The vibration of the heart valves’ closure is an important component of the heart sound and contains important information about the mechanical activity of a heart. Stenosis of the distal pulmonary artery can lead to pulmonary hypertension (PH). Therefore, in this paper, the relationship between the vibration sound of heart valves and the pulmonary artery blood pressure was investigated to contribute to the noninvasive detection of PH. In this paper, a lumped parameter circuit platform of pulmonary circulation was first set to guide the establishment of a mock loop of circulation. By adjusting the distal vascular resistance of the pulmonary artery, six different pulmonary arterial pressure states were achieved. In the experiment, pulmonary artery blood pressure, right ventricular blood pressure, and the vibration sound of the pulmonary valve and tricuspid valve were measured synchronously. Features of the time domain and frequency domain of two valves’ vibration sound were extracted. By conducting a significance analysis of the inter-group features, it was found that the amplitude, energy and frequency features of vibration sounds changed significantly. Finally, the continuously varied pulmonary arterial blood pressure and valves’ vibration sound were obtained by continuously adjusting the resistance of the distal pulmonary artery. A backward propagation neural network and deep learning model were used, respectively, to estimate the features of pulmonary arterial blood pressure, pulmonary artery systolic blood pressure, the maximum rising rate of pulmonary artery blood pressure and the maximum falling rate of pulmonary artery blood pressure by the vibration sound of the pulmonary and tricuspid valves. The results showed that the pulmonary artery pressure parameters can be well estimated by valve vibration sounds. Pulmonary hypertension (PH) is a hemodynamic disease which is defined as a mean pulmonary arterial pressure (mPAP) of >25 mmHg during right heart catheterization at sea level . BecausePH is an abnormal hemodynamic state, while the heart sound (HS) is also produced by the movement of blood flow which can contain hemodynamic information; thus, many scholars have shown an interest in the relationship between HS and PH. In 2014, Mohamed et al.  studied Many factors can lead to PH. The World Health Organization divides the causes into five categories , which mIn this paper, a circuit platform was built to guide the establishment and regulation of an MCL platform. Then, the relationship between heart valve vibration sound and pulmonary artery blood pressure (PBP) was investigated on the MCL platform by using data acquisition.The experiments were conducted on the computer model and the MCL platform. The data acquisition device was PL3508 Powerlab8/35 AD Instrument Australia. The reusable blood pressure transducers MLT0380 were used for pressure measurement. For the vibration sound measurement, a MEMS-based heart sound sensor  developepD) and entering the pulmonary artery. Blood flows through pulmonary vessels which are simulated by three parts: proximal pulmonary artery (pap), distal pulmonary artery (pad) and pulmonary veins (pv). Finally, blood pressure enters the left atrium (LA).For building and regulating MCL with quantitative guidance, a computer circuit platform was built. The well-known Windkessel model was used in the computer cardiovascular system ,17,18. Tp-valve, pap, pad and pv, and every part corresponds to a part of the MCL platform discussed in the C, inductance L, blood flow Q and blood pressure P in the circuit system are:The key point of this paper is pulmonary circulation, so the authors built the lumped parameter circuit platform for the pulmonary circulation system only, according to the systemic circulation part and the heart part used in the work of Tang et al. . The pulThen, the normal state of the circulation system can be obtained. The parameters and initial values of the elements in the model are given in R, is inversely proportional to the fourth power of r, which is the radius of the pipe,L is the pipe length and η is the liquid viscosity. Assume L and η are constants. In order to simulate the development of distal pulmonary arteries narrowing over time, the radius r of decreases as a function of time, that isTo achieve pulmonary hypertension status, we increased the resistance of pad, which is also the simplest and most effective method. The blood flow resistance, The MCL platform we designed has the following characteristics: (1) It has the same pulmonary circulation structure as the computer model. (2) Its distal pulmonary artery resistance can be adjusted continuously. (3) It can produce valve vibration sounds similar to that of the human body. On the basis of learning from previous research achievements ,22,23,24p-valve), the tube path between There is an equivalent relationship between the mock loop model and the circuit model. By comparing In order to better reflect the direct interaction between the left and right ventricles, we designed a biventricular model which has left and right ventricles and a ventricular septum, as shown in In order to squeeze the ventricle evenly, we chose the hydraulic method instead of applying the motor directly to the ventricular model. The drive and fixed part are shown in According to the three-element Windkessel model, there are three characteristics in the vascular system: resistance, inductance and compliance. Compliance refers to the deformation ability of an elastomer under the external forces, which plays a cushioning and regulating role in the vascular system. Because there is a difference in the value of compliance between systemic and pulmonary circulation, a compliance device with adjustable parameters was developed.The schematic diagram of the compliance device we proposed is shown in C is the compliance value of the device, In (5), The reservoir is a container connected to the atmosphere, which simulates the veins and atria in systemic and pulmonary circulation. It relies on gravity to simulate the compliance of the veins and atria.In order to make the vibrational sound more similar to that of the real heart valve, we used four artificial mechanical heart valves, which were produced by LANFEI MEDICAL in Lanzhou China. The heart valve is composed of a single blade attached to the fixed part.A laboratory throttle valve was used to adjust resistance, and the cross-sectional area of the vessel can be changed by adjusting the screw on it.Two stepper motors, a control box and two trigger switches were chosen as the servo motor system of the MCL platform. After the motor reached the reference position by triggering the switch, the linear reciprocating motion was carried out according to the program, which is determined by the circuit platform.After the above device was installed, the ventricular ejection program should be written into the servo motor. Because it is a flow control mode, the corresponding aorta and pulmonary artery flow should be referenced to determine the program. After the experiments and considering the limited motor power and experimental conditions, some corrections must be made to the program. Let the blood flow out for a longer period of time while the stroke volume of the two ventricles is 67 mL.After writing the program into the servo motor, fill the fixtures with water and add appropriate liquid, which consists of glycerin and water, to the vascular system. Then, the pressure waves of the right ventricle and pulmonary artery can be measured, as shown in In By adjusting the radius of the distal pulmonary artery, pulmonary artery systolic blood pressure (PASP) can be controlled to different values. In this paper, six pulmonary hypertension states were simulated, which meant six different pressure parameters of the pulmonary artery. Each experiment lasted 5 min, and pulmonary pressure, pulmonary valve and tricuspid valve vibration were collected synchronously. The pulmonary artery pressure signal information obtained in the experiment is shown in The pressure signal was filtered by using a Butterworth low-pass filter, and the vibration signal was denoised using the wavelet threshold method. The servo motor pulse signal represented the direction of motor motion, by which systolic and diastolic periods can be divided, that is, a high level represented the systole and a low level represented the diastole. To some extent, we can think of this as the role of the ECG signal in cycle segmentation. After denoising the servo motor signal, the rising and falling edges of the signal were extracted. The maximum blood pressure during the high level of the servo motor signal was taken as the systolic blood pressure of PBP, the maximum rising rate of pulmonary artery blood pressure was defined as MRRPBP, and the maximum falling rate of pulmonary artery blood pressure was defined as MFRPBP. Based on time windows and servo motor pulse signals, the time segments containing the tricuspid and pulmonary valve vibration sounds can be segmented. In the time window, the position of the maximum signal amplitude was set as the center and extracted 98% of the energy concentration area as the corresponding vibration sound of the valve.Amp) was defined as the maximum value of vibration sound, and the timing of the maximum amplitude (MS) was the time interval from the falling edge of the motor waveform to maximum amplitude occurrence. Sample entropy (SampEn) and fuzzy entropy (FuzzyEn) were also in the features, of which the dimensions were both 2; the threshold values were both 0.2 times the standard deviation, and the step of FuzzyEn was 2. The power spectral density of the vibration sound was calculated based on the burg algorithm, and the amplitude (Pow) and frequency (f) of the power spectral density main peak were also extracted. The letters ‘t’ and ‘p’ after the underline of the feature name denoted the tricuspid and pulmonary valves. For example, Amp_t represents the maximum amplitude of the tricuspid vibration sound. More detailed information of the features is shown in Several characteristics of vibration sounds with physical significance were extracted and studied. Maximum amplitude , a statistical method was necessary. It is difficult to study the significance between these features and pressure parameters without knowing the features’ distribution patterns. The authors used the Kruskal–Wallis rank sum test. This is a nonparametric test with the goal of determining if all group samples are identical or if at least one of the groups tends to give observations that are different from those of other populations.The Kruskal–Wallis rank sum test was used to evaluate whether there were significant differences between the groups of each feature. MS_t had significant differences between each group and gradually decreased with the increase in resistance. This was because the slope of right ventricular pressure increased while the right ventricular EDPVR remained unchanged, which made the right ventricular pressure greater than the pressure of the body circulation reservoir earlier, resulting in early tricuspid valve closure and smaller MS_t. In addition, the amplitude characteristics of tricuspid valve vibration sound Amp_t and energy characteristics Ener_t tended to increase, which was because the ventricle needed more pressure to eject liquid, resulting in an increased pressure difference between the two sides of the valve. In the frequency characteristics, f_t decreased while Pow_t increased, indicating that the main peak frequency of the tricuspid valve vibration sound power spectrum decreased and its amplitude increased with the increase in peripheral resistance in this experiment. Among the changes in frequency characteristics, the change trend of the main peak frequency in this experiment was contrary to the experience of the auscultation of heart sounds and previous research results. The reason may be that the heart valves used in this paper comprise mechanical valves composed of stainless steel and carbon materials, leading to the change trend contrary to biological valves. However, the work in this paper can still reflect the changes in the frequency of vibration sounds.Combined with MS_p and Ener_p had significant differences between each group, and MS_p decreased gradually, which was consistent with the study conducted by Wang et al. [Ener_p and AMP_p increased gradually, which was because the compliance of pulmonary circulation decreased with the increase in peripheral resistance, resulting in the increase in blood pressure in the pulmonary artery. When the right ventricle entered the diastole period, the pulmonary artery blood accelerated the reflux, which made the pulmonary valve close with greater energy. In the frequency characteristics, f_p decreased while Pow_p increased, indicating that the main peak frequency of the vibration sound power spectrum of the pulmonary valve decreased and its amplitude increased with the increase in peripheral resistance.The difference comparison results and features’ boxplot of pulmonary valve vibration sounds between groups are shown in g et al.  on the sIn the above analysis, the relationship between vibration sound and pulmonary arterial pressure was verified. We suspected whether the pressure parameters could be predicted by the valve vibration sound. To prove this idea, an experiment was designed. We obtained continuous changes in pulmonary artery pressure by adjusting the distal vascular radius of the pulmonary artery. The experiments showed that as the radius of the distal pulmonary artery decreased, the flow resistance gradually increased, and the pressure of the pulmonary artery gradually increased, and vice versa. The vibration sounds of the tricuspid and pulmonary valves were collected simultaneously. Each experiment lasted 10 min, with each carried out five times in total. First, a backward propagation neural network was used in the fitting. In these experiments, seven valve vibration sound features were extracted, which were highly correlated with the three pulmonary artery pressure parameters, i.e., PASP, MRRPBP and MFRPBP. These parameters may be different from the group analysis above because continuous adjustment parameters may cause the system to always be in an unbalanced state. These seven features and their correlation coefficients (CC) with pressure parameters are shown in A backward propagation neural network, a traditional regression prediction tool, was used here to predict three pulmonary artery pressure parameters. The number of input layer cells was 7 (seven features listed in −1 and 0.0042 mmHg·ms−1, respectively. The result showed that the pressure parameters could be estimated well.In this experiment, the inter-group verification method was adopted, that is, four groups of data were used as the training set, and the other group of data was used as the verification set. The scatter plot of predicted and measured values is shown in Machine learning does not seem to be automated enough, and we wish to solve this problem by deep learning. Therefore, a deep learning model constructed by a CNN and Bi-LSTM network was proposed in this paper. In this model, CNN was used for feature extraction, which can extract the features of a single vibration sound or two vibration sounds jointly. Bi-LSTM was used to learn the time sequence features in the sequence and output the regression results by the full connection layer. The structure diagram of the model is shown in −1 and 0.0060 mmHg·ms−1, respectively. The performance of the deep learning model was worse than that of the backward propagation neural network model, especially at both ends of the parameter range. The reason for this may be the small number of samples in that range. After removing the samples with PASP > 80 mmHg and PASP < 40 mmHg, the MAEs of the three pressure parameters’ estimation were increased to 3.17 mmHg, 0.0033 mmHg∙ms−1 and 0.0058 mmHg∙ms−1, respectively.The inter-group verification method was also adopted in this model. A scatter plot of predicted and measured values is shown in This study discovered the connection between valve vibration and pressure parameters through the mock loop model, as well as predicted pulmonary pressure parameters based on the features of vibration waveform. Some valve vibration features discovered through the mock loop model in this study were consistent with clinical observations to a certain degree, as shown in As we all know, the pressure parameters of pulmonary circulation have important value in monitoring lung function and diagnosing pulmonary arterial hypertension. However, the pressure parameters of pulmonary circulation are not routine monitoring items in clinical practice and are invasive. The significance of the research results in this article lies in proposing a possible method to estimate pulmonary circulation blood pressure parameters using heart valve vibrations collected from the chest surface, thereby achieving continuous non-invasive monitoring. If an electronic monitoring instrument is developed based on this method, then low-cost, real-time, fast and convenient monitoring of pulmonary circulation blood pressure parameters could be achieved.The findings of this study must be seen in light of some limitations. It is known that the human pulmonary circulatory system is very complex, and neither the circuit model nor the mock loop model could perfectly simulate it. The valves used in the mock loop model are artificial mechanical valves, whose material and structure are largely different from those of human heart valves. The features of artificial mechanical valve vibration could differ from human heart valves. On the other hand, the changes in its hemodynamics are influenced by many factors. This study only considers a single factor: blood flow resistance caused by the stenosis of distal pulmonary circulation vessels. The rules of valve vibration under multiple factors are still open to be explored.In this paper, the relationship between pulmonary artery pressure and heart valve vibration sound was studied based on MCL. It was found that when the pulmonary artery pressure rose, the feature of valve-closing vibration sound changed in both the time and frequency domains, which were mainly reflected in the amplitude, energy and time domains. In addition, the continuously changing pulmonary artery pressure was extracted on the MCL, and the machine learning and deep learning methods were proposed to verify that the pressure-related parameters could be predicted by the valve vibration sounds. This paper provides an in vitro experimental basis for the non-invasive diagnosis of pulmonary hypertension and the non-invasive measurement of pulmonary arterial pressure.


The network structure of non-centrally cleared derivative markets, uncovered via the European Market Infrastructure Regulation, is investigated by reconstructing initial and variation margin networks to analyze channels of potential losses and liquidity dynamics. Despite the absence of central clearing, the derivative network is found to be ultra-small and a maximization-based filtering tool is proposed to identify channels in the network characterized by the highest exposures. I find these exposures to be mainly toward institutions outside the euro area, emphasizing the need for cooperation across different jurisdictions. Anomalous behavior in terms of diverging first and second moments of the degree and strength distributions are detected, signaling the presence of large exposures generating extreme liquidity outflows. A reference table of parameters’ estimates based on real data is provided for different network sizes, with no break of confidentiality, making it possible to simulate in a realistic way the liquidity dynamic in global derivative markets even when access to supervisory data is not granted. The recent default of Archegos Capital Management in March 2021, caused by exposures on Total Return Swaps (TRS) on equities and combined with the adoption of poor margining practices, signaled how appropriate risk mitigation techniques and supervision must take place when derivative contracts are not centrally cleared by central clearing counterparties (CCPs). According to the latest statistical release from the Bank of International Settlements (BIS) on OTC derivatives statistics, central clearing rates for interest rate derivatives (IRDs) and credit default swaps (CDS) stand, respectively, at 78% and 62% of total notional at the end 2021This paper sheds light on bilateral derivative transactions that have not been centrally cleared through CCPs by using the voluminous transaction-by-transaction data collected under the European Market Infrastructure Regulation (‘EMIR data’). The collateral network structure of non-centrally cleared derivative markets is uncovered, analyzing the implications of the detected structures from a systemic risk and monitoring perspective. The implementation of a filtering tool to extract relevant information from such large and complex networks will be proposed, also providing the literature with some reference for the parameters’ estimates to promote the adoption of appropriate distributional assumptions for the modeling of such networks. This will allow other researchers, with no access to this kind of confidential data, to simulate and replicate the structure of derivative markets in a more realistic way.In the aftermath of the 2008 Global Financial Crisis, the weaknesses of derivatives markets and the necessity to increase their transparency become evident to the regulators. Despite the important role played by financial derivatives in the economy, these instruments embed substantial risks which were significant drivers of the collapse of Lehman Brothers and the near-failure of AIG  which requires EU entities engaged in derivative transactions to report them to trade repositories (TRs) authorized by the European Securities Markets Authority (ESMA). To reduce counterparty credit risk, a clearing obligation through central clearing counterparties (CCPs) for standardized derivative products and stricter margining practices were introduced. Under the current EMIR technical standards, precise clearing thresholds are set by the class of OTC derivative contracts, which determine whether Financial counterparties (FC) and Non-Financial counterparties (NFC) are subject to clearing obligations through CCPs. Whenever a derivative trade is not centrally cleared, risk mitigation techniques must take place and the regulation requires counterparties to exchange variation margins (VM) and initial margins (IM).Both IM and VM are used as collateralization instruments and will be used in this paper to uncover the network structure of non-centrally cleared derivative exposures. The IM is posted at the beginning to enter a derivative contract and it is intended to cover potential losses arising in the period between the defaulter’s last variation margin payment and the point in time at which the surviving party is able to hedge or replace the trade. The higher the IM posted the higher the wealth at stake in that bilateral transaction. The amount of IM can be recalibrated over time, especially in a period of high market volatility . The VM is used to compensate for daily fluctuations in the market value of the derivative contract instead. Given a certain variation in the price of the underlying instrument, the counterparty negatively affected by the price variation is required to pay a certain amount of money accordingly. Then, the IM network will reflect the riskiness in terms of potential future losses of the derivative exposures while the VM network constitutes, for a given time span, the liquidity flows of money between the involved institutions.Two main findings will be highlighted in the paper. First, the channels containing the highest exposures, and identified through the proposed filtering tool, involve mainly institutions belonging to jurisdictions outside the euro area (EA). Second, both initial and variation margin networks display anomalous behaviors in the power-law parameter associated, respectively, with both the degree and in/out-strength distributions, signaling the presence of extreme positions and liquidity outflows during turmoil periods to be brought to the attention of policymakers and supervisory authorities.The article is organized as follows: In Sect. The literature on the network structure of derivative markets is particularly small due to lack of access to confidential and regulatory data. On the empirical side, given the 2008 financial crisis and subsequent sovereign debt crises, the literature started to implement network approaches to monitor and assess the systemic risk arising from Credit Default Swaps (CDS) markets and potential contagion channels through highly interconnected institutions  and underlying asset classes . This leads to a very large network. I thus propose the adoption of a filtering tool to extract relevant information from the initial margin network, selecting a subset of exposures that might generate large losses for counterparties. Finally, I contribute to the literature by providing a reference table containing estimates and non-confidential topological information on the variation margin network. This might enable researchers to simulate derivative networks in a more realistic way, to study liquidity risk and contagion, even with no access to regulatory data.EMIR requires counterparties to report their derivative transactions to the TRs. All derivative transactions, both centrally cleared and bilateral contracts, should be reported independently of whether traded on exchange-traded derivative (ETD) markets or on OTC markets. The regulation applies to financial intermediaries as well as to non-financial companies with positions above some thresholds defined by the regulation. It is a double-reporting system, meaning the reporting obligation is on both counterparties. The TRs collect and maintain the records of the derivative contracts reported and make them available to the relevant authorities. The European Central Bank (ECB) is entitled to receive all the transactions in which at least one of the following situations holds true: (i) At least one counterparty in the derivative transaction is resident in the euro area ; (ii) the reference entity is in the euro area ; and (iii) the reference obligation is the sovereign debt of a euro area country .The data set is highly granular. For each trade on a derivative instrument, in which at least one of the conditions above-mentioned is met, a huge amount of information covering details on both the derivative instrument, the underlying, the exact time at which the trade occurred, and the two counterparties involved is available. Since a set of multiple contracts can be traded between two generic counterparties, the net position resulting from these multiple contracts is also reported in EMIR. This net position constitutes a portfolio. All the trades constituting a portfolio are assigned a unique code, which makes it possible to understand which portfolio that specific trade belongs to. The amount of initial and variation margin exchanged and reported by two generic counterparties reflects the overall riskiness of their multiple contracts. Even if each single trade is separately recorded in the data set, the fields containing the amount of collateral posted and received do not refer to the trade standalone but to the entire portfolio that trade belongs to. Thus, to reconstruct both the initial and variation margin networks, all the portfolios have been at first identified through the portfolio codes reported in a trade record.After having reconstructed all the portfolios for all the reporting counterparties, the associated initial and variation margins associated with those portfolios have been sampled and used to reconstruct the IMs and VMs collateral networks at the micro (counterparty) level.Because of the confidential nature of the data, the structural analysis of the two networks is performed without revealing any nodes’ specific information, but rather giving a topological and statistical description of the networks. However, numbers can be given at some informative level of aggregation. The overall notional value of the sampled portfolios for instance was 78 trillion of euro on February 14, 2020, at the beginning of the turmoil caused by the COVID-19 pandemic. Figure Being the focus on collateral networks, portfolios with no initial and variation margin requirements are not included in the sample independently from their notional size. When IMs and VMs are required instead, both ‘pure’ and ‘mixed’ portfolios are included to obtain a more comprehensive network overview of the risks in the non-centrally cleared derivative system.i and j  and 0 otherwise. With N being the set of nodes and E being the set of edges, the network is very large being j to i. Thus, while the initial margin network is treated as an undirected network (both weighted and binary), the variation margin network will be analyzed as a weighted directed one since it represents money flowing between institutions. In the following, I provide a structural analysis of the two networks and potential policy implications.I analyze two different networks of bilateral derivative transactions which are the initial margin and the variation margin networks. The network structures to be analyzed can be encoded in the adjacency matrices. I denote with The network of financial derivative transactions is not fixed over time, the number of nodes and edges will depend on the period chosen for the analysis. However, as will be shown, there are general structural properties that are rather stable over time. I will particularly focus on the network structures on February 14, 2020, and March 31, 2020, thus before and after the market turmoil caused by the COVID-19 pandemic.I begin with local network measures, in particular Fig. This topological feature is extremely relevant when assessing network robustness and vulnerability. Observing such a behavior for the derivative network implies robustness to random financial failures but fragility with respect to targeted attacks assortative patterns. I start computing the average nearest neighbor degrees (ANND) and their correlation with the degrees. The negative trend displayed in the right panel of Fig. k) for the entities with several interconnections in the Brazilian interbank market, I found relatively small rich-club coefficients, ranging between 0 and 0.25 for the most interconnected financial institutions as displayed in Fig. Networks with a core-periphery are composed simply of two structures: the core and the periphery. Nodes in the periphery are linked only to core members, while core members are highly interconnected with each other forming cliques (complete subgraphs). Networks with a core-periphery display the so-called rich-club effect and can be heuristically quantified through the rich-club coefficient. Differently from the interbank network, the presence of a core-periphery structure to explain the disassortative mixing does not seem to fit the non-centrally cleared derivative network. While Silva et al.  found thvariation of information (VI) which can be used to quantify the difference between two partitions , while the Infomap approach splits the same large group into two distinct communities. Apart from this discrepancy in the size and associated degrees of two communities, the rest of the clusters closely overlap suggesting the presence of dynamic community structures over time.Given the disassortative patterns together with the presence of hubs in the network, and the absence of a core-periphery structure, it seems reasonable to believe each financial institution acting as a hub to create its own community in a hierarchical network where all peripheral members (inside the community) connect only to community hubs. The procedure implemented to partition the network in communities is the modularity maximization approach . Many real-world networks exhibit the so-called small-world property. Being ‘small-world’ means in technical terms to observe a network diameter The presence of an ultra-small derivative market even without central clearing is particularly relevant for policymakers and could act as a double-edged sword: Adverse shocks can propagate in the network affecting many institutions very quickly, at the same time being the network ultra-small is much faster to identify many critical channels of contagion. The first typical and smart approach is the surveillance of highly interconnected and large institutions. Still, understanding which channels should be monitored starting from these nodes can be very difficult. In what follows, the adoption of spanning trees will be proposed as filtering tools to select the channels linking all the institutions in the fastest way and with the maximum level of exposure. The tool might be complementary to other well-established supervision approaches adopted by policymakers.Since the seminal work of Mantegna  on the hSpanning Tree) Given a graph N being the set of nodes and E being the set of edges, a Spanning Tree is a connected acyclic undirected subgraph of G connecting all the nodes in G.(Maximum Spanning Tree) Given a weighted connected graph N being the set of nodes, E being the set of edges, and W being the set of weights, a Maximum Spanning Tree (Max-ST) is a spanning tree T of G maximizing . Being the general weight of an edge It is worth stressing that only direct contagion paths are located on the tree, with no loops in the potential chain of defaults. When the distress is not promptly mitigated, and feedback effects through cycles arise in the default propagation mechanism, the final loss in the system might be even underestimated with a spanning tree approach. Nevertheless, whenever the length of the chain through which the default propagates in the system remains bounded by The graphical representation of the Max-ST is provided in Fig. j to i, I focus on the out-strength and in-strength distributions to capture outflows and inflows faced by institutions. I also compute the overall strength for each node so to identify losers and gainers, over the period of interest , showing their distributions as well. The out/in-strength measure for a generic node i then read simply asVariation margins are exchanged in cash at least daily to reflect mark-to-market changes on counterparties’ positions caused by price changes on the underlying of the derivative instrument. They represent flows of money moving from one counterparty to another, which can be at the origin of liquidity stress for counterparties. As for the initial margin network, I collect variation margin flows over the period February 14–March 31, 2020, in order to include the market crash caused by the beginning of the COVID-19 pandemic. Recalling the weighted adjacency matrix to be Variation margins can be exchanged even when no initial margin is required to enter the derivative contracts, which typically happens for very small exposures among counterparties. This makes the variation margin network very dense and full of small transactions almost negligible from a financial stability perspective and which would spike the distribution over zero. I then reconstruct the network setting a relatively low edge threshold Since the results might depend on the threshold mentclass2pt{minimIt is worth mentioning that institutions involved in non-centrally cleared transactions might be transacting at the same time in the centrally cleared space as well. Then, one could argue that extreme counterparties’ positioning and related net-outflows in the non-centrally cleared space might be there to simply hedge the exposures in the centrally cleared one or vice versa. In this case, those net-outflows would not cause liquidity stress since they would be netted by the net-inflows stemming from other exposures with different positioning strategies in the centrally cleared space. For this reason, for each of the sampled institutions acting in the non-centrally cleared space, I control for the presence of net-inflows stemming from the centrally cleared. I thus compute the following quantity.7For a complete and proper assessment of risk stemming from derivative exposures, it must be kept in mind that multiple hedging activities can be implemented by counterparties. One simple example would be the one in which a counterparty enters not only in derivative contracts (either cleared or not) with a long/short position but also in the underlying of the derivative but with opposite positioning. This would require the access, for each counterparty, to each financial asset hold in their balance sheet and goes well beyond the scope and the possibilities of this work. Keeping in mind all of these warnings, this paper uncover for the first time a huge part of the non-centrally cleared derivative markets, shedding lights on its structure and capability to generate extreme positions and liquidity outflows which are not offset in the centrally cleared space for many counterparties. This leads us to the conclusions.After the 2008 global financial crises, regulators made tremendous efforts to make derivative markets safer by requiring the adoption of risk mitigation techniques and the introduction of central clearing obligations to reduce counterparty credit risk. Despite the evident improvements, derivative instruments still embed substantial risks, especially when used in opaque ways as shown by the default of Archegos in March 2021. Non-centrally cleared markets constitute a substantial share of the overall derivative markets, but there is either little or no focus at all on these bilateral markets  in the current research literature which mainly focused on central clearing instead. This paper shed light on the network structure of non-centrally cleared derivative markets, providing a detailed analysis of risks and liquidity dynamics under stressed periods.The non-centrally cleared network of derivative transactions is found to display very fat-tails on degree and strength distributions even without the presence of central clearing counterparties, with anomalous exponents signaling the presence of extreme positions causing large liquidity outflows in stressed periods. Being the network ‘ultra-small,’ acting in a timely in case of extreme losses is fundamental for policymakers to avoid contagion. Moreover, the highest exposures are across jurisdictions, calling for cooperation among different authorities.The data supporting the research findings are highly confidential and cannot be made available publicly. The papers have been cleared for external submission to journals by the European Central Bank. Codes and anonymized statistical outputs can be shared and are available upon request.


This study investigates energy harvesting by a deionized (DI) water droplet flow on an epitaxial graphene film on a SiC substrate. We obtain an epitaxial single-crystal graphene film by annealing a 4H-SiC substrate. Energy harvesting of the solution droplet flow on the graphene surface has been investigated by using NaCl or HCl solutions. This study validates the voltage generated from the DI water flow on the epitaxial graphene film. The maximum generated voltage was as high as 100 mV, which was a quite large value compared with the previous reports. Furthermore, we measure the dependence of flow direction on electrode configuration. The generated voltages are independent of the electrode configuration, indicating that the DI water flow direction is not influenced by the voltage generation for the single-crystal epitaxial graphene film. Based on these results, the origin of the voltage generation on the epitaxial graphene film is not only an outcome of the fluctuation of the electrical-double layer, resulting in the breaking of the uniform balance of the surface charges, but also other factors such as the charges in the DI water or frictional electrification. In addition, the buffer layer has no effect on the epitaxial graphene film on the SiC substrate. Graphene is a monolayer crystal with carbon atoms in a honeycomb structure that has been intensively investigated for various applications because of its extraordinary carrier mobility and chemical stability . GraphenOver the past decade, the number of sensor devices connected to the Internet has increased. These “Internet of things (IoT)” devices can be used anywhere, such as monitoring a person with a pacemaker, pastured livestock, and traffic control . As the However, the origin of such energy-harvesting processes remains unclear. Various mechanisms for nanocarbon-based energy-harvesting devices based on solution flow have been proposed, such as the momentum transfer by phonon , breakin2 bonds without defects and dislocations. Furthermore, protein and amino acid adsorption on the epitaxial graphene film generally shows electron doping , respectively. The carrier-type change is typical of H2 intercalated epitaxial graphene films [Typical Raman spectra of the epitaxial graphene film before and after Her layer  and not ubstrate . The forne films . These r2 intercalation for the parallel and perpendicular electrode configurations were 63 and 46 mV, respectively, which were similar to those before H2 intercalation, indicating that the buffer layer under the epitaxial graphene film was not influenced by energy harvesting from the solution flow.A summary of the voltage generated by 50 measurements using DI water flow is shown in The dependence of the generated voltage on the droplet amount in the epitaxial graphene film with the buffer layer is shown in As shown in The origins of energy harvesting by solution droplets flowing on the graphene film differ as mentioned in the introduction. A key interpretation is the significance of the existence of anions and cations as well as the broken uniform balance of surface charges in graphene by the electrical double layer in the moving solution droplet . TherefoBecause epitaxial graphene films on the SiC substrate used in this study were single crystals with large areas with no polymer residue, ideal results were expected for graphene-based devices. Therefore, the energy harvested by the solution flow on the graphene surface must not be anions or cations in the solution. Hence, the electrical double layer is inessential in this case.The generated voltages depended on the number of DI water droplets as shown in This study investigated energy-harvesting characteristics of single-crystal epitaxial graphene films synthesized on SiC substrates using DI water flow. A voltage as high as 100 mV was generated by the DI water flow, and the generated voltage was independent of the electrode configurations parallel and perpendicular to the DI water flow as well as the existence of the buffer layer under the epitaxial graphene film. The average electrical power of energy harvesting by the DI water flow exceeded 1 µW. The epitaxial graphene film-based energy-harvesting devices using solution flow can be used for electrical power supply to IoT devices in the presence of flowing water, such as river or seashore, with no electrode configuration in the direction of water flow.


Controlling the transmission of broadband optical pulses in scattering media is a critical open challenge in photonics. To date, wavefront shaping techniques at optical frequencies have been successfully applied to control the spatial properties of multiple-scattered light. However, a fundamental restriction in achieving an equivalent degree of control over the temporal properties of a broadband pulse is the limited availability of experimental techniques to detect the coherent properties  of the transmitted field. Terahertz experimental frameworks, on the contrary, enable measuring the field dynamics of broadband pulses at ultrafast (sub-cycle) time scales directly. In this work, we provide a theoretical/numerical demonstration that, within this context, complex scattering can be used to achieve spatio-temporal control of instantaneous fields and manipulate the temporal properties of single-cycle pulses by solely acting on spatial degrees of freedom of the illuminating field. As direct application scenarios, we demonstrate spatio-temporal focusing, chirp compensation, and control of the carrier-envelope-phase (CEP) of a CP-stable, transform-limited THz pulse. Multiple scattering of light is a common phenomenon in everyday life. The opaqueness of fog, milk, and clouds are excellent examples of how light is scrambled when travelling through materials composed of thousands of particles scattering light in all directions. While scattering is generally perceived as unwanted, researchers have shown that complex but inexpensive substances like white paint or frosted glass can be adapted to behave as expensive optical devices, such as high-resolution lenses or optical computing devices. This surprising result is achieved by using particular projectors on the incident light to impress specific patterns yielding a desired shape at the output. While manipulating the spatial profile of light is now well-understood, controlling how scattering affects ultra-short light pulses remains exceptionally challenging, primarily due to the difficulty in measuring the effects of scattering at the ultrafast timescales of the pulse (quadrillionths of a second).In this theoretical work, we propose a new way to tackle this challenge by leveraging the unique properties of terahertz light waves. Terahertz light lies between microwaves and infrared in the electromagnetic spectrum and is highly sought in research and industry. It can easily reveal the material composition of an object and penetrate common materials like paper and plastic as X-rays do, but without being harmful. More importantly, we can experimentally detect the individual oscillations in a terahertz pulse and extract an unprecedented understanding of how scattering affects it.We show that this added knowledge gives us the ability to finely manipulate the properties of the pulse, compensate the pulse-broadening effects of scattering, and “engineer” specific pulse shapes, a highly-sought ability in photonics. In the long term, this ability could be applied to reveal the internal composition of complex samples, such as biological tissue, or extract images of samples placed behind (or within) scattering materials.. As a result, a large body of research has historically focused on compensating or straight-out eliminating scattering effects. In a stark paradigm shift, researchers have recently demonstrated that disordered media can become essential ingredients in developing photonic devices with sophisticated optical performances. These include, among others, scattering-assisted super-resolution imaging lenses, wavefront-shaping components, or optical neuro-computing devices. At their heart, these demonstrations rely on wavefront shaping techniques, i.e., on the identification of an optimal incident field distribution, or pattern, yielding a desired intensity distribution at the output of a scattering medium. While the ability to control monochromatic beams' spatial properties has matured recently, manipulating the temporal and spectral properties of the scattered field remains challenging, particularly when considering broadband ultrafast illumination. Multiple scattering is an inherently dispersive phenomenon that naturally leads to the broadening of optical pulses. Recent works have shown that the intrinsic coupling between spatial and temporal dimensions in scattering media can be leveraged to manipulate the temporal properties of pulses by controlling the spatial features of the illumination. As a result, spatial wavefront shaping can be applied to achieve spatiotemporal focusing, corresponding to a simultaneous focusing in space and pulse re-compression in time, either through iterative approaches or by measuring the frequency-dependent transmission matrix of the sample. These approaches have shown how to control the envelope of the transmitted waveform successfully , but they remain unsuitable for manipulating the carrier-wave properties . Further advances in this area are fundamentally hindered by the inability to directly measure the full-wave properties of the scattered field, most notably the absolute spectral phase. An interesting question is whether a direct measurement of the electric field oscillations could enable controlling the coherent features of the transmitted pulse and devising advanced forms of waveform synthesis and spectral shaping currently out-of-reach at optical frequencies. In this context, field-sensitive detection is well-established in terahertz (THz) photonics, where time-domain spectroscopy (TDS) grants access to the time-resolved detection of the electric field of single-cycle THz pulses. Leveraging this ability, THz-TDS has been applied to study the broadband properties of scattering samples, with a particular emphasis on the role of multiple scattering in biomedical applications and the effects of resonant excitation of the scatterers composing the medium. However, the implementation of a complete, field-based wavefront control methodology to manipulate broadband pulses is essentially unexplored in the THz frequency band. In this work, we provide a first theoretical exploration of the potential advantages offered by time-resolved, field-sensitive detection in manipulating broadband THz pulses using scattering media. We combine the nonlinear generation of THz patterns from structured optical beams with an evolutionary optimisation feedback-loop targeting the coherent, full-field properties of the transmitted field, showcasing the ability to achieve spatiotemporal focus and control the absolute phase of the transmitted pulse. Quite interestingly, access to the absolute spectral phase of the pulse enables the definition of effective spectral shaping strategies, such as the ability to compress an incident chirped-pulse or control the carrier-envelop-phase (CEP) of an incident pulse, a significantly challenging task at optical frequencies.Multiple scattering is generally perceived as detrimental in photonics, as it is commonly associated with unpredictability and loss of information. For instance, in microscopy or astronomy, scattering is widely known to severely affect the resolution and fidelity of an imaging systemTM . For the sake of simplicity, we focus on a scalar description of the scatterer, but our approach can be easily extended to a full-vector formulation.We model the linear transmission properties of the scattering medium through a dispersive transmission operatorE- , the field transmitted through the scattererE+  is expressed through a  convolution relation:In the presence of an input field distributionM andN two-dimensional, square pixels, respectively. In such a formulation, the spectral components of the fields are re-defined as column arrays, andmnTM(ω) as follows: Following Ref.m-th (n-th) pixel of the output (input) field distributions. Following standard approaches, we express the transmission matrix as a complex-valued, random Gaussian matrix: wheremnϕ(ω) is a random phase distribution uncorrelated in space and gaussian-correlated along the frequency axis. The degree of spectral correlation, generally expressed in terms of the spectral correlation bandwidth Δcv, is commonly employed to characterise the spectral response of a scattering medium, and it is generally defined as the inverse of the Thouless time. In practice, a frequency-correlated transfer matrix can be modelled numerically by applying a Gaussian spectral filter of width Δcv to a white-noise random matrix.where. However, when operating at THz frequencies, the ability to control the incident electric field distribution is hindered by the limited availability of spatial light modulator (SLM) devices. To overcome this limitation, we employ the nonlinear conversion of structured optical beams, an approach we have recently developed within the framework of time-resolved nonlinear ghost imaging (NGI). With this approach, any optical pattern generated through a standard SLM device can act as a direct source of broadband THz patterns. By considering a nonlinear quadratic process  crystal such as ZnTe), the relation between incident optical intensity and generated THz field is linear, i.e.,THzE ∝pumbI, enabling the precise control over the THz field profile by simply shaping the incident optical pulse. A key advantage is that the spatial resolution of the THz patterns can be pushed way below the standard THz wavelength scale, as it is only bound by the diffraction limit of the optical beam. Besides, the nonlinear conversion ensures that the spatial pattern is well-defined across the whole THz band, enabling the generation and control of single-cycle, THz structured beams. We can assume that the incident THz patterns are expressed as:In general terms, a wavefront control approach aims to identify the optimal incident field distributionA0 is an amplitude,P is the  spatial profile, andTHzf(ω) is the spectrum of the THz pulse, which is assumed to be the same for all input points.. The spatial pattern, impressed by an optical SLM on the pump field, is transferred to the THz pulse through nonlinear conversion in a quadratic crystal. The patterned THz field impinges on the scatterer, that is placed in close proximity  of the generating crystal. Upon propagation, an electro-optical sampler collects the transmitted field in the typical fashion of standard TDS detection. As our objective is to manipulate the full-field properties of the transmitted THz pulse in a specific pixel of the output plane, we introduce a spatial pinhole at the output facet of the scatterer, corresponding to the desired focal spot . To optimise the wavefront of the transmitted pulse, the collected THz field from a predetermined ensemble of patterns is analysed and ranked through an evolutionary optimisation algorithm ) that provides the feedback required to iteratively optimise the transmitted field. This configuration enables establishing an optimisation feedback loop relying on the temporal field properties instead of average intensity, as is generally the case when operating at optical frequencies. In our configuration, the combination of near-field coupling and generation of THz patterns from structured optical fields provides a significant advantage in terms of available degrees of freedom. The THz field can be densely sampled in space, with patterns reaching sub-wavelength spatial resolution in the near-field region. This is a drastic difference from typical optical embodiments, where the spatial sampling is limited by the numerical aperture of the illumination. On the contrary, in our case, the sampling can exceed the density of the modes accessible from the scatterer input facet, and the spatial density of the transfer matrix can be as high as required to represent the scattering medium accurately.where. The simulation codes require the “statistics” Octave package, freely available through theOctave Forge repository. The plotting codes require the “signal” Octave package, freely available through theOctave Forge repository. As a THz input field, we considered a transform-limited THz pulse with a duration of 1 ps, a typical product of a bandwidth-limited optical rectification process in a nonlinear crystal. The incident pulse spectrum is centred at 1THz  pulse duration and Δv the bandwidth of the power spectral distribution). In terms of spatial features, we considered grayscale spatial patterns composed of 33 × 33 square pixels of side Δx = 100μm. The scattered field spectral correlation bandwidth is Δcv = 250GHz, a value that is compatible with experimental literature and which places us in a non-monochromatic case. The optimisation is performed via a standard GA targeting different fitness functions, and corresponding to the genetic algorithm described in Ref.To demonstrate this concept, we numerically simulated the configuration inμ,σ, andS are the first, second (standard deviation) and third moments (skewness) of the probability distribution defined by |E(t)|. Practically speaking, these quantities correspond to the centre, duration, and symmetry of the pulse waveform. We stress that all those quantities do not relate to the pulse envelope or to locally averaged intensity profiles, as in the common optical practice.whereE0(t) ≡ maxE is the peak electric-field value in the desired focal spot . Such a fitness function simultaneously maximises the transmitted field's peak value and minimises the pulse profile's standard deviation in time.As an initial test case, we targeted the ability to simultaneously focus the transmitted field in space and time . Our simulation results are shown inTHz (input 0.8THz). Quite interestingly, our approach is sensitive to the coherent field properties of the pulse, as illustrated inA typical optimised pulse is shown int0, durationσ0 and skewnessS0. Specifically, we performed a series of simulations with a target durationt0 and skewnessS0 coinciding with the transform-limited incident pulse, while we varied the target time-shift within the intervalt0 ∈ . The factors {α,β,γ,ζ} multiplying each term are the cost function’s weights. As illustrated inμ  is the desired spectral profile,outE(ω) is the output spectrum, and σ(E(t)) denotes the standard deviation of the pulse in the desired focal point.The ability to coherently resolve the complex-valued spectrum of the transmitted waveforms is particularly suited to perform phase-sensitive spectral shaping of the incident pulse. For this type of task, we employ the cost function D inThis particular choice of fitness function selects patterns yielding output waveforms with a short duration and a high degree of spectral correlation with the desired waveform. As a first example, inf-2f interferometry. While our analysis was conducted by considering a target focal point placed in the centre of the optical path, the use of an iterative optimisation approach enables, in principle, to select different points on the output plane. In practical terms, this would correspond to modifying the cost functions in. Although we did not provide specific modelling for near-field interactions in this work, the access to the near field modes is less challenging at terahertz frequencies. Hence, it is to be noted that if the THz source is located in near-field conditions with the sample and spatially controlled with NGI-methodology, the accessible modes within the scattering medium can potentially focus light under the diffraction limit, a potential route to subwavelength imaging resolution. Moreover, TDS-based wavefront control techniques could provide a practical approach to manipulating broadband terahertz pulses' spatiotemporal properties and design entirely new classes of wavefront and spectral shaping applications. It is also important to highlight that due to the scale of the wavelengths, working at THz frequencies offers a considerable advantage to have a precise and determinist approach in sample realisation . Additionally, the size of each scattering particle would be bigger  compared to what is usually used in optical frequencies , therefore rendering samples intrinsically more robust to thermal and mechanical effects. Finally, the combination of THz technology with concepts and methodologies from complex photonics opens up the intriguing (and unexplored) possibility of performing time-resolved, full-wave scattering matrix retrieval experiments.In this work, we theoretically investigate a field-sensitive wavefront shaping methodology to control the spatiotemporal properties of terahertz pulses transmitted through a scattering medium. Our approach combines the field detection capabilities of TDS techniques with the generation of terahertz structured beams through nonlinear conversion of optical beams. Our simulations show how the full access to the coherent properties of the transmitted terahertz field enables defining phase-sensitive evolutionary optimisation strategies to manipulate the carrier-wave properties of THz pulses as they travel through complex media. As in relevant case studies, we considered different wavefront control applications, including spatiotemporal focusing, phase inversion, temporal shifting control, and re-compression of a chirped THz pulse. Quite remarkably, we demonstrated the ability to manipulate the CEP of a single-cycle, CP-stable incident pulse. Controlling the CEP of ultrafast pulses is a highly challenging task in photonics that usually requires the ability to independently control the group and phase velocity of CP-stable pulse or implementing advanced detection techniques such asEthical approval and consent were not required.  The manuscript "Nonlinear field-control of terahertz waves in random media for spatiotemporal focusing" presents a theoretical and numerical demonstration of a technique for the full-wave control of a Terahertz pulse propagating in a random media. In the last ten years, the spatial manipulation of an electromagnetic wave to control its propagation through turbid media has raised many researchers' interest in photonics. This has brought significant improvement in the techniques aimed at overcoming and eventually exploiting the structural disorder at the scale of optical wavelength. At these frequencies, the success of these techniques is mainly due to the availability of spatial light modulators (SLM) that, combined with optimizing algorithms, enabled an approach to the inverse scattering problem and obtained results such as super focusing and imaging through opaque media. In this framework, the novelty of the work authored by Cecconi et al. is to achieve spatio-temporal shaping of ultra-short pulse in the THz range, combining the well-established outcomes obtained to control the spatial distribution of optical field with the advantage of the full-field detection of time-domain-spectroscopy (TDS). Specifically, the Authors propose using an optical SLM to modulate the wavefront of the optical pump that, impinging on the nonlinear crystal that generates the THz pulse, transmits to this latter the modulation. The optimization of such a modulation is obtained by a scheme that foresees feedback, provided by a genetic algorithm, between the pulse transmitted and the pattern to impress on the optical pump .  The Authors simulated some test cases to demonstrate the validity of their theoretical approach and of the proposed scheme to realize it. Specifically by playing with the genetic algorithm (GA) chosen as optimization algorithm, they demonstrate e sub-wavelength focusing of the pulse and simultaneously the ability to control the pulse centre, keeping fix the focusing point. Remarkable is also that, leveraging the phase sensitive TDS detection and by suitable choice of the fitness function of the GA, they succeed in optimizing the spectral shape of the pulse transmitted by the disordered sample performing a control on the chirp of the pulse and of its carrier-envelope-phase. The work is reported with accuracy and provides details helpful to interested researchers to implement the clever strategy proposed for other applications in the THz range.  The work also raised a series of interesting question to address in future as the existence of a disorder threshold to use the methodology. I'm also wondering if it was possible to implement the technique to obtain multi-point focusing by translating the collection system in order to obtain a scan of the output surface.I don't understand the meaning of the infinity symbol in Eq.(4).Some misreferences to the figures in the text.  - In the second paragraph of the Results, on page 5, the Authors refer to Figure 2e for the spectrum of the incident beam. I think that the correct reference figure is Figure 2d. - In the second paragraph on page 7, the Authors refer to Figure 3b for the pulse centre. I think that the correct reference is Figure 3c.In the title of the second subsection of the "Results", I think the CEO has to be changed in CEP. Below I report some minor revisions that the Authors could address in the text:Is the study design appropriate and does the work have academic merit?YesIs the work clearly and accurately presented and does it cite the current literature?YesIf applicable, is the statistical analysis and its interpretation appropriate?YesAre all the source data underlying the results available to ensure full reproducibility?YesAre the conclusions drawn adequately supported by the results?YesAre sufficient details of methods and analysis provided to allow replication by others?YesReviewer Expertise:Photonic of complex systemsI confirm that I have read this submission and believe that I have an appropriate level of expertise to confirm that it is of an acceptable scientific standard. We are glad that the reviewer appreciated the work we have performed, and we thank the reviewer for their positive assessment. In relation to the interesting suggestion to obtain multi-point focusing , in our approach, it is possible to focus the THz pulse in different spatial target points by writing different cost functions related to different spatial positions. The ability to manipulate different points of the scattered field is indeed a key advantage of using an iterative optimisation algorithm, and it could enable us to find the optimal patterns producing foci in different points. We note, however, that in actual experiments finding an optimal solution far away from the centre of the optical path might be more challenging. In the presence of non-uniform illumination, for example, points close to the edge of the illumination region might be characterised by a lower signal-to-noise ratio. To clarify this point, we added the sentence “While our analysis was conducted by considering a target focal point placed in the centre of the optical path, the use of an iterative optimisation approach enables, in principle, to select different points on the output plan. In practical terms, this would correspond to modifying the cost functions in Table 1 to consider the scattered electric field at different positions. We note, however, that in real-life experiments, the ability to obtain an optimal solution at any point on the output plane might be restricted by the properties of the scattering medium and the uniformity of the optical illumination.” in the Discussion and Conclusions section. Please find below our point-by-point answer to the further suggestion for revision: 1) Regarding the infinity symbol in equation (4), it is a rendering error when generating the PDF. We thank the reviewer for pointing it out and have amended it in the new version. 2, 3) Thanks for the note; we have corrected the references. 4) Regarding the title of the second subsection of the ‘Results’, the Referee is correct. We changed it to ‘Field-sensitive spectral shaping: chirp and CEP control’. The manuscript "Nonlinear field-control of terahertz waves in random media for spatiotemporal focusing" describes a theoretical and numerical work describing an innovative implementation of super focusing in scattering disordered media in the terahertz frequency band. Imaging and tight focusing directly inside disordered media was assumed to be impossible mostly due to the multiple scattering events making the photon path almost impossible to predict. However since the scattering processes remain coherent and time reversible, works of the past decades showed that thanks to an inverse problem approach one can retrieve information at a very high resolution. Such an approach had several theoretical outcomes and applied consequences as in Optical coherence tomography. One of the key levers to achieve such an approach is to control the shape of the wave front of the beam. The author of the papers propose a very smart way to do it using nonlinear generation of Terahertz radiation and instead of imprinting the pattern on the THZ beam they proposed to imprint it on the infrared beam used to generate the THz through nonlinear optics effect. In this way, one only needs conventional spatial light modulators and not THz ones. The manuscript provides numerical analysis based on simulated scattering samples showing subwavelength focusing on a broad band. Not only that but the authors managed to focus, but they also shifted the pulse to a desired time delay in a few picoseconds range and modulated the carrier envelope phase. The conclusions are well supported and the text is very clear. This work is a real advance in the field and would suggest many questions among them : If scattering is more and more understood in the visible and near infrared with scatterers corresponding to this wavelength range, it is less the case for the scatterer in the THz frequency ranges. The model proposed are well known in the higher energy band but I wonder if they have already been applied in the THz since ref 37 to 40 of the papers does not discuss it. In other words, are there any arguments for this model to work in the THz range especially compared to the analysis in ref 37? Is it possible to focus the THz spot elsewhere than in the middle of the optical path?Is the study design appropriate and does the work have academic merit?YesIs the work clearly and accurately presented and does it cite the current literature?YesIf applicable, is the statistical analysis and its interpretation appropriate?Not applicableAre all the source data underlying the results available to ensure full reproducibility?YesAre the conclusions drawn adequately supported by the results?YesAre sufficient details of methods and analysis provided to allow replication by others?YesReviewer Expertise:Terahertz PhotonicsI confirm that I have read this submission and believe that I have an appropriate level of expertise to confirm that it is of an acceptable scientific standard. We thank the reviewer for the thorough analysis of our manuscript and their positive assessment of our results. In the following, we address the reviewer’s comments: 1) Thanks for the interesting question. As correctly pointed out by the reviewer, there are no experimental studies on the broadband transmission matrix representation of a scattering medium at THz frequencies. In the state-of-the-art (cf. Refs. 37-40), researchers have mostly analysed the scattering response in terms of average diffusion models by collecting the total transmitted field at the output. A key challenge in obtaining a full transfer matrix representation of the scattering is the requirement of resolving the scattered electric field in space, which is extremely challenging in THz experiments. At optical frequencies, however, it has been shown that the transfer matrix representation is equivalent to the diffusion approximation results for a space-dependent response. The transfer matrix framework,  in general, is derived and validated in accordance with the diffusion approximation [R1]. The experimental validation of our transfer matrix model will be the subject of our future work. Our objective in this manuscript is to review the theoretical implications of time-resolved, field-sensitive detection for manipulating broadband THz pulses, and until now, no complete, field-based wavefront control methodology has been developed for manipulating broadband pulses at THz frequencies. 2) We thank the author for raising this excellent point. In our approach, it is possible to focus the THz pulse in different spatial target points by writing an appropriate cost function. The ability to manipulate different points of the scattered field is indeed a key advantage of using an iterative optimisation algorithm. In practical terms, this would correspond to changing the desired focal point where E0 is calculated or expressing different cost functions for different points at the output. We note, however, that in actual experiments finding an optimal solution far away from the centre of the optical path might be more challenging. In the presence of non-uniform illumination, for example, points close to the edge of the illumination region might be characterised by a lower signal-to-noise ratio. To clarify this point, we added the sentence “While our analysis was conducted by considering a target focal point placed in the centre of the optical path, the use of an iterative optimisation approach enables, in principle, to select different points on the output plan. In practical terms, this would correspond to modifying the cost functions in Table 1 to consider the scattered electric field at different positions. We note, however, that in real-life experiments, the ability to obtain an optimal solution at any point on the output plane might be restricted by the properties of the scattering medium and the uniformity of the optical illumination.” in the Discussion and Conclusions section.   [R1] S M Popoff, et al., 2011 New J. Phys. 13 123021. DOI 10.1088/1367-2630/13/12/123021


This paper presents a method for estimating the position of a target under jammed conditions using the Time Difference of Arrival (TDOA) method. The algorithm utilizes a deep neural network to overcome the challenges posed by the jammed conditions. The simulations and results indicate that the presented method is more accurate and efficient than the traditional TDOA methods. Time Difference of Arrival (TDOA) is a technique used to determine the location of a transmitter by measuring the time difference of arrival (TDOA) of a signal at multiple receivers. TDOA location estimation is based on the principle that the signal from the transmitter will arrive at each receiver at a slightly different time due to the distance between the transmitter and the receivers. By measuring the time difference of arrival of the signal at each receiver, it is possible to determine the transmitter’s location. TDOA location estimation can be performed using either a time-based or frequency-based approach. In a time-based approach, the time difference of arrival is directly measured by comparing the signal arrival times at each receiver. This can be done using high-precision clocks to measure the arrival time of the signal at each receiver. In a frequency-based approach, the frequency difference of arrival is measured and used to calculate the time difference of arrival. This can be done by measuring the frequency shift of the signal due to the Doppler effect caused by the relative motion between the transmitter and the receivers. TDOA location estimation can also be performed using either a single-tone or a multi-tone approach. In a single-tone approach, a single frequency is used for the transmitted signal, while in a multi-tone approach, multiple frequencies are used. The use of multiple frequencies allows for the use of frequency-based TDOA estimation, which can be more accurate than time-based TDOA estimation in certain situations.One of the challenges in TDOA location estimation is the need to accurately synchronize the clocks of the receivers, as even small clock errors can significantly impact the accuracy of the TDOA measurements. To mitigate the impact of clock errors, TDOA location estimation can be performed using a network of receivers rather than a single receiver, which allows for calculating clock error compensation values.Another challenge in TDOA location estimation is the presence of multi-path interference, which occurs when the transmitted signal takes multiple paths to reach the receivers due to reflections off of nearby objects. This can cause errors in the TDOA measurements and degrade the accuracy of the location estimation. Multi-path interference can be mitigated through the use of advanced signal processing techniques such as matched filtering and least squares estimation .TDOA location estimation can also be affected by the presence of noise and interference in the environment , which cA key challenge with contemporary radar systems is their requirement for high spatial resolution, which necessitates the use of wide-band sampling. However, the transfer of sampled signals to a central processing node can be an arduous and demanding task. While optical links can be utilized to aggregate several receiving nodes, such an approach is often impractical. To address this issue, this paper presents a novel method that employs a deep neural network to compress the sampled signal into a latent space, which can then be transferred to a central processing node for data processing, where the signal is expanded and analyzed.Furthermore, the incorporation of convolution layers in the neural network enables the system to be robust against jamming. This approach is explored in the subsequent sections of this paper and evaluated using the constructed simulator.Overall, TDOA location estimation is a powerful tool for determining the location of a transmitter in a wireless communication system, with applications in a wide range of fields, including military and defense, transportation, and emergency response. Ongoing research in TDOA location estimation aims to improve accuracy, reliability, and efficiency, as well as to explore new applications and integration with other technologies.TDOA location estimation can be traced back to the early 20th century with the development of the hyperbolic positioning system by Marconi and Braun in 1903. In the 1950s, the development of radar systems led to the use of TDOA for target tracking and location estimation  for sateTwo techniques for three-dimensional target localization using bistatic range readings from several transmitter-receiver pairs in a passive radar system were first introduced by Malanowski and K. Kulp in 2012. The algorithms, called spherical interpolation (SI) and spherical intersection (SX), are based on methods used in TDOA systems and use closed-form equations. The paper includes a theoretical accuracy analysis of the algorithms, verified through Monte-Carlo simulations and a real-life example .In 2015 A. Noroozi and M. A. Sebt presented a closed-form weighted least squares method for determining the position of a target in a passive radar system with multiple transmitters and receivers using TDOA measurements. The method involves intersecting ellipsoids defined by bistatic range (BR) measurements from various transmitters and receivers. The localization formula is derived from minimizing the weighted equation error energy. To improve the method’s performance, the paper proposes two weighting matrices, one leading to an approximate maximum likelihood (ML) estimator and the other to a best linear unbiased estimator (BLUE). The paper includes numerical simulations to support the theoretical developments .An improved approach for localizing a moving target utilizing a noncoherent multiple-input multiple-output (MIMO) radar system with widely dispersed antennas was presented in 2016 by H. Yang and J. Chun. The method is based on the two-stage weighted least squares (2SWLS) approach but only requires a single reference transmitter or receiver and can easily incorporate time-of-arrival (TOA), frequency-of-arrival (FOA), TDOA, and frequency-difference-of-arrival (FDOA) data. The authors also introduce auxiliary variables to improve numerical stability and demonstrate that their method is more stable than the Group-2SWLS method while achieving the Cramer–Rao lower bound (CRLB) at higher noise levels .In 2017 A. Noroozi and M. A. Sebt presented a method for estimating the location of a single target using bistatic range measurements in a multistatic passive radar system. The proposed method uses a weighted least squares (WLS) approach to eliminate nuisance parameters, which are parameters that are unknown and cannot be estimated from the data, and to obtain an estimate of the target location. The method involves several WLS minimizations, and two different weighting matrices are derived to improve the method’s performance. One of these matrices leads to the maximum likelihood estimator (MLE), while the other leads to the best linear unbiased estimator (BLUE) .In 2020 F. Ma, F. Guo, and L. Yang addressed the problem of directly determining the positions of moving sources using the received signals. Traditional methods for localization of moving sources involve two steps. To identify the location of the moving sources, estimations of the intermediate TDOA and FDOA characteristics are performed. In contrast, the authors propose a new method that directly estimates the locations and velocities of moving sources from the received signals. To solve the problem of simultaneously estimating the high-dimensional unknown parameters, the authors propose a multiple particle filter-based method, in which the positions and velocities of the moving sources are updated alternately using separate local particle filters. The proposed method requires fewer particles compared to classic particle filters, and its convergence is proved both theoretically and numerically. The Cramer–Rao lower bound for the proposed moving source localization method is also developed. Simulation results show that the proposed method is computationally efficient and accurate in estimating the positions of moving sources .A method for calculating the location characteristics of a moving aerial target in an Internet of Vehicles (IoV) system employing space-air-ground-integrated networks was proposed by Liu et al. in 2022. (SAGINs) . The proIn recent years, advances in signal processing algorithms and machine learning techniques have led to improved accuracy and efficiency in TDOA location estimation. TDOA location estimation has also been integrated with other location estimation techniques, such as angle of arrival (AOA) and signal strength (RSS) measurements, to improve accuracy and reliability ,14,15.TDOA location estimation is now used in a wide range of applications, including military and defense, transportation, emergency response, and the development of advanced technologies such as autonomous vehicles and smart cities. In the future, TDOA location estimation is expected to play a key role in developing intelligent transportation systems and advancing communication technologies such as 5G and beyond. Ongoing research in TDOA location estimation aims to improve accuracy, reliability, and efficiency, as well as to explore new applications and integration with other technologies. Some of the current areas of research in TDOA location estimation include the development of advanced signal processing algorithms, the use of machine learning techniques, and the integration of TDOA with other location estimation techniques such as AOA and RSS measurements.Passive electronic support measurement tracker (PET) systems are also known as passive surveillance systems (PSS), and their principles and technology are highly similar to radar technology from a passive radar point of view . Many PEAll receiving stations are placed in terrain with radio visibility towards the target, and the exact coordinates  applied ,18. The A neural network is a type of artificial intelligence system that is inspired by the structure and function of the human brain. An input layer, one or more hidden layers, and an output layer are only a few of the layers of interconnected neurons or nodes that make up this system. Numerous tasks, including as classification, regression, and function approximation, are carried out using neural networks. They are particularly well-suited for tasks where the input and output are fixed-length, and the relationships between them are well-defined .Neural networks are trained using an optimization algorithm, such as stochastic gradient descent (SGD), which adjusts the weights and biases of the network to minimize the error between the predicted output and the true output. This process is known as backpropagation, which involves propagating the error back through the network and updating the weights and biases in each layer .The capacity of neural networks to learn from and adjust to incoming data is one of its main advantages. They can learn complex relationships between the input and output data and generalize to new data, making them effective at tasks such as image classification and speech recognition .Despite their success, neural networks do have some limitations. They can be sensitive to the quality and scale of the input data and may require preprocessing or data augmentation to achieve good results. In addition, neural networks can be computationally expensive to train, requiring specialized hardware and optimization techniques to achieve good performance .Feed-forward neural networks, recurrent neural networks, and convolutional neural networks are a few of the several types of neural networks. Each type is designed for specific types of tasks and data, and selecting the appropriate type of neural network for a given task is an important consideration in the design and implementation of an AI system .In this research, we suggest combining several neural networks. Since neural networks are nowadays penetrating all fields of science, we wondered if they could have a benefit in TDOA systems. Therefore, in the following paragraphs, we describe in general terms the different neural networks we have used in the design of the network architecture .One layer of neurons or nodes makes up a perceptron, an artificial neural network. Frank Rosenblatt developed it in the 1950s as a way to simulate the learning process of the human brain. Perceptrons are used for various tasks, including classification, regression, and function approximation. They are particularly well-suited for tasks where the input and output are fixed-length, and the relationships between them are well-defined  m, #2 antenna  m, #3 antenna  m, and #4 antenna  m. The carrier frequency is The block diagram describing the principle can be seen in Signals received by antennas can be seen in The neural network is used for two specific tasks. First, it is used to compress the signal from the receiving antenna to the central node. Secondly, it is used for resistance against jamming. For this purpose, the authors have designed RadarNET, as described below. At the input of each antenna node, there is a buffer of 8000 samples, and the output is encoded only to 16 samples. To provide the capability to be scaled, the input node is cloned  to four receiving antennas. The real input signal is injected into the 1D convolution layer, followed by the Max-pooling layer to provide filtration of the artifacts. Then the signal is processed by a LSTM. This series of layers works as a filter—finding specific patterns related exclusively with the reflected radar signals. Then the LSTM cell encodes the filtered signal in to a latent subspace made of 16 real-valued samples representing the features of the reflected signal. The cell remembers values over arbitrary time intervals and compresses the signal further to 16 samples. In general, the input part of the network can be seen as a autoencoder. Another important idea is incorporated in the image, which is to clone coefficients to other input units, the reason being to make on-site implementation possible (implementation directly to a receiving antenna unit). Hence, each antenna node provides 16 samples, that is, 64 samples in total, from 4 receiving antennas to the central node. The structure of the neural network can be seen in The central node collects compressed data from the antenna nodes, then increases the vector size from 64 to 128 samples. This part can be seen as a autodecoder network structure scaling the latent space to 12 samples. The layer is followed by fully connected layers providing a time-difference estimation outputting three samples that represent the time differences. The differences are used in Equation  to calcuTo overcome the challenges posed by a large number of coefficients and memory limitations, the data was loaded and processed on demand. To guarantee the convergence of both the evaluation and training datasets, a dynamic loading strategy was implemented. The data for training was generated anew for each evolution, comprising 200 batches for training and 100 batches for evaluation. The training process employed the Mean Squared Error (MSE) criterion, utilizing the ADAM optimizer within the Keras framework for optimal performance. This approach not only allows for the efficient utilization of computational resources but also ensures that the network’s performance continually improves over time as it processes new and diverse data.To evaluate the proposed algorithm, using neural networks, the simulator for receiving reflected signals from a moving target was created. The scripts written in Python language can be found on GitLab . In the The proposed algorithm was evaluated on a linear trajectory of the target to provide meaningful results. The jammer was strategically located at the position  m. The evaluation results were visually represented in the form of plots in In this paper, a method for estimating the position of a target under jammed conditions using the Time Difference of Arrival method is presented. Additionally, a significant reduction of data transmission between the antenna nodes and the central node is achieved through advanced signal processing techniques. The algorithm utilizes a deep neural network to overcome the challenges posed by the jammed conditions. The neural network employed boasts a highly sophisticated architecture featuring a total of 10,277,763 trainable parameters. Each antenna node has a buffer of 8000 samples at its input, and the output is compressed to only 16 samples. Despite the compression, the network still demonstrates superior performance compared to traditional methods, such as cross-correlation for delay estimation. This approach not only allows for the efficient utilization of computational resources but also ensures that the network’s performance continually improves over time as it processes new and diverse data.Furthermore, the network is designed to be robust against noise and interference, ensuring accurate and reliable results even in challenging jammed environments. The results of the simulations show that the proposed method outperforms the conventional TDOA method in terms of accuracy and computational efficiency. The use of deep neural networks in this application opens up new possibilities for developing advanced signal-processing algorithms for positioning systems and other related fields. The proposed method can be applied to various scenarios, such as indoor and outdoor localization, navigation, and tracking of moving targets.The receiver antennas are distributed in the square perimeter and for convenience, the target is only moving inside. However it is possible to be outside the perimeter. The reader may observe significant maximum position error of the so-called classical method . The claIn this paper, the authors have presented the concept of using a neural network to compress the sampled signal into a latent space, which can then be transferred to a central processing node for data processing, where the signal is expanded and analyzed.Furthermore, the incorporation of convolution layers in the neural network enables the system to be robust against jamming. The network is designed to have an antenna compressing (processing) node with a neural network independent in the field. The compressed signals from several nodes are aggregated in the main node and are analyzed.Many papers, such as Refs. ,13,30, hThe results suggest that the radar with RadarNET is capable of estimating the position of the target even under heavy jamming. In the simulator, the average error of the proposed method is 50% smaller then using the classical approach as described in Ref. . The reaIn conclusion, the scripts used in this paper are readily available on GitLab  for furt