud. To materialize these quantum effects in the actual ab initio calculations, we study practical implementation of relevant electronic matrix elements that are related to the derivatives with respect to the nuclear coordinates. Applications of the present scheme are performed in terms of the configuration state functions (CSF) using the canonical molecular orbitals as basis functions without transformation to particular diabatic basis. In the CSF representation, the nonadiabatic interaction due to the kinematic coupling is anticipated to be rather small, and instead it should be well taken into account through the off-diagonal elements of the electronic Hamiltonian matrix. Therefore it is expected that the nonadiabatic dynamics based on this CSF basis neglecting the kinematic coupling may work. To verify this anticipation and to quantify the actual effects of the kinematic coupling, we compare the dynamics with and without the kinematic-coupling terms using the same CSF set. Applications up to the fifth electronically excited states in a nonadiabatic collision between H(2) and B(+) shows that the overall behaviors of these two calculations are surprisingly similar to each other in an average sense except for a fast fluctuation reflecting the electronic time scale. However, at the same time, qualitative differences in the collision events are sometimes observed. Therefore it turns out after all that the kinematic-coupling terms cannot be neglected in the CSF-basis representation. The present applications also demonstrate that the nonadiabatic electronic wave-packet dynamics within ab initio quantum chemical calculation is feasible.

Journal Article↗
PubMed2005

An equation-free probabilistic steady-state approximation: dynamic application to the stochastic simulation of biochemical reaction networks.

Stochastic chemical kinetics more accurately describes the dynamics of "small" chemical systems, such as biological cells. Many real systems contain dynamical stiffness, which causes the exact stochastic simulation algorithm or other kinetic Monte Carlo methods to spend the majority of their time executing frequently occurring reaction events. Previous methods have successfully applied a type of probabilistic steady-state approximation by deriving an evolution equation, such as the chemical master equation, for the relaxed fast dynamics and using the solution of that equation to determine the slow dynamics. However, because the solution of the chemical master equation is limited to small, carefully selected, or linear reaction networks, an alternate equation-free method would be highly useful. We present a probabilistic steady-state approximation that separates the time scales of an arbitrary reaction network, detects the convergence of a marginal distribution to a quasi-steady-state, directly samples the underlying distribution, and uses those samples to accurately predict the state of the system, including the effects of the slow dynamics, at future times. The numerical method produces an accurate solution of both the fast and slow reaction dynamics while, for stiff systems, reducing the computational time by orders of magnitude. The developed theory makes no approximations on the shape or form of the underlying steady-state distribution and only assumes that it is ergodic. We demonstrate the accuracy and efficiency of the method using multiple interesting examples, including a highly nonlinear protein-protein interaction network. The developed theory may be applied to any type of kinetic Monte Carlo simulation to more efficiently simulate dynamically stiff systems, including existing exact, approximate, or hybrid stochastic simulation techniques.

Computer Simulation↗
PubMed2007

Aging in a Laponite colloidal suspension: a Brownian dynamics simulation study.

The authors report Brownian dynamics simulation of the out-of-equilibrium dynamics (aging) in a colloidal suspension composed of rigid charged disks, one possible model for Laponite, a synthetic clay deeply investigated in the last few years by means of various experimental techniques. At variance with previous numerical investigations, mainly focusing on static structure and equilibrium dynamics, the authors explore the out-of-equilibrium aging dynamics. They analyze the wave vector and waiting time dependence of the dynamics, focusing on the single-particle and collective density fluctuations (intermediate scattering functions), the mean-squared displacement, and the rotational dynamics. Their findings confirm the complexity of the out-of-equilibrium dynamical behavior of this class of colloidal suspensions and suggest that an arrested disordered state driven by a repulsive Yukawa potential, i.e., a Wigner glass, can be observed in this model.

Journal Article↗
PubMed2005

Gelation-driven component selection in the generation of constitutional dynamic hydrogels based on guanine-quartet formation.

The guanosine hydrazide 1 yields a stable supramolecular hydrogel based on the formation of a guanine quartet (G-quartet) in presence of metal cations. The effect of various parameters (concentration, nature of metal ion, and temperature) on the properties of this gel has been studied. Proton NMR spectroscopy is shown to allow a molecular characterization of the gelation process. Hydrazide 1 and its assemblies can be reversibly decorated by acylhydrazone formation with various aldehydes, resulting in formation of highly viscous dynamic hydrogels. When a mixture of aldehydes is used, the dynamic system selects the aldehyde that leads to the most stable gel. Mixing hydrazides 1, 9 and aldehydes 6, 8 in 1:1:1:1 ratio generated a constitutional dynamic library containing the four acylhydrazone derivatives A, B, C, and D. The library constitution displayed preferential formation of the acylhydrazone B that yields the strongest gel. Thus, gelation redirects the acylhydrazone distribution in the dynamic library as guanosine hydrazide 1 scavenges preferentially aldehyde 8, under the pressure of gelation because of the collective interactions in the assemblies of G-quartets B, despite the strong preference of the competing hydrazide 9 for 8. Gel formation and component selection are thermoreversible. The process amounts to gelation-driven self-organization with component selection and amplification in constitutional dynamic hydrogels based on G-quartet formation and reversible covalent connections. The observed self-organization and component selection occur by means of a multilevel self-assembly involving three dynamic processes, two of supramolecular and one of reversible covalent nature. They extend constitutional dynamic chemistry to phase-organization and phase-transition events.

Aldehydes↗
PubMed2006

Highly designable phenotypes and mutational buffers emerge from a systematic mapping between network topology and dynamic output.

Deciphering the design principles for regulatory networks is fundamental to an understanding of biological systems. We have explored the mapping from the space of network topologies to the space of dynamical phenotypes for small networks. Using exhaustive enumeration of a simple model of three- and four-node networks, we demonstrate that certain dynamical phenotypes can be generated by an atypically broad spectrum of network topologies. Such dynamical outputs are highly designable, much like certain protein structures can be designed by an unusually broad spectrum of sequences. The network topologies that encode a highly designable dynamical phenotype possess two classes of connections: a fully conserved core of dedicated connections that encodes the stable dynamical phenotype and a partially conserved set of variable connections that controls the transient dynamical flow. By comparing the topologies and dynamics of the three- and four-node network ensembles, we observe a large number of instances of the phenomenon of "mutational buffering," whereby addition of a fourth node suppresses phenotypic variation amongst a set of three-node networks.

Biophysical Phenomena↗
PubMed2006

Predicting stochastic gene expression dynamics in single cells.

Fluctuations in protein numbers (noise) due to inherent stochastic effects in single cells can have large effects on the dynamic behavior of gene regulatory networks. Although deterministic models can predict the average network behavior, they fail to incorporate the stochasticity characteristic of gene expression, thereby limiting their relevance when single cell behaviors deviate from the population average. Recently, stochastic models have been used to predict distributions of steady-state protein levels within a population but not to predict the dynamic, presteady-state distributions. In the present work, we experimentally examine a system whose dynamics are heavily influenced by stochastic effects. We measure population distributions of protein numbers as a function of time in the Escherichia coli lactose uptake network (lac operon). We then introduce a dynamic stochastic model and show that prediction of dynamic distributions requires only a few noise parameters in addition to the rates that characterize a deterministic model. Whereas the deterministic model cannot fully capture the observed behavior, our stochastic model correctly predicts the experimental dynamics without any fit parameters. Our results provide a proof of principle for the possibility of faithfully predicting dynamic population distributions from deterministic models supplemented by a stochastic component that captures the major noise sources.

Escherichia coli↗
PubMed1979

From deterministic dynamics to probabilistic descriptions.

THE PRESENT WORK IS DEVOTED TO THE FOLLOWING QUESTION: What is the relationship between the deterministic laws of dynamics and probabilistic description of physical processes? It is generally accepted that probabilistic processes can arise from deterministic dynamics only through a process of "coarse graining" or "contraction of description" that inevitably involves a loss of information. In this work we present an alternative point of view toward the relationship between deterministic dynamics and probabilistic descriptions. Speaking in general terms, we demonstrate the possibility of obtaining (stochastic) Markov processes from deterministic dynamics simply through a "change of representation" that involves no loss of information provided the dynamical system under consideration has a suitably high degree of instability of motion. The fundamental implications of this finding for statistical mechanics and other areas of physics are discussed. From a mathematical point of view, the theory we present is a theory of invertible, positivity-preserving, and necessarily nonunitary similarity transformations that convert the unitary groups associated with deterministic dynamics to contraction semigroups associated with stochastic Markov processes. We explicitly construct such similarity transformations for the so-called Bernoulli systems. This construction illustrates also the construction of the so-called Lyapounov variables and the operator of "internal time," which play an important role in our approach to the problem of irreversibility. The theory we present can also be viewed as a theory of entropy-increasing evolutions and their relationship to deterministic dynamics.

Journal Article↗