Association Scheme Research Articles

Computing Zeta Functions of Table Algebra Orders Using Local Zeta Integrals

We investigate Solomon’s zeta function for orders in the special case of orders generated by the standard basis of an integral table algebra, a special case of which is the integral adjacency algebra of an association scheme. As Solomon’s elementary method for computing this zeta function runs into computational difficulties for ranks 3 or more, a more efficient method is desired. We give several examples to illustrate how the local zeta integral approach proposed by Bushnell and Reiner can be applied to compute explicit zeta functions for these orders.

Online multi-target intelligent tracking using a deep long-short term memory network

Multi-target tracking is facing the difficulties of modeling uncertain motion and observation noise. Traditional tracking algorithms are limited by specific models and priors that may mismatch a real-world scenario. In this paper, considering the model-free purpose, we present an online Multi-Target Intelligent Tracking (MTIT) algorithm based on a Deep Long-Short Term Memory (DLSTM) network for complex tracking requirements, named the MTIT-DLSTM algorithm. Firstly, to distinguish trajectories and concatenate the tracking task in a time sequence, we define a target tuple set that is the labeled Random Finite Set (RFS). Then, prediction and update blocks based on the DLSTM network are constructed to predict and estimate the state of targets, respectively. Further, the prediction block can learn the movement trend from the historical state sequence, while the update block can capture the noise characteristic from the historical measurement sequence. Finally, a data association scheme based on Hungarian algorithm and the heuristic track management strategy are employed to assign measurements to targets and adapt births and deaths. Experimental results manifest that, compared with the existing tracking algorithms, our proposed MTIT-DLSTM algorithm can improve effectively the accuracy and robustness in estimating the state of targets appearing at random positions, and be applied to linear and nonlinear multi-target tracking scenarios.

Coherent Plasma in a Lattice

We present a fully second-quantized calculation showing the emergence of spontaneous coherent configurations of the electromagnetic field interacting with charged bosons in a regular lattice. The bosons tend to oscillate at their plasma frequency, and in addition are subjected to electrostatic forces which keep them confined close to the lattice sites while causing a frequency shift in the oscillation. Under certain conditions upon these frequencies, we find that a suitably defined set of coherent states (coherent both in the field and matter degrees of freedom) exhibit a negative energy gap with respect to the perturbative ground state. This is true in the RWA approximation and for position-independent fields to both the first and second order in the interaction Hamiltonian. We compare this result with other recent findings from cavity QED, and note that (1) consideration of full 3D wavefunctions and a careful definition of the coherent states are essential for obtaining the energy gap, and (2) although our calculation is made in reference to bosons, it may apply to protons bound in a crystal matrix as well if their density is very low compared to the density of available states.

Synthesis and Interlayer Assembly of a Graphenic Bowl with Peripheral Selenium Annulation

Pentagonal cyclization at the bay positions of armchair-edged graphenic cores can build molecular bowls without the destruction of hexagonal lattices. However, this synthesis remains challenging due to unfavorable strain and the multiple reactions required. Here, we show that a new type of graphenic molecular bowl with a depth of 1.7 Å and a diameter of 1.2 nm is constructed by sextuple Se annulation at the bay positions of armchair-edged hexa-peri-hexabenzocoronene. This graphenic bowl is functionalized with phenylseleno groups that stack into a discrete bilayer dimer in solution. Such a dimer exhibits high stability and survives in the gas phase after laser ablation. Strikingly, the asymmetric one-dimensional supramolecular columns of graphenic bowl with coherent stacking configuration are observed in the solid state, which results in a strong second harmonic generation with prominent polarization dependence. Our findings present a concise synthesis of a giant molecular bowl with a graphenic core and demonstrate the unique supramolecular assembly of extended graphenic bowls.

Anthracycline Cardiotoxicity: From Mechanisms to Prevention Strategies

Introduction: Anthracyclines are among the most powerful antineoplastic drugs ever developed and, even today, they are widely used according to various association schemes in the onco-hematological field. However, cardiotoxicity remains one of the most feared and characteristic side effects, both short and long term, often causing the premature interruption of therapy or irreversible effects after their suspension. In this article, we want to explain the underlying biological mechanisms, the clinical presentation characteristics and the possible strategies to prevent it. Materials and Methods: A computerized research was carried out for the articles to be inserted through use of international databases PUBMED, RESEARCHGATE and GOOGLE SCHOLAR, by typing in keywords such as “anthracyclines cardiotoxicity” and “cardioprotection strategies for anthracycline toxicity” and related articles. Discussion and Conclusions: The toxicity of these drugs on the heart represents the limiting factor both for their indications and for the success of the therapy, sometimes being the cause of premature interruption or impossibility of use in some patients. It depends especially on the cumulative dose used in the single patient and on the pre- existing risk conditions for the development of these ADRs, both in the short and long term. However, there are strategies that can avoid or reduce the damage, both related to the formulation of the compounds and to the co- administration of other drugs.

Load Balanced User Association Scheme in Planned Non-bias Small Cell Deployment

The work presented in this paper focuses on developing a load-balanced user association scheme in a single Radio Access Technology (RAT) Heterogeneous Networks (HetNet). The optimization algorithm maximizes network capacity and optimal user association in a planned small cell deployment framework, considering Quality of Service (QoS) and network load balance. Planned deployment of small cells has many advantages, including controlled interference levels within the HetNet. The proposed Branch and Bound (BAB) based algorithms provide a more realistic interference scenario through the non-use of bias in the small cells. The proposed algorithm achieved higher load balancing than current schemes in literature and high spectral efficiency values.

The search for small association schemes with noncyclotomic eigenvalues

In this article we determine feasible parameter sets for (what could potentially be) commutative association schemes with noncyclotomic eigenvalues that are of smallest possible rank and order. A feasible parameter set for a commutative association scheme corresponds to a standard integral table algebra with integral multiplicities that satisfies all of the parameter restrictions known to hold for association schemes. For each rank and involution type, we generate an algebraic set for which any suitable integral solution corresponds to a standard integral table algebra with integral multiplicities, and then try to find the smallest suitable solution. The main results of this paper show the eigenvalues of association schemes of rank 4 and nonsymmetric association schemes of rank 5 will always be cyclotomic. In the rank 5 cases, the results rely on calculations done by computer for Gröbner bases or for bases of rational vector spaces spanned by polynomials. We give several examples of feasible parameter sets for small symmetric association schemes of rank 5 that have noncyclotomic eigenvalues.

Some subfield codes from MDS codes

<p style='text-indent:20px;'>Subfield codes of linear codes over finite fields have recently received a lot of attention, as some of these codes are optimal and have applications in secrete sharing, authentication codes and association schemes. In this paper, a class of binary subfield codes is constructed from a special family of MDS codes, and their parameters are explicitly determined. The parameters of their dual codes are also studied. Some of the codes presented in this paper are optimal or almost optimal.</p>

WiMA: Towards a Multi-Criterion Association in Software Defined Wi-Fi Networks

Despite the planned installation and operations of the traditional IEEE 802.11 networks, they still experience degraded performance due to the number of inefficiencies. One of the main reasons is the received signal strength indicator (RSSI) association problem, in which the user remains connected to the access point (AP) unless the RSSI becomes too weak. In this paper, we propose a multi-criterion association (WiMA) scheme based on software defined networking (SDN) in Wi-Fi networks. An association solution based on multi-criterion such as AP load, RSSI, and channel occupancy is proposed to satisfy the quality of service (QoS). SDN having an overall view of the network takes the association and reassociation decisions making the handoffs smooth in throughput performance. To implement WiMA extensive simulations runs are carried out on Mininet-NS3-Wi-Fi network simulator. The performance evaluation shows that the WiMA significantly reduces the average number of retransmissions by 5%–30% and enhances the throughput by 20%–50%, hence maintaining user fairness and accommodating more wireless devices and traffic load in the network, when compared to traditional client-driven (CD) approach and state of the art Wi-Balance approach.

Quasi self-dual codes over non-unital rings from three-class association schemes

<abstract><p>Let $ E $ and $ I $ denote the two non-unital rings of order 4 in the notation of (Fine, 93) defined by generators and relations as $ E = \langle a, b \mid 2a = 2b = 0, a^2 = a, b^2 = b, ab = a, ba = b\rangle $ and $ I = \langle a, b \mid 2a = 2b = 0, a^2 = b, ab = 0\rangle $. Recently, Alahmadi et al classified quasi self-dual (QSD) codes over the rings $ E $ and $ I $ for lengths up to 12 and 6, respectively. The codes had minimum distance at most 2 in the case of $ I $, and 4 in the case of $ E $. In this paper, we present two methods for constructing linear codes over these two rings using the adjacency matrices of three-class association schemes. We show that under certain conditions the constructions yield QSD or Type Ⅳ codes. Many codes with minimum distance exceeding 4 are presented. The form of the generator matrices of the codes with these constructions prompted some new results on free codes over $ E $ and $ I $.</p></abstract>

A Matching Game-Based Laboratory Learning System for Resources Management in Remote Laboratories

Recently, increasing demand for remote laboratories is noticed, due to the shifting of the educational systems from face-to-face education to online education through the internet. A Remote-controlled laboratory is based on the use of real instrumentations and components, in which experiments are completely conducted and controlled remotely by the students through the internet. Thus, it provides a hands-on learning experience for students on an online basis. In order to realize this increasing demand for remote laboratories, efficient management of the laboratory resources should be considered. In this work, a novel laboratory learning system is proposed, which provides the flexibility of deployment on any physical infrastructure, integrability with other different physical laboratory resources, and scalability. Moreover, a mathematical model for the laboratory learning system is formulated, to provide the basis for defining the optimization problem. The problem of minimizing the number of blocked time slots per acquiring student, by optimizing the association between the reserving students and the available resources at different time slots is also formulated, which reflects the maximization of resources utilization. Then, a matching game-based framework is proposed to optimally solve the formulated problem. Simulation results show the significance of the proposed matching game-based framework compared to other students to resources association schemes, in minimizing the number of blocked time slots per acquiring student and maximizing the resources utilization efficiency.

Completion Time Minimization for Data Collection in a UAV-enabled IoT Network: A Deep Reinforcement Learning Approach

In this paper, we study the completion time minimization in an unmanned aerial vehicle (UAV)-enabled Internet of Things (IoT) network, where the UAV tries to collect all the data generated by the ground IoT devices for further processing. To simplify the analysis, the continuous time horizon is discretized into several time slots. The duration of each time slot is set to be less than the pre-defined threshold such that the UAV's location can be considered as unchanged during each time slot. In our work, we aim to minimize the completion time of the UAV by optimizing the association scheme of the IoT devices, the location (i.e., the trajectory) and velocity of the UAV at each time slot. However, the formulated problem is challenging to solve by traditional optimization methods considering the unknown number of time slots (which leads to the unknown number of decision variables) and non-convex functions. We thus reformulate it as a Markov decision process (MDP) and propose a deep deterministic policy gradient (DDPG)-based method to efficiently solve it. The DDPG-based algorithm uses deep function approximators instead of finding the action that maximizes the state-action value, and is therefore well suited to solve high-dimensional, continuous control problems. Extensive numerical results are presented to validate the effectiveness of our proposed algorithm.

Thermodynamic modeling of gas solubility in ionic liquids using equations of state

This work aimed at the thermodynamic modeling of gas solubility in ionic liquids (ILs) using the Soave-Redlich-Kwong (SRK), cubic-plus-association (CPA), and perturbed-chain statistical associating fluid theory (PC-SAFT) equations of state. Wherefore, the routines were developed for the parameterization of ILs. Then, the ILs were implemented in the Aspen plus simulator to evaluate the equations of state and explore the phase equilibrium data with the predictive equations and the correlation of the binary interaction parameter. Hence, it was verified the correlation of the density and speed of sound curves presented limitations to correcting the slope of the curves of pure ILs. Nonetheless, the PC-SAFT with the 4C associative scheme demonstrated a better fit for the thermophysical properties. As for the prediction of phase equilibrium for the [EMIM][TfO], the PC-SAFT with the 2B scheme showed a better fit with CO2, while the CPA with the 2B scheme presented the best result for H2S. For [OMIM][NTf2], the PC-SAFT with the 1A scheme showed better results with CO2, and the CPA with the 2B scheme showed the lowest deviation with H2S.

On pseudofrobenius imprimitive association schemes

An (association) scheme is said to be Frobenius if it is the (orbital) scheme of a Frobenius group. A scheme which has the same tensor of intersection numbers as some Frobenius scheme is said to be pseudofrobenius. We establish a necessary and sufficient condition for an imprimitive pseudofrobenius scheme to be Frobenius. We also prove strong necessary conditions for existence of an imprimitive pseudofrobenius scheme which is not Frobenius. As a byproduct, we obtain a sufficient condition for an imprimitive Frobenius group G with abelian kernel to be determined up to isomorphism only by the character table of G. Finally, we prove that the Weisfeiler-Leman dimension of a circulant graph with n vertices and Frobenius automorphism group is equal to 2 unless $$n\in \{p,p^2,p^3,pq,p^2q\}$$ , where p and q are distinct primes.

Association schemes arising from table algebras

Association schemes arising from table algebras

Euclidean designs obtained from spherical embedding of coherent configurations

AbstractCoherent configurations are a generalization of association schemes. Motivated by the recent study of Q‐polynomial coherent configurations, in this paper, we study the spherical embedding of a Q‐polynomial coherent configuration into some eigenspace by a primitive idempotent. We present a necessary and sufficient condition when the embedding becomes a Euclidean ‐design (on two concentric spheres) in terms of the Krein numbers for . In addition, we obtain some Euclidean 2‐ or 3‐designs from spherical embedding of coherent configurations including tight relative 4‐ or 5‐designs in binary Hamming schemes and the union of derived designs of a tight 4‐design in Hamming schemes.

Partial geometric designs arising from association schemes

The basic relations of an association scheme induce block designs in a natural way. There are many (commutative or non-commutative) association schemes in which some basic relations induce partial geometric designs or 2-designs. In this paper we study how the algebraic structures of association schemes determine partial geometric designs. We will first establish a necessary and sufficient condition under which some basic relations of an association scheme induce partial geometric designs. Then by using the representation theory of association schemes, we will show that the parameters of these partial geometric designs have some special properties. We will also use the characters of commutative association schemes to determine which basic relations induce partial geometric designs or 2-designs. Isomorphisms of partial geometric designs will also be discussed.

Developing reliable urban flood hazard mapping from LiDAR data

Digital surface models (DSMs) are crucial in providing accurate urban flood hazard maps. The ubiquitous availability of LiDAR data (where accessible) makes constructing geometrically sound DSMs feasible. However, little attention has been paid to developing approaches for producing geometrically consistent DSMs. Herein is described an application-driven procedure for creating a geometrically robust DSM (DSM1). Two further DSMs were created, one for portraying streets using breaklines as ancillary information (DSM2) and the other through direct interpolation of LiDAR data (DSM3). The geometrical correctness and vertical accuracy of these DSMs were examined qualitatively and quantitatively by plotting longitudinal profiles and cross-sections onto major runoff pathways and determining statistical error. The effect of these DSMs’ geometric consistency on flood hazard maps was also evaluated. For this, hydraulic outputs from DSM1 were used as a benchmark to compare hydraulic outputs from DSM2 and DSM3. This comparison was conducted at two spatial resolutions: i) at the total area flooded using the F statistic; and ii) at the pixel level by employing global indices and category-level indices extracted from a confusion matrix. Our findings revealed that: 1) DSM1 defined the most geometrically coherent configurations for runoff pathways; 2) in urban areas with the most densely packed streets and buildings, DSM2 and particularly DSM3 featured the most unrealistic geometric representations of the urban domain, displaying fake water flow barriers and lower than real runoff pathway cross-sections; and 3) the geometric quality of the DSMs created had a significant impact on flood hazard maps reliability (i.e., the disagreement in flood hazard categories between DSM2 and DSM3 and DSM1 varied from 28% to 82%). These findings can be very valuable in achieving further reductions and better flood risk management.

Vehicle-cluster-based opportunistic relays for data collection in intelligent transportation systems

Intelligent transportation system (ITS) is envisioned to greatly improve traffic and enhance safety on roads. ITS relies on a huge amount of data generated from roadside sensor devices to make decisions. Due to the limited channel resources, the base station (BS) that connects with an ITS server can only collect data from parts of sensor devices at a time. To improve the number of device associations, we regard vehicle clusters as relays to collect data, which can avoid high capital expenditure and operating expenses from dedicated relays. Due to the frequently varying channel interference and the limited communication coverage of a vehicle cluster relay (VCR), it is challenging to guarantee the transmission rates and the fairness of sensor devices, which will affect the decisions of ITS. For this reason, we propose a Movement- and Fairness-Aware Heuristic (MFAH) algorithm to tackle the above challenges. MFAH sequentially conducts two novel channel allocation schemes, i.e., exclusive channel allocation scheme and compatible channel allocation scheme, to fast allocate channels and improve the channel utilization, which increases the number of device associations while guaranteeing the transmission rates. Regarding the fairness of each device’s associations, we propose a device association scheme based on the cumulative number of device associations and the distance from the target VCR to select appropriate sensor devices to upload data. We theoretically analyze the lower bound of the obtained network utility. Extensive simulations show that compared with benchmarks, the proposed MFAH algorithm converges fast and effectively improves the network utility (i.e., increasing the number of device associations while guaranteeing the fairness of device associations).

Leveraging Graph and Deep Learning Uncertainties to Detect Anomalous Maritime Trajectories

Understanding and representing traffic patterns are key to detecting anomalous trajectories in the transportation domain. However, some trajectories can exhibit heterogeneous maneuvering characteristics despite confining to normal patterns. Thus, we propose a novel graph-based trajectory representation and association scheme for extraction and confederation of traffic movement patterns, such that data patterns and uncertainty can be learned by deep learning (DL) models. This paper proposes the usage of a recurrent neural network (RNN)-based evidential regression model, which can predict trajectory at future timesteps as well as estimate the data and model uncertainties associated, to detect anomalous maritime trajectories, such as unusual vessel maneuvering, using automatic identification system (AIS) data. Furthermore, we utilize evidential deep learning classifiers to detect unusual turns of vessels and the loss of transmitted signal using predicted class probabilities with associated uncertainties. Our experimental results suggest that the graphical representation of traffic patterns improves the ability of the DL models, such as evidential and Monte Carlo dropout, to learn the temporal-spatial correlation of data and associated uncertainties. Using different datasets and experiments, we demonstrate that the estimated prediction uncertainty yields fundamental information for the detection of traffic anomalies in the maritime and, possibly in other domains.