In this paper, we propose and validate with data extracted from the city of Santiago, capital of Chile, a methodology to assess the actual impact of lockdown measures based on the anonymized and geolocated data from credit card transactions. Using unsupervised Latent Dirichlet Allocation (LDA) semantic topic discovery, we identify temporal patterns in the use of credit cards that allow us to quantitatively assess the changes in the behavior of the people under the lockdown measures because of the COVID-19 pandemic. An unsupervised latent topic analysis uncovers the main patterns of credit card transaction activity that explain the behavior of the inhabitants of Santiago City. The approach is non-intrusive because it does not require the collaboration of people for providing the anonymous data. It does not interfere with the actual behavior of the people in the city; hence, it does not introduce any bias. We identify a strong downturn of the economic activity as measured by credit card transactions (down to 70%), and thus of the economic activity, in city sections (communes) that were subjected to lockdown versus communes without lockdown. This change in behavior is confirmed by independent data from mobile phone connectivity. The reduction of activity emerges before the actual lockdowns were enforced, suggesting that the population was spontaneously implementing the required measures for slowing virus propagation. After appropriate anonymization, CCR provide high-resolution spatiotemporal information on the economic life of the city. The geo-location of credit card transactions is achieved through the Point of Sale Terminal (POST) where the transaction is made, which provides additional information about the economic sector involved in the transaction.There is literature emerging about the observation of the economic impact of COVID-19 through the lens of consumer spending obtained from CCR information. For instance, CCR data from the second biggest bank in Spain shows a sharp v-shape in the aggregated consumption due to the strict lockdown measures imposed by the Spanish government , while tHowever, little research at a microscopic level has been done about the impact on consumer behavior of stay-at-home mandates and other NPI measures. A relevant research question addressed in this paper is whether the NPI anti-COVID-19 measures have induced behavioral changes in the spending habits of the inhabitants of Santiago. We use results from independent studies based on cell-phone calls  to confirm/validate our results ,27. AddiIn this paper, we deal with data from the city of Santiago, Chile, which can be defined at three geographic levels. Administratively, the city of Santiago is organized into communes, the borders of which are shown in Computational experiments were carried out over an anonymized dataset provided by a major Chilean bank collected under strict personal data protection protocols. The study has been approved by the Ethics and Biosecurity Committee of the Facultad de Ciencias Físicas y Matemáticas of the University of Chile. Before being used in this study, customer identifiers, credit card identifiers, and any personal data were removed before entering the data analysis described below. There is no possibility that personal information can be leaked and no result of our analysis can be associated to any particular cardholder because the analysis is only based on the number of transactions made in every time window at each business location.A Point of Sale Terminal (POST) is an electronic device that is used to process card payments at business locations. Each time a customer pays with a credit or debit card, the transaction is processed by the POST and is geographically tagged with the latitude and longitude of the associated business location. Each record in the dataset contains the card type (credit or debit), ID, latitude and longitude of POST where the transaction was made, day and hour of the transaction. Furthermore, the record contains the economic sector related to the company where the transaction was made. The dataset contains credit card transactions made during the years 2017, 2019, and 2020 associated with more than 100 thousand POSTs. Specifically, we have 85, 60, and 45 million credit card transactions for the years 2017, 2019, and 2020, respectively.p over a specified period of time. In this study, we will consider that each p during period t. Then, the raw activity pattern of the terminal p is given by the vector T is the set of activity blocks. In this study, we set T into hourly periods during a week; therefore, each raw activity pattern p processed in the hourly time window t.A POST Activity Pattern (AP) is a vector characterizing the activity of each terminal Using the economic sector information of each POST, we can determine the distribution of card usage over the economic sectors, as shown in In order to visualize the geographical distribution of the volume of transactions, we carry out a spatial aggregation that is the result of imposing upon the city a grid of ll known  that hexUnder this spatial aggregation scheme, we define To better illustrate how different economic sectors are geographically distributed in the area under study, in https://www.statsmodels.org/stable/generated/statsmodels.tsa.seasonal.seasonal_decompose.html) (accessed on 20 May 2021). The trend is obtained by applying a convolutional filter that implements a moving average, and the seasonal component corresponds to the average for each period of the de-trended series. The trend component shows an increment at the end of each month, explained because a significant fraction of Chilean citizens is paid precisely at the end of the month. The trend also shows a moderate increment by the end of the year, associated with Christmas shopping. The seasonal component has a strong weekly frequency. Based on this weekly regularity, we define K activity topics t and p extend over the hours in the week and all POSTs, respectively, without duplicated values. Activity topics are composed of activity blocks, with mixing parameters t of the activity pattern Topic modeling research originates from natural language processing of documents. It is a probabilistic approach for discovering latent topics in a collection of documents. The basic premise is that the words that compose the documents are a linear combination of these latent topics. The most successful technique for topic modeling is the Latent Dirichlet Allocation (LDA) . In thishttps://radimrehurek.com/gensim/) (accessed on 20 May 2021). The LDA discovery of latent topics is unsupervised; therefore, there is no guarantee regarding the order of discovery or the identity of the topics. In order to establish correspondences among topics in different sets, e.g., discovered from data extracted at different times, we use the cosine similarity metric between two activity patterns (AP) defined as follows:To build up the LDA model, i.e., to discover the latent activity topics and the decomposition of the POST activity patterns into them, we used a python implementation provided by gemsim .Topic 0 “residential” is characterized by two high activity peaks during weekdays, localized around lunch and dinner times. Notice that the second peak on Fridays occurs later around 11 p.m., reflecting that people used to have a later dinner on this day. Also notice that the second peak on Sundays is much less pronounced, indicating that citizens were less prone to go out dining on Sunday evening.Topic 1 “leisure/commerce” presents three peaks during the weekdays located at 9 a.m., lunchtime, and around 7 p.m., roughly corresponding to times when people used to commute to or from school or work. During weekends, this pattern is more evenly distributed throughout the day. Notice that there are high activities in the early hours of Saturday and Sunday, corresponding to nightlife habits before the pandemic.Topic 2 “office areas” is characterized by a high and uniform activity during weekdays and less activity during weekends. During the day the main activity is between 09:00 a.m. and 18:00 p.m. and there is increasing activity at lunchtime (13:00 p.m.), corresponding to office areas activity.Topic 3 “rush hour” has peaks that roughly correspond to times when people are moving from or to the working place in office/business areas.The interpretation of these topics is as follows:For further confirmation of the above interpretation of the CCR activity topics, we compare them with CDR activity topics reported in previous analyses of human activity patterns in Santiago . The resk contributes to the overall activity pattern of POST p, such that Additional confirmation of our interpretation of the CCR activity topics comes from the observation of the spatial distribution of the topic in the area of Santiago. Recall that LDA’s output can be interpreted as the degree In order to assess the effect of NPI for COVID-19 on the behavior of the habitants of Santiago, we collected the CCR data in pre-pandemic (year 2019) and pandemic (year 2020) periods. We remind the reader that Chile has been in commune-based lockdown ever since mid-March 2020, so there is no global post-lockdown period. In order to have a picture of the evolution of the activity topics, we proceed to extract the LDA topics ) that may fall into poverty with ensuing systemic health critical issues.The analysis of the CCR data identifies an economic sector that has hardly been hit by the pandemic-induced economic crisis, that of Leisure/Commerce out of the four activity topics identified on the pre-pandemic data. Our results comparing this activity topic in the year previous to the pandemic and the year of the pandemic show that Santiago citizens have changed their behaviors according to the lockdown and curfew policies. Though there is some literature on the disruption of supply chains due to COVID-19 , the impOne of the facts that we have found is the voluntary reduction of activity that was apparent several days before the implementation of coercive measures from the administrations. This result is in agreement with reported voluntary reductions in mobility estimated from the Google human mobility dataset . It seemThis paper shows how the anonymized information about credit card transactions can be used to assess the follow-up and impact of non-pharmaceutical interventions implemented to curb the COVID-19 pandemic. We show how unsupervised latent topic analysis uncovers the main patterns of credit card transaction activity that explain the behavior of the inhabitants of Santiago City. Topics identified in the pre-pandemic year of 2017 are used to identify the topics produced by the analysis in years 2019–2020, including the pandemic. Specifically, we are able to assess the impact on the leisure/commerce sector, which has suffered a strong loss of activity due to the pandemic. Additionally, the examination of the aggregated activity allows assessing significant differences among communes that did impose lockdown from those that did not. Lockdown and curfew interventions lead to a reduction of 70% in credit card transaction activity. Additionally, we found a spontaneous reduction of activity before the implementation of lockdown of the same magnitude of the reduction achieved with the mandatory restrictions. The need for coercive measures to achieve mobility reduction to stop the virus spread may be reexamined in light of these findings. Future works will be directed to the disaggregate analysis of the information of the points of sale according to their nominal industrial activity, in order to ascertain the variable impact of the pandemic on the industry. This analysis will include the distinction between essential and non-essential services. In addition, a detailed analysis of the recovery after lockdown should be carried out independently for each commune.


The aim of this study was to investigate the distribution of crimp in new jacquard fabric structures (in which one-layer and two-layer weaves are combined) in the fabric width and to create a method of crimp prediction. It was established that crimp was around 18.80% and changed within the limits of errors, i.e., a range of only ~4%, in the fabric width. It can therefore be said that the warp crimp was constant in the fabric width. Because the warp crimp of jacquard fabric changed insignificantly (within the limits of errors), it can be stated that the fabric-setting parameters and structural solutions were chosen and matched correctly, and such fabric can be woven on any jacquard weaving loom. There are several definitions of crimp. Percentage crimp is defined as the mean difference between the straightened thread length and the distance between the ends of the thread while in the cloth, expressed as a percentage . The shoWarp and weft crimp percentage are two factors that have an influence on a fabric’s abrasion resistance, shrinkage, and fabric behaviour during strength testing .Physical properties such as elasticity, rigidity, bending behaviour, etc. of fibres and yarns;Count of warp and weft threads;Setting of the threads;Tension on the threads during weaving;Yarn and fabric structure;Physical and chemical treatment of the fabric after weaving .Factors that affect crimp include the following:Crimp frequency, amplitude, crimp stability, crimp elongation, and crimping point are some of the important properties that determine crimp. A fibre’s crimp characteristics have a strong influence on the processing performance of the fibres .The construction of the warp and weft yarns are determined by various factors, such as the type and setting of weaving loom, the weaving conditions , the fabric weave, linear densities, the raw material of the threads, the flexibility of the warp and weft, and the pressure strength of the warp and weft threads in the positions of the floats. Thread crimp changes during weaving, fabric relaxation, and finishing . RecentlWarp and weft crimp is important because it has an influence on weaving technology, warp and weft expenditure, fabric shrinkage during weaving and fabric properties  .During warping, it is important that all warp threads warped on the warp beam are equally taut. This is to ensure that the fabric’s properties during weaving do not change and remain the same throughout the entire fabric length. Without ensuring the same warp system tension across the whole width of the fabric, unequal fabric properties will be obtained. This not only affects the weaving process but can also negatively influence the weaving loom. Uneven tension in the thread system unequally affects their crimp and its distribution in the fabric .Because warp and weft threads are oriented in two directions in the fabric, stretching fabric in the directions of warp and weft lengthens or widens the fabric in the direction of tension and shrinks it in the opposite direction. Elongation of the fabric is directly related to the decrease in crimp shrinkage in the same direction. Threads lengthen in the direction of load after removal of crimp, and the opposite thread system gains higher crimp. This will increase until one thread system does not interfere with the other .Topalbekiroglu and Kaynak performed research  in whichCrimp also influences the fabric’s strength. Any modification of the fabric structure, which spreads the friction over a larger area improves abrasion resistance. Abrasion resistance increases when the friction load affects a larger number of threads and fibre removal or transfer from the fabric during friction decreases. Of course, floating threads, which are higher in comparison with the fabric surface, will suffer the most from abrasion load. In order to save the fabric’s tensile properties, fabric abrasion resistance should be increased; fabric appearance and/or mass loss are secondary factors. By increasing fabric crimp, abrasion resistance decreases. It is thought that this occurs because the crimp is lower when length of floats is higher. Fabric weaves and high crimp values, which would make some floats higher than others, thus concentrating abrasion loads, are not wanted. The locations of these floats would become the main weak links in the whole fabric .The aim of Stig‘s and Hallström‘s research  was to fThe aim of this paper was to investigate the distribution of crimp in jacquard fabrics across the fabric width and to create a method of predicting crimp in jacquard fabrics.−1 twist in the Z direction, the breaking force was 5.286 N and the elongation at break was 1.7%. The warp setting was 21 ends/cm and the weft setting was 16 picks/cm. In the weft direction, every second thread was bleached and every other second thread was of a natural colour. The warp was bleached. The number of jacquard machine hooks was 3360. The fabric width in the reed was 160 cm. The initial warp tension was 7.43 mN/tex, the healds’ cross-advance was at 10 degrees of the main loom shaft. Fabrics were woven in seven different designs . The warp and weft yarns were linen; their linear density was 50 tex. They were single-ply yarns with 523 m designs .The dimensions of all designs were 1.5 m × 2.0 m. All the designs were woven using five different weaves, which are presented in Examples of fragments of jacquard fabric Design 1 from the right a and wrosl is the length of the warp thread and audl is the length of fabric specimen.A known problem of all jacquard fabrics’ weavability is that the weaving design has to be such that uniform warp yarn crimp over the entire width of the fabric can be achieved. This problem exists in every jacquard fabric but this question is particularly relevant when combining one-layer and two-layer weaves in one fabric. In order to distribute one-layer and two-layer weaves evenly in the fabric’s width, warp crimp was established in different places of the fabric width. A random part of the fabric length was chosen and a segment of a certain length was measured. We tried to ensure that this place was not the beginning of the repeat and that the fabric repeat did not finish in the whole segment. The fabric was divided into six approximately equal parts, distributed equally across the fabric width. When the fabric had been divided into separate specimens, 10 warp threads were unpicked in the right side of the specimen. Their length was measured. Equation (2) was used for calculating the crimp:When weaving jacquard fabrics, it is very important that the warp crimp in different places in the fabric’s width should be the same or differ insignificantly. In such a case, the jacquard fabric’s weavability will be good. In other cases, some warp yarns or their groups will be stretched and other ones will be loose. This fact is especially important in fabrics in which one-layer and two-layer weaves are combined. However, the investigation of fabric crimp across the width is very relevant to all jacquard fabrics.In order to investigate crimp distribution in the fabric’s width, warp crimp in various parts of the fabric was established. A random location in the fabric length was chosen and a segment 40 cm in length was measured. The fabric was divided into six parts, which were distributed across the fabric width as follows: 25 cm, 20 cm, 20 cm, 20 cm, 20 cm, 20 cm, and 25 cm. A schematic view of specimen partitioning is shown in After dividing the fabric into separate specimens, 10 warp threads were unpicked from the right side of each specimen. The length of these 10 threads was measured. The crimp of the warp threads was calculated according to Equation (2).The distribution of crimp across the fabric width is demonstrated in In order to explain how crimp changes in parts of fabric woven in different weaves, an original method is suggested. By applying this method, the crimp was calculated in certain segments. Specimens 10 cm in length were manufactured in which sections woven with different weaves were found. In the case of new Jacquard fabric structures, the parts woven in one-layer and two-layer weaves were analysed separately, because the float distribution inside these groups was similar. Ten different warp threads were pulled out from four different specimens and the crimp was calculated according to Equation (2) separately for one-layer and two-layer fabric sections.The crimp of one-layer weaves should be the same because the floats’ lengths and their distribution are the same in one-layer weaves; only the character of the floats differs. The same situation also occurs with two-layer weaves because the floats are only shifted through a single thread and the floats’ distribution in the weave are the same. The results of calculating the crimp for one-layer and two-layer weaves are presented in In order to calculate the crimp, we determined the percentage of warp threads interwoven in one-layer and two-layer weaves along their length in the specimen. In the case of another jacquard fabric structure, the percentage of warp threads interwoven in each different weave will be calculated. Adobe Photoshop CS6 software , which allowed us to visualise the created fabric at the pixel level, was used for calculating this parameter. It was established during this investigation that one pixel equals one warp thread. Next, a newly created jacquard fabric design was divided across the entire fabric width into the same six parts as the real fabric , the length of which is 40 cm. Ten pixel columns from the specimen’s right side were calculated. The proportion of one-layer and two-layer weaves in separate warp threads is presented in When proportion of one-layer and two-layer weaves in the chosen warp threads is known, the crimp of chosen warp threads can be calculated according to Equation (3):ves from , d2−sl ives from .Moreover, General warp crimp consists of a few one-layer and a few two-layer weaves, and their proportions in a jacquard fabric are evaluated in Equation (3), when crimps of each separate weave are known. Thus, the warp crimp of each separate warp thread in jacquard fabric can be predicted according to Equation (3) just by looking at the draft fabric pattern.nth weave in a certain thread (%), nth weave, nth weave along the warp thread in the draft jacquard pattern, and If the jacquard fabric is woven using another weave and structure, Equations (3)–(5) can be rewritten as:The results of calculating the crimp are demonstrated in In a comparison between the experimental and calculated crimp results, comparable crimp results are shown in The results showed that warp crimp changed within the limits of errors in the jacquard fabric’s width. Thus, it can be stated that the fabric’s structural parameters and structural solutions had been chosen correctly.The same investigation of crimp was performed with seven different jacquard fabrics patterns woven with the same weaves but with different distributions in the fabric. The results are presented in As can be seen from After evaluation of jacquard fabrics’ crimp in the warp direction, it was established that the crimp was 18.80% and changed within the limits of errors, i.e., a range of only 4% percent, in the fabric width. Thus, it can be said that the warp crimp was constant across the fabric width.Because the warp crimp of Jacquard fabric changed insignificantly (within the limits of errors), it can be stated that the fabric’s setting parameters and structural solutions were chosen and matched correctly and such a fabric could be woven on any Jacquard weaving loom.After a comparison of the experimental and calculated warp crimps, it was established that calculated crimp in all cases was higher than the experimental crimpy by 5–10% across the fabric width. The reason for this may be the lower accuracy of establishing the calculated crimp, because the crimp of different weaves was established from shorter segments of the warp threads.


Swarm Intelligence journal is dedicated to the publication of extended versions of some of the best papers presented at ANTS 2020, Twelfth International Conference on Swarm Intelligence, which took place in Barcelona, Spain, on October 26–28, 2020. Due to the COVID-19 pandemic, the conference was held online.This special issue of the Swarm Intelligence journal.ANTS is the first and most established conference series dedicated to the dissemination of swarm intelligence research. Its first edition took place in 1998, at the Université Libre de Bruxelles, Brussels, Belgium. Since then, it has been held every other year and, since 2010 , the authors of full conference papers have been invited to submit an extended version for possible inclusion in a dedicated special issue of the Five articles from the 2020 edition of the ANTS conference were accepted for publication in the special issue after at least two rounds of reviews with comments by at least three referees. The papers co-authored by a guest editor of this special issue have been managed anonymously by one of the other guest editors. In the following, each paper is briefly introduced by the guest editor who managed it.Robot swarm democracy: the importance of informed individuals against zealots.” In this paper, Giulia De Masi, Judhi Prasetyo, Raina Zakir, Nikita Mankovskii, Eliseo Ferrante, and Elio Tuci study the interplay between three types of agents—zealots, informed, and uninformed—in the context of the well-known best-of-n collective decision-making problem. Their results show that when all robots are informed , the swarm converges to the best option even if the number of zealot agents steering the swarm toward low-quality options is higher than those steering the swarm toward the high-quality option, provided the unbalance of zealots is not too high. They also show that informed agents can be effectively used to counteract the negative effect of zealot agents that try to steer the swarm towards low-quality options. The study was performed using mathematical models and simulations, and the obtained results were confirmed with real robot experiments.The special issue opens with “HuGoS: A virtual environment for studying collective human behavior from a swarm intelligence perspective,” Nicolas Coucke, Mary Katherine Heinrich, Axel Cleeremans, and Marco Dorigo present a multi-user virtual environment that supports the study of human interactions and group behaviors. Human interactions and group behaviors are often more complex and variated than those displayed by animals or artificial agents. Moreover, human relations have unique aspects of human psychology that are not usually studied in swarm intelligence research. The presented multi-user virtual environment named HuGoS—Humans Go Swarming—is an open-source software tool implemented using the Unity game development platform. HuGoS turns out to be a versatile tool that allows the implementation of a large number of possible scenarios, making it a comprehensive tool for experimentation. The authors show the functionality of HuGoS experimentally via a coordination task performed by anonymous human participants. The performance of the task includes group activities such as dynamic best-of-n collective decision making, messaging or signaling, and stigmergic interactions. HuGoS is a step forward into the research on human swarm intelligence, and it will hopefully help in acquiring a better understanding of the new and complex behaviors arising in larger human collectives.In “Discrete collective estimation in swarm robotics with distributed Bayesian belief sharing,” Qihao Shan and Sanaz Mostaghim present a novel approach to collective decision making in robot swarms based on Bayesian hypothesis testing. While most of the previous work has focused on the study of simple methods with minimal requirements in terms of computational complexity and communication bandwidth, this novel approach explores the benefits of a more complex method that is a decentralized variant of a previously published approach that required a leader. As benchmarking scenario, the authors chose the well-known collective perception task where robots in a swarm estimate a globally distributed environmental feature: the ratio of black and white tiles covering the experimental floor. Individual robots rely on Bayesian statistics to assess the most likely state of the environment and exchange their beliefs by communicating with neighbors. The authors compare their approach to state-of-the-art methods, such as direct comparison and voter-based decision making. The results show that this new approach shows good accuracy and speed at the cost of more communication between the robots.In “Ant colony optimization for feasible scheduling of step-controlled smart grid generation,” Jörg Bremer and Sebastian Lehnhoff describe the application of ant colony optimization to an interesting real-life problem: the scheduling of step-controlled devices in the management of energy resources. This problem, which is NP-hard from a mathematical perspective, will become more and more relevant in the near future due to the gradual shift in the electrical energy grid from a few large power plants to many rather small and decentralized energy producers. One of the main challenges for solving the problem considered in the paper is the construction of feasible solutions. For this purpose, the authors enhance the proposed ant colony optimization algorithm with a simulation model used for the identification of feasible paths during solution construction. The authors also present a study on the complexity and structure of the underlying feasibility landscape.In “Resource ephemerality influences effectiveness of altruistic behavior in collective foraging,” Johannes Nauta, Yara Khaluf, and Pieter Simoens study the link between altruism and foraging efficiency. In the altruistic behavior they study, an agent prioritizes collective intake over individual intake–it will recruit other members of its species to feed on a resource patch instead of feeding itself. The authors show that the net gain of engaging in altruistic foraging behavior depends on the durations of impermanent resource patches. When a patch has a longer duration, the patch should induce altruistic behavior to increase foraging efficiency. Conversely, when a patch has a shorter duration, an agent should feed on it individually before it disappears. The authors show that the net gain also depends on the overall availability of resource patches. Altruistic behavior increases foraging efficiency when patches are sufficiently difficult to locate but not when patches are readily available. The authors also show that the effectiveness of altruistic behavior during foraging depends on the density and communication range of the agents. Altruistic behavior is more effective than other strategies when the incidence rate of agent-to-agent communication is low but not necessarily when the incidence rate is high.In “The high quality of the five papers contained in this special issue is the result of the collaboration of a large number of people: the authors, who submitted their best work to the journal; the referees, who helped in the selection of the published papers; and finally, the many people at Springer who assisted us in the production phase. We thank them all for their help to make this special issue possible.


Fault detection and identification are vital for guaranteeing the precision and reliability of tightly coupled inertial navigation system (INS)/global navigation satellite system (GNSS)-integrated navigation systems. A variance shift outlier model (VSOM) was employed to detect faults in the raw pseudo-range data in this paper. The measurements were partially excluded or included in the estimation process depending on the size of the associated shift in the variance. As an objective measure, likelihood ratio and score test statistics were used to determine whether the measurements inflated variance and were deemed to be faulty. The VSOM is appealing because the down-weighting of faulty measurements with the proper weighting factors in the analysis automatically becomes part of the estimation procedure instead of deletion. A parametric bootstrap procedure for significance assessment and multiple testing to identify faults in the VSOM is proposed. The results show that VSOM was validated through field tests, and it works well when single or multiple faults exist in GNSS measurements. The inertial navigation system (INS) and global navigation satellite system (GNSS) compose the tightly coupled integrated navigation system directly. The fusion of the raw navigation information (pseudo-range or carrier phase measurements) of the GNSS and the inertial measurements of IMUs  is implemented in some nonlinear filters ,2, such Two main types of fault detection and identification are usually employed in tightly coupled integrated navigation systems. The most common methods are fault detection and isolation (FDI), fault detection and exclusion (FDE) and fault detection and recovery (FDR). When a fault of the raw sensor signal in the integrated navigation system occurs, the FDE can provide an alarm and enable the navigation system to exclude the faulty measurements. A fault detection algorithm based on hypothesis testing in parity space was investigated by Sturza . IntegriAn adaptive filter guarantees the precision and reliability of the integrated navigation system through adaptive adjustments of the noise covariance matrix and reduction of the weights of faulty measurements, and avoids hypothesis testing. There are various kinds of adaptive estimation methods, such as the generalized maximum likelihood estimator , the sofArtificial intelligence has been applied to enhance the performance of fault detection, and benefits from rapid development. A data-driven adaptive neuron fuzzy inference system for predefined faults was used for the detection of navigation sensor faults in unmanned aerial vehicles . GaussiaThe variance shift outlier model (VSOM) combined with an extended Kalman filter (EKF) in this paper is utilized for the detection of GNSS measurement faults and the estimation of the variance shift for each measurement, which down-weights the measurement if required. The innovation of the EKF was fitted to the VSOM used to detect and identify the faulty measurements. The VSOM can be considered as the middle ground between FDI/FDE/FDR and robust estimation . Unlike The remainder of the paper is organized as follows. In A tightly coupled, INS/GNSS-integrated navigation system with a closed-loop error-state, extended Kalman filter is described in this paper. The tightly coupled approach processes the raw pseudo-range GNSS measurement in a single filter, and the estimated position errors are utilized to correct the INS’s navigation solution . The arcThe linear dynamic equation for the error state in a time-varying linear system can be given as follows:The state vector in the filter is given byThe linear observation equation is given byAssuming the discrete-time process, the system error dynamic equation and the observation equation can be rewritten as follows:I denotes the identity matrix. The Kalman gain matrix is:When the observations are available, The innovation vector isWhen a closed loop EKF is deployed, the value of the estimated state vector feeds back to the system, and the predicted state vector mes zero ,21. The Under the fault-free condition, the innovation vector The horizontal alert limit (HAL) and the horizontal protection level (HPL) need to be compared with each other. When some faults in the measurements are not detected and identified, HAL and HPL could give the system protection. HAL is the maximal tolerable value of horizontal position error. When it is exceeded, an alert will be raised. The value of HAL is specified as 40 m in this paper. HPL is an upper bound. If the horizontal position error exceeds HPL, it shall be detected with a 99.9% probability. HPL needs to be computed in real time to check the integrity available and analyze the position-domain to determine whether the estimation could be used for the solution. Two computational passes are required for HPL in this tightly coupled, INS/GNSS-integrated navigation system, the first for checking integrity and the second for checking the availability of the final navigation solutions. A detailed calculation process for HPL is given in H is x is a x under the linear model (14). The REML estimate The variance shift outlier model defined in this paper is the same as that in ,22,23. Tith measurement has an inflated error variance. i is the number less than or equal to the dimensions of z, which denotes the position of the fault in the measurements. The measurement has error variance ith measurement. A variance shift model for the ith measurement takes the formith ith element and 0 elsewhere; I is a z the data under a VSOM model (16) isSuppose the ith element of z inflates The variance corresponding to the ith VSOM (16) can be expressed as follows:The REML log-likelihood function (REML LLF) for the ith VSOM can be given in another way:ith measurement under the null model (14), respectively. Since The REML LLF for the ctor are (20)σ^2=infinity .A linear model that follows is used here.Equation . xframe fined in ,26.Normalize the measurement equation as follows (22) ,27:(23)zThenith satellite measurement; see ith measurement, testing of the hypotheses is established as follows:Equation  has the ith measurement.The alternative model is fitted under the VSOM of the ith measurement. i denotes the ith VSOM.To test the hypothesis, the likelihood ratio test (LRT) statistic is established by ,23(28)LUnder the null hypothesis, the REML LLF could be given byHence,LRT is a monotonically increasing function of There is an asymptotical equivalence between the LRT and the score test under the null hypothesis. However, there is a computational advantage to the score test statistic. The score test statistic does not need to fit the model specified under the alternative hypothesis, and it is only required to estimate under the null model ,22. A scEquation  with resUnder the null hypothesis, ith VSOM, and the information matrix can be partitioned as follows:The negative expected value of the second derivatives of (19) is specified as the information matrix for Using Equations (23)–(26), the expected information matrix under the null hypothesis is given byFor testing The score test statistic can be rewritten asThere are two situations in the practical scenario : a measuS1: Estimate (23) under the null hypothesis, obtaining parameter estimates S2: Generate new measurementsS3: Fit the null hypothesis (23) and obtain bootstrap LR test statistic S4: B times, for B is reasonably large. An empirical distribution(ED) of size B for each order statistic is generated.Step 2 and step 3 are required to be repeated S5: Calculate the To determine how many and which measurements are faulty, the LR and score test statistics for each measurement are calculated. Then, testing more than one hypothesis simultaneously becomes the primary problem. For the appropriate sampling distribution of the LR and score test statistics, a parametric bootstrap method is implemented for significance assessments of the tests and multiple testing of the statistics. The parametric bootstrap procedure is can be divided into five steps:When the LR test statistics exceed their respective thresholds , these measurements are deemed to be all faulty and should fit the modified model, including a variance shift. The measurements that are deemed to be faulty will be down-weighted in the estimation procedure.D is a ith position and 0 elsewhere, The flow chart of detecting faulty measurements based on the VSOM approach is shown in After obtaining the inflated factor Equation , the dowThe computation of HPL is described as follows ,29. HPL1ith element of diagonal matrix The calculation of HPL2 is similar to that of traditional receiver autonomous integrity monitoring (RAIM) HPL . HPL2 obHPL2 can be calculated byHPL can be given byB was set at 1000. The significance level In this section, the proposed method is proven to be feasible by the a static test and a vehicular dynamic test of the tightly coupled, INS/GNSS-integrated navigation system. The fiber-optic-gyroscope-based SINS in both two experiments was independently developed by Harbin Engineering University. The sampling rate for the IMU was set at 100 Hz. The parameters of the INS are shown in  at 0.01 .The INS was placed on a marble isolation table, and the antenna of the receiver was placed outdoors. The GNSS receiver tracked dual-constellation navigation signals: GPS L1: 1575.42 MHz; BDS B1: 1562.098 MHz. The raw navigation data from the IMU and GNSS receiver were collected for 21,600 s. The arrangement is shown in Take the data at 670 s as examples to show how VSOM detects and identifies faulty measurements. A comparison of the statistics and their respective thresholds is shown in ith measurement is just a potential fault when The comparison of the position solutions with and without fault detection and identification based on VSOM is shown in A vehicular dynamic test was performed in an urban environment. The test equipment is shown in Both GPS and BDS were employed in this experiment, and the number of observed satellites was the sum of that of two systems. To further reveal the details, the distance from the initial position to the current position over time is shown in A fault detection and identification method for tightly coupled, INS/GNSS-integrated navigation systems is proposed in this paper. The method emphasizes the faults in GNSS measurements. This method is beneficial to ensuring the precision and reliability of a tightly coupled, integrated navigation system. The VSOM employed in this paper can be viewed as a trade-off between a faulty detection and exclusion algorithm and robust estimation. The size of the variance shift in the measurement is the key to partial exclusion or inclusion of the measurements in the estimation process. Either the LR statistics or score test statistics are presented as objective measures for determining whether the measurements are faulty. Parametric bootstrapping was employed in this paper to assess the significance and the handling of multiple testing. The performance of the proposed method was verified by a static field test and a dynamic field test. As shown in the results, the faults occurring during the navigation process can be detected and identified accurately. After down-weighting the fault with proper weight factors in the estimation procedure, the performance and precision can be ensured. However, the fault detection and identification based on the variance shift outlier model still need to be improved. More applicable scene tests and more flexible test criteria will be explored to perfect the method in the future.


In this paper, we investigate modification of transmission spectra of long-period fiber grating structures with an acoustic shock front propagating along the fiber. We simulate transmission through inhomogeneous long-period fiber gratings, π-shift and reflective π-shift gratings deformed by an acoustic shock front. Coupled mode equations describing interaction of co-propagating modes in a long-period fiber grating structures with inhomogeneous deformation are used for the simulation. Two types of apodization are considered for the grating modulation amplitude, such as uniform and raised-cosine. We demonstrate how the transmission spectrum is produced by interference between the core and cladding modes coupled at several parts of the gratings having different periods. For the π-shift long-period fiber grating having split spectral notch, the gap between the two dips becomes several times wider in the grating with the acoustic wave front than the gap in the unstrained grating. The behavior of reflective long-period fiber gratings depends on the magnitude of the phase shift near the reflective surface: an additional dip is formed in the 0-shift grating and the short-wavelength dip disappears in the π-shift grating. In the past two to three decades, fiber gratings have been intensively studied for applications in optical communications and sensing ,2,3. In Conversely, the interaction of ultrasound with grating sensors can be used to identify leakage of medical gas delivery systems in health care facilities. This issue has a tremendous financial impact, which is even more demanding in the current pandemic situation.For the case of step-changed acoustic fronts, calculating transmission spectra is similar to the problem of inhomogeneous step-changed LPFGs where some part of the grating is strained, while the strain sensitivity of LPFGs has been analyzed in Ref. ; meanwhiThe spectral response of LPFGs can be controlled by adding a phase shift in the middle of the grating ,28,29, wThe standard LPFG works in transmission and requires access to both end-sides of the fiber: one brings the light from a source and the other returns the remaining light to a photo-detector. In terms of sensing, it is more convenient to create a sensing head having access to a single end of the fiber. This can be attained by using a reflective surface at the end of the optical fiber with the LPFG in a self-interference Michelson configuration ,44,45,46In this work, we investigate modification of transmission spectra of long-period fiber grating structures with an acoustic shock front propagating along the fiber. We simulate transmission through homogeneous long-period fiber gratings, π-shift, and reflective gratings with propagating acoustic shock front producing non-uniform deformation along the optical fiber. Coupled mode equations describing interaction of co-propagating modes in a long-period fiber grating structures with inhomogeneous deformation are written and used for the simulation. We consider the influence of smoothness of the acoustic front and the magnitude of the phase shift on the spectra of various types of LPFG structures.The long-period fiber grating has periodical modulation of its refractive index with period between 100 and 1000 μm a. The trThe phase-shifted LPFG has a section with modified fiber structure, where the grating has an additional space between the grating lines or changed propagation constants of the core and cladding modes b. Each sThe reflective LPFG has a reflective coating at the end face of the optical fiber near the grating. If the grating ends exactly at the end face, no phase shift is introduced for the propagating modes c. Such aIf there is some space between the grating and the end face, a phase shift is formed d. We obtWe assume that a longitudinal compressive shock front of acoustic shock wave propagates along the fiber and deforms the grating starting from z=L . The speThe front of the shock wave may have different profiles, which is determined by the time profile of the initial impact and by diffusion of the shock front due to dispersion of the speed of sound in the fiber and surrounding material. Assuming that the initial shock front is described by the step function, it can be represented as a Fourier transform of waves with different frequencies. These waves propagating in a dispersive medium have different speeds and arrive to the grating in different moments. The resulting sum of the waves is some smoothed stepwise function. The magnitude of smoothing is determined by the dispersion of the medium and the distance from the source to the grating. We consider only the effect of the leading edge of compression of the shock wave, which is much sharper compared to the trailing edge of expansion. Slow expansion has space distribution larger than the grating length and covers the whole grating, which acts as a homogeneous structure in this case.The strain can be strong enough so that the wavelength shift is large and resonances of cladding mode with adjacent mode numbers can overlap. This is an alternative kind of interference, because cladding modes with different mode numbers do not interfere themselves; indeed, it would take place only interference between them when they couple back to the core mode. Another situation is possible when the LPFG excites modes of different types : the oveThe refractive index modulation in a fiber with a LPFG can be written as follows:To simulate the process of propagation of acoustic shock front through the LPFG, we assume that the amplitude of the front profile is described by the following function, which changes the strain from one level to another with controllable smoothness defined by the parameter Here, The refractive index modulation in the deformed fiber takes the formThe period of the deformed grating is determined by the function In addition to displacement of the fiber grating, the refractive index of the fiber is modified due to strain-optic effect byThe dielectric permittivity and its change in the deformed and strained fiber can be expressed from Equation (4) asHere we have neglected the terms of the second order of smallness in the change of dielectric permittivity.1μ and HEν1 modes, respectively, The long-period fiber gratings couple modes propagating in the same direction. We consider the case of one core mode that is coupled to the forward propagating cladding modes. The interaction with backward propagating modes may occur only at the endface of the fiber for reflective LPFGs. The coupling coefficient between two co-propagating modes is defined as the following overlap integral over the fiber cross-section:The coupled mode equations that describe the amplitudes of modes can be written asThe two coupling constants 1μ modes without azimuthal structure interact, because the fiber is straight and has no birefringence and the grating is radially symmetric. The coupled mode equations are obtained by ignoring quickly oscillating terms and describe slowly varying amplitudes of two co-propagation modes:11 and HE1ν, respectively, and the detuning parameter isWe have assumed here that only HEFor obtaining Equation (12), we use the equality of coupling constants The resonance condition for mode coupling isThe effective refractive indices For simulation, we use parameters of SMF-28 fiber at wavelength The coefficient 0.78 in the self-coupling constant he fiber . The crovely see .As follows from Equation (14), when the fiber is strained, the wavelength shift of a spectral dip is determined by the difference of self-coupling constants depending on strain:We take nd 35 in ). As com15 is centered at 1550 nm. At this wavelength, we can find the effective refractive index of the fifth cladding mode –1. All parameters that we used in the simulation are listed in We begin simulation with a uniform grating having constant modulation amplitude of induced refractive index along the length of the fiber. Let the grating has a period of 430 μm. Then the resonance of the fifth mode HEThe transmission spectra of a regular LPFG are shown in The acoustic front propagating through the grating divides the grating into two parts with different parameters. Such a grating is equivalent to a step-changed grating , and theLet us consider the dependence of spectral characteristics of the LPFG with an acoustic front in its center. When the length increases, the transmission loss grows overall. The spectrum is wide for short grating lengths and forms a band centered at 1530 nm , by detection of ultrasound waves (frequency < 100 kHz and 40–60 dB) produced in pipeline systems exhibiting different kinds of anomalies.


There is a trend toward minimally invasive and more automated procedures in orthopedic surgery. An important aspect in the further development of these techniques is the quantitative assessment of the surgical approach. The aim of this scoping review is to deliver a structured overview on the currently used methods for quantitative analysis of a surgical approaches' invasiveness in orthopedic procedures. The compiled metrics presented in the herein study can serve as the basis for digitization of surgery and advanced computational methods that focus on optimizing surgical procedures.In-vivo and ex-vivo studies that quantitatively assess the invasiveness of the surgical approach were included with a special focus on radiological methods. We excluded studies using exclusively one or multiple of the following parameters: risk of reoperation, risk of dislocation, risk of infection, risk of patient-reported nerve injury, rate of thromboembolic event, function, length of stay, blood loss, pain, operation time.We performed a blinded literature search in November 2020. in-situ” (14) and their use “in-vivo” or “ex-vivo” was analyzed. Additionally, we explain the basic principles of each modality and match it to the anatomical structures it has been used on.The final selection included 51 articles. In the included papers, approaches to 8 different anatomical structures were investigated, the majority of which examined procedures of the hip (57%) and the spine (29%). The different modalities to measure the invasiveness were categorized into three major groups “biological” (23 papers), “radiological” (25), “measured in-situ measurements but are non-invasive and possible to perform in-vivo. Additionally, radiological metrics require substantial expertise and are not cost-effective. Owed to their high accuracy and low invasiveness, radiological methods are, in our opinion, the best suited for computational applications optimizing surgical procedures. The key to quantify a surgical approach's invasiveness lies in the integration of multiple metrics.An ideal metric used to quantify the invasiveness of a surgical approach should be accurate, cost-effective, non-invasive, comprehensive and integratable into the clinical workflow. We find that the radiological methods best meet such criteria. However, radiological metrics can be more prone to confounders such as coexisting pathologies than  Surgical approaches represent the foundation on which specific interventions are built, with about 100 common surgical approaches in orthopedic surgery alone . The surWith the goal of minimizing tissue damage, new surgical approaches are continuously being developed –7. GenerOpen approach: direct exposure of the injured parts of the target structure.Mini-open approach: direct exposure of the injured parts of the target structure with a small incision or multiple small incisions.Percutaneous approach: straight corridor from the skin to the target structure guided by medical imaging.Arthroscopy: camera guided technique requiring two- to three-point incisions.Assessing the invasiveness in a more comprehensive way can be challenging given the complexity of the anatomical structures and the lack of objective and quantitative criteria based on which the surgical approach can be evaluated. The extent of the surgical incision and the quality of surgical approach can be affected by multiple factors such as: the complexity of the target anatomy and the pathology, the surgeon's level of experience and the nature of the intervention . In current clinical practice either qualitative criteria  or post-operative patient outcome measures . In. In57)].Electromyography measures the electrical potential generated by a muscle after neurological or electrical activation. In contrast to surface electromyography, needle electromyography allows for the measurement of single motor-units by recording the generated electrical signal. Monitoring these signals before and after an incision provides a means for evaluating the surgical approach based on the damage to the underlying muscle or nerve tissue. For example, rhythmical, spontaneous contractions such as positive sharp waves and fibrillation potentials were used in Waschke et al.  and consThe development of muscle fiber diameter correlates with the muscle atrophy of the damaged muscle fibers or compensatory muscle hypertrophy of the functional muscle fibers, respectively. The assessment of the change of the muscle fiber composition due to surgical damage  has not produced any significant results to our knowledge. Histological analysis as done in Pumberger et al.  needs toMuscle strength can be measured using pressure sensitive sensors called dynamometers  as a su(fatty) atrophy can be ambiguous, as it is sometimes used to describe the process of conversion from muscle to fat tissue [e.g., (development of muscle-to-fat ratio (= fatty degeneration) or volume atrophy, respectively. An increased muscle-to-fat ratio as well as volume atrophy are the consequences of pathological processes such as immobility  best meet those criteria. However, such metrics can be more prone to confounders such as coexisting pathologies than We can thus conclude that there is no metric that delivers a complete and objective quantitative analysis of the surgical approach. The key lies in the integration of multiple metrics, allowing an extensive analysis of the invasiveness of a surgical approach. Moreover, further research needs to be conducted for assessing the quality of the proposed methods by comparing their correlation with the functional outcomes of the procedures.PF, HE, and NB contributed to the ideation of the review. NB and HE performed the literature research and made the selection of papers. NB extracted and structured the relevant contents of each paper of the selection and wrote the first draft of the manuscript. HE wrote sections of the manuscript. All authors contributed to manuscript revision, read, and approved the submitted version.HE salary was partially funded by the SURGENT project which was financed by a University Medicine Zurich, University of Zurich seed funding.The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.All claims expressed in this article are solely those of the authors and do not necessarily represent those of their affiliated organizations, or those of the publisher, the editors and the reviewers. Any product that may be evaluated in this article, or claim that may be made by its manufacturer, is not guaranteed or endorsed by the publisher.


To synthesize and evaluate lockdown policies, we develop a multiscale susceptible, infected, recovered, and deceased model that partitions a given MSA into geographic subregions, and that incorporates data on the behaviors of the populations of these subregions. This modeling approach allows for the analysis of heterogeneous lockdown policies that vary across the different types of activity sites within each subregion of the MSA. We formulate the synthesis of optimal lockdown policies as a nonconvex optimization problem and we develop an iterative algorithm that addresses this nonconvexity through sequential convex programming. We empirically demonstrate the effectiveness of the developed approach by applying it to six of the largest MSAs in the United States. The developed heterogeneous lockdown policies not only reduce the number of deceased individuals by up to 45 percent over a 100 day period in comparison with three baseline lockdown policies that are less heterogeneous, but they also impose lockdowns that are less severe.We study the problem of synthesizing  The COVID-19 pandemic has caused over 180 million confirmed cases and over 3.96 million deaths globally as of June 30, 2021. Since the outbreak of COVID-19, various public health control strategies have been proposed and tested against the coronavirus SARS-CoV-2. However, existing COVID-19 control synthesis approaches typically either apply optimal control techniques using models that largely neglect interactions between individuals living in different geographic regions, or focus on evaluating relatively simple control strategies with no optimality guarantees.9. However, studies of the spread of COVID-19 in India, France, and Italy have demonstrated the important role that heterogeneity between geographic regions plays in attempts to predict and to control the pandemic12. It is essential that any interventions to slow the spread of the COVID-19 distinguish between different geographic regions, which may have differing demographics, available medical equipment, and rates of transmission. The exclusion of such geographic information in the modeling and analysis of control policies may result in significant discrepancies between the model-predicted outcomes, and the practical results observed when the control policies are deployed.Approaches that apply optimal control techniques largely rely on models that neglect important spatial-temporal dynamics associated with regional differences in the pandemic’s spread, and with people’s movement16. Instead, these works evaluate given control policies without any consideration of their optimality. Note that such optimality becomes very important when our objective is not only to minimize deaths, but also to reduce the severity of the imposed lockdown.Conversely, the research that incorporates detailed spatial-temporal geographic information does not focus on the synthesis of optimal control policieslockdown policies that explicitly take such geographic consideration into account. A lockdown policy specifies the maximum number of allowable concurrent visitors to various types of activity sites accross a given metropolitan statistical area (MSA). We define activity sites to be the physical locations throughout the MSA, such as grocery stores and fitness centers, where interactions between members of the population frequently occur and thus where the disease is likely to spread.In this work, we study the synthesis of optimal To synthesize optimal lockdown policies while incorporating the aforementioned geographic considerations, we first develop a multiscale susceptible, infected, recovered, and deceased  model of the spread of a disease through a given MSA. The model explicitly incorporates geographic data describing the spatial distribution of the population, and interactions between individuals from different subregions within the MSA. The visualization on the left of Fig. heterogeneous lockdown policies. Each of these policies specifies the allowable number of visitors to a specific type of activity site within a given subregion. We formulate the problem of computing optimal heterogeneous lockdown policies as a nonconvex optimization problem. We then develop an iterative algorithm addressing this nonconvexity through sequential convex programming17. Building on related results20, we linearize the underlying nonconvex problem around the solution from the previous iteration and check whether the synthesized policy obtains a better objective value. The algorithm can synthesize a heterogeneous lockdown policy that is locally optimal with respect to the nonconvex optimization problem.By explicitly modeling the activity sites at which the disease is likely to spread, the developed approach allows for the synthesis of optimal We evaluate the developed modeling framework and optimal policy synthesis algorithm using data from six of the largest MSAs in the United States: Phoenix, New York, Chicago, Los Angeles, Dallas-Fort Worth, and Seattle. Figure 26. Commonly used compartmental models partition the population into labeled groups, each of which describes a different phase of infection32. For example, the SIR model separates the population into three compartments, those who are susceptible to the virus 33. Given such a partition of the population, systems of ordinary differential equations are often used to model the dynamics of the disease’s spread. By including additional compartments in the model, and thus refining the partition of the population into more detailed categories, predictions and analysis of specific changes and quantities of interest can be made. For example, partitioning the population into different age categories allows for the analysis of age-specific targeted lockdown policies2. Giordano et al.32 consider eight categories in their compartmental model, allowing for discrimination between infected individuals depending on whether they have been diagnosed and on the severity of their symptoms; this refinement aims to enable the model to reflect the observed high number of asymptomatic individuals who are still able to cause transmissions.Since the initial outbreak of COVID-19, there has been extensive research into modeling its spread within a population40. Agent-based models allow for simulation of the effectiveness of behavioral interventions on the level of individual members of the population, such as mask-wearing and social distancing requirements within an enclosed space.While such compartmental models provide an easy-to-interpret means of analyzing the spread of COVID-19, they may only be used in the context of relatively large populations. Conversely, agent-based models instead encode rules for agents—simulated members of the population—to follow. These models simulate the spread of the disease resulting from these behaviors41 model transmission within a network where households make contact at common points of interest. Karaivanov42 incorporates a social network model with an SIR model to provide a more realistic model of the interactions within a population, as opposed to the uniform mixing assumed by most SIR models. However, none of the above papers consider the problem of optimal control. Table Several papers have considered further extensions of compartmental models. Chang et al.53 use compartment-style pandemic models to study the effect of lockdowns on the spread of COVID-19. However, they do not synthesize lockdown control policies, nor do they study geographically heterogeneous lockdowns. Chatzimanolakis et al.54 and Buhat et al.55 both study the problem of optimally distributing test kits under limited supply. Other works study the trade-offs between focusing allocation of vaccinations to either high-risk or high-transmission age-groups in the context of SIR models6. Goldenbogen et al.56 study a human-human interaction network and analyzes the optimal policy for vaccine distribution.Several papers have investigated the problem of control analysis for various COVID-19 related policies, including lockdowns, testing, and vaccine distribution. Sardar et al.1 study the problem of minimizing the deceased people in a basic SIR model while controlling the impact on the economy. Acemoglu et al.2 extends this work to consider differing dynamics and control among age groups. Both of these works, along with other COVID-19 control-related papers58, only consider a spatially homogeneous population and control policy. Similar to the regional model considered by Della Rossa12, we consider a hierarchical model allowing for region-specific dynamics and control. Table Similar to our work, several papers have studied the problem of synthesizing or evaluating lockdown policies within various epidemiological models to balance the tradeoff between viral spread and economic impact. Alvarez et al.59.We formulate a multiscale SIRD pandemic model that uses a directed graph to capture the spread of the disease through a given MSA. The model also captures how the disease’s spread is affected by the lockdown of various types of activity sites. Each node of this graph represents a distinct geographic subregion and contains an independent SIRD model, which captures the spread of COVID-19 within the corresponding population. We represent the interactions between the populations of the subregions, i.e., the SIRD models, by the directed edges in the graph. The weight of a given edge encodes the fraction of the origin subregion’s population that frequently interact within the subregion represented by the destination node; these weights are obtained from SafeGraph data32, we include the following types of activity sites in our model: Grocery stores, restaurants, fitness centers, hotels, pharmacies, and physicians.In this work, we assume that all interactions causing the spread of COVID-19 within the MSA population occur at various types of activity sites. These activity sites represent the physical spaces within a community in which it is common for people, often from different households and potentially from different subregions, to gather in close proximity. In this work, similarly to Giordano et al.demand rates for each type of activity site within each subregion. The demand rates are defined as the average number of people from a given subregion that visit a particular type of activity site per day. For each type of activity site within each subregion, we then use the corresponding estimated demand rate to define a nominal capacity, which represents the maximum number of visits per day that can be sustained by all activity sites of this type within the particular subregion. To help visualize the how the multiscale SIRD model partitions an example MSA into subregions, Fig. We used the foot traffic information of activity sites in April 2020, collected from SafeGraph, to estimate the To control the spread of the disease we specify a separate time-varying lockdown policy for each type of activity site within each subregion. At each point in time, the lockdown policy takes a value between 0 and 1, representing a fraction of the nominal capacity of the corresponding activity site type and subregion. For example, a lockdown policy might specify that all grocery stores within a particular subregion of the MSA may only allow half as many visitors per day as their nominal capacity. On the other hand, in a neighboring subregion, restaurants may only serve up to a quarter of their nominal capacity. So, specifying the lockdown for activity sites reduces their allowable number of visitors per day. This in turn reduces the spread of the disease in the model by reducing the number of interactions occurring in the population. However, in response to the reduction in available capacity at the various activity sites, we assume that members of the population will begin to travel to other subregions. Specifying lockdown policies may therefore also indirectly influence the inter-regional interactions occurring throughout the MSA.We assume that the selected lockdown policy cannot blindly shut down all activity sites. In particular, we enforce the constraint that, after accounting for the travel between subregions, there must be enough capacity throughout the MSA to satisfy all of the existing demand. This constraint corresponds to the idea of imposing a lockdown while still ensuring that the needs of the population are being met. For example, every member of the population should have the chance to shop for groceries.economic impact parameter. A higher value of this parameter implies a higher relative weight on the economic cost in the objective.Our objective is to solve for a heterogeneous lockdown policy that minimizes the number of deaths in the MSA over some finite time horizon, while limiting the severity of the imposed lockdown. We formulate the computation of an optimal lockdown policy as a nonlinear optimization problem. The variables of the optimization problem encode, at each moment in time, the number of people in each subregion that are susceptible, infected, recovered, and deceased, the fraction of each subregion’s population that visit activity sites within each of the subregions, and the lockdown value for each type of activity site within each subregion. The objective of the optimization problem is a weighted sum of the cumulative deaths in the MSA and the economic cost of the lockdown policy over a finite time horizon. We model the economic cost of imposing a lockdown on a given type of activity site within a given subregion as being proportional to the frequency at which it is visited by members of the MSA’s population. We represent the relative weight of the economic cost in the optimization objective by an 19. To compute a locally optimal solution, we successively linearize the nonconvex optimization problem by computing a local approximation of the problem at each iteration20. We provide more details on the formulation of the multiscale pandemic model, on the resulting optimization problem, and on our solution approach in the supplementary material.The resulting optimization problem is nonconvex due to the nonlinear dynamics of the multiscale SIRD model. In general, it is computationally hard to compute an optimal lockdown policy for such nonconvex problemsIn this section, we implement the developed approach using SafeGraph data from Phoenix, Seattle, New York, Chicago, Los Angeles, and Dallas-Fort Worth MSAs. We show detailed results for the Phoenix MSA in this section, and we include the results for the other MSAs in the supplementary material.In Figs. For each of the six types of activity sites included in the multiscale SIRD model, Fig. daily activities; we assume that after visiting an activity site in another subregion, members of the population will return to their home subregion.Figure In the remainder of this section we examine the benefits of heterogeneous lockdown policies, the tradeoff between the number of infected individuals and the economic cost of the imposed lockdowns, and the tradeoff between the accuracy of the multiscale SIRD model and the computational performance of the optimization algorithm. For consistency, we present these results only for the Phoenix MSA.Heterogeneous lockdown (HL): Separate lockdowns are imposed for each type of activity site within each subregion.Regional lockdown (RL): Each subregion may impose different lockdowns, but within a given subregion, all activity sites impose the same lockdown.Activity site lockdown (ASL): Each type of activity site may impose different lockdowns, but the lockdown for a particular type of activity site is identical across all of the subregions.MSA lockdown (MSAL): All activity sites within all subregions impose the same lockdown.Figure In Figure Practically speaking, the reason that HL policies are more performant than their more homogeneous counterparts, is because they allow for more granular control of the lockdowns imposed throughout the MSA. This granularity can help to individually address different geographic, demographic, and epidemiological characteristics of the disease’s spread across the different subregions and types of activity sites. Mathematically, this intuitive explanation corresponds to the fact that the class of all HL policies is a superset of the classes of all ASL, RL, and MSAL policies, respectively. That is, any ASL, RL, or MSAL policy can also be considered to be an HL policy. For this reason, it must be the case that the optimal HL policy is at least as performant as the optimal policy from each of these other classes.Figure outgoing edges from each subregion in the multiscale SIRD model of the MSA. An outgoing edge from subregion In order to improve the computational performance of the optimization algorithm, we may limit the number of We observe that by including 5 outgoing edges per subregion in the model instead of 3, we can solve for an optimal lockdown policy with 26% fewer deaths. Conversely, the average lockdown value is very similar for the different number of edges. In other words, including more outgoing edges per subregion leads to solutions that reduce the number of deaths, without imposing more severe lockdown policies. However, this benefit comes at the expense of an increase in computation time; the computation times for 4 and 5 edges are 80% and 240% larger than for 3 edges, respectively.We also note that the lockdown value and the number of deaths are very similar for the models that use 4 and 5 outgoing edges for each subregion. This is likely because our methods compute a locally optimal solution as opposed to a globally optimal one, which would be intractable.Figure We present a modeling framework and an optimization algorithm for the synthesis of multiscale heterogeneous lockdown policies. Our numerical results demonstrate the effectiveness of these lockdown policies, which individually address the different geographic, demographic, and epidemiological characteristics of the disease’s spread across the different subregions and activity sites within an MSA. The resulting policies provide practical and actionable insights surrounding the incorporation of geographic information into epidemic control strategy synthesis.Through our numerical results, we demonstrate that lockdown policies that distinguish between different activity sites and geographical subregions not only reduce the number of deceased individuals due to the pandemic but also decrease the severity of the induced lockdowns across the entire MSA, in comparison to less heterogeneous lockdown policies. This result highlights the importance of heterogeneous control strategies in slowing the spread of the pandemic. We also observe an increasing relationship between the demand rate of a particular type of activity site, and the average lockdown value that is assigned to those activity sites by the optimal heterogeneous lockdown policy. Similarly, we observe that the activity sites within subregions with large populations are locked down more severely than those in subregions with small populations. Finally, we observe that the optimal lockdown policy tends to become most severe at the point in time when the number of infections in the population is at its peak value, before gradually easing up over time. In summary, our numerical results suggest that lockdown policies are most effective when they distinguish between different types of activity sites and geographic subregions, when the severity of the lockdown increases with the popularity of the activity site and the population of the subregion, and also when severity of the lockdown increases with the number of infected individuals in the population.Furthermore, we observe a direct tradeoff between the severity of a lockdown and the resulting number of deceased individuals at the end of the considered time horizon. The proposed lockdown policy synthesis algorithm provides a method to control this tradeoff through the economic impact parameter. By varying the value of this parameter, decision-makers can assess the predicted biological and economic outcomes of an entire suite of lockdown policies, before deploying any of them in practice.The framework we present is flexible; it can be adapted to incorporate additional modeling considerations and data sources, when such information becomes available. For example, we assume that the economic impact of a lockdown policy is proportional to the demand rate of the corresponding activity sites. However, a more complex economic cost function could easily be incorporated into the optimization objective. Furthermore, additional considerations surrounding the lockdown policy for specific activity sites can be incorporated by adding constraints to the optimization problem. The granularity of the model can also be refined by incorporating additional types of activity sites and a finer partition of the MSA into subregions. Finally, we demonstrate that by including more edges in the multiscale SIRD model, we can significantly reduce the predicted number of deceased individuals at the sole expense of a higher computational cost.Supplementary Information.


Viruses are pathogens that have evolved to hijack the cellular machinery to replicate themselves and spread to new cells. During the course of evolution, viruses developed different strategies to overcome the cellular defenses and create new progeny. Among them, some RNA and many DNA viruses require access to the nucleus to replicate their genome. In non-dividing cells, viruses can only access the nucleus through the nuclear pore complex (NPC). Therefore, viruses have developed strategies to usurp the nuclear transport machinery and gain access to the nucleus. The majority of these viruses use the capsid to manipulate the nuclear import machinery. However, the particular tactics employed by each virus to reach the host chromatin compartment are very different. Nevertheless, they all require some degree of capsid remodeling. Recent notions on the interplay between the viral capsid and cellular factors shine new light on the quest for the nuclear entry step and for the fate of these viruses. In this review, we describe the main components and function of nuclear transport machinery. Next, we discuss selected examples of RNA and DNA viruses  that remodel their capsid as part of their strategies to access the nucleus and to replicate. Xenopus laevis [2 and ≈5 × 107 NPCs/nucleus in total [The cytoplasmic and the nuclear bi-directional exchange of molecules and proteins is ensured by the Nuclear Pore Complexes (NPCs). These structures are large multiprotein complexes composed by approximately thirty different nucleoporins in mammalian cells  organizes laevis . The NPCs laevis . The NPCs laevis . Indeed,in total ; this nuin total . The humin total ,15.Two mechanisms determine the passage of molecules through the NPC: facilitated and passive diffusion. Macromolecules lacking nuclear transport signals (NLS), which create a specific amino acid sequence, are transported in the nucleus by passive diffusion. The structure and organization of the NPC allows the passive diffusion of small molecules and ions smaller than 9 nm. On the other hand, molecules larger than 39 nm require an active process to be imported or exported through the NPC . HoweverIn addition, several molecular dynamics simulations have been extensively performed over the past decade to shed light on the transport mechanism. Usually, simulations are conducted over a time scale of micro seconds to determine how FG Nups stretch out and form rapid bundles of multiple FG Nups. It has been proposed that the hydrophobic region of FG Nups is protected from being exposed to the aqueous environment by being coiled up into a globular structure ,33,34.A more recent study highlights that FG-nucleoporins from different Nups undergo liquid–liquid phase separation and form liquid droplets that mimic the permeability barrier properties of NPCs ,35. In aSo far, we have reached a good understanding of how proteins are imported to the nucleus, but much less is known about the strategies and tactics that viruses employ to cross the nuclear barrier. In the next sections, we expose some examples of how different viruses have evolved alternative ways to access the host nucleus. We will particularly focus on the role of the capsid to lead the viral genome into the host chromatin compartment, which is an essential step for the life cycle of several viruses.The hepatitis B virus (HBV) is an enveloped DNA virus with a size of 42–47 nm that belongs to the hepadnaviridae family . Inside The viral capsid is usually a key player in the viral infection, especially in viruses that need to access the nucleus to replicate. It is not surprising that the HBV capsid requires a change in its structure to meet the requirement of crossing the NPC, which is the main bottleneck for several viruses to complete their life cycle. Thus, the HBV remodeled capsid kidnaps cellular factors to access the nucleus. Observations showing that the capsid should be phosphorylated to change the conformation and interact with Nup153 highlight the importance of capsid remodeling and its interplay with nuclear pore factors to ensure the viral nuclear entry.The herpes simplex virus 1 (HSV-1) is a virus that belongs to the herpesviridae family. Its prevalence in the human population is high  and freqThe HSV-1 enters into the cells assisted by the proteins located in the viral envelope. The protein gB is mainly responsible, together with other proteins , for interacting with the cellular receptors and forming the core fusion machinery ,60,61,62The HSV-1 capsid shields the viral DNA in a space of 125 nm of diameter in mature angular shells (triangulation number T = 16) ,68. The The HSV-1 strategy to access the nucleus represents another example of different adaptations to overcome the cellular barriers. As we have highlighted, the capsid of HSV-1 is a main player in the infection process and is fundamental to gain access to the nucleus. Similar to other viruses, the interplay between the capsid and the components of the NPC provides adequate conditions for the preservation and nuclear translocation of viral genome. Interestingly, the EM techniques as well as host–viral interaction studies on HSV-1 have been instrumental for increasing our knowledge about the HSV-1 nuclear import ,68. BiocThe plethora of new and classical technologies will contribute altogether to provide new pieces of information on the process of HSV-1 nuclear import.The adenoviruses are a family of viruses that can infect mammals, birds, and even fish. The adenoviruses that infect humans are divided in different categories named A, B, D, E, F, and G and 57 different serotypes . Among tThe human immunodeficiency virus (HIV) is an RNA virus that belongs to the retroviridae family. This family of viruses has the particularity of reverse transcribing the RNA genome into DNA, which is the only viral form capable of integration into the host DNA ,93. The The relevance of Nup153 in HIV nuclear import has been demonstrated by Nup153 depletion experiments. The knockdown of Nup153 severely affects the HIV nuclear import ,109,132.LLPS gives rise to membraneless organelles (MLOs) that we found in the nucleus of infected cells triggered by viral infection; in particular, these MLOs are formed by CPSF6, viral RNA genome, viral integrase, viral CA, and nuclear speckle factors, while the host chromatin is excluded from them ,114. It Viruses evolved multiple mechanisms to overcome the physical barriers that cell compartments impose for its own protection. This is especially critical for viruses that require access to the nucleus to complete their life cycle. In non-dividing eukaryotic cells, the only door to this compartment is the NPC, which is hijacked by various viral strategies in order to gain access to the nucleus. Some of them such as HBV rely on the manipulation of importins and some nucleoporins such as Nup153 to reach the nuclear compartment. Others viruses such as HSV employ the interaction with nucleoporins of the cytoplasmic side of the NPC, such as Nup214 and Nup358. This interaction helps HSV to inject its genome in the nuclear compartment. On the other hand, the adenoviruses use a combination of binding to the cytoplasmic Nups and to the components of the microtubules to disrupt the capsid and release the genome in the nucleus. Of particular interest is the case of HIV-1 due to the crucial importance of its capsid for nuclear import and the subsequent nuclear steps required for its integration. The HIV-1 virus also hijacks the NPC components located on both sides of the NE (notably Nup358 and Nup153) to efficiently enter the host nuclear compartment. The importance of the capsid in the nuclear import is further highlighted by the observation that even when the retrotranscription is inhibited by nevirapine, the nuclear import still takes place . Once inThe nuclear import of viruses is still an unexplored universe with few exceptions that account for a great amount of information such as HIV-1. In many other cases such as adenoviruses, herpesvirus, or HBV, some pioneer studies illustrate novel and interesting aspects of this processes. However, there is much more to discover to generate the complete picture of how different viruses achieve the nuclear access. In the last few years, the continuous optimization of electron microscopy techniques have provided a wealth of information about previously unknown structures and mechanisms employed by viruses. It is likely that in the future, more researchers would have access to these new technologies that combined with more traditional techniques are essential tools to reach new goals in virology. The nuclear import step is essential for establishing a productive infection and viral persistence, so new knowledge on these fundamental aspects of virology will warrant new advances in the field.


Phononic crystals with phononic band gaps varying in different parameters represent a promising structure for sensing. Equipping microchannel sensors with phononic crystals has also become a great area of interest in research. For building a microchannels system compatible with conventional micro-electro-mechanical system (MEMS) technology, SU-8 is an optimal choice, because it has been used in both fields for a long time. However, its mechanical properties are greatly affected by temperature, as this affects the phononic bands of the phononic crystal. With this in mind, the viscous dissipation in microchannels of flowing liquid is required for application. To solve the problem of viscous dissipation, this article proposes a simulation model that considers the heat transfer between fluid and microchannel and analyzes the frequency domain properties of phononic crystals. The results show that when the channel length reaches 1 mm, the frequency shift caused by viscous dissipation will significantly affect detecting accuracy. Furthermore, the temperature gradient also introduces some weak passbands into the band gap. This article proves that viscous dissipation does influence the band gap of phononic crystal chemical sensors and highlights the necessity of temperature compensation in calibration. This work may promote the application of microchannel chemical sensors in the future. Phononic crystals (PnC) are analogous to photonic crystals, which are composed of periodic arrays of elastic materials. In phononic crystals, phononic bandgaps can be generated throughout the Brillouin zone, which make it possible to realize a vibrationless environment at a specific frequency. Given diverse parameters influencing the band’s structure, it also has applications in sensing ,2,3. As In binary cermet topology, phononic bandgaps can be generated by materials with high sound velocity as the host and material with low sound velocity as the internal periodic array . Such prIn the field of microchannel chemical sensors, the previous works are mainly based on the cavity mode ,8,9, in The eigen frequency of a finite periodic structure is dependent on the frequency band with a pure imaginary propagation coefficient, which means its passband is only related to frequency. COMSOL multiphysics with the finite element method (FEM) can be used to analyze the structure’s waveguide. The advantages of this lie in its flexibility. After providing appropriate element routines, various structural configurations can be examined . The subA crossover schematic diagram of components used in the simulation is shown in As the focus of this simulation is the effect of temperature on phononic crystal microchannels, an acoustic wave-generating device composed of an interdigital transducer and piezoelectric crystal is replaced with a background pressure field at blk3 as the sound pressure source, with the absolute pressure set as Arr1 is set as the fluid domain, and the property we mainly focus on is sound velocity. As for the temperature, dynamic viscosity coefficient and other parameters, we adopt the corresponding values of water that are built into the software. The other domains are set as SU-8, and its parameters are set as shown in Before viscous dissipation, the relevant simulation is performed, and the frequency domain response of the model to liquids with different sound velocity properties (the sound velocity in an aqueous solution of organic matter varies with the ratio of solvents) is tested in a 100 μm channel. In the pressure acoustic frequency domain study, the absolute sound pressure on the upper interface of ext2 is integrated, which illustrates the change in the passband in the phononic crystal. Before that, a band diagram of the tetragonal superlattice element is constructed as a 2D model is measured, as shown in The equations above are used to calculate the eigenvalue The analysis of frequency domain is then performed. The result is shown in According to reference , the mecAbove are fluid heat transfer equations for a rectangular microchannel , where ρThe viscous dissipation effect of fluids is often neglected in macroscopic channels. Equation (5) illustrates that the viscous dissipation value is inversely proportional to the cross-sectional area of the channel for a given fluid. The viscous dissipation increases as the channel becomes smaller. Therefore, in the microchannel, even fluids with a laminar Reynolds number can cause considerable temperature field variations . After teference .In the previous simulation, the temperature change is not obvious, so the length of the channel is extended to 1 mm. According to reference , an incrConjugate heat transfer in the 1 mm microchannel is simulated. As shown in Because the frequency spectrum of the 1-mm-long channel is essentially the same as that of the 100 μm channel, only the phononic band edge can be simulated accurately. As shown in A microchannel chemical sensor based on a phononic crystal has excellent application prospect. The main principle is that the band edge structure of the phononic crystal changes with the change in sound velocity caused by different chemical compositions in the liquid. A phononic crystal chemical sensor built in cavity mode may face some problems, such as mutual interference in multiple measurements, difficulty in multiple sample injection, and difficulty in filling the cavity repeatedly. In order to meet the practical needs, it may be necessary to drive the liquid flow through the phononic crystal by means of pressure or electroosmosis. In the microchannel, the viscous dissipation of flow with a low Reynolds number can also cause obvious temperature field changes, which will have a significant impact on the mechanical properties of SU-8. Therefore, this article proposes a model for the viscous dissipation and the conjugate heat transfer between fluid and microchannel. Furthermore, the frequency domain properties of phononic crystal are also analyzed. Through numerical analysis, it can be found that when the channel length reaches 1 mm, the frequency shift brought about by viscous dissipation will significantly affect the detection accuracy. Therefore, in standard band edge calibration, the standard operating conditions of the sensor, such as the Reynolds number and the temperature, should be clearly defined. When making high-precision measurements, temperature compensation mechanisms should be considered. The temperature gradient related to the viscous dissipation effect may give rise to a weak passband in the phononic gap, whose effect may be more obvious in a longer flow channel. This work has proposed a reliable model and proven that viscous dissipation does influence the band gap of phononic crystal chemical sensors. Moreover, it declares the necessity of temperature compensation during calibration, which will promote the application of microchannel chemical sensors in the future.