Noncommutative Function-Theoretic Operator Theory and Applications

This concise monograph explores how core ideas in Hardy space function theory and operator theory continue to be useful and informative in new settings, leading to new insights for noncommutative multivariable operator theory. Beginning with a review of the confluence of system theory ideas and reproducing kernel techniques, the book then covers representations of backward-shift-invariant subspaces in the Hardy space as ranges of observability operators, and representations for forward-shift-invariant subspaces via a Beurling–Lax representer equal to the transfer function of the linear system. This pair of backward-shift-invariant and forward-shift-invariant subspace form a generalized orthogonal decomposition of the ambient Hardy space. All this leads to the de Branges–Rovnyak model theory and characteristic operator function for a Hilbert space contraction operator. The chapters that follow generalize the system theory and reproducing kernel techniques to enable an extension of the ideas above to weighted Bergman space multivariable settings.

Using Embedded Feature Selection and CNN for Classification on CCD-INID-V1—A New IoT Dataset

As Internet of Things (IoT) networks expand globally with an annual increase of active devices, providing better safeguards to threats is becoming more prominent. An intrusion detection system (IDS) is the most viable solution that mitigates the threats of cyberattacks. Given the many constraints of the ever-changing network environment of IoT devices, an effective yet lightweight IDS is required to detect cyber anomalies and categorize various cyberattacks. Additionally, most publicly available datasets used for research do not reflect the recent network behaviors, nor are they made from IoT networks. To address these issues, in this paper, we have the following contributions: (1) we create a dataset from IoT networks, namely, the Center for Cyber Defense (CCD) IoT Network Intrusion Dataset V1 (CCD-INID-V1); (2) we propose a hybrid lightweight form of IDS—an embedded model (EM) for feature selection and a convolutional neural network (CNN) for attack detection and classification. The proposed method has two models: (a) RCNN: Random Forest (RF) is combined with CNN and (b) XCNN: eXtreme Gradient Boosting (XGBoost) is combined with CNN. RF and XGBoost are the embedded models to reduce less impactful features. (3) We attempt anomaly (binary) classifications and attack-based (multiclass) classifications on CCD-INID-V1 and two other IoT datasets, the detection_of_IoT_botnet_attacks_N_BaIoT dataset (Balot) and the CIRA-CIC-DoHBrw-2020 dataset (DoH20), to explore the effectiveness of these learning-based security models. Using RCNN, we achieved an Area under the Receiver Characteristic Operator (ROC) Curve (AUC) score of 0.956 with a runtime of 32.28 s on CCD-INID-V1, 0.999 with a runtime of 71.46 s on Balot, and 0.986 with a runtime of 35.45 s on DoH20. Using XCNN, we achieved an AUC score of 0.998 with a runtime of 51.38 s for CCD-INID-V1, 0.999 with a runtime of 72.12 s for Balot, and 0.999 with a runtime of 72.91 s for DoH20. Compared to KNN, XCNN required 86.98% less computational time, and RCNN required 91.74% less computational time to achieve equal or better accurate anomaly detections. We find XCNN and RCNN are consistently efficient and handle scalability well; in particular, 1000 times faster than KNN when dealing with a relatively larger dataset-Balot. Finally, we highlight RCNN and XCNN’s ability to accurately detect anomalies with a significant reduction in computational time. This advantage grants flexibility for the IDS placement strategy. Our IDS can be placed at a central server as well as resource-constrained edge devices. Our lightweight IDS requires low train time and hence decreases reaction time to zero-day attacks.

Functional Connectivity Density for Radiation Encephalopathy Prediction in Nasopharyngeal Carcinoma

The diagnostic efficiency of radiation encephalopathy (RE) remains heterogeneous, and prediction of RE is difficult at the pre-symptomatic stage. We aimed to analyze the whole-brain resting-state functional connectivity density (FCD) of individuals with pre-symptomatic RE using multivariate pattern analysis (MVPA) and explore its prediction efficiency. Resting data from NPC patients with nasopharyngeal carcinoma (NPC; consisting of 20 pre-symptomatic RE subjects and 26 non-RE controls) were collected in this study. We used MVPA to classify pre-symptomatic RE subjects from non-RE controls based on FCD maps. Classifier performances were evaluated by accuracy, sensitivity, specificity, and area under the characteristic operator curve. Permutation tests and leave-one-out cross-validation were applied for assessing classifier performance. MVPA was able to differentiate pre-symptomatic RE subjects from non-RE controls using global FCD as a feature, with a total accuracy of 89.13%. The temporal lobe as well as regions involved in the visual processing system, the somatosensory system, and the default mode network (DMN) revealed robust discrimination during classification. Our findings suggest a good classification efficiency of global FCD for the individual prediction of RE at a pre-symptomatic stage. Moreover, the discriminating regions may contribute to the underlying mechanisms of sensory and cognitive disturbances in RE.

Multichannel absorption compensation with a data-driven structural regularization

Seismic absorption compensation is an important processing approach to mitigate the attenuation effects caused by the intrinsic inelasticity of subsurface media and to enhance seismic resolution. However, conventional absorption compensation approaches ignore the spatial connection along seismic traces, which makes the compensation result vulnerable to high-frequency noise amplification, thus reducing the signal-to-noise ratio (S/N) of the result. To alleviate this issue, we have developed a structurally constrained multichannel absorption compensation (SC-MAC) algorithm. In the cost function of this algorithm, we exploit an [Formula: see text] norm to constrain the reflectivity series and an [Formula: see text] norm to regularize the reflection structural characteristic of the compensation data. The reflection structural characteristic operator, extracted from the observed stacked seismic data, is the core of the structural regularization term. We then solve the cost function of SC-MAC by the alternating direction method of multipliers. Benefiting from the introduction of reflection structure constraint, SC-MAC improves the stability of the compensation result and inhibits the amplification of high-frequency noise. Synthetic and field data examples demonstrate that our proposed method is more robust to random noise and can not only improve the resolution of seismic data, but also maintain the S/N of the compensation seismic data.

About the general solution of a linear homogeneous differential equation in a Banach space in the case of complex characteristic operators

A linear inhomogeneous differential equation (LIDE) of the n th order with constant bounded operator coefficients is studied in Banach space. Finding a general solution of LIDE is reduced to the construction of a general solution to the corresponding linear homogeneous differential equation (LHDE). Characteristic operator equation for LHDE is considered in the Banach algebra of complex operators. In the general case, when both real and complex operator roots are among the roots of the characteristic operator equation, the n -parametric family of solutions to LHDE is indicated. Operator functions eAt ; sinBt ; cosBt of real argument t ∈ [0;∞) are used when building this family. The conditions under which this family of solutions form a general solution to LHDE are clarified. In the case when the characteristic operator equation has simple real operator roots and simple pure imaginary operator roots, a specific form of such conditions is indicated. In particular, these roots must commute with LHDE operator coefficients. In addition, they must commute with each other. In proving the corresponding assertion, the Cramer operator-vector rule for solving systems of linear vector equations in a Banach space is applied