Discrete Dynamical Systems: A Brief Survey

Dynamical system is a mathematical formalization for any fixed rule that is described in time dependent fashion. The time can be measured by either of the number systems - integers, real numbers, complex numbers. A discrete dynamical system is a dynamical system whose state evolves over a state space in discrete time steps according to a fixed rule. This brief survey paper is concerned with the part of the work done by José Sousa Ramos [2] and some of his research students. We present the general theory of discrete dynamical systems and present results from applications to geometry, graph theory and synchronization

Mitochondrial Dynamics in the Drosophila Ovary Regulates Germ Stem Cell Number, Cell Fate, and Female Fertility

This project has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation program (H2020-ERC-2017-STGGA 759853-StemCellHabitat), Wellcome Trust and Howard Hughes Medical Institute (HHMI-208581/Z/17/Z-Metabolic Reg SC fate), EMBO Installation grant (H2020-EMBO3311/2017/G2017), and by Fundação para a Ciência e Tecnologia (IF/01265/2014/CP1252/CT0004 and PD/BD/128003/2016 to MG).The fate and proliferative capacity of stem cells have been shown to strongly depend on their metabolic state. Mitochondria are the powerhouses of the cell being responsible for energy production via oxidative phosphorylation (OxPhos) as well as for several other metabolic pathways. Mitochondrial activity strongly depends on their structural organization, with their size and shape being regulated by mitochondrial fusion and fission, a process known as mitochondrial dynamics. However, the significance of mitochondrial dynamics in the regulation of stem cell metabolism and fate remains elusive. Here, we characterize the role of mitochondria morphology in female germ stem cells (GSCs) and in their more differentiated lineage. Mitochondria are particularly important in the female GSC lineage. Not only do they provide these cells with their energy requirements to generate the oocyte but they are also the only mitochondria pool to be inherited by the offspring. We show that the undifferentiated GSCs predominantly have fissed mitochondria, whereas more differentiated germ cells have more fused mitochondria. By reducing the levels of mitochondrial dynamics regulators, we show that both fused and fissed mitochondria are required for the maintenance of a stable GSC pool. Surprisingly, we found that disrupting mitochondrial dynamics in the germline also strongly affects nurse cells morphology, impairing egg chamber development and female fertility. Interestingly, reducing the levels of key enzymes in the Tricarboxylic Acid Cycle (TCA), known to cause OxPhos reduction, also affects GSC number. This defect in GSC self-renewal capacity indicates that at least basal levels of TCA/OxPhos are required in GSCs. Our findings show that mitochondrial dynamics is essential for female GSC maintenance and female fertility, and that mitochondria fusion and fission events are dynamically regulated during GSC differentiation, possibly to modulate their metabolic profile.publishersversionpublishe

Comparison of Flight Simulators Based on Human Motion Perception Metrics

In flight simulation, motion filters are used to transform aircraft motion into simulator motion. When looking for the best match between visual and inertial amplitude in a simulator, researchers have found that there is a range of inertial amplitudes, rather than a single inertial value, that is perceived by subjects as optimal. This zone, hereafter referred to as the optimal zone, seems to correlate to the perceptual coherence zones measured in flight simulators. However, no studies were found in which these two zones were compared. This study investigates the relation between the optimal and the coherence zone measurements within and between different simulators. Results show that for the sway axis, the optimal zone lies within the lower part of the coherence zone. In addition, it was found that, whereas the width of the coherence zone depends on the visual amplitude and frequency, the width of the optimal zone remains constant

Relationship Between Optimal Gain and Coherence Zone in Flight Simulation

In motion simulation the inertial information generated by the motion platform is most of the times different from the visual information in the simulator displays. This occurs due to the physical limits of the motion platform. However, for small motions that are within the physical limits of the motion platform, one-to-one motion, i.e. visual information equal to inertial information, is possible. It has been shown in previous studies that one-to-one motion is often judged as too strong, causing researchers to lower the inertial amplitude. When trying to measure the optimal inertial gain for a visual amplitude, we found a zone of optimal gains instead of a single value. Such result seems related with the coherence zones that have been measured in flight simulation studies. However, the optimal gain results were never directly related with the coherence zones. In this study we investigated whether the optimal gain measurements are the same as the coherence zone measurements. We also try to infer if the results obtained from the two measurements can be used to differentiate between simulators with different configurations. An experiment was conducted at the NASA Langley Research Center which used both the Cockpit Motion Facility and the Visual Motion Simulator. The results show that the inertial gains obtained with the optimal gain are different than the ones obtained with the coherence zone measurements. The optimal gain is within the coherence zone.The point of mean optimal gain was lower and further away from the one-to-one line than the point of mean coherence. The zone width obtained for the coherence zone measurements was dependent on the visual amplitude and frequency. For the optimal gain, the zone width remained constant when the visual amplitude and frequency were varied. We found no effect of the simulator configuration in both the coherence zone and optimal gain measurements

aPKC regulates apical constriction to prevent tissue rupture in the Drosophila follicular epithelium

Funding: We thank Daniel St Johnston, Juergen Knoblich, Patrick Laprise, Stefano de Renzis, Xiaobo Wang, Yohanns Bellaiche, and the Bloomington and Kyoto Drosophila Stock Centers for reagents. We also thank Yohanns Bellaiche, Ivo Telley, and Romain Levayer for insightful comments on the manuscript. This work is funded by National Funds through FCT—Fundação para a Ciência e a Tecnologia, I.P., under the project PTDC/BIA-CEL/ 1511/2021. E.M.-d.-S.’s salary is funded by the ‘‘FCT Scientific Employment Stimulus’’ program. M.O.,A.B.-C., and A.M.C. were supported by PhD fellowships from FCT. M.O.’s salary was also supported by the Maria de Sousa Award Research in the J.J. lab was supported by Wellcome Trust, the Royal Society, and BBSRC (BB/V001353/1). The authors acknowledge the i3S Scientific Platform ALM, member of the national infrastructure Portuguese Platform of Bioimaging, and the Dundee Imaging Facility for excellent support.Apical-basal polarity is an essential epithelial trait controlled by the evolutionarily conserved PAR-aPKC polarity network. Dysregulation of polarity proteins disrupts tissue organization during development and in disease, but the underlying mechanisms are unclear due to the broad implications of polarity loss. Here, we uncover how Drosophila aPKC maintains epithelial architecture by directly observing tissue disorganization after fast optogenetic inactivation in living adult flies and ovaries cultured ex vivo. We show that fast aPKC perturbation in the proliferative follicular epithelium produces large epithelial gaps that result from increased apical constriction, rather than loss of apical-basal polarity. Accordingly, we can modulate the incidence of epithelial gaps by increasing and decreasing actomyosin-driven contractility. We traced the origin of these large epithelial gaps to tissue rupture next to dividing cells. Live imaging shows that aPKC perturbation induces apical constriction in non-mitotic cells within minutes, producing pulling forces that ultimately detach dividing and neighboring cells. We further demonstrate that epithelial rupture requires a global increase of apical constriction, as it is prevented by the presence of non-constricting cells. Conversely, a global induction of apical tension through light-induced recruitment of RhoGEF2 to the apical side is sufficient to produce tissue rupture. Hence, our work reveals that the roles of aPKC in polarity and actomyosin regulation are separable and provides the first in vivo evidence that excessive tissue stress can break the epithelial barrier during proliferation.proofepub_ahead_of_prin

Local piezoresponse and polarization switching in nucleobase thymine microcrystals

Thymine (2-oxy-4-oxy-5 methyl pyrimidine) is one of the four nucleobases of deoxyribonucleic acid (DNA). In the DNA molecule, thymine binds to adenine via two hydrogen bonds, thus stabilizing the nucleic acid structure and is involved in pairing and replication. Here, we show that synthetic thymine microcrystals grown from the solution exhibit local piezoelectricity and apparent ferroelectricity, as evidenced by nanoscale electromechanical measurements via Piezoresponse Force Microscopy. Our experimental results demonstrate significant electromechanical activity and polarization switchability of thymine, thus opening a pathway for piezoelectric and ferroelectric-based applications of thymine and, perhaps, of other DNA nucleobase materials. The results are supported by molecular modeling of polarization switching under an external electric field. (C) 2015 AIP Publishing LLC

Analysis of sheet metal formability through isotropic and kinematic hardening models

The present paper aims at analysing the sheet metal formability through several isotropic and kinematic hardening models. Specifically, a special attention is paid to the physically-based hardening model of Teodosiu and Hu (1995), which accounts for the anisotropic work-hardening induced by the microstructural evolution at large strains, as well as to some more conventional hardening models, including the isotropic Swift strain-hardening power law, and the Voce saturation strain-hardening law, combined with a non-linear kinematic hardening described by the Armstrong-Frederick law. The onset of localized necking is simulated by an advanced sheet metal forming limit model which connects, through the Marciniak-Kuczinsky analysis, the hardening models with the anisotropic yield criterion Y1d2000-2d (Barlat et al., 2003). Both linear and complex strain paths are taken into account. The selected material is a DC06 steel sheet. The validity of each model is assessed by comparing the predicted forming limits with experimental results carefully obtained on this steel. The origin of discrepancy in the predicted results using different hardening models is thoroughly analyzed. (C) 2011 Elsevier Masson SAS. All rights reserved.X111816sciescopu