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Abstract Chronic obstructive pulmonary disease (COPD) is one of the leading causes of death worldwide. Current COPD diagnosis (i.e., spirometry) could be unreliable because the test depends on an adequate effort from the tester and testee. Moreover, the early diagnosis of COPD is challenging. The authors address COPD detection by constructing two novel physiological signals datasets (4432 records from 54 patients in the WestRo COPD dataset and 13824 medical records from 534 patients in the WestRo Porti COPD dataset). The authors demonstrate their complex coupled fractal dynamical characteristics and perform a fractional‐order dynamics deep learning analysis to diagnose COPD. The authors found that the fractional‐order dynamical modeling can extract distinguishing signatures from the physiological signals across patients with all COPD stages—from stage 0 (healthy) to stage 4 (very severe). They use the fractional signatures to develop and train a deep neural network that predicts COPD stages based on the input features (such as thorax breathing effort, respiratory rate, or oxygen saturation). The authors show that the fractional dynamic deep learning model (FDDLM) achieves a COPD prediction accuracy of 98.66% and can serve as a robust alternative to spirometry. The FDDLM also has high accuracy when validated on a dataset with different physiological signals. 

Epilepsy affects approximately 50 million people worldwide. Despite its prevalence, the recurrence of seizures can be mitigated only 70% of the time through medication. Furthermore, surgery success rates range from 30% - 70% because of our limited understanding of how a seizure starts. However, one leading hypothesis suggests that a seizure starts because of a critical transition due to an instability. Unfortunately, we lack a meaningful way to quantify this notion that would allow physicians to not only better predict seizures but also to mitigate them. Hence, in this paper, we develop a method to not only characterize the instability of seizures but also to leverage these conditions to stabilize the system underlying these seizures. Remarkably, evidence suggests that such critical transitions are associated with long-term memory dynamics, which can be captured by considering linear fractional-order systems. Subsequently, we provide for the first time tractable necessary and sufficient conditions for the global asymptotic stability of discrete-time linear fractional-order systems. Next, we propose a method to obtain a stabilizing control strategy for these systems using linear matrix inequalities. Finally, we apply our methodology to a real-world epileptic patient dataset to provide insight into mitigating epilepsy and designing future cyber-neural systems. 

The gap between chronological age (CA) and biological brain age, as estimated from magnetic resonance images (MRIs), reflects how individual patterns of neuroanatomic aging deviate from their typical trajectories. MRI-derived brain age (BA) estimates are often obtained using deep learning models that may perform relatively poorly on new data or that lack neuroanatomic interpretability. This study introduces a convolutional neural network (CNN) to estimate BA after training on the MRIs of 4,681 cognitively normal (CN) participants and testing on 1,170 CN participants from an independent sample. BA estimation errors are notably lower than those of previous studies. At both individual and cohort levels, the CNN provides detailed anatomic maps of brain aging patterns that reveal sex dimorphisms and neurocognitive trajectories in adults with mild cognitive impairment (MCI, N  = 351) and Alzheimer’s disease (AD, N  = 359). In individuals with MCI (54% of whom were diagnosed with dementia within 10.9 y from MRI acquisition), BA is significantly better than CA in capturing dementia symptom severity, functional disability, and executive function. Profiles of sex dimorphism and lateralization in brain aging also map onto patterns of neuroanatomic change that reflect cognitive decline. Significant associations between BA and neurocognitive measures suggest that the proposed framework can map, systematically, the relationship between aging-related neuroanatomy changes in CN individuals and in participants with MCI or AD. Early identification of such neuroanatomy changes can help to screen individuals according to their AD risk. 

Finding strongly connected components (SCCs) and the diameter of a directed network play a key role in a variety of discrete optimization problems, and subsequently, machine learning and control theory problems. On the one hand, SCCs are used in solving the 2-satisfiability problem, which has applications in clustering, scheduling, and visualization. On the other hand, the diameter has applications in network learning and discovery problems enabling efficient internet routing and searches, as well as identifying faults in the power grid. In this paper, we leverage consensus-based principles to find the SCCs in a scalable and distributed fashion with a computational complexity of O(Ddmaxin−degree) , where D is the (finite) diameter of the network and dmaxin−degree is the maximum in-degree of the network. Additionally, we prove that our algorithm terminates in D+1 iterations, which allows us to retrieve the diameter of the network. We illustrate the performance of our algorithm on several random networks, including Erdö-Rényi, Barabási-Albert, and Watts-Strogatz networks. 

Assessing the stability of biological system models has aided in uncovering a plethora of new insights in genetics, neuroscience, and medicine. In this paper, we focus on analyzing the stability of neurological signals, including electroencephalogram (EEG) signals. Interestingly, spatiotemporal discrete-time linear fractional-order systems (DTLFOS) have been shown to accurately and efficiently represent a variety of neurological and physiological signals. Here, we leverage the conditions for stability of DTLFOS to assess a real-world EEG data set. By analyzing the stability of EEG signals during movement and rest tasks, we provide evidence of the usefulness of the quantification of stability as a bio-marker for cognitive motor control. 

Abstract Network theory helps us understand, analyze, model, and design various complex systems. Complex networks encode the complex topology and structural interactions of various systems in nature. To mine the multiscale coupling, heterogeneity, and complexity of natural and technological systems, we need expressive and rigorous mathematical tools that can help us understand the growth, topology, dynamics, multiscale structures, and functionalities of complex networks and their interrelationships. Towards this end, we construct the node-based fractal dimension (NFD) and the node-based multifractal analysis (NMFA) framework to reveal the generating rules and quantify the scale-dependent topology and multifractal features of a dynamic complex network. We propose novel indicators for measuring the degree of complexity, heterogeneity, and asymmetry of network structures, as well as the structure distance between networks. This formalism provides new insights on learning the energy and phase transitions in the networked systems and can help us understand the multiple generating mechanisms governing the network evolution. 

Solving optimization problems is a recurrent theme across different fields, including large-scale machine learning systems and deep learning. Often in practical applications, we encounter objective functions where the Hessian is ill-conditioned, which precludes us from using optimization algorithms utilizing second-order information. In this paper, we propose to use fractional time series analysis methods that have successfully been used to model neurophysiological processes in order to circumvent this issue. In particular, the long memory property of fractional time series exhibiting non-exponential power-law decay of trajectories seems to model behavior associated with the local curvature of the objective function at a given point. Specifically, we propose a NEuro-inspired Optimization (NEO) method that leverages this behavior, which contrasts with the short memory characteristics of currently used methods (e.g., gradient descent and heavy-ball). We provide evidence of the efficacy of the proposed method on a wide variety of settings implicitly found in practice. 

Abstract Recent advances in network science, control theory, and fractional calculus provide us with mathematical tools necessary for modeling and controlling complex dynamical networks (CDNs) that exhibit long-term memory. Selecting the minimum number of driven nodes such that the network is steered to a prescribed state is a key problem to guarantee that complex networks have a desirable behavior. Therefore, in this paper, we study the effects of long-term memory and of the topological properties on the minimum number of driven nodes and the required control energy. To this end, we introduce Gramian-based methods for optimal driven node selection for complex dynamical networks with long-term memory and by leveraging the structure of the cost function, we design a greedy algorithm to obtain near-optimal approximations in a computationally efficiently manner. We investigate how the memory and topological properties influence the control effort by considering Erdős–Rényi, Barabási–Albert and Watts–Strogatz networks whose temporal dynamics follow a fractional order state equation. We provide evidence that scale-free and small-world networks are easier to control in terms of both the number of required actuators and the average control energy. Additionally, we show how our method could be applied to control complex networks originating from the human brain and we discover that certain brain cortex regions have a stronger impact on the controllability of network than others.