Minimal Vectors Research Articles

Stability of optimal spherical codes

For many extremal configurations of points on a sphere, the linear programming approach can be used to show their optimality. In this paper we establish the general framework for showing stability of such configurations and use this framework to prove the stability of the two spherical codes formed by minimal vectors of the lattice E8\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$E_8$$\\end{document} and of the Leech lattice.

Generalised evasive subspaces

AbstractWe introduce and explore a new concept of evasive subspace with respect to a collection of subspaces sharing a common dimension, most notably partial spreads. We show that this concept generalises known notions of subspace scatteredness and evasiveness. We establish various upper bounds for the dimension of an evasive subspace with respect to arbitrary partial spreads, obtaining improvements for the Desarguesian ones. We also establish existence results for evasive spaces in a nonconstructive way, using a graph theory approach. The upper and lower bounds we derive have a precise interpretation as bounds for the critical exponent of certain combinatorial geometries. Finally, we investigate connections between the notion of evasive space we introduce and the theory of rank‐metric codes, obtaining new results on the covering radius and on the existence of minimal vector rank‐metric codes.

Mono-Higgs and Mono-Z Production in the Minimal Vector Dark Matter Model

The minimal vector dark matter is a viable realization of the minimal dark matter paradigm. It extends the standard model by the inclusion of a vector matter field in the adjoint representation of SU(2)L. The dark matter candidate corresponds to the neutral component of the new vector field (V0). Previous studies have shown that the model can explain the observed dark matter abundance while evading direct and indirect searches. At colliders, the attention has been put on the production of the charged companions of the dark matter candidate. In this work, we focus on the mono-Higgs and mono-Z signals at Hadron colliders. The new charged vectors (V±) are invisible unless a dedicated search is performed. Consequently, we assume that the mono-Higgs and mono-Z processes correspond to the pp→hV+,0V−,0 and pp→ZV+,0V−,0 reactions, respectively. We show that, while the pp→hV+,0V−,0 is more important, both channels may produce significant signals at the HL-LHC and colliders running at s=27 TeV and 100 TeV, probing almost the complete parameter space.

A novel generative–predictive data-driven approach for multi-objective optimization of horizontal axis tidal turbine

Tidal turbines play a critical role in converting the kinetic energy of water into electricity, contributing significantly to energy conversion. However, the current optimization design of these turbines involves computationally intensive simulations, leading to higher design costs. Additionally, traditional parameterized modeling methods, constrained by predefined design parameters, limit the exploration of innovative designs. In response, this study introduces an innovative data-driven “generative–predictive” design approach comprising a generative model and a predictive model. The generative model autonomously learns feature representations from existing turbines and leverages this knowledge to generate a novel set of turbines with superior hydrodynamic performance. Subsequently, an efficient performance evaluation is conducted using a predictive model for the generated turbines. Compared to the current parameterized modeling approaches, the proposed approach is combined with multi-objective optimization algorithm to optimize the tidal turbine hydrodynamic performance. Research results demonstrate that the generative model, trained on gradients, can generate highly complex turbines with minimal latent vectors. Through transfer learning, the predictive model exhibits robustness and accuracy, effectively guiding the design process. In the final optimization comparison, the proposed generative–predictive design approach requires only 4% of the optimization time while achieving results similar to or surpassing traditional design approaches. This approach proves to be a powerful tool for guiding the efficient and optimized design of turbines.

MMV method: a new approach to compare protein sequences under binary representation

In the present work, a new form of descriptor using minimal moment vector (MMV) is introduced to compare protein sequences in the frequency domain under their component wise binary representations. From every sequence, 20 different binary component sequences are formed, each corresponding to 20 amino acids. Each such vector is now shifted from the time domain to the frequency domain by applying the Fast Fourier Transform (FFT). Next, the power spectrum calculated from the FFT values for each component sequence is so normalized that the sum of the components equals 1. The descriptor is defined as a 20-component vector composed of the 20 second-order minimal moments calculated from the normalized spectrum of the 20 component sequences. Once the descriptor is known, the distance matrix is created by applying the Euclidean Distance measure. The phylogenetic tree is generated by applying the unweighted pair group method with the arithmetic mean (UPGMA) algorithm using Molecular Evolutionary Genetics Analysis11 (MEGA11) software. In this work, the datasets used for similarity studies are 9 NADH dehydrogenase 5 (ND5), 12 Baculoviruses, 24 Transferrins (TF) proteins, and 50 Spike Protein of coronavirus. A qualitative measure using rationalized perception is used to compare the effectiveness of the proposed method. Quantitative measure based on symmetric distance (SD) is used to compare the phylogenetic trees of the present method with those obtained by other methods. It is observed that the phylogenetic trees generated by the proposed technique are at par with their known biological references, and they produce results better than those of the earlier methods. Communicated by Ramaswamy H. Sarma

Maximum likelihood estimation and natural pairwise estimating equations are identical for three sequences and a symmetric 2-state substitution model

Consider the problem of estimating the branch lengths in a symmetric 2-state substitution model with a known topology and a general, clock-like or star-shaped tree with three leaves. We show that the maximum likelihood estimates are analytically tractable and can be obtained from pairwise sequence comparisons. Furthermore, we demonstrate that this property does not generalize to larger state spaces, more complex models or larger trees. Our arguments are based on an enumeration of the free parameters of the model and the dimension of the minimal sufficient data vector. Our interest in this problem arose from discussions with our former colleague Freddy Bugge Christiansen.

Usage of task and data parallelism for finding the lower boundary vectors in a stochastic-flow network

In a stochastic-flow network, a minimal system state vector under which the maximum flow of the network from a source node to a destination node is equal to d is called a lower boundary vector (LBV). As the number of LBVs increases exponentially with the size of the network, the available algorithms in the literature could be improved to be more practical for real-world large-sized systems. We employ task and data parallelism to propose an efficient algorithm for determining all the LBVs to tackle this problem. We present an efficient approach for removing duplicate solutions to improve an available algorithm to find all the LBVs. We show the correctness and compute the complexity results of the proposed approach and demonstrate its efficiency. Then, we propose vectorized, parallelized, and vectorized–parallelized versions of the main algorithm. We illustrate the standard version through a benchmark example and discuss the other proposed versions’ correctness. We conduct several experimental results on two known benchmark networks and more than one thousand random problems to demonstrate the practical efficiency of the vectorized–parallelized version. Moreover, Dolan and Moré’s performance profile is used to provide a more intuitive comparison between all four versions.

On the combinatorial nature of tree representations of Euclidean quivers

We verify computationally a conjecture on the field independence of tree representations of Euclidean quivers, with dimension vector bounded by the minimal radical vector of the quiver. This includes a large class of exceptional representations, in particular all the regular non-homogeneous exceptionals. In addition we also present some thought-provoking findings, which further confirms the combinatorial nature of the category of representations of tame quivers.

Absolute minima of potentials of certain regular spherical configurations

We use methods of approximation theory to find the absolute minima on the sphere of the potential of spherical (2m−3)-designs with a non-trivial index 2m that are contained in a union of m parallel hyperplanes, m≥2, whose locations satisfy certain additional assumptions. The interaction between points is described by a function of the dot product, which has positive derivatives of orders 2m−2, 2m−1, and 2m. This includes the case of the classical Coulomb, Riesz, and logarithmic potentials as well as a completely monotone potential of the distance squared. We illustrate this result by showing that the absolute minimum of the potential of the set of vertices of the icosahedron on the unit sphere S2 in R3 is attained at the vertices of the dual dodecahedron and the one for the set of vertices of the dodecahedron is attained at the vertices of the dual icosahedron. The absolute minimum of the potential of the configuration of 240 minimal vectors of E8 root lattice normalized to lie on the unit sphere S7 in R8 is attained at a set of 2160 points on S7 which we describe.

Calibrations for the Volume of Unit Vector Fields in Dimension 2

We use the theory of calibrations to write an equation of a minimal volume vector field on a given Riemann surface.

A generalized model to generate d-MP for a multi-state flow network

Network reliability is defined as the probability that a demand d can successfully be sent through a multi-state flow network (MSFN). Several practical systems, including manufacturing, supply chain, and computer networks, can be modeled as the MSFN for evaluating network reliability. Calculating network reliability belongs to an NP-hard problem. Existing algorithms based on minimal paths (MP) are developed to systematically obtain all d-MP for the further network reliability evaluation. The d-MP are minimal necessary capacity-state vectors for a demand level d in short. When facing more complex and practical MSFN, we always have a motivation to improve the efficiency to calculate network reliability by generating all the d-MP. A generalized MSFN model is proposed in this study to generate all the d-MP efficiently. All the solutions satisfying the constructed formulations are all the d-MP. That is, the evaluation of the network reliability can be accelerated based on the solutions generated from the proposed model. Besides, recursive procedures with a demonstrated example are provided to offer hints to implement the proposed model. Numerical experiments, including the MSFN from references and random generation, and time complexity analysis are conducted to show that the improvement of the d-MP generation by using the proposed generalized MSFN model, compared with the existing algorithm with the linear time complexity.

On the Douglas–Rachford Algorithm for Solving Possibly Inconsistent Optimization Problems

More than 40 years ago, Lions and Mercier introduced in a seminal paper the Douglas–Rachford algorithm. Today, this method is well-recognized as a classic and highly successful splitting method to find minimizers of the sum of two (not necessarily smooth) convex functions. Whereas the underlying theory has matured, one case remains a mystery: the behavior of the shadow sequence when the given functions have disjoint domains. Building on previous work, we establish for the first time weak and value convergence of the shadow sequence generated by the Douglas–Rachford algorithm in a setting of unprecedented generality. The weak limit point is shown to solve the associated normal problem, which is a minimal perturbation of the original optimization problem. We also present new results on the geometry of the minimal displacement vector. Funding: The research of H. H. Bauschke and W. M. Moursi was partially supported by Discovery Grants of the Natural Sciences and Engineering Research Council of Canada [Grants RGPIN-2018-03703 and RGPIN-2019-04803], respectively.

Gauss maps of harmonic and minimal great circle fibrations

We investigate Gauss maps associated to great circle fibrations of the euclidean unit 3-sphere mathbb {S}^3. We show that the associated Gauss map to such a fibration is harmonic, respectively minimal, if and only if the unit vector field generating the great circle foliation is harmonic, respectively minimal. These results can be viewed as analogues of the classical theorem of Ruh and Vilms about the harmonicity of the Gauss map of a minimal submanifold in the euclidean space. Moreover, we prove that a harmonic or minimal unit vector field on mathbb {S}^3, whose integral curves are great circles, is a Hopf vector field.

Deep Learning-Based Metaheuristic Weighted K-Nearest Neighbor Algorithm for the Severity Classification of Breast Cancer

ObjectiveThe most widespread and intrusive cancer type among women is breast cancer. Globally, this type of cancer causes more mortality among women, next to lung cancer. This made the researchers to focus more on developing effective Computer-Aided Detection (CAD) methodologies for the classification of such deadly cancer types. In order to improve the rate of survival and earlier diagnosis, an optimistic research methodology is required in the classification of breast cancer. Consequently, an improved methodology that integrates the principle of deep learning with metaheuristic and classification algorithms is proposed for the severity classification of breast cancer. Hence to enhance the recent findings, an improved CAD methodology is proposed for redressing the healthcare problem. Material and MethodsThe work intends to cast a light-of-research towards classifying the severities present in digital mammogram images. For evaluating the work, the publicly available MIAS, INbreast, and WDBC databases are utilized. The proposed work employs transfer learning for extricating the features. The novelty of the work lies in improving the classification performance of the weighted k-nearest neighbor (wKNN) algorithm using particle swarm optimization (PSO), dragon-fly optimization algorithm (DFOA), and crow-search optimization algorithm (CSOA) as a transformation technique i.e., transforming non-linear input features into minimal linear separable feature vectors. ResultsThe results obtained for the proposed work are compared then with the Gaussian Naïve Bayes and linear Support Vector Machine algorithms, where the highest accuracy for classification is attained for the proposed work (CSOA-wKNN) with 84.35% for MIAS, 83.19% for INbreast, and 97.36% for WDBC datasets respectively. ConclusionThe obtained results reveal that the proposed Computer-Aided-Diagnosis (CAD) tool is robust for the severity classification of breast cancer.

ON/OFF control for reaching a steady state attractive region in batches Petri nets

This paper addresses an event-driven control problem of controlled generalized batches Petri nets without discrete nodes, i.e., a class of hybrid Petri net formalisms. The goal of the controller is to reach a given steady state from an initial marking qualified as blocking, by controlling the flow of transitions. To this end, we firstly characterize an attractive region of the steady state as an optimal solution of a linear programming problem (LPP). Next, based on the ON/OFF state of transitions, which depends on the enabling conditions and the firing quantities, an ON/OFF event-driven control strategy is proposed for reaching, from a blocking initial marking quantity, the nearest marking quantity in the attractive region. The admissible controlled firing flow vector is computed according to a LPP which maximizes the firing flow of ON-transitions to its maximal firing flow while it imposes a null firing flow to OFF-transitions. The proposed strategy is event-driven and the control actions are updated only when specific events occur. The basic idea of this new control strategy is to fire each transition as fast as possible at any event step until the minimal firing quantity vector is reached.

Paragraph-antibody paratope prediction using graph neural networks with minimal feature vectors.

The development of new vaccines and antibody therapeutics typically takes several years and requires over $1bn in investment. Accurate knowledge of the paratope (antibody binding site) can speed up and reduce the cost of this process by improving our understanding of antibody-antigen binding. We present Paragraph, a structure-based paratope prediction tool that outperforms current state-of-the-art tools using simpler feature vectors and no antigen information. Source code is freely available at www.github.com/oxpig/Paragraph. Supplementary data are available at Bioinformatics online.

On average coherence of cyclotomic lattices

We introduce maximal and average coherence on lattices by analogy with these notions on frames in Euclidean spaces. Lattices with low coherence can be of interest in signal processing, whereas lattices with high orthogonality defect are of interest in sphere packing problems. As such, coherence and orthogonality defect are different measures of the extent to which a lattice fails to be orthogonal, and maximizing their quotient (normalized for the number of minimal vectors with respect to dimension) gives lattices with particularly good optimization properties. While orthogonality defect is a fairly classical and well-studied notion on various families of lattices, coherence is not. We investigate coherence properties of a nice family of algebraic lattices coming from rings of integers in cyclotomic number fields, proving a simple formula for their average coherence. We look at some examples of such lattices and compare their coherence properties to those of the standard root lattices.

Investigate exact reliability under limited time and space of a multistate online food delivery network

In recent years, especially during the outbreak of COVID-19, there have witnessed the emergence of online food delivery (OFD) services that allow customers to place orders via Internet-connected devices to obtain door-to-door delivered meals. In this service, on-time delivery to the right customer with high-quality fresh meals is deemed the primary factor. This paper investigates the reliability of OFD through its ability to meet customer needs in a specific context. During the delivery process, the courier receives the food at the store, packs it into a delivery box, and then delivers it to the customer. Note that, the delivery boxes are limited in space. Customers prefer having their orders delivered within a given time threshold. Thus, reliability is defined as the probability to complete non-integer and multiple orders under a limited time and space. Besides, the OFD system belongs to the gig economy, which allows couriers to select their shifts and working regions. Hence, the capacity of each region, which indicates the number of available couriers, is regarded as multistate. We, thus, construct the OFD system as a multistate online food delivery network (MOFN). Under the limitation of time and space, all feasible minimal capacity vectors are determined to compute the reliability. With the proposed investigation, managers can understand their MOFN’s ability to meet specific customer demands. Accordingly, they can make appropriate adjustments for better performance.

Low feature dimension in image steganographic recognition

Steganalysis <span>aids in the detection of steganographic data without the need to know the embedding algorithm or the "cover" image. The researcher's major goal was to develop a Steganalysis technique that might improve recognition accuracy while utilizing a minimal feature vector dimension. A number of Steganalysis techniques have been developed to detect steganography in images. However, the steganalysis technique's performance is still limited due to their large feature vector dimension, which takes a long time to compute. The variations of texture and properties of an embedded image are clearly seen. Therefore, in this paper, we proposed Steganalysis recognition based on one of the texture features, such as gray level co-occurrence matrix (GLCM). As a classifier, Ada-Boost and Gaussian discriminant analysis (GDA) are used. In order to evaluate the performance of the proposed method, we use a public database in our proposed and applied it using IStego100K datasets. The results of the experiment show that the proposed can improve accuracy greatly. It also indicates that in terms of accuracy, the Ada-Boost classifier surpassed the GDA. The comparative findings show that the proposed method outperforms other current techniques especially in terms of feature size and recognition accuracy</span>.

Self-Repairing Herpesvirus Saimiri Deletion Variants.

Herpesvirus saimiri (HVS) is discussed as a possible vector in gene therapy. In order to create a self-repairing HVS vector, the F plasmid vector moiety of the bacterial artificial chromosome (BAC) was transposed via Red recombination into the virus genes ORF22 or ORF29b, both important for virus replication. Repetitive sequences were additionally inserted, allowing the removal of the F-derived sequences from the viral DNA genome upon reconstitution in permissive epithelial cells. Moreover, these self-repair-enabled BACs were used to generate deletion variants of the transforming strain C488 in order to minimalize the virus genome. Using the en passant mutagenesis with two subsequent homologous recombination steps, the BAC was seamlessly manipulated. To ensure the replication capacity in permissive monkey cells, replication kinetics for all generated virus variants were documented. HVS variants with increased insert capacity reached the self-repair within two to three passages in permissive epithelial cells. The seamless deletion of ORFs 3/21, 12–14, 16 or 71 did not abolish replication competence. Apoptosis induction did not seem to be altered in human T cells transformed with deletion variants lacking ORF16 or ORF71. These virus variants form an important step towards creating a potential minimal virus vector for gene therapy, for example, in human T cells.