Simulation-based reachability analysis for nonlinear systems using componentwise contraction properties

A shortcoming of existing reachability approaches for nonlinear systems is the poor scalability with the number of continuous state variables. To mitigate this problem we present a simulation-based approach where we first sample a number of trajectories of the system and next establish bounds on the convergence or divergence between the samples and neighboring trajectories. We compute these bounds using contraction theory and reduce the conservatism by partitioning the state vector into several components and analyzing contraction properties separately in each direction. Among other benefits this allows us to analyze the effect of constant but uncertain parameters by treating them as state variables and partitioning them into a separate direction. We next present a numerical procedure to search for weighted norms that yield a prescribed contraction rate, which can be incorporated in the reachability algorithm to adjust the weights to minimize the growth of the reachable set

Simple choreographies of the planar Newtonian NN-body Problem

In the $N$-body problem, a simple choreography is a periodic solution, where all masses chase each other on a single loop. In this paper we prove that for the planar Newtonian $N$-body problem with equal masses, $N \ge 3$, there are at least $2^{N-3} + 2^{[(N-3)/2]}$ different main simple choreographies. This confirms a conjecture given by Chenciner and etc. in \cite{CGMS02}.Comment: 31pages, 6 figures. Refinements in notations and proof

Lagrangian Reachabililty

We introduce LRT, a new Lagrangian-based ReachTube computation algorithm that conservatively approximates the set of reachable states of a nonlinear dynamical system. LRT makes use of the Cauchy-Green stretching factor (SF), which is derived from an over-approximation of the gradient of the solution flows. The SF measures the discrepancy between two states propagated by the system solution from two initial states lying in a well-defined region, thereby allowing LRT to compute a reachtube with a ball-overestimate in a metric where the computed enclosure is as tight as possible. To evaluate its performance, we implemented a prototype of LRT in C++/Matlab, and ran it on a set of well-established benchmarks. Our results show that LRT compares very favorably with respect to the CAPD and Flow* tools.Comment: Accepted to CAV 201

The Nanostructure of Myoendothelial Junctions Contributes to Signal Rectification between Endothelial and Vascular Smooth Muscle Cells

Micro-anatomical structures in tissues have potential physiological effects. In arteries and arterioles smooth muscle cells and endothelial cells are separated by the internal elastic lamina, but the two cell layers often make contact through micro protrusions called myoendothelial junctions. Cross talk between the two cell layers is important in regulating blood pressure and flow. We have used a spatiotemporal mathematical model to investigate how the myoendothelial junctions affect the information flow between the two cell layers. The geometry of the model mimics the structure of the two cell types and the myoendothelial junction. The model is implemented as a 2D axi-symmetrical model and solved using the finite element method. We have simulated diffusion of Ca2+ and IP3 between the two cell types and we show that the micro-anatomical structure of the myoendothelial junction in itself may rectify a signal between the two cell layers. The rectification is caused by the asymmetrical structure of the myoendothelial junction. Because the head of the myoendothelial junction is separated from the cell it is attached to by a narrow neck region, a signal generated in the neighboring cell can easily drive a concentration change in the head of the myoendothelial protrusion. Subsequently the signal can be amplified in the head, and activate the entire cell. In contrast, a signal in the cell from which the myoendothelial junction originates will be attenuated and delayed in the neck region as it travels into the head of the myoendothelial junction and the neighboring cell

Guaranteed optimal reachability control of reaction-diffusion equations using one-sided Lipschitz constants and model reduction

We show that, for any spatially discretized system of reaction-diffusion, the approximate solution given by the explicit Euler time-discretization scheme converges to the exact time-continuous solution, provided that diffusion coefficient be sufficiently large. By "sufficiently large", we mean that the diffusion coefficient value makes the one-sided Lipschitz constant of the reaction-diffusion system negative. We apply this result to solve a finite horizon control problem for a 1D reaction-diffusion example. We also explain how to perform model reduction in order to improve the efficiency of the method

A theoretical model of the high-frequency arrhythmogenic depolarization signal following myocardial infarction

Theoretical body-surface potentials were computed from single, branching and tortuous strands of Luo-Rudy dynamic model cells, representing different areas of an infarct scar. When action potential (AP) propagation either in longitudinal or transverse direction was slow (3-12 cm/s), the depolarization signals contained high-frequency (100-300 Hz) oscillations. The frequencies were related to macroscopic propagation velocity and strand architecture by simple formulas. Next, we extended a mathematical model of the QRS-complex presented in our earlier work to simulate unstable activation wavefront. It combines signals from different strands with small timing fluctuations relative to a large repetitive QRS-like waveform and can account for dynamic changes of real arrhythmogenic micropotentials. Variance spectrum of wavelet coefficients calculated from the composite QRS-complex contained the high frequencies of the individual abnormal signals. We conclude that slow AP propagation through fibrotic regions after myocardial infarction is a source of high-frequency arrhythmogenic components that increase beat-to-beat variability of the QRS, and wavelet variance parameters can be used for ventricular tachycardia risk assessment

Wdrożenie technik rolnictwa precyzyjnego na przykładzie wielkopowierzchniowego gospodarstwa rolnego

An attempt to assess the use of modern technique in multi-surface agricultural farm and an attempt to compare the system of precise farming management with conventional was made. Based on the research, which was carried out, it was determined that the purchase cost of the precise farming devices will bring measurable advantages as soon as in the second year of use. Introduction of the precise fertilization treatment and application of pesticides brought the highest savings in a farm. The use of the parallel move system in the investigated farm brings approx. 10% of savings in consumption of production means, that is, sowing material, fertilizers, pesticides and fuel. Advantages arising from the use of precise farming application are estimated to account to approx. 37 PLN·ha-1 per year.W pracy podjęto próbę oceny zastosowania nowoczesnych technik w wielkopowierzchniowym gospodarstwie rolnym oraz porównania systemu gospodarowania rolnictwa precyzyjnego do konwencjonalnego. Na podstawie przeprowadzonych badań stwierdzono, że koszt zakupu urządzeń zwrócił się w drugim roku jego użytkowania. Największe oszczędności w gospodarstwie przyniosło wdrożenie zabiegu precyzyjnego nawożenia oraz stosowanie środków ochrony roślin. Miało to również swoje odbicie w mniejszej ilości zużytego oleju napędowego. Stwierdzono, że minimalna powierzchnia gospodarstwa, od jakiej stosowanie technologii rolnictwa precyzyjnego przyniesie dochody wynosi 310 ha. Korzyści płynące z precyzyjnego gospodarowania szacuje się na ok. 75 PLN·ha-1

Modern technological and functional solutions used in dairy cows breeding on the example of the selected farms of Łomżyński province

W 2012 roku przeprowadzono analizę wybranych gospodarstw specjalizujących się w chowie krów mlecznych. Celem badań była ocena rozwiązań technologiczno-funkcjonalnych stosowanych w chowie bydła mlecznego na terenie powiatu łomżyńskiego. Dokonano oceny warunków środowiskowych w pomieszczeniach dla bydła, systemów utrzymania zwierząt, zadawania pasz, usuwania odchodów oraz pozyskiwania mleka. Na podstawie przeprowadzonych badań należy stwierdzić, że na przestrzeni ostatnich dziesięciu lat nastąpiły istotne zmiany, które wpłynęły na stosowane technologie oraz rozwiązania funkcjonalne budynków inwentarskich gospodarstw specjalizujących się w produkcji mleka. Wdrożenie nowoczesnych technologii poprawiło dobrostan zwierząt, co przełożyło się na zwiększenie ich wydajności mlecznej, poprawę jakości otrzymywanego surowca, a także znacznie skróciło czas pracy rolnika. Na podstawie przeprowadzonych badań stwierdzono, że rolnicy przekonani są co do istoty i ważności inwestowania w nowoczesne rozwiązania technologiczne.In 2012, analysis of the selected farms specialising in dairy cows breeding was carried out. The objective was an assessment of technological and functional solutions used in the dairy cattle breeding on the area of Łomżyński province. Assessment of environmental conditions in facilities for cattle, systems of animals maintenance, feeding, removal of excrements and obtaining milk was carried out. Based on the research which was carried out, one should state that within the range of the last ten years, significant changes occurred, which influenced applicable technologies and functional solutions of livestock buildings of farms specialising in milk production. Implementation of modern technologies improved animals welfare, which translated into the increase of their milk efficiency, improvement of the quality of the obtained raw material and also considerably shortened farmer's work time. Based on the research, it was found out that farmers are convinced about the significance and importance of investing in modern technological solutions