In late 2019, the novel and highly infectious coronavirus SARS-CoV-2 caused a worldwide outbreak of a severe respiratory infectious disease, known as COVID-19. The disease has started in China and turned into one of the worst pandemics in human history. Due to the very fast global spread of the pathogen, COVID-19 is a great challenge for the Public Health Systems. It had led to a variety of severe limitations in private and public life worldwide. There is a lively public debate about possible sources of SARS-CoV-2. This article aims at providing a better understanding of controversial biological and political issues regarding COVID-19. Recommendations are made for possible actions under the umbrella of the World Health Organization and in respect to the Biological Weapons Convention. Coronaviridae (Coronavirus Disease 2019 (COVID-19). Since its official reporting in December 2019 globally, more than 273 Mio cases and more than 5.35 Mio COVID-19 related deaths  are registered . Scientific publications, media reports, and official governmental statements were analyzed to investigate possible solutions for strengthening public health responses to the COVID-19 pandemic. A special focus was put on instruments discussed within the BWC regime and the academic biosecurity community. Possible investigation scenarios based on current international accepted mechanisms and initial steps how to investigate the source of a pandemic like COVID-19 were also elaborated.Several publications conclude that SARS-CoV-2 originated from nature and was not man-made or released accidently from a research laboratory –22. Nevei. the outbreak was a consequence of a laboratory accident?Scientific reports have documented a few accidental coronavirus releases from Chinese laboratories in the past –25. In 2ii. SARS-CoV-2 is a genetically engineered virus?One of the most urgent questions related to the COVID-19 pandemic was, if this infectious disease outbreak was caused by a genetically modified coronavirus. Scientists at WIV indeed conducted extensive research projects on coronaviruses including virus strains closely related to SARS-CoV-2. They used standard methods in virus cell culture as well as genetic engineering. Several manuscripts were published including so-called gain-of-function (GOF) experiments –33. Curr1) The ACE2 receptor-binding domain of the spike protein: This protein is exposed to the viroid surface and acts as a ligand for the host cell angiotensin-converting enzyme 2 (ACE2) receptor. Binding of the viral spike protein to the ACE2 receptor is a key step for virus entry into the host cell , 37.2) The second notable region is a furin cleavage site, which is located at the junction of S1 and S2 subunit of the spike unit. This peptide insertion is involved in the proteolytic cleavage of the spike protein. Enveloped viruses like the coronaviruses require proteolytic cleavage of the spike unit to be able to infect the host cell , 39. SARiii. SARS-CoV-2 was already circulating for longer, but infections were not made public.There are also reports pointing to a much earlier occurrence of SARS-CoV-2 than December 2019, as has been communicated by the Chinese health authorities. There was one case reported from a 55-year-old resident from Hubei province published in the South China Morning Post on 17 November 2019 , 44. FurInterestingly, a possible precursor virus related to SARS-CoV-2 could be the causative agent for the infection of six mineworkers in Mojiang, Yunnan province, in April 2012 , 50. TheIn sum, there is scientific evidence pointing to a natural spillover of SARS-CoV-2, but there is also other evidence supporting manmade sources of the COVID-19 pandemic. Therefore, it is important to investigate thoroughly the COVID-19 outbreak on a sound scientific basis [see for example the critics of Graner et al.  of the pWhich international organization could be taken responsible for the unambiguous investigation of a pandemic outbreak? Independently obtained results of an investigation would ideally be recognized by the international community as a whole. The United Nations (UN) as the largest and most powerful international organization represents 193 countries in the world. In general, the UN could initiate such an investigation  54). As. As54). End of January and mid of February 2020, two WHO-China Joint Missions were carried out. During the first mission, visits of different facilities in Hubei province were conducted. Furthermore, ongoing epidemiological surveillance processes were analyzed. Infection prevention and control measures as well as the deployment of a RT-qPCR test kit for the detection of the new coronavirus were discussed with Chinese officials . EpidemiThe COVID-19 pandemic could act as a model for efficient international assistance and future cooperation in the public health sector and beyond. What emerged evident during the first months of this pandemic is the need for improvements in communication and better-synchronized containment measures by all countries worldwide. In this respect, the delayed reporting of human-to-human spreading of the disease did cost valuable time  before appropriate health protection measures such as social distancing, masks, and isolation of clusters of infected people were put into action. It should be noted that the time required for efficient disease containment measures mandatory for an efficient infectious disease containment might be quite reasonable. This holds even truer in cases where asymptomatic disease carriers already shed sufficient amounts of the virus to initiate new chains of infection. Here, an improved epidemiological – and less political – driven reporting system would allow to keep pace with such dynamic disease outbreaks. In the following section, we contemplate investigative procedures linked to the BWC regime.The Biological and Toxins Weapons Convention (BWC) of 1972 is a multilateral arms control treaty banning the development, production, stockpiling and - in addition to the Geneva Protocol of 1925 - use of biological weapons (BW) . Currentad hoc establishment of large-scale medical infrastructure like field hospitals, and the installation of field laboratories could be used to improve public health systems responses to severe epidemics/pandemics. But most importantly, BWC Member States offering assistance to a country challenged by a disastrous biological event or incident is meant to enhance confidence among States Parties.In particular, Article VII of the ConventionIn 2020, United Nations Secretary-General António Guterres highlighted the danger of a deliberate use of diseases as weapons at a Security Council video conference. Especially, diseases that were deliberately altered to be more virulent or intentional released are of concern, as we are not yet prepared to deal with such viruses on a global scale. The Secretary-General also commented on the requirement of a verification mechanism to implement confidence-building measures within the framework of the convention. The BWC regime should be better prepared to cope with upcoming biological threats by improved preventative measures, enhanced response capacities and effective countermeasures .In case of an alleged use of biological warfare agents, the UN Security Council (UNSC) should have the obligation to take action and to initiate an investigation. However, in the current political situation the UNSC often has difficulties to find consensus on urgent questions related to human safety and security. For example, there is no common understanding within the UNSC on procedures to investigate alleged chemical weapons attacks, e.g., during the Syrian civil war.en detail on how BWC States Parties should act in the event of an abusive spread of pathogens. In the case of alleged use of biological weapons States Parties could approach the UN Security Council (UNSC) and asks for investigation of the complaints, but this procedure has never been evoked and given the political tensions frequently seen in the UNSC it appears difficult to predict the outcome of such an appeal. Negotiations of BWC verification protocol failed in 2001 and currently there are no clear indications for a restart of this process. It would be more than desirable to see an impulse set by the COVID-19 pandemic for BWC Member States to again engage in strengthening of the BWC. At the 2021 BWC Meeting of Experts, the US Under Secretary of State for Arms Control and International Security provided ideas for such a move forward in her statementDue to the absence of any legally binding verification mechanism within the BWC regime there are no procedures implemented The amendment of the BWC by an additional protocol would be another possibility to provide States Parties to react fast and efficient on incidents related to possible uses of BW. Such an addendum could regulate standardized investigative measures and, if necessary, sanctions or obligations of the international community in such an event.Another approach is the UN Secretary-General's Mechanism (UNSGM) mechanism, which was established as a verification instrument of the Geneva Protocol for investigating an alleged use of chemical and biological weapons. UN General Assembly established this mechanism with resolution A/RES/42/37 C (1987). The UN Secretary-General can react on appeals also by single UN Member States in the case of alleged use of chemical and biological weapons. Several Member States of the BWC consider the UNSGM also as a valuable tool for an investigation of unusual outbreaks of infectious diseases in case of a potential alleged use as a bioweapon. Although the UNSGM is currently the key instrument in the international toolbox of the investigation of unusual biological incidents, it is limited to the investigation of the alleged use of bioweapons. In comparison to the strict quality standards within the investigations of chemical weapons, no quality standards are existing for biological weapons. In case of an investigation of the alleged use of a potential bioweapon laboratory results might be therefore easily questioned or even rejected.The idea of activating the UNSGM is not accepted by all BWC States Parties, therefore its final authority to investigate biological incidents would be highly controversial. In 2020 and 2021, for example, Member States of the BWC have attempted to weaken the UNSGM and the power of the UN Secretary-General by submitting working papers and voting on their contents in the First Committee of the UN General Assembly. If a biological event was caused deliberately must therefore be assessed with high confidence before the UNSGM is applied to prevent political damage to this investigative instrument. However, the public debate about the origin of SARS-CoV-2 shows how difficult this might be to achieve. In order to further investigate the possibility of an incidential release of SARS-CoV-2 a transparent investigation would be required. Research at the WIV was partly funded in by the US money and conducted in collaboration with US scientists.In the light of this complex situation, free international scientific exchange of scientists is essential, which is also supported by Article X of the BWC calling upon States Parties to cooperate for the peaceful use of biotechnology. In order to strengthen and cultivate scientific friendships in the areas of relevance to the BWC, a framework should be established. Within this framework scientists could meet and interact more closely – inspired by political questions related to the BWC, but not dominated by political tensions.Cooperation of States under the WHO umbrella to further investigate the origins of SARS-CoV-2 appears to be the most intriguing way forward. Elements of the BWC regime might be give orientation on how to further proceed. In the following, we provide recommendations for an internationally agreeable investigation of the COVID-19 outbreak.Desirably, in agreement with all WHO Member States, a multidisciplinary international task force could be established within a new mandate to take medical, environmental, and biomedical samples in states parties of interest, e.g. China. This task force would be required to obtain and study available information relating to these allegations including interviews. It could further perform or delegate (with the support of the UNSGM laboratory network) the analysis of the beforehand acquired samples. Unfortunately, during the WHO-China joint investigation in 2021, limited capacity to investigate thoroughly resulted in unattainable objectives. In the future, the demand to agree on an mutual accepted mandate will also include a specific framework in which to operate successfully. Moreover, it must be clarified to what extend a country, by the time of an outbreak, would have the obligation to fully support such an investigation. The implementation of an internationally agreed procedure for a WHO investigative mechanism is for sure a most difficult endeavor. Strengthening public health and swift support as well as transparent investigation of severe infectious disease outbreaks should be investigated while considering the responsibility of all states regarding a sustainable global health. However, it would also be important that investigations into a pandemic origin would include a joint effort between WHO member states and experts from the country of interest. These measures could ensure a basis of trust. In addition, the support of the investigation team might assist affected countries with disease surveillance measures. The discussion of an investigated outcome will be held on a neutral and professional level and it must always be assumed that the presumption of innocence applies. If need for action is identified e.g. the improvement of essential laboratory infrastructure and the implementation of an appropriate biosafety and biosecurity management, it should be promoted within the international community .In the BWC regime, there is still an ongoing political debate about the requirement for a verification mechanism. Nevertheless, BWC Member States should take every necessary step to further extend the agreed confidence-building measures by novel approaches including technical means. Another relevant aspect could be fostering international scientific cooperation under the umbrella of the Convention. In this respect, the COVID-19 pandemic could be a trigger for such activities. Clearly, a naturally occurring infectious disease outbreak is not a matter for the BWC. But treaty members frequently confirmed that capabilities for the detection of biological weapons attacks must be in place before such an incident might take placeIn the hypothetical case of the unintended release of a pathogen from a laboratory or biotechnological installation subsequently leading to an epidemic/pandemic, it is of utmost importance to quickly identify the corresponding facility. A network of governmental laboratories working at BSL-3 or even BSL-4 level would be of help. A database of research capabilities of these labs could be established. Database entries should focus on biosafety and biosecurity assessments of the work but would give no exact details about sensitive information in order to respect intellectual property and national security concerns. Network members could provide guidance how to monitor research activities of the listed labs, for example, in the context of a still-to-come Scientific Advisory Board of the BWC. Moreover, such mechanism could improve international standards in biosafety and biosecurity and ultimately support an open scientific exchange within the international community . BuildinThis process could be started by organizing scientific conferences organized by a UN organization , which would be focused on various fora for a rather informal personal exchange between scientific and technical experts, politicians and diplomats. The idea is that there are no diplomatic constraints within the discussions of scientists. The annual BWC Meeting of Experts could be used as template for such conference, which would be held readily in advance to the next BWC Review Conference. At the scientific conference and in support by a newly founded science advisory board of the BWC working groups could be set up. Tasks of relevance to the BWC would include assessing the impact of new (bio-)technologies, requirements for internationally agreed safety and security standards in biological laboratories. Furthermore, internationally agreed standard procedures for the epidemiological and bioforensic investigation of outbreaks caused by the potential misuse of pathogens.The mechanisms outlined above would allow for an improved open exchange on developments in science and technology between the three BWC regional groups . Precondition for the proposed measures is, of course, the political will to further develop the BWC regime in a cooperative manner. Nevertheless, an enhanced scientific exchange along with better opportunities for less well-equipped BWC States Parties to participate and benefit from this process might increase the political commitment to the BWC regime including the required financial support.The COVID-19 pandemic exposes frictions in the international system to counteract biological threats. Loss of confidence in internationally agreed mechanisms for reporting, monitoring and management of epidemics/pandemics is of great concern, especially for the WHO. Lack in transparency and delayed reporting of key epidemiological and biological data by some states in the course of the emerging COVID-19 pandemic clearly showed the need for improving international mechanisms counteracting biological threats. In the view of the current tense political situation, which is marked by mutual allegations of inappropriate COVID-19 countermeasures and negligent inadequate monitoring measures in biosafety and biosecurity between leading countries, the return to cooperative action for an unbiased SARS-CoV-2 outbreak analysis following scientific standards is highly desirable. In this respect, re-strengthening of the role of the WHO and its investigative mechanisms would be of utmost importance. The BWC, being primarily an arms control treaty, offers rather an outline than detailed practical steps to be taken for the analysis of unusual infectious disease outbreaks. Instruments such as the UNSGM could provide valuable tools for performing required scientific and technical analyses without necessarily triggering the mechanism. Nevertheless, there is still no internationally accepted running workflow how to perform the bioforensic investigation of pandemic outbreaks. The international community should take the responsibility for improving and protection global public health by activating relevant political instruments, which are designed for that very purpose.All authors listed have made a substantial, direct, and intellectual contribution to the work and approved it for publication.The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.All claims expressed in this article are solely those of the authors and do not necessarily represent those of their affiliated organizations, or those of the publisher, the editors and the reviewers. 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In this study, a novel collaborative method is developed to optimize hybrid sensor networks (HSN) for environmental monitoring and anomaly search tasks. A weighted Gaussian coverage method hs been designed for static sensor allocation, and the Active Monitoring and Anomaly Search System method is adapted to mobile sensor path planning. To validate the network performance, a simulation environment has been developed for fire search and detection with dynamic temperature field and non-uniform fire probability distribution. The performance metrics adopted are the detection time lag, source localization uncertainty, and state estimation error. Computational experiments are conducted to evaluate the performance of HSNs. The results demonstrate that the optimal collaborative deployment strategy allocates static sensors at high-risk locations and directs mobile sensors to patrol the remaining low-risk areas. The results also identify the conditions under which HSNs significantly outperform either only static or only mobile sensor networks in terms of the monitoring performance metrics. Sensor networks are the focus of an increasingly vigorous research area with extensive applications in environmental monitoring and anomaly detection ,2, in maThere are three challenges in the current research on HSNs. First, the deployment strategy of HSN does not fully consider the collaboration between static and mobile sensors, and optimization has not yet been investigated for the portfolio mix of the two types of sensors under cost constraints. Second, the currently adopted environment models are fairly basic with static fields, uniform risk distribution, and a disk-shaped sensing model. Real environments that require monitoring are more complex and rarely conform to these simple assumptions. Third, general performance metrics, such as coverage percentage and communication efficiency, are generally adopted to evaluate the sensor networks. What is missing are more direct assessment in terms of the optimal monitoring performance for specific applications, such as anomaly detection time. A more detailed discussion of the related work is provided in The work focuses on the design and optimization of collaborative hybrid sensor networks (HSNs). This work addresses the aforementioned open issues for general sensor networks. More specifically, a novel collaborative method is developed and validated to optimize HSNs for environmental monitoring and anomaly search tasks. A weighted Gaussian coverage (WGC) method has been designed for the static sensor allocation, and the Active environmental Monitoring and Anomaly Search System  has beenThe results (1) demonstrate that the optimal collaborative deployment strategy allocates the static sensors at high-risk locations and directs the mobile sensors to patrol the remaining low-risk areas; (2) identify a set of conditions under which HSNs significantly outperform purely static and purely mobile sensor networks in terms of the ultimate monitoring performance; (3) establish how the cost constraints and mobile sensor speed affect the optimal sensor portfolio.A general optimization problem is formulated for HSNs with static and mobile sensors and solved to identify the optimal portfolio mix and its main drivers.A collaborative deployment strategy of HSN is developed to improve the monitoring performance in complex environments with obstacles and non-uniform risk distribution.A realistic simulation environment is built to provide a more direct assessment of the ultimate performance objectives of monitoring and anomaly search tasks.The main contributions of this work are the following:The remainder of the article is organized as follows. A literature review is provided in The design of HSNs can be naturally classified into two parts: a static sensor allocation part and a mobile sensor path planning part. The questions in the introduction indicated the need for a collaborative combination of these two parts. Most previous works considered the collaboration between mobile sensors only ,19, or jAnother important aspect that has not received adequate attention in the literature is the environment model. Previous works generally assumed a simple environment and focused on sensor networks. For example, refs. ,23 invesTo evaluate the performance of monitoring sensor networks, previous works proposed several metrics, which can be divided into three general groups, as follows: sensor coverage, network connectivity, and energy efficiency . For exaTo address these three challenges, in this work, first, a general optimization problem for HSN with static and mobile sensors is formulated. Second, a collaborative HSN deployment strategy is developed to improve the monitoring performance in complex environments with obstacles and non-uniform risk distribution. Third, a realistic simulation environment is built to provide a direct assessment of the ultimate objectives of specific monitoring and anomaly search tasks.In this section, a general optimization problem for HSN is formulated. Curious readers may refer to The objective of this work can be succinctly expressed as follows: to design and optimize the performance of a hybrid sensor network (HSN) by collaborative static sensor allocation and mobile sensor path planning. Before elaborating on the specific research objectives, the main design parameters considered  and assuFirst, the cost parameters are considered. The total budget for the sensor network is set as Second, the sensor portfolio parameters are considered. The number of static and mobile sensors in the sensor network are defined as Note that for environments with an arbitrary size, sensor density is a more appropriate parameter to describe the quantity of sensors. Since the focus here is on one environment with a fixed size, sensor density is considered to be the same as sensor number, and they are used interchangeably in the later discussion. Given the linearity of Equation (1), the iso-cost curve in the Having established these design parameters, the problem formulation is presented. Previous works have generally formulated the design of sensor networks as optimization problems ,32,36. IA sensor portfolio Next, Equation (3) has been simplified to an equivalent optimization problem. Since the optimal performance is achieved by using the maximum budget The optimal portfolio mix There are three research objectives. First, to devise a collaborative sensor deployment method  sensors ,37. The ortfolio ,38. In tThe design of the deployment method Note that the focus here is on the first research objective (O1). The sensor portfolio The HSN deployment method consists of two parts, static sensor allocation (SSA) and mobile sensor path planning (MSPP). The high-level HSN architecture is shown in Most realistic environments have a non-uniform risk map. For example, cooking in the kitchen, electric heaters in the bedrooms, and dryers (wherever they are placed) exhibit a higher risk of fire. With this observation, the collaboration between static and mobile sensors is achieved by allocating the static sensors at high-risk locations and utilizing the mobile ones to patrol the rest of the area. In the absence of a risk map or for an unknown environment, the default method is to use a uniform risk map, which is a special feature of the more general solution. The following discussion addresses HSN deployment problems with a uniform and non-uniform risk map.A weighted Gaussian coverage (WGC) metric is designed to solve the SSA problem. The active monitoring and anomaly search system  is adaptIn this subsection, the first step of the deployment method is discussed, which is static sensors allocation. Previous works studied the uniform sensor allocation problem ,40. ThisThe sensor coverage To address these drawbacks, a weighted Gaussian coverage (WGC) is proposed as shown in Equations (8)–(10):First, at each sensor location ch as A* . Figure After the static sensors are allocated, the active monitoring and anomaly search system (AMASS)  is adaptAs shown in The last piece of information, the anomaly risk The reward function is formulated by the extracted information with a balance of exploitation and exploration: A critical problem for a system of mobile sensors is the possibility of multiple sensors being in the same location. Crowded mobile sensors result in system inefficiency and have higher risk of collisions. The computational complexity of the global optimum path planning for a multi-agent system increases exponentially with the number of agents . PracticThe dynamic value iteration method  is used This concludes our discussion on the collaborative HSN deployment method by combining the static sensor allocation and mobile sensor path planning. In the next section, the simulation environment developed for the application and the performance metrics used for the sensor networks are discussed.In The application is for temperature monitoring and fire detection in a 2D multi-room apartment. The floorplan of the apartment is shown in There are three key characteristics of this application. First, the temperature field is dynamic. The purpose of building the simulation environment is to obtain a dynamic temperature field inside a room when a fire event occurs. A conduction heat propagation process is adopted to simulate realistic indoor conditions . A detai47 ℃ . The senNext, the performance metrics that are used as the objective functions are discussed.As noted in the introduction, previous sensor network deployment methods focused on improving sensor coverage, network connectivity, and energy efficiency. However, for a given application in a complex environment, the aforementioned metrics do not necessarily reflect the ultimate aim of the monitoring tasks, such as detection time and state estimation error. In this work, the three performance metrics listed in First, detection time lag represents the temporal sensitivity of the sensor network. Early detections grant people more reaction time. Second, alarm distance indicates the spatial uncertainty of the anomaly source when it is detected. The reasoning behind using this metric is that when an alarm is triggered, the source of the anomaly is often uncertain. For example, it took several months to localize the source of a leak on-board the International Space Station after its detection . It willNote that calculating these metrics requires the ground truth provided by the simulation environment. These metrics serve as an evaluation of the sensor network for the testing purpose.Next, these three metrics are used as the objective functions to evaluate the performance of the sensor networks.In this section, the results of the computational experiments are discussed in light of the three research objectives O1–O3 discussed in In this example, 6 static sensors and 2 mobile sensors with a moving speed of In this example, all six static sensors are located at high-risk locations. The sensors are allocated this way to achieve the highest weighted Gaussian coverage (WGC). The two mobile sensors are set to avoid each other as well as the static sensors to explore the environment more efficiently. This simple result illustrates how the static sensors can be used to monitor fixed high-risk locations, and the mobile sensors can patrol a larger area that has a dynamic risk uncertainty. The fire is detected after 14 min because the heat transport is relatively slow under the defined conditions. This level of performance is compared with other sensor portfolios in the following experiments and optimal portfolios are identified under various cost conditions.The optimization of the sensor portfolio is a central problem for HSNs with cost constraint. It is important to determine the benefit of adding each type of sensor and to balance the tradeoffs between them. A performance saturation point can be reached when adding sensors of the same type beyond a certain point. The performance of a large combination of different sensor numbers Adding more sensors of any type will improve all performance metrics. However, this improvement is highly non-linear, and it indicates a decreasing marginal benefit with higher sensor density. Consider curve B (mobile sensors) in The marginal improvement is different for static and mobile sensors  outperform purely static and mobile sensor networks under specific cost conditions. The sensor portfolio mix The speed of the mobile sensors is an important parameter that affects the network monitoring performance. The extent of this effect, however, is not negligible and will depend on the sensor density and portfolio mix in a complex manner. In the previous experiments, the mobile sensor speed was held constant at The performance surfaces for different mobile sensor speeds are provided in A similar general trend is observed for different mobile sensor speeds, such that higher moving speeds generally result in better monitoring performance across the three metrics. To better visualize this performance differential for different speeds, the performance ratio, for example, between In region 1, where both static and mobile sensor densities are limited, the performance ratio is the highest among the four regions when the speed is increased from When comparing region 2 with region 1, the static sensor density is higher. The detection time ratio decreases to around 1.4 because the mobile sensor proportion When comparing region 3 with region 1, the mobile sensor density is found to be higher. The detection time ratio decreases to around 1.6 because of the saturation effect. As discussed in In region 4, both mobile sensor density and static sensor density are high. The performance ratio gradually plateaus, around and below 1.4.Several observations can be made based on the results in In short, higher mobile sensor speed results in better monitoring performance, and that speed has a nonlinear effect on performance, which varies with sensor density and portfolio mix The optimal portfolio mix The most significant result in Beyond these detailed results, it is useful to reflect on the main high-level findings this section demonstrated: (1) that a simulation-based analysis of sensor networks provides a more direct assessment of the ultimate objectives of specific monitoring and anomaly search tasks. It is myopic to restrict the analysis to indirect measures of the performance, such as area coverage; (2) that given specific cost parameters, hybrid sensor networks can provide significant and robust advantages over purely static or mobile sensor networks; (3) that identifying the optimal sensor portfolio mix requires careful analysis and is driven by cost parameters and mobile sensors speed.The analyses and results provided here offer a fruitful basis for significant more developments in the future, and they raise an expansive set of additional questions briefly described in the conclusion.In this work, a collaborative static sensor allocation and mobile sensor path planning method was devised for the design and performance optimization of a hybrid sensor network (HSN). First, a weighted Gaussian coverage (WGC) method was designed for static sensor allocation, and the Active environmental Monitoring and Anomaly Search System (AMASS) was adapted to the path planning problem for the mobile sensors. Second, the optimal sensor portfolio mix was identified under different cost constraints. Third, the effect of mobile sensor speed on the network performance and optimal sensor portfolio was investigated. To analyze and validate the performance of the collaborative deployment method, a realistic simulation environment of fire searching in a 2D multi-room apartment was developed. The results demonstrate that: (1) a simulation-based analysis and the validation of sensor networks provide direct assessment of the ultimate objectives of specific monitoring and anomaly search tasks; (2) given specific cost parameters, collaborative hybrid sensor networks can provide significant advantages over either static or mobile sensor networks; (3) identifying the optimal sensor portfolio mix requires careful analysis and determined by cost parameters and mobile sensor speed.This work addressed several research questions, and it raised a host of others, which point the way toward several future avenues for research. For example, the deployment strategy was developed for the purpose of detecting a single type of anomaly with a single type of sensor . The examination of a heterogeneous suite of sensors, that monitor multiple states and detect multiple types of anomalies , can be performed in future studies. Another important research direction involves not just the performance of the sensing network, but an analysis of its robustness and resilience in the face of different failure types or classes of threats. Such analyses help to further enrich an understanding of sensing network design trade space, and can further strengthen the appeal of hybrid sensor networks.


Grasping the historical volatility of stock market indices and accurately estimating are two of the major focuses of those involved in the financial securities industry and derivative instruments pricing. This paper presents the results of employing the intrinsic entropy model as a substitute for estimating the volatility of stock market indices. Diverging from the widely used volatility models that take into account only the elements related to the traded prices, namely the open, high, low, and close prices of a trading day (OHLC), the intrinsic entropy model takes into account the traded volumes during the considered time frame as well. We adjust the intraday intrinsic entropy model that we introduced earlier for exchange-traded securities in order to connect daily OHLC prices with the ratio of the corresponding daily volume to the overall volume traded in the considered period. The intrinsic entropy model conceptualizes this ratio as entropic probability or market credence assigned to the corresponding price level. The intrinsic entropy is computed using historical daily data for traded market indices . We compare the results produced by the intrinsic entropy model with the volatility estimates obtained for the same data sets using widely employed industry volatility estimators. The intrinsic entropy model proves to consistently deliver reliable estimates for various time frames while showing peculiarly high values for the coefficient of variation, with the estimates falling in a significantly lower interval range compared with those provided by the other advanced volatility estimators. In other words, the dispersion of the price values across the time frame taken into account provides multiple types of information, and is perceived in various ways:These are only a few aspects that naturally derive from following the price variation of a financial instrument in a given time window. This price dispersion over time is identified as the historical volatility of a financial security over a period of time. It has a salient importance in practice for assessing portfolio risk and pricing derivative products . Many diThe most common method used to estimate the historical volatility is the close-to-close method. In this approach, the historical volatility is defined as either the annualized variance or standard deviation of log returns ,3. In orn-period historical data is given by the standard deviation:With these assumptions, the classical volatility estimator based on close-to-close prices of T is considered as being the time frame between two consecutive closing prices: from the previous day closing price until the current day closing price. Since within this interval T there is an “overnight” period of time during which the market is closed, regardless of the meridian on which the particular stock exchange is located, this duration is commonly modeled as a fraction f of the trading interval T. Hence, there is an interval of length Based on close-to-close approach, the trading interval f does not necessarily quantify the time length of the market closing period, but the fraction f is rather meant to model the relative size of the opening jump in comparison to the price evolution during the period of continuous trading. We note that the opening jump may occur due to inclusion of the dividend value when it comes to a traded stock, as in (1) when computing the log returns. Consequently, the notations that we adopt in this paper follow those that were initially used by Garman and Klass ;f, 1];In terms of notations, we follow the seminal study by Yang and Zhang (2000) , as theynd Klass :C0 or Cin-periods T:In addition to the above notations, we introduce the following extensions concerning a succession of equally sized n-period interval T is expressed as:With these notations, the drift or the average of log returns for an With this notation, the classical close-to-close volatility estimator becomes:The classical close-to-close estimator does handle drift , and in the same journal issue as Parkinson, Garman and Klass  proposedThe Garman–Klass estimator includes opening and closing prices for the current trading day. From this perspective, the Both the Parkinson and Garman–Klass advanced volatility estimators assume that there is no drift  based on (4)–(6), we obtain the following form of Rogers–Satchell volatility estimation, which is simply based on the current day open, high, low, and close prices:According to Rogers and Satchell, the Garman–Klass estimator seems to present two major drawbacks: first, the estimator is biased when there is a non-zero drift rate for the stock return in the period, and second, the empirical observations of stock prices are not continuous, as the Brownian motion model approach stipulates . While tn = 1) estimators, whereas the classical n > 1):k in order to minimize the variance of the Yang and Zhang noted in  that VGK in 2000  a new mik can never reach zero or one, and this fact proves that neither the classical close-to-close estimator k applied on Yang and Zhang commented in  that k c weights . Yang anOver the past decades, the use of entropy in modeling various economic phenomena, along with the emergence of econophysics as a scientific discipline , has resWe conceived the intrinsic entropy model initially based on the intraday trading data, namely the execution data generated by the stock exchange matching engine once one buy and one sell orders are put in correspondence . For eact. Let X be a traded symbol on the market. Based on these considerations, the intraday intrinsic entropy model has the following formalization:X at moment t;X in the current trading session up to moment t;k is ordinal trade number;k for symbol X;k for symbol X;X up to moment t, refp is reference price for symbol X, corresponding to the trading data prior to the moment t.With this perspective in mind, the total executed (traded) quantity of a given security is not known until the trading day is over. Therefore, the intrinsic entropy value for a given security is determined every time a new trade is made, and all of the ratios are recalculated for all trades that were made during the day up to the latest one considered at time The ratios The intraday intrinsic entropy model proves to gauge the investors’ interest in a given exchange-traded security. Furthermore, the intrinsic entropy provides an indication regarding the direction and intensity of this interest, either in buying or selling the security. Regarding the employed reference prices, we conclude in  that theIn the case of the intraday trading, the total traded quantity of the entire day is not an a priori known value, hence the intrinsic entropy model proposed for the intraday trading employs ratios that have a moving base. The denominator of the series increases with each exchange-executed quantity for the underlying security:t. We note that t is a timestamp and does not have the meaning of equally distanced time intervals, since it represents the actual moment during the trading day when the trade was made. Similarly, if we compute the Consequently, the value of the fraction becomes smaller as we advance in the trading day and with the number of executed trades, regardless of how big the executed quantity is at any given moment In other words, depending on the direction in which the trading data for the considered period are taken into account, either from the oldest to the most recent or from the most recent to the oldest, the information provided by the traded volume correspondingly favors the older prices or the more recent ones.Employing the price of the preceding transaction as a reference price preserves the atomicity of each trade within the overall pool of transactions that constitute the trading day on the stock exchange. Consequently, a Markov chain is thereby constructed, in which the price of each individual trade is compared only to the price of the preceding trade.n > 1) and on the intrinsic entropy model that we introduced in [We proposed a new unbiased volatility estimator based on multiperiod data —the intrinsic entropy model takes into account the traded volumes during the considered time frame as well.We adjusted the intraday intrinsic entropy model that we introduced earlier for exchange-traded securities in order to connect daily OHLC prices with the ratio of the corresponding daily volume to the overall volume traded in the considered period. The intrinsic entropy model conceptualizes this ratio as entropic probability or market credence assigned to the corresponding price level.The intrinsic entropy is computed using historical daily data for traded market indices . We compared the results produced by the intrinsic entropy model with the volatility obtained for the same data sets using widely employed industry volatility estimators, namely close-to-close (C), Parkinson (HL), Garman–Klass (OHLC), Rogers–Satchell (OHLC), and Yang–Zhang (OHLC) estimators ,19.We consequently studied the efficiency of the intrinsic entropy-based volatility and the other variance-based volatility estimates by comparing them with the volatility of the standard close-to-close estimate. It will be shown that this intrinsic entropy-based volatility model proved to consistently deliver a minimal estimation error, i.e., the minimal variance of the estimates for time frames of 5 to 11 days.T, respectively. The intrinsic entropy-based volatility model uses the constant k determined by Yang and Zhang with the same purpose of weighting the component that handles the opening jumps The intrinsic entropy-based model for estimating volatility follows the Yang and Zhang approach regarding the treatment of the overnight jumps, opening jumps, and the drift manifested during the trading day:n-period interval T. Therefore, the estimator that we introduced is independent of drift  then the volume ratios can be computed using (23). This seems to be a more natural approach from the whole market perspective, given that an n-period interval is not large enough to completely cancel the contribution of the order data. On the other hand, knowing exactly the number of trading days for which one computes the volatility estimator, a simpler and fairer approach may be more appropriate, for example by calculating the overall traded quantity (volume) from the very beginning, and thereafter performing calculations for the fraction of each day’s volume in the total trade volume of the period. In the intrinsic entropy model, the In the case of the historical volatility, the We used the probabilities provided by (23) and (31) throughout this paper to compute the intrinsic entropy-based volatility estimator.Given the fact that the intrinsic entropy-based estimator of historical volatility does not produce results in a comparable range of values with the variance-based estimators, this raises the question regarding how these estimators could actually be compared in a relevant manner that would allow decisive discrimination ,21.We note that the intrinsic entropy-based estimates are consistently in a lower range of values compared to the estimates produced by the other volatility estimators, while changing relevantly from one day to another.The information that is brought in by the daily traded volume and the entropic mechanism through which the intrinsic entropy-based estimations are computed provide for more dynamic changes, although we note that these estimates can offer a more valuable perspective of the overall market evolution for short time horizons. Moreover, the traded volume can be taken into account by investors when focusing on a technical analysis approach ,23,24. Fn day intervals that we considered .We note that the other volatility estimators that we considered in our analysis, namely the classical close-to-close, Parkinson, Garman–Klass, and Rogers–Satchell estimators, exhibited the same pattern as the Yang–Zhang estimator in terms of providing higher estimates than the intrinsic entropy-based one, and all showed little change of volatility on a daily basis. Furthermore, this pattern is reflected in the volatility estimates computed for all the stock market indices that we took in account  and for all the n-period intervals, going back from 31 January 2021: 5, 10, 15, 20, 30, 60, 90, 150, 260, and 520. The estimates are computed on a daily basis, by rolling back n-period time windows, corresponding to the considered intervals.We now present our empirical findings and compare the estimates produced by the intrinsic entropy-based volatility model against the volatility provided by the classical close-to-close, Parkinson, Garman–Klass, Rogers–Satchell, and Yang–Zhang estimators. We considered for this comparison the historical daily trading data for S&P 500, Dow 30, NYSE Composite, NASDAQ Composite, Russell 2000, Hang Seng Index, and Nikkei 225 indices. The estimates are computed for the following As the intrinsic entropy-based model of volatility consistently delivers lower estimates for each time interval and stock market index, we first investigated the following set of indicators to serve for the purpose of comparison, namely the average (Mean), variance (Var), and coefficient of variation (CV).These indicators are computed for each volatility estimator Mean, Var, and CV of volatility estimates computed for all of the volatility estimators considered for the following stock market indices: Dow 30, NYSE Composite, NASDAQ Composite, Russell 2000, Nikkei 225, and Hang Seng Index. We emphasize the fact that the volatility estimates provided by the intrinsic entropy consistently show the mean in a lower value range, while the coefficient of variation (CV) confirms the earlier observation that the intrinsic entropy estimates change on a daily basis. These empirical results were replicated for all of the stock market indices observed and all of the time intervals considered.In n-period time interval, these functions have the following representations, where i in the interval:The empirical evidence shows that the volatility estimates based on intrinsic entropy fall in lower value ranges for all of the stock market indices and the time intervals considered; a comparison established on a referential indicator might be worth investigating. In particular, we highlight Molnar, who mentioned in  the meanWe note that not having access to the true, unobserved volatility of the market In addition to the MSE and PB indicators, we note the volatility estimators’ efficiency. The efficiency of an estimator is defined as the variance of a benchmark estimator divided by the variance of that particular estimator:We note that the intrinsic entropy-based estimator’s efficiency is consistently higher than the other volatility estimators, particularly for short time intervals of between 5 and 11 days, representing roughly one to two weeks of trading. In order to explore this observation in more detail, we computed the volatility estimators’ efficiency for a series of successive time intervals from 5 to 20 days, along with a 30 day window. We note that the volatility estimators’ efficiency was not consistent with regard to the stock market indices. The empirical data show no volatility estimator as having the best efficiency for all market indices considered in our analysis. For example, In In We cannot precisely pinpoint the unit of measure for the intrinsic entropy-based estimation of volatility. We perceive this aspect as a limitation of the estimator in the sense that it does measure the dispersion of daily price changes with respect to the daily traded volumes, but not as a pure variance-based estimator; its estimates cannot be directly compared to other volatility estimators that we considered in our research. It does offer a higher coefficient of variance for a lower mean of the estimates, which may suggest a better purpose for its usage as an investment decision support tool, rather than a descriptive reporting tool for historical volatility.From this different perspective of market volatility, we note that the intrinsic entropy-based volatility estimates may have a more useful role in emphasizing the fractured nature of the market ,29. RobeLevy also commented in  that theThis paper presents the results from employing the intrinsic entropy model for volatility estimation of stock market indices. Diverging from the widely used volatility models that take into account only the elements related to the traded prices, —namely the open, high, low, and close prices of a trading day (OHLC)—the intrinsic entropy model includes the traded volumes during the considered time frame as well. We adjusted the intraday intrinsic entropy model that we introduced earlier for exchange-traded securities in order to connect daily OHLC prices with the ratio of the corresponding daily volume to the overall volume traded in the considered period. The intrinsic entropy model conceptualizes this ratio as an entropic probability or market credence assigned to the corresponding price level. The intrinsic entropy is computed using historical daily data for traded market indices . We compared the results produced by the intrinsic entropy model with the volatility obtained for the same data sets using widely employed in the markets volatility estimators. The intrinsic entropy model proved to consistently deliver lower volatility estimations for various time frames we experimented with, compared with those provided by the other advanced volatility estimators. We note that while producing estimates in a significantly lower range compared with the other considered volatility estimators, the intrinsic entropy-based volatility offers consistently higher values for the coefficient of variation of its estimates. The tests that we conducted using historical trading data concerning the major international stock market indices provide empirical evidence that the intrinsic entropy-based volatility estimator offers more information regarding the market volatility, particularly for short time intervals of 5 to 11 days of trading data.We comment that the identified limitations of the intrinsic entropy-based volatility estimator, namely the precise nature of its unit of measure and its high variability within a low average of the estimates, could provide a complementary perspective of the market in comparison with the variance-based volatility estimators.


The fast tool servo (FTS) control strategy is the control core of high-speed noncircular turning. This method should ensure high-speed and precision positioning and have the corresponding anti-interference ability in the micro-stroke motion with dynamic changes of tool feed and load. Most of the previous FTS control studies used the repetitive control and speed feedforward control strategy, which achieved promising results under ideal machining conditions. However, this strategy showed some defects in the real-world complex and changeable working conditions such as time-varying cutting force, intermittent cutting and fluctuating machine spindle speed. This paper proposed and implemented a compound proportional integral derivative control strategy based on input feedforward and dynamic compensation in noncircular turning. This technique successfully met the motion requirements of the high responsiveness of micro-stroke in noncircular turning and overcame disturbances from complex time variations of the cutting force, intermittent cutting case of the product and fluctuations of machine spindle speed. According to the findings, the machining tracking error was less than ±2 µm. Experimental results demonstrated the excellent tracking performance and machining effect of this control strategy. U-axis on the X-axis of a typical CNC lathe, with the X-axis performing the preliminary motion and the U-axis performing the high-frequency micro-motion that is synchronised with the spindle rotation and the motion of the Z-axis to cut the noncircular part.The motion characteristics of high-speed noncircular turning necessitate that the fast tool servo (FTS), which performs cutting feed, have high positioning accuracy and dynamic response performance. Importantly, the most challenging control criterion is that the FTS should not only ensure high speed and precision positioning but also have the anti-interference ability in the micro-stroke motion with dynamic changes of tool feed and load. Therefore, the control strategy of FTS in noncircular turning is crucial. Researchers have studied FTS in various ways. Some scholars proposed novel FTS mechanisms to facilitate noncircular turning. They developed a new piezoelectric actuator (PEA)-based FTS mechanism to incorporate additional functions to the general CNC system . DiffereMost previous FTS control studies based on various control strategies, such as speed feedforward control strategy, achieved good results under ideal machining conditions. However, when these strategies were applied to machining in actual working conditions, the machining effect was not ideal due to time-varying cutting forces, intermittent cutting and poor machining accuracy. After comparing the advantages and disadvantages of the speed feedforward control strategy, this paper proposed and applied a compound PID control strategy based on input feedforward and dynamic compensation in noncircular turning. This strategy successfully meets the motion requirements of the high response of micro-stroke in noncircular turning and overcomes disturbances from the time-varying complexities of the cutting force, the intermittent cutting case of the product and fluctuations in the machine spindle speed.U-axis and mounted on the rough-positioned X-axis. Notably, the tool position along the X-axis must be properly synchronised with the spindle position for cutting the noncircular cross-section, which requires a high-speed, high-precision and high-frequency performance of the cutter control device. It is necessary to study the mathematical models of the motor and cutting force for effective control of the FTS.The mathematical model of the linear motor includes the voltage equation, the electromagnetic thrust equation and the mechanical motion equation.A closer look at the motor structure reveals that a rotating motor can be referred to to construct a mathematical model of a permanent magnet synchronous linear motor. The specific idea is to use Clarke transformation to transform the system variable obtained ,19. Figu(1) Voltage equations for a linear motorAccording to the conversion relation of the three coordinate systems shown in  follows :(1){ud=R(2) Electromagnetic thrust equation of the linear motorThe electromagnetic thrust equation of a permanent magnet synchronous linear motor can be expressed as follows:Ideally, the inductances of the (3) Mechanical motion equation of the linear motorAccording to the analysis of the motion force of the linear motor, the mechanical motion equation can be expressed as follows:To sum up, Equations (1), (4) and (5) constitute a brief mathematical model of the permanent magnet synchronous linear motor.The FTS system is a closed-loop system with position feedback driven by a linear motor. The control system uses a three-ring control structure of position, speed and current, with PID/PI/PI as the control mode, respectively. The basic PID control model of the FTS can be obtained via the linear motor mathematical model, as in In Because the cross-section of the noncircular part is usually elliptical, its high-frequency noncircular turning uses the multi-axis control feed mode, as in The equation of the polar diameter  follows :(6)R=a2cIn Equation (6), The tool’s starting position is set at the long axis vertex of the elliptical contour and its initial value is set to zero. The motion trajectory equation of the tool can be deduced as follows:Based on Equation (8), the velocity and acceleration mathematical model of the tool can be calculated further.The turning force of the noncircular surface part is the main interference force, which directly affects the motion control of the cutting tool. In noncircular turning, the cutting force of the tool is uneven and dynamic. However, the force on a static point is similar to that on a normal circular section, which contains tangential force Equation (9) shows that, although the force analysis of noncircular turning is the same as that of the normal turning at a particular moment, the Many researchers combined feedforward and PID control to solve the problem of control lag and improve the tracking effect of the system on the input signal. The closed-loop transfer function of compound feedforward PID control can be expressed as follows:The transfer function of the system control deviation It is necessary to make the control deviation The compensation signal of the speed feedforward is used for improving the response precision of system speed in the control of FTS based on the combination of PID control and speed and acceleration feedforward. The compensation signal of the acceleration feedforward can effectively suppress the overshoot caused by the speed feedforward control.The PID control strategy of velocity and acceleration feedforward can achieve a good control effect when there is no load and no consideration of cutting force. However, the cutting force acting as the main interference constantly changes in the actual turning process. As a result, the PID control strategy of velocity and acceleration feedforward cannot effectively deal with these disturbances. The above experiment analysis shows some nonlinear factors, such as time-varying cutting force and broken cutting, among others, in the noncircular turning process. The PID control strategy with speed and acceleration feedforward is not ideal under load machining; hence, the nonlinear factors in noncircular turning must be considered and solved.Compound feedforward can be divided into feedforward control that is compensated by input and feedforward control that is compensated by disturbance . The inpThe input compensation feedforward control with speed feedforward and acceleration feedforward can achieve a good control effect without considering disturbance in high-speed noncircular turning. In contrast, the cutting tool’s most important disturbance signal (cutting force) can be used for the feedforward control of disturbance compensation according to the pre-calculated dynamic model. Therefore, the compound PID control strategy based on input feedforward and dynamic compensation can achieve a good tracking control effect in high-speed noncircular turning while also meeting the requirements of high response motion control of high-speed noncircular turning.In the noncircular turning process, the cutting force disturbance is compensated on the current ring of the PID controller to achieve a more rapid and effective control effect based on the original input feedforward compensation. As depicted in According to Equation (14), the transfer function At the same time, based on the analysis of cutting force in This paper only studied the cutting force of noncircular turning, which is expressed as follows:If the workpiece is a middle convex variable elliptical piston, then Equation (17) can be further expressed as follows:This section details the machining test based on the compound PID control strategy of input feedforward and dynamic compensation. The dynamic prospective compensation is directly compensated before the current loop of the servo driver after real-time calculation. In the experiment, the middle convex variable elliptical piston of aluminium alloy is taken as the machining object whose main parameters are shown in The compound PID control strategy with input feedforward and dynamic compensation can effectively improve the tracking performance of machining under complex and changeable noncircular turning conditions. (1)The mathematical model of the FTS is proposed to investigate the control method and cutting force. The PID control model of the FTS is derived from the analysis of a mathematical model of a linear motor that includes voltage equation, electromagnetic thrust equation and mechanical motion equation. The force analysis shows that the cutting force is constantly changing because of the changes in speed and acceleration. It can be concluded that noncircular turning is more complex than ordinary turning.(2)The test results show that the machining tracking error is improved from ±14 µm to less than ±2 µm by using the compound PID control strategy based on input feedforward and dynamic compensation. The depth and shallow consistency of the piston skirt are neat and compliant. The findings demonstrate that this strategy fully considers the time-varying complexity of the actual cutting force, the diversity of intermittent cutting and fluctuations in the machine spindle speed. The experimental results also demonstrate that the strategy has a very good tracking performance and machining effect.The control strategy of an FTS is the control core of high-speed noncircular turning. Based on the mathematical model of FTS and a comparison of the advantages and disadvantages of the repetitive control and the speed feedforward PID control in noncircular turning, a compound PID control strategy based on input feedforward and dynamic compensation is proposed in this paper to meet the motion characteristics of high-speed noncircular turning with high response and micro-stroke. The main contributions of this study are summarised as follows: