Incidence Matrix Research Articles

Invariants for incidence matrix of a tree

Invariants for incidence matrix of a tree

Dynamic Analysis of Metamorphic Mechanisms with Impact Effects During Configuration Transformation

Metamorphic mechanisms have attracted considerable attention owing to their capability to switch their topology to adapt to different operational tasks. One feature of topological change is the re-contact of different bodies, which inevitably causes collisions affecting operation accuracy and service life. Consequently, in this study, a collision incidence matrix was introduced to describe the topology of a system involved in collisions, and a method for reducing the closed-loop system to an open-loop system was proposed. The complex movement of the metamorphic mechanism in a changing topology was classified into two different running stages of the source metamorphic mechanism. Based on the relative coordinate method, dynamic modeling of the source metamorphic mechanism considering the impact effects was conducted. Combining the classical collision theory and Newton–Euler equation, the generated impact impulse and the motion after collision were determined. Subsequently, a dynamic analytical method for the full configuration of metamorphic mechanisms was proposed to reflect the changes in the topological structure in the dynamic model. Finally, two typical metamorphic mechanisms used in packaging and spinning were considered as examples to verify the correctness and effectiveness of the proposed method, and their impact characteristics during configuration transformation were analyzed. The proposed analytical method of internal impact for a variable topology process provides effective theoretical guidance for the stability analysis of configuration transformation and structural design aimed at minimizing impacts.

Application of Diverse Silicon Sources to Soil for Reducing Wheat Blast Disease

Despite the economic potential of wheat for food security, blast disease is one of the major constraints to wheat production in warm and humid areas. Silicon (Si) increases crop yields and resistance to both biotic and abiotic stresses. The effect of various Si sources, including Na2SiO3, MgSiO3, CaSiO3, and rice hull ash (RHA), on suppressing wheat blast (WB) incidence was studied at Bangladesh Institute of Nuclear Agriculture field from November 2019 to March 2020 using a complete randomized design (CRD) with three replications. Total 42 plastic pots were filled with the recommended doses of fertilizers and Si. On 17 days after inoculation (DAI), the lowest WB incidence (83.16%) and severity matrix (80.20%) were found with the treatment of CaSiO3 @ 100 kg ha-1. At 15 DAI, the same treatment reduced the WB incidence and severity matrix by 21.10% and 41.73%, respectively. Most yield indicators were significantly improved by the Si fertilizers, except for grain spike-1 quantity, weight, and thousand grain weight (g). However, pots that were fertilized with Si distinguished out from both the control and absolute control groups. While CaSiO3 at 75 kg ha-1, RHA at 6.0 t ha-1, and MgSiO3 at 100 kg ha-1 produced respectable yields, the maximum was achieved by CaSiO3 at 100 kg ha-1. There was a significant positive relationship between the leaf concentrations of K and Si, with the highest concentration found in plants treated with CaSiO3. A large number of yield metrics showed moderate to strong positive associations with leaf K and Si concentrations, whereas the disease severity matrix revealed the maximum significant negative correlation with these elements. The best outcomes were obtained by applying Si as CaSiO3 @100 kg ha-1, which has potential as an environmentally acceptable source for controlling WB disease and increasing wheat yields. J Bangladesh Agril Univ 22(3): 295–309, 2024

Exploring high-order correlation for hyperspectral image denoising with hypergraph convolutional network

High-order correlation is an important property of hyperspectral images (HSIs) and has been widely investigated in model-based HSI denoising. However, the existing deep learning-based HSI denoising approaches have not fully utilized the high-order correlation. Hypergraph convolutional networks have shown great potential in capturing the high-order correlation. Therefore, in this paper, we propose a novel HSI denoising method by employing hypergraph convolution to characterize the high-order correlation at the patch level. Specifically, our framework is a symmetrically skip-connected 3D encoder–decoder architecture, which enhances the extraction and utilization of local features. Furthermore, to integrate competently the hypergraph convolutional modules into the 3D framework, we devise a dimensional transformation module that facilitates the fusion of 3D convolution and hypergraph convolution. Notably, in the hypergraph convolution operation, we use a data-driven technique to acquire the incidence matrix of a hypergraph, efficiently constructing the HSI into a high-order structure. Our proposed method excels in HSI denoising performance compared to state-of-the-art approaches, evidenced by extensive experiments on synthetic and real-world noisy HSIs.

Risk Assessment of Selected CCS Wells through Feature, Event, and Process Method and Comparison of the Barrier Effect.

To reduce the CO2 release in the atmosphere, the carbon capture and sequestration (CCS) technique presents a solution in which the CO2 is captured from the emitting source and injected into a suitable geological formation in the subsurface. For the CCS project to be successful, CO2 must be trapped underground for hundreds of years. In that respect, good integrity plays an important role as it ensures that the injected CO2 remains sequestrated in the subsurface. Hence, this study presents a risk assessment technique with the help of which critical elements that can compromise the integrity of the CCS well can be identified. The approach taken for the risk assessment is based on the feature, event, and process (FEP). However, this method gives a qualitative analysis, and to convert it to a semiquantitative one, FEP is integrated with an interaction matrix, incident potential matrix (IPM), and cause-effect plot diagram. In this paper, risk assessment was conducted on two fictitious wells with different well configurations. It was found that cement and casing were the most vulnerable components, while formation water and subsidence were the most problematic elements in the given well system. It was also concluded that the number of plugs and their location in the well could increase or decrease the intensity of the risk levels in the CCS wells.

An estimation method for bias error of measurements by utilizing process data, an incidence matrix and a reference instrument for data validation and reconciliation: Part 2 Extension to the energy balance relation

Abstract Ensuring data reliability is becoming increasingly important for further applications of AI, IoT, and digital twins. One promising technology for ensuring data reliability is data validation and reconciliation (DVR), which minimizes the uncertainty of measurements based on statistics. DVR has been widely used for the operation and maintenance of nuclear power plants in Europe and the United States in recent years. The most important input for DVR analysis is measurement uncertainty. The catalog value provided by sensor manufacturers includes the measurement uncertainty, but in reality, the actual measurement uncertainty is often smaller. Previous studies have proposed several methods for evaluating the actual measurement uncertainty based on process data, which have been confirmed to be effective for evaluating random errors. It is important to note that bias errors also contribute significantly to the measurement uncertainty. In our previous paper, we proposed a method for estimating bias error using process data, an incidence matrix, and a reference instrument. The proposed method was limited to a mass balance relation, i.e., flow rate measurements. In this paper, we extend the method to include an energy balance relation by considering energy conservation in addition to mass conservation. This extension enables the evaluation of measurement uncertainty for flow rate and temperature. The proposed method was validated with two benchmark problems. It was found to be applicable to various flow conditions, including physically fluctuating flow, such as that observed in the feedwater flow in nuclear power plants.

The determinant of {±1}-matrices and oriented hypergraphs

The determinants of {±1}-matrices are calculated via the oriented hypergraphic Laplacian and summing over incidence generalizations of vertex cycle-covers. These cycle-covers are signed and partitioned into families based on their hyperedge containment. Every non-edge-monic family is shown to contribute a net value of 0 to the Laplacian, while each edge-monic family is shown to sum to the absolute value of the determinant of the original incidence matrix. Simple symmetries are identified as well as their relationship to Hadamard's maximum determinant problem. Finally, the entries of the incidence matrix are reclaimed using only the signs of an adjacency-minimal set of cycle-covers from an edge-monic family.

Effects of Ar ion bombardment on the structure and properties of β-quartz

β-quartz is an important component that affects the physical and chemical properties of glass-ceramics. The material removal process of ion beam machining is complicated as one of the ultra-precision machining forms. Therefore, it is important to understand the removal mechanism of ion beam machining materials. The methods of molecular dynamics (MD) and first-principles were adopted to investigate the microscopic mechanism of ion beam bombardment of the β-quartz structure. The damage evolution of structures and the evolution of material properties caused by defects respectively from the atomic and electronic levels. Through MD analysis, we find that the random collision between incident ions and matrix atoms can lead to the formation of sputtered atoms. The incidence of ions will increase the disorder degree of the matrix, and the influence on the disorder degree at different depths of the matrix is different. The degree of disorder increases obviously in the range of 50–70 Å from the surface of the matrix. It has a significant impact on the surface topology of the matrix, the number of defects, surface roughness, and matrix density. The results of first-principle calculation show that the refraction, absorption and other characteristics of the system are significantly different with different doping forms, and the energy loss is most affected by substituted doping. And the substituted doping defects have the most significant effects on the structural energy loss. Among, the Ar-substituted O doping structure leads to higher energy loss, and the peak energy loss intensity reaches 5.146. In contrast, the Ar-substituted Si doping structure causes the least energy loss, the intensity is 2.543. This study provides a theoretical basis for the selection of parameters and the realization of ultra-smooth surface in actual ion beam machining.

On Spectral Portraits of Incidence Matrices of Nearest Neighbor Graphs

On Spectral Portraits of Incidence Matrices of Nearest Neighbor Graphs

Symmetric 2‐(36,15,6) $(36,15,6)$ designs with an automorphism of order two

AbstractBouyukliev, Fack and Winne classified all 2‐ designs that admit an automorphism of odd prime order, and gave a partial classification of such designs that admit an automorphism of order 2. In this paper, we give the classification of all symmetric 2‐ designs that admit an automorphism of order two. It is shown that there are exactly nonisomorphic such designs, of which are self‐dual designs. The ternary linear codes spanned by the incidence matrices of these designs are computed. Among these codes, there are near‐extremal self‐dual codes with previously unknown weight distributions.

Mutual incidence matrix of two balanced incomplete block designs

AbstractWe propose to consider a mutual incidence matrix of two balanced incomplete block designs built on the same finite set. In the simplest case, this matrix reduces to the standard incidence matrix of one block design. We find all eigenvalues of the matrices and and their eigenspaces.

COUNTING PATHS OF GRAPHS VIA INCIDENCE MATRICES

Operating only by means of the incidence matrix of a connected graph G, a new algebraic combinatorial method for determining the paths of length (q−1) of G together with the generators of the corresponding generalized graph ideal Iq(G) is discussed and developed. The stated formulae are obtained and shown even by changing techniques appropriately when the difficulties of calculation increased.

Construction of Qــ Ary(n,Μ,d )ــ Codes in PG (2,9)

This study's main objective is to offer the connection between the projective plane of order nine & the field of coding theory. An incidence matrix has been developed using the parameters n (code length), d (code min. distance), and e (code error correcting). The greatest value of size code M across a limited field of the ninth order has also been determined. There are a few theorems and examples provided.

The use of ecological niche models improves biogeographic regionalization of the Balsas Depression, Mexico

AbstractAimBiogeographic regionalization classifies zones in terms of their biotas and contributes to understanding the ecological and historical factors that affect the distribution of species. We use Ecological Niche Modeling (ENM) to complement missing information on species distribution and thus improve the accuracy of biogeographic boundaries.LocationBalsas Depression Floristic Province, Mexico.MethodsBased on parameters documented in herbarium collections and environmental variables, ENM was carried out to determine the most suitable environmental conditions for a species to thrive (i.e., the species' ecological niche). The ENM and spatial analysis were used to obtain the biogeographic regionalization of the seasonally dry tropical forest (SDTF) in the Balsas Depression (BD), Mexico, through spatial analysis. Using the Maxent algorithm, we constructed ecological niche models (ENMs) of 134 flowering plant species distributed preferentially in the SDTF (characteristic species), most of them endemic to the BD. Subsequently, we obtained an incidence matrix based on the information from the 134 ENMs, which was used to analyze the turnover of species in Biodiverse software. The turnover matrix was used for Non‐metric Multidimensional Scaling (NMDS) ordination and clustering analyses. Finally, the environmental predictors most related to species turnover were identified using the relative environmental turnover method.ResultsThe clustering analysis divided the SDTF in the BD into four floristic districts — two located in its western part and two in the eastern region. The NMDS differentiated, in the first component, two districts in the western region and one in the eastern. Seven environmental variables contributed significantly to explaining the turnover of species in these districts; the most significant were the elevation, pH, and precipitation of the coldest quarter.Main ConclusionsThe use of ENM for the regionalization of areas with high species richness allows for a more detailed classification of subregions and the distribution patterns of the species that define their limits. This provides a more solid theoretical basis for the investigation of biogeographic patterns.

Joint Optimization of Measurement Point Intelligent Selection and End-to-End Network Traffic Calculation in Datacenters

The effective design and management of data centers needs to follow the end-to-end traffic characteristics of data center networks (DCNs). However, directly measuring the end-to-end traffic of the network requires huge software and hardware costs. Since the particularity of the structure of DCNs, the flow estimation method used in the traditional computer network cannot be applied to existing DCNs. In this paper, we study the end-to-end traffic calculation of cloud computing DCNs. We propose <bold xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">LLS-TC</b> , which is an intelligent end-to-end traffic inference algorithm based on network tomography. Only using SNMP (simple network management protocol) data generally supported by switches, end-to-end traffic information can be calculated quickly and accurately. <bold xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">LLS-TC</b> first devices a network traffic measurement point intelligent selection scheme based on node weighting. It first assigns weight to nodes through node criticality, and then uses node weighted incidence matrix approximation algorithm to calculate initial solution. <bold xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">LLS-TC</b> then designs a network tomography method suitable for cloud computing network traffic calculation. It uses the time correlation of data center traffic to model the algorithm problem into a linear state space model, and finally calculates the traffic carried by each path through the improved Kalman filtering algorithm. Our evaluation and analysis demonstrate that <bold xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">LLS-TC</b> can effectively use the extracted coarse-grained traffic characteristics, and greatly improve the accuracy of the calculation on the premise of ensuring the computational efficiency.

Real-time prediction of transit origin–destination flows during underground incidents

Efficient transportation planning and management are critical for ensuring the smooth operation of rail transit systems, particularly in urban areas with high passenger demand. Real-time prediction of transit flow during underground incidents is vital for ensuring passenger safety, minimizing disruptions, and optimizing resource allocation. This study presents a comprehensive framework to address the considerable challenges associated with short-term origin–destination (OD) flow prediction, particularly during incidents. We propose integrating convolutional long short-term memory cells with self-attention cells to learn the long-range spatiotemporal information of historical OD flows. To overcome the absence of a real-time OD matrix, we introduce an improved graph convolution operation, considering the local connection of ridership, to capture vital spatiotemporal interaction patterns. Quantitative and qualitative analyses were conducted to evaluate the performance of the framework, providing insights into the role of each module. Experimental results suggest that incorporating incident matrix theory enhances the accuracy of capturing declining OD flows during incidents by up to approximately 25%. Furthermore, integrating external features like weather and time comprehensively assesses the impact of erratic change factors, especially during off-peak periods. Additionally, introducing more than one cycle of historical OD flow as an input may introduce noise, and increased attention is needed for OD flows with average daily flows exceeding 30 passengers. Designed with a high degree of modularity and adaptability, the proposed framework serves as a valid tool for transportation professionals and researchers to address evolving challenges in the management and operation of urban transportation systems.

Signed graphs and inverses of their incidence matrices

The Laplacian matrix L of a signed graph G may or may not be invertible. We present a combinatorial formula of the Moore-Penrose inverse of L. This is achieved by finding a combinatorial formula for the Moore-Penrose inverse of an incidence matrix of G. This work generalizes related known results on incidence and Laplacian matrices of an unsigned graph. Several examples are provided to show the usefulness of these combinatorial formulas.

Multiple aspects of tree beta diversity in coastal ecosystems in Brazil

AbstractAimPatterns of beta diversity reflect the formation dynamics of ecological communities. Here, we integrated geographic, phylogenetic, and phenotypic information of coastal woody vegetation to investigate (1) whether the observed dissimilarity between assemblages differs from that expected by chance, examining the roles of spatial and deterministic processes; (2) the relative contribution of beta‐diversity components (turnover and nestedness) for taxonomic, phylogenetic, and functional beta diversity; and (3) what environmental factors drive the differences in composition between assemblages for all these dimensions.LocationBrazil.TaxonAngiosperm trees.MethodsWe built dissimilarity matrices and partitioned the taxonomic, phylogenetic, and functional beta diversity from an incidence matrix, a phylogeny including the region's plants, and a matrix expressing functional distances. Using linear regressions, we tested the effects of different environmental predictors representative of the effects of water availability, thermal energy, habitat heterogeneity, edaphic constraints, climatic stability, and human influence on beta‐diversity patterns.ResultsTaxonomic, phylogenetic, and functional dissimilarities exhibited a typical pattern of greater dissimilarity with distance (i.e., as expected by chance). However, these patterns showed different contributions of beta‐diversity components, predominating turnover in taxonomic and phylogenetic dissimilarity, and nestedness in functional dissimilarity. Water availability had a slight effect on patterns of taxonomic and phylogenetic dissimilarities.Main conclusionsThe Brazilian coastal woody vegetation appears to have emerged through a dynamic of colonisation of evolutionarily distinct but functionally similar lineages that originated from adjacent phytogeographic domains, proportional to their diversity. This is consistent with a combination of both neutral and non‐neutral processes. Our findings underscore the complementary roles of different dimensions of beta diversity in explaining the dynamics of these vegetation communities.

On Lagrangian Grassmannian Variety and Plücker Matrices

The Plücker matrix BL(n,E) of the Lagrangian Grassmannian L(n,E), is determined by the linear envelope ⟨L(n,E)⟩ of the Lagrangian Grassmannian. The linear envelope ⟨L(n,E)⟩ is the intersection of linear relations of Plücker of Lagrangian Grassmannian, defined here. The Plücker matrix BL(n,E) is a direct sum of the incidence matrix of the configuration of subsets. These matrices determine the isotropy index rn and rn-atlas which are invariants associated with the symplectic vector space E.

Taxonomic, phylogenetic, and functional nestedness of mammal assemblages in the Zhoushan Archipelago, China

Abstract Nestedness is an important part of the theoretical framework of island biogeography and community ecology. However, most previous studies focused on taxonomic dimension and overlooked functional and phylogenetic nestedness. Here, we simultaneously investigated taxonomic, functional, and phylogenetic nestedness of terrestrial mammals on 39 land-bridge islands in the Zhoushan Archipelago, China. As mammals’ response to the environment may depend on their body size, we performed analyses for three mammal assemblages separately: overall species, large and medium-sized species, and small species. The taxonomic nestedness was quantified by organizing the species incidence matrix, while the functional and phylogenetic nestedness were estimated by combining the similarity of their ecological traits and phylogeny. Island characteristics (island area, three isolation indices, land use intensity, and habitat diversity) and species traits (body size, litter size, habitat specificity, geographic range size, and minimum area requirement) were used as predictors of nestedness. Overall and small species were significantly nested in 3 facets of nestedness, and results supported the selective extinction, selective colonization, and habitat nestedness hypotheses. Large and medium-sized species were functionally and phylogenetically nested when matrices were ordered by increasing distance to mainland, supporting the selective colonization hypothesis. Overall, differences in nestedness and its underlying mechanisms were detected not only in 3 facets of nestedness but also in the 3 mammal assemblages. Therefore, frameworks that incorporate taxonomic, phylogenetic, and functional nestedness can contribute to a more comprehensive understanding of nestedness processes. Additionally, it also improves our ability to understand the divergent responses of mammal assemblages to the insular environment.