Dimensional Vector Research Articles

Finite dimensional Frobenius–Perron algebras

Motivated by the Frobenius–Perron (FP) theory of endofunctors of a [Formula: see text]-linear category, we introduce the notion of a FP algebra. This notion can be seen as a generalization of a fusion algebra, and is related to the PP theory of endofunctors of the categories of finite dimensional representations of Taft algebras. Our main result is to classify such algebras with small dimensions according to their FP dimension vectors. Moreover, we introduce the notion of a FP Hopf algebra which can be used to categorify a FP algebra via the Green ring of the Hopf algebra.

On some pre-orders and partial orders of linear operators on infinite dimensional vector spaces

AbstractThis article is devoted to the generalization of the Drazin pre-order and the G-Drazin partial order to Core-Nilpotent endomorphisms over arbitrary k-vector spaces, namely, infinite dimensional ones. The main properties of this orders are described, such as their respective characterizations and the relations between these orders and other existing ones, generalizing the existing theory for finite matrices. In order to do so, G-Drazin inverses are also studied in this framework. Also, it includes a generalization of the space pre-order to linear operators over arbitrary k-vector spaces.

The use of pretrained neural networks for solving the problem of reverse searching of X-ray images of prohibited items and substances

The paper considers the application of pretrained neural networks to solve the problem of reverse searching of X-ray images of prohibited items and substances. The purpose of the work is to conduct an analysis and substantiate ways to improve the efficiency of baggage and passenger hand luggage X-ray image recognition systems. An analysis of existing domestic and foreign works in the field of baggage and passenger hand luggage X-ray image recognition is presented. It has been revealed that, despite the achieved results in the development of algorithms for recognizing prohibited items and substances, they do not fully cope with such a complexity factor as the overlay of objects. To solve this problem, the paper proposes to additionally analyze X-ray images with low confidence in object recognition. This stage includes the following steps: image segmentation, extraction of features of segmented image elements; search for similar images in the database; decision-making on the class of segmented image elements. This article discusses the last three steps. Variants of approaches to feature extraction from images are analyzed, particularly those based on the application of convolutional autoencoders and pretrained neural networks. The approach based on the application of pretrained neural networks is chosen. The ResNet-50 architecture neural network, pretrained on the ImageNet collection, is used during the work. In order to apply this model to extract image feature vectors, the last classification layer was preliminarily removed. All the previous layers of the model encode the image into a vector. ResNet-50 generates a 2048-dimensional feature vector of images. The principal component analysis is used to reduce the dimensionality of the image feature vectors. The decision of whether the segmented image element is a prohibited item or substance is considered as a reverse search problem using the k-nearest neighbor algorithm. In this case, the class of the X-ray image element is the class most frequently encountered among the K nearest neighbors. In order to test the proposed approach, a training dataset, including 4,635 images of individual items and substances that may be encountered in baggage and passenger hand luggage, was generated. A comparative analysis of image indexing and image search under different algorithms and feature number is presented. A comparative analysis of the model accuracy is provided. It is concluded that the most acceptable is the “Brute force” algorithm in combination with the principal component analysis.

Trajectory Similarity Measurement: An Efficiency Perspective

Trajectories that capture object movement have numerous applications, in which similarity computation between trajectories often plays a key role. Traditionally, trajectory similarity is quantified by means of non-learned measures, e.g., Hausdorff, that operate directly on the trajectories. Recent studies exploit deep learning to map trajectories to d -dimensional vectors, called embeddings. Then, some distance measure, e.g., Manhattan, is applied to the embeddings to quantify trajectory similarity. The resulting similarities are inaccurate: they only approximate the similarities obtained using the non-learned measures. As embedding distance computation is efficient, focus has been on obtaining embeddings of high accuracy. Adopting an efficiency perspective, we analyze the time complexities of both the non-learned and the learning-based approaches, finding that the time complexities of the former approaches are not necessarily higher. Through extensive experiments on open datasets, we find that only a few learning-based approaches can deliver the promised higher efficiency, when the embeddings can be pre-computed, while non-learned approaches are more efficient for one-off computations. Among the learning-based approaches, the self-attention-based ones are the fastest and the most accurate. These results have implications for the use of trajectory similarity approaches given different application requirements.

A novel thermal turbulence reconstruction method using proper orthogonal decomposition and compressed sensing coupled based on improved particle swarm optimization for sensor arrangement

With the development of offshore wind turbine single power toward levels beyond 10 MW, the increase in heat loss of components in the nacelle leads to a high local temperature in the nacelle, which seriously affects the performance of the components. Accurate reconstruction and control of thermal turbulence in the nacelle can alleviate this problem. However, the physical environment of thermal turbulence in the nacelle is very complex. Due to the intermittent and fluctuating nature of turbulence, the turbulent thermal environment is highly nonlinear when coupled with the temperature field. This leads to large reconstruction errors in existing reconstruction methods. Therefore, we improve the sparse reconstruction method for compressed sensing (CS) based on the concept of virtual time using proper orthogonal decomposition (POD). The POD-CS method links the turbulent thermal environment reconstruction with matrix decomposition to ensure computational accuracy and computational efficiency. The improved particle swarm optimization (PSO) is used to optimize the sensor arrangement to ensure stability of the reconstruction and to save sensor resources. We apply this novel and improved PSO-POD-CS coupled reconstruction method to the thermal turbulence reconstruction in the nacelle. The effects of different basis vector dimensions and different sensor location arrangements (boundary and interior) on the reconstruction errors are also evaluated separately, and finally, the desired reconstruction accuracy is obtained. The method is of research value for the reconstruction of conjugate heat transfer problems with high turbulence intensity.

SEMANTIC SEGMENTATION AND CONTENT-BASED RETRIEVAL IN MULTIMEDIA IMAGE DATABASES

Brain tumors, particularly gliomas, pose a significant threat to global health, necessitating accurate and efficient diagnostic methods. Magnetic Resonance Imaging (MRI) serves as a crucial tool for diagnosing glioma grades, but interpretation is subject to variability, hindering treatment planning. Intra and inter-observer variability in radiological image interpretation impede effective therapeutic strategies for brain tumor patients. Accessing relevant images from vast medical databases for comparison and treatment planning is cumbersome and time-consuming. This paper proposes a Content-Based Medical Image Retrieval (CBIR) system utilizing Convolutional Neural Network (CNN)-based feature extraction, specifically employing the AlexNet architecture. The system employs KNN clustering for indexing the feature map database and implements Gain-based feature selection to reduce feature vector dimensionality. The proposed system underwent evaluation using BraTS 2018 and 2020 datasets with five-fold cross-validation. Achieving state-of-the-art performance, the system demonstrated a mean Average Precision of 98% and Precision of 97%, showcasing its efficacy in accurately retrieving similar pathological MRI brain images.

Quantum-inspired framework for computational fluid dynamics

Computational fluid dynamics is both a thriving research field and a key tool for advanced industry applications. However, the simulation of turbulent flows in complex geometries is a compute-power intensive task due to the vast vector dimensions required by discretized meshes. We present a complete and self-consistent full-stack method to solve incompressible fluids with memory and run time scaling logarithmically in the mesh size. Our framework is based on matrix-product states, a compressed representation of quantum states. It is complete in that it solves for flows around immersed objects of arbitrary geometries, with non-trivial boundary conditions, and self-consistent in that it can retrieve the solution directly from the compressed encoding, i.e. without passing through the expensive dense-vector representation. This framework lays the foundation for a generation of more efficient solvers of real-life fluid problems.

A preserving accuracy two-grid reduced-dimensional Crank-Nicolson mixed finite element method for nonlinear wave equation

In this paper, we mainly resort to a proper orthogonal decomposition (POD) method to study the reduced-dimension of unknown mixed finite element (MFE) solution coefficient vectors in the two-grid Crank-Nicolson MFE (TGCNMFE) method for the nonlinear wave equation and build a preserving accuracy reduced-dimension extrapolated TGCNMFE (RDETGCNMFE) method for the nonlinear wave equation. For this purpose, we first build a new TGCNMFE method for the nonlinear wave equation and demonstrate the existence, unconditional stability, and error estimates for the TGCNMFE solutions. From there, we build a preserving accuracy RDETGCNMFE method for the nonlinear wave equation by using the POD method to decrease the dimension of unknown TGCNMFE solution coefficient vectors and employ the matrix analysis to analyze the existence, unconditional stability, convergence, and errors for the RDETGCNMFE solutions. We finally make use of numerical experiments to verify our theoretical results and to show the advantages of RDETGCNMFE method.

Existence conditions for functional ODE observer design of descriptor systems revisited

This paper is devoted to the problem of designing functional observers for linear time-invariant (LTI) descriptor systems. The observers are realized by using state–space systems governed by ordinary differential equations (ODEs). Available existence results for functional ODE observers in the literature are extended by introducing new and milder sufficient conditions. These conditions are purely algebraic and provided directly in terms of the system coefficient matrices. The proposed observer has an order less than or equal to the dimension of the functional vector to be estimated. The observer parameter matrices are obtained by using simple matrix theory, and the design algorithm is illustrated by numerical examples.

The Block-Correlated Pseudo Marginal Sampler for State Space Models

Pseudo Marginal Metropolis-Hastings (PMMH) is a general approach to Bayesian inference when the likelihood is intractable, but can be estimated unbiasedly. Our article develops an efficient PMMH method that scales up better to higher dimensional state vectors than previous approaches. The improvement is achieved by the following innovations. First, a novel block version of PMMH that works with multiple particle filters is proposed. Second, the trimmed mean of the unbiased likelihood estimates of the multiple particle filters is used. Third, the article develops an efficient auxiliary disturbance particle filter, which is necessary when the bootstrap disturbance filter is inefficient, but the state transition density cannot be expressed in closed form. Fourth, a novel sorting algorithm, which is as effective as previous approaches but significantly faster than them, is developed to preserve the correlation between the logs of the likelihood estimates at the current and proposed parameter values. The performance of the sampler is investigated empirically by applying it to nonlinear Dynamic Stochastic General Equilibrium models with relatively high state dimensions and with intractable state transition densities and to multivariate GARCH diffusion-driven volatility in the mean models. Although we only apply the method to state space models, the approach will be useful in a wide range of applications such as large panel data models and stochastic differential equation models with mixed effects.

Fermat surfaces and hypercubes

<p>Fermat’s last theorem appears not as a unique property of natural numbers but as the bottom line of extended possible issues involving larger dimensions and powers when observed from a natural vector space viewpoint. The fabric of this general Fermat’s theorem structure consists of a well-defined set of vectors associated with <strong> </strong>dimensional vector spaces and the Minkowski norms one can define there. Here, a special vector set is studied and named a Fermat surface. Besides, a connection between Fermat surfaces and hypercubes is unveiled.</p>

Micro- and Macroevolution: A Continuum or Two Distinct Types of Change?

How microevolution and macroevolution are related is one of the major unanswered questions in evolutionary biology. The most prevalent view is that microevolution and macroevolution are part of a continuum of one type of change and that macroevolution is the cumulative result of microevolution. Mathematics, however, distinguishes two fundamentally different, singular types of change: change of a vector in its parameters versus its dimensions. This mathematical distinction may help to articulate the concept of evolution by distinction of two fundamentally different types of evolution: the change of the state vector of an organism in 1) its parameters (= ‘first-order evolution’) and 2) its dimensions (= ‘second-order evolution’). This distinction can be operationalized by identifying genes and regulatory elements in the nucleotide code of an organism as dimensions and the level of expression as parameters of its state vector. This operationalization allows us to substitute the phenotype-based analysis of evolution with a genotype-based analysis and draws attention to the molecular mechanisms that change the parameters or the dimensions of the state vector, respectively. We illustrate the distinction between first- and second-order evolution with a simulation of the adaptive dynamics of a population of digital amoebae. Our genotype-based systems approach reveals that micro- and macroevolution are largely similar to first- and second-order evolution respectively, and are not a continuum of change.

Fast quadratic model predictive control based on sensitivity analysis and Wolfe method

AbstractThis paper proposes a new algorithm based on sensitivity analysis and the Wolfe method to solve a sequence of parametric quadratic programming (QP) problems such as those that arise in quadratic model predictive control (QMPC). The Wolfe method, based on Karush–Kuhn–Tucker conditions, has been used to convert parametric QP problems to parametric linear programming (LP) problems, and then the sensitivity analysis is applied to solve the sequence of the parametric LP problems. This strategy obtains sensitivity analysis‐based QMPC (SA‐QMPC) algorithm. It is proved that the computational complexity of SA‐QMPC is for a region of the initial conditions and for sufficiently small sampling time and all initial conditions, where and are the horizon time and dimension of the state vector, respectively. Numerical results indicate the potential and properties of the proposed algorithm.

Controllability and observability of conformable fractional finite dimensional linear systems

In this research paper, we investigate the controllability and observability of continuous-time fractional dynamical systems. The characterisation of all fractional continuous one-parameter semi groups on a finite dimensional vector space as fractional matrix-valued exponential functions is given. This characterisation is used to express the solution of continuous-time fractional dynamical system. Furthermore, we analyse controllability and observability of linear conformable fractional systems in the mathematical context of linear operators on a finite dimensional vector space. By defining the controllability and observability maps, we establish necessary and sufficient conditions for controllability and observability of this type of systems. We also present the Hautus test for controllability and observability, and introduce controllability and observability Gramians, both for finite and infinite time interval. Finally, we present several illustrative applications and examples to validate all the obtained results.

Network-based System of Mechanical Vibration Fault Diagnosis

Nowadays researchers are investing in electrical machines fault diagnosis area. The users and manufacturers are strong for containing diagnostic features for reliability and scalability improvement. The regular monitoring enables machine faults early detection and hence helpful for automation by providing process control. The fault detection performance and machine-learning algorithms classification are highly dependent on features involved. The aim of this paper is to solve the network mechanical vibration problem and for that a research on mechanical vibration fault diagnosis is proposed. The first is to use the vibration signal receiving device to record the vibration signal of the target device. In the process of receiving the signal, the measurement point is related to the accuracy of the received signal, so it is necessary to prepare the measurement point. Secondly, the principle of fault detection based on vibration detection is introduced. The main purpose of this method is to identify the fault characteristics, simulate the fault with MATLAB, and obtain the error time-frequency diagram behavior. The feature vector dimension obtained by the idling confirmation example is the same as that of the rotor, which is 14, including 8 relative wavelet packet intensity entropy feature indexes and higher values, minimum value, peak-to-peak value, mean value, mean square error and variance. Finally, the deficiencies of the detected vibration faults are identified and similar improvements are proposed. Improvements only reduce signal vibration, disrupting feature isolation and identifying patterns.The observed percentage accuracy for classification of faults through proposed approach is 98.2%.

Distance Functions in Some Class of Infinite Dimensional Vector Spaces

Distance Functions in Some Class of Infinite Dimensional Vector Spaces

A muti-modal feature fusion method based on deep learning for predicting immunotherapy response

Immune checkpoint therapy (ICT) has greatly improved the survival of cancer patients in the past few years, but only a small number of patients respond to ICT. To predict ICT response, we developed a multi-modal feature fusion model based on deep learning (MFMDL). This model utilizes graph neural networks to map gene-gene relationships in gene networks to low dimensional vector spaces, and then fuses biological pathway features and immune cell infiltration features to make robust predictions of ICT. We used five datasets to validate the predictive performance of the MFMDL. These five datasets span multiple types of cancer, including melanoma, lung cancer, and gastric cancer. We found that the prediction performance of multi-modal feature fusion model based on deep learning is superior to other traditional ICT biomarkers, such as ICT targets or tumor microenvironment-associated markers. In addition, we also conducted ablation experiments to demonstrate the necessity of fusing different modal features, which can improve the prediction accuracy of the model.

Algorithm for ocean surface pollution detection based on the results of video surveillance image processing

The problems of timely detection of environmental disturbances caused by the consequences of various man-made disasters on land and on the water surface of water areas of seas and oceans are based on imperfect methods of control and monitoring of large spaces. Therefore, it is relevant to search for approaches for learning procedures used in the construction of monitoring systems. The aim of article to consider approaches to the formation of feature spaces based on the processing of multiple-scale distributions of signals from drone cameras and the application of discrete series of continuous-time wavelets. An approach to the formalization of the recognition task is proposed. The results of using discrete series of continuous-time wavelets are presented, which allows obtaining a result similar to the use of a multi-dimensional filter bank loaded on integrators. Results of a practical experiment are presented, which showed that increasing the dimensionality of feature vectors reduces their contrast. The directions of further research are formed. The presented results open new possibilities for realization of recognition systems at the software level.

A Framework for Unsupervised Profiling of Malaria Vectors' Insecticide Resistance Using Machine Learning Technique.

Background: There is a need to identify different insecticide resistance profiles that represent circumscription-encapsulation of knowledge about malaria vectors' insecticide resistance to increase our understanding of malaria vectors' insecticide resistance dynamics. Methods: Data used in this study are part of the aggregation of over 20,000 mosquito collections done between 1957 and 2018. We applied two data preprocessing steps. We developed three clustering machine learning models based on the K-means algorithm with three selected datasets. The elbow method was used to fine-tune the hyperparameters. We used the silhouette score to assess the clustering results produced by each of the three models. The proposed framework incorporates continuous learning, allowing the machine learning models to learn continuously. Results: For the first model, the optimal number of clusters (profiles) k was 17. For the second model, we found four profiles. For the third model, the optimal number of profiles was 7. Discussion: We found that the insecticide resistance profiles have dynamic resistance levels with respect to the insecticide component, species component, location component, and time component. This profiling task provided knowledge about the evolution of malaria vectors' insecticide resistance in the African continent by encapsulating the information on the complex interaction between the different dimensions of malaria vectors' insecticide resistance into different profiles. Policy makers can use the knowledge about the different profiles found from the analysis of available insecticide resistance monitoring data (through profiling) by using our proposed approach to set up malaria vector control strategies that consider the locations, species present in those locations, and potentially efficient insecticides.

130 Developing a Conceptual Data Model for Nursing Workload

OBJECTIVES/GOALS: Nurses are leaving the profession at an alarming rate due to increased workload and burnout.#_msocom_1 Computational models that are reliable and reproducible are needed to quantitatively examine nursing workload and estimate potential effect of interventions. This project developed a logical data model to represent nursing EHR interactions. METHODS/STUDY POPULATION: With nursing EHR interactions as a starting point, we expand upon literature that examined the EHR workload of physicians. We conducted an exploratory analysis of nursing EHR audit log data at a large academic medical center, and explored components of nursing workload that can be extracted from other health system data. Using concepts derived from the studying temporal biomedical data patterns, we formulated a data structure that describes nurse EHR interactions, nurse intrinsic and situational characteristics, and nurse outcomes of interest in a scalable and extensible manner. RESULTS/ANTICIPATED RESULTS: Temporal machine learning models are grounded in the concept of vectors. We developed a logical data model that describes tasks performed by nurses (NTask), nurse types (NType), and nursing outcomes (NOutcome). For each nurse (k), we define a function <NTask (k, i)>, i=1 to N as a vector of dimension N, where N is the number of time periods in the study. The i component corresponds to the activity that the nurse is doing. The model will allow the quantitative classification of activity patterns for any finite number of nurses for an arbitrary set of tasks and for time at any specified resolution. The expected outcome is a set of vectors that can then be utilized to quantitatively model nurse activity trajectories and other patterns of nurse EHR interactions. DISCUSSION/SIGNIFICANCE: By instantiating the logical data model, we will demonstrate how nurse EHR interactions can be studied using temporal unsupervised learning and state-of-the-art artificial intelligence methods. We plan to simulate the potential impact of workload interventions and predict risk for nurse burnout.