Characterizing stochastic cell cycle dynamics in exponential growth

Two powerful and complementary experimental approaches are commonly used to study the cell cycle and cell biology: One class of experiments characterizes the statistics (or demographics) of an unsynchronized exponentially-growing population, while the other captures cell cycle dynamics, either by time-lapse imaging of full cell cycles or in bulk experiments on synchronized populations. In this paper, we study the subtle relationship between observations in these two distinct experimental approaches. We begin with an existing model: a single-cell deterministic description of cell cycle dynamics where cell states (i.e. periods or phases) have precise lifetimes. We then generalize this description to a stochastic model in which the states have stochastic lifetimes, as described by arbitrary probability distribution functions. Our analyses of the demographics of an exponential culture reveal a simple and exact correspondence between the deterministic and stochastic models: The corresponding state lifetimes in the deterministic model are equal to the exponential mean of the lifetimes in the stochastic model. An important implication is therefore that the demographics of an exponential culture will be well-fit by a deterministic model even if the state timing is stochastic. Although we explore the implications of the models in the context of the Escherichia coli cell cycle, we expect both the models as well as the significance of the exponential-mean lifetimes to find many applications in the quantitative analysis of cell cycle dynamics in other biological systems.

Generalized Probabilistic Theories in a New Light

In this paper we will present a modified formulation of generalized probabilistic theories that will always give rise to the structure of Hilbert space of quantum mechanics, in any finite outcome space, and give the guidelines to how to extend this work to infinite dimensional Hilbert spaces. Moreover, this new formulation which we will call extended operational-probabilistic theories, applies not only to quantum systems, but also equally well to classical systems, without violating Bell’s theorem, and at the same time solves the measurement problem. This is why we will see that the question of why our universe is quantum mechanical rather than classical is misplaced. The only difference that exists between a classical universe and a quantum mechanical one lies merely in which observables are compatible and which are not. Besides, this extended probability theory which we present in this paper shows that it is non-determinacy, or to be more precise, the non-deterministic description of the universe, that makes the laws of physics the way they are. In addition, this paper shows us that what used to be considered as purely classical systems and to be treated that way are in fact able to be manipulated according to the rules of quantum mechanics –with this new understanding of these rules- and that there is still a possibility that there might be a deterministic level from which our universe emerges, which if understood correctly, may open the door wide to applications in areas such as quantum computing. In addition to all that, this paper shows that without the use of complex vector spaces, we cannot have any kind of continuous evolution of the states of any system.

Exact description of SIR-Bass epidemics on 1D lattices

<p style='text-indent:20px;'>This paper is devoted to the study of a stochastic epidemiological model which is a variant of the SIR model to which we add an extra factor in the transition rate from susceptible to infected accounting for the inflow of infection due to immigration or environmental sources of infection. This factor yields the formation of new clusters of infections, without having to specify a priori and explicitly their date and place of appearance.</p><p style='text-indent:20px;'>We establish an exact deterministic description for such stochastic processes on 1D lattices (finite lines, semi-infinite lines, infinite lines) by showing that the probability of infection at a given point in space and time can be obtained as the solution of a deterministic ODE system on the lattice. Our results allow stochastic initial conditions and arbitrary spatio-temporal heterogeneities on the parameters.</p><p style='text-indent:20px;'>We then apply our results to some concrete situations and obtain useful qualitative results and explicit formulae on the macroscopic dynamics and also the local temporal behavior of each individual. In particular, we provide a fine analysis of some aspects of cluster formation through the study of patient-zero problems and the effects of time-varying point sources.</p><p style='text-indent:20px;'>Finally, we show that the space-discrete model gives rise to new space-continuous models, which are either ODEs or PDEs, depending on the rescaling regime assumed on the parameters.</p>

Correctness of the Chord protocol

Internet of Things (IoT) can be seen as a cooperation of various devices with limited performances that participate in the same system. IoT devices compose a distributed architecture system. The core of every IoT system is its discovery and control services. To realize such services, some authors used the developed solutions from the different domains. One such solution is the Chord protocol, one of the first, the simplest and the most popular distributed protocols. Unfortunately, the application of the Chord protocol was realized using the correctness of the Chord protocol for granted, or by the very hard assumptions. In this paper we prove the correctness of the Chord protocol using the logic of time and knowledge with the respect to the set of possible executions, called regular runs. We provide the deterministic description of the correctness of the Chord protocol and consider Chord actions that maintain ring topology while the nodes can freely join or leave.

PREDICTING THE EFFECTS OF THE DIDACTIC PROCESS USING FORGETTING CURVES

The paper presents the method of predicting the effects of the didactic process using the forgetting curves. In the didactic process, learning and forgetting processes play an important role. The learning time, the number of repetitions and their distribution over time are important. These issues can be analyzed using a deterministic description. The flow of information and the learning process can be described thanks to the educational environment developed by the author, enabling the creation of a model of the didactic process described by differential equations. The differential equations can be represented in the form of a network of connected elements in a similar way to the electrical circuits and represented in the form of an intuitive schematic. The network can be simulated using a microsystem simulator. The use of the microsystems simulator enables simulation of the didactic process in time and prediction of effects also after its completion in the long-term. It also enables prediction of the repetitions also during the didactic process. The presented approach enables the easy creation of the macro models and enables the use of many advanced simulation algorithms. The examples of simulations of the didactic process based on the real data are included. Short and long-term simulations for individual students and groups of students are presented. An example of the prediction of the optimal repetitions is shown. Based on the results, appropriate conclusions were drawn. The issues discussed in the work may be of interest to those involved in the analysis and mathematical description of the didactic process. They can also be interesting for developers of the e-learning systems especially e-learning platforms.

Analysis of electron density calculations using deterministic-probabilistic model of the ionospheric D-region

The work is devoted to the development of a fundamentally new way of modeling the ionospheric D-region – deterministic-probabilistic. The results of Ne calculations using this technique are analyzed. Research of this kind is of fundamental importance, related to the rejection of a purely deterministic description of a continuously changing environment such as the ionosphere. In this work, the electron density is calculated using a five-component system of ionization-recombination cycle equations. Probability density functions (PDFs) of input parameters of the model are used to solve the system. The most important sources of the D-region ionization are taken into account to calculate PDFs of the ionization rate. The necessary number of iterations is determined by the convergence of PDFs of the electron density from 50 km to 85 km at midlatitudes under different heliogeophysical conditions. Theoretical Ne PDFs have been shown to be in good agreement with two experimental databases on electron density, especially at large D-region heights. The next important stage of modeling is the thorough verification of Ne PDFs from experimental radiophysical data on VLF–LF propagation.

Bohr, Niels (1885–1962)

One of the most influential scientists of the twentieth century, the Danish physicist Niels Bohr founded atomic quantum theory and the Copenhagen interpretation of quantum physics. This radical interpretation renounced the possibility of a unified, observer-independent, deterministic description in the microdomain. Bohr’s principle of complementarity – the heart of the Copenhagen philosophy – implies that quantum phenomena can only be described by pairs of partial, mutually exclusive, or ‘complementary’ perspectives. Though simultaneously inapplicable, both perspectives are necessary for the exhaustive description of phenomena. Bohr aspired to generalize complementarity into all fields of knowledge, maintaining that new epistemological insights are obtained by adjoining contrary, seemingly incompatible, viewpoints.

Ryanodine receptor gating controls generation of diastolic calcium waves in cardiac myocytes

The role of cardiac ryanodine receptor (RyR) gating in the initiation and propagation of calcium waves was investigated using a mathematical model comprising a stochastic description of RyR gating and a deterministic description of calcium diffusion and sequestration. We used a one-dimensional array of equidistantly spaced RyR clusters, representing the confocal scanning line, to simulate the formation of calcium sparks. Our model provided an excellent description of the calcium dependence of the frequency of diastolic calcium sparks and of the increased tendency for the production of calcium waves after a decrease in cytosolic calcium buffering. We developed a hypothesis relating changes in the propensity to form calcium waves to changes of RyR gating and tested it by simulation. With a realistic RyR gating model, increased ability of RyR to be activated by Ca2+ strongly increased the propensity for generation of calcium waves at low (0.05–0.1-µM) calcium concentrations but only slightly at high (0.2–0.4-µM) calcium concentrations. Changes in RyR gating altered calcium wave formation by changing the calcium sensitivity of spontaneous calcium spark activation and/or the average number of open RyRs in spontaneous calcium sparks. Gating changes that did not affect RyR activation by Ca2+ had only a weak effect on the propensity to form calcium waves, even if they strongly increased calcium spark frequency. Calcium waves induced by modulating the properties of the RyR activation site could be suppressed by inhibiting the spontaneous opening of the RyR. These data can explain the increased tendency for production of calcium waves under conditions when RyR gating is altered in cardiac diseases.