Dimensional Vector Research Articles

Enhancing network lifespan in wireless sensor networks using deep learning based Graph Neural Network

Inadequate energy of sensors is one of the most significant challenges in the development of a reliable wireless sensor network (WSN) that can withstand the demands of growing WSN applications. Implementing a sleep-wake scheduling scheme while assigning data collection and sensing chores to a dominant group of awake sensors while all other nodes are in a sleep state seems to be a potential way for preserving the energy of these sensor nodes. When the starting energy of the nodes changes from one node to another, this issue becomes more difficult to solve. The notion of a dominant set-in graph has been used in a variety of situations. The search for the smallest dominant set in a big graph might be time-consuming. Specifically, we address two issues: first, identifying the smallest possible dominant set, and second, extending the network lifespan by saving the energy of the sensors. To overcome the first problem, we design and develop a deep learning-based Graph Neural Network (DL-GNN). The GNN training method and back-propagation approach were used to train a GNN consisting of three networks such as transition network, bias network, and output network, to determine the minimal dominant set in the created graph. As a second step, we proposed a hybrid fixed-variant search (HFVS) method that considers minimal dominant sets as input and improves overall network lifespan by swapping nodes of minimal dominating sets. We prepared simulated networks with various network configurations and modeled different WSNs as undirected graphs. To get better convergence, the different values of state vector dimensions of the input vectors are investigated. When the state vector dimension is 3 or 4, minimum dominant set is recognized with high accuracy. The paper also presents comparative analyses between the proposed HFVS algorithm and other existing algorithms for extending network lifespan and discusses the trade-offs that exist between them. Lifespan of wireless sensor network, which is based on the dominant set method, is greatly increased by the techniques we have proposed.

1-dimensional Embedding Approach for Adolescent Psychosis Prediction from EEG Brain Waves using Support Vector Machines and Deep Learning

Objective: Schizophrenia is a form of psychosis which is prevalent within the population and affects both adults and adolescents, where it has also been noted that the conventional means towards diagnosing the disorder involve a high degree of subjectivity, can yield false positive results and are overall difficult to replicate. The use of electroencephalography (EEG) brain waves has been seen to carry promise as a means towards a non-invasive diagnosis of brain states via the acquisition of the bioelectrical manifestation of neuronal activities from across the skull. The acquisition of EEG signals involves a high number of electrode channels alongside the extraction of a relatively broad number of signal features which ultimately yields a high dimensional vector that scales upwards with the addition of data from subsequent subjects. Methods: As a means around dealing with this issue, this paper proposes a combination of signal decomposition prior to feature extraction, alongside dimensionality reduction, to obtain a low dimensional representation and embedding which is sufficient to allow for an improved prediction performance with a low dimensional projection capable of distinguishing between schizophrenic and non-schizophrenic adolescents. Results: The results from the pilot carried out, showed that a combination of a metaheuristic signal decomposition, linear dimensionality reduction and the long short-term memory deep learning model provided the best classification performance for the recognition of adolescent schizophrenia from a 1-dimensional embedding representation with a prediction accuracy of 88%. Conclusion: Further work in this area would now look into the application of probabilistic modelling as a means towards inferring an associated stage of the schizophrenia psychosis where predicted to be present in an adolescent subject.

Abstract 5361: Deep learning models capture high dimensional features for cell morphology analysis

Abstract Many methods for imaging and sorting tumor cells require biomarker labels that perturb cells and may create a selection bias. The Deepcell platform can characterize and sort cells using only brightfield images of unlabeled single cells, thereby enabling more comprehensive and unbiased assessment of tumor cell morphology and heterogeneity. Cells are imaged with a high-speed camera during microfluidic flow and brightfield images are analyzed in real-time by deep learning models to generate quantitative embeddings, which are reproducible and multi-dimensional descriptions of cell morphology. One of the key technical challenges in building this platform was the development of an AI model to extract features from cell images from diverse human cells without prior knowledge of specific cell types, cell preparation, or other application-specific knowledge for an exploratory approach. Deepcell’s ‘Human Foundation Model’ (HFM) is a feature encoder that transforms cell images into 128 dimensional embedding vectors. The model backbone, responsible for extracting image features, is based on the ResNet18 convolutional deep neural network architecture. Training utilizes a multi-task semi-supervised training framework that combines the VicReg self-supervised learning model, which learns images features without labels, along with supervised auxiliary models using labeled data. These sub-models enable the backbone model to recognize specific cell attributes such as granulation, pigmentation, characteristics of malignancy, attributes related to cellular states like apoptosis and necrosis. We augment the deep learning embeddings with computer vision derived cellular features, such as area, perimeter, intensity, and texture features to improve model interpretability and accuracy. Here, we describe how the HFM self-supervised backbone model was trained, the discriminatory power added by the supervised tasks, and validation of the reproducibility and generalization capabilities of the resulting model. We also demonstrate how the resulting embeddings can be visualized using the Deepcell Cloud software and how clusters of cells in our embedding space can be related to cell images, interpretable morphological features, and actionable biological characteristics. Potential applications of the Deepcell platform are diverse and promising, such as label-free enrichment of malignant cells and discovery of morphologically distinct subpopulations of heterogeneous cancer cell samples. Citation Format: Kevin B. Jacobs, Kiran Saini, Nianzhen Li, Senzeyu Zhang, Ryan Carelli, Amy Wong-Thai, Stephane C. Boutet, Anastasia Mavropoulos, Andreja Jovic, Jeanette Mei, Mahyar Salek, Maddison Masaeli. Deep learning models capture high dimensional features for cell morphology analysis. [abstract]. In: Proceedings of the American Association for Cancer Research Annual Meeting 2023; Part 1 (Regular and Invited Abstracts); 2023 Apr 14-19; Orlando, FL. Philadelphia (PA): AACR; Cancer Res 2023;83(7_Suppl):Abstract nr 5361.

Abstract 5408: AI powered-platform to predict gene modifications from prostate and breast cancer whole slide images

Abstract There is little published evidence of predicting cancer genotypes directly from tissue histology, especially for breast and prostate cancers. Artificial intelligence (AI) enables discriminating and extracting morphological features reflective of the underlying genomic alterations at visual and subvisual levels. We have built a morphology-based and AI-powered platform for cancer genotyping, risk stratification and outcome prediction that addresses the needs for treatment decision-making in a cost effective and timely fashion. A cohort of 390 prostate and 742 invasive breast cancer patients with known molecular status of key genes, such as TP53, PIK3CA, MYC, ERBB2, TMPRSS2-ERG and PTEN from The Cancer Genome Atlas were included in this study. Hematoxylin and eosin (H&E) stained whole slide images (WSI) of the cancer tissue sections were available at 20x or 40x. The WSI from the two cancer cohorts were split 2:1 into a training and test dataset, respectively. Our platform involved two different deep Convolutional Neural Network (DCNN) architectures. The platform first divided each WSI into multiple tiles. Each tile was then analyzed using a DCNN that graded the tile and generated a high dimensional vector to provide a mathematical representation of the morphology. The combination of high dimensional vectors across the WSI was then fed into a second DCNN that generated a morphological score, which predicted whether the gene under consideration was wild type or modified. Our platform has achieved 70 - 80% accuracy as defined by the Area under the Curve for the receiver operating characteristics curves for the genetic markers on the test cohorts (Table 1). Our platform can predict genotypes/molecular alterations directly from H&E stained WSI with high accuracy. This technology presents a novel, practical and cost-effective approach for cancer molecular classification and risk stratification, enabling timely and optimal treatment decision-making for positive clinical outcomes. Genotype Prediction for Breast Cancer (BrCa) and Prostate Cancer (PCa) from WSI Cohort Molecular Biomarker Training Dataset (n) Test Dataset (n) Test ROC AUC Score (%) Gene Modification/Loss Intact/Wild type Gene Modification/Loss Intact/Wild type BrCa TP53 196 302 96 149 80 PIK3CA 153 344 75 170 74 MYC 68 414 33 204 77 ERBB2 66 416 32 205 78 PCa TMPRSS2-ERG 104 157 51 78 70 PTEN 57 201 28 99 73 Citation Format: Wei Huang, Parag Jain, Chensu Xie, Hassan Muhammad, Hirak Basu, George Wilding, Rajat Roy. AI powered-platform to predict gene modifications from prostate and breast cancer whole slide images. [abstract]. In: Proceedings of the American Association for Cancer Research Annual Meeting 2023; Part 1 (Regular and Invited Abstracts); 2023 Apr 14-19; Orlando, FL. Philadelphia (PA): AACR; Cancer Res 2023;83(7_Suppl):Abstract nr 5408.

322 Distributed Vector Representations of Neurosurgical Admission Notes Predict Discharge Disposition

INTRODUCTION: Natural language processing (NLP) aims to extract information from unstructured language input for use in machine learning, without the need for laborious manual review of text to retrieve data of potential interest. An NLP-based model utilizing term frequency-inverse document frequency (TF-IDF) vectoral representations of pre-operative clinical notes has previously been shown to predict discharge disposition following meningioma resection. The TF-IDF vectorization scheme is based on word counts across documents but does not account for word order or semantic information. An alternative algorithm, paragraph vectorization, utilizes an unsupervised neural network to learn document vector representations. METHODS: We analyzed 7,122 admission notes. We trained a neural network to derive paragraph vector representations of notes and trained a classifier to predict home vs non-home discharge disposition based on these representations. Out-of-sample performance was assessed on a held-out testing set. We repeated the analysis using TF-IDF document representations to compare the two approaches. Performance was quantified using area under the receiver operating characteristic curve (ROC-AUC). RESULTS: Model performance increased with vector dimensionality. A 200-dimensional distributed document vectorization was highly predictive of nonhome discharge with an ROC-AUC of 0.82 ± 0.01 (mean ± standard error over 5-fold nested cross-validation). When the dimensionality of the embedding vector space was relatively low (e.g. <100), learned paragraph vectors predicted discharge disposition better than TF-IDF vectors. CONCLUSIONS: Natural language processing of admission notes via neural network-learned distributed vectoral representations is a viable strategy of information extraction from neurosurgical clinical documentation. This embedding scheme overcomes some of the limitations of TF-IDF and encodes more information in lower-dimensional embedding vector spaces. It holds promise as a method of using free text to train machine learning algorithms for prediction of clinically relevant outcomes.

FIMBISAE: A Multimodal Biometric Secured Data Access Framework for Internet of Medical Things Ecosystem

Information from the Internet of Medical Things (IoMT) domain demands building safeguards against illegitimate access and identification. Existing user identification schemes suffer from challenges in detecting impersonation attacks which leave systems vulnerable and susceptible to misuse. Significant advancement has been achieved in the domain of biometrics and health informatics. This can take a step ahead with the usage of multimodal biometrics for the identification of healthcare system users. With this aim, the proposed work explores the fingerprint and iris modality to develop a multimodal biometric data identification and access control system for the healthcare ecosystem. In the proposed approach, minutiae-based fingerprint features and a combination of local and global iris features are considered for identification. Further, an index space based on the dimension of the feature vector is created, which gives a 1-D embedding of the high-dimensional feature set. Next, to minimize the impact of false rejection, the approach considers the possible deviation in each element of the feature vector and then stores the data in possible locations using the predefined threshold. Besides, to reduce the false acceptance rate, linking of the modalities has been done for every individual data. The modality linking thus helps in carrying out an efficient search of the queried data, thereby minimizing the false acceptance and rejection rate. Experiments on a chimeric iris and fingerprint bimodal database resulted in an average of 95% reduction in the search space at a hit rate of 98%. The results suggest that the proposed indexing scheme has the potential to substantially reduce the response time without compromising the accuracy of identification.

Grouping Intrinsic Mode Functions and Residue for Pathological Classifications via Electroglottograms

The electroglottogram (EGG) is a signal used for measuring the change of the relative contact area in the vocal cord during the throat production. In the recent years, the low cost and the non-invasive applications have been derived. Hence, the EGG has been applied in various science, engineering and medical fields such as in the basic voice science including the phonetics, the singing and the hearing as well as in the speech and the language therapy and the related clinical works including the voice production physiology, the swallowing and the psychology. However, the pathological classifications using the EGGs usually yield the poor performances. This is because the EGGs are required to decompose into the various components for extracting the features for performing the classifications. Nevertheless, the total numbers of the components decomposed by some time frequrncy representation such as the empirical mode decomposition (EMD) for different EGGs are different. Hence, the dimension of the feature vectors extracted from different EGGs is different. This introduces to the difficulty for building a machine learning model for performing the classification. This paper is to address this issue. This paper proposes a method for grouping the intrinsic mode functions (IMFs) and the residue obtained by applying the EMD to the EGGs for classifying between the healthy subjects and the pathological subjects. More precisely, this paper proposes a clustering based method to group the IMFs and the residue so that the total numbers of the grouped IMFs of different EGGs are the same. First, the IMFs and the residue of the EGGs are catergorized into a desired number of groups based on their correlation coefficients. Second, the IMFs or the residue in each group are summed together to obtain the grouped IMF. Third, the mean frequency and the first formant of each grouped IMF are computed. Finally, a random forest is employed for performing the classification. To our best knowledge, this joint EMD and clustering based method is firstly proposed to preform the pathological voice detection. The computer numerical simulations are conducted using the online availiable Saarbrücken voice database. Here, five cross validations have been performed. The mean accuracy, the mean specificity and the mean sensitivity among these five validations are 86.98, 79.92 and 91.57, respectively. The standard deviation of the accuracy, the specificity and the sensitivity among these five validations are ±2.00%, ±3.71% and ±2.13%, respectively. The simulation results show that our proposed method outperforms the common EGG or speech processing based methods. This paper proposes a clustering based method for grouping the IMFs and the residue for performing the pathological classifications via the EGGs. The grouping criterion is based on the correlation coefficients. It is found that our proposed method can achieve the highest classifications for the majority signal to noise ratios compared to the state of the arts methods. • This paper proposes a clustering based method for grouping the IMFs and the residue. • It applies to classify between the healthy and the pathological subjects. • The total numbers of the grouped IMFs of different EGGs are the same. • The mean frequency and the first formant of each grouped IMF are computed. • A random forest is employed for performing the classification.

Multicomponent gauge-Higgs models with discrete Abelian gauge groups

We consider a variant of the charge-Q compact Abelian-Higgs model, in which an N f -dimensional complex vector is coupled with an Abelian gauge field. For and Q = 1 we observe several transition lines that belong to the O(4), O(3), and O(2) vector universality classes, depending on the symmetry breaking pattern at the transition. The universality class is independent of q as long as . The universality class of the transition is uniquely determined by the behavior of the scalar fields; gauge fields do not play any role. We also investigate the system for and Q = 2. In the presence of U(1) gauge fields, the system undergoes transitions associated with charged fixed points of the Abelian-Higgs field theory. These continuous transitions turn into first-order ones when the U(1) gauge fields are replaced by the discrete fields: in the present compact model charged transitions appear to be very sensitive to the nature of the gauge fields.

Coating Damage Detection of Vessels Using Machine Learning-Based Underwater Electric Field

There has been extensive research on corrosion electric fields because of their special characteristics. There are apparent distribution characteristics corresponding to different coating damage regions of a vessel. To accurately detect where the coating damage region is located on vessels using underwater electric field signature, in this study, a method called “refined composite multivariate multiscale fluctuation reverse dispersion entropy (RCMMFRDE)” was proposed. This method effectively extracted the multichannel signal in a complex environment of poor stability and high noise. By combining RCMMFRDE and hierarchical prototype (HP), a novel coating damage detection method was developed. First, the accumulated differential value was calculated to determine the side on which the vessel had the damaged coating. Second, RCMMFRDE was used to extract the features of electric field signals. Then, feature vector dimensionality reduction was carried out using pair-wise feature proximity (PWFP). The low-dimensional features were given as input to the HP classifier to detect the damaged region. Finally, a series of numerical and physical scale experiments were conducted to validate the feasibility of the proposed method. The damaged region was efficiently predicted, achieving satisfactory accuracy of 96.67% and 92.00% in numerical and measurement data respectively; thus, it is a suitable alternative to conventional methods, especially when there is a lack of previous environmental information.

The Eurasian Vector as a Priority of Russia’s Parliamentary Diplomacy

The article discusses certain special aspects of Russia’s parliamentary diplomacy in the context of global confrontation with the West. It demonstrates that the Eurasian vector of the parliamentary dimension should become the priority thereof. The article researches multilateral and bilateral inter-parliamentary relations aimed at the formation of Eurasian law and the creation of conditions for functioning of Eurasian courts and arbitration tribunals. Certain features of the work of Eurasian parliamentary institutions are revealed, such as: the CSTO Parliamentary Assembly, IPA CIS, the Parliamentary Assembly of the Union of Belarus and Russia on economic, political, military, humanitarian integration in the post-Soviet territory.Aim. Disclosure of the content of the Eurasian vector of Russia’s parliamentary diplomacy as a priority dimension in the context of global confrontation with the West.Tasks. Analyze features of the Western and Eurasian vectors of parliamentary diplomacy of Russia; explore forms and methods of parliamentary diplomacy in the post-Soviet territory; determine ways to strengthen the role of the parliamentary dimension in the processes of Eurasian integration.Methods. Systematic approach, comparative analysis, compilation of the best practices.Results. The study showed the need for a transition to bilateral forms of inter-parliamentary cooperation between Russia and unfriendly countries of the West and the effectiveness of multilateral cooperation with the countries of the East in order to develop Eurasian integration. The relevance of creating a parliamentary dimension in the EAEU and completing the formation of parliamentary institutions in the CSTO and the Union State has been substantiated.

Modeling of multi-factory dependences in complex control systems by SUGENO fuzzy knowledge base

The creation of intelligent control systems based on soft computing for complex real-time systems is considered. Usually, the control of many objects and technological processes is performed by a human operator based on instructions and personal experience. Due to the uncertainty and incompleteness of information about the parameters of the object, the impossibility of their direct measurement and the natural diversity of the environment, the use of classical mathematical methods for the automation of control is impossible. Adaptive methods are used to solve the management problem under conditions of uncertainty. The most effective is the implementation of fuzzy control based on production rules, which does not require knowledge of the object model. The concept of fuzzy control is widely used because of its ability to operate according to conditions. The object is evaluated using fuzzy rules from the knowledge base that create a fuzzy decision domain. The stage of structural identification of the system when modeling an unknown dependency by Sugeno's fuzzy knowledge base is presented, which allows implementing a control algorithm based on a neural network. To take into account the maximum number of influencing factors, the hierarchical structure of the fuzzy control system is applied. Granulation by certain properties of the object and the environment at the level of input variables allows to reduce the dimensionality of the data vector and the number of rules of the knowledge base, making it possible to build fuzzy control systems with an unlimited number of inputs. According to this model, the decision-making process is divided into two levels. The first level reduces the amount of information to define the situations to be processed in the second level by the Sugeno knowledge base. A preliminary fuzzy model of control of complex dynamic objects with incomplete determination is built.

A sparse matrix formulation of model-based ensemble Kalman filter

We introduce a computationally efficient variant of the model-based ensemble Kalman filter (EnKF). We propose two changes to the original formulation. First, we phrase the setup in terms of precision matrices instead of covariance matrices, and introduce a new prior for the precision matrix which ensures it to be sparse. Second, we propose to split the state vector into several blocks and formulate an approximate updating procedure for each of these blocks. We study in a simulation example the computational speedup and the approximation error resulting from using the proposed approach. The speedup is substantial for high dimensional state vectors, allowing the proposed filter to be run on much larger problems than can be done with the original formulation. In the simulation example the approximation error resulting from using the introduced block updating is negligible compared to the Monte Carlo variability inherent in both the original and the proposed procedures.

Effective observables for electromagnetic duality from novel amplitude decomposition

We introduce a decomposition of $D$-dimensional vector amplitudes in terms of building blocks that preserve all partial amplitude relations of the parent gauge theory. Using this decomposition, we derive a new set of amplitude relations between nonlinear sigma model pions and the pure-scalar sector of Yang-Mills scalar theory. These new relations indicate an equivalence between Born-Infeld duality invariance and that of Einstein-Maxwell theory, considering their known double-copy construction from the two scalar theories with Yang-Mills. This observation motivates a general framework for constructing duality-invariant effective field theory observables at any multiplicity using the building blocks in our amplitude decomposition. Finally, we conjecture a subtle relationship between these duality-invariant building blocks and the bosonic sector of $\mathcal{N}=4$ super Yang-Mills.

Модальный синтез регуляторов полиномиальным методом для систем автоматического управления с избыточной размерностью вектора управления

When using polynomial methods of synthesis of multichannel regulators, there is a need for polynomial matrix calculus. However, when using this method, objects with the number of output channels equal to the number of input channels are mainly considered. This is necessary for the convenience of solving a system of linear algebraic equations in matrix polynomial computation. At the same time, a fairly large number of real technical systems have an unequal number of input and output channels. At the same time, the issue of the synthesis of generators by the polynomial method for multichannel objects with an unequal number of input and output impacts has not been worked out sufficiently deeply. One of the special cases of such systems can be considered systems with excessive dimension of the control vector. Within the framework of this work, examples of such systems and the purposes of their use are given. An illustrative example of a linear model of an unstable object with three channels for input action and two channels for output action is given. It is necessary to achieve certain quality indicators of the output vector quantity, while the control is carried out in the feedback of the system and is summed up with the input effect. The simplicity of the system under consideration is connected with the convenience of demonstrating on this example a modal synthesis method using a polynomial matrix decomposition of the transfer functions of an object and a controller for such a class of objects. In accordance with the recommendations presented in the algorithm for synthesizing regulators for objects with a non-square matrix transfer function, to solve the problem of synthesizing a regulator for systems with an excessive dimension of the control vector, the transfer function of the control object is represented as a right polynomial matrix decomposition, and the regulator is represented as a left one. During the demonstration of the example of the algorithm, some clarifications and edits are proposed in it.

Detection of Movement Related Cortical Potentials from Single Trial EEG Signals

Movement-Related Cortical Potentials (MRCP) are signals that begin to appear approximately two seconds before the onset of voluntary movements and can be recorded with EEG. MRCP is an important sign that the movement will begin. Determining the movement intention before the action is extremely important information especially for real-time BCI systems. By using MRCP, Brain-Computer Interface (BCI) users' movement intention can be determined prior to the move and this sign can be used as a control signal. In this study, it was aimed to determine the movement and resting states with high accuracy with MRCP signals. Furthermore, the effects of filter cutoff frequencies, number of electrodes, and MRCP time interval window on the success of distinguishing movement/resting states in the preprocessing stage were investigated. For this purpose, Katz fractal dimension and nonlinear support vector machine methods were used in the feature extraction and classification stages, respectively. The proposed method was tested on the attempted hand and arm movements dataset containing EEG signals of 10 participants with spinal cord injury. Katz fractal dimension and support vector machines methods can determine movement and resting states with an average of 96.47% accuracy using MRCP signals. If the number of electrodes to be used in signal analysis was 3, 9 and 61, the obtained accuracy rates were determined as 83.71%, 90.67%, and 96.47%, respectively. The experimental results also showed that the filter cutoff frequencies used in the preprocessing had a significant effect on the accuracy.

Dynamic Convolution-based Encoder-Decoder Framework for Image Captioning in Hindi

In sequence-to-sequence modeling tasks, such as image captioning, machine translation, and visual question answering, encoder-decoder architectures are state of the art. An encoder, convolutional neural network (CNN) encodes input images into fixed dimensional vector representation in the image captioning task, whereas a decoder, a recurrent neural network, performs language modeling and generates the target descriptions. Recent CNNs use the same operation over every pixel; however, all the image pixels are not equally important. To address this, the proposed method uses a dynamic convolution-based encoder for image encoding or feature extraction, Long-Short-Term-Memory as a decoder for language modeling, and X-Linear attention to make the system robust. Encoders, attentions, and decoders are important aspects of the image captioning task; therefore, we experiment with various encoders, decoders, and attention mechanisms. Most of the works for image captioning have been carried out for the English language in the existing literature. We propose a novel approach for caption generation from images in Hindi. Hindi, widely spoken in South Asia and India, is the fourth most-spoken language globally; it is India’s official language. The proposed method utilizes dynamic convolution operation on the encoder side to obtain a better image encoding quality. The Hindi image captioning dataset is manually created by translating the popular MSCOCO dataset from English to Hindi. In terms of BLEU scores, the performance of the proposed method is compared with other baselines, and the results obtained show that the proposed method outperforms different baselines. Manual human assessment in terms of adequacy and fluency of the captions generated further determines the efficacy of the proposed method in generating good-quality captions.

Safe Rules for the Identification of Zeros in the Solutions of the SLOPE Problem

In this paper we propose a methodology to accelerate the resolution of the so-called Sorted L-One Penalized Estimation (SLOPE) problem. Our method leverages the concept of “safe screening", well studied in the literature for group-separable sparsity-inducing norms, and aims ato identify the zeros in the solution of SLOPE. More specifically, we derive a set of inequalities for each element of the -dimensional primal vector and prove that the latter can be safely screened if some subsets of these inequalities are verified. We propose moreover an efficient algorithm to jointly apply the proposed procedure to all the primal variables. Our procedure has a complexity , where is a problem-dependent constant and is the number of zeros identified by the test. Numerical experiments confirm that, for a prescribed computational budget, the proposed methodology leads to significant improvements in the solving precision.

Zonotopal Algebras, Orbit Harmonics, and Donaldson–Thomas Invariants of Symmetric Quivers

Abstract We apply the method of orbit harmonics to the set of break divisors and orientable divisors on graphs to obtain the central and external zonotopal algebras, respectively. We then relate a construction of Efimov in the context of cohomological Hall algebras to the central zonotopal algebra of a graph $G_{Q,\gamma }$ constructed from a symmetric quiver $Q$ with enough loops and a dimension vector $\gamma $. This provides a concrete combinatorial perspective on the former work, allowing us to identify the quantum Donaldson–Thomas (DT) invariants as the Hilbert series of the space of $S_{\gamma }$-invariants of the Postnikov–Shapiro slim subgraph space attached to $G_{Q,\gamma }$. The connection with orbit harmonics in turn allows us to give a manifestly nonnegative combinatorial interpretation to numerical DT invariants as the number of $S_{\gamma }$-orbits under the permutation action on the set of break divisors on $G$. We conclude with several representation-theoretic consequences, whose combinatorial ramifications may be of independent interest.

Performance Enhancement of a Spin-Wave-Based Reservoir Computing System Utilizing Different Physical Conditions

We numerically study how to enhance reservoir computing performance by thoroughly extracting the spin-wave device potential for higher-dimensional information generation. The reservoir device has a 1-input exciter and 120-output detectors on the top of a continuous magnetic garnet film for spin-wave transmission. For various nonlinear and fading-memory dynamic phenomena distributing in the film space, small in-plane magnetic fields are used to prepare stripe domain structures and various damping constants at the film sides and bottom are explored. The ferromagnetic resonant frequency and relaxation time of spin precession clearly characterizes the change in spin dynamics with the magnetic field and damping constant. The common input signal for reservoir computing is a 1-GHz cosine wave with random 6-valued amplitude modulation. A basic 120-dimensional reservoir output vector is obtained from time-series signals at the 120-output detectors under each of three magnetic field conditions. Then, 240- and 360-dimensional reservoir output vectors are also constructed by concatenating two and three basic ones, respectively. In nonlinear autoregressive moving average (NARMA) prediction tasks, the computational performance is enhanced as the dimension of the reservoir output vector becomes higher and a significantly low prediction error is achieved for the tenth-order NARMA task using the 360-dimensional vector and optimum damping constant. The results are clear evidence that the collection of diverse output signals efficiently increases the dimensionality of the integrated reservoir state vector (i.e. reservoir-state richness) and thereby contributes to high computational performance. This paper demonstrates that performance enhancement through various configuration settings is a practical approach for on-chip reservoir computing devices with small numbers of real output nodes.

Lagrangian Grassmannians, CKP Hierarchy and Hyperdeterminantal Relations

This work concerns the relation between the geometry of Lagrangian Grassmannians and the CKP integrable hierarchy. The Lagrange map from the Lagrangian Grassmannian of maximal isotropic (Lagrangian) subspaces of a finite dimensional symplectic vector space $V\oplus V^*$ into the projectivization of the exterior space $\Lambda V$ is defined by restricting the Pl\"ucker map on the full Grassmannian to the Lagrangian sub-Grassmannian and composing it with projection to the subspace of symmetric elements under dualization $V \leftrightarrow V^*$. In terms of the affine coordinate matrix on the big cell, this reduces to the principal minors map, whose image is cut out by the $2 \times 2 \times 2$ quartic {\em hyperdeterminantal} relations. To apply this to the CKP hierarchy, the Lagrangian Grassmannian framework is extended to infinite dimensions, with $V\oplus V^*$ replaced by a polarized Hilbert space $ {\mathcal H} ={\mathcal H}_+\oplus {\mathcal H}_-$, with symplectic form $\omega$. The image of the Plucker map in the fermionic Fock space ${\mathcal F}= \Lambda^{\infty/2}{\mathcal H}$ is identified and the infinite dimensional Lagrangian map is defined. The linear constraints defining reduction to the CKP hierarchy are expressed as a fermionic null condition and the infinite analogue of the hyperdeterminantal relations is deduced. A multiparametric family of such relations is shown to be satisfied by the evaluation of the $\tau$-function at translates of a point in the space of odd flow variables along the cubic lattices generated by power sums in the parameters.