Limit theorems for discounted convergent perpetuities II

Let $(\xi_1, \eta_1)$, $(\xi_2, \eta_2),\ldots$ be independent identically distributed $\mathbb{R}^2$-valued random vectors. Assuming that $\xi_1$ has zero mean and finite variance and imposing three distinct groups of assumptions on the distribution of $\eta_1$ we prove three functional limit theorems for the logarithm of convergent discounted perpetuities $\sum_{k\geq 0}e^{\xi_1+\ldots+\xi_k-ak}\eta_{k+1}$ as $a\to 0+$. Also, we prove a law of the iterated logarithm which corresponds to one of the aforementioned functional limit theorems. The present paper continues a line of research initiated in the paper Iksanov, Nikitin and Samoillenko (2022), which focused on limit theorems for a different type of convergent discounted perpetuities.Comment: 23 page

Adaptation of NEMO-LIM3 model for multigrid high resolution Arctic simulation

High-resolution regional hindcasting of ocean and sea ice plays an important role in the assessment of shipping and operational risks in the Arctic Ocean. The ice-ocean model NEMO-LIM3 was modified to improve its simulation quality for appropriate spatio-temporal resolutions. A multigrid model setup with connected coarse- (14 km) and fine-resolution (5 km) model configurations was devised. These two configurations were implemented and run separately. The resulting computational cost was lower when compared to that of the built-in AGRIF nesting system. Ice and tracer boundary-condition schemes were modified to achieve the correct interaction between coarse- and fine grids through a long ice-covered open boundary. An ice-restoring scheme was implemented to reduce spin-up time. The NEMO-LIM3 configuration described in this article provides more flexible and customisable tools for high-resolution regional Arctic simulations

Complex partial synchronization patterns in networks of delay-coupled neurons

We study the spatio-temporal dynamics of a multiplex network of delay-coupled FitzHugh–Nagumo oscillators with non-local and fractal connectivities. Apart from chimera states, a new regime of coexistence of slow and fast oscillations is found. An analytical explanation for the emergence of such coexisting partial synchronization patterns is given. Furthermore, we propose a control scheme for the number of fast and slow neurons in each layer.DFG, 163436311, SFB 910: Kontrolle selbstorganisierender nichtlinearer Systeme: Theoretische Methoden und Anwendungskonzept

Injection locking in self-oscillating magnetometers

Injection locking (IL) is a well-known phenomenon that occurs in nonlinear oscillators subject to external periodic or non-periodic signals. It is a phenomenon of induced synchronization that occurs when an external (injection) signal locks the frequency of the oscillator to the frequency of the external signal. This form of synchronization is relatively straightforward to implement because it does not require specially organized feedback as is the case with phase locked loop. Circuits that exploit IL can have very simple designs and be applied to a broad range of applications, such as to synchronize frames and lines in early television sets, to synchronize lasers, and to function as ac voltmeters, field-intensity meters, amplifier-limiters and AM and FM detectors. However, the focus of this article is the recent application of IL to magnetic field sensors. This novel application highlights the potential benefits of the IL approach but also some of the complexities and opportunities for further development. As with all measurement systems, the consideration of noise is paramount in the design of magnetic sensors. Noise reduction and mitigation strategies are essential. IL can be employed as a noise mitigation strategy in magnetometers that utilize self-oscillations as part of their detection paradigm; it can stabilize the oscillation frequency, potentially simplifying the measurement circuitry, and in some circumstances improve the signal-to-noise ratio. Here we review some magnetometers that have successfully exploited IL principles and highlight design options. We also propose a new circuit that is simple to implement and more straightforward to analyze

Phase locking below rate threshold in noisy model neurons

The property of a neuron to phase-lock to an oscillatory stimulus before adapting its spike rate to the stimulus frequency plays an important role for the auditory system. We investigate under which conditions neurons exhibit this phase locking below rate threshold. To this end, we simulate neurons employing the widely used leaky integrate-and-fire (LIF) model. Tuning parameters, we can arrange either an irregular spontaneous or a tonic spiking mode. When the neuron is stimulated in both modes, a significant rise of vector strength prior to a noticeable change of the spike rate can be observed. Combining analytic reasoning with numerical simulations, we trace this observation back to a modulation of interspike intervals, which itself requires spikes to be only loosely coupled. We test the limits of this conception by simulating an LIF model with threshold fatigue, which generates pronounced anticorrelations between subsequent interspike intervals. In addition we evaluate the LIF response for harmonic stimuli of various frequencies and discuss the extension to more complex stimuli. It seems that phase locking below rate threshold occurs generically for all zero mean stimuli. Finally, we discuss our findings in the context of stimulus detection

Interaction between counter-propagating quantum Hall edge channels in the 3D topological insulator BiSbTeSe2_2

The quantum Hall effect is studied in the topological insulator BiSbTeSe$_2$. By employing top- and back-gate electric fields at high magnetic field, the Landau levels of the Dirac cones in the top and bottom topological surface states can be tuned independently. When one surface is tuned to the electron-doped side of the Dirac cone and the other surface to the hole-doped side, the quantum Hall edge channels are counter-propagating. The opposite edge mode direction, combined with the opposite helicities of top and bottom surfaces, allows for scattering between these counter-propagating edge modes. The total Hall conductance is integer valued only when the scattering is strong. For weaker interaction, a non-integer quantum Hall effect is expected and measured

Paleo-Balkan and Slavic Contributions to the Genetic Pool of Moldavians

Moldova has a rich historical and cultural heritage, which may be reflected in the current genetic makeup of its population. To date, no comprehensive studies exist about the population genetic structure of modern Moldavians. To bridge this gap with respect to paternal lineages, we analyzed 37 binary and 17 multiallelic (STRs) polymorphisms on the non-recombining portion of the Y chromosome in 125 Moldavian males. In addition, 53 Ukrainians from eastern Moldova and 54 Romanians from the neighboring eastern Romania were typed using the same set of markers. In Moldavians, 19 Y chromosome haplogroups were identified, the most common being I-M423 (20.8%), R-M17* (17.6%), R-M458 (12.8%), E-v13 (8.8%), RM269* and R-M412* (both 7.2%). In Romanians, 14 haplogroups were found including I-M423 (40.7%), R-M17* (16.7%), RM405 (7.4%), E-v13 and R-M412* (both 5.6%). In Ukrainians, 13 haplogroups were identified including R-M17 (34.0%), I-M423 (20.8%), R-M269* (9.4%), N-M178, R-M458 and R-M73 (each 5.7%). Our results show that a significant majority of the Moldavian paternal gene pool belongs to eastern/central European and Balkan/eastern Mediterranean Y lineages. Phylogenetic and AMOVA analyses based on Y-STR loci also revealed that Moldavians are close to both eastern/central European and Balkan-Carpathian populations. The data correlate well with historical accounts and geographical location of the region and thus allow to hypothesize that extant Moldavian paternal genetic lineages arose from extensive recent admixture between genetically autochthonous populations of the Balkan-Carpathian zone and neighboring Slavic group

Enhanced processing in arrays of optimally tuned nonlinear biomimetic sensors : a coupling-mediated Ringelmann effect and its dynamical mitigation

Inspired by recent results on self-tunability in the outer hair cells of the mammalian cochlea, we describe an array of magnetic sensors where each individual sensor can self-tune to an optimal operating regime. The self-tuning gives the array its “biomimetic” features. We show that the overall performance of the array can, as expected, be improved by increasing the number of sensors but, however, coupling between sensors reduces the overall performance even though the individual sensors in the system could see an improvement. We quantify the similarity of this phenomenon to the Ringelmann effect that was formulated 103 years ago to account for productivity losses in human and animal groups. We propose a global feedback scheme that can be used to greatly mitigate the performance degradation that would, normally, stem from the Ringelmann effect