Association Scheme Research Articles

Marker-based C-arm self-calibration with unknown calibration pattern.

Accurate tomographic reconstructions require the knowledge of the actual acquisition geometry. Many mobile C-arm CT scanners have poorly reproducible acquisition geometries and thus need acquisition-specific calibration procedures. Most of geometric self-calibration methods based on projection data either need prior information or are limited to the estimation of a low number of geometric calibration parameters. Other self-calibration methods generally use a calibration pattern with known geometry and are hardly implementable in practice for clinicalapplications. We present a three-step marker based self-calibration method which does not require the prior knowledge of the calibration pattern and thus enables the use of calibration patterns with arbitrary markerspositions. The first step of the method aims at detecting the set of markers of the calibration pattern in each projection of the CT scan and is performed using the YOLO (You Only Look Once) Convolutional Neural Network. The projected marker trajectories are then estimated by a sequential projection-wise marker association scheme based on the Linear Assignment Problem which uses Kalman filters to predict the markers 2D positions in the projections. The acquisition geometry is finally estimated from the marker trajectories using the Bundle-adjustmentalgorithm. The calibration method has been tested on realistic simulated images of the ICRP (International Commission on Radiological Protection) phantom, using calibration patterns with 10 and 20 markers. The backprojection error was used to evaluate the self-calibration method and exhibited sub-millimeter errors. Real images of two human knees with 10 and 30 markers calibration patterns were then used to perform a qualitative evaluation of the method, which showed a remarkable artifacts reduction and bone structures visibilityimprovement. The proposed calibration method gave promising results that pave the way to patient-specific geometric self-calibrations inclinics.

A Survey of Coronal Mass Ejections Measured In Situ by Parker Solar Probe during 2018–2022

Abstract We present a statistical investigation of the radial evolution of 28 interplanetary coronal mass ejections (ICMEs), measured in situ by the Parker Solar Probe spacecraft from 2018 October to 2022 August. First, by analyzing the radial distribution of ICME classification based on magnetic hodograms, we find that coherent configurations are more likely to be observed close to the Sun. By contrast, more complex configurations are observed farther out. We also notice that the post-ICME magnetic field is more impacted following an ICME passage at larger heliocentric distances. Second, with a multilinear robust regression, we derive a slower magnetic ejecta (ME) expansion rate within 1 au compared to previous statistical estimates. Then, investigating the magnetic field fluctuations within ICME sheaths, we see that these fluctuations are strongly coupled to the relative magnetic field strength gradient from the upstream solar wind to the ME. Third, we identify ME expansion as an important factor in the formation of sheaths. Finally, we determine the distortion parameter (DiP), which is a measure of magnetic field asymmetry in an ME. We discover lower overall asymmetries within MEs. We reveal that even for expanding MEs, the time duration over which an ME is sampled does not correlate with DiP values, indicating that the aging effect is not the sole contributor to the observed ME asymmetries.

The Terwilliger algebras of the group association schemes of three metacyclic groups

AbstractFor any finite group , the Terwilliger algebra of the group association scheme satisfies the following inclusions: , where is a specific vector space and is the centralizer algebra of the permutation representation of induced by the action of conjugation. The group is said to be triply transitive if . In this paper, we determine the dimensions of and for being , and , and show that and are triply transitive. Additionally, we give a complete characterization of the Wedderburn components of the Terwilliger algebras of , and when they are triply transitive.

Tri-hierarchical incomplete block designs

A tri-hierarchical incomplete block (TriHIB) design is defined as an arrangement of v equi-replicated treatments in three levels of blocking such that each block of the first level contains m1 blocks of second level and that of second level contains m2 blocks of the third level. Every level of a TriHIB design, treated independently, is an incomplete block design (IBD) and ignoring any one level of blocking, results into a bi-hierarchical incomplete block (BiHIB) design. Here, two general methods of construction of TriHIB designs are proposed. In the first method, popular association schemes (viz., triangular, Latin square and rectangular) of partially balanced IBDs have been used for developing three series of designs with equal/unequal block sizes at higher levels of blocking. Second method yields another series of designs, through cyclic development of two initial sequences, with equal block sizes at first two levels and equal/unequal block sizes at the third level of blocking. A list of parameters of TriHIB designs for number of treatments up to 30 is presented, along with efficiency factors. Further, for easy accessibility and wider adaptability of these designs, an R package ‘Tri.Hierarchical.IBDs’ has been developed for the generation of the proposed designs.

A congestion-aware user–cell association scheme to assist with traffic offloading in a three-tier heterogeneous network

In this work, we aim to expand the cell range in congestion areas. To achieve this goal, we integrate UAV network into macro–micro cellular network to enhance coverage. However, the gain of deploying heterogeneous nodes is limit if there are no CRE (cell range expanding)-based method to steer users towards low-power nodes. Therefore, in order to further improve system access capacity, we propose a congestion-aware UA (user–cell association) scheme to offload queued traffic of cellular network into UAV network. To verify the superiority of proposed scheme, we utilize the low-complexity SG (stochastic-geometry) methods. Then in simulation analysis phase, we obtain five primary results: (a). The SG-based methods have lower computation complexity, and the convergence of derived expressions are verified. (b). The SG-based methods do not need the exact users’ location but the users’ density, which have improved the operability and robustness in infrastructure construction of wireless network. (c). The congestion-aware UA scheme can prompt network to adjust association tier flexibly, which is very suitable for traffic unevenly-distributed regions. (d). The optimal offsets of virtual power are estimated as B2 = −4 dB for small-cell and B3 = 3 dB for drone-cell, the resulting improvement in communication capacity is 8%. (e). We suggest the deployment density of UAV sites will no need to exceed λ3 = 41 (pks/km2).

Strongly Regular Graphs from Pseudocyclic Association Schemes

Strongly Regular Graphs from Pseudocyclic Association Schemes

Quantitative analysis method for absorption mechanism and energy consumption of CO2 capture by amino acid ionic liquids

Amino acid ionic liquids (AAILs) are attractive candidates for CO2 capture due to their high solubility for CO2. Quantitatively analyzing the interaction of amino groups in AAILs with CO2 and evaluating the energy consumption of CO2 capture is critical to the molecular design of ideal AAILs. In this work, a thermodynamic model based on the cubic plus association equation of state was proposed to calculate the contribution from the chemical reactions between various stoichiometric ratios of CO2 and AAIL (Nm:n,m:n is stoichiometric ratio) on CO2 solubility. The results show that the larger contribution to the CO2 solubility in [Glu], [Tyr] and [Gln]-IL with strong polar groups is derived from association scheme N1:2, while the N1:1 association interaction is the dominant contribution of [Gly], [Ala], [Val] and [Pro]-IL with hydrogen atom or short alkyl side chains, and [VBIm]-IL with multiple amino groups. The N2:1 association interaction is primary between CO2 and [Cho][His] or [Cho][Arg]. Besides, the contributions of these association effects are greater than that of dispersion and repulsion to CO2 solubility. Then, the solvent cyclic capacity and regeneration energy of AAILs in the pressure swing and temperature swing CO2 capture system were estimated. More amino groups result in higher regeneration energy consumption and do not necessarily increase solvent cyclic capacity. Among the studied AAILs, [Cho][Gly] which exhibits high cyclic capacity and low energy consumption has great potential in CO2 capture solvent.

Water content in CO2–CH4 mixtures: New saturation setup and measurements using a quartz-crystal microbalance.

This study presents experimental data on water content in CO2, methane, and their mixtures. A new saturation process was developed using a PVT cell connected to a variable-volume cylinder filled with deionized water. Dry gas with a known composition was injected into the cylinder, and the temperature and pressure conditions were adjusted accordingly. The water content of the saturated gas was then analyzed using a quartz-crystal microbalance (QCM). Various mixtures with different CO2 and methane mole ratios were investigated at different pressures for a given temperature. The PC-SAFT and CPA equations of state were applied to correlate the moisture data. The association scheme employed included 2B, 3B, and 4C types, considering the cross-association between water and CO2. The results for pure methane showed that the water content increased as the pressure decreased across all pressure ranges. However, for pure CO2 above 70 bar, the water content increased due to the condensation behavior of CO2. The same trend was observed for mixtures, where the water content increased with increasing pressure for CO2 mole fractions above 0.74. For all the systems studied, the PC-SAFT and CPA equations of state successfully correlated the water content data using a single constant binary interaction parameter and considering the cross-association between water and CO2.

A Triboelectric Nanogenerator Based on Pendulum‐Rotation Transmission Mechanism for Harvesting Continuous Low‐Frequency Mechanical Energy

AbstractHarvesting the omnipresent mechanical energy emerges as an essential solution in combating environmental pollution and alleviating energy deficits. However, the ultra‐low frequencies and variable amplitudes of most ambient mechanical energy pose significant challenges to effective energy harvesting. To address this issue, this paper reports an innovative triboelectric nanogenerator based on pendulum‐rotation transmission mechanism (PR‐TENG) designed for efficacious harvesting of continuous low‐frequency mechanical energy. It comprises two synergistic units: a transmission unit and a power‐generating unit. The transmission unit is capable of converting external low‐frequency mechanical excitations into unidirectional rotation. Through an internal speed‐increasing mechanism, the rotational speed of the rotor can be further elevated, thereby enabling the power‐generating unit to produce a frequency‐multiplied output and markedly improving the energy transduction efficiency. The mechanism of triboelectrification employed by the power‐generating unit further reduces the total weight of the device, thus advancing its portability. In addition, the coherent coaxial configuration of the device's components significantly enhances compactness and optimizes spatial efficiency. As a practical power source, the PR‐TENG is shown to be capable of directly powering LEDs. Owing to its distinctive operational mechanism and structural innovation, the PR‐TENG is a promising method to efficiently harvest low‐frequency mechanical energy from the ambient environment.

Partially balanced nested block designs based on 2-associate-class association schemes for test-control comparisons

In this article, nested partially balanced treatment incomplete block (NPBTIB) designs are introduced for making test treatments-control treatment comparisons. Several methods of constructing such designs are presented. These methods of constructions utilize group divisible treatment (GDTD) designs, nested balanced incomplete block (NBIB) designs, and nested partially balanced incomplete block (NPBIB) designs. A catalogue of efficient NPBTIB designs with 2-associate classes for the number of treatments v ≤ 16 , replications of test treatments r ≤ 15 , and replications of control treatment r 0 ≤ 30 is also included.

Mobile association scheme based on auction algorithm in heterogeneous wireless networks

With the rapid development of mobile communications, the dense deployment of small base stations (SBSs) in heterogeneous wireless networks (HW-Nets) has met the explosive growth in demand from terminals. However, due to the irregular deployment of SBSs, users frequently handover base stations in pursuit of high-quality services, which inevitably leads to load imbalance among SBSs. To alleviate load imbalance in HW-Nets and improve the efficiency of seamless handover, this paper proposes a distributed auction algorithm scheme based on dual active protocol stack (DAPS), which transforms the wireless access selection of terminals into the terminal-base station association process during movement to globally optimize network resource utilization. At the same time, this paper constructs a terminal-base station association graph and uses auction algorithms to solve the maximum weighted matching of the graph. The DAPS-based scheme can effectively avoid the problem of excessively long outage time caused by handovering outages. Simulation results show that compared with general distributed algorithms, the distributed auction algorithm based on DAPS can effectively balance the load of base stations and reduce the mobile outage latency by 59% .

Wreath Products and Projective System of non-Schurian Association Schemes

A wreath product is a method to construct an association scheme from two association schemes. We determine the automorphism group of a wreath product. We show a known result that a wreath product is Schurian if and only if both components are Schurian, which yields large families of non-Schurian association schemes and non-Schurian $S$-rings. We also study iterated wreath products. Kernel schemes by Martin and Stinson are shown to be iterated wreath products of class-one association schemes. The iterated wreath products give examples of projective systems of non-Schurian association schemes, with an explicit description of primitive idempotents.

On the diameter and zero forcing number of some graph classes in the Johnson, Grassmann and Hamming association scheme

We determine the diameter of generalized Grassmann graphs and the zero forcing number of some generalized Johnson graphs, generalized Grassmann graphs and the Hamming graphs. Our work extends several previously known results.

Condensation and evaporation of boson stars

Axion-like particles, including the QCD axion, are well-motivated dark matter candidates. Numerical simulations have revealed coherent soliton configurations, also known as boson stars, in the centers of axion halos. We study evolution of axion solitons immersed into a gas of axion waves with Maxwellian velocity distribution. Combining analytical approach with controlled numerical simulations we find that heavy solitons grow by condensation of axions from the gas, while light solitons evaporate. We deduce the parametric dependence of the soliton growth/evaporation rate and show that it is proportional to the rate of the kinetic relaxation in the gas. The proportionality coefficient is controlled by the product of the soliton radius and the typical gas momentum or, equivalently, the ratio of the gas and soliton virial temperatures. We discuss the asymptotics of the rate when this parameter is large or small.

Existence of schematic arrays under a novel criterion

. As an important combinatorial structure, association scheme plays an important role in many fields, such as coding theory, graph theory, and combinatorial design. An array is called a schematic if its runs form an association scheme with respect to a certain classification criterion. However, at present, the existing research results about the schematic array are only based on the distance classification criterion, which dramatically limits the existing results on schematic arrays. This article presents a novel matching classification criterion, called MC-criterion, which, together with the existing distance classification, forms a general framework for classification. An array is called G-schematic if its runs form an association scheme with respect to MC-criterion. Subsequently, this article proves that the existence of two types of G-schematic arrays.

Graph Crypto‐Stego System for Securing Graph Data Using Association Schemes

Cryptography has recently become a critical area to research and advance in order to transmit information safely and securely among various entities, especially when the transmitted data is classified as crucial or important. This is due to the increase in the use of the Internet and other novel communication technology. Many businesses now outsource sensitive data to a third party because of the rise of cloud computing and storage. Currently, the key problem is to encrypt the data such that it may be stored on an unreliable server without sacrificing the ability to use it effectively. In this paper, we propose a graph encryption scheme by using cryptography and steganography. Data is encrypted using association schemes over finite abelian groups and then hiding the encrypted data behind randomly chosen cover image. We implemented and evaluated the efficiency of our constructions experimentally. We provide experimental results, statistical analysis, error analysis, and key analysis that demonstrates the appropriateness and efficiency of the proposed technique.

Optimal topology control for grounding protection sensor networks in shipboard electrical systems.

Intelligent monitoring of environmental information in ships is an important prerequisite for reducing and avoiding accidents and is of great importance for safety at sea. The use of a ship environmental monitoring system based on wireless sensor networks has the unique advantages of low cost, stability, and reliability, allowing real-time monitoring of many environmental factors in ships. This article proposes an optimal topology control to maximize collected data satisfaction and reduce energy consumption and transmission latency. First, the cluster head selection method is obtained by initializing the wireless sensor network with a fuzzy clustering algorithm, then the amount of collection data is obtained by a sub-gradient descent algorithm, and a sensor association scheme based on ant colony optimization is proposed to solve the knapsack problem. Finally, simulation results show that the proposed algorithm in this article can effectively reduce the energy consumption and transmission delay of the wireless sensor network while ensuring the monitoring of the grounding protection in the electrical system of the offshore ship.

A census of small Schurian association schemes

Using the classification of transitive groups of degree n, for [Formula: see text], we classify the Schurian association schemes of order n, and as a consequence, the transitive groups of degree n that are 2-closed. In addition, we compute the character table of each association scheme and provide a census of important properties. Finally, we compute the 2-closure of each transitive group of degree n, for [Formula: see text]. The results of this classification are made available as a supplementary database.

New eigenvalue bound for the fractional chromatic number

AbstractGiven a graph , we let denote the sum of the squares of the positive eigenvalues of the adjacency matrix of , and we similarly define . We prove that and thus strengthen a result of Ando and Lin, who showed the same lower bound for the chromatic number . We in fact show a stronger result wherein we give a bound using the eigenvalues of and whenever has a homomorphism to an edge‐transitive graph . Our proof utilizes ideas motivated by association schemes.

Self-orthogonal codes over a non-unital ring from two class association schemes

There is a non-unital ring [Formula: see text] of order 4 defined by generators and relations as [Formula: see text] In this paper, we present special constructions of linear codes over [Formula: see text] from the adjacency matrices of two class association schemes. These consist of either Strongly Regular Graphs (SRGs) or Doubly Regular Tournaments (DRTs). We investigate the conditions under which these codes are self-orthogonal, quasi self-dual, or Type IV. As a byproduct of this study, some diophantine relations on the weight of sum of vectors with coefficients in [Formula: see text] are derived. Some examples of codes with minimum distance better than that of Type IV codes over unital rings of the same order in modest lengths are given.