Peak -to -average power ratio reduced parallel interference cancellation Multicarrier-Code Division Multiple Access system with anti -interference property

Orthogonal Frequency-Division Multiplexing (OFDM) has been proved to be a promising technology that enables the transmission of higher data rate. Multicarrier Code-Division Multiple Access (MC-CDMA) is a transmission technique which combines the advantages of both OFDM and Code-Division Multiplexing Access (CDMA), so as to allow high transmission rates over severe time-dispersive multi-path channels without the need of a complex receiver implementation. Also MC-CDMA exploits frequency diversity via the different subcarriers, and therefore allows the high code rates systems to achieve good Bit Error Rate (BER) performances. Furthermore, the spreading in the frequency domain makes the time synchronization requirement much lower than traditional direct sequence CDMA schemes. There are still some problems when we use MC-CDMA. One is the high Peak-to-Average Power Ratio (PAPR) of the transmit signal. High PAPR leads to nonlinear distortion of the amplifier and results in inter-carrier self-interference plus out-of-band radiation. On the other hand, suppressing the Multiple Access Interference (MAI) is another crucial problem in the MC-CDMA system. Imperfect cross-correlation characteristics of the spreading codes and the multipath fading destroy the orthogonality among the users, and then cause MAI, which produces serious BER degradation in the system. Moreover, in uplink system the received signals at a base station are always asynchronous. This also destroys the orthogonality among the users, and hence, generates MAI which degrades the system performance. Besides those two problems, the interference should always be considered seriously for any communication system. In this dissertation, we design a novel MC-CDMA system, which has low PAPR and mitigated MAI. The new Semi-blind channel estimation and multi-user data detection based on Parallel Interference Cancellation (PIC) have been applied in the system. The Low Density Parity Codes (LDPC) has also been introduced into the system to improve the performance. Different interference models are analyzed in multi-carrier communication systems and then the effective interference suppression for MC-CDMA systems is employed in this dissertation. The experimental results indicate that our system not only significantly reduces the PAPR and MAI but also effectively suppresses the outside interference with low complexity. Finally, we present a practical cognitive application of the proposed system over the software defined radio platform.

An epistemic event -based correlation scheme for pervasive network management

Computer networks produce tremendous amounts of event-based data that can be collected and managed to support an increasing number of new classes of pervasive applications. Examples of such applications are network monitoring and crisis management. Although the problem of distributed event-based management has been addressed in the non-pervasive settings such as the Internet, the domain of pervasive networks has its own characteristics that make these results non-applicable. Many of these applications are based on time-series data that possess the form of time-ordered series of events. Such applications also embody the need to handle large volumes of unexpected events, often modified on-the-fly, containing conflicting information, and dealing with rapidly changing contexts while producing results with low-latency. Correlating events across contextual dimensions holds the key to expanding the capabilities and improving the performance of these applications. This dissertation addresses this critical challenge. It establishes an effective scheme for complex-event semantic correlation. The scheme examines epistemic uncertainty in computer networks by fusing event synchronization concepts with belief theory. Because of the distributed nature of the event detection, time-delays are considered. Events are no longer instantaneous, but duration is associated with them. Existing algorithms for synchronizing time are split into two classes, one of which is asserted to provide a faster means for converging time and hence better suited for pervasive network management. Besides the temporal dimension, the scheme considers imprecision and uncertainty when an event is detected. A belief value is therefore associated with the semantics and the detection of composite events. This belief value is generated by a consensus among participating entities in a computer network. The scheme taps into in-network processing capabilities of pervasive computer networks and can withstand missing or conflicting information gathered from multiple participating entities. Thus, this dissertation advances knowledge in the field of network management by facilitating the full utilization of characteristics offered by pervasive, distributed and wireless technologies in contemporary and future computer networks.

Theoretical Investigation of Intra- and Inter-cellular Spatiotemporal Calcium Patterns in Microcirculation

Microcirculatory vessels are lined by endothelial cells (ECs) which are surrounded by a single or multiple layer of smooth muscle cells (SMCs). Spontaneous and agonist induced spatiotemporal calcium (Ca2+) events are generated in ECs and SMCs, and regulated by complex bi-directional signaling between the two layers which ultimately determines the vessel tone. The contractile state of microcirculatory vessels is an important factor in the determination of vascular resistance, blood flow and blood pressure. This dissertation presents theoretical insights into some of the important and currently unresolved phenomena in microvascular tone regulation. Compartmental and continuum models of isolated EC and SMC, coupled EC-SMC and a multi-cellular vessel segment with deterministic and stochastic descriptions of the cellular components were developed, and the intra- and inter-cellular spatiotemporal Ca2+ mobilization was examined. Coupled EC-SMC model simulations captured the experimentally observed localized subcellular EC Ca2+ events arising from the opening of EC transient receptor vanilloid 4 (TRPV4) channels and inositol triphosphate receptors (IP3Rs). These localized EC Ca2+ events result in endothelium-derived hyperpolarization (EDH) and Nitric Oxide (NO) production which transmit to the adjacent SMCs to ultimately result in vasodilation. The model examined the effect of heterogeneous distribution of cellular components and channel gating kinetics in determination of the amplitude and spread of the Ca2+ events. The simulations suggested the necessity of co-localization of certain cellular components for modulation of EDH and NO responses. Isolated EC and SMC models captured intracellular Ca2+ wave like activity and predicted the necessity of non-uniform distribution of cellular components for the generation of Ca2+ waves. The simulations also suggested the role of membrane potential dynamics in regulating Ca2+ wave velocity. The multi-cellular vessel segment model examined the underlying mechanisms for the intercellular synchronization of spontaneous oscillatory Ca2+ waves in individual SMC. From local subcellular events to integrated macro-scale behavior at the vessel level, the developed multi-scale models captured basic features of vascular Ca2+ signaling and provide insights for their physiological relevance. The models provide a theoretical framework for assisting investigations on the regulation of vascular tone in health and disease.

Pulsed parabolic equation model of acoustic transmission (PPEMAT)

Underwater sound is very important in the field of oceanography where it is used for remote sensing in much the same way that radar is used in atmospheric studies. One way to mathematically model sound propagation in the ocean is by using the parabolic-equation method, a technique that allows range dependent environmental parameters. More importantly, this method can model sound transmission where the source emits either a pure tone or a short pulse of sound. Based on the parabolic approximation method and using the split-step Fourier algorithm, a computer model for underwater sound propagation was designed and implemented. This computer model differs from previous models in its use of the interactive mode, structured programming, modular design, and state-of-the-art graphics displays. In addition, the model maximizes the efficiency of computer time through synchronization of loosely coupled dual processors and the design of a restart capability. Since the model is designed for adaptability and for users with limited computer skills, it is anticipated that it will have many applications in the scientific community.

Peak-to-Average Power Ratio Reduced Parallel Interference Cancellation Multicarrier-Code Division Multiple Access System with Anti-Interference Property

Orthogonal Frequency-Division Multiplexing (OFDM) has been proved to be a promising technology that enables the transmission of higher data rate. Multicarrier Code-Division Multiple Access (MC-CDMA) is a transmission technique which combines the advantages of both OFDM and Code-Division Multiplexing Access (CDMA), so as to allow high transmission rates over severe time-dispersive multi-path channels without the need of a complex receiver implementation. Also MC-CDMA exploits frequency diversity via the different subcarriers, and therefore allows the high code rates systems to achieve good Bit Error Rate (BER) performances. Furthermore, the spreading in the frequency domain makes the time synchronization requirement much lower than traditional direct sequence CDMA schemes. There are still some problems when we use MC-CDMA. One is the high Peak-to-Average Power Ratio (PAPR) of the transmit signal. High PAPR leads to nonlinear distortion of the amplifier and results in inter-carrier self-interference plus out-of-band radiation. On the other hand, suppressing the Multiple Access Interference (MAI) is another crucial problem in the MC-CDMA system. Imperfect cross-correlation characteristics of the spreading codes and the multipath fading destroy the orthogonality among the users, and then cause MAI, which produces serious BER degradation in the system. Moreover, in uplink system the received signals at a base station are always asynchronous. This also destroys the orthogonality among the users, and hence, generates MAI which degrades the system performance. Besides those two problems, the interference should always be considered seriously for any communication system. In this dissertation, we design a novel MC-CDMA system, which has low PAPR and mitigated MAI. The new Semi-blind channel estimation and multi-user data detection based on Parallel Interference Cancellation (PIC) have been applied in the system. The Low Density Parity Codes (LDPC) has also been introduced into the system to improve the performance. Different interference models are analyzed in multi-carrier communication systems and then the effective interference suppression for MC-CDMA systems is employed in this dissertation. The experimental results indicate that our system not only significantly reduces the PAPR and MAI but also effectively suppresses the outside interference with low complexity. Finally, we present a practical cognitive application of the proposed system over the software defined radio platform.

Development of hardware in the loop real-time control techniques for hybrid power systems involving distributed demands and sustainable energy sources

The future power grid will effectively utilize renewable energy resources and distributed generation to respond to energy demand while incorporating information technology and communication infrastructure for their optimum operation. This dissertation contributes to the development of real-time techniques, for wide-area monitoring and secure real-time control and operation of hybrid power systems. ^ To handle the increased level of real-time data exchange, this dissertation develops a supervisory control and data acquisition (SCADA) system that is equipped with a state estimation scheme from the real-time data. This system is verified on a specially developed laboratory-based test bed facility, as a hardware and software platform, to emulate the actual scenarios of a real hybrid power system with the highest level of similarities and capabilities to practical utility systems. It includes phasor measurements at hundreds of measurement points on the system. These measurements were obtained from especially developed laboratory based Phasor Measurement Unit (PMU) that is utilized in addition to existing commercially based PMU’s. The developed PMU was used in conjunction with the interconnected system along with the commercial PMU’s. The tested studies included a new technique for detecting the partially islanded micro grids in addition to several real-time techniques for synchronization and parameter identifications of hybrid systems. ^ Moreover, due to numerous integration of renewable energy resources through DC microgrids, this dissertation performs several practical cases for improvement of interoperability of such systems. Moreover, increased number of small and dispersed generating stations and their need to connect fast and properly into the AC grids, urged this work to explore the challenges that arise in synchronization of generators to the grid and through introduction of a Dynamic Brake system to improve the process of connecting distributed generators to the power grid.^ Real time operation and control requires data communication security. A research effort in this dissertation was developed based on Trusted Sensing Base (TSB) process for data communication security. The innovative TSB approach improves the security aspect of the power grid as a cyber-physical system. It is based on available GPS synchronization technology and provides protection against confidentiality attacks in critical power system infrastructures. ^

Methane and stable isotope record of ice core EDML from Dronning Maud Land, Antarctica

Precise knowledge of the phase relationship between climate changes in the two hemispheres is a key for understanding the Earth's climate dynamics. For the last glacial period, ice core studies have revealed strong coupling of the largest millennial-scale warm events in Antarctica with the longest Dansgaard-Oeschger events in Greenland through the Atlantic meridional overturning circulation. It has been unclear, however, whether the shorter Dansgaard-Oeschger events have counterparts in the shorter and less prominent Antarctic temperature variations, and whether these events are linked by the same mechanism. Here we present a glacial climate record derived from an ice core from Dronning Maud Land, Antarctica, which represents South Atlantic climate at a resolution comparable with the Greenland ice core records. After methane synchronization with an ice core from North Greenland, the oxygen isotope record from the Dronning Maud Land ice core shows a one-to-one coupling between all Antarctic warm events and Greenland Dansgaard-Oeschger events by the bipolar seesaw. The amplitude of the Antarctic warm events is found to be linearly dependent on the duration of the concurrent stadial in the North, suggesting that they all result from a similar reduction in the meridional overturning circulation.

Metodologia de estimação de estados para tratamento de medições errôneas e registros não sincronizados em algoritmos de localização de faltas em linhas de transmissão

The performance of algorithms for fault location i n transmission lines is directly related to the accuracy of its input data. Thus, fa ctors such as errors in the line parameters, failures in synchronization of oscillographic recor ds and errors in measurements of voltage and current can significantly influence the accurac y of algorithms that use bad data to indicate the fault location. This work presents a new method ology for fault location in transmission lines based on the theory of state estimation in or der to determine the location of faults more accurately by considering realistic systematic erro rs that may be present in measurements of voltage and current. The methodology was implemente d in two stages: pre-fault and post- fault. In the first step, assuming non-synchronized data, the synchronization angle and positive sequence line parameters are estimated, an d in the second, the fault distance is estimated. Besides calculating the most likely faul t distance obtained from measurement errors, the variance associated with the distance f ound is also determined, using the errors theory. This is one of the main contributions of th is work, since, with the proposed algorithm, it is possible to determine a most likely zone of f ault incidence, with approximately 95,45% of confidence. Tests for evaluation and validation of the proposed algorithm were realized from actual records of faults and from simulations of fictitious transmission systems using ATP software. The obtained results are relevant to show that the proposed estimation approach works even adopting realistic variances, c ompatible with real equipments errors.

Mecanismos de sincronia social no ritmo circadiano de atividade durante a coabitação em casais de saguis (Callithrix jacchus)

In marmosets, it was observed that the synchrony among circadian activity profiles of animals that cohabite in family groups is stronger than those of the same sex and age of different families. Inside the group, it is stronger between the younger ones than between them and their parents. However, the mechanisms involved in the social synchrony are unknown. With the aim to investigate the synchronization mechanisms involved in the synchrony between the circadian activity profiles during cohabitation in pairs of marmosets, the motor activity was continuously registered by the use of actmeters on three dyads. The pairs were maintained in two different conditions of illumination: light-dark cycle LD 12:12 (LD cohabitation I – 21 days), and thereafter in LL (~350 lux). Under LL, the pairs were submitted to four experimental situations: 1. Cohabitation (LLJ I – 24 days), 2. Removal of one member of the pair to another room with similar conditions (LLS I – 20 days), 3. Reintroduction of the separated member in the cage of the first situation (LLJ II – 30 days) and 4. Removal of a member from each pair to another experimental room (LLS II – 7 days), to evaluate the mechanisms of synchronization. Ultimately, the members of each pair were reintroduced in the cage and were kept in LD cycle 12:12 (LDJ II – 11 days). The rhythms of pairs free-ran in LL, with identical periods between the members of each pair during the two stages of cohabitation. In the stages in which the animals were separated, only the rhythms of two females free-ran in the first stage and of three animals in the second one. In those conditions, the rhythms of animals of each pair showed different endogenous periods. Besides, during cohabitation in LD and LL, the members of each pair showed a stable phase relationship in the beginning of the active phase, while in the stages in which the animals were separated it was noticed a breaking in the stability in the phase relationships between the circadian activity profiles, with an increase in the difference in the phase angles between them. During cohabitation, at the transition between LD and LL, all animals showed free-running rhythms anticipating progressively the beginning and the end of the active phase in a phase similar to the previous condition, showing signs of entrainment to the previous LD. While in the posterior stages this was observed in only three animals between: LLT I and LLS I, and LLT II and LLS II, evidencing signs of entrainment to social cues between the members of each pair. On the other hand, one animal delayed progressively between LLT I and LLS I, three animals delayed between LLS I and LLT II, and three animals between LLT II and LLS II, perhaps by entrainment to the animals maintained outdoors in the colony. Similar process was observed in four animals between LLS II and LDT II, indicating entrainment to LD. In the transition between LLS I and LLT II, signs of masking was observed in the rhythm of a female in response to the male and in another pair in the rhythm of the male in regard to that of the female. The general and maximum correlations in the circadian activity profiles were stronger during cohabitation in LD and LL than in the absence of social contact in LL, evidencing the social effect. The cohabiting pairs had higher values of the maximum correlation in LD and LL than when the profiles were correlated to animals of different cages, with same or different sexes. Similar results were observed in the general correlation. Therefore, it is suggested that cohabitation induces a strong synchrony between circadian activity profiles in marmosets, which involves entrainment and masking. Nevertheless, additional studies are necessary to evaluate the effect of social cues on the synchronization of the circadian rhythm in pairs of marmosets in the absence of external social cues in order to confirm this hypothesis.

Caracterização do ritmo circadiano de atividade e repouso em saguis idosos (Callithrix Jacchus)

Advanced age may become a limiting factor for the maintenance of rhythms in organisms, reducing the capacity of generation and synchronization of biological rhythms. In this study, the influence of aging on the expression of endogenous periodicity and synchronization (photic and social) of the circadian activity rhythm (CAR) was evaluated in a diurnal primate, the marmoset (Callithrix jacchus). This study had two approaches: one with longitudinal design, performed with a male marmoset in two different phases: adult (three years) and older (9 y.o.) (study 1) and the second, a transversal approach, with 6 old (♂: 9.7 ± 2.0 y.o.) and 11 adults animals (♂: 4.2 ± 0.8 y.o.) (study 2). The evaluation of the photic synchronization involved two conditions in LD (natural and artificial illuminations). In study 1, the animal was subjected to the following stages: LD (12:12 ~ 350: ~ 2 lx), LL (~ 350 lx) and LD resynchronization. In the second study, the animals were initially evaluated in natural LD, and then the same sequence stages of study 1. During the LL stage in study 2, the vocalizations of conspecifics kept in natural LD on the outside of the colony were considered temporal cue to the social synchronization. The record of the activity was performed automatically at intervals of five minutes through infrared sensor and actimeters, in studies 1 and 2, respectively. In general, the aged showed a more fragmented activity pattern (> IV < H and > PSD, ANOVA, p < 0.05), lower levels of activity (ANOVA, p < 0.05) and shorter duration of active phase (ANOVA, p < 0.05) in LD conditions, when compared to adults. In natural LD, the aged presented phase delay pronounced for onset and offset of active phase (ANOVA, p < 0.05), while the adults had the active phase more adjusted to light phase. Under artificial LD, there was phase advance and greater adjustment of onset and offset of activity in relation to the LD in the aged (ANOVA, p < 0.05). In LL, there was a positive correlation between age and the endogenous period () in the first 20 days (Spearman correlation, p < 0.05), with prolonged  held in two aged animals. In this condition, most adults showed free-running period of the circadian activity rhythm with  < 24 h for the first 30 days and later on relative coordination mediated by auditory cues. In study 2, the cross-correlation analysis between the activity profiles of the animals in LL with control animals kept under natural LD, found that there was less social synchronization in the aged. With the resubmission to the LD, the resynchronization rate was slower in the aged (t-test; p < 0.05) and in just one aged animal there was a loss of resynchronization capability. According to the data set, it is suggested that the aging in marmosets may be related to: 1) lower amplitude and greater fragmentation of the activity, accompanied to phase delay with extension of period, caused by changes in a photic input, in the generation and behavioral expression of the CAR; 2) lower capacity of the circadian activity rhythm to photic synchronization, that can become more robust in artificial lighting conditions, possibly due to the higher light intensities at the beginning of the active phase due to the abrupt transitions between the light and dark phases; and 3) smaller capacity of non-photic synchronization for auditory cues from conspecifics, possibly due to reducing sensory inputs and responsiveness of the circadian oscillators to auditory cues, what can make the aged marmoset most vulnerable, as these social cues may act as an important supporting factor for the photic synchronization.

Caracterização do ritmo circadiano de atividade e repouso em saguis idosos (Callithrix Jacchus)

Advanced age may become a limiting factor for the maintenance of rhythms in organisms, reducing the capacity of generation and synchronization of biological rhythms. In this study, the influence of aging on the expression of endogenous periodicity and synchronization (photic and social) of the circadian activity rhythm (CAR) was evaluated in a diurnal primate, the marmoset (Callithrix jacchus). This study had two approaches: one with longitudinal design, performed with a male marmoset in two different phases: adult (three years) and older (9 y.o.) (study 1) and the second, a transversal approach, with 6 old (♂: 9.7 ± 2.0 y.o.) and 11 adults animals (♂: 4.2 ± 0.8 y.o.) (study 2). The evaluation of the photic synchronization involved two conditions in LD (natural and artificial illuminations). In study 1, the animal was subjected to the following stages: LD (12:12 ~ 350: ~ 2 lx), LL (~ 350 lx) and LD resynchronization. In the second study, the animals were initially evaluated in natural LD, and then the same sequence stages of study 1. During the LL stage in study 2, the vocalizations of conspecifics kept in natural LD on the outside of the colony were considered temporal cue to the social synchronization. The record of the activity was performed automatically at intervals of five minutes through infrared sensor and actimeters, in studies 1 and 2, respectively. In general, the aged showed a more fragmented activity pattern (> IV < H and > PSD, ANOVA, p < 0.05), lower levels of activity (ANOVA, p < 0.05) and shorter duration of active phase (ANOVA, p < 0.05) in LD conditions, when compared to adults. In natural LD, the aged presented phase delay pronounced for onset and offset of active phase (ANOVA, p < 0.05), while the adults had the active phase more adjusted to light phase. Under artificial LD, there was phase advance and greater adjustment of onset and offset of activity in relation to the LD in the aged (ANOVA, p < 0.05). In LL, there was a positive correlation between age and the endogenous period () in the first 20 days (Spearman correlation, p < 0.05), with prolonged  held in two aged animals. In this condition, most adults showed free-running period of the circadian activity rhythm with  < 24 h for the first 30 days and later on relative coordination mediated by auditory cues. In study 2, the cross-correlation analysis between the activity profiles of the animals in LL with control animals kept under natural LD, found that there was less social synchronization in the aged. With the resubmission to the LD, the resynchronization rate was slower in the aged (t-test; p < 0.05) and in just one aged animal there was a loss of resynchronization capability. According to the data set, it is suggested that the aging in marmosets may be related to: 1) lower amplitude and greater fragmentation of the activity, accompanied to phase delay with extension of period, caused by changes in a photic input, in the generation and behavioral expression of the CAR; 2) lower capacity of the circadian activity rhythm to photic synchronization, that can become more robust in artificial lighting conditions, possibly due to the higher light intensities at the beginning of the active phase due to the abrupt transitions between the light and dark phases; and 3) smaller capacity of non-photic synchronization for auditory cues from conspecifics, possibly due to reducing sensory inputs and responsiveness of the circadian oscillators to auditory cues, what can make the aged marmoset most vulnerable, as these social cues may act as an important supporting factor for the photic synchronization.

Uma proposta de solução para funcionamento offline em aplicações android

Given the growing demand for the development of mobile applications, driven by use increasingly common in smartphones and tablets grew in society the need for remote data access in full in the use of mobile application without connectivity environments where there is no provision network access at all times. Given this reality, this work proposes a framework that present main functions are the provision of a persistence mechanism, replication and data synchronization, contemplating the creation, deletion, update and display persisted or requested data, even though the mobile device without connectivity with the network. From the point of view of the architecture and programming practices, it reflected in defining strategies for the main functions of the framework are met. Through a controlled study was to validate the solution proposal, being found as the gains in reducing the number of lines code and the amount of time required to perform the development of an application without there being significant increase for the operations.

Uma proposta de solução para funcionamento offline em aplicações android

Given the growing demand for the development of mobile applications, driven by use increasingly common in smartphones and tablets grew in society the need for remote data access in full in the use of mobile application without connectivity environments where there is no provision network access at all times. Given this reality, this work proposes a framework that present main functions are the provision of a persistence mechanism, replication and data synchronization, contemplating the creation, deletion, update and display persisted or requested data, even though the mobile device without connectivity with the network. From the point of view of the architecture and programming practices, it reflected in defining strategies for the main functions of the framework are met. Through a controlled study was to validate the solution proposal, being found as the gains in reducing the number of lines code and the amount of time required to perform the development of an application without there being significant increase for the operations.

Isotopic data of atmospheric methane from EDML and Vostok ice cores over a full glacial cycle

The response of natural CH4 sources to climate changes will be an important factor to consider as concentrations of this potent greenhouse gas continue to increase. Polar ice cores provide the means to assess this sensitivity in the past and have shown a close connection between CH4 levels and northern hemisphere temperature variability over the last glacial cycle. However, the contribution of the various CH4 sources and sinks to these changes is still a matter of debate. Contemporaneous stable CH4 isotope records in ice cores provide additional boundary conditions for assessing changes in the CH4 sources and sinks. Here we present new ice core CH4 isotope data covering the last 160,000 years, showing a clear decoupling between CH4 loading and carbon isotopic variations over most of the record. We suggest that d13CH4 variations were not dominated by a change in the source mix but rather by climate- and CO2-related ecosystem control on the isotopic composition of the methane precursor material, especially in seasonally inundated wetlands in the tropics. In contrast, relatively stable d13CH4 intervals occurred during large CH4 loading changes concurrently with past climate changes implying that most CH4 sources (most notably tropical wetlands) responded simultaneously.

Survivability of Deterministic Dynamical Systems

Acknowledgements We acknowledge gratefully the support of BMBF, CoNDyNet, FK. 03SF0472A, of the EIT Climate-KIC project SWIPO and Nora Molkenthin for illustrating our illustration of the concept of survivability using penguins. We thank Martin Rohden for providing us with the UK high-voltage transmission grid topology and Yang Tang for very useful discussions. The publication of this article was funded by the Open Access Fund of the Leibniz Association.