Lung adenocarcinoma (LUAD) is a typical disease regarded as having multi-stage progression. However, many existing methods often ignore the critical differences among these stages, thereby limiting their effectiveness for discovering key biological molecules and biological functions as signals at each stage. In this study, we propose a method to discover the evolution between biological molecules and biological functions by investigating the multi-stage biological molecules of LUAD. The method is based on the random walk algorithm and the Monte Carlo method to generate clusters as the modules, which were used as subgraphs of the differentiated biological molecules network in each stage. The connection between modules of adjacent stages is based on the measurement of the Jaccard coefficient. The online gene set enrichment analysis tool (DAVID) was used to obtain biological functions corresponding to the individual important modules. The core evolution network was constructed by combining the aforementioned two networks. Since the networks here are all dynamic, we also propose a strategy to visualize the dynamic information together in one network. Eventually, 12 core modules and 11 core biological functions were found through such evolutionary analyses. Among the core biological functions that we obtained, six functions are related to the disease, the biological function of neutrophil chemotaxis is not directly associated with LUAD but can serve as a predictor, two functions may serve as a predictive signal, and two functions need to be verified through more biological evidence. Compared with two alternative design methods, the method proposed in this study performed more efficiently. Lung cancer is a type of malignant tumor with the highest morbidity and mortality in the world at present , while lRecent developments in experimental procedures have resulted in several mature methods to analyze biological molecules. One approach involves directly using gene set enrichment analysis (GSEA) to identify crucial biological molecules in LUAD  and age-To overcome this limitation, the present work aims to identify the crucial biological molecules of LUAD and the biological functions that accompany LUAD through its four stages, ultimately aiming to improve the diagnosis, treatment, and prognosis of LUAD. The aim is to discover the evolution between biological molecules and biological functions by investigating the multi-stage biological molecules of LUAD.Many current methods for clustering biological molecules in order to identify key biological molecules use the random walk algorithm. However, differing from the traditional random walk algorithm, we combine the Monte Carlo method with a random walk approach, which does not record the start vertex and the end vertex of the walking path but instead assigns a weight to every step in the walking. Moreover, studies on networks that use the traditional random walk algorithm can provide only a generic solution, lacking in specificity. Thus, we consider the degree of the vertices to help define the weight by introducing the penalty coefficient.Specifically, the steps followed in the present work are as follows. The stage-specific differentiated biological molecule network was first built, which contains genes, miRNA, and lncRNA, respectively. An innovative clustering method based on the random walk  algorithhttps://portal.gdc.cancer.gov/), including tumor and normal groups, and we obtained the data for mRNA, miRNA, and lncRNA. The genome annotation for Homo sapiens was downloaded from the Gencode database (https://www.gencodegenes.org/). Duplicate genes were removed and standardized using the trimmed mean of M-values (TMM) normalization . The datasets were downloaded from The Cancer Genome Atlas (TCGA) database . The last step (building the core networks) concerned how to build the global module network by connecting modules in each stage, further using similarity to connect modules in adjacent stages, and how to build the functional interaction network using the Gene Ontology (GO) database and the Kyoto Encyclopedia of Genes and Genomes (KEGG) in GSEA to obtain the biological functions corresponding to the modules. This step also concerned how to build the core evolution network through the combination of the two aforementioned networks, as well as how to find the core biological molecule modules and the core biological functions. The general framework of the proposed method is shown in The analysis process comprised three steps: 1) building the stage-specific differentiated biological molecule network, 2) module identification, and 3) building the core networks. In the first step , the dataset was transformed into the differentiated biological molecule network in each stage, including not only the differentiated genes but also the miRNA and lncRNA. In the module-identification step, modules of the differentiated biological molecule network were obtained by clustering the vertices and edges in the network through the innovative walking algorithm. The source code for the algorithm in this step is available on Github   , and theSubsequently, the selected biological functions were taken as vertices, and we used the Jaccard coefficient to evaluate their similarity to generate a functional interaction network for further analysis.The global module network and the functional interaction network both present the statistical information about the disease. Since we obtained the functions in the modules, it can be proven that there is a relationship between the functions and the modules. Therefore, the aforementioned two kinds of networks can be combined to generate a comprehensive network. In this comprehensive network, we combined the two networks with the relationship between the modules and functions as new edges. The comprehensive network combines the two aspects of the disease , as well as combining information about the four stages. We thus took both modules and functions as vertices and took three kinds of relationships  as edges.μ − σ, μ + σ) in the normal distribution, which corresponds to 68.26%  and also better than that of Design2 (which shows that it is better to build modules than to put vertices together).In this study, we have proposed a method to investigate the evolution of LUAD from the perspective of the combination of graph theory knowledge and biological knowledge. The global module network, the functional interaction network, and the core evolution network were presented from the dynamic evolution point of view. In the core evolution network, there are 12 core modules and 11 core biological functions. Among the core biological functions, six are related to the disease, the biological function of neutrophil chemotaxis is not straightly associated with LUAD but can serve as a prediction, two functions may serve as a predictive signal, and two functions need to be verified through more biological evidence. The core evolution network highlights the evolution information for the multi-stage disease.The advantages of the proposed method are as follows. First, we chose an innovative clustering algorithm based on the random walk algorithm and the Monte Carlo method for the network clustering and designed a set of parameters for each step of the experiment to find the best parameter setting based on statistical principles. Additionally, many objective factors were considered in each step of the algorithm design, and some simple ideas or models were used to solve problems. Second, compared with other methods, our method not only presented the information of each stage statically, but also presented the evolution dynamically. Third, the idea of “focusing on the main factors” is implied in every step, which greatly reduced the amount of work and harvested the most typical results.The limitations of the proposed method are as follows. The algorithm can be further optimized to overcome the high time complexity of the method. Moreover, in the cluster-screening step, we directly combined the union as the clustering results, without considering the corresponding problems of irrelevant vertices, which should be further investigated.


With the constant need for the development of smart devices, Micro-Electro-Mechanical Systems (MEMS) based smart sensors have been developed to detect hazard materials, micro-particles or even toxic substances. Identifying small particles using such micro-engineering technology requires designing sensors with high sensitivity, selectivity and ease of integration with other electronic components. Nevertheless, the available detection mechanism designs are still juvenile and need more innovative ideas to be even more competitive. Therefore, this work aims to introduce a novel, smart and innovative micro-sensor design consisting of two weakly electrostatically coupled microbeams (both serving as sensors) and electrically excited using a stationary electrode assuming a dc/ac electric signal. The sensor design can be tuned from straight to eventually initially curved microbeams. Such an arrangement would develop certain nonlinear phenomena, such as the snap-through motion. This behavior would portray certain mode veering/mode crossing and ultimately mode localization and it would certainly lead in increasing the sensitivity of the mode-localized based sensing mechanism. These can be achieved by tracking the change in the resonance frequencies of the two microbeams as the coupling control parameter is varied. To this extent, a nonlinear model of the design is presented, and then a reduced-order model considering all geometric and electrical nonlinearities is established. A Long-Time Integration (LTI) method is utilized to solve the static and dynamics of the coupled resonators under primary lower-order and higher-order resonances, respectively. It is shown that the system can display veering and mode coupling in the vicinity of the primary resonances of both beams. Such detected modal interactions lead to an increase in the sensitivity of the sensor design. In addition, the use of two different beam’s configurations in one device uncovered a possibility of using this design in detecting two potential substances at the same time using the two interacting resonant peaks. Micro-Electro-Mechanical Systems (MEMS) designate a smart and innovative technology integrating small devices with a combination of miniature mechanical and electrical components. Most of these devices are fabricated using bulk micro-machining, surface micro-machining and lithography processes and their assembly is based on integrating semiconductors’ circuitry processes, such as PolyMUMPs, SOIMUMPs and PiezoMUMPs ,2,3,4. TThere are different methods to excite MEMS devices, such as electrothermal, electromagnetic, piezoelectric and electrostatic. Among these methods, the electrostatic actuation has been developed and utilized in a wide variety of applications due to its many inherent advantages. For example, it offers good coupling between different energy domains in the micro-scale, requires small current compared to other actuation methods, reduces the overall power consumption, produces a controllable distance and requires a simple fabrication process ,3,4. TheThe electrostatic actuation has several arrangements, such as parallel electrodes (microbeams) based capacitor and even interdigitated comb-fingers, where in both, the force can be attractive when the two electrodes are of opposite charges and repulsive when they are carrying the same electrical charges. However, this actuation mechanism results in some nonlinear phenomena, such as dynamic pull-in instability where the electrostatic actuating force becomes higher than restoring mechanical force and limits the travel ranges of MEMS devices ,7,8,9. TTo overcome this challenge and to increase the electrostatically actuated micro-structures travel range, flexible and slightly curved beams  have been suggested and then thoroughly examined ,13,14,15Due to the interaction between the geometry nonlinearity (mid-plane stretching) and the force nonlinearity, the curved structure exhibits multiple stable equilibria, snap-through motion and pull-in instabilities along with modal interaction ,20,21,22However, the instability usually coexists with any large nonlinear behavior, and therefore, it is indispensable to explore how to increase the vibration amplitude without reducing the stability of the designed micro-sensor. Nevertheless, and despite the challenging concerns coming from the nonlinear behavior, electrostatically actuated MEMS resonators have been utilized as sensors mainly utilizing the resonance frequency shift to measure forces, accelerations and masses ,25. To tIndeed, some research works ,40,41,42In this regard, the aim of the proposed work is to suggest and examine a novel MEMS sensor design consisting of two microbeams coupled and excited electrostatically via one lower in-plane stationary electrode. The design has the advantage of coupling electrostatically two microbeams serving as sensors to reduce the required input power and the device input power and footprint compared to that driven by comb-drive fingers. The two beams can be fabricated as straight and/or initially curved beams considering the advantages mentioned earlier in the literature review survey. The use of two different beam configurations in one device is beneficiary toward detecting two potential substances at the same time. The system would be a representative design of a mode-localized based sensor consisting of two weakly electrostatically coupled microbeams. A comprehensive analytical model incorporating all possible nonlinear terms is presented and solved based on the Galerkin method combined with the Long-Time Integration (LTI) method. The dynamic characteristics of two coupled resonators are investigated around their respective primary resonances.The proposed sensor consists of two microbeams, both designed as straight or initially curved, denoted as upper and lower beams and actuated by one sidewall electrode, as shown in The sensor uses the phenomenon of mode localization and measures the change in the vibration mode of coupled resonators to detect a small perturbation. Its sensitivity depends on the ratio between the mechanical properties of the microbeams and the electrostatic coupling force. We expect that any small perturbation in the added mass will lead to veering and/or crossover phenomena, and therefore a change in the resonance frequency can be measured. The sensor’s sensitivity also depends on the operational mode where there are two fundamental modes. The first one is the quasi-static mode known in the literature as binary sensors with ON and OFF states. The second mode is based on a harmonic signal where the sensor can be operated as a traditional linear frequency-shift-based sensor or bifurcation-type based sensor depending on the actuation levels. We expect that the bifurcation-type sensors are significantly sensitive compared to the quasi-static and linear-frequency shift sensors to changes in mass interpreted as changes in the location of the bifurcation nodes in the nonlinear frequency responses.The operational principle of the proposed design depends on the vibrating modes of the microbeams, as shown in the simple lumped model of h is the thickness and b is the width. Knowing that both beams are anchored and as a first step, we draw the free-body-diagram (F.B.D) for each beam as shown in The problem formulation and derivation of the equations of motion describing the transverse motion of the above sensor have been carried out following the Newton’s mechanics approach. The two beams are coupled electrostatically as shown in The forcing terms appearing in both two figures  yiel yiel(5)wlower microbeamupper microbeamquations  and 8)  (8)w¨u+cEquations  and 8)  8) are dSimilarly, the equation describing the static equilibria of the upper beam under the effect of the static voltage can be written as:Then, we descretize the static deflections of the two microbeams in terms of the Galerkin approximation asquations –14) and and(15)wquations  by [17) by thThese equations are then solved for In this investigation, two main actuation scenarios will be considered. The first scenario is to vary the lower beam’s actuation signal and keep it at a constant level for the upper beam. Then, we will revert the process by applying a varying signal to the upper beam and keep the lower beam actuation signal at a constant value. This is a required step to study the nonlinear dynamics and modal interactions of the two beams and how the variation in the control parameter would affect their static, eigenvalues and dynamic responses.Here, we investigate the static and dynamic responses of the coupled beams when the excitation signal varies along the lower beam and the upper beam quations  and 19)Vudc voltSimilar behavior is also observed when the static voltage of the upper beam increases to 20 V. However, its mid-point deflection starts changing from a new setting-point corresponding to To further validate this, we increase the upper microbeam voltage to 40 V. This leads to a highly nonlinear static response characterized by a snap through where the stable branches of the solution meet the unstable branches of the solution, as shown in Next, we explore the effect of these excitation signals on the fundamental frequencies of both microbeams. This is performed by substituting the static results obtained above, employing a ROM with three symmetric modes into the equation described in We note that the veering phenomenon may occur when one of the eigenvalues of the two beams approach each other as the excitation signal varies. This is a similar behavior to that presented in ,22,34,39Increasing the upper static voltage to Furthermore, we examine the frequency-response curves of the first lower  and jump at A similar behavior is also observed when the lower voltage sets to We note that, under this actuation scheme, the lower beam starts its deflection from a new biased position corresponding to Moreover, the variation of the fundamental frequencies of the both microbeams under excitation waveforms similar to that used in the static analysis has been studied. This will give more insight as to whether the modes are veering or crossing each other under these excitation conditions. Setting the lower static voltage to Then, it increases as the upper voltage further increases along the second branch of equilibria, corresponding to the initial counter curvature, until it reaches a maximum value of 14.88 kHz. After that, it suddenly drops and reaches zero at the pull-in instability voltage of On the other hand, the upper beam fundamental frequency continuously drops along the first stable equilibria, marked with orange line, as the voltage increases until it reaches a zone where its value become closer to the lower beam fundamental frequency. This is a classical behavior of the veering phenomenon where two modes are approaching each other and then veer away as the control parameters change. In the neighborhood of veering zone, we have found that the minimum frequency gap between the two frequencies is approximately A similar behavior is also observed when the lower static voltage increases to The dynamic response under this excitation scenario has been investigated by subjecting the two beams to a frequency sweep test in the vicinity of the veering zone, as described in The variation of the two beam mid-point velocities obtained under a voltage waveform with Further increasing the upper static voltage leads to a fast attraction toward the veering zone with frequency gap starting to decrease, as shown in As the excitation force leaves the veering zone, the two modes start growing with energy showing a mode localization like in the vicinity of the lower beam primary resonance due to its shortcoming as shown in Replication of the above analysis with the lower voltage set to This investigation has explored the vibration of weakly electrostatically coupled clamped-clamped straight and initially curved microbeams. Linear (veering and crossing) and nonlinear  modal interactions under primary resonance were examined for potential use of the design as a mode-localized based sensor. A comprehensive analytical model incorporating all nonlinearities was established and then numerically solved based on the Galerkin modal expansion method superimposed to a long-time integration technique. The dynamic characteristics of the two coupled resonators under primary resonance were generated, and the contributions of their respective primary resonances in the overall response were analyzed accordingly. The static results under dc voltages only showed possibilities of having a mix of one-stable and even two-stables operating conditions, both adjustable through slightly perturbing the assumed lower stationary electrode dc voltage. Subsequently, this control parameter showed as well, throughout an eigenvalue problem analysis, that for the coupled resonators, mode veering can occur, offering potentials of nonlinear modal interaction, such as mode localization. Then, a dynamic analysis was carried out and showed that under the same excitation conditions and around the system primary resonance, linear and even softening behaviors can be obtained by adjusting the overall actuating dc and/or ac voltage amplitudes. In addition, when assuming a dc voltage at the lower electrode that triggers possible modes veering, it was noticed that as this excitation force drives the coupled system in the neighborhood of such a veering zone, the two primary resonant modes are at maximum amplitudes, showing a non-trivial frequency gap. They start varying and show a mode localization like in the vicinity of the upper and/or lower beam primary resonance. This confirmed that as the two resonant peaks are penetrating the veering zone, the upper and lower microbeams’ respective frequencies gap reduces and they sort of exchange the peak-like dominance accordingly. Such interesting modal interactions could lead to an increase in the sensitivity of such a sensing mechanism and the computed results showed that this can be achieved by just varying a simple control dc voltage parameter. The use of two different beam configurations in one device showed the possibility of detecting two potential substances at the same time with two interacting distinct resonant peaks.


Recent studies have examined the relationship between economic policy uncertainty and exchange rate. We contribute to this literature by considering the effect of minor positive and major positive changes as well as minor negative and major negative changes in the economic policy uncertainties on the exchange rates. In this regard, we use a recently developed multiple asymmetric threshold nonlinear ARDL model along with Granger causality in quantile test. Our estimates support the asymmetric effect in three countries only when an asymmetric ARDL model is used. However, these estimates support asymmetric effects for all the sample countries when the multiple asymmetric threshold nonlinear ARDL model is used. Moreover, the effect varies across various quantiles when Granger causality in quantile test is used. Overall, the extended model helps us to examine more minutely the impact of EPU and GEPU on the exchange rate in G7 countries. The results of this study can be useful for the central banks to devise appropriate policies to intervene in the foreign exchange market. Uncertainty plays a negative role in economic activity. For instance, during uncertainty, firms do not make investment decisions until more information arrives in the future because the cost of investment decisions is irreversible  and exchange rate. For example, Bartsch  used GARThe limitation of the above literature is that it does not differentiate the effect of positive and negative changes in the EPU on the exchange rate. More specifically, it does not distinguish the impact of minor to major positive shocks in the EPU and minor to major adverse shocks in the EPU on the exchange rates. However, investors demand more risk premium for bearing additional risk. Therefore, the investors and other stakeholders react more abruptly to negative news, such as increasing policy uncertainty, than positive news. In other words, foreign investors will make quick adjustments in their investment decisions when there is rising policy uncertainty in a foreign country compared to a stable policy. Moreover, since the change in the investment and policy decisions involve cost, investors may not change their choices during minor policy changes. In contrast, they may change decisions when there are significant changes in the foreign policy uncertainties.This study extends the literature by using extended methodologies such as a recently developed multiple asymmetric threshold nonlinear ARDL (MATMARDL) model proposed by Uche et al. . The MATOur study contributes to the existing literature in various ways: First, using a nonlinear ARDL cointegration modeling approach, this study examines the asymmetric impact of domestic EPU on the exchange rates in G7 countries. Second, since foreign shocks also influence the domestic exchange rate, we also look at the effect of global EPU (GEPU) on the exchange rate. Finally, we differentiate the impact of minor to major positive shocks in EPU and GEPU and the effect of minor to major negative shocks in EPU and GEPU on the exchange rates in G7 countries.2The present study explores the effect of domestic EPU and Global EPU (GEPU) on the exchange rate in G7 countries. The selection of the G7 countries as a venue for research is based on the following reasons. First, The G7 countries’ sample is the most industrialized and represents 58%  of the Global net worth OECD, . Second,The remainder of the paper is structured as follows: Section “Data and methodology” describes the data and explains the methods to carry out this study, section “Empirical results” presents the empirical findings, and section “Conclusion, policy implications and limitations of the study” concludes the research and proposes policy recommendations.This study investigates whether the effect of EPU and global EPU (GEPU) on exchange rate varies from minor to major positive shocks in the EPU and GEPU and from minor to major adverse shocks in the EPU and GEPU in G7 countries. To do this, we use monthly data from January 1998 to January 2021. The sample period is selected based on the data availability of the variables under study. The current study uses monthly data to contain more information than quarterly data. Besides, monthly data is less noisy than the daily data series  on the real effective exchange rate in G7 countries. For this purpose, we use the nonlinear ARDL (NARDL) model proposed by Shin et al.  and the μ shows intercept, Xt shows all the independent variables in Kx1 vector form. The long-run coefficients are represented by ρ and θ, whereas the short-run coefficients are represented by α and β. The lag order of the dependent and independent variables is shown by p and q, respectively. Finally, ρ = θ = 0) against the alternative hypothesis of cointegration  way to both positive (increase) and negative (decrease) shocks to the explanatory variables. The general form of the standard linear ARDL model is expressed as follows:n et al.  to test The primary assumption of the above ARDL model is that all independent variables have symmetric effects on the dependent variable. However, in real life, this may not be the case. Shin et al.  proposedp, q, r, and s represent the lag order against each variable in the short run, the long-run asymmetry is examined using Wald-test under the null hypothesis: F-test and the Wald-test for the joint cointegration test. The null hypothesis under this test is that all the long-run coefficients are jointly equal to zero.Using Eqs. Pal and Mitra , 2016 inTherefore, the present study uses this advanced model to understand the comprehensive relationship between EPU and exchange rate in G7 countries. In this regard, the EPU variable is decomposed into three positive and three adverse shocks series as follows:I{T} represents the indicator function where its value is equal to 1 if the condition in parenthesis is satisfied or 0 otherwise. The decomposition of EPU into three negative partial sum series  and three positive partial sum series  can be expressed using the multiple asymmetric thresholds NARDL (MATNARDL) model proposed by Uche et al.  regarding all We also use the Granger causality test in our analysis. Granger causality test is used to examine the causal relationship among the given variables. This test assumes that the dependent variable is explained independently of the lags of the independent variables. Researchers have extended the Granger causality test using advanced and diverse techniques. Our study uses the Granger causality test in quantiles proposed by Troster  to examiIn Eq. R-square is used to determine whether the models are a good fit.Moreover, to examine the goodness of fit of the models and other requirements of the models used in this study, we use stability and other diagnostic tests. Ramsey RESET is used to examine whether the models are correctly specified, the serial correlation test is used to determine whether there is no autocorrelation issue in the models, and CUSUM and CUSUMQ tests are used to examine whether the models are stable. Finally, an adjusted We report the descriptive statistics and other preliminary stationarity tests before conducting the primary analysis. Table I (0) or one I (1), or mixed order . Therefore, to check the order of integrating the variables, we use standard unit root tests, such as augmented Dickey-Fuller (ADF) and Kwiatkowski PhillipsSchmidt Shin (KPSS) tests. The null hypothesis under the ADF test is that the series has a unit root, whereas the null hypothesis under KPSS test statistics shows that the series has no unit root. Table Since NARDL and multiple asymmetric thresholds NARDL . Therefore, using the recently developed MATNARDL model by Uche et al. , we decoAdditionally, we check the short- and long-run asymmetry between EPU and exchange rate using the Wald-test and present results in Table Next, we present the NARDL estimates in Table +) in Canada and Japan significantly and positively affects the exchange rate. In contrast, a decrease in the EPU does not significantly affect the exchange rate. These results, therefore, suggest long-run asymmetry in Canada and Japan. On the contrary, the long-run estimates in the UK indicate a significant and negative effect of both positive and negative shocks in the EPU, whereas, in France, Germany, Italy, and the US, insignificant results are found for both positive and negative surprises in the EPU. The possible reason for the insignificant effect in these countries may be that these countries have implemented practical hedging tools to avoid the risks associated with economic uncertainties. Krol  test, a chi-square distribution with two degrees of freedom. The LM test statistic for each sample country is also reported in panel C Table . The tesR-square is used to check the goodness of the fit of each model. These values (panel C) indicate that the NARDL model enjoys a good fit.Moreover, to check the stability of the models, we employ the CUSUM and CUSUMQ tests. In these tests, ‘S’ indicates the parameters are stable while “US” shows that parameters are not stable. Our estimates suggest that the model is stable in most cases except in Japan and the UK with the CUSUM and CUSUMQ tests, respectively. Next, the ECM test is used to check the convergence or the speed of adjustment towards the long-run equilibrium. ECM values are negative and statistically significant, which supports the model requirements. Finally, an adjusted As mentioned earlier, the standard NARDL model does not consider the effect of minimal and substantial positive and negative changes in the exogenous variable on the dependent variable. However, the foreign exchange market reacts differently to small and large positive and small and large negative changes in the economic uncertainties. Therefore, to consider the effect of minimal and extensive changes in the EPU, we use the multiple asymmetric threshold nonlinear ARDL (MATNARDL) model proposed by Uche et al. . For theNext, Table Table Moreover, panel B Table  presentsIn the above estimates, we use the EPU of each country to examine its effect on the exchange rate. However, we also use Global EPU (GEPU) for robustness purposes, re-estimate both NARDL and MATNARDL models, and present these results in Appendix A Tables . The finOverall, our study is based on assumptions of purchasing power parity theory of the equilibrium exchange rate. This theory was developed by Gustav Kassel in 1920, and it is based on the law of one price. Overall the researchers claim that “The theory is based on Law of One Price (LOOP), and simply claims that the exchange rate is determined by relative developments of domestic and foreign prices”. As for as our findings are concerned, we support this argument and most of the results are consistent with the arguments stated by purchasing power parity.Uncertainties in economic activities have a negative role on the economic growth of any country. It becomes challenging for firms to make investment decisions during economic uncertainties as economic policy uncertainties affect international trade and other macroeconomic variables, including the exchange rate. Bloom  providedRecent literature has shifted to examining the nonlinear effect of EPU on the economic and financial variables. However, no study has been conducted so far which focuses explicitly on the asymmetric impact of EPU on the exchange rate, with a particular focus on the effect of extreme changes in the EPU. This study extends the existing literature by examining the asymmetric impact of EPU on the exchange rate in G7 countries. It further extends the literature by examining the effect of minimal and substantial positive and minimal and substantial negative changes in the EPU on the exchange rate. Moreover, we use global EPU (GEPU) for robustness purposes and discuss its impact on the exchange rate. To investigate the effects of positive and negative shocks in EPU and GEPU on the exchange rate, we use the NARDL model Shin et al.  proposedNARDL estimates indicate that, in the long run, EPU asymmetrically affects the exchange rate in the context of Canada and Japan only. In contrast, in the short run, it asymmetrically affects the context of Canada, Japan, and the UK only. Moreover, MATNARDL estimates indicate all sample countries’ short-run and long-run asymmetric effects. Overall, these results significantly change when the MATNARDL model is used, showing superiority over the standard NARDL model. These findings indicate that the MATNARDL model helps examine the effect more minutely than the standard NARDL model fails to investigate.Following Vuong et al.  and VuonThe findings of our study can be helpful for the governments, policymakers, and other relevant stakeholders. Specifically, our results indicate that the effect of EPU significantly changes when a MATNARDL model is used, which, therefore, suggests taking into account the impact of substantial and small changes in the economic policy uncertainties. Ignoring the effect of these significant changes may lead to misleading conclusions. Moreover, making the same investment decisions across all extremes of the uncertainties may lead to unfavorable consequences. For example, our MATNARDL estimates indicate that positive shocks in the EPU significantly affect the exchange rate, whereas adverse shocks in the EPU do not significantly affect the exchange rate. Therefore, these differences in economic policies must be considered while formulating the relevant guidelines. We expect the governments of the relevant countries to consider the proper implementation of the policies.Following the suggestions by Vuong , we ment


This paper estimates the impact of public guarantees on crisis predictive indicators among small and mid-size enterprises (SMEs). We use a confidential database provided by the Italian Ministry of Economic Development on the universe of guarantees granted by the Central Guarantee Fund. We apply difference-in-difference regressions and propensity-score matching estimators to a sample of approximately 40,000 SMEs over the 2010–2018 period. We find that obtaining a public guarantee improves profitability both in the short- and medium-term. On the other hand, SMEs’ financial health worsens in the short run, but financial burdens are alleviated 2 years after the issuance of a guarantee. The economic and financial effects of government-backed loans are amplified for micro-sized firms, companies operating in the service sector and direct guarantees. Our results can thus support public authorities in designing credit guarantee schemes capable of preventing SMEs’ zombification and protecting them from the risk of debt overhang. Access to public credit guarantee schemes negatively impact SMEs’ financial equilibrium, but their recovery occurs 2 years after guarantee issue. How does one select eligible firms to prevent zombification? Using a confidential dataset provided by the Italian Ministry of Economic Development on guarantees issued by the Central Guarantee Fund, we investigate this topic with an unprecedented level of salience. Our findings reveal the need for cautious interventions on firms in financial distress and for the introduction of stress tests to select beneficiaries. Our results show that specific guarantee lines could be applied for direct guarantees granted to micro-sized enterprises and companies operating in the service sector to maximize the additionality of public resources. This study has practical, policy and societal implications, guiding SMEs in their assessment of the overall medium-term effects of guarantees and policy-makers in their rethinking of guarantee schemes to resolve trade-offs between effectiveness and sustainability. Throughout European countries, plans for recovery and resilience following the coronavirus disease (COVID-19) pandemic have included the strengthening of public guarantee programmes. In addition to moratoria on loan repayments, tax deferrals, grants, equity facilities and wage subsidies, public guarantee schemes represent a fundamental instrument within the countercyclical public policy toolkit deployed by governments to support the liquidity needs of firms, particularly small and mid-size enterprises (SMEs) ?This study aims to evaluate the effects of government-backed finance on SMEs’ crisis indicators 1 year and 2 years after guarantees are issued. We attempt to understand whether public guarantees are able to impact the business continuity prospects of guaranteed SMEs by comparing them to non-guaranteed SMEs. We specifically address the following research questions:To answer these questions, we use a confidential database provided by the Italian Ministry of Economic Development that includes all guarantees issued by the Italian Central Guarantee Fund (CGF) from 2012 to 2016, which we integrate with data downloaded from the Aida Bureau van Dijk database for a period ending in 2018. We use difference-in-difference regressions (DiD or diff-in-diff) and propensity-score matching estimators to compare a proprietary sample of 17,810 guaranteed firms with a sample of approximately 21,000 comparable SMEs.Papers that analyse the impacts of government-sponsored credits typically focus on a specific country given the need to compare transactions regulated by the same legislation  to obtain predictive signals of corporate crises. Public guarantee funds pursue economic policy objectives but must simultaneously ensure sustainability in the use of public funds for the benefit of the taxpayers. Therefore, the selection of eligible companies while considering business continuity prospects over time from a forward-looking perspective is essential. Then, the study measures the impacts of new guaranteed loans on the overall health of the company as measured by predictive indicators of corporate crises. The overall package of these indicators was not previously investigated by the international literature and represents one of the first empirical tests applying the recent Code of the Business Crisis and Insolvency . The Code aims to create functional instruments to facilitate the early identification of the debtor’s financial crisis to prevent insolvency and, when such efforts fail, manage the insolvency with the aim of overcoming the crisis and restoring the company to profitability. Therefore, the warning signals to prevent a crisis investigated in this study include not only economic and capital adequacy indicators but also debt sustainability indices, which are particularly relevant in evaluating the effectiveness of public support for access to new financing. Regarding this issue, the literature has paid limited attention to the impact of public programmes on firms’ liquidity and the overall structure of corporate debts. We attempt to contribute to filling this gap by studying the impact of guarantees on the overall cost of corporate debt and debt sustainability with cash flows.The effects of public guarantees on SMEs’ going concern were investigated in the context of economic and financial crises  and the repayment periods of guaranteed loans and reducing guarantee fees and documentation requirements AECM, .Public guarantee programmes are among the main tools used to support access to finance during and after a recession period. As a strategic response to a financial and economic crisis, these schemes seem to be more effective than other direct public interventions  a direct guarantee can be activated to cover a loan granted by a bank, a leasing company or other financial intermediaries without directly intervening in the lender-borrower relationship; or (2) a counterguaranteeSMEs that exceed a predefined probability of default cannot access the Fund. Eligible firms, on the other hand, have different conditions for accessing the Fund based on their obtained score. For example, national regulations establish the maximum coverage percentages of the guarantee to the total amount of the loan and the maximum guaranteed amount, which can vary based on the obtained score. The guarantee never covers 100% of the loan, but the coverage rate can reach 80% of the loan for direct guarantees and 90% for a counter-guarantee to an MGI whose guarantee cannot, however, exceed 80% of the loan. Such conditions also differ according to the amount and type of operation guaranteed, in the short- or medium–long-term, for liquidity or investments.During and after relevant economic or financial shocks, when firms’ survival is exposed to growing risks, the CGF has experienced significantly increasing rates in both the applications for admission received and accepted. In particular, the role of the CGF was strengthened during the international financial crisis started in 2008 and after the European sovereign debt crisis started in 2010. It was refinanced with approximately two billion euros between 2008 and 2012 and then again between 2013 and 2014 with 1.2 billion euros. Afterwards, during the COVID-19 pandemic, the Italian government adopted extraordinary measures that reinforced and significantly expanded the programme by broadening its coverage, relaxing its eligibility criteria and increasing its endowment.During the period covered in this study, the number of requests forwarded to the CGF increased by approximately 60%, the number of requests accepted has risen by almost 70%, while the number of companies guaranteed grew by approximately 60%.During the COVID-19 emergency, the functioning of the CGF has been temporarily modified. Currently, it could be necessary to rethink the structure of the programme during the post-pandemic era.This paper is related to the literature that studies the effects of public interventions in terms of supporting the access to finance of micro-sized enterprises and SMEs. This focus on smaller companies is particularly relevant since such companies are a crucial element of most European countries: in 2020, they accounted for more than 99.8% of all the businesses in the EU-27 non-financial business sector, contributed more than half of the value added of the Union and accounted for approximately two thirds of the total employment of the private sector with over 90 million employees  economic additionality and (2) financial additionality.Employment by considering increases in the number of employees or the employment growth rate , the accessed loan and the sector and geographical area of the guaranteed firm. In the dataset, we include the balance sheet information of the guaranteed firms, which is sourced from the Aida Bureau van Dijk database. To cover the periods before and after each guarantee was granted, we collect data from 2010 to 2018. The values are downloaded from the 2 years before the issuance of each guarantee for bias correction; financial and economic data from 2017 and 2018 are used to measure the impacts of the public guarantees. Table We develop a consistent control sample of comparable firms that did not receive public guarantees during the same period Rubin, . We downTo identify the determinants of access to the CGF, we refer to variables used in the literature to evaluate firms’ creditworthiness Altman, . AccordiPrevious studies  and SMEs’ ongoing concern indicators (measured by crisis indicators). To evaluate economic additionality, we choose the ROI because it can be used to measure, in terms of profitability, the effect of new investments financed by guaranteed loans , we choose the covariates by conducting a probit regression. The formula is as follows:We use a matching estimator, ithm Li, . The ATTi observed in the year before the guarantee is granted (t-1). We use the k-nearest matching algorithm and identify k-matched (control) observations from the sample of non-guaranteed firms, namely the “untreated” firms, for each observation. The control observations are the non-guaranteed firms that are closest to the treated observations in terms of propensity score. The number of control observations, k, is arbitrarily determined. We estimate the average treatment of the sample with four equally weighted matches, controlling for heteroskedasticity . Indeed, Abadie & Imbens  and industry  of each firm. We proxy the size of each firm based on its number of employees: micro-sized enterprises have up to 10 employees; small firms have between 11 and 50 employees; and medium firms have between 51 and 250 employees. Using the aforementioned k-nearest matching estimator, for each subsample, we estimate the effect of guarantees on the changes in profitability and the indicators of business crisis 1 and 2 years after the issuance of the guarantees. Then, we apply propensity score matching to each subsample.i at time t; n is equal to 1 and 2; To overcome the potential limitations of propensity score matching, we also apply the DiD methodology. Equation  represenFirst, a probit regression is conducted to verify the relevance of the covariates. Table Table The guarantees help increase the difference between guaranteed and non-guaranteed firms. First, the guarantees have a strong effect on the ROI growth rate during the year after the intervention of the CGF. The impact on this variable is even greater 2 years after the issuance of the guarantee. The loans obtained due to the credit-support programme contribute, with a high level of statistical significance, to the improvement of ROI for guaranteed firms, both in the short- and medium-term. These results confirm the main findings of the accredited literature on economic additionality /total assets growth rate.The consideration of further important aspects related to the ongoing concern of SMEs is the main contribution of our study. Therefore, first, our analysis reveals a relevant effect on the liquidity position of the examined guaranteed companies. The growth rate of the current ratio among the firms that have been granted public support is higher than that of companies without this support. No direct impact is recorded on the ratio of cash flow to total assets. According to our results, guarantees are not able to directly impact the ability of companies to generate cash flow. On the other hand, a significant effect is produced on the ratios related to the firms’ financial health:The relation between interest expenses and total sales seems to worsen in the short- and medium-term. In particular, for micro-sized enterprises, obtaining a guarantee involves a significant increase in the growth rate of this ratio.Firms that use state-backed credit incur costs. Usually, guarantees are not provided free of charge, but their costs in the focal period range from 0.25 to 1% of the guaranteed amount.On the other hand, the interest rates of guaranteed loans should reflect the presence of a public guarantee as follows: a guaranteed loan should be more inexpensive than it would have been without the guarantee. This is also related to the inclusion of all the main public guarantee programmes on the list of credit risk mitigators of the EU Capital Requirement Regulation. Nevertheless, in addition to the guarantee fees passed onto borrowers, companies can face an increase in the interest rates applied to other unsecured loans due to the potential worsening of their financial structure and creditworthiness. Indeed, once they are accepted for public guarantees, supported companies change their financial structures and increase their debt-to-equity ratios, as shown by our main results. Growth is particularly exhibited by micro- and medium-sized enterprises in the short-term and by small firms in the medium run. There is not only an increase in the leverage of guaranteed firms compared to that of unsecured companies but also an improvement in the composition of corporate debts. The growth in a company’s “/total assets” ratio decreases when it obtains a guarantee, improving its financial structure. This may be related to an increase in assets due to the new investments made possible by the guaranteed loan and/or to a partial reimbursement of old tax debts and social security debts that occurs once the new liquidity has been obtained.Such a firm’s financial health is thus partly threatened by this new access to finance but with some positive aspects. Moreover, this deterioration in financial health is not persistent in the medium-term. The effects on the ratios “financial interest/sales” and “debt/equity” lose significance, and the coefficients decrease in the second year after the issuance of guarantees. For medium-sized companies, there is no significant relationship in the medium-term.In summary, obtaining a guarantee helps increase the differences between guaranteed and unsecured firms, except in relation to the capacity to produce cash flow. However, while the ROI growth rate continues to grow significantly 2 years after the issuance of a guarantee, the negative effects on financial health lessen over time. Regarding the overall impact on business ongoing concerns, guarantees do not lead to an increase in business continuity risks in the medium-term. Table The signs of the relationships are the same for every industry. Nevertheless, relevant differences in terms of magnitude are detected. In the service industry, the effects of guarantees are more evident, both in terms of profitability and in terms of crisis indicators. In particular, positive and significant increases in the growth rates of the “financial interest/sales” growth rate ratio and the “short-term assets/short-term liabilities” growth rate ratio are recorded , and a relevant decrease in the growth rate of the “/total assets” ratio is highlighted. On the other hand, a higher growth rate in the debt-to-equity ratio is exhibited by the trade sector.In general, services are usually characterized by higher long-term barriers to investment due to financial constraints. This was confirmed by a recent survey conducted by the European Investment Bank (EIB), according to which obstacles to investment activities related to the availability of finance are more significant in the services sector than other industries EIB, . This maTable The results are similar for the two forms of guarantees, but as assumed, the effects have different magnitudes. Both the impact on profitability and that on the crisis indicators are more pronounced in the case of direct guarantees. The bank directly requests public guarantees mainly for companies able to achieve more substantial profit improvements in the short- and medium-term. Nevertheless, the impact of direct guarantees, on the whole, put the financial health of companies at greater risk. Higher profitability can be achieved in the face of greater negative impacts on firms’ financial structures and burdens of financial charges. However, the intervention of an MGI is able to reduce the overall risk borne by the bank and the risks to companies’ business continuity prospects simultaneously.t-test to examine differences in observable characteristics between the treatment firms and the control firms before the matching  in addition to the type of intervention (direct guarantee or counterguarantee/reinsurance). Therefore, specific portions of public funds could be applied where the effects produced by such guarantees are stronger as is the case of direct guarantees granted to micro-sized enterprises and companies operating in the service sector to maximize the additionality of public resources in the context of curtailed budgets.Currently, the CGF considers the differences among business sectors only for better assessing the probability of default among eligible firms. The kinds of ratios and thresholds used to evaluate each variable vary according to the industry in which the focal company applying for the fund operates. Considering the impact of guarantees on different sectors, to improve its economic additionality and its effects on business continuity, the CGF could consider firms’ industries also as a variable in determining the specific amounts to be allocated to establish defined economic policy objectives.Nevertheless, during recovery phases, it is essential that public guarantee schemes do not interfere with efficient downsizing or consolidation within specific sectors to prevent dangerous zombification effects. Hence, the search for maximizing the effectiveness of public intervention must be limited to the subset of illiquid companies with viable business models in the context of targeted credit-support programmes. The use of crisis prevention indicators, which combine the analysis of economic and financial profiles, seems to be a useful reference for solving the trade-offs in the design and implementation of public guarantee funds. Our main findings thus have relevant implications for policy-makers, contributing to the public debate on rethinking credit guarantee schemes after the pandemic to find an equilibrium between effectiveness and sustainability.Moreover, our results may have important practical implications for SMEs that are potentially eligible for a public guarantee. When applying for a public guarantee, SMEs should assess not only the impact on access to a specific financing type but should also properly estimate the medium-term effect on the overall economic and financial conditions. In this regard, our study points out that firms characterized by high levels of debt and financial distress should carefully consider their application for a public guarantee to avoid raising warning signs of a potential corporate crisis.Despite the relevance of our results and the robust methodologies we have applied, our empirical analysis has some limitations that may be overcome by future research. First, our analysis explores the Italian context. Although this choice is useful in comparing guarantees issued in the same regulatory context and granted to eligible firms selected according to uniform criteria, a cross-country analysis could effectively verify the impact of macroeconomic and financial country-specific conditions on our main results. Such variables could help justify regulatory differences and a different level of public support for SMEs at an international level.Second, we carried out this analysis over the period 2010–2018. It could be interesting to explore a broader period, including the most recent years, to determine if our results vary according to changed economic context. In particular, future research could test the medium-term effects of the easing of eligibility criteria and the temporary changes to the functioning of the CGF introduced during the pandemic emergency period, applying the methodology based on crisis predictive indicators presented in this paper. This is particularly important in a context of global inflation and energy crisis, where the debate on the design and implementation of support measures for SMEs is highly topical.


Polistes wattii, an open nesting paper wasp species, builds planar hexagonal structures. Here, using the pair correlation function approach, we show that their nests exhibit short-range hexagonal order (no long-range order) akin to amorphous materials. Hexagonal orientational order was well preserved globally. We also show the presence of topological defects such as dislocations (pentagon-heptagon disclination pairs) and Stone-Wales quadrupoles, and discuss how these defects were organised in the nest, thereby restoring order. Furthermore, we suggest the possible role of such defects in shaping nesting architectures of other social insect species.Social insects have evolved a variety of architectural formations. Bees and wasps are well known for their ability to achieve compact structures by building hexagonal cells.  These nests have captivated mathematicians and ecologists alike for their structural complexity and the mechanisms behind the coordinated building7. How do multiple individuals in a group or a colony come together to construct these tiled layouts? The principle of stigmergy explains this as the formation of patterns by emergence8, including self-organisation and self-assembly mechanisms10. In most species, the construction rules depend on environmental  or pheromone gradients11. In this context, the relative importance of self-organised13 vs template-based interactions has been examined, and current evidence points towards architectural mechanisms being an interactive effect of both these interactions14. It is paramount to place these mechanisms in the context of behavioural and cognitive processes to understand nest construction comprehensively. The repertoires required for complex nest architectures are often characterised by simplified clusters of direct steps. However, the processes involved in planning construction in various environmental conditions, detecting errors and their remediation, working around novel obstructions, etc., require substantial cognitive abilities that outwit simple algorithms15.Animal nests and their architecture are crucial for the development of the young, protection from predators, and storage of resources. The diversity and complexity in architecture signify how these functions are fulfilled in diverse habitats and environmental conditions. Such complexity is exemplified by the nests of social insects  owing to their ability to use or modify the surroundings, and create ordered and plastic structures16). Such optimal utilisation of space and energy has been proposed as the significant selection pressure for shaping these structures19. Honeybees use wax to shape their cells, while most wasp species use either mud or fibrous materials of plant origin for construction. Though the cells are hexagonal in both cases, the construction materials possess strikingly distinct properties. Therefore, the underlying processes could be different. Construction of bees’ wax-based cells is postulated to begin as an array of circles (laid over packed cylinders as a base) that are modified to rounded hexagons purely by mechanical/thermodynamic means21. However, experimental work from nests of European honeybees suggests that bees actively construct hexagonal cells by handling the wax and controlling its temperature22. Given the plasticity of wax, any disruptions to tiling in these structures can be rectified, thereby reducing the possibility of overall defects in the nests. Hence the legend of honeycomb ordering. On the other hand, nests made up of plant fibres such as those of paper wasps are unlikely to follow similar modes of construction. The reduced plasticity makes them interesting as ordered physical systems prone to topological defects. A topological defect in systems of broken symmetry, like crystals, magnets, liquid crystals, etc., is defined as a disruption of order throughout the system in a way that defies restoration via any continuous deformation24. In contrast, defects such as vacancies, hilly terrain in a flat land, etc., are geometric defects as they affect order locally in their neighbourhood without any signature far away from them. A key characteristic of topological defects is that they cannot be repaired by local rearrangements alone but instead require changes to the system globally. Geometric defects can be amended by making changes locally at the scale of basic elements or constituents25. Here, we refer to topological defects as those that occur and affect at length scales beyond a single unit/element, such as a single cell within a nest. The emergence and evolution of such topological defects in paper wasps’ nests have never been studied. Some of the most common topological defects in crystals and liquid crystals manifest as disclinations and dislocations27. Examples of such disclinations have been shown in living systems such as protein coats of viruses28 and insect corneal nanostructures29, where insertion of pentagons into an array of packed hexagons results in Gaussian curvature and breaks the sixfold rotational symmetry. Similarly, the Stone-Wales defect, characterised by two pentagons and two heptagons30, is a well-known defect in graphene, fullerene, and carbon nanotubes32.In bees and wasps, cells within the nest are usually circular or hexagonal. Hexagonal tiling provides a compact structure and is proven to cover a planar region with regular units of equal area whilst minimising the total perimeter , we ask the following questions: What is the nature of ordering  and spatial arrangement of cells within and between the nests? In the current context, order describes the regularity in the tiling of the cells within the nests. Short-range order (SRO) represents the arrangements of nearest neighbours in the nest, while long-range order (LRO) represents the regularity over a longer distance. More quantitatively, a nest is said to have long-range order if there is a nonzero probability of finding the corners of two cells on the same regular lattice, even for large separations between the cells.What are the topological defects found in theses nests?Paper wasps of Polistes have a widespread distribution and are a well-studied example for the evolution of sociality and dominance hierarchies in insects. It is a primitive and speciose genus with more than 200 species38. P.wattii is known to be distributed across central and South Asia39. They are inactive during the winter, and nest building begins once they emerge from hibernation. The construction of nests often lasts till late summer. In our study, all the analysed P.wattii nests were from anthropogenic habitats. Nesting height was typically within the range of 5-15 m. Images of nests were taken in the summer of 2020 and 2021. Adult nests that were fully constructed and completed the season were considered for analysis . These nests were photographed with a reference scale. Images were further analysed by subtracting the background and binarisation using ImageJ40. The positions of all the individual vertices (corners shared by at least three cells) were marked on the images, and their x, y coordinates were exported for subsequent analysis. Here, we have taken the structure to be planar (see Results and Discussion for details). To avoid the effect of boundary which includes incomplete cells, a few layers of vertices along the edges were excluded. Apart from these, a few cells with cylindrical projections where identifying the underlying vertices was difficult were excluded from the final analyses. Overall, 25 nests were used to characterise the degree of ordering. The presence of topological defects was identified by inspecting the number of vertices for the cells within 35 different nests. We characterised the defects by identifying their basic features (number of vertices and neighbouring cells) and calculating the internal angles of the first neighbouring hexagonal layer from coordinates. For a region without defects, we would expect these angles to be close to 120The study was conducted within the campus of Ashoka University, Sonepat, India (28.9457g(r) (henceforth PCF) based on Ripley’s K function derivative method in the spatstat package with default smoothing parameter41. The approach relies on the probability of finding a pair of vertices separated by a distance r. This results in an average representation of the local spatial neighbourhood at a distance r from any given vertex. PCF of a regular lattice exhibits sharp peaks at the lattice spacing distances . Such sharp peaks indicate perfect ordering. On the other hand, an amorphous structure will show some reduced degree of order; in particular, it would have g(r) approaching 1 for large values of r. The limiting value of 1 indicates no correlation between the positions of vertices when they are far apart. In a PCF, the peak heights are generally related to the number of neighbours. The first two peaks were discernible in nests of different sizes, allowing us to focus on the location and width of these peaks for each of the nests. The following function consisting of two Gaussians with amplitudes g(r)-vs-r curve for each nest,To quantify ordering and analyse the spatial distribution of cells, we used pair correlation function 43. Cell-orientational order parameter j centered at k to the centre and the chosen x-axis, and n is an index for orientational ordering . Based on the the fitted values of Eq. , the walmentclass2pt{minim45. As shown in Fig. r increases, this overlap disappears. This pattern of the PCF illustrates the SRO in the structure of nests. The presence of a peak in a PCF confirms that any given vertex would have neighbouring vertices at distances provided by the peak position. This is an example of SRO. Moreover, the decaying envelope of the PCF to The number of cells in the analysed nests ranged between 50 and 740. For each nest, we characterised the nature of ordering by calculating pair correlation function for the vertices. For a regular hexagonal lattice, sharp peaks  of location and width of the first peak compared to the second peak . In few nests of 48. If structural disorders such as topological defects are left uncorrected, they affect the overall planarity of the nest. The missing link of a pentagon in a hexagonal net necessarily requires the removal of a wedge of hexagons, producing a cone-like structure as shown in Fig. Defects such as one pentagon or one heptagon amidst hexagons disrupt the planarity of a honeycomb structure as shown in Figure 49. For cells with defects that occur in pairs or as groups, we measured the angles of the neighbouring vertices for upto one shell of nearest neighbours. For a regular hexagonal lattice, these angles would be 120Figures ide Fig. . This co50, which destroy the residual bond-orientational order. For instance, when these defects are induced by thermal energy, one sees a two-step melting process of a two dimensional crystal. In colloidal crystals, dislocations or disclination dominated phases can be produced by external agencies like laser. In short, topological defects significantly influence a system’s behavior. In this spirit, the disposition of the two-dimensional nests is ultimately determined by the nature of the individual cells and the topological defects, which are generated by the construction rules adopted by the wasps.A dislocation for a two-dimensional system consists of a pentagon-heptagon pair . The presence of such a defect necessarily entails an extra row of hexagons that vitiates the translational order at large distances but not the bond-orientational order. Consequently, a proliferation of dislocations can produce a state of bond-orientational order without any translational order (a distinct phase of matter well known as the hexatic phase). A liquid is formed when the dislocations break into disclinations (independent pentagons and heptagons)52. Cells of different sizes are routinely observed in honeycombs as larvae of drones and workers are of different sizes. Retaining order with cells of different sizes that are being built independently by different individuals poses a challenge, and the honeybees counter this by local sensing and introducing non-hexagonal cells where required54. The introduction of a pentagon or a heptagon adjacent to each other is only possible by a regular set of local inspections carried out by wasps to identify possible deviations from hexagonality. There are two alternatives to explain the emergence of these defects that require further investigations. These alternatives are as follows: a) As the angle of a regular heptagon is 128.5P. fuscatus have shown the presence of an elaborate building programme that is beyond a set of linear steps, including repairing cell walls when damaged, adding pulp, and strengthening the stalk when required, which is done by multiple inspections55. This suggests that deviations from 6-sidedness are also possibly assessed via such inspections. However, it is unknown if these inspections involve identifying the number of vertices, measuring the internal angles or by Burgers vector.While pentagon-heptagon pairs were found to occur in nests, the configuration where hexagons separate a pentagon and a heptagon was never observed in our dataset. Interestingly, some of the described defects and their properties are utilised by honeybees to attain curvature as well as to merge cells of different sizesPolistes wattii show orientational order without any translational long-range order in the placement of the hexagonal cells on a planar surface. However, the ordering is well preserved in the immediate neighborhood of the cells (short-range order). Furthermore, topological defects were identified in the form of dislocations and disclinations  in the nests. We showed that these defects were organised such that the planarity of the nests was maintained. We used the approach of pair correlation function and topological methods to analyse these structural features of wasp nests.Our results suggest that the nests of Two key features that were never violated in the nests were a) convexity of individual cells and b) planar global structure. We postulate that wasps conduct systematic localised inspections, detect changes in local symmetry or order, and make changes to the adjoining cells to restore order. Going further, we intend to test the role of cell size heterogeneity on the emergence of topological defects and the relationship between the decay length of pair correlation function with the size of the nests. Future studies could place the nests in captivity and characterise the behaviours that precede and succeed the construction of cells around the defects. The introduction of defects experimentally in such captive nests would help understand the response of individuals and the group. While our study establishes the presence and repair of the defects, it is unclear if all the wasps equally participate in this process or certain keystone individuals are efficient at inspection and repair processes. These additional studies would therefore allow us to understand the behavioral mechanisms encompassing the repair of topological defects.Supplementary Information.


The fisheye camera has a field of view (FOV) of over 180°, which has advantages in the fields of medicine and precision measurement. Ordinary pinhole models have difficulty in fitting the severe barrel distortion of the fisheye camera. Therefore, it is necessary to apply a nonlinear geometric model to model this distortion in measurement applications, while the process is computationally complex. To solve the problem, this paper proposes a model-free stereo calibration method for binocular fisheye camera based on neural-network. The neural-network can implicitly describe the nonlinear mapping relationship between image and spatial coordinates in the scene. We use a feature extraction method based on three-step phase-shift method. Compared with the conventional stereo calibration of fisheye cameras, our method does not require image correction and matching. The spatial coordinates of the points in the common field of view of binocular fisheye camera can all be calculated by the generalized fitting capability of the neural-network. Our method preserves the advantage of the broad field of view of the fisheye camera. The experimental results show that our method is more suitable for fisheye cameras with significant distortion. The ordinary camera has a limited FOV. It can no longer meet the needs of some research projects without adding other auxiliary facilities. The appearance of the fisheye camera overcomes this shortcoming. The fisheye camera has a small focal length, and the field of view can generally reach more than 180° . Due to The research on stereo calibration technology of fisheye cameras is more meaningful. Compared with ordinary camera, the structure of fisheye camera is more complicated. Fisheye cameras introduce severe distortion, especially barrel distortion, during imaging . This stThe traditional stereo calibration method for fisheye cameras requires an imaging model in a specific mathematical format. Before this paper, there were some studies on stereo calibration techniques for fisheye cameras. For example, first combined fisheye camera calibration and epipolar rectification applied in a stereo fisheye camera system. They accomplished 3D reconstruction of specific points from authentic fisheye images With the development of artificial intelligence, Deep Learning (DL) is increasingly used in the field of computer vision . There hTo overcome these shortcomings, we propose the application of neural-network to the stereo calibration of binocular fisheye camera. Take the image coordinates of the left and right fisheye cameras as the input training set. The spatial coordinates corresponding to the image coordinates in the scene are used as the output training set. The trained neural-network can implicitly describe the mapping relationship from the 2D image plane to the 3D space. With the nonlinear fitting ability of the neural-network, it can directly predict the spatial coordinates of the target point based on the trained network. Compared with traditional stereo calibration, the proposed method is model-free. There is no need to establish an accurate mathematical imaging model, nor does it need to know the intrinsic and extrinsic parameters of the fisheye camera. Experiments have been conducted, and their results verify the performance of the proposed method.To obtain the training set of the neural-network, a large number of feature points with known image coordinates and spatial coordinates are required. Some 2D targets such as chessboard are the most commonly used. The chessboard-based calibration method has good calibration accuracy for ordinary cameras . HoweverThe remained parts of the paper are as follows. Fisheye cameras take non-similar imaging and introduce large barrel distortion in the imaging process. Compressing the diameter space breaks the limitation of the imaging field of view to achieve wide-angle imaging . The proThe projection equation for equidistant projection is shown as: The projection equation for equisolid-angle projection is shown as: The projection equation for orthographic projection is shown as: The projection equation for stereographic projection is shown as: Traditional distortion models cannot guarantee the accuracy of fisheye camera. Several models have been developed to represent the distortion of the fisheye camera, including the polynomial model, the field-of-view (FOV) model , and the=RrPw+Trwhere RTherefore, the rotation vector of the left fisheye camera to the right fisheye camera is The solution ibration .In recent years, the emergence of some bio-inspired algorithms that simulate natural ecosystems provide new ideas for solving complex optimization problems. These bio-inspired algorithms include genetic algorithms , particlThe forward propagation process can be understood as follows: the output of the previous layer is used as the input of the next layer, and the output of the next layer is calculated until the operation reaches the output layer. Let the activation value of the Before explaining the back propagation algorithm, it is first necessary to define the loss function. The loss function can measure the loss between the output computed by the training samples and the actual output.The purpose of the back propagation process is to adjust the network parameters. Its essence is to find the optimal weights and biases by minimizing the loss function. So it is necessary to calculate the partial derivatives of the loss function to the weights and biases. The gradient of the variables in each layer of the neural-network can be obtained by finding the partial derivatives. The stochastic gradient descent algorithm (SGD) is commonly used to update the network parameters. The SGD algorithm can be summarized as: This paper uses a neural-network to implicitly describe the nonlinear mapping relationship between image coordinates and their corresponding spatial coordinates in the scene. The settings of neural-network parameters include the structure of the neural-network, loss function, activation function, and optimizer. With the training sets keep constant, different network parameters can significantly impact the convergence speed and prediction accuracy of the network.The neural-network structure proposed in this paper contains five layers, as shown in This study is essentially a regression problem. The most commonly used loss functions for regression problems are the mean square error (L2loss) and the mean absolute error (L1loss). L2loss function curve is smooth and can converge quickly to a minimum even at meager learning rates. However, when outliers exist in the training set, L2loss gives higher weight to the outliers, affecting the overall performance . L1loss Optimizers can optimize neural-network to improve training accuracy and save training time. The most basic optimizer is the SGD algorithm, initially introduced in the previous subsection. The SGD algorithm is computationally efficient and only requires solving the first-order derivatives of the loss function. However, The SGD algorithm makes the results fall into saddle points and find local optimal solutions because of the direction. Consequently, this paper uses an adaptive optimization algorithm that can update the learning rate automatically. To further verify the effect of the optimizer on the neural-network, The input set is 1) Generate three-frequency three-step stripe images with equal-step phase shift increments of 2π⁄3. Their intensities can be expressed as: 2) Two fisheye cameras are fixed on the overhead camera mount, and the LCD monitor is fixed on the high-precision horizontal elevator. The fisheye cameras can shoot the LCD overhead. The high-precision horizontal elevator controls the LCD to move in the 3) According to 4) Any point on the stripe image, calculate its absolute phase 5) The absolute phase is converted to spatial coordinates for each feature point with the following equation: q represents the pixel size of the LCD. Use the reading of the high-precision horizontal elevator as the To solve the above problems, the active phase target is used. Firstly, the wrapped phase of the sinusoidal periodic stripe image is solved using the three-step phase shift equation. According to the multi-frequency method, the phase is unwrapped to obtain the absolute phase. Finally, we select the eligible pixel points as feature points according to the absolute phase. A set of exactly matched image coordinates and spatial coordinates will be obtained if the unwrapping is successful. The feature points extracted using our method have the advantage of quantity and are minimally affected by the fisheye camera distortion. After determining the input and output data sets, the image and spatial coordinates have different value ranges. So it is necessary to normalize the data. Normalization can improve the convergence speed of the neural-network and the model’s accuracy. We use the polar difference transformation method.To verify the accuracy of the proposed method, an experimental platform was built. The first experiment compares the neural-network-based fisheye camera stereo calibration (the proposed method) with traditional fisheye camera stereo calibration. As shown in The training set is obtained by following the steps described in Based on the trained network, the sample data can be predicted. We perform the traditional fisheye camera stereo calibration using the fisheye camera calibration method in opencv3.0. The specific principle can be referred to  and is nThe second experiment compares two different methods of obtaining the training set for the neural-network. One is to use active phase targets as proposed in this paper, and the other is to use a chessboard as the target. The experimental procedure using the active phase target has been described in The experimental chessboard contains 88 corner points with a spacing of 15 mm and a manufacturing error of 0.01 mm. The Harris corner point detection algorithm can obtain the sub-pixel image coordinates of the chessboard corner points. The corner points of the chessboard are used as feature points. To ensure the consistency of the experimental conditions, the positions of the fisheye cameras are not changed. The chessboard is fixed on the high-precision horizontal elevator. The high-precision horizontal elevator controls the chessboard to move in the The sample data are then predicted based on the trained network model. To further verify the practicability of the proposed method, 3D reconstructions of the chessboard corners and a partial plane of the sphere are performed.The experimental chessboard contains 88 corner points with a spacing of 4.9 mm. The binocular fisheye camera takes pictures of the chessboard in different poses at the same time. The subpixel image coordinates of the chessboard corners are obtained using the Harris corner detection algorithm. The spatial coordinates of these corners are then reconstructed using the trained neural-network model. Similarly, we reconstructed a partial plane of the sphere. We recover the absolute phase of the sphere by projecting a fringe image on the upper surface of the sphere. According to the matching relationship between the absolute phases of the sphere in the left and right cameras, the pixel points are matched . Then weThis paper applies a neural-network to the fisheye camera stereo calibration technique. There is no need to pre-build the fisheye camera model. The proposed method is model-free. A nonlinear mapping relationship between image coordinates and spatial coordinates is established using neural-network. The use of the active phase target enables the extraction of feature points with a larger number and higher precision, which is more suitable for the calibration of fisheye cameras. Due to the flexible structure of the neural-network, the neural-network model can be easily extended to the joint calibration of multiple fisheye cameras and the joint calibration of asymmetric fisheye camera layouts. These are expected to be further investigated and implemented in the future.