Representation of time-dependent correlation and recurrence time functions

Correlation functions based on time averaging are not suited to study non-stationary point processes (e.g. the electric organ discharge activity of weakly-electric pulse fish). To overcome this problem, we present here a time-dependent correlation method, which can also be applied to study complicated correlations of moderately non-stationary point processes (e.g. neuronal spike trains). Indication of recurrence time aspects of the point processes provides a more complete representation of the correlation functions. In addition higher order correlations between two point processes are represented.     

Long-Term Changes of a Coastal Bird Breeding Community on a Small Island – Does Natural Succession Compromise Conservation Values?

Limited spatial resources available for conservation lead to controversy about whether to apply single-species management or ecosystemary approaches in order to maintain biodiversity. In this study I analyse changes in a community of breeding coastal birds over a 90-year period, in order to examine whether natural processes on an unmanaged island are in accordance with requirements to save endangered species. Both diversity and species richness of the community increased significantly over time, and evenness increased after having been severely reduced by human impact. Diversity, evenness and species richness seemed to approach an equilibrium in the past decade, but number of breeding pairs declined as a consequence of altered natural disturbance regime. Species identity changed over time, with two initially very common species recently becoming locally extinct. These species are of high conservation concern, and their disappearance causes a problem for the concept of naturalness on islands. I conclude that natural processes need to be applied to the entire landscape in order to maintain dynamic processes that are essential for the survival of these species. The natural changes on the island should not be interrupted, but rather demonstrated to the public in order to increase conservation mindedness and gain support for changes in anthropogenic influences on a larger spatial scale.     

Pressure jump relaxation investigations of lipid membranes using FTIR spectroscopy

The relaxation kinetics of aqueous lipid dispersions after a pressure jump (p-jump) were investigated using time-resolved FTIR spectroscopy. The methylene stretching vibrational band and the carbonyl band were analyzed to detect changes in conformational order of the hydrocarbon chains and to follow the degree of hydration of the head group, respectively. The kinetics of the transition was found to consist of multiple processes with relaxation constants from seconds down to milliseconds. Faster processes are also present, but could not be resolved by our instrument. This is the first investigation showing directly the time resolved change in chain order in lipid bilayers induced by a p-jump. The results obtained with this IR detection method support previous results that the change in chain order after a perturbation is a multi-step process with the initial molecular events occurring with time constants shorter than milliseconds.     

Contact-Mode High-Resolution High-Speed Atomic Force Microscopy Movies of the Purple Membrane

High-speed atomic force microscopy (HS-AFM) is becoming a reference tool for the study of dynamic biological processes. The spatial and time resolutions of HS-AFM are on the order of nanometers and milliseconds, respectively, and allow structural and functional characterization of biological processes at the single-molecule level. In this work we present contact-mode HS-AFM movies of purple membranes containing two-dimensional arrays of bacteriorhodopsin (bR). In high-resolution movies acquired at a 100 ms frame acquisition time, the substructure on individual bR trimers was visualized. In regions in between different bR arrays, dynamic topographies were observed and interpreted as motion of the bR trimers. Similarly, motion of bR monomers in the vicinity of lattice defects in the purple membrane was observed. Our findings indicate that the bR arrays are in a mobile association-dissociation equilibrium. HS-AFM on membranes provides novel perspectives for analyzing the membrane diffusion processes of nonlabeled molecules.     

Kinetic investigations on the phase transition of phospholipid bilayers

Pressure-jump experiments were performed on vesicles and liposomes of dimyristoyl phosphatidylcholine and dipalmitoyl phosphatidylcholine following the time course of solution turbidity. For both lipids two relaxation effects were evaluated the time constants of which exhibit clear maxima at the midpoint of the phase transition. The time constants lie for vesicles in the 100 μs and 1 ms ranges and for liposomes in the 1 ms and 10 ms ranges. The processes are slightly faster for dimyristoyl phosphatidylcholine than for dipalmitoyl phosphatidylcholine. All relaxation times are concentration-independent. The time constant and amplitude behaviours indicate that all processes are cooperative in agreement with previous interpretations. It is demonstrated that cooperative units can be evaluated from the relaxation amplitudes. These are of the same order of magnitude as those obtained from static experiments. On the grounds of the present kinetic investigation we can state that the application of the linear Ising model to two-dimensional processes as attempted for the static lipid phase transition is inadequate.     

Dynamics extraction in multivariate biomedical time series

A nonlinear analysis of the underlying dynamics of a biomedical time series is proposed by means of a multi-dimensional testing of nonlinear Markovian hypotheses in the observed time series. The observed dynamics of the original N-dimensional biomedical time series is tested against a hierarchy of null hypotheses corresponding to N-dimensional nonlinear Markov processes of increasing order, whose conditional probability densities are estimated using neural networks. For each of the N time series, a measure based on higher order cumulants quantifies the independence between the past of the N-dimensional time series, and its value r steps ahead. This cumulant-based measure is used as a discriminating statistic for testing the null hypotheses. Experiments performed on artificial and real world examples, including autoregressive models, noisy chaos, and nonchaotic nonlinear processes, show the effectiveness of the proposed approach in modeling multivariate systems, predicting multidimensional time series, and characterizing the structure of biological systems. Electroencephalogram (EEG) time series and heart rate variability trends are tested as biomedical signal examples. Received: 2 July 1997 / Accepted in revised form: 26 March 1998     

Designing an A* algorithm for calculating edit distance between rooted-unordered trees.

Tree structures are useful for describing and analyzing biological objects and processes. Consequently, there is a need to design metrics and algorithms to compare trees. A natural comparison metric is the "Tree Edit Distance," the number of simple edit (insert/delete) operations needed to transform one tree into the other. Rooted-ordered trees, where the order between the siblings is significant, can be compared in polynomial time. Rooted-unordered trees are used to describe processes or objects where the topology, rather than the order or the identity of each node, is important. For example, in immunology, rooted-unordered trees describe the process of immunoglobulin (antibody) gene diversification in the germinal center over time. Comparing such trees has been proven to be a difficult computational problem that belongs to the set of NP-Complete problems. Comparing two trees can be viewed as a search problem in graphs. A* is a search algorithm that explores the search space in an efficient order. Using a good lower bound estimation of the degree of difference between the two trees, A* can reduce search time dramatically. We have designed and implemented a variant of the A* search algorithm suitable for calculating tree edit distance. We show here that A* is able to perform an edit distance measurement in reasonable time for trees with dozens of nodes.     

Integration of order picking and vehicle routing in a B2C e-commerce context

E-commerce sales are increasing every year and customers who buy goods on the Internet have high service level expectations. In order to meet these expectations, a company’s logistics operations need to be performed carefully. Optimizing only internal warehouse processes will often lead to suboptimal solutions. The interrelationship between the order picking process and the delivery process should not be ignored. Therefore, in this study, an order picking problem and a vehicle routing problem with time windows and release dates are solved simultaneously using a single optimization framework. To the best of our knowledge, it is the first time that an order picking problem and a vehicle routing problem are integrated. A mixed integer linear programming formulation for this integrated order picking-vehicle routing problem (OP-VRP) is provided. The integrated OP-VRP is solved for small instances and the results are compared to these of an uncoordinated approach. Computational experiments show that integration can lead to cost savings of 14% on average. Furthermore, higher service levels can be offered by allowing customers to request their orders later and still get delivered within the same time windows.     

Dietary change and stable isotopes: a model of growth and dormancy in cave bears.

In order to discuss dietary change over time by the use of stable isotopes, it is necessary to sort out the underlying processes in isotopic variation. Together with the dietary signal other processes have been investigated, namely metabolic processes, collagen turnover and physical growth. However, growth and collagen turnover time have so far been neglected in dietary reconstruction based on stable isotopes. An earlier study suggested that cave bears (Ursus spelaeus) probably gave birth to cubs during dormancy. We provide an estimate of the effect on stable isotopes of growth and metabolism and discuss collagen turnover in a population of cave bears. Based on a quantitative model, we hypothesized that bear cubs lactated their mothers during their first and second winters, but were fed solid food together with lactation during their first summer. This demonstrates the need to include physical growth, metabolism and collagen turnover in dietary reconstruction. Whereas the effects of diet and metabolism are due to fractionation, growth and collagen turnover are dilution processes.     

Mass Spectrometry‐Based Analysis of Time‐Resolved Proteome Quantification

The aspect of time is essential in biological processes and thus it is important to be able to monitor signaling molecules through time. Proteins are key players in cellular signaling and they respond to many stimuli and change their expression in many time‐dependent processes. Mass spectrometry (MS) is an important tool for studying proteins, including their posttranslational modifications and their interaction partners—both in qualitative and quantitative ways. In order to distinguish the different trends over time, proteins, modification sites, and interacting proteins must be compared between different time points, and therefore relative quantification is preferred. In this review, the progress and challenges for MS‐based analysis of time‐resolved proteome dynamics are discussed. Further, aspects on model systems, technologies, sampling frequencies, and presentation of the dynamic data are discussed.     

Growth with regulation in fluctuating environments

In this paper deterministic growth laws of a logistic-like type are initially introduced. The growth equations are expressed by first order differential equations containing a third order nonlinear term. Such equations are then parameterized in a way to allow for random fluctuations of the intrinsic fertility and of the environmental carrying capacity, thus leading to diffusion processes of new types. Their transition p.d.f. and asymptotic moments are then obtained and a detailed study of the extinction problem is performed within the framework of the first passage time problem through arbitrarily fixed threshold values. Some statistically significant quantities, such as the mean time necessary for the process to attain an assigned state, are obtained in closed form. The behavior of the diffusion processes here derived is finally compared with that of the well known diffusion processes obtained by parameterizing logistic and Gompertz growth equations.Work supported in part by the Group for Mathematical Information Sciences (GNIM) of the National Research Council and by Progetto Finalizzato Sofmat, Contract No. 82.00845.97     

Entropy and information in evolving biological systems

Integrating concepts of maintenance and of origins is essential to explaining biological diversity. The unified theory of evolution attempts to find a common theme linking production rules inherent in biological systems, explaining the origin of biological order as a manifestation of the flow of energy and the flow of information on various spatial and temporal scales, with the recognition that natural selection is an evolutionarily relevant process. Biological systems persist in space and time by transfor ming energy from one state to another in a manner that generates structures which allows the system to continue to persist. Two classes of energetic transformations allow this; heat-generating transformations, resulting in a net loss of energy from the system, and conservative transformations, changing unusable energy into states that can be stored and used subsequently. All conservative transformations in biological systems are coupled with heat-generating transformations; hence, inherent biological production, or genealogical proesses, is positively entropic. There is a self-organizing phenomenology common to genealogical phenomena, which imparts an arrow of time to biological systems. Natural selection, which by itself is time-reversible, contributes to the organization of the self-organized genealogical trajectories. The interplay of genealogical (diversity-promoting) and selective (diversity-limiting) processes produces biological order to which the primary contribution is genealogical history. Dynamic changes occuring on times scales shorter than speciation rates are microevolutionary; those occuring on time scales longer than speciation rates are macroevolutionary. Macroevolutionary processes are neither redicible to, nor autonomous from, microevolutionary processes.Authorship alphabetical     

A fractional calculus approach to self-similar protein dynamics.

Relaxation processes and reaction kinetics of proteins deviate from exponential behavior because of their large amount of conformational substrates. The dynamics are governed by many time scales and, therefore, the decay of the relaxation function or reactant concentration is slower than exponential. Applying the idea of self-similar dynamics, we derive a fractal scaling model that results in an equation in which the time derivative is replaced by a differentiation (d/dt)beta of non-integer order beta. The fractional order differential equation is solved by a Mittag-Leffler function. It depends on two parameters, a fundamental time scale tau 0 and a fractional order beta that can be interpreted as a self-similarity dimension of the dynamics. Application of the fractal model to ligand rebinding and pressure release measurements of myoglobin is demonstrated, and the connection of the model to considerations of energy barrier height distributions is shown.     

Non-homogeneous Markov processes for biomedical data analysis

Some time ago, the Markov processes were introduced in biomedical sciences in order to study disease history events. Homogeneous and Non-homogeneous Markov processes are an important field of research into stochastic processes, especially when exact transition times are unknown and interval-censored observations are present in the analysis. Non-homogeneous Markov process should be used when the homogeneous assumption is too strong. However these sorts of models increase the complexity of the analysis and standard software is limited. In this paper, some methods for fitting non-homogeneous Markov models are reviewed and an algorithm is proposed for biomedical data analysis. The method has been applied to analyse breast cancer data. Specific software for this purpose has been implemented.     

Correlation of space-time ranges in ecological hierarchies of various nature

Relations between characteristic scales of time and space are analyzed for the hierarchical systems of a various nature. The available data fit well to the power relation: [T] = a[L]b, where [T] and [L] are characteristic ranges of time and space, b--scaling exponent, a--conversion coefficient. The spatio-temporal scales of ocean physical and biological (pelagic) processes are closely overlapped. Contrastingly, the scale for terrestrial and benthic ecosystems and their environments differ noticeably. For terrestrial and benthic ecological systems, and also for atmospheric phenomena, the b values significantly less than 1, that indicates a significant coherence of structure-generating processes integrating lower-level hierarchical units to a higher-level entity. For geomorphological structures, both terrestrial and oceanic, the scaling parameters has appeared close to 1 (a "direct transfer" type of generating processes). For plankton systems, which are related with water masses, the b values vary from 1 (processes of direct transfer) up to 2 (random dispersal or diffusion processes). The author attributes this difference to the principle distinctions in dynamic properties of the physical environments for terrestrial (and probably, benthic) and plankton organisms. Finally, for the units (structures or processes) of one and the same organization level, scaling exponents are significantly higher and close to 2 (diffusive dynamics) or more (rigid spatial limitation). Thus, the development of many ecological structures looks dynamically like diffusion or gradual growth, but their putting in the higher-level order (integrity) is a qualitative leap forward and demands appropriate cooperative organizational processes.     

On the autocorrelation of one class of non-stationary random point processes

The autocorrelation of those non-stationary random point processes that can be transformed by a time transformation into a stationary process is derived. As an application, a closed form formula is obtained for the autocorrelation of those processes where the average number of points is sinusoidally modulated and the corresponding stationary process is defined by independent intervals identically distributed according to a gamma density of integer order.     

Timing‐Mechanismen in der Natur: Biologische Uhren

Increasingly timing mechanisms are detected on all levels of organisation which control the temporal order and coordination of biological processes. The respective mechanisms are designated as „biological clocks”︁. They are based on two principles: oscillations and unidirectional processes (hour‐glass). Oscillating biological clocks such as circadian,clunar or annual clocks coordinate biological events with respect to certain time points (phases)of external daily, lunar or annual hanges in the environment, while hourglass mechanisms mainly determine the duration of steps in development or aging.Complex biological timing mechanisms may comprise endogenous clocks and hourglass processes as well as external signals. Timing of biological events is often coupled with reaching defined thresholds within the underlying clock mechanism.     

Setting Objectives and Defining Outputs for Ecological Restoration and Habitat Creation

The past 40 years have seen the legal and policy framework for nature conservation in Britain extend from protection and preservation to include enhancement through techniques such as ecological restoration and habitat creation. Clear objectives need to be set for ecological restoration and habitat creation schemes because the processes involve human intervention in combination with natural factors operating over time. Objectives are required for both management and monitoring in order to enable measurement of success or failure. The most effective way to achieve high-quality restoration and creation schemes is to define the output of the process—a habitat, vegetation type, or biological community. The better the definition of the output, the greater the need to define the inputs and the nature of the intervening processes. Ecologists and environmental managers have a key role to play in establishing the degree of definition necessary in order to achieve a particular objective.     

From macroscopic measurements to microscopic mechanisms of protein aggregation

The ability to relate bulk experimental measurements of amyloid formation to the microscopic assembly processes that underlie protein aggregation is critical in order to achieve a quantitative understanding of this complex phenomenon. In this review, we focus on the insights from classical and modern theories of linear growth phenomena and discuss how theory allows the roles of growth and nucleation processes to be defined through the analysis of experimental in vitro time courses of amyloid formation. Moreover, we discuss the specific signatures in the time course of the reactions that correspond to the actions of primary and secondary nucleation processes, and outline strategies for identifying and characterising the nature of the dominant process responsible in each case for the generation of new aggregates. We highlight the power of a global analysis of experimental time courses acquired under different conditions, and discuss how such an analysis allows a rigorous connection to be established between the macroscopic measurements and the rates of the individual microscopic processes that underlie the phenomenon of amyloid formation.     

A Derivative Matching Approach to Moment Closure for the Stochastic Logistic Model

Continuous-time birth-death Markov processes serve as useful models in population biology. When the birth-death rates are nonlinear, the time evolution of the first n order moments of the population is not closed, in the sense that it depends on moments of order higher than n. For analysis purposes, the time evolution of the first n order moments is often made to be closed by approximating these higher order moments as a nonlinear function of moments up to order n, which we refer to as the moment closure function. In this paper, a systematic procedure for constructing moment closure functions of arbitrary order is presented for the stochastic logistic model. We obtain the moment closure function by first assuming a certain separable form for it, and then matching time derivatives of the exact (not closed) moment equations with that of the approximate (closed) equations for some initial time and set of initial conditions. The separable structure ensures that the steady-state solutions for the approximate equations are unique, real and positive, while the derivative matching guarantees a good approximation, at least locally in time. Explicit formulas to construct these moment closure functions for arbitrary order of truncation n are provided with higher values of n leading to better approximations of the actual moment dynamics. A host of other moment closure functions previously proposed in the literature are also investigated. Among these we show that only the ones that achieve derivative matching provide a close approximation to the exact solution. Moreover, we improve the accuracy of several previously proposed moment closure functions by forcing derivative matching.