This study investigates the internal architecture of Asian hornet nests (AHNs) using advanced imaging techniques, such as CT scanning and X-ray radiography, to understand their construction and function. The primary objective and significance of this study centre on drawing inspiration from the creative way Asian hornets construct their nests, with a particular focus on the architecture, design, functionality, and building materials of these nests. The architectural principles governing the construction of these nests, such as the arrangement of hexagonal cells, pedicels for load bearing, and adhesive materials, serve as a source of inspiration for innovative and sustainable design practices. The pedicels in Asian hornet nests play a crucial role in transferring load and ensuring stability. Additionally, AHNs’ adhesion to tree branches is essential for preventing collapse, and the pedicels provide necessary structural support. The knowledge gained from studying AHNs’ internal architecture could be applied directly to the architecture and civil engineering fields to improve structure stability and durability. The microstructure analysis of the paper-like material that hornets produce to build their nests indicates a complex and heterogeneous structure, composed of various plant fragments and fibres. This unique composition creates intricate grooves and pores, which are essential for regulating temperature and humidity levels within the outer envelope of the nest. The study of Asian hornet nests’ internal structure demonstrated that nature’s engineering principles inspire the design of durable and resilient structures in the construction industry. Civil engineers can incorporate similar principles into their designs to enhance the structural integrity and performance of buildings, bridges, and other infrastructure. Nature offers instances of robust materials and structures that possess optimised morphologies and topologies, thereby enabling exceptional mechanical and structural properties. These instances present sustainable alternatives for the construction sector . Animal Vespa velutina Lepeletier, 1836 (Hymenoptera: Vespidae) is an Asian hornet native to the mountains of Southeast Asia, from Kashmir to Malaysia, spreading eastwards to Taiwan and south-eastwards to Sulawesi, the Sunda Islands, and Timor. There are 14 subspecies of this taxon ,6, whichAsian hornets are social insects that live in a hierarchical community structure consisting of three classes: queens, workers, and males. The males have single copies of their species’ chromosomes (haploids), while the females have double copies (diploids). Towards the end of summer, multiple queens are produced from each nest and then mate. After mating with one or more males, the queen stores the sperm in an abdominal container. When the time is right, the queen lays fertilised and unfertilised eggs in large numbers, with a single queen capable of laying thousands of eggs and creating thousands of offspring. The original mated queen emerges during the initial warm days of spring and constructs the primary nest for the starting colony using materials such as wood pulp and leaves. The main Asian hornet nest (AHN) is typically compact and circular. It is located in a secure area where food is easily accessible, particularly honeybees, as they are a vital part of the larvae’s diet. After 4–5 weeks, the first female workers emerge and assist the queen. At this point, the wasps often leave the primary nest and construct a larger secondary nest on top of trees. The colony experiences growth during the summer, with the population increasing to thousands. Newly mated queens depart from the nest to establish a new colony elsewhere. The abandoned nest is likely to disintegrate during winter; however, a recent study found evidence of surviving individuals from all castes, as well as eggs and broods, inside the nests. Secondary nests should be removed during the winter to eliminate any residual colonies that may regrowth in the spring ,17,18,19This study utilises a range of non-destructive techniques, such as CT scans and X-rays, to explore the intricate details of the architecture, shape, and size characteristics of an AHN. These methods enable researchers to examine both the internal and external structures of the AHN without causing any damage or alteration, thus ensuring the preservation of the nest and the retention of its intricate details for current and future studies and examinations. Additionally, the microstructure of nest-building materials was analysed using SEM-EDS. These findings have the potential to significantly contribute to future biomimetics studies, offering valuable information about the construction techniques used by Asian hornets. The implications of this research extend beyond the world of entomology, with applications in engineering, architectural design, and the development of innovative and sustainable materials for the building sector.The Asian hornet nest in this study case is an oval-shaped structure with several centimetres in diameter. It is made of a paper-like material produced by the hornets using wood pulp and saliva . The nesThe current study focuses on an Asian hornet nest (AHN) that was situated atop a tree branch, as shown in The present study aimed to analyse and describe various aspects of an AHN. The Asian hornet nest in this case study has an oval-shaped structure. The disc-shaped comb is enclosed in an envelope, with a single entrance at the top of the outer envelope (the upper combs), as shown in NL) of 72.4 cm, a height (NH) of 40.2 cm, and a width (NW) of 39.6 cm. The weight of the nest was found to be 2.40 kg. The volume of the nest (NV) was calculated using the formula of a prolate spheroid (1):The measurements revealed that the nest had an overall length , also known as a computed tomography (CT) scan, is a radiological imaging technique that uses X-rays to analyse the internal structure of the Asian hornet nest (Vespa velutina nigrithorax) in a non-destructive manner .Computed tomography (CT) assessment was performed using a Revolution™ ACT–16 slices scanner , using a helicoidal acquisition with a slice thickness of 1.25 mm.CT scans create highly detailed, cross-sectional images of the nest, which can be reconstructed into a 3D model of its internal structure . During The radiographic study was performed using an X-ray generator Philips Optimus 80  and a computed digital X-ray device . Two perpendicular views were performed using an X-ray beam of 60 kVp and 5 mAs, with a focal distance of about 1 m and a 12:1 ratio moving grid. The Veterinary Hospital of UTAD conducted this analysis with meticulous attention to detail.X-ray analysis is a non-invasive methodology that enables non-destructive investigation of the internal structure of an AHN without causing any disruption to its composition. During the X-ray analysis, the nest is strategically positioned on an X-ray plate and scanned from a specific angle, producing a two-dimensional image of the nest’s internal structure in two distinct positions, as depicted in The Scanning Electron Microscopy (SEM) with Energy Dispersive Spectroscopy (EDS) analysis of the AHN’s paper-like material was conducted using small fragments cut from the outer envelope of the AHN, which were then observed using a scanning electron microscope (SEM-EDS) Hitachi S-4800 coupled with an EDX detector. The analysis was performed in the Optical Centre of the University of Beira Interior (UBI), Covilhã, Portugal.SEM-EDS is a powerful tool for studying the microstructure and chemical composition of the AHN’s paper-like materials. SEM-EDS can reveal the morphological structure of the material and the chemical composition characteristics of the nest-building materials.To obtain a thorough understanding of the internal structure of the hornet nest and to produce higher-quality 3D images, the data collected from the CT scan were processed using the “RadiAnt DICOM Viewer” software. The 3D volume rendering (3D VR) technique was employed to create detailed images, and the “Angio” parameter in the 3D presets tool was used to enhance the images further.The 3D VR technique and the “Angio” parameter enabled a more comprehensive understanding of the nest’s internal structure, which is challenging to discern with conventional imaging methods. The “Angio” parameter, short for angiography, enabled the visualisation of the nest’s tissue structure. These tools proved highly effective for studying the intricate details of the hornet nest’s structure and function.The Vespa velutina nigrithorax hornet seems to have built its nest differently from other types of wasps in the region, enclosing the combs in an outer envelope to shield them from external elements . Each leThe X-rays exhibit varying degrees of absorption by different types of tissue due to their differential electron densities, with denser tissues such as bone, metal, or tree branches absorbing a more significant amount of X-rays ,32,33. LThe combs are arranged in a symmetrical pattern. The shape of the combs is similar to that of mushrooms with an umbonate pileus, which have a rounded protrusion in the centre of their caps. The combs are a key structural component of a hornet nest, consisting of five series of parallel combs stacked vertically and held together by columns. The adhesion of the hornet nest to the tree branches is fundamental to preventing the collapse of the nest onto the ground.All the combs in the hornet nest are almost disc-shaped . This shThe hexagonal shape of Asian hornet comb cells allows for a regular, gap-free division of a plane surface. Although other shapes, such as squares and triangles, can achieve this, the hexagon encloses the same area with the least circumference. As a result, hexagonal cells require less adhesion material than triangular or square cells with the same volume, making them more economical . AdditioInsulation plays a crucial role in the space between the combs, as it helps maintain a stable temperature within the nest . The insVentilation is another fundamental function of the space between the combs, as it facilitates the regulation of temperature and humidity levels within the nest . The spaMovement is also enabled by the space between the combs, providing a pathway for the adult hornets to attend to the needs of the developing larvae and eggs.Expansion refers to the space between the combs, which also allows for the expansion of the colony. As the colony grows, hornets can construct additional combs and add them to the existing space between the combs, ensuring that the colony can accommodate more members as needed .The space between the combs in an AHN serves several pivotal functions essential for colony survival and proliferation. These functions include insulation, ventilation, movement, and expansion:The aim of examining the pedicels’ structural properties would be to gain a deeper understanding of the stability and construction of the AHN, which could lead to the development of innovative biomimetic designs and engineering solutions that have practical applications. Depending on the level of the nest at which the pedicels are attached, their thickness and accumulation occur at varying rates in different areas of the nest. The accumulation of pedicels reinforces the nest structure and distributes its weight evenly across the tree branch, thus preventing it from breaking or detaching. The material used for adhesion, as well as the mode of attachment of the combs to the outer envelope and tree branches, also contribute to the structure’s overall stability by acting as pillars. As the comb layers increase in size and height, the number and thickness of pedicels also increase, ultimately resulting in the attachment of the nest to the tree branch at the top. Social wasps employ various thermoregulatory mechanisms, such as fanning their wings to enhance them and “curling” behaviour, in which the queen curls her body around the pedicels of the nest ,43. The In the Vespa velutina nigrithorax’s nest, the pedicels are long enough to allow the clear passage of hornets from one comb to another. The pedicel, for instance, functions as a barrier against walking insects and reduces the contact surface area between the nest and the substrate to a minimum. This reduction allows hornets to easily monitor the small potential invasion zone and quickly respond to threats ,45.The investigation of the adhesion material used by hornets to attach their nest to the tree branches is not only interesting from a biological point of view but also from the point of view of the materials science and engineering fields. The hornet’s ability to produce a highly adhesive and durable material with local and limited resources is a great inspiration for developing sustainable and eco-friendly building materials.In engineering, the centre of gravity is a fundamental concept in determining the stability and equilibrium of structures. The location of the centre of gravity in relation to the base of support is crucial for both static and dynamic stability, as it determines the ability of an object to maintain its balance and prevent it from falling over . Hornet The hornets’ remarkable ability to comprehend physics and engineering principles is awe-inspiring. Placing columns at the centre of gravity in the comb structure is a testament to their intelligence and ingenuity. This design strategy allows hornet combs to remain securely attached to their supports.cbA) was estimated using the standard mathematical formula for the area of an ellipsoid, assuming that their shapes were elliptical and similar, as shown in Equation (2).This study examined five combs within an AHN, measuring their respective maximum ( CT scan . The area) measured 4.3 mm, and the height (h) ranged from 17 mm to 25 mm, as illustrated in This section presents the measurements of the comb’s cells, including the thickness of the walls (0.99 mm), the design and size of the hexagonal prism, the area of cells, and the volume of the hexagonal prism. The measurements of the nest combs are as follows: the base edge of the hexagonal prism shape (2.Area of the cell: 2V) 2, depending on the hexagonal prism height (h).Volume of the hexagonal prism: As illustrated in To calculate the number of cells in each comb, a simple computation is required by dividing the area of the comb by the area of each individual cell, assuming that each cell is of equal size and shape. Although this estimate may not be entirely precise, any discrepancies between the estimated and actual cell numbers are likely negligible.The observed variation in cell count across the different comb levels can be interpreted as a strategic building process by the hornets. The primary comb at Level 5 is constructed with a smaller area and fewer cells, after which the hornets build larger combs (Level 3 and Level 4) with more cells to expand the nest. The size and cell count in Levels 1 and 2 are then reduced to enhance nest stability and prevent detachment. This variation in cell count is a crucial design feature for the structural integrity of the nest. It is imperative that the nest remain stable during extreme weather events or when exposed to external forces. The hornets’ strategic building process is a prime example of how engineering principles are inherent in nature and can be applied to design durable and robust structures.Through the use of CT scan technology, we can create a schematic diagram of the Asian hornet nest after a comprehensive examination as it is shown in The resultant X-ray image, referred to as X-ray radiograph or simply radiograph, is created by passing X-rays through the AHN and capturing the resulting transmission of radiation on a digital detector. This process generates a monochromatic image that displays the internal structure of the Asian wasp nest, with denser materials, such as the tree branch and the lower edge of the combs, appearing in bright white. In contrast, less dense materials, such as soft tissue (cells of combs and the outer envelope), appear darker.Multiple X-ray images taken from varying angles highlight the intricate connections between the tree branch and the AHN b. NotablCT scans and X-ray analyses are two radiological imaging techniques used to examine the internal structure of Asian hornet nests non-destructively. Both techniques utilise X-rays to penetrate the object and create images of its internal structure.CT scans use advanced techniques such as 3D volume rendering, and the “Angio” parameter refines the CT scan images for a comprehensive understanding of the nest’s internal structure. X-rays produce a two-dimensional image of the nest’s internal structure from a specific angle, allowing for the identification of different comb layers and intricate connections between the nest and the tree branch. While both techniques have advantages and disadvantages, CT scans provide a more detailed and comprehensive view of the internal structure of the hornet nest, including a 3D reconstruction. At the same time, X-ray analysis is less time-consuming and less expensive, but it only provides a 2D image of the internal structure. However, X-rays have limited ability to distinguish between materials with similar densities, making it challenging to differentiate between the layers that make up the outer envelope and the pedicels of the Asian hornet nest. In contrast, CT scans differentiate between materials with similar densities, ensuring a more accurate assessment of the different layers that make up the Asian hornet nest, including the outer envelope.CT scans reveal the structural components of the nest, such as the arrangement and shape of the combs, which resemble mushrooms with an umbonate pileus. The circular, disc-shaped, and gravity-centred combs distribute the weight of the nest evenly, reducing stress on the overall structure. Additionally, CT scans offer several advantages over X-rays when it comes to examining the outer envelope of AHNs. CT scans utilise a series of X-ray images taken from multiple angles and combine them to create a detailed 3D image of the object being scanned. This allows for a more accurate assessment of the different layers that make up the AHN, including the outer envelope. CT scans also offer a more detailed image of the nest, facilitating a more comprehensive understanding of its structure and function. Another advantage of CT scans is their ability to generate images of the AHN in different planes, such as coronal or sagittal. This offers additional information about the shape and orientation of the comb inside the outer envelope and any abnormalities or irregularities that may be present.Asian hornet combs are enveloped with a paper-like material made of plant fibres and oral secretions, which is primarily derived from sieve tubes or vessels in plant tissues. These vessels provide a natural source of material for the nest envelope, and oral secretions help to bind the fibres together . This enThe EDS analysis conducted on the paper-like material provides the chemical composition of the material that hornets used to build up the nest. The paper-like material analysed includes elements such as carbon (52.74 mass.%), oxygen (45.02 mass.%), aluminium (1.33 mass.%), potassium (0.12 mass.%), and calcium (0.52 mass.%), as shown in Cellulose, hemicellulose, and lignin are lignocellulosic materials made up of C and O elements. Cellulose is composed of long chains of sugar molecules that are held together by strong bonds between the carbon and oxygen atoms. Hemicellulose is composed of shorter chains of sugar molecules, while lignin is composed of complex polyphenolic molecules ,53. CellIn a comparative study, a difference was noted in the chemical makeup of the Asian hornet nest paper when compared to N. Crespo et al.’s  researchThe construction of Asian hornet nests involves the use of paper-like material gathered from the surrounding environment, including wood and tree leaves. As such, it is possible for inorganic elements to be present in the nests due to the potential contamination of this material during the construction process . These contaminants may come from the surrounding environment, where the materials were originally sourced, and have the potential to affect the chemical composition of the Asian hornet nest. Therefore, it is important to consider potential sources of contamination when analysing the chemical composition of the Asian hornet nest paper. It is also possible that the difference in organic matter content could be due to natural variations in the environment or differences in the availability of materials used to build the nest. Further studies may be necessary to fully understand the factors that contribute to variations in the chemical makeup of AHNs’ paper-like material.In conclusion, this study of AHNs offers a deep understanding of the materials, design, and engineering principles used by hornets to create their intricate structures. The key findings of this research contribute to the understanding of the complex architecture of these nests, which serve as both shelter and home to the hornets. The construction process of the Asian hornet nest, completed in a notably short timeframe considering the builders’ size, serves as a source of inspiration for the construction and materials industries.The AHN’s outer envelope has a vital, multifaceted role in protecting, regulating, and supporting the nest, making it crucial for colony survival and development.The disc-shaped combs serve an essential role in distributing the weight of the nest more evenly, and the space between the combs fulfils various significant functions such as insulation, ventilation, movement, and expansion. This comprehension of the functional morphology of the nest shows the specific adaptations that enable these hornets to survive and thrive in their natural environment. The adhesion of the nest to the tree branches is critical to preventing collapse, and the pedicels in the nest serve as critical structural components, providing stability and support for the different levels of combs. These findings offer important insights into the biomechanics of the nest and the complex interplay between its different components.The strategic placement of columns around the centre of gravity is essential for ensuring the stability of the combs, and the hornets’ adhesive material has the potential to inspire sustainable building materials. This finding has important implications for the field of biomimicry, which seeks to develop new and sustainable technologies based on natural designs and systems.Both X-rays and CT scans facilitate the non-destructive testing of materials and structures. While both techniques are valuable, CT scans offer several advantages over X-rays in terms of examining the outer envelope and pedicels of AHNs, making them a superior tool for evaluating the structure and function of nests.SEM-EDS is a reliable method to acquire detailed information on the microstructure and the chemical composition of nests’ paper-like material. Plant fibres and oral secretions are used to make the paper-like cover of Asian hornet combs. As a natural source of material for the nest envelope, oral secretions help bind the fibres.The exceptional architectural design, rapid construction abilities, adhesive materials, and unique material properties found in these nests have the potential to significantly transform the civil engineering field, leading to more efficient and sustainable solutions in the construction sector.This research demonstrates hornets’ exceptional intelligence and ingenuity in creating their nests and the potential for biomimicry in developing sustainable and eco-friendly materials and structures. These findings carry substantial implications for understanding insect behaviour and evolution, as well as for the development of new civil engineering and architectural technologies inspired by the natural world.


Turbulence can cause effects such as light intensity fluctuations and phase fluctuations when a laser is transmitted in the atmosphere, which has serious impacts on a number of optical engineering application effects and on climate improvement. Therefore, accurately obtaining real-time turbulence intensity information using lidar-active remote sensing technology is of great significance. In this paper, based on residual turbulent scintillation theory, a Mie-scattering lidar method was developed to detect atmospheric turbulence intensity. By extracting light intensity fluctuation information from a Mie-scattering lidar return signal, the atmospheric refractive index structure constant,  Atmospheric turbulence is one of the most prominent features in the atmospheric boundary layer . The maiIn recent years, lasers have been widely used in communication and remote sensing, which has also greatly promoted research into light wave transmission in turbulent atmospheres. When light waves are transmitted in the atmosphere, the relevant features are affected by atmospheric turbulence and show an irregular changing state . The ranThe physical quantity measurements commonly used to describe atmospheric turbulence effects include the scintillation index, the refractive index structure constant, and coherence length ,11,12. Aon model ,14. Lidar, as an active remote-sensing technology, uses a laser as the light source and obtains atmospheric distribution information along the laser beam transmission path by detecting the backscattering signals of the interaction between the laser and the atmosphere. At present, the lidar technologies commonly used to detect atmospheric turbulence mainly include differential image motion lidar (DIM), differential column image motion lidar (DCIM), and differential wavefront lidar (DW). DIM lidar is designed according to the principle of differential image motion measurement (DIMM). The atmospheric coherence length  limited . In rece limited . In 2018 limited . DICM li limited . The aboMie-scattering lidar is an atmospheric lidar system designed based on the Mie-scattering theory proposed by Gustav Mie . CompareThe Kolmogorov turbulence theory is a local isotropic turbulence theory, which is an idealized theory. It is widely used in the inversion of turbulence intensity in the process of detecting atmospheric turbulence with lidar. However, some experiment results show that the turbulence characteristics of the tropopause and the stratosphere are significantly different when using Kolmogorov theory ,24. In tIn this paper, based on residual turbulent scintillation (RTS) theory, a Mie-scattering lidar method suitable for measuring the atmospheric turbulence profile is proposed. The scintillation index of different heights was obtained by calculating the fluctuation in light intensity, and the atmospheric turbulence profile was calculated. Some experiments were performed. The turbulence theory was extended from the Kolmogorov theory to the non-Kolmogorov theory, and the atmospheric turbulence profiles under the two theories were obtained and compared with the The detection principle of Mie-scattering lidar is based on the residual turbulent scintillation theory. When light waves are transmitted in the atmosphere, they will interact with atmospheric molecules and aerosols, and the subsequent scattered signals will be received by Mie-scattering lidar. Due to the existence of turbulence, the received return signal fluctuates. According to the residual turbulent scintillation theory, the signal fluctuation caused by aerosols can be smoothed out by adding a small iris diaphragm to the telescope, retaining only the signal fluctuation information caused by turbulence to measure the atmospheric turbulence intensity. The residual turbulent scintillation theory and its limitations are introduced below.Belen’kii et al. proposed the RTS theory for measuring atmospheric turbulence, expressed as when the light propagates in the atmosphere, if the radius, ll exist .Under the following four conditions:(1) Single scattering approximation and uniform aerosol particle size distribution, average path length (2) Atmospheric optical thickness: (3) The relevant scale of radial light intensity (4) Under the condition of weak fluctuations  and the transmitted signal passes through a filter with an optical density of 0.2 to the flat, convex lens and then converges into the PMT2. The purpose of using different optical density filters is to test the built Mie-scattering lidar system and to judge the amplification of the strong and weak signals.For the data acquisition system, the PMT selected in this study and the high-voltage power supply were produced by Licel in Germany and can convert weak optical signals into electrical signals. In order to facilitate the collection and display of the PMT-converted voltage signal by the data acquisition unit, an amplifier is installed to amplify the electrical signal and eliminate the signal oscillation. The data acquisition unit is a high-speed fluorescent oscilloscope, which has a bandwidth of 1 GHz, a sampling frequency of 100 M/s, and a recording length of 10,000 points and can sample the data points after 512 times that of the average return signal. According to the RTS theory described above, the spatial correlation scale According to the calculations, the aerosol spot scale In this study, light intensity fluctuation is used to detect atmospheric turbulence. The fluctuation in light intensity on the receiving plane is called scintillation, which is the most important effect of turbulent atmospheric transmission. The scintillation index is used to describe the intensity of light intensity fluctuations, namely the normalized variance of light intensity fluctuations:Under a weak fluctuation condition Since the weak fluctuation condition is always satisfied in the actual detection process of Mie-scattering lidar, the emitted Gaussian beam can be approximately regarded as a spherical wave, and most propagation problems meet the conditions of the turbulent inertia region . Under tOn the vertical detection path, the scintillation index of the spherical wave is written asIn summary, the atmospheric turbulence detection method adopted is as follows: based on RTS theory, first, the scintillation index rameters ,31.Yinchuan is located in northwest China in the central and northern parts of the Ningxia Plain, surrounded by the Yellow River in the east and the Helan Mountains in the west. It is also surrounded by the Badain Jaran, Ulanbuh, Tengger, and Maowusu deserts and has a typical temperate continental semi-arid climate, as shown in ¯=1.0 μm ; howeverRandom fluctuations in the atmospheric refractive index lead to random fluctuations in laser beam intensity. As a specific random process, light intensity fluctuation can be quantitatively described by the probability density distribution of light intensity, and the probability density distribution is also the most basic method to describe the statistical characteristics of light intensity fluctuation. The working principle of Mie-scattering lidar is to obtain the scintillation index of the beam by analyzing the intensity fluctuation in the received return signal and then obtain the atmospheric turbulence intensity information by inversion. Therefore, it is of great significance to study the statistical characteristics of the light intensity fluctuation in the return signal to detect atmospheric turbulence using Mie-scattering lidar and to improve the working performance of the lidar.A large number of theoretical and experimental studies have shown that, under weak turbulence fluctuation conditions, the probability density distribution of signal light intensity fluctuations meets the log-normal distribution; that is, the logarithmic intensity follows the normal distribution . In ordeThe built Mie-scattering lidar is used to measure turbulence in the vertical direction. For the vertical detection path, the atmospheric turbulence intensity varies with height, so obtaining the probability density distribution of the back-wave light intensity signal can provide a theoretical basis for the inversion of the atmospheric refractive index structure constant.The wavelength of the laser source is 532 nm, and the emission frequency is 10 Hz. As the probability density distribution of light intensity is a statistical feature of light intensity fluctuation, a large sample size is required. In this paper, 10,000 sample points composed of 10,000 pulses were analyzed as a group. By taking the 1.5 km transmission path as an example, the probability distribution characteristics of the light intensity received via Mie-scattering lidar were analyzed.First, the data collected in the experiment were normalized to make the average logarithmic light intensity  0, that is, <As can be seen from It can be seen from As mentioned above, the scintillation index The experiment was conducted from August to September 2022, and the observation lasted for approximately 20 days. Most of the time, the weather was clear and the visibility was high, and there were no obvious clouds in the detection path. Due to the strong sky background light noise received via lidar during the day, the observation was only conducted after 20:00 LST  every night, lasting until 22:00 LST, for two hours a day.A high-speed fluorescent oscilloscope was used to collect the return signal received via lidar. The change in scintillation index in the vertical transmission path was calculated using the collected Mie-scattering lidar return signal. In the vertical direction, the turbulence intensity of the far-field signal is very weak. In the process of laser transmission, the amount of light intensity flicker caused by the turbulence of far-field signals will be relatively small. Moreover, the background sky light noise, granular noise, amplifier noise, and other noise will cause a fluctuation in light intensity changes, and the calculated scintillation index is not only caused by turbulence changes. Therefore, vertical detection by Mie-scattering lidar requires a high signal-to-noise ratio to obtain an accurate far-field signal. In this study, the Mie-scattering lidar return signal was denoised by the sliding window average method to some extent. As can be seen from Usually, the scintillation index age form :(6)βI2=σTherefore, the scintillation index is calculated by measuring the mean <The scintillation index of different heights was calculated by the return signal. As can be seen from In this study, the scintillation index profile was used to obtain the atmospheric refractive index constant profile In this study, the Newton iteration method is used to invert the As can be seen from rbulence . Within As can be seen from In the experimental observation, the atmospheric turbulence intensity profile under different weather conditions was also detected. On 21 August 2022, the weather changed from overcast to light rain, with thick clouds in the sky and low temperatures. The diameter of the iris diaphragm is The Kolmogorov turbulence intensity It is clear that the scintillation index and turbulence intensity under cloudy conditions are significantly lower than those under sunny conditions, and the Kolmogorov turbulence intensity on cloudy days is approximately one order of magnitude smaller than that on sunny days. This is because the random fluctuation in atmospheric temperature is the main cause of the random fluctuation in the atmospheric refractive index, the temperature fluctuation on cloudy days is lower than that on sunny days, and the temperature fluctuation is less obvious than that on sunny days. On sunny days, solar radiation keeps heating the surface during the daytime, and the heat keeps transmitting upward, resulting in strong temperature fluctuations and a significant turbulence effect.Some research shows that for the atmospheric measurements of the tropopause, stratosphere, and near the ground, the turbulence structure-function or turbulence spectrum obtained in experiments still has power law characteristics, but the power law value deviates from –11/3 of the Kolmogorov turbulence spectrum in most cases ,37. Ther density :(8)ΦnA(α)=For non-Kolmogorov turbulence, under weak fluctuation conditions, the relationship between the variance in normalized light intensity fluctuation (scintillation index) and the variance in logarithmic amplitude fluctuation still satisfies Equation (3). However, the variance in the logarithmic amplitude fluctuation in spherical waves under non-Kolmogorov turbulence is no longer as is shown in Equation (4) but is turned into the following form :(10)σχ2 model, which allows for changes in the upper air speed and near-ground turbulence levels to be applied to atmospheric conditions at different locations. The model is given by (13)Cn2, the first term represents the strong turbulent layer conditions that often occur in the tropopause, the second term represents the turbulent layer conditions in the boundary layer, and the third term represents the turbulent layer conditions in the free atmosphere . AccordiThe laser light source was 532 nm, the emission frequency was 10 Hz, and the diameter of the telescope diaphragm Regarding the comparison, it can be seen that the overall variation trend of the This phenomenon has been analyzed in detail, and there are two reasons for this. The first reason is the selection of the HV-night model coefficient. Since there is no real-time high-resolution data, only the meteorological data of that day were used to estimate the wind speed, near-surface turbulence intensity, and boundary layer turbulence intensity, resulting in the difference between the model and the actual detection results. Moreover, due to the overlap of the field of view, the turbulence intensity in the low-altitude range was different from the theoretical value. Another reason is that the turbulence has internal and external scale changes, but the change in the internal and external scales with height was not considered in the inversion process. It is assumed that the inner scale is 0 and the outer scale is infinite for the entire detection path, thus resulting in measurement errors. The However, in general, the detected atmospheric turbulence intensity profile is basically consistent with the trend of the HV-night model, and the detection results are distributed near the theoretical value, indicating that it is feasible for the Based on RTS theory, Mie-scattering lidar technology was designed and built for the detection of atmospheric turbulence, and the vertical atmospheric refractive index constant profiles of Kolmogorov turbulence and non-Kolmogorov turbulence were detected and calculated, respectively.The return light intensity signal on the vertical path was analyzed statistically, and the actual probability distribution of the light intensity was fitted. The results show that the actual probability density distribution of logarithmic light intensity on the vertical path roughly obeys the normal distribution under weak fluctuations.The atmospheric turbulence was classified into Kolmogorov turbulence and non-Kolmogorov turbulence, and the inversion of the Moreover, the detection results of Mie-scattering lidar were compared with the HV-night model in the Yinchuan area. The results show that the Kolmogorov turbulence and non-Kolmogorov turbulence intensity profiles were consistent with the variation trend of the HV-night model, and the detected turbulence intensity fluctuated around the model. The reasons for this phenomenon can be summarized as two aspects: one is that the parameter selection in the model is not accurate enough, and the other is that the turbulence has internal and external scale changes. However, in general, it is feasible to use Mie-scattering lidar to detect atmospheric turbulence.In the future, the influence of the internal and external scales of turbulence varying with height should be taken into account, and more accurate and applicable inversion algorithms for the


Despite the frequent changes in household composition in Sub-Saharan Africa, the literature on the household division process is sparse, with no evidence of its effect on food security. This paper addresses the topic in Malawi, where the fission process is evident and malnutrition is a severe problem. Using the Integrated Household Panel Dataset, this study applies the difference-in-difference model with the propensity score matching technique to compare matched groups of households that did and did not split between 2010 and 2013. The results suggest that coping strategies adopted by poor households and life course events determine household fission in Malawi, a process that benefits household food security in the short term. On average, the food consumption score is 3.74 units higher among households that split between 2010 and 2013 compared to the matched households that did not. However, the household division might have long-run adverse effects on food insecurity, especially for poor households due to the adoption of coping strategies that might compromise their human capital and income-generating activities. Therefore, this process warrants attention for the more accurate understanding, design, and evaluation of food security interventions. This study investigates the effect of household fission on food security in Malawi. In Sub-Saharan Africa, households exhibit frequent changes in their composition due to the evolving nature of life course events and the dynamics of demographic and contextual factors. This phenomenon is also evident in Malawi. However, despite its possible effect on household welfare levels, the process has received less attention in the literature owing to data limitations ,2,3. TheIn addition, the majority of these studies exclude the household fission that occurs within the administrative area of the origin household. This omission provides an incomplete characterization of the process, and as a consequence its effects on household food security. This aspect is relevant in Sub-Saharan Arica and especially in Malawi, where, for example, marriage is a dominant factor contributing to the household splitting process . Most maBased on the literature ,10,11, tThe empirical analysis in this study compares the 1028 intact and 318 original households in the IHPS dataset to detect and verify whether the household fission process benefits the food security status of original households. However, the comparison is not without challenge, as the households might be systematically different in the characteristics that might determine their food security status, and these characteristics might change over time. As a consequence, the group of original and non-split households might not be comparable. This study addresses this methodological challenge by using a difference-in-difference (DID) method on a matched sample of original and intact households , which iMalawi is an ideal country to study the household splitting process and its consequent effect on household food security. The country suffers a significant risk of malnutrition , with 51This analysis has at least three important aspects. First, the possible effect of fission on household food security contributes to a better understanding of the phenomenon and the impact and design of food security interventions. Failure to account for the unobserved household fission process might overestimate the impact of food security interventions on household food security, especially if the latter is a function of the household division process. Second, it expands the understanding of the overall household splitting process in Malawi and its implications for household food security, solving the limitations of the existing migration literature. Third, it allows for resolving one of the possible selectivity biases in panel data models in the existent empirical literature, where the household structure is assumed to remain constant over time .The first step in the empirical analysis was understanding the household splitting process and its potential implications for the food security status of the original household to select the appropriate determinants of household splitting in the econometric model. These determinants were identified based on the literature review, including those described by Piotrowski  and key The concept of the household is central to the present study. The household is considered an economic unit; it constitutes a group of people who live together and have a common housekeeping arrangement, which means that they pool their money and eat at least one meal together each day . The stuRegarding the life course events, marriage and the tendency among male youths to seek economic independence were identified as the driving factors behind the household splitting process in Malawi. The country exhibits a pattern of nearly universal marriage, which is the dominant reason for leaving the household and generating a new one . This exAlmost all marriages in Malawi are contracted under the rules of African customary law. For this reason, there is a strong tie between marriage and land. The association between agricultural livelihood and marriage observed in Sub-Saharan Africa finds confirmation in Malawi .The two forms of customary marriages practiced in the country are patrilineal and matrilineal . In patrHowever, the household splitting process does not occur immediately after the marriage in Malawi. Instead, the key informants revealed that household splitting manifests once the couple gains economic independence, usually after the harvesting season. In the prevalent matrilineal system, the husband moves into the wife’s house, and the wife’s uncle provides the couple with a plot of land, which helps them achieve economic independence after harvesting. Moreover, in matrilineal societies, the chinkhoswe (the engagement ceremony) has become a fundraising function for households over the years. The collected funds provided to the newly wedded couple encourage their economic independence and the formation of a new household.Similarly, in the patrilineal system, the household splitting process transpires with the achievement of economic independence. However, in this system, the man’s family allocates him the land during childhood, and the bride moves into the groom’s house after marriage. More generally, household size reduction following marriage is also seen as a coping mechanism to improve consumption levels in Malawi. However, during the key informant interviews, respondents noted that a possible negative side effect of this mechanism could be a reduced household income if the individual who moved out of the family were a working member. This side effect was mainly associated with the tendency among male youths to seek independence. The literature also asserts this tendency where household fission and the generation of a split-off household is linked to the pursuit of independence, especially among boys at the age of marriage .The present study further identified that household fission in Malawi is also linked to the coping mechanisms employed by poor households. These coping mechanisms include the practice of child marriage and sending members away to form new housing arrangements. Malawi is one of the top ten countries with the highest incidence of child marriage in Africa . ApproxiThe key informant interviews also highlighted another coping strategy that the poorest households implement; they send their members permanently to eat elsewhere and form a separate housekeeping arrangement. However, despite its possible positive effects regarding better within-household resource allocation, our respondents highlighted that this coping mechanism is insufficient to allow the original and newly generated split-off households to escape poverty.The data used in this study come from the IHPS conducted in Malawi by the National Statistical Office (NSO) as a part of the Integrated Household Survey. The publicly available IHPS dataset covers four waves of a panel survey implemented every three years from 2010 to 2019. Our analysis used the two rounds implemented in 2010 and 2013. This study refers to these survey years as rounds 1 and 2, respectively. It is imperative to note that the present study only used the IHPSs implemented in 2010 and 2013 and omitted those conducted in 2016 and 2019 for the following reasons. First, the panel analysis covering the entire survey period between 2010 and 2019 would require consistent data, across all survey years, for all households, including the newly generated split-off households. However, the original households split multiple times during the period 2010–2019, and the split-off households generated in any subsequent survey rounds would not have data for the preceding survey periods. Second, Malawi witnessed extreme environmental shocks in 2014–2015 (flood) and 2015–2016 (drought). The environmental shocks themselves could influence the determinants of the household splitting process. Consequently, the effects of the household splitting process on food security observed between the survey periods 2013 and 2016 or 2016 and 2019 might suffer sample selection bias and might not be generalizable over other periods without significant shocks. Therefore, this study focused only on the first two surveys, implemented in 2010 and 2013, to minimize such sample selection bias. Third, the household splitting process between the survey years 2010 and 2016 or 2013 and 2019 was not studied, as households might witness substantial changes in their characteristics in the 6-year gap between these survey periods. This paper analyzed the following two mutually exclusive groups of households. The first group comprised original households that generated split-off households between rounds 1 and 2, and the second group included the intact households that did not split during the respective two periods—the intact households. The original household in round 2 was identified by tracking the household head’s unique identification code provided in the dataset. The IHPS panel dataset contained 318 original households, 1028 intact households, and 470 split-off households. The 470 split-off households were dropped in the used dataset, as the present study only concerned the effect of household fission on the original households. The final dataset that was prepared and analyzed contained 318 and 1028 original and intact households with balanced panel data for rounds 1 and 2.Following the literature and the key informant interviews, the present study considered the household splitting process in Malawi as supported by three categories of determinant factors related to the individual-level, household-level, and contextual characteristics of the households. This study estimates the effect of the household splitting process on household food security as measured by the Food Consumption Score (FCS), the outcome variable in this analysis. The FCS is a composite indicator constructed to account for the household dietary diversity, food frequency, and relative nutritional importance of the food groups consumed . The scoThe food items of the collected 7-day food frequency data were grouped into the nine standard food groups . Afterwards, all consumption frequencies of food items in the same group were summed up and their values were top-coded at 7. Then, the consumption frequency obtained for each food group was multiplied by a standard weight, the value of which depended on the level of energy, quality of protein, and range of micronutrients provided by the food group. These standard weights were 2 for main staples, 3 for pulses, 4 each for meat and fish and milk, 1 each for vegetables and fruit, 0.5 each for oil and sugar, and 0 for condiments. Finally, the weighted food group score for each food category was summed up to determine the household FCS. Households were classified as food-secure if the FCS was above 35, moderately food-insecure if the indicator was between 21 and 35, and severely food-insecure if the FCS was below 21. On average, the original and intact households considered in this study were food-secure in both rounds 1 and 2.As this indicator is standardized, it can be used to compare the state of households’ food security in different locations and over time . MoreoveRegarding the household splitting process determinants, the first variable that captures the individual-level characteristics is the household head’s age expressed in years. In this study, we further added two dummy variables, ‘male (16–25)’ and ‘female (16–25)’, indicating the presence of male and female members in the 16–25 age category. This age range was selected based on the literature and available data to represent the typical age for youths inclined to leave the parental family and generate a new household ,34,35. AThis present study represented the household characteristics in terms of its socio-economic status, as proxied by the household size and wealth index. This latter indicator is a widely used composite measure of households’ cumulative living standards in low- and middle-income countries due to difficulties in collecting reliable data on income and expenditure . The household size was computed as the total count of members in the household. For the computation of the wealth index, we selected a set of proxy indicators on the households’ ownership of durables and furniture and their dwelling characteristics following the literature ,38. The The data confirm the evidence from the key informant interviews on the use of the splitting process as a coping mechanism by the poorest household, and that a poor original household generates a poor split-off household. This tendency was verified using household access to social safety net programs targeted toward the poorest and most vulnerable households in Malawi ,42. ThesIn this paper, it was noted that the original households receiving social safety net programs in both survey rounds tended to generate split-off households in round 2 as new beneficiaries of these programs. Therefore, the study included a dummy variable, ‘social assistance’, with values equal to 1 if the original household received at least one of the institutionally organized household-level social safety net programs in round 2 and 0 otherwise. This variable was used as a proxy indicator of the households’ tendency to utilize coping mechanisms related to sending members permanently away to form separate housekeeping arrangements. This study also adopted two dummy indicators for the households’ geographical areas of residence representing the central and southern regions of Malawi to capture the possible confounding factors related to the contextual characteristics of the households. According to the research question of this study, the household splitting process between rounds 1 and 2 was considered as the treatment variable. As described in the previous section, this study hypothesized that the treatment affects household food security, our outcome variable.The econometric analysis evaluated this hypothesis by referring to the literature on the treatment–effect estimation that ideally requires a randomized assignment of the treatments into two mutually exclusive groups . The groThe implementation of the difference-in-differences (DID) method permitted the treatment effect to be estimated by comparing changes in the household FCS in the two periods analyzed in the treated and control groups . The DIDThis study combined the DID method with the propensity score matching (PSM) technique to improve the common trend assumption, as suggested in the literature ,45. The S is a binary treatment variable, such that its value equals 1 if the household h participated in the splitting process between the two rounds and 0 otherwise. Further, I, H, and C represent the set of the households’ individual-level, household-level, and contextual characteristics in round 1, respectively, as presented and discussed in j, βkβ, and lβ are the coefficients of these characteristics, and ε is the residual term.The study implemented the combined PSM-DID in the following steps, as the literature suggested ,47. It fS in (1) produced an estimated propensity score, which is a composite measure of a household’s pre-treatment characteristics determining its participation in the splitting process [The predicted probability of  process ,46. Thes process . As highlighted in the previous section, this study selected the variables in (1) through literature reviews and key informant interviews. The appropriateness of the PSM model (1) was ascertained by ensuring that the treated and control households fulfilled the common support and balancing conditions. The common support condition requires that households have overlapping propensity scores so that an original household can be matched and compared with an intact household with a similar probability of splitting. The balancing condition requires that the pre-treatment characteristics are, on average, similar both in the overall treated and control groups. The study graphically assessed the common support condition by plotting the propensity scores and asserted the balancing condition using a standardized difference test across the overall treated and control groups. FCS is the observed food consumption score for household h in survey round t = {1,2}; S is the treatment variable, with values of 1 and 0 for original and intact households h, respectively. Further, p is a dummy variable indicating either the pre-treatment (coded as 0) or post-treatment (coded as 1) period, and (hS × tP) is the interaction term that informs on the average treatment effect of the splitting process on the FCS among households who participated in the splitting process. In technical terms, this treatment effect is referred to as the average treatment effect on the treated (ATT), which is captured by the coefficient α3 and is the estimate of our interest.Finally, a DID analysis was conducted for the matched treated and control households using the following regression model:This study implemented the combined PSM-DID in STATA using a single command ‘diff’, which computed the propensity scores for households, matched original and intact households using a default kernel function, constructed the treated and control groups, and conducted a DID estimation for households fulfilling the common support condition. However, the comparability of the treated and control households depends on the quality and reliability of the matching procedure. Therefore, this study computed the standardized differences in the covariates included in the PSM model (1) to assess the matching procedure, as presented in t-test in the matched sample confirms that the treated and control groups of households are statistically similar after the matching procedure, which ensures their comparability. The estimates also highlight that the treated and control groups of households are balanced in all covariates. This aspect is indicated by the overall covariate balance tests presented in the second section of Column (ii) of The PSM also identified and evaluated the determinants of the household splitting process and their implications for household food security in Malawi. Therefore, next, the following sub-paragraph presents the probit regression results for the PSM model (1) in Regarding individual-level characteristics, the results suggest that the probability of splitting increases with the increase in the household head’s age. The age squared variable qualifies this process better. Its negative sign indicates that as the household head becomes older, the effect of age on the household division process is lessened. As marriage is the dominant reason for household splitting in Malawi, this non-linear relationship was expected because with the increase in the household head’s age, the household structure changes with the reduction in the number of members in the marriageable age category (16–25). This hypothesis showed a possible confirmation in the dataset used by this study. In fact, there is a negative and statistically significant correlation (−0.43) between the household head’s age and the number of members in the marriageable age category (16–25).p-value equaling 0.84 signaled no significant gender differences in the probability of household splitting due to the presence of marriageable male or female members in the household.Further, the possible relevance of marriageable members in explaining the household splitting process was also maintained by the positive coefficient of the two specific variables, ‘male (16–25)’ and ‘female (16–25)’. This analysis distinguished between male and female members in the marriageable age category to verify a probable gender component in the splitting process. For this purpose, the t-test of coefficient equality was computed for these dummy indicators. Its The significant and positive coefficient of the ‘female child (8–15)’ indicated that households with an unmarried girl child have a higher propensity to split. This associative effect aligns with the literature that correlates the presence of an unmarried girl child in households and their decision to migrate . The preThe positive association of the household size with the household splitting process reinforces this role of poverty in household division. As previously noted, household size is correlated with poverty in Malawi. According to NSO-Malawi , 60.6 peThe evidence on ‘social assistance’ seems to confirm the use of the household division process by the poorest and most vulnerable households in their attempt to improve their economic conditions. This evidence also sheds light on a mechanism associated with the spread of poverty in the area, despite its possible positive effect on household resource distribution. As previously noted, this group of poor households in the sample tend to generate poor split-off households. However, this coping strategy does not result in their escape from poverty and food insecurity. On the contrary, it might prolong the adverse effects of the household splitting process in the long term.The positive sign of the estimated wealth index seems to contradict the previous considerations on the role of poverty in the household splitting process. However, the wealth index captures another important aspect of the household splitting process in Malawi, related to the socio-economic status and spouse similarity, as highlighted during our key informant interviews and confirmed by the literature. According to the literature, better educated women are more likely to have better educated husbands, and households with high levels of wealth have more educated members and greater household educational attainment ,54. AccoThe positive association between the two region-specific dummies and the household splitting process affirms the role of the households’ contextual characteristics in their decision to split. In particular, this study highlights that households residing in the central and southern regions are more likely to split than those in the northern regions. These observations are critical in explaining the household splitting process in Malawi, especially considering the heterogeneous cultural and socio-economic contexts across the country’s central, northern, and southern regions. For example, girls in the southern region are observed to marry earlier than those in the northern region, whereas the average marriage age is highest in the central region. In addition, the matrilineal societies dominate the country’s southern region, whereas the patrilineal system prevails in its central areas. The evidence from the present study implies that these contextual characteristics translate into household-level differences, including disparities in the average age of marriage and forms of customary marriages, with specific effects on household wealth ,56 and tFurthermore, the regional dummies also captured the varying levels of multidimensional poverty across the three regions, measured along the dimensions of health, population, education, environment, and work. In fact, according to recent estimates, the southern region presents the highest multidimensional poverty index value, the northern region the lowest, and the central region is at an intermediate position . TherefoThe first three results in The DID-PSM estimation result, reported in the final rows of The DID-PSM indicated a statistically significant increase of 3.74 units in the FCS among the original households in the treated group compared to the non-split households in the control group. This increase corresponds to an average of 7% higher FCS values in 2013 among split households with respect to the base year (2010) net of any increase in the control group. We found that the FCS among the intact households, on average, remained stable across the two analyzed periods. Therefore, any food security improvements observed across these two periods could mostly be attributed to the improvements among original households due to the household splitting process. Such improvements may seem to indicate that the splitting process benefits household food security. However, statistical significance does not necessarily imply practical significance, especially given the lower magnitude of the effect of the splitting process on household food security.Furthermore, despite any possible beneficial effects, it is also important to consider that the household splitting process might negatively affect some households, especially in the long term. Most of the household splitting process determinants identified in the present study, like child marriage and dependence on social protection systems, are implemented by poor households as coping strategies. These strategies, however, might perpetuate the vicious cycle of poverty and food insecurity for already destitute households. For example, child marriage adversely affects the daughters’ long-term social, economic, and health outcomes due to a lack of schooling, pregnancies, and limited decision-making capabilities at their young age . These eThe present study confirms the analytical framework presented in However, the observed tendency among poor households to generate split-off households as new beneficiaries for the social protection programs might further exacerbate poverty and food insecurity. As the interviews with key informants asserted, such a coping strategy, implemented mainly by poor households, further generates another poor split-off household. At the same time, the strategy could further reduce the human capital in the original household with the exit of income earners. Nevertheless, the significant and positive effect of the household splitting process on household food security implies the need to understand the role of this phenomenon in evaluating any food security interventions to avoid a possible confounding bias. The present study’s findings also call for an understanding of the overall household splitting process in the analysis, design, and implementation of food security interventions in Malawi in ways that could help poor households minimize the use of certain coping strategies that might harm them in the long run. These coping strategies include child marriage practices and the tendency of poor households to generate split-off households as beneficiaries of social protection programs.Future research studies could expand this analysis by quantifying the long-run effects of these coping strategies and the household splitting process on the original and split-off households, along the pathways proposed in our study. Moreover, the methodological approach adopted by this study made an unconfoundedness assumption in the PSM procedure and DID estimation. This assumption entails a similar distribution of unobserved determinants of the household splitting process and household food security situation across the original and intact households. Therefore, future studies could incorporate richer sets of predictors in the econometric models with the possible inclusion of variables indicating intra-household resource distribution and food consumption across both original and intact households. These variables were, however, unavailable in the IHPS dataset. Therefore, the data limitations of this study also warrant the need for future surveys to consider the household splitting process and its consequences in devising questionnaires and data collection tools.


Disarmament treaties have been the driving force towards reducing the large nuclear stockpile assembled during the Cold War. Further efforts are built around verification protocols capable of authenticating nuclear warheads while preventing the disclosure of confidential information. This type of problem falls under the scope of zero-knowledge protocols, which aim at multiple parties agreeing on a statement without conveying any information beyond the statement itself. A protocol capable of achieving all the authentication and security requirements is still not completely formulated. Here we propose a protocol that leverages the isotopic capabilities of NRF measurements and the classification abilities of neural networks. Two key elements guarantee the security of the protocol, the implementation of the template-based approach in the network’s architecture and the use of homomorphic inference. Our results demonstrate the potential of developing zero-knowledge protocols for the verification of nuclear warheads using Siamese networks on encrypted spectral data. Since then, several treaties like the Strategic Arms Reduction Treaty (START) and Strategic Offensive Reduction Treaty (SORT) have reduced this number to a global amount of 13,000, with the USA and Russia holding about 6000 each3. Further reduction efforts are built around verification procedures capable of authenticating nuclear warheads while preventing the disclosure of confidential information. Despite decades of research, an optimal verification protocol capable of achieving these goals is still not entirely formulated. The primary constraint related to such protocols stands in the seemingly contradictory formulation of the task: demonstrate to a third party that the item in your possession is authentic without disclosing any information about the item.The Cold War’s escalating tensions have seen the world’s superpowers stockpiling over 60,000 nuclear warheads at their peak in 19864. The first approach is based on defining a set of absolute attributes as unique identifiers of the warhead. Such attributes contained physical features, like the mass or size of the object, and compositional information, such as isotopic ratios, hidden behind information barriers. The fact that some layer of abstraction contains absolute values that can be correlated to the physical properties of the warhead has left such implementations at risk of tampering. Secondly, given that the attributes are hand-picked, there is the possibility that the selected set of attributes does not uniquely define the nuclear warhead, allowing the chance of fake warheads passing as genuine. The drawbacks of attribute-based methods have forced a shift to template-based verification protocols, which use an already proven sample (template) to validate the warhead under testing. A template-based method implies the ability to quantify the relative difference between two objects on some predefined metrics. Measurements of the appropriate metrics without disclosing any information about the objects ensure zero-knowledge verification.In the context of nuclear warhead verification, zero-knowledge protocols aim to prove to an external inspector that the warhead under testing is genuine and has not been tampered with in any way. A hoax warhead can be broadly classified into compositional or geometrical hoaxes. A compositional hoax is a nuclear warhead in which any element was replaced with a surrogate, or the isotopic composition of any component has been altered. On the other hand, in the geometrical hoax case, the elemental/isotopic composition is preserved, but changes to the structural integrity of the warhead have been made. Up to this point, two types of verification protocols capable of identifying hoax warheads have been proposed8. The proposed Princeton protocol is based on fast neutron radiography to achieve zero-knowledge validation using preloaded superheated bubble detectors6. Using preloaded detectors ensures the method’s security as the sensitive information is never measured directly. While powerful in its approach, the technique lacks the isotopic specificity to identify compositional hoaxes. An MIT-based group has proposed a different protocol that employs the superior isotopic discrimination capabilities of Nuclear Resonance Fluorescence (NRF) and targets compositional as well as geometrical verification4. The method is based on the detection of resonant photons produced in the interaction of an incident beam with a sample material. The photons are generated in specific nuclear transitions that can be uniquely assigned to particular isotopes9. The proposed protocol employs a transmission NRF configuration10, in which the witness foil characteristics are withheld from the verifier and are used to encrypt the measured spectrum. Unlike the Princeton protocol, the MIT protocol cannot achieve the zero-knowledge standard as the verifier will have access to hashed measurement results.Several groups have provided template-based protocols using different imaging modalities14 to achieve zero-knowledge verification. This algorithm combines for the first time machine learning and homomorphic inference to authenticate nuclear warheads. Two elements ensure the security of the protocol, the implementation of the template-based protocol at the architecture level, using Siamese networks, and the use of homomorphic encryption at inference time. The results of this work are presented in two parts: an extensive 2D example demonstrating the capability of Siamese neural networks to address the warhead verification problem and a single-point analysis highlighting the advantages and current limitations of homomorphic inference.This work proposes a new template-based protocol built on the isotopic capabilities of NRF measurements coupled with the feature selection and classification abilities of neural networksMonte Carlo simulations data were used to generate the training, testing, and validation datasets, required to evaluate the capabilities of the proposed verification protocol. The measurement setup was composed of eight detectors uniformly distributed on two rings at 45mentclass2pt{minimTwo distinct datasets were the basis for the training, testing, and validation splits. The training and testing datasets were sampled from a randomly generated dataset composed of 100 scene configurations. The generated scenes contained randomly selected spectral features, like NRF lines, intensities, and branch ratios, as well as geometrical features, like the shape and size of the object. The shape of the objects was sampled out of four possible outcomes: concentric spheres and cylinders, sequential cylinders and rectangular plates 18. The Concrete library19, a TFHE-based scheme that implements the concept of programmable bootstrap was used throughout this work. The programmable bootstrapping is a key concept that allows fine control of the associated noise and enables the possibility to evaluate any arbitrary function homomorphically.Homomorphic encryption algorithms are constructed around noisy ciphertexts that support performing mathematical operations without the loss of encryption. The ability to perform encrypted computations guarantees the preservation of data privacy for each step in the processing pipeline. The main limitation associated with homomorphic encryption was the increasing amount of noise with each operation; any additional step above the maximum noise level renders the ciphertext undecryptable. These schemes, known as somewhat homomorphic schemes, would allow only a finite number of homomorphic operations. The first implementation of a fully homomorphic encryption scheme is described by the seminal work of GentryIn its current implementation, the Concrete library contains most of the elements required to implement neural network architectures. In terms of mathematical operations, the library allows addition and subtraction between ciphertexts, addition and multiplication between ciphertext and plaintext, and evaluation of an arbitrary function on a ciphertext through programmable bootstrapping. A homomorphic inference scheme can be implemented using these capabilities in which the weights and biases are plaintexts, while the input, output, and all the intermediate values are encrypted. Two main limitations currently restrict the use of homomorphic inference on complex network architectures: the computational overhead and the 7-bit computational threshold. The computational overhead does not pose a significant issue for the current work, as real-time inference is not necessarily required for the protocol. The 7-bit limit imposes significant constraints on the maximum network accumulator values, restricting the size of the network.In order to demonstrate the potential of using homomorphic inference for the warhead verification problem while satisfying the 7-bit limitation of the library, a scaled-down version of the network shown in Fig. The network was trained in plain using samples from all 100 training/testing with a quantization level of 5 bits  and ring-LWE, which are naturally quantum-resistant20.Constructing realistic protocols around the described methodology does require extensive details about dismantlement treaties and implementation requirements, which fall outside the scope of this work. The following description represents a simplistic view of such a procedure. The proposed protocol involves three entities participating in the verification procedure: host, inspector, and an overseeing authority. The host is the owner of the warhead under testing and of the measurement setup. It is assumed that the measurement will be made in the host’s facility. The inspector is the entity that aims to verify the authenticity of the sample in the possession of the host. The inspector will arrive at the host’s facility accompanied by a genuine warhead authenticated by other meansIn the context of nuclear spectroscopy, several factors can interfere with a measurement’s integrity. A neural network that can be used for an automatic verification procedure should be able to account for experimental edge cases and correctly assess the validity of the sample. In a zero-knowledge protocol scenario, the problem is amplified as histograms cannot be visualized in plain to identify common experimental problems, like poor resolution due to noise or improper sample positioning. The neural networks selected in this work are capable of dealing with these issues, as it is detailed in the following sections.The proposed verification protocol uses input data from 2D scenes obtained in a single projection measurement. However, to satisfy the homomorphic library’s 7-bit limitation, a downscaled version of our network was used for the single-point analysis. Hence the discussion is focused on the performance evaluation for the 2D analysis using plain inference and for the single-point analysis using both plain and encrypted data. The results of the inference procedure for the 2D scene are shown in Fig. 4. The capability of a neural network to analyze high dimensional data also enables the possibility to use tomographic data as input that can yield additional improvements in accuracy.In terms of the overall accuracy, the verification protocol can be significantly enhanced if multiple projections are involved. The generality of the Siamese architecture enables the possibility of analyzing measurement samples for an arbitrary number of projections. This might be required as protection against geometric hoaxes that could mimic the template along a predefined projectionThe outcome of the inference procedure using plain and encrypted data for single-point analysis is summarized in Fig. The performance metrics for the single-point analysis using plain and encrypted inference on the validation dataset are shown in Fig. 21, and at the hardware level with optical computing. Specialized hardware would enable inference on complex full precision networks as several orders of magnitude improvements in processing times are expected19.Despite the reduced complexity of the input, the single-point neural network underperforms in comparison to the 2D neural network on the training and testing dataset. This is directly correlated to the 7-bit limitation of the homomorphic library. An additional increase in the bit rate will alleviate these problems and will allow the possibility of performing homomorphic inference using the full-sized network. The current 7-bit limitation its imposed by the computational load of the bootstrapping operation, which grows roughly exponentially with the length of the plain message. Solutions for speeding up FHE schemes are proposed on the software level, like parallel arithmetic12. Moreover, the generality of our approach enables the ability to further extend the model with additional modalities based on spectral comparison, like neutron-induced nuclear resonance measurements8.The results of our work demonstrate the potential of using Siamese neural networks for zero-knowledge verification of nuclear warheads. Developing simulation-based models with excellent performance is a key building block for constructing models based on experimental data. An ideal training scenario for a proof of concept implementation would make use of realistic Monte Carlo simulations for generating pre-training data, followed by training on experimental measurementsThe second key feature that guarantees the security of the proposed protocol is the use of homomorphic inference. The ability to perform mathematical operations on encrypted data enables the possibility to apply complex algorithms while preserving data privacy. Our work demonstrates the possibility of achieving zero-knowledge homomorphic inference on spectral data using a complex Siamese architecture. Good accuracy results were obtained for the single-point analysis, using a limited implementation of our model, despite the 7-bit limitation currently imposed by the library. Solutions for extending the current limit are already in the works and will provide the ability to perform homomorphic inference of highly complex architectures.22. G4Penelope classes were used to model the low-energy electromagnetic interactions. The NRF interaction was simulated using the experimentally validated implementation described by Negm24. The incident beam was modeled as an approximation for a continuous spectrum that can be experimentally obtained using bremsstrahlung or laser Compton scattering. The detectors, part of the measurements setup, were modeled after a 150% relative efficiency high-purity germanium detector. Each of the 900 pixels of a sample was simulated using The datasets used for the training, testing, and validation of the proposed models were generated using Geant4 version 10.0625. The training was done using Adam, with a 26. The weight values were restricted to The neural network architectures were implemented using the Keras framework27 for plain and encrypted inference. All the array operations required for the inference were carried out using the ndarray library 0.15.4. The encrypted inference process was implemented using the FHE library Concrete version 0.1.11. The encoder ranges required for the encrypted inference were obtained based on the minimum/maximum values observed during the plain inference on the training and testing datasets. The selected encryption parameters offer a 128-bit security level. The validation dataset for the plain inference was composed of 34 samples. The validation for the encrypted inference was carried out 16 times, using the complete dataset in order to account for the evaluation uncertainties. The encrypted inference compute time required to run the validation dataset was about 350 h on a single CPU thread.The training procedure for the single-point neural network was made using the procedure described above. Following the training, the single-point neural network architecture was implemented in RustThe assumptions of the proposed protocol lead to the following threat model. First, the exchange of sensitive information between the involved parties and the overseeing authority is made using encrypted data, which preserves data privacy. A semi-honest overseeing authority could extract information from the plain-text model, related to the training data and model stability but cannot generate adversarial samples. Second, we assume that the protocol steps from the experimental measurement to the analysis algorithm are not compromised. In that case, the attack path for a malicious host requires the generation of a hoax object. In a black-box scenario where the host does not have direct access to the network, generating adversarial samples would require an abundant number of queries. Such attacks cannot be considered a vulnerability as the number of queries could be easily limited at the protocol level. The system is susceptible to gradient-based attacks in a white-box scenario in which the host gains direct access to the network. Under these conditions, the host can use the genuine warhead to generate adversarial spectra that could deceive the classifier. However, given the statistical nature of spectroscopic measurements and the specificity of nuclear resonances, most of the generated adversarial spectra will not describe realistic objects and cannot be used to reconstruct hoax objects. Currently, the proposed protocol describes the verification process at a conceptual level. The threat model outlines only a limited view of the challenges associated with the verification of nuclear warheads. Several key elements, such as physical security and encryption key handling, fall outside the scope of this paper. These implementation details are essential to ensure the protocol’s security and will be considered in future studies.28. Robust training techniques and ensemble learning have been proposed to generate models with improved stability, and state-of-the-art performance30. Additionally, network instabilities can be further reduced by using multiple projections and imaging modalities that will significantly decrease the uncertainties associated with the inference of a single measurement. Further studies are required to assess and enhance the stability of homomorphic inference for Siamese networks in the context of zero-knowledge verification of nuclear warheads using spectroscopic data.The use of neural networks in security-critical environments raises additional challenges as the lack of interpretability and model stability. The robustness of the network is especially important in the context of our work, as small perturbations associated with the homomorphic inference can lead to incorrect predictionsSupplementary Information.


Indocyanine Green (ICG) fluorescence-guided surgery is widely used for intraoperative visualization of lymphatic structures. To date, there are no reports indicating this dye being used in lymph node biopsies for suspected or relapsed lymphoma.Between October 2021 and June 2022, 12 patients underwent a fluorescence-guided laparoscopic lymph node biopsy (FGLLB) using ICG. The following was retrospectively evaluated: the dosage of ICG, the injection site, the number of patients where fluorescence was obtained after ICG administration, and additionally, the parameters indicating the outcome of the surgical procedure.The median duration of the surgery was 90 min. A laparotomy conversion was required in one case due to bleeding. Fluorescence was obtained in 10/12 (83.3%) patients by means of subcutaneous/perilesional injection in six of the patients, and intravenously in the other four. Hospitalization had a mean duration of three days. There were no major postoperative complications. FGLLB was used in seven patients to follow lymphoproliferative disease progression, and in five patients to establish a diagnosis. In all cases, FGLLB provided the information necessary for the correct diagnosis.Fluorescence with ICG offers a simple and safe method for detecting pathological lymph nodes. FGLLB in suspected intra-abdominal lymphoma can largely benefit from this new opportunity which has not yet been tested to date. Further studies with large case series are needed to confirm its efficacy. Sentinel lymph node biopsy has been validated as a standard of care in breast cancer, melanoma and gynaecological malignancies –3. With In the gynaecological field, recently published systematic reviews recommend the use of ICG as the tracer of choice for most gynaecological cancers .However, the use of this dye in primary lymph node diseases has not yet been sufficiently studied. To date, there are only a few anecdotal reports indicating its use to detect pathological lymphatic tissue when a lymph node biopsy is performed for suspected lymphoproliferative disease , 7.Taking advantage of the known properties of an elective tropism for the lymph node tissue of the ICG, the decision was made to study the use of this fluorophore for the intraoperative identification of pathological lymphatic tissue. In case of abdominal lymph nodes affected by primary lymphoproliferative diseases, the hypothetical advantage, since not yet fully studied, would be to simplify the search for the lymph nodes themselves and to be able to choose the biopsy site with greater precision by targeting the vital tissue needed to obtain a contributory pathological examination. Thus, a prospective series of patients undergoing a fluorescence-guided laparoscopic lymph node biopsy (FGLLB) to rule out, or to follow the progression of a lymphoma, was studied.In October 2021, FGLLB was introduced for the first time in our division. By October 2022, twelve procedures had been performed and collected in a prospective database. The clinical characteristics of the patients included sex, age, previous abdominal surgery, and associated comorbidities. The purpose of the biopsy was to establish a diagnosis or confirm the progression of lymphoma. All patients had intra-abdominal lymphadenopathy and an absence of lymphadenopathy accessible to a superficial biopsy. The pre-operative work-up included a computer tomography (CT) scan and a positron emission tomography (PET) for all patients. During the laparoscopic procedure a solution obtained by diluting a 25 g vial of indocyanine green powder  with 10 ml of sterile water was used. The concentration of the solution to be injected was kept constant for all patients in the study. The site of administration of the ICG dye varied with the anatomical site of the specimen to be retrieved. In case of inframesocolic lymph nodes (ILN) biopsy, the injection of 2 mL of the aforementioned solution was carried out in each of the inguinal regions, in the subcutaneous/intra lymph node position , followed by the evaluation of the fluorescence and subsequent lymph node excision. Fig. .The indicators of the procedure outcome taken into consideration were: the operative time, the estimated blood loss, the associated interventions, the surgical conversion, the insertion of additional trocars, the positioning of an abdominal drain, the length of hospital stay and the post-operative complications. To evaluate the effectiveness of the use of the ICG in fluorescence-guided surgery, the drug dosages, the injection site of the drug and the number of patients with fluorescence obtained after ICG administration were also considered.In the case of ILN biopsy, after induction of anaesthesia, 2 mL of the aforementioned ICG solution was injected subcutaneously at both inguinal regions, at the level of the femoral triangle of Scarpa. The pneumoperitoneum was achieved through the umbilicus via an open technique; a 10-mm trocar was inserted to accommodate a 30°-angle telescope. A 10-mm trocar was inserted in the right iliac fossa and a 5-mm trocar in the right hypochondrium. The surgeon and camera holder stood on the right side of the patient. A right tilt and mild Trendelemburg position were given to the table. Taking advantage of the lymphatic drainage that first drains to the external iliac lymph nodes from the superficial inguinal lymph nodes, then to the pelvic lymph nodes, and finally to the paraaortic lymph nodes twenty minutes after the injection, observations were made of the lymph nodes stained with ICG in the subserosa along these vessels. Para-aortic lymphadenopathy was reached by an incision of the peritoneum covering the superior part of the right common iliac artery. This incision was guided along the left aspect of the aorta, just above the inferior mesenteric artery. A Thunderbeat™  device was used for dissection. A dedicated clinical endoscopic system  equipped with infra-red (IR) light source and IR UHD telescope was used to illuminate regional lymph nodes . Median BMI of the patients was 26.3 (range: 20.4–38.6). Previous abdominal surgery was present in five patients. FGLLB was completed laparoscopically in 11 cases. A laparotomy conversion was required in one case due to bleeding and an abdominal drainage was left in place in this patient. Generally, three trocars were needed, however, two patients needed a supplementary trocar to better expose the field. The estimated blood loss was absent in all patients except in those converted from laparoscopy to laparotomy.The abdominal lymph nodes sampled were ILN (periiliac and periaortic) in nine cases and SLN (coeliac trunk and gastrohepatic ligament) in three. The biopsy was excisional in seven cases, incisional in three cases and both methods were used in two cases. Fluorescence was obtained in 10/12 (83.3%) patients by means of subcutaneous/perilesional injection in six of the patients and intravenously in the other four. No fluorescence was noted in cases of perilesional injection. The clinical features are detailed in Table Median duration of surgery was 90 min (range: 60–120 min). Length of hospitalization was 1.5 days (range: 1–11 days). Morbidity was null.A prolonged postoperative stay of 11 days was due to the development of complete ureteral obstruction as a result of tumoral compression needing a nephrostomy and a stent. A preoperative positron emission tomography/computed tomography (PET/CT) scan showed solid lymphomatous tissue enveloping the terminal portion of the subrenal abdominal aorta and the left common iliac artery.In seven patients FGLLB was used to follow the progression of a lymphoproliferative disease, and in five patients to establish a diagnosis. The histopathological diagnosis was non-Hodgkin lymphoma in nine patients, a specific inflammatory reaction in two patients and metastasis from an undifferentiated solid tumour in one case, respectively. In each retrieval of the 9 cases where a non-Hodgkin lymphoma diagnosis was obtained, the samples were multiple and all were positive, both when the sampling was incisional and when it was excisional. In all cases FGLLB provided adequate specimens of lymphatic tissue and a correct diagnosis with subsequent therapeutic decisions being achieved.The subdivision of the abdominal lymph nodes sites involved in the laparoscopic biopsy essentially reflects the different pathways of the lymphatic flow. In fact, for the ILNs the injection of the dye took place in the inguinal region. However, this route of administration is not effective for the SLNs since the paths of the lymph flow are more complex.Unfortunately, for the SLNs an injection in the regions adjacent to the lymph nodes proved to be ineffective in staining the lymph nodes and in two out of three cases the staining was obtained only after the intravenous injection, i.e., with the “rescue procedure”.The subcutaneous injection at the groin certainly proved to be more effective in cases of ILN. In fact, in six out of nine cases, the para-iliac and periaortic chains were coloured which made the sampling easier. In the remaining three cases, fluorescence was obtained in two, and only thanks to the “rescue procedure” of intravenous dye injection. It should be noted that in these last three cases the disease was in the form of a large tumour mass and of extra lymph node origin.Extranodal involvement can be seen with lymphoma in approximately 25–40% of cases and almost any organ can be involved . This coAnother peculiarity that was observed during laparoscopic biopsy of pathologic ILNs was the possibility that lymph nodes greatly enlarged due to the disease constitute a “stop” to the up flow of the dye by preventing its entry into the lymph node itself and into the lymphatic chain immediately downstream.The issue of whether the dye is retained by the pathological lymph node in the same way as it is in healthy ones is currently unknown. In colo-rectal or gastric cancer, after the peritumoral injection of ICG, the dye follows the lymphatic pathways and colours the lymph nodes it finds along the collectors. The presence of cancer cells within the metastatic lymph node does not seem to decrease the intensity of staining .However, this statement is not univocal. Widespread lymph node metastases have been observed to induce an obstruction of lymphatic channels, and lymphatic drainage is bypassed to other (nonsentinel) lymph nodes . PerhapsIn conclusion, the issue whether the elective tropism of the dye towards the lymph nodes is maintained in cases of primary lymph node disease has been proven. Concerns remain about the ideal dosages of ICG and the injection sites. A potential advantage to be investigated is the ability, thanks to the dye, to carry out the surgical sampling on a defined vital area, avoiding false negatives due to the sampling of necrotic tumours or acellular fibrous areas, thus improving the diagnostic accuracy. Furthermore, in the case of abdominal lymph nodes affected by primary lymphoproliferative diseases, ICG-enhanced fluorescence seems to provide several advantages in FGLLB by allowing both to better identify the surgical anatomy and to potentially reduce the surgical time due to a safer dissection. Further studies with large case series are needed to confirm these promising data.