Learning and development in real brains typically happens over long timescales, making long-term exploration of these features a significant research challenge. One way to address this problem is to use computational models to explore the brain, with Spiking Neural Networks a popular choice to capture neuron and synapse dynamics. However, researchers require simulation tools and platforms to execute simulations in real- or sub-realtime, to enable exploration of features such as long-term learning and neural pathologies over meaningful periods. This article presents novel multicore processing strategies on the SpiNNaker Neuromorphic hardware, addressing parallelization of Spiking Neural Network operations through allocation of dedicated computational units to specific tasks  to optimize performance. The work advances previous real-time simulations of a cortical microcircuit model, parameterizing load balancing between computational units in order to explore trade-offs between computational complexity and speed, to provide the best fit for a given application. By exploiting the flexibility of the SpiNNaker Neuromorphic platform, up to 9× throughput of neural operations is demonstrated when running biologically representative Spiking Neural Networks. The human brain is capable of operating using less energy than a light bulb  to process all network activity. Another strong limitation is given by long-range connections between different brain areas  is constant. Increasing the number of neurons per computational unit extends the green bar. When the input firing activity is high (commonly when the number of input connections is high), or P is increased, the blue bar grows. The length of the blue bar therefore varies according to the amount of synaptic inputs received during the timestep. In order to maintain real-time processing, both the bars need to complete the execution before the beginning of the subsequent timestep (therefore before the next green bar is due to start). During a simulation, the length of the green bar  can be achieved by reducing the number of neurons per computational unit. However, this operation has the effect of requiring additional hardware, since the network becomes more distributed and adds burdens to the communication fabric, increasing the number of destinations for the generated spikes. The time taken to process spikes, as indicated by the length of the blue bar in A more efficient partitioning strategy  many-core digital Neuromorphic platform, specifically designed to simulate SNNs in real time  format Mead, , therefoSNNs on SpiNNaker are commonly partitioned following a Homogeneous parallelization approach  the time required to update the neural state (tupd) of all the neurons simulated on core. The time required to process a single spike is defined by tspike. This value is expressed by Equation (3) and can be broken in a fixed contribution (cs), which is paid once per spike packet, corresponding to context switches, synaptic row location in the shared memory and transfer time, and a variable contribution (ms) which corresponds to the cost of processing a single synaptic event. Spike processing on SpiNNaker is handled through a pipelined approach, therefore the cost of processing the first and the last spike in the pipeline are different due to different API calls –(3), where tspike to obtain the processed spikes per timestep. This number is then incremented by 2, to account for tlast previously subtracted. The number of synaptic events that can be processed in a single timestep is, therefore, given by multiplying the number of spikes by the connectivity probability (P), which indicates the number of postsynaptic connections per spike and then by the number of postsynaptic neurons on core (n).The processing time  coming from the receptors simulated by the core. The Neuron core reads all the contributions in a single memory block read and computes the total input currents by adding together the values from different Synapse cores.The Heterogeneous Programming Model  receives inputs from the lower 6 presynaptic neurons (dark green in Synapse core (S21) from the higher 6 –(7), adapted from Equation (1). For this model, tp represents the spike processing window, which is obtained by subtracting from the duration of the timestep (Δt) the time required by the Synapse cores to write the synaptic contributions to shared memory (tw), minus the time taken by the postsynaptic Neuron core to read the contributions from shared memory (tr). These last two components represent a fraction of the timestep which is wasted, as during tw no additional spikes can be processed, and during tr the Neuron core has to wait, as it is retrieving the information necessary to update neuron state. The number of neurons is indicated by n. These are simulated by the Neuron core of the ensemble. The spike processing times tspike, tlast follow the same rule presented in Equation (3).The number of synaptic events that can be processed in a timestep under this approach per Synapse cores (Sc). This dependency can be easily explained by the increase in size of the memory block containing the synaptic contributions  to be read by the Neuron core every timestep, and by memory access contention, arising when multiple Synapse cores try to write to memory at the end of each timestep simultaneously. The lower case coefficients  are hardware specific values. Previously measured quantities, obtained from experimental analysis on SpiNNaker, are shown in Synapse core. The total number of synaptic events per ensemble is calculated by adding together the values for each Synapse core belonging to the ensemble. Compared to the Homogeneous partitioning case, with the same number of postsynaptic neurons, this represents a pseudo-linear increase in the processed events per timestep. A demonstration of this can be seen in Synapse cores. Here, the blue line shows the 1 ms case and the green line 0.1 ms. For the latter it is not possible to include more than 8 Synapse cores per ensemble, as the synaptic contribution reading time from the Neuron core's perspective becomes predominant, therefore preventing real-time execution.A description of the read and write times is given by Equations (6) and (7) and they depend on the number of involved Synapse cores (S12 and S22), to simulate the last four columns, resulting in additional resources being allocated and a sub-optimal partitioning of the matrices. Furthermore the number of synaptic events that can be processed for 0.1 ms timestep simulations is limited to the throughput of 8 Synapse cores, which does not allow to fully exploit the available parallelism.The Heterogeneous Programming model can achieve impressive performance improvements, however it also presents limitations, as seen in the example shown in Here, we present a novel parallelization approach enabling more efficient use of the available system resources, to address peak synaptic throughput performance and increased sparsity in synaptic connections.Multi-target Partitioning, extends the concept of Synapse cores introduced in Section 3.3, by assigning multiple Neuron core targets. Therefore, each neural ensemble will have multiple Synapse cores implementing the postsynaptic receptors of multiple Neuron cores, instead of matching the neurons of a single Neuron core. This technique improves partitioning of the synaptic matrices, by allowing longer rows. This therefore reduces the chance of empty rows for very sparse networks, and, at the same time, allows to amortize the fixed cost of processing a spike  over a larger number of synapses.This new approach, termed Synapse cores now span over a much larger synaptic matrix, covering the entire rows in the example. The partitioning is performed presynaptically , similarly to the Heterogeneous Model. However for the Multi-target partitioning, each Synapse core can target multiple postsynaptic Neuron cores, implementing all receptors for all target Neuron cores . This approach allows to save resources  by the number of connected Neuron cores (Nc). This reflects also on the spike processing times, as shown in Equation (13), where the variable cost is now multiplied by the total number of neurons targeted by the spike, therefore by the Synapse core. The reading (tr) and writing (tw) times now depend on the structure of the ensemble, as both contention and size of the transfer play a key role. The lower case coefficients (a to g) are hardware specific values, which therefore change according to the chosen platform. The components are similar to the Heterogeneous model case, however Synapse cores each targeting 3 Neuron cores.A schematic of the core interactions and memory structures for the Multi-target partitioning implementation is shown in Neuron cores can now be included in a single matrix. Therefore, Synapse cores allocate the shared memory region for the current timestep synaptic contributions , according to delay and postsynaptic index. Synaptic input buffers , to reduce contention on the SDRAM memory controller. The destination is decided according to the physical core ID,evenly spreading the contributions between the two memories. Both memories are part of the system memory map, therefore the allocation can be performed simply by specifying the correct memory heap, and the address retrieval is transparent to this operation.During simulation initialization, Neuron cores perform reads of the sub-regions. Upon completion, the input currents for each postsynaptic neuron are calculated by adding together all contributions from the Synapse cores for the specific neuron. The synaptic currents are then used to update the neuron state, according to the implemented neuron model and, if the model mandates it, a spike is generated.At the beginning of the subsequent timestep, all Neuron core can generate the first spike. In fact until all the contributions are read, the Neuron cores cannot start processing the neural state updates. This reflects on when postsynaptic Synapse cores can start receiving spikes, effectively reducing the spike processing window. It is therefore of paramount importance to reduce this reading interval as much as possible. In order to address this issue, Neuron cores are instructed to perform out-of-order read operations of the sub-regions. This means that, based on the Neuron core ID, the first read region will be either from SysRAM or SDRAM. This effectively halves the Neuron cores accessing the same memory at the same time, by explicitly instructing half of them to first read from SDRAM and half of them from SysRAM. After each read is completed, each Neuron core sends the subsequent request to the other memory.The time required to read the memory regions is a crucial design parameter, because it sets a boundary on when the Synapse cores, which implement the chosen rule for a simulation. The Heterogeneous model and the Multi-target partitioning can be extended to include simulations of plastic SNNs. For plastic networks, the time required to process synaptic events is higher compared to the static case, as a weight update phase is needed. Therefore, simulations of plastic SNNs would also benefit from reduced processing time per synaptic event. Here, we present the steps to extend the plasticity framework, in order to include the Multi-target partitioning. This framework is independent from the implemented plasticity rule, and the synaptic update is fully handled by Neuron cores, which contains one slot per postsynaptic neuron, and is updated every time a neuron fires. The introduction of plasticity into the Multi-target approach adds complexity, since the Neuron cores need to communicate back to the Synapse cores which neurons have spiked during the timestep, to correctly update the synaptic weights. This operation is again performed through shared memory. All Synapse cores share the same postsynaptic region , which contains information on whether each neuron has spiked or not, is written to SDRAM by each Neuron core. The Synapse cores can read this region and update the postsynaptic history (purple buffers in Synapse cores (as only these have visibility of the timing of incoming spikes). Only after this read operation is completed is it possible to update the weights and to process the incoming spikes. Therefore, the received spikes before this operation are buffered and ready to be processed when the read is completed. The Synapse core read is scheduled to happen after a fixed amount of time (for a given configuration), as the Neuron cores require a fixed amount of time to update the neural state and write back the postsynaptic buffers.During each timestep, after all the neurons on core have been updated, the postsynaptic buffer , peak synaptic event throughput (Section 4.2) and the effect of connection sparsity (Section 4.3).Synapse and Neuron cores under the new ensembles scheme, showing timings for each possible combination of Neuron and Synapse cores on a chip. Each Neuron core is set to simulate 64 Leaky Integrate-and-Fire  integer, meaning the contributions of a Synapse core targeting a single Neuron core amount to 64 × 2 B = 128 B (each DMA read has this fixed length).Reading time measurements are shown in Synapse cores , the number of reads per timestep per Neuron core increases. Reads are scheduled by the Neuron cores at the beginning of the timestep and performed sequentially, since there is a single DMA engine. As expected, for both the plots, the case with a single Neuron core (first line), shows linearly increasing reading times. The use of two separate memories does not influence this aspect, as one read at a time is performed. However it is observed that times in the dual memories plot are slightly lower. This is due to half of the Synapse cores contributions being stored into SysRAM which has a lower access time than SDRAM, therefore providing faster access. By increasing the number of Neuron cores , the contention increases, as multiple Neuron cores try to access shared memory to retrieve their synaptic contributions simultaneously. This case demonstrates the benefits of having two different memories in use with separate access. The SysRAM + SDRAM case indeed performs generally better than the single memory case allowing a gain up to 4 μs. There are, however, some isolated allocations where the single memory case performs better. This is probably due to a bad allocation of the cores on the chip, which results in a slower access to memory. Core allocation affects the memory access time, as to grant fairness, access to memory is regulated by a binary tree with arbiters at every junction point. The cores are on the leaves of the tree. A situation where the allocation of Synapse cores is unbalanced can cause higher contention between memory requests, as requests coming from more populated branches of the tree need to be filtered by multiple arbitration steps. This results in additional delays, which increase the total memory transfer time from the cores' perspective. Cores are assigned by the SpiNNaker toolchain during the placement phase. The values reported here represent the measured worst case reading times, therefore they are likely to represent the worst allocation of cores.By increasing the number of Synapse cores, which represents the placement with the highest number of sequential reads, performed by a single Neuron core. Furthermore, by keeping the number of Synapse cores constant, and increasing the Neuron cores, the transfer time becomes higher, as the reading contention increases. This reduces the portion of the timestep available for neural processing. It is therefore of paramount importance to understand the requirement of the SNN to be simulated, in order to determine the appropriate number of Synapse cores to allocate per Neuron core. It is noted that the values shown here represent the worst case scenario, thus presenting the highest recorded reading times. A more detailed analysis including best and average cases, is provided in the The worst case for both the experiments happens with 14 Neuron cores will start to fire, as the read phase must precede the neural state update and therefore Neuron cores must wait until this phase is completed before processing the neuron state update.The worst case analysis is important from a reading perspective to understand when the Synapse cores are displayed horizontally, while increasing Neuron cores on the vertical axis. By increasing the number of Synapse cores, the contention grows, as multiple cores attempt to write to shared memory simultaneously. By increasing the number of Neuron cores however, the size of each write becomes larger. This is because each Synapse core performs one single write per timestep. Therefore, by increasing the number of postsynaptic receptors (connected Neuron cores), the number of synaptic contributions to be written grows as well. The size of each write is expressed by Equation (14), where n is the number of neurons per Neuron core (64 in this case), w is the size of a contribution (2 B for standard SNNs) and T is the number of target Neuron cores for each Synapse core. Therefore, in T increases vertically from top to bottom.The measurements for the writing times are shown in Synapse core contributions are partially located in SysRAM and partially in SDRAM. Although SysRAM provides a faster access, it has a slower transfer rate, therefore, for larger transfers, it can result in similar or worse performance compared to SDRAM. This, combined with a bad cores placement, can result in losing the advantages of using SysRAM, negating the faster memory access, due to contention on the memory controller. Average and best case measurements however highlight that this is an isolated case, and show that the dual memory approach is more effective for the arrangements of interest. For more details and analysis, please refer to the Similarly to the read case, the reported times are the worst case measured writing times, and, for some cases, the access time is worse for the dual memory case. This can be due to several factors, as Synapse cores on when to stop processing incoming spikes and start writing the synaptic contributions to shared memory . The highest recorded writing time is when using SDRAM only with 6 Synapse cores targeting 7 Neuron cores. This time amounts to 26.98 μs. This does not represent an issue in 1 ms timesteps simulations, but amounts to more than a quarter of the timestep for real-time simulations with 0.1 ms timesteps.From a writing perspective, the worst case scenario is useful to instruct Synapse and Neuron cores per ensemble. This avoids overestimations which would further reduce the processing time shown in Equation (9). This analysis shows the importance of balancing the number of Synapse and Neuron cores according to the application requirements, in order to incur minimal memory access penalties. Network sparsity and firing activity also play a key role in the choice of core allocations, therefore the next sections focus on these aspects.The worst case writing and reading measurements therefore allow to Taylor synaptic contribution writing and reading times to the required number of Synapse cores and target Neuron cores. A third configuration is also presented, referred to as single target expanded. This consists of a standard Heterogeneous partitioning which maintains the same number of Neuron cores as the previous two cases, but allocates the same input Synapse cores capacity per Neuron core as the Multi-target approach. This last configuration provides a useful comparison, as the number of cores required for the single target Heterogeneous partitioning is adjusted to match the input capability of the Multi-target partitioning. The aim of including these cases is, therefore, twofold: first to compare the Multi-target partitioning to its Heterogeneous counterpart employing the same hardware resources, evaluating the performance difference; second, to show that, to achieve the input processing capability of the Multi-target approach, while using the Heterogeneous partitioning, is necessary to employ a larger number of hardware resources. This is represented by the single target expanded case.The most useful metric when evaluating throughput performance of the Multi-target partitioning is the maximum number of processed synaptic events per timestep. This experiment therefore compares the peak throughput performance for the Multi-target partitioning to previous works. To perform a fair comparison, the same SNN is profiled using the different approaches: Multi-target and Heterogeneous models. The same number of cores is allocated for both configurations, but with different internal connections between Sc, Nc], where Sc is the number of Synapse cores and Nc the number of Neuron cores – the case shown in Synapse cores are connected to all the Neuron cores. The Heterogeneous partitioning is shown on the right, including the two different mappings explored: single target and single target expanded. The single target Heterogeneous partitioning presents 3 Neuron cores receiving input from a single Synapse core each, showing an input capacity reduced by a third compare to the Multi-target case. The single target expanded in the experiment is therefore comparable with the  cases for the two other configurations, however the number of cores allocated is . This single-target expanded configuration matches the input capacity per Neuron core of the Multi-target partitioning, keeping the same number of neurons and Neuron cores . The intent here is to show that the Multi-target partitioning can reach similar performance compared to this extended configuration, requiring only a fraction of the allocated resources.A schematic of core allocations for the three approaches is shown in Neuron cores in this case) on the other hand, generate spike packets every time a neuron is updated and the model equations require it to spike, therefore distributing the spike packet generation over the timestep.The SNN model used for this experiment consists of 2 populations of neurons, configurable with a range of sizes and connectivity (similar to that shown in Synapse cores per ensemble) of the postsynaptic Population. These Population sizes have been obtained experimentally, such that the postsynaptic Population receives more spike packets than it can process. This allows saturation of the receivers in order to determine their limits. The number of generated spike packets however needs to be limited, due to limitations set by the SpiNNaker communication infrastructure . Different connectivity patterns have been tested to demonstrate the robustness of the approach. Here, the 1% connectivity case is shown, as it is commonly found in biologically-representative SNNs , which is not amortized by a smaller number of neurons or synaptic receptors.The simulated network in this experiment was the same for both 1 and 0.1 ms timestep cases, with the exception of the presynaptic Population size, which was scaled down of a factor ≈10×  and the single target (green). The upper axis shows values for the single target expanded (purple). The chosen configurations of cores allow direct comparison of the approaches. The left number in each tuple represents the Synapse cores of that test case, the right number the Neuron cores . This replicates the input capabilities of the Multi-target partitioning per ensemble, but requires a considerably higher amounts of cores compared to the Multi-target case, resulting in the worst case of 56 total cores compared to 14 (8th test case).Both the single target cases (green and purple) make use of the Heterogeneous model. The number of employed cores for each test case is indicated on the horizontal axes. The lower axis refers to the Multi-target approach (blue) performs better compared to the single target model (green). This is because the Multi-target partitioning performs a more efficient use of the available system resources compared to the Heterogeneous partitioning, allocating a higher input processing capacity to each Neuron core.In all the cases the Synapse core in the Multi-target case receives inputs from one seventh of the presynaptic neurons and targets all the 448 postsynaptic neurons. The single target partitioning on the other hand, has each Synapse core receiving inputs from all the presynaptic neurons, but targets only 64 neurons. Because the connectivity is very sparse, a reduced input traffic achieves better results.For the 1 ms timestep experiment the highest synaptic event throughput is given by the  configuration, where the Multi-target partitioning processes ≈9× more synaptic events than the heterogeneous partitioning. The reason why this happens is due to a full exploitation of the source-based partitioning offered by the approach. Each Multi-target approach performs well also compared to the single target expanded (purple), which represents a remarkable result, since the amount of resources in use is much lower, especially in the  case. The single target expanded approach employs the same number of Synapse cores per ensemble as the Multi-target partitioning, but has a single target per ensemble. Therefore, in the  case , each Synapse core receives input from one seventh of the presynaptic neurons and targets 64 postsynaptic neurons only.The Multi-target partitioning performing better than the single target case. However, with higher numbers of Synapse cores targeting higher numbers of Neuron cores, performance compared to the single target expanded case tends to be lower. This is due to the tight constraints set by the timestep resolution and the fact that memory read and write times for the synaptic contributions do not scale down with the timestep resolution.The trend is similar for 0.1 ms timesteps, with the single target expanded case, but with a fraction of the hardware resources . Furthermore, with the same amount of resources it is possible to achieve considerably higher synaptic event throughput.This experiment shows that, by efficiently using the Multi-target partitioning, it is possible to achieve comparable results to the Multi-target approach shows the best gain, having the steepest increase compared to the other three approaches, performing the best use of the available resources. Additional analysis is performed in the The general trend for the three approaches, together with the Homogeneous partitioning baseline is compared in Multi-target approach shows better performance than the single target case for all simulated configurations, demonstrating again that the approach makes better use of the available resources. For very sparse networks, with plastic synapses, the Multi-target approach achieves peak synaptic event throughput very close to the single target expanded simulations. This is due to the differences in processing plastic synapses compared to static synapses. Plasticity, requires the updated weights to be written back to shared memory, therefore doubling the accesses to SDRAM compared to the static case. This operation becomes extremely costly when the number of receptors per row are limited. Therefore, having longer synaptic rows, as in the case of the Multi-target approach, allows to further increase the number of synaptic events that can be processed per timestep. Similarly to the static case, the Neuron cores. The number of Synapse cores is kept fixed and the target Neuron cores are gradually increased. In order to provide a good balance (and according to the peak performance shown in Section 4.2), the chosen number of Synapse cores is 7 and the target Neuron cores range from 1 to 7, guaranteeing to fit on a single chip. This allocation also allows equal comparison between simulations with 1 ms timestep resolution and 0.1 ms, having set the number of neurons per Neuron core in both cases to 64. The connectivity probabilities investigated are: 0.1, 1, 10, and 50%. Connectivity patterns above 50% are beyond the scope of this study, as they are extremely rare in biology .The results for this experiment are shown in For the 1 ms case  right, aNeuron cores gives advantage similarly to the 1 ms case, however, when the network becomes denser the trend starts to invert, as the cost of processing a single incoming spike dominates over the gain introduced by this approach.The 0.1 ms case  left folNeuron processing units for sparser applications and increasing the number of Synapse processing units when the fan-in dominates. Thanks to these improvements it is possible to maximize the performance, while using minimal hardware resources and therefore reducing power consumption.This work presents a novel parallelization approach for neural processing on Neuromorphic hardware, which improves the performance of SNN simulations by acting on the way synaptic matrices are partitioned and processed. The Multi-target partitioning approach provides additional freedom when designing SNN simulations, by allowing to target applications more specifically, according to their requirements. By allowing parameterization of synaptic and neural processing units, it is possible to allocate the appropriate amount of resources for a given requirement, prioritizing the number of Through a SpiNNaker implementation of the Multi-target partitioning approach, it is possible to improve the peak synaptic processing throughput up to 9× compared to previous results for the same hardware resources. Furthermore, it is possible to obtain comparable processed synaptic events per ms, by reducing the hardware resources to a quarter, resulting in a much smaller machine (and energy consumption) dedicated to the simulation (as detailed in Section 4.2).Neuron cores, expanding the limit beyond a single postsynaptic Neuron core. This has the effect of reducing, by a factor Nc the number of destination processors per spike packet, facilitating the routing of spike packets and so reducing the pressure on the communication fabric. Furthermore, this increased number of targets per spike packet allows to amortize the dominating fixed cost of processing a spike (cs) . This is shown by Equations (8) and (13), where the number of target neurons of each spike grows according to the number of target tw) and reading (tr) times (Equations 9–11) to increase with the number of cores in the ensemble, consuming approximately half the timestep duration for high timestep resolution simulations such as 0.1 ms. For this reason the need for faster access to shared memory is proven, by showing that there is a large potential gain in having access to multiple separate shared memories, compared to a single shared memory. This consideration opens up to the possibility of using more advanced memory architectures for Neuromorphic hardware, such as multiport memories, since structures like synaptic matrices and synaptic contributions are non-overlapping and therefore would benefit from the capability of separate independent accesses.The Multi-target partitioning approach is optimal as it comes with minimal additional costs compared to previous approaches. However, the SpiNNaker implementation is limited by the different access patterns to shared memory. The shared memory access time plays a key role in the fraction of the timestep available for spike processing, as shown by Equation (9) and by the recorded values presented in Sections 4.1.2 and 4.1.3. The relatively old technology employed by SpiNNaker represents a bottleneck in this context, resulting in both memory contention and transfer size limiting the total system throughput. This causes the synaptic contributions writing , limiting the memory contention to a quarter of the cores in use, which combined with the much higher memory throughput (6 vs. 1 GB/s for the SpiNNaker SDRAM) would have a large impact on the synaptic contributions reading and writing times.The flexibility of the approach also makes it portable and extendable for the next generation of digital Neuromorphic platforms. SpiNNaker 2, by exploiting its chip organization of cores in quartets, namely QPEs  under grant EP/D07908X/1 and EP/G015740/1, in collaboration with the universities of Southampton, Cambridge, and Sheffield and with industry partners ARM Ltd., Silistix Ltd., and Thales. Ongoing development of the software is supported by the EU ICT Flagship Human Brain Project (H2020 785907 and 945539), in collaboration with many university and industry partners across the EU and beyond. LP was funded by an EPSRC DTA studentship in the Department of Computer Science.The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.All claims expressed in this article are solely those of the authors and do not necessarily represent those of their affiliated organizations, or those of the publisher, the editors and the reviewers. Any product that may be evaluated in this article, or claim that may be made by its manufacturer, is not guaranteed or endorsed by the publisher.


Expansionary monetary policies, which started to be implemented after the global crisis in 2008 and became widespread during the COVID-19 period, lowered global interest rates and increased the stock market indexes. This study aims to investigate the effects of expansionary monetary policies implemented before and during COVID-19 on foreign direct investment (FDI) flows to emerging economies. In this context, the effect of expansionary monetary policies on FDI has been tried to be determined through the changes created in financial indicators such as interest rate and stock market index. Accordingly, the effects of the developments in the global stock market index and interest rates on the FDI for Brazil, China, Turkey, and Poland were estimated using the autoregressive distributed lag (ARDL) model for the period 2008–2021. Empirical findings show that expansionary monetary policy practices before and during COVID-19 causing high global stock market index and low-interest rates encourage FDI inflows to developing countries. The empirical results on the effects of expansionary monetary policies applied before and during COVID-19 on FDI allow important implications to be made when considered together with the contractionary monetary policies to be implemented after COVID-19. So much so that our empirical results in favour of FDI flows to developing countries regarding the expansionary monetary policies implemented before and during COVID-19 imply that the transition to contractionary monetary policy in the post-COVID-19 period may cause significant constraints on the FDI inflows to developing countries. Therefore, it may be expected that favourable financial conditions for foreign direct capital inflows to developing countries will disappear in the post-COVID-19 period. In other words, the falling global stock market index and increasing interest rates along with the contractionary monetary policies implemented in the post-COVID-19 period will be able to have the potential to cause a significant change in the investment preferences of international companies towards developing economies. The general policy prescription obtained from the results of the study shows that developing countries would need much more FDI-attracting policies in order to compensate for the negative financial effects of contractionary monetary policies implemented in the post-COVID-19 period. Foreign Direct Investment (FDI) is considered an important component of their development strategy for emerging economies. Accordingly, policymakers give huge significance to the design of policy to stimulate inward FDI flows. FDI not only provides developing countries the much-needed capital but also enhances employment and production as well as the transfer of technology. Besides, some other benefits for the host country have been identified like the introduction of improved management techniques, international trade integration, and the evolution of a more competitive business environment. FDI has also been more stable or less risky compared to other capital flows like portfolio investments and debt flows : 9–19). With the global economic crisis experienced in 2008, unconventional monetary policy practices are widely applied all over the world. In this way, expansionary monetary policy tools have started to be used more powerfully and widely than ever before. The fact that Central Banks have the opportunity to respond to the crisis more quickly by increasing liquidity compared to fiscal policy instruments has led to the implementation of expansionary monetary policy by a wide group of countries. Accordingly, after the 2008 crisis, the Federal Reserve System (FED) adopted a series of unconventional policies as an alternative to traditional measures to stimulate aggregate demand and restore the functioning of the financial system. In addition, with the COVID-19 epidemic that started in China in 2019 and spread all over the world, the economies experienced another great shock. Thereupon, almost all countries continued to implement expansionary monetary policies more vigorously in order to eliminate the negative effects of the COVID-19. Thus, the expansionary monetary policy, which started to be implemented in 2008 with the global crisis, was also widely adopted throughout the world during the COVID-19 period.Due to the expansionary monetary policies implemented before and during COVID-19, significant changes were created in global financial indicators such as the interest rate and stock market index. The abundance of liquidity, which became abundant with the expansionary monetary policies, decreased the interest rates and increased the stock market indexes at a global level. It has been revealed by many studies in the literature that the expansionary monetary policies implemented by the central banks in this period decreased the interest rates and increased the stock market index ; 11, 3737, 8]..8].The aim of this study is to reveal the impact of expansionary monetary policies applied before and during the COVID-19 on FDI inflows to developing countries. In this framework, it will be tried to determine how the applied expansionary monetary policies affect the amount of FDI towards emerging markets through the changes in the interest rate and stock market index. Accordingly, data from emerging markets such as Brazil, China, Turkey and Poland between the years 2008–2021 were analysed using the ARDL method. The examined countries were chosen to represent examples of developing countries in different continents of the world.In the framework of empirical analysis, we try to determine not only the basic financial dynamic of FDI flows to emerging markets before and during COVID-19 but also policies needed in order to sustain the inflow of FDI to developing countries in the post-COVID 19 period. In the last period, with the loss of importance of the COVID-19 and inflation increases, it seems that most of the central banks have started to return to contractionary monetary policies. Of course, the drastic change in monetary policies implemented before and during the COVID-19 in the upcoming post-COVID-19 period will undoubtedly have a profound impact on the FDI inflows to developing countries. Therefore, the findings of this study will enable us to make some inferences about the possible effects of the contractionary monetary policies implemented in the post-COVID-19 period on FDI flows to developing countries.The rest of the paper proceeds as following plan. Section “Literature review” reviews the main related literature. Section “Data and methodology” presents data, methodology, and empirical results. The final section concludes and makes some policy implications in order to maintain stable FDI inflows to the emerging market.There has been a significant increase in foreign direct investment because of the world becoming a single global village with globalization. Especially, FDI has increasingly become an important source of economic growth and development for emerging economies. In addition to increasing employment and production in developing countries, FDI has also led to significant changes in the production structure through information and technology diffusion. For this reason, developing countries all over the world have made a great effort to attract foreign direct investments to their countries. Due to the increasing importance of FDI in the world economy in terms of developing economies, the factors affecting the FDI trend have begun to be studied extensively in the economics literature.In order for multinational companies to invest abroad, certain conditions that will increase their profit expectations must be met. In the literature, besides the global economic conjuncture, many factors related to the economic situation of both the home country and the foreign country in which the multinational company will invest have been determined. While an important part of these factors is related to real economic indicators, another important part considers financial indicators.Indeed, looking at the literature it seems that determinants of FDI movements are closely tied to emerging countries’ real and financial-economic conditions. Accordingly, in reviewing the empirical evidence it is crucial to distinguish between the real and financial factors driving capital flows to emerging markets. This distinction is important because the drivers of capital flows differ crucially depending on the real and financial sector of the economy. Thus, the distinction between the real and financial factors for capital flows has been the dominant intellectual framework for classifying drivers : 516–517There is a wide literature on the real economic determinants of FDI inflows to an emerging economy. In this context, although many economic variables have been discussed, market volume, growth rate, human capital, openness, and foreign trade balance have been the most used variables in the literature. Adhikary  and KumaApart from real economic factors, many studies in the literature determine many financial factors influencing FDI flows into an economy. According to these studies, financial markets can play a vital role as much as a real economic system in attracting FDI to the host country. Many studies show that a well-developed financial system acts as a catalyst to increase FDI inflow into developing economies. The financial system of a country includes the banking sector and the stock market. An efficient banking sector can contribute to FDI inflows by providing lower costs loans availability. The efficient stock market provides foreign investors better gains from "public offering." In this regard, it is significant to identify financial system variables that contribute to FDI inflows.Naceur et al.  especialIn the framework of financial factors affecting global FDI movements, some studies in the literature also add the effect of monetary policy on financial indicators to analyses. Thus, this part of the literature has also indicated the interaction between monetary policy and financial indicators affecting FDI inflows to host countries. According to these studies, changes in financial indicators depending on monetary policies play a big role not only in domestic investments but also in the realization of foreign direct investments. In other words, monetary policy preferences and their effects on financial indicators can be one important determinant in the investment decisions of domestic entrepreneurs, and they can undoubtedly significantly affect the investments made by multinational companies.When the related literature is examined, it is seen that monetary policy practices affect foreign direct investments, especially with the changes they create on financial variables such as interest rate and stock market index. Thus, it can be argued that interest rate and stock market index determined by the monetary policy are two important financial indicators that all entrepreneurs consider when making investment decisions. In this context, expansionary monetary policies implemented after the 2008 economic crisis and during the pandemic had increased the liquidity in global markets and therefore created significant positive effects on foreign direct investments by decreasing interest rates and increasing the stock market index.Based on the findings indicated above, it is possible to examine the literature examining the effects of expansionary monetary policies applied before and during the COVID-19 on foreign direct capital inflows to developing countries under two groups. In the framework of classical investment theory, the first group examining the interest rate channel implies that the expansionary monetary policy of the central bank reduces the cost of capital lowering the interest rate, and thus promoting global foreign direct investment. The second group analysing the asset price channel uses Tobin's q theory. The expansionary monetary policy of the central bank increases the asset prices promoting the demand for assets in the stock market, and thus promoting global foreign direct investment. In summary, the recent literature focussing on the impact of expansionary monetary policies on FDI inflows to emerging markets considers two main channels: the interest rate channel and the asset price channel.Considering the interest rate channel, classical economic approach asserts that one of the most important financial variables affecting the advantage of investing overseas is the cost of capital or interest rate for MNCs. In general, the results of economic research highlight the profit expectations of entrepreneurs as the most important factor affecting the investment level. In cases where the economic environment offers high-profit expectations for entrepreneurs, it is seen that the investment level in the country increases. Thus, it is not possible to increase private sector investments in an environment where high-profit expectations for entrepreneurs are not met. Economists from the classical economics tradition also argue that while creating high-profit expectations, entrepreneurs focus on low investment costs. In other words, the classical approach assumes that entrepreneurs try to maximize profits by minimizing costs. Thus, low-interest rates in the economy can reduce the financing cost of the investment and therefore the total costs, raising the profit expectations of the entrepreneurs and directing them to invest more. When this fact is evaluated together with monetary policy by which the central banks control money supply and credit in order to adjust the interest rate, it is clearly pointed out that the central bank’s expansionary policy significantly influences multinational companies' investment decisions.Fornah and Yuehua  aim to dRegarding the asset price channel, economists argue that the positive effect of monetary expansion on direct physical investments can also arise from the stock market index. Due to the increasing demand for stock markets with monetary expansion, the stock market index increases and makes it more profitable for both domestic and foreign entrepreneurs to turn to real investments. Tobin theorized this fact in the framework of the “q ratio”. The q ratio can be defined as the “Market Value of Firm's Capital Stock” divided by the “Replacement Cost of the Capital Stock”. The increase in the market value of firms according to the replacement costs of their capital causes the q ratio to be higher than 1. This indicates that the installed capital value exceeds the replacement cost in the market, resulting in higher returns. Thus, the more value the q ratio gets above 1, the more firms are willing to add to their installed capital stock. Undoubtedly, the value of q ratio greater than one depends on the increase in the stock value of the investment in the stock market. That means the firm makes more investments if the value of its stock market increases. When this phenomenon is evaluated together with the policies implemented before and during the pandemic, it can be concluded that the expansionary monetary policies implemented before and during the pandemic period had a positive effect on FDI inflows to emerging markets by increasing the stock market index.Batten and Vo  found thIn this section, we empirically examine the effects of expansionary monetary policies implemented before and during the COVID-19 on FDI inflows to developing countries. The effects of expansionary monetary policies on FDI inflows to developing countries will be determined through changes in financial indicators such as interest rates and stock market indices. Accordingly, we will try to empirically reveal the effects of financial variables on FDI inflows to emerging markets by using international data for four developing countries such as Brazil, China, Turkey and Poland for the period 2008–2021.In the study, the data of the four countries that attract the most foreign direct investment in their regions, representing the developing countries in different continents of the world, were used. In this context, data from China, Brazil, Poland and Turkey, which attract the most foreign direct investment in their regions, were included in the analysis, representing the regions of Asia, Latin America, Europe and the Middle East, respectively . The resThe financial indicators such as interest rate and stock market index in determining the effects of expansionary monetary policies on FDI have very strong theoretical justifications within the framework of classical investment theory and Tobin's Q theory, respectively. The classical investment theory argues that entrepreneurs give more importance to low investment costs while creating high-profit expectations. Thus, the low-interest rates in the economy reduce the financing cost of the investment and therefore the total costs, which raises the profit expectations of the entrepreneurs and directs them to invest more. Tobin's Q theory asserts that the Q ratio, which equals the stock market value of a company divided by its assets' replacement cost, is significant in taking new investment decisions for companies. High stock prices causing higher Tobin's q values encourage companies to invest more in physical capital. Because, in this case, physical capital investments gain "worth" in the stock markets more than the price companies paid for them.In our study, the effect of financial indicators on FDI was basically estimated within the framework of Model-1 and as shown in Eq. The logarithmic form of all variables was used in the analysis. The dependent variable in the model is the foreign direct investment It is theoretically expected that there will be a negative relationship between FDI and interest rate and a positive relationship between the stock market index and FDI within the framework of the classical investment approach and Tobin's Q theory, respectively. Accordingly, within the framework of Model 1, it was investigated whether the implementation of expansionary monetary policy causing to decrease in interest rates and increase in stock market indexes positively affected the FDI flow towards developing countries.We also estimated the Model-2 shown in Eq. In Model-2, the regression specification in Model-1 has been modified by adding a new real economic indicator such as Gross Domestic Product (lngdp). Thus, we also tested how precisely the coefficients of financial variables estimate the impact of expansionary monetary policies on FDI inflows to developing countries. Theoretically, there is a positive relationship between national income and investments. The Keynesian approach argues that when calculating the profit expectations of entrepreneurs, it is more important to maximize expected revenue rather than cost minimization. Accordingly, in a situation where the national income increases, the demand in the market is revived due to consumer income. Such a situation increases the revenue and profit expectations of entrepreneurs and leads them to make more physical investments.In the estimation of Model-1 and Model-2, the quarterly frequency data set between 2008:Q4-2021:Q3 covering the post-2008 economic crisis and the pandemic period was used. The FDI variable is used as the ratio of inward foreign direct investment to the country’s GDP. Data on the FDI variable of all countries were obtained from The Organisation for Economic Co-operation and Development (OECD) database. The Standard & Poor's (S&P) 500 index is preferred as the indicator of the global stock markets variable. The S&P 500 was introduced in 1957 by Standard & Poor's, as a stock market index to track the value of 500 large corporations listed on the New York Stock Exchange. The US 10-year government bond interest rate is chosen as the indicator of global interest rates the second independent variable. This ratio also indicates the unconventional monetary policy implemented by FED after the 2008 financial crisis. The datasets of S&P 500 and US 10-year government bond interest rates were obtained from St. Louis FED , 53. GDPThe sample of the study includes emerging markets including Brazil, China, Turkey, and Poland. The countries examined were chosen to represent developing countries on different continents of the world based on the availability of data.Table In our study, the effects of independent variables on foreign direct investments for developing countries are estimated by ARDL methodology. Pesaran and Pesaran , PesaranThere are three important stages in the ARDL methodology. Initially, the stationarity of the time series is checked. Because the series to be used in the ARDL methodology should be stationary in the level or first difference. In the second stage, the long-term interaction among the variables is examined with the cointegration test. The cointegration relationship is investigated with the Bound Test. In the last step, if there is a cointegration relationship between the variables, the coefficients showing the correlation between the variables are estimated in the long and short run.Since the series is to be stationarity for times series analysis, it should be investigated the stationary degree of series before estimations. Within the scope of empirical analysis, first, Augmented Dickey–Fuller (ADF), Phillips–Perron (PP) unit root tests developed by Dickey and Fuller , PhillipBound Test is estimated based on the Unrestricted Error Correction Model (UECM) shown in Eq. . In the After indication of the cointegration relationships among the variables, the long-term coefficients are calculated. The long-term relationship between the variables is determined by estimating the ARDL model shown in Eq. . In thisIn the last section, short-term relationships are estimated with the error correction model in Eq. . In thisThe stationarity of the series is investigated with ADF and PP unit root tests, and the results are presented in Table The cointegration relationship between the variables has been investigated by using the bound test. In the framework of the bound test, Model 1 and Model 2 indicated in Eq. . EmpiricAfter the cointegration relationship is found, we apply the ARDL technique to estimation the long-term coefficients. In this framework, Model 1 and Model 2 indicated in Eq. . Table 4The estimation results obtained within the framework of Model 1 were generally compatible with theoretical expectations. Accordingly, it is observed that interest rates (lni) in the before and during COVID-19 when expansionary monetary policies were implemented, within the framework of classical investment theory, increased foreign direct capital inflows (lnfdi) in China, Poland and Turkey, except Brazil. The effect of interest rates on capital inflows in Brazil was not statistically significant. Interest rates made the most significant contribution to foreign direct capital inflows in China during the period when expansionary monetary policies were implemented. Poland was the second country benefiting from abundant money and low-interest rates. Turkey, on the other hand, was the country that benefited the least from the interest rate advantage in terms of foreign direct investment. On the other hand, within the framework of Tobin's Q theory, it is determined that the rising stock market index during the implementation of expansionary monetary policies positively affected foreign direct capital inflows in China, Brazil and Turkey, except Poland. In Poland, the effect of stock market index (lnstockp) on foreign capital inflows (lnfdi) was not statistically significant. The stock market index made the most significant contribution to foreign direct capital inflows in Brazil during the implementation of expansionary monetary policies. The second country benefiting from the stock market index was China. Turkey, on the other hand, was the country that benefited the least from the interest rate advantage in terms of foreign direct investment.The results in Model 2 estimated for robustness check were similar to the original Model 1. Thus, the robustness of the results obtained from the original Model 1 was demonstrated. The results in Model 2 showed that, similar to Model 1, interest rates (lni) increased foreign direct capital inflows (lnfdi) in China, Poland and Turkey, except for Brazil. Again, while the interest rates had the greatest impact on China, the least impact was on Turkey. In addition, in the estimation of Model 2, the rising stock market index during the implementation of expansionary monetary policies positively affected foreign direct capital inflows in China, Brazil and Turkey, excluding Poland. The GDP control variable included in Model 2 for robustness testing was insignificant in all countries except Brazil.Concerning the diagnostic tests related to the estimations, the results of the Jarque–Bera normality test mentclass2pt{minimIn general, Model 1 and Model 2 short-term forecast results were in harmony with long-term forecasts in terms of the stock market index, but it was not possible to reach the same conclusion in terms of interest rates. The short-term estimation results are in Table Model-1 and Model-2 short-term estimation results of the stock market index are statistically significant to a large extent. In addition, developments in the stock market index, in line with theoretical expectations, affect capital inflows positively, except for China. Thus, it can be said that short-term forecasts are generally compatible with long-term forecast results. Model-1 short-term estimation results indicate that the estimation results showing the relationship between the stock market index and capital inflow in China and Turkey are statistically significant. However, while the increases in the stock market index positively affect capital inflows to Turkey, it is determined that it has the opposite effect in China. The short-term estimation results of Model 1 stock market index could not be determined in Brazil and Poland. Model-2 short-term estimation results determined that the estimation results for the stock market index in all countries are statistically significant. In addition, developments in the stock market index positively affect capital inflows in all countries except China. Similar to the results of Model 1, increases in the stock market index in China affect capital inflows negatively in Model 2.Short-term estimates of the interest rate, on the other hand, are not statistically significant to a large extent within the framework of both Model 1 and Model 2. Only in China, the interest rate values are statistically significant in the short-term forecasts made within the framework of Model 1 and Model 2. This situation revealed that the short-term and long-term forecast values for interest rates do not match. Therefore, it can be said that the relationship between the interest rate and capital inflows is more valid in the long-run than in the short run.Finally, estimation results of ECT indicate that the speed of adjustment is computed simply as a percentage of the equilibrium error that is corrected each period. Coefficients of ECT are negative and statistically significant. The results from error correction models also show that changes in variables of models the short-term dynamic adjustment path of FDIs towards their long-run equilibrium levels. In addition, it can be said that the speed of adjustment towards the equilibrium is rapid for China and Turkey and is in the form of decreasing fluctuations for Brazil and Poland.Overall, the evidence from time-series analysis revealed that interest rate and stock prices play an important role in FDI inflows to four developing countries before and during the COVID-19. In other words, the expansionary monetary policies implemented before and during the COVID-19 had significant effects on foreign direct investments with the changes they created in financial indicators such as interest rate and stock market prices. More specifically, in this period when liquidity was plentiful, falling interest rates, within the framework of classical investment theory, reduced investment financing costs and positively affected the volume of foreign direct investments. In addition, the liquidity abundance has also increased the stock market indexes, creating a very positive environment for foreign direct investment within the framework of Tobin's Q theory.When the effects of the interest rate and stock price are compared, it has been revealed that the effect of the stock market index on capital inflows to developing economies is more important than the effect of interest rates. In other words, expansionary monetary policies have had an impact on capital inflows to developing countries more through the stock market index than the interest rate. Because the coefficients of the stock market index were found to be higher than the coefficients of the interest rates. In addition, the positive effect of stock market indices on capital inflows has been determined in both long- and short-term forecasts. However, the positive effect of the interest rate is mostly revealed in long-term forecasts. Short-term estimates of the impact of interest rates, on the other hand, were generally statistically insignificant.The results of the study also enabled us to make some inferences about the possible effects of contractionary monetary policies implemented in the post-COVID-19 period on FDI flows to developing countries. In the last period, with the loss of importance of the COVID-19 and inflation increases, it seems that most of the central banks have started to return to contractionary monetary policies. In other words, both the weakening of the pandemic and the inflation problem in the recent period forced Central Banks to implement a contractionary monetary policy in the post-COVID-19 period. Accordingly, it is expected that interest rates will increase and stock market indexes will decrease in all countries in the post-COVID-19 period. Therefore, favourable financial conditions for foreign direct capital inflows to developing countries will probably disappear in the post-COVID-19 period.The results obtained allow important implications for policy design towards attracting FDI. In general, policymakers in developing countries should pay special attention to attracting foreign direct investment to offset the negative impact of interest rate and stock price resulting from the post-COVID-19 contractionary monetary policy. In this context, some policies towards the real economy can be implemented in order to ensure that foreign direct investments to developing countries continue uninterruptedly in the post-COVID-19 period. In this context, as frequently mentioned in the literature, improving the physical infrastructure of energy, transportation and communication , increasThe determination of the expansionary monetary policies implemented before and during COVID-19 on FDI flows to emerging economies is crucial to design policies in post-pandemics period to attract FDI in emerging markets. Accordingly, this study analyses the effect of monetary expansion before and during pandemics on foreign direct investment inflow to emerging market economies. ARDL method has been used to present evidence of the relationship between foreign direct investment inflows and financial variables for four emerging markets including Brazil, China, Turkey, and Poland during the period from 2008 to 2021.The empirical analysis examined the effect of the expansionary monetary policy applied before and during the COVID-19 on foreign direct investments in emerging economies, through two financial channels such as the interest rate and the stock market index. In the framework of classical economic approach, the interest rate channel implies that the expansionary monetary policy of the central bank reduces the cost of capital lowering the interest rate, and thus promoting global foreign direct investment. The asset price channel works under Tobin's q theory. The expansionary monetary policy of the central bank increases the asset prices promoting the demand for assets in the stock market, and thus promoting global foreign direct investment.The evidence from time-series analysis revealed that interest rate and stock prices play an important role in FDI inflows to developing countries before and during the COVID-19. When the effects of the interest rate and stock price are channels compared, it seems that the effect of the stock market index on capital inflows to developing economies is more important than the effect of interest rates. Thus, during the research period when expansionary monetary policies were implemented, the stock market index channel, which was put forward within the framework of Tobin's Q theory, worked more strongly on FDI inflows to emerging economies.The empirical findings of the study are not only important for illustrating the fundamental dynamics of capital flows before and during COVID-19, but also provide important policy implications for continued FDI inflows into emerging economies in the post-COVID-19 era. So much so that today, with the decrease of the effect of COVID-19 and the increase in inflation, central banks all over the world are starting to return to contractionary monetary policies. Of course, tightening monetary policy in the post-COVID-19 era will bring notable changes in the impact of interest rate and stock price on FDI flows to developing countries. Therefore, it can be expected that favourable financial conditions for foreign direct capital inflows to developing countries will disappear in the post-COVID-19 period. In this period, it will not be possible for developing countries to attract foreign capital to their economies by taking advantage of low-interest rates and high stock prices.In terms of policy inference, policymakers in emerging economies should focus more on policies that attract FDI in order to eliminate the disadvantages of financial indicators resulting from the contractionary policy implemented in the post-COVID-19 era. Therefore, policy-makers in developing countries should pay special attention to policies aimed at improving factors other than financial indicators that affect FDI inflows. These policies may include improving physical infrastructure, strengthening human capital, tax cuts and investment incentives to increase the profitability of investment in the country. In addition, such policies may include legal and institutional arrangements that will ensure the effective functioning of the free market, and practices aimed at ensuring political and social stability.


In the last decades, mobile robotics has become a very interesting research topic in the field of robotics, mainly because of population ageing and the recent pandemic emergency caused by Covid-19. Against this context, the paper presents an overview on wheeled mobile robot (WMR), which have a central role in nowadays scenario. In particular, the paper describes the most commonly adopted locomotion strategies, perception systems, control architectures and navigation approaches. After having analyzed the state of the art, this paper focuses on the kinematics of three omnidirectional platforms: a four mecanum wheels robot (4WD), a three omni wheel platform (3WD) and a two swerve-drive system (2SWD). Through a dimensionless approach, these three platforms are compared to understand how their mobility is affected by the wheel speed limitations that are present in every practical application. This original comparison has not been already presented by the literature and it can be used to improve our understanding of the kinematics of these mobile robots and to guide the selection of the most appropriate locomotion system according to the specific application.


Sensing systems are becoming less and less invasive. In this context, flexible materials offer new opportunities that are impossible to achieve with bulky and rigid chips. Standard silicon sensors cannot be adapted to curved shapes and are susceptible to big deformations, thus discouraging their use in wearable applications. Another step forward toward minimising the impacts of the sensors can be to avoid the use of cables and connectors by exploiting wireless transmissions at ultra-high frequencies (UHFs). Thin-film bulk acoustic wave resonators (FBARs) represent the most promising choice among all of the piezoelectric microelectromechanical system (MEMS) resonators for the climbing of radio frequencies. Accordingly, the fabrication of FBARs on flexible and wearable substrates represents a strategic step toward obtaining a new generation of highly sensitive wireless sensors. In this work, we propose the design and fabrication of a flexible gravimetric sensor based on an FBAR on a polymeric substrate. The resonator presents one of the highest electromechanical coupling factors in the category of flexible AlN-based FBARs, equal to 6%. Moreover, thanks to the polymeric support layer, the presence of membranes can be avoided, which leads to a faster and cheaper fabrication process and higher robustness of the structure. The mass sensitivity of the device was evaluated, obtaining a promising value of 23.31 ppm/pg. We strongly believe that these results can pave the way to a new class of wearable MEMS sensors that exploit ultra-high-frequency (UHF) transmissions. The industry of electronics has been drastically revolutionised over the years. The need for smaller devices has resulted in highly miniaturised chips, opening the door to new applications that were unimaginable with the older technologies . In the In this context, flexible and stretchable electronics can address scenarios in which the standard bulky and rigid materials cannot be applied in the attachment of systems to the human body, which is characterised by non-flat surfaces . MoreoveSeveral works in the literature have reported flexible and wearable sensors ,7,8,9; nFor radio-frequency (RF) integration, among the types of microelectromechanical (MEM) resonators, thin-film bulk acoustic wave resonators (FBARs) offer the highest working frequencies combined with the lowest footprints. FBARs confine thickness-extension waves in a vertical cavity formed by a piezoelectric material sandwiched between two electrodes. A reflecting layer at the bottom edge is used to limit the standing wave to the piezoelectric region . The pie3) has been used for decades with optimal results [In this regard, there are several materials suitable for this scope. Lithium niobate  presents the highest phase velocities in the literature and very low losses. By exploiting sputtering to obtain high-quality thin-film coatings on flexible substrates, AlN represents the best choice for applying piezoelectricity in RF integration for wearable systems ,18.In the literature, several works have demonstrated the feasibility of AlN-based sensing platforms. Indeed, thanks to their very high mass sensitivities, these resonators can be exploited for the development of a huge variety of sensors for antigen detection ,20, sweaIn this scenario, the fabrication of flexible FBARs with a demonstrated mass sensitivity allows the development of highly sensitive sensing platforms for wearable and ingestible applications.The authors of  proposedSeveral works reported the fabrication of FBARs on flexible polyimide membranes by using a silicon donor wafer and transfer printing on a flexible substrate ,24,25. TThe authors of  detailedAnother solution that sped up the fabrication process was reported in , where aThe same approach was applied to an AlN-based FBAR in . NeverthIn this work, we propose a gravimetric mass sensor made with an AlN-based flexible FBAR on an 8 μm thick polyimide substrate whose resonance is at 2.55 GHz. The resonator was designed by using a finite element method (FEM) solver and fabricated using three lithographic processes. Unlike in , the worFinally, the mass sensitivity of the sensor was proven by spin-coating different amounts of polymethylmethacrylate (PMMA) on the active region of the resonator. The sensor demonstrated a linear decrease in the anti-resonance frequency with the increase in the mass loading, with a very high responsivity of 23.31 ppm/pg.d is the thickness of the piezoelectric layer. The stack was designed by using a solver based on the finite element method (FEM), which was developed by using the electrostatic and mechanical domains offered by Comsol Multiphysics. In particular, the cross-section was defined as detailed in A breakdown of the device’s components is detailed in The admittance is reported in The fabrication process of the flexible FBAR is detailed in 3-based inductively coupled plasma (ICP) etching. The piezoelectric layer was obtained by using the same approach, but in this case, a 1.2 μm AlN layer was deposited and patterned (see rned see c. The torned see d. The reQ) and electromechanical coupling factor  with the setup illustrated in As can be seen, our resonator presented the highest electromechanical coupling factor combined with the lowest number of fabrication steps. Unlike the device in ,25, our The mass sensitivity of the resonator and its feasibility as a gravimetric sensor were proved through the spin-coating deposition of PMMA layers with thicknesses from 0 to 650 nm on top of the FBAR. The response of the resonator was measured for all of the mass loadings, and the results are shown in e sensor c was obtA linear dependence between mass loading and the anti-resonance value could be observed, proving the feasibility of the resonator as a gravimetric sensor with a responsivity of about 23 ppm/pg.The fabrication of flexible MEMS resonators that work in the GHz range is a crucial challenge to overcome in the quest for wearable and wireless sensors. In this work, a gravimetric sensor based on a flexible AlN-based FBAR resonator was presented. The device was designed by using an FEM model to estimate the electrical and mechanical responses. The high effectiveness of the fabrication protocol was demonstrated, as it resulted in an optimal-quality resonator with a response that was perfectly in line with the simulation results. The resonator showed an optimal performance with a Q-factor of 218 and an electromechanical coupling factor of 6%. In addition, the mass responsivity of the resonator was estimated by spinning several amounts of PMMA in layers that were from 0 to 650 nm thick. The device was demonstrated to have a linear dependence on mass variation, thus proving its suitability as a gravimetric sensor. The sensitivity was evaluated, and a promising value of 23.31 ppm/pg was obtained. We strongly believe that these results can pave the way to a new class of wearable MEMS sensors that exploit UHF transmissions.