Convergence Time Towards Periodic Orbits in Discrete Dynamical Systems

We investigate the convergence towards periodic orbits in discrete dynamical systems. We examine the probability that a randomly chosen point converges to a particular neighborhood of a periodic orbit in a fixed number of iterations, and we use linearized equations to examine the evolution near that neighborhood. The underlying idea is that points of stable periodic orbit are associated with intervals. We state and prove a theorem that details what regions of phase space are mapped into these intervals (once they are known) and how many iterations are required to get there. We also construct algorithms that allow our theoretical results to be implemented successfully in practice.Comment: 17 pages; 7 figure

Composition law of cardinal order permutations

In this paper the theorems that determine composition laws for both cardinal ordering permutations and their inverses are proven. So, the relative positions of points in a hs-periodic orbit become completely known as well as in which order those points are visited. No matter how a hs-periodic orbit emerges, be it through a period doubling cascade (s=2^n) of the h-periodic orbit, or as a primary window (like the saddle-node bifurcation cascade with h=2^n), or as a secondary window (the birth of a $s-$periodic window inside the h-periodic one). Certainly, period doubling cascade orbits are particular cases with h=2 and s=2^n. Both composition laws are also shown in algorithmic way for their easy use

Short-term synaptic plasticity regulates the level of olivocochlear inhibition to auditory hair cells

In the mammalian inner ear, the gain control of auditory inputs is exerted by medial olivocochlear (MOC) neurons that innervate cochlear outer hair cells (OHCs). OHCs mechanically amplify the incoming sound waves by virtue of their electromotile properties while the MOC system reduces the gain of auditory inputs by inhibiting OHC function. How this process is orchestrated at the synaptic level remains unknown. In the present study, MOC firing was evoked by electrical stimulation in an isolated mouse cochlear preparation, while OHCs postsynaptic responses were monitored by whole-cell recordings. These recordings confirmed that electrically evoked IPSCs (eIPSCs) are mediated solely by α9β10 nAChRs functionally coupled to calcium-activated SK2 channels. Synaptic release occurred with low probability when MOC-OHC synapses were stimulated at 1 Hz. However, as the stimulation frequency was raised, the reliability of release increased due to presynaptic facilitation. In addition, the relatively slow decay of eIPSCs gave rise to temporal summation at stimulation frequencies >10 Hz. The combined effect of facilitation and summation resulted in a frequency-dependent increase in the average amplitude of inhibitory currents in OHCs. Thus, we have demonstrated that short-term plasticity is responsible for shaping MOC inhibition and, therefore, encodes the transfer function from efferent firing frequency to the gain of the cochlear amplifier.Fil: Ballestero, Jimena Andrea. Consejo Nacional de Investigaciones Científicas y Técnicas. Instituto de Investigaciones en Ingeniería Genética y Biología Molecular "Dr. Héctor N. Torres"; ArgentinaFil: Zorrilla de San Martín, Javier. Consejo Nacional de Investigaciones Científicas y Técnicas. Instituto de Investigaciones en Ingeniería Genética y Biología Molecular "Dr. Héctor N. Torres"; ArgentinaFil: Goutman, Juan Diego. Consejo Nacional de Investigaciones Científicas y Técnicas. Instituto de Investigaciones en Ingeniería Genética y Biología Molecular "Dr. Héctor N. Torres"; ArgentinaFil: Elgoyhen, Ana Belen. Consejo Nacional de Investigaciones Científicas y Técnicas. Instituto de Investigaciones en Ingeniería Genética y Biología Molecular "Dr. Héctor N. Torres"; Argentina. Universidad de Buenos Aires. Facultad de Medicina; ArgentinaFil: Fuchs, Paul A.. The Johns Hopkins University School of Medicine; Estados UnidosFil: Katz, Eleonora. Consejo Nacional de Investigaciones Científicas y Técnicas. Instituto de Investigaciones en Ingeniería Genética y Biología Molecular "Dr. Héctor N. Torres"; Argentina. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Fisiología, Biología Molecular y Celular; Argentin

Field Crops Research

Downy brome (Bromus tectorum L.) is a problematic weed for the conventional fallow/winter wheat (F/W) production system in the low precipitation-region (\u3c 350mm yr−1) of the Pacific Northwest. A 4-yr field experiment was conducted to determine if incorporating spring barley (B, Hordeum vulgare L.) or spring carinata (C, Brassica carinata A. Braun) into 3-yr crop rotations with W would benefit weed management. The experimental design was a split-plot with four replications where each phase was present every year for the following rotations: 1) F/W, 2) F/W/B, and 3) F/W/C. Reduced tillage, consisting of a single undercutting operation with a wide-blade sweep, and herbicides were used to control weeds during the fallow period. The seeded plots were subdivided in three different weed management areas: a weed-free area where weeds were pulled by hand, a weedy area with no weed control and a general area where weeds were chemically controlled. Weed density and cover per species and W yield were evaluated in each rotation. Grass cover and density after one and two complete cropping cycles were significantly higher in F/W than in F/W/B and F/W/C. Reduction in density and cover of total weeds was found after two cycles. However, differences in community biodiversity were only found between F/W, and F/W/B or F/W/C in 2017. Winter wheat plots of F/W had more downy brome than F/ W/B or F/W/C indicating the greater capacity of the latter to control this weed. In 2018, the 3-yr rotation with barley had greater winter wheat grain yield compared with F/W when weeds were not present though weeds were more competitive in F/W/B. Intensifying the F/W cropping system into a 3-yr crop rotation of W followed by spring barley or spring carinata may reduce weed infestations of winter annual grasses that are difficult to control in W and the most competitive due to larger similarities in their life cycle with this crop