Distribution Of Vectors Research Articles

Bayesian spatio-temporal modeling to assess the effect of land-use changes on the incidence of Cutaneous Leishmaniasis in the Brazilian Amazon

Cutaneous Leishmaniasis (CL) is a vector-borne disease caused by a protozoan of the genus Leishmania and is considered one of the most important neglected tropical diseases. The Brazilian Amazon Forest harbors one of the highest diversity of Leishmania parasites and vectors and is one of the main focuses of the disease in the Americas. Previous studies showed that some types of anthropogenic disturbances have affected the abundance and distribution of CL vectors and hosts; however, few studies have thoroughly investigated the influence of different classes of land cover and land-use changes on the disease transmission risk. Here, we quantify the effect of land use and land-cover changes on the incidence of CL in all municipalities within the Brazilian Amazon Forest, from 2001 to 2017. We used a structured spatiotemporal Bayesian model to assess the effect of forest cover, agriculture, livestock, extractivism, and- deforestation on CL incidence, accounting for confounding variables such as population, climate, socioeconomic, and spatiotemporal random effects. We found that the increased risk of CL was associated with deforestation, especially modulated by a positive interaction between forest cover and livestock. Landscapes with ongoing deforestation for extensive cattle ranching are typically found in municipalities within the Amazon Frontier, where a high relative risk for CL was also identified. These findings provide valuable insights into developing effective public health policies and land-use planning to ensure healthier landscapes for people.

A Novel Resource-Aware Distributed Cooperative Decision-Making Mechanism for Connected Automated Vehicles

<div>This article proposes a new model for a cooperative and distributed decision-making mechanism for an ad hoc network of automated vehicles (AVs). The goal of the model is to ensure safety and reduce energy consumption. The use of centralized computation resource is not suitable for scalable cooperative applications, so the proposed solution takes advantage of the onboard computing resources of the vehicle in an intelligent transportation system (ITS). This leads to the introduction of a distributed decision-making mechanism for connected AVs. The proposed mechanism utilizes a novel implementation of the resource-aware and distributed–vector evaluated genetic algorithm (RAD-VEGA) in the vehicular ad hoc network of connected AVs as a solver to collaborative decision-making problems. In the first step, a collaborative decision-making problem is formulated for connected AVs as a multi-objective optimization problem (MOOP), with a focus on energy consumption and collision risk reduction as example objectives. RAD-VEGA then cooperatively solves this MOOP, taking into account the availability of AV’s onboard resources and the application layer characteristics of today’s ITS communication tools. The performance of the proposed mechanism is evaluated by solving the ZDT1 test problem and studying pareto-frontier solutions to the true front over time. The scalability of the proposed solution is estimated to be 305 CAVs, considering a communication bandwidth of 6 MB/s. Additionally, cooperative AV planning scenario examples are simulated, and the effectiveness of the proposed mechanism is demonstrated by comparing final and initial solutions after solving the MOOP using RAD-VEGA.</div>

Weighted-Neighborhood-Information-Network-Enabled Anomaly Detection Method for Electronic Sensors and Sensor Networks

As electronic sensors and sensor networks advance, perception data are increasingly characterized by mixed attributes. Traditional anomaly detection methods predominantly focus on numerical attributes. In this paper, we introduce a weighted neighborhood information network (WNIN)-enabled anomaly detection method tailored for mixed-attribute data from electronic sensors and sensor networks. Firstly, we employ the analytic hierarchy process (AHP) to analyze the security of sensor networks, leveraging a hierarchical electronic sensor network model to construct a hierarchical perception security architecture for anomaly detection. Subsequently, a neighborhood information system is established to ascertain the relationships between data objects with mixed attributes. We then develop the WNIN to encapsulate the relationships, and a state-transferring probability matrix based on data object similarity is derived. Ultimately, a random wandering process within the WNIN is executed, and the importance of data objects is evaluated using the steady-state distribution vector, thereby determining the anomaly data. Simulation outcomes reveal that our proposed method attains superior anomaly detection rates compared with existing methods.

Schistosomiasis and Geographical Distribution of Aquatic Mollusks and Disease Vectors in the Gharb Plain (Morocco)

Schistosomiasis and Geographical Distribution of Aquatic Mollusks and Disease Vectors in the Gharb Plain (Morocco)

A probabilistic approach to Lorentz balls [formula omitted]

We develop a probabilistic approach to study the volumetric and geometric properties of unit balls Bq,1n of finite-dimensional Lorentz sequence spaces ℓq,1n. More precisely, we show that the empirical distribution of a random vector X(n) uniformly distributed on its volume normalized unit ball converges weakly to a compactly supported symmetric probability distribution with explicitly given density; as a consequence we obtain a weak Poincaré-Maxwell-Borel principle for any fixed number k∈N of coordinates of X(n) as n→∞. Moreover, we prove a central limit theorem for the largest coordinate of X(n), demonstrating a quite different behavior than in the case of the ℓqn balls, where a Gumbel distribution appears in the limit. Finally, we prove a Schechtman-Schmuckenschläger type result for the asymptotic volume of intersections of volume normalized ℓq,1n and ℓpn balls.

Tomographic redshift dipole: testing the cosmological principle

The cosmological principle posits that the universe is statistically homogeneous and isotropic on large scales, implying all matter shares the same rest frame. This principle suggests that velocity estimates of our motion from various sources should agree with the cosmic microwave background (CMB) dipole's inferred velocity of 370 km/s. Yet, for over two decades, analyses of radio galaxy and quasar catalogs have found velocities at odds with the CMB dipole, with tensions up to 5σ. In a blind analysis of BOSS and eBOSS spectroscopic data from galaxies and quasars across 0.2 < z < 2.2, we applied a novel dipole estimator for a tomographic approach, robustly correcting biases and quantifying uncertainties with realistic mock catalogs. Our findings with eBOSS data (0.6 < z < 2.2), indicating a velocity of 196+92 -79-79 km/s, demonstrate a 2σ agreement with the CMB dipole when considering the full 3D vector distribution and a 3-to-6σ tension with previous number count studies. This result supports the cosmological principle, emphasizing the consistency of our motion with the CMB across vast cosmic distances. On the other hand, the BOSS data revealed potential unmodeled systematics; the estimator could not be minimized using the LOWZ set (0.2 < z < 0.4), and the CMASS set (0.4 < z < 0.6) presented results that pointed towards the southern hemisphere, conflicting with the CMB dipole. Addressing the disparities with earlier number count analyses and understanding possible systematics in spectroscopic measurements will be essential to further validate the cosmological principle.

Bayesian estimation for mean vector of multivariate normal distribution on the linear and nonlinear exponential balanced loss based on wavelet decomposition

This paper addresses the problem of Bayesian wavelet estimating the mean vector of multivariate normal distribution under a multivariate normal prior distribution based on linear and nonlinear exponential balanced loss functions. The covariance matrix of multivariate normal distribution is considered known. Bayes estimators of mean vector parameter of multivariate normal distribution are achieved. Then two soft shrinkage wavelet threshold estimators based on Stein’s unbiased risk estimate (SURE) and Bayes estimators are provided. Finally, the performance of the soft shrinkage wavelet estimators was checked through simulation study and Electrical Grid Stability Simulated data set. Simulation and real data results showed the better performance of SURE thresholds based on linear and nonlinear exponential balanced loss functions compared to other classical wavelet methods. Also, they showed better performance for SURE threshold based on nonlinear exponential balanced loss function in multivariate normal distribution with small dimensions.

Multi-granularity attribute similarity model for user alignment across social platforms under pre-aligned data sparsity

Cross-platform User Alignment (UA) aims to identify accounts belonging to the same individual across multiple social network platforms. This study seeks to enhance the performance of UA tasks while reducing the required sample data. Previous research has focused excessively on model design, lacking optimization throughout the entire process, making it challenging to achieve performance without heavy reliance on labeled data. This paper proposes a semi-supervised Multi-Granularity Attribute Similarity Model (MGASM). First, MGASM optimizes the embedding process through multi-granularity modeling at the levels of characters, words, articles, structures, and labels, and enhances missing data by leveraging adjacent text attributes. Next, MGASM quantifies the correlation between attributes of the same granularity by constructing Multi-Granularity Attribute Cosine Distance Distribution Vectors (MA-CDDVs). These vectors form the basis for a binary classification similarity model trained to calculate similarity scores for user pairs. Additionally, an attribute reappearance score correction (ARSC) mechanism is introduced to further refine the ranking of candidate users. Extensive experiments on the Weibo-Douban and DBLP17-DBLP19 datasets demonstrate that compared to state-of-the-art methods, The hit-precision of the MGASM series has significantly improved by 68.15% and 27.02%, almost reaching 100% precision. The F1 score has increased by 37.6% and 21.4%.

Modelling bluetongue and African horse sickness vector (Culicoides spp.) distribution in the Western Cape in South Africa using random forest machine learning.

Culicoides biting midges exhibit a global spatial distribution and are the main vectors of several viruses of veterinary importance, including bluetongue (BT) and African horse sickness (AHS). Many environmental and anthropological factors contribute to their ability to live in a variety of habitats, which have the potential to change over the years as the climate changes. Therefore, as new habitats emerge, the risk for new introductions of these diseases of interest to occur increases. The aim of this study was to model distributions for two primary vectors for BT and AHS (Culicoides imicola and Culicoides bolitinos) using random forest (RF) machine learning and explore the relative importance of environmental and anthropological factors in a region of South Africa with frequent AHS and BT outbreaks. Culicoides capture data were collected between 1996 and 2022 across 171 different capture locations in the Western Cape. Predictor variables included climate-related variables (temperature, precipitation, humidity), environment-related variables (normalised difference vegetation index-NDVI, soil moisture) and farm-related variables (livestock densities). Random forest (RF) models were developed to explore the spatial distributions of C. imicola, C. bolitinos and a merged species map, where both competent vectors were combined. The maps were then compared to interpolation maps using the same capture data as well as historical locations of BT and AHS outbreaks. Overall, the RF models performed well with 75.02%, 61.6% and 74.01% variance explained for C. imicola, C. bolitinos and merged species models respectively. Cattle density was the most important predictor for C. imicola and water vapour pressure the most important for C. bolitinos. Compared to interpolation maps, the RF models had higher predictive power throughout most of the year when species were modelled individually; however, when merged, the interpolation maps performed better in all seasons except winter. Finally, midge densities did not show any conclusive correlation with BT or AHS outbreaks. This study yielded novel insight into the spatial abundance and drivers of abundance of competent vectors of BT and AHS. It also provided valuable data to inform mathematical models exploring disease outbreaks so that Culicoides-transmitted diseases in South Africa can be further analysed.

A novel approach to quantitate biodistribution and transduction of adeno-associated virus gene therapy using radiolabeled AAV vectors in mice

An understanding of recombinant adeno-associated viruses (AAVs) biodistribution profiles is an important element of a preclinical development program. Here, we have developed a radiolabeling strategy utilizing the co-delivery of 125I (non-residualizing) and 111In (residualizing) radionuclides conjugated AAVs to provide a detailed distribution quantification at tissue level delineating between the cellular internalized AAV (degraded, 111In-125I) and AAV remaining in the extracellular matrix (intact, 125I). This labeling method has been successfully applied to AAV9 and AAV-PHP.eB as tool molecules without altering the physical properties and biological activities of the AAVs. Upon labeling with either of the radioactive probes, these molecules were systemically injected into C57BL/6 mice. The biodistribution results indicate AAVs, with a fast distribution profile, were mainly located in the extracellular matrix of highly perfused organs such as liver and spleen at early time points, leading to a difference between capsid quantification and vector genome quantification. The results suggest that the 125I-AAV/111In-AAV co-delivery approach offers a robust and efficient analytical strategy to investigate the detailed tissue distribution of AAV vectors, including both vector genome and protein capsids. This novel method has the potential to be applied to capsid optimization, selection, and lead candidate development.

Trypanosoma infection and bloodmeal analysis in post-feeding sand flies across Thailand

Phlebotomine sand flies are recognized as a primary vector of Leishmania and are also suspected vectors of Trypanosoma. The transmission cycle of these parasites relies on the distribution of sand fly vectors, parasites, and reservoir animals. This study aimed to detect Leishmania and Trypanosoma DNA and identify the sources of bloodmeals in post-feeding sand flies captured across Thailand. A total of 42,911 field female sand flies were collected from 11 provinces across Thailand using CDC light traps. Among these, 253 post-feeding sand flies were selected for analysis. The predominant species in this study was Sergentomyia khawi (33.60 %). The DNA was extracted from individual female sand flies. Polymerase chain reaction (PCR), specific to the internal transcribed spacer 1 (ITS1) and the small subunit ribosomal RNA (SSU rRNA) gene regions were used to detect the presence of Leishmania and Trypanosoma DNA, respectively. Additionally, cytochrome c oxidase subunit I (COI) gene region was utilized to identify the sources of host bloodmeals. Leishmania DNA was not detected in any specimens. The analysis of SSU rRNA sequences revealed the presence of Trypanosoma DNA (11.46 %, 29/253) in sand fly samples. Among these samples, T. noyesi (1.58 %, 4/253) was identified in Idiophlebotomus longiforceps and Phlebotomus asperulus, Trypanosoma Anura01+02/Frog2 (1.18 %, 3/253) in Se. khawi, and Trypanosoma Anura04/Frog1 (8.70 %, 22/253) in Se. khawi, Se. hivernus and Grossomyia indica. Bloodmeal analysis utilizing the COI gene revealed a diverse range of vertebrate hosts’ blood, including bird, bat, frog and sun skink. Our findings confirm the presence of Trypanosoma DNA and identify the sources of bloodmeals from vertebrate hosts in various sand fly species, suggesting their potential as possible vectors for Trypanosoma in Thailand. Furthermore, our study is the first to provide molecular evidence using the COI gene to identify frogs as a host blood source for sand flies in Thailand. Further studies focusing on the isolation of live parasites in sand flies to confirm vector potential and examining the role of animal reservoirs will enhance our understanding of the host-parasite relationship and enable more efficient control for disease transmission.

Bovine trypanosomosis, vector distribution and infection rate in three districts of Gamo Zone, southwestern Ethiopia

African animal trypanosomosis is one of the main obstacles to the development of livestock and agricultural output in Ethiopia. It usually results in a severe, frequently fatal sickness, and the infected animals were more weakened as the disease progress and become unfit for work. A cross sectional study design was conducted from December 2021 to April 2022 with the aim of estimating the prevalence of trypanosome infection both in Glossina spp. and cattle, and to assess apparent density of Glossina spp. A total of 298 cattle were selected and examined for trypanosome by using buffy coat technique. The overall prevalence of bovine trypanosomosis was 19.1%; and two species of trypanosomes, T. congolense and T. vivax, were identified in the study area. The prevalence of T. congolense and T. vivax were 15.8% and 2.3%, respectively. The prevalence of trypanosomosis was significantly higher in adult animals (OR = 2.7; p < 0.05) than in younger cattle and poor body condition (OR = 3.18; p < 0.05) than medium body condition animals. The mean PCV value of infected animals was 14.3% (13.3–15.4) significantly lower than the non-infected animals 18.5% (17.8–19.2). Glossina pallidipes is the only tsetse species encountered in all the study areas. In total, 2992 flies were caught of which 90.8% belong to G. pallidipes and 9.2% were other biting flies. The overall apparent density of G. pallidipes was 20.1 F/T/D and other biting flies were 2.0 F/T/D. A total of 307 live Glossina pallidipes were dissected. The overall prevalence of Glossina pallidipes infection rate was 9.1% (95% CI = 5.9–12.4). The prevalence of G. pallidipes infection was significantly higher in Kucha district (OR = 3.2, χ2 = 2.6, p < 0.05) than the other two districts, Daramalo and Arba Minch Zuria. Also it was significantly higher in flies trapped from riverine forest areas (OR = 5.5, χ2 = 2.86, p < 0.05). Therefore, to reduce the impact of trypanosomosis and Glossina, vector control and treating infected cattle with prophylactic or chemotherapeutic drugs and active community participation can play a key role.

Distribution and seasonal fluctuation of visceral leishmaniasis vectors sandflie in Lüliang City of Shanxi Province in 2023

To investigate the distribution and seasonal fluctuations of visceral leishmaniasis vectors sandflies in Lüliang City, Shanxi Province, so as to provide insights into assessment of the visceral leishmaniasis transmission risk and formulation of visceral leishmaniasis control measures. A total of 12 natural villages were sampled from Shilou County, Lishi District, Lanxian County, Linxian County and Wenshui County in Lüliang City, Shanxi Province from June to September, 2023, and sandflies were captured using light traps from 7 breeding habitats, including farmers' houses, sheep pens, cattle pens, chicken coops, pig pens, mule and horse pens, and loess-cave dwellings. Following morphological identification of the sandfly species, the distribution of sandflies and the seasonal fluctuations of the sandfly density were analyzed. In addition, the Leishmania was detected in sandflies using a real-time fluorescence quantitative PCR assay. A total of 2 831 sandflies were captured with 156 light traps in Lüliang City from June to September, 2023, including 2 638 female sandflies (93.18%) and 193 male sandflies (6.82%), and the average density was 16.91 sandflies/(light-night). The seasonal fluctuations of the sandfly density all appeared a unimodal distribution in all survey sites, and the sandfly density peaked in July and then declined rapidly. Among all types of breeding habitats, the greatest sandfly density was found in sheep pens [39.04 sandflies/(light-night)]. In addition, 4.08% (2/49) of the sandfly samples were tested positive for Leishmania nucleic acid as revealed by the real-time fluorescence quantitative PCR assay. Sandflies were widely distributed in Lüliang City, Shanxi Province in 2023, and the peak of the sandfly density was observed in July, which had a visceral leishmaniasis transmission risk. Intensified surveillance of visceral leishmaniasis and sandfly vectors is required and targeted vector control is recommended.

Application of Geophysical Methods in the Identification of Mineralized Structures and Ranking of Areas for Drilling as Exemplified by Alto Guaporé Orogenic Gold Province

Mineral exploration works conducted in the Alto Guaporé Gold Province (AGGP), situated in the southwest region of the Amazon Craton in Brazil, faces the challenges of many gold provinces around the world, i.e., declines in the discoveries of new economic deposits and increases in exploration costs. Ground geophysical methods, combined with structural analyses and geological mapping, are valuable tools that have potential to improve accuracy in selecting exploration targets and in determining drilling locations. AGGP deposits are primarily associated with regional N20°–W50° inverse faulting and sheared geologic contacts between Meso-Neoproterozoic siliciclastic metasedimentary rocks and Mesoproterozoic basement (granite and volcano–sedimentary sequences). Mining currently occurring in the central portion of the province drives exploration works towards the many existing targets at the area. Among them, the ABP target is one of the most promising for being located few kilometers north of the Pau-a-Pique mine. At the ABP target, gold is associated with hydrothermal alteration located in the sheared contacts and in the hinge zone of folded metasedimentary sequence. Hydrothermal phases include Fe-oxides, sulfide (py), muscovite and quartz veins. In this study, we use magnetic and geoelectric (induced polarization) surveys coupled with structural and geological mapping to identify potential footprints within the ABP target. The results from induced polarization (IP) profiles successfully mapped the shape and orientation of the main structures down to approximately 350 m at the ABP target, indicating potential locations for hydrothermal alteration hosting gold. Additionally, 3D magnetic data inversions illustrated the distribution of magnetic susceptibilities and magnetization vectors associated with shear zone structures and isolated magnetic bodies. Magnetic data highlighted fault zones along the contacts between metamorphic rocks and granites, while IP data identified areas with high chargeability, correlating with sulfidation zones mineralized with gold. These findings suggest a metallogenic model where gold deposits are transported through deep structures connected to regional faults, implying significant tectonic and structural control over gold deposition. The results underscore the potential of multiparameter geophysics in identifying and characterizing deposits in both deep and strike, thereby advancing our understanding of mineral occurrences in the region and enhancing the search for new mineralized zones.

Paris 2024 Olympic Games: A risk enhancer for autochthonous arboviral diseases epidemics?

ObjectivesThe anticipated increase in international tourist flows and the first locally acquired dengue cases in the Paris region in October 2023 have raised concerns about potential arbovirus outbreaks during the 2024 Olympics. Unlike previous mass sporting events at risk of arbovirus outbreaks, Paris is a nonendemic arbovirus area, requiring a unique investigation. MethodsTherefore, we analyzed factors conducive to possible arbovirus epidemics in temperate regions: vector distribution in the Paris area, seasonal global arboviral disease patterns, projected visitor demographics, and international flight bookings. Results and conclusionOur results suggest that the expected visitors’ profile for the summer of 2024 should not increase the risk of arbovirus importation into the Paris region compared to a typical year. Conversely, the primary risk of arbovirus outbreaks is likely to come from within France, particularly from the French West Indies, where a notable, albeit declining, dengue outbreak is underway. Vigilant surveillance by French health authorities will ensure that this trend continues.

Influence of environmental, geographic, socio-demographic, and epidemiological factors on presence of malaria at the community level in two continents

The interactions of environmental, geographic, socio-demographic, and epidemiological factors in shaping mosquito-borne disease transmission dynamics are complex and changeable, influencing the abundance and distribution of vectors and the pathogens they transmit. In this study, 27 years of cross-sectional malaria survey data (1990–2017) were used to examine the effects of these factors on Plasmodium falciparum and Plasmodium vivax malaria presence at the community level in Africa and Asia. Monthly long-term, open-source data for each factor were compiled and analyzed using generalized linear models and classification and regression trees. Both temperature and precipitation exhibited unimodal relationships with malaria, with a positive effect up to a point after which a negative effect was observed as temperature and precipitation increased. Overall decline in malaria from 2000 to 2012 was well captured by the models, as was the resurgence after that. The models also indicated higher malaria in regions with lower economic and development indicators. Malaria is driven by a combination of environmental, geographic, socioeconomic, and epidemiological factors, and in this study, we demonstrated two approaches to capturing this complexity of drivers within models. Identifying these key drivers, and describing their associations with malaria, provides key information to inform planning and prevention strategies and interventions to reduce malaria burden.

Tunable Near-Field Radiative Heat Transfer between Graphene-Coated Magneto-Optical Metasurfaces.

The highly structured design of metasurfaces greatly facilitates the manipulation of near-field radiative heat transfer (NFRHT). In this study, we incorporate magneto-optical materials into metasurfaces to theoretically explore the mechanism for controlling NFRHT between anisotropic magneto-optical metasurfaces. Our findings indicate that the interaction between the magnetization-induced modes, arising from interband transitions of graphene, and the surface modes of InSb under a magnetic field leads to a transition in the heat transfer spectrum from a dual band to a triple band. The modification of the distribution and magnitude of transmission wave vectors in surface electromagnetic modes by magnetic fields serves to modulate the radiative heat flux. By combining active control by a magnetic field with passive structural design of metasurfaces, the regulation of heat flux can be increased by more than 8-fold compared with the planar configuration. Additionally, the magnetic field amplifies the anisotropy of the photon energy distribution induced by the symmetry breaking of the metasurface structure. This study is anticipated to provide a pathway for achieving flexible tuning of NFRHT by combining active and passive regulation. It also opens up possibilities for multiband information transmission and for improving the performance of energy conversion devices.

Modeling Medium-Term Debris Cloud of Satellite Breakup via Probabilistic Method

Accurately modeling the evolution of debris clouds from satellite breakups is necessary for assessing the collision risk to space assets. Generally, the evolution of debris clouds can be divided into short-, medium-, and long-term phases. Compared to the short- and long-term phases, the study on the medium-term phase was insufficient. This paper proposes a probabilistic method to model the medium-term evolution of a debris cloud. First, a satellite breakup event can be characterized by a probabilistic density distribution of the initial velocity vectors of all fragments. Then, the distribution in the initial velocity can be transformed to that in three classic orbital elements, i.e., semimajor axis, eccentricity, and inclination. Given that the driving force of medium-term evolution is the J2 perturbation and that J2 has no secular contribution to these three classic orbital elements, the distribution of classic orbital elements remains stationary during the evolution. This feature can be exploited to express the probabilistic density distribution of any given target position in terms of the density distribution of the classic orbital elements by changing variables. Finally, 16 one-variable equations with analytical first derivatives were formulated to find the proper inverse mapping from the given position to the classic orbital elements, and the Jacobian matrix of the inverse mapping was derived. Medium-term debris clouds resulting from two typical breakup velocity distributions were tested using the proposed method. Results show that the proposed method can accurately simulate the evolution of the clouds’ geometrical extent and density flow.

Effective method for photonic jet shaping in reflection mode

We report an effective method to shape a photonic jet (PJ) generated by a dielectric cuboid scatterer on a hollow reflection screen. The study focuses on the shaping of PJ by hollow and cuboid geometries, including side length, depth, and position. The results show that all the geometric parameters can effectively shape the PJ in characteristic parameters of intensity, focal length (FL), and lateral size. The comparison shows that the present shaping method is much superior to the previously reported one based on a change of cuboid height, characterized by three times larger of the varying ranges of the PJ characteristic parameters. The shaping by the side length and depth of hollow and cuboid is explained from viewpoints of ray optics and electromagnetic field theory in terms of hollow-induced phase singularity in Poynting vector distribution. The hollow position mainly shapes the propagation trajectory of PJ. The deviation of the hollow position results in the curvature of the propagation trajectory of PJ, and the curvature is correlated with the asymmetric extent of the scattering system.

EXCEPTIONAL SIMPLE REAL LIE ALGEBRAS AND VIA CONTACTIFICATIONS

Abstract In Cartan’s PhD thesis, there is a formula defining a certain rank 8 vector distribution in dimension 15, whose algebra of authomorphism is the split real form of the simple exceptional complex Lie algebra $\mathfrak {f}_4$ . Cartan’s formula is written in the standard Cartesian coordinates in $\mathbb {R}^{15}$ . In the present paper, we explain how to find analogous formulae for the flat models of any bracket generating distribution $\mathcal D$ whose symbol algebra $\mathfrak {n}({\mathcal D})$ is constant and 2-step graded, $\mathfrak {n}({\mathcal D})=\mathfrak {n}_{-2}\oplus \mathfrak {n}_{-1}$ . The formula is given in terms of a solution to a certain system of linear algebraic equations determined by two representations $(\rho ,\mathfrak {n}_{-1})$ and $(\tau ,\mathfrak {n}_{-2})$ of a Lie algebra $\mathfrak {n}_{00}$ contained in the $0$ th order Tanaka prolongation $\mathfrak {n}_0$ of $\mathfrak {n}({\mathcal D})$ . Numerous examples are provided, with particular emphasis put on the distributions with symmetries being real forms of simple exceptional Lie algebras $\mathfrak {f}_4$ and $\mathfrak {e}_6$ .