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Markerless motion capture offers several benefits over traditional marker-based systems by eliminating the need for physical markers, which are prone to misplacement and artifacts. Utilizing computer vision and deep learning algorithms, markerless systems can directly detect human body landmarks, reducing manual processing and errors associated with marker placement. These systems are adaptable, able to track user-defined features, and practical for real-world applications using consumer-grade devices such as smartphone cameras. This study compares the performance of OpenCap, a markerless motion capture system, with traditional marker-based systems in assessing cycling biomechanics. Ten healthy adults participated in experiments to capture sagittal hip, knee, and ankle kinematics and dynamics using both methods. OpenCap used videos from smartphones and integrated computer vision and musculoskeletal simulations to estimate 3D kinematics. Results showed high agreement between the two systems, with no significant differences in kinematic and kinetic measurements for the hip, knee, and ankle. The correlation coefficients exceeded 0.98, indicating very strong consistency. Errors were minimal, with kinematic errors under 4 degrees and kinetic errors below 5 Nm. This study concludes that OpenCap is a viable alternative to marker-based motion capture, offering comparable precision without extensive setup for hip (flexion/extension), knee (flexion/extension), and ankle (dorsiflexion/plantarflexion) joints. Future work should aim to enhance the accuracy of ankle joint measurements and extend analyses to 3D kinematics and kinetics for comprehensive biomechanical assessments.

Simulation studies, such as finite element (FE) modeling, offer insights into knee joint biomechanics, which may not be achieved through experimental methods without direct involvement of patients. While generic FE models have been used to predict tissue biomechanics, they overlook variations in population-specific geometry, loading, and material properties. In contrast, subject-specific models account for these factors, delivering enhanced predictive precision but requiring significant effort and time for development. This study aimed to facilitate subject-specific knee joint FE modeling by integrating an automated cartilage segmentation algorithm using a 3D Swin UNETR. This algorithm provided initial segmentation of knee cartilage, followed by automated geometry filtering to refine surface roughness and continuity. In addition to the standard metrics of image segmentation performance, such as Dice similarity coefficient (DSC) and Hausdorff distance, the method's effectiveness was also assessed in FE simulation. Nine pairs of knee cartilage FE models, using manual and automated segmentation methods, were developed to compare the predicted stress and strain responses during gait. The automated segmentation achieved high Dice similarity coefficients of 89.4% for femoral and 85.1% for tibial cartilage, with a Hausdorff distance of 2.3 mm between the automated and manual segmentation. Mechanical results including maximum principal stress and strain, fluid pressure, fibril strain, and contact area showed no significant differences between the manual and automated FE models. These findings demonstrate the effectiveness of the proposed automated segmentation method in creating accurate knee joint FE models., Comment: arXiv admin note: substantial text overlap with arXiv:2312.00169

Simulation studies like finite element (FE) modeling provide insight into knee joint mechanics without patient experimentation. Generic FE models represent biomechanical behavior of the tissue by overlooking variations in geometry, loading, and material properties of a population. On the other hand, subject-specific models include these specifics, resulting in enhanced predictive precision. However, creating such models is laborious and time-intensive. The present study aimed to enhance subject-specific knee joint FE modeling by incorporating a semi-automated segmentation algorithm. This segmentation was a 3D Swin UNETR for an initial segmentation of the femur and tibia, followed by a statistical shape model (SSM) adjustment to improve surface roughness and continuity. Five hundred and seven magnetic resonance images (MRIs) from the Osteoarthritis Initiative (OAI) database were used to build and validate the segmentation model. A semi-automated FE model was developed using this semi-automated segmentation. On the other hand, a manual FE model was developed through manual segmentation (i.e., the gold standard approach). Both FE models were subjected to gait loading. The predicted mechanical response of manual and semi-automated FE models were compared. In the result, our semi-automated segmentation achieved Dice similarity coefficient (DSC) over 98% for both femur and tibia. The mechanical results (max principal stress, max principal strain, fluid pressure, fibril strain, and contact area) showed no significant differences between the manual and semi-automated FE models, indicating the effectiveness of the proposed semi-automated segmentation in creating accurate knee joint FE models. ( https://data.mendeley.com/datasets/k5hdc9cz7w/1 ).

This paper presents a multi-agent Deep Reinforcement Learning (DRL) framework for autonomous control and integration of renewable energy resources into smart power grid systems. In particular, the proposed framework jointly considers demand response (DR) and distributed energy management (DEM) for residential end-users. DR has a widely recognized potential for improving power grid stability and reliability, while at the same time reducing end-users energy bills. However, the conventional DR techniques come with several shortcomings, such as the inability to handle operational uncertainties while incurring end-user disutility, which prevents widespread adoption in real-world applications. The proposed framework addresses these shortcomings by implementing DR and DEM based on real-time pricing strategy that is achieved using deep reinforcement learning. Furthermore, this framework enables the power grid service provider to leverage distributed energy resources (i.e., PV rooftop panels and battery storage) as dispatchable assets to support the smart grid during peak hours, thus achieving management of distributed energy resources. Simulation results based on the Deep Q-Network (DQN) demonstrate significant improvements of the 24-hour accumulative profit for both prosumers and the power grid service provider, as well as major reductions in the utilization of the power grid reserve generators., Comment: 16 pages, 10 figures

Controlled frames which presented to improve the numerical output of iterative algorithms for inverting the frame operator, have been introduced by Balazs and et al. Also, these frames are used by Bogdanova and et al. for spherical wavelets. In this note, we aim to study some new results about controlled fusion frames and behavior of them under erasures. Finally, we will introduce the approximation operator for these frames and a result of the composition of the operators of two controlled fusion frames will be proved.

This paper presents a Reinforcement Learning (RL) based energy market for a prosumer dominated microgrid. The proposed market model facilitates a real-time and demanddependent dynamic pricing environment, which reduces grid costs and improves the economic benefits for prosumers. Furthermore, this market model enables the grid operator to leverage prosumers storage capacity as a dispatchable asset for grid support applications. Simulation results based on the Deep QNetwork (DQN) framework demonstrate significant improvements of the 24-hour accumulative profit for both prosumers and the grid operator, as well as major reductions in grid reserve power utilization.

Demand Response (DR) has a widely recognized potential for improving grid stability and reliability while reducing customers energy bills. However, the conventional DR techniques come with several shortcomings, such as inability to handle operational uncertainties and incurring customer disutility, impeding their wide spread adoption in real-world applications. This paper proposes a new multiagent Reinforcement Learning (RL) based decision-making environment for implementing a Real-Time Pricing (RTP) DR technique in a prosumer dominated microgrid. The proposed technique addresses several shortcomings common to traditional DR methods and provides significant economic benefits to the grid operator and prosumers. To show its better efficacy, the proposed DR method is compared to a baseline traditional operation scenario in a small-scale microgrid system. Finally, investigations on the use of prosumers energy storage capacity in this microgrid highlight the advantages of the proposed method in establishing a balanced market setup.

k-frames were recently introduced by Gavruta in Hilbert spaces to study atomic systems with respect to a bounded linear operator. A continuous frame is a family of vectors in Hilbert space which allows reproductions of arbitrary elements by continuous super positions. We construct a continuous k-frame, so called ck-frame along with an atomic system for this version of frames. Also we introduce a new method for obtaining the dual of a ck-frame and we prove some new results about it.

In this note, we first introduce the notation of weaving cfusion frames in separable Hilbert spaces. After reviewing the conditions for maintaining the weaving c-fusion frames under the bounded linear operator and also, removing vectors from these frames, we will present a necessarily and sufficient condition about c-woven and c-fusion woven. Finally, perturbation of these frames will be introduced.

In this paper, we introduce orthonoramal and Riesz bases for g-fusion frames and will show that the weights have basic roles. Next, we prove an effective theorem between frames and g-fusion frames by using an operator. Finally, perturbations of g-fusion frames will be presented.

Frames for operators or k-frames were recently considered by Gavruta (2012) in connection with atomic systems. Also generalized frames are important frames in the Hilbert space of bounded linear operators. Fusion frames, which are a special case of generalized frames have various applications. This paper introduces the concept of generalized fusion frames for operators aka k-g-fusion frames and we get some results for characterization of these frames. We further discuss on duals and Q-duals in connection with k-g-fusion frames. Also we obtain some useful identities for these frames. We also give several methods to construct k-g-fusion frames. The results of this paper can be used in sampling theory which are developed by g-frames and especially fusion frames. In the end, we discuss the stability of a more general perturbation for k-g-fusion frames.

After introducing g-frames and fusion frames by Sun and Casazza, combining these frames together is an interesting topic for research. In this paper, we introduce the generalized fusion frames or g-fusion frames for Hilbert spaces and give characterizations of these frames from the viewpoint of closed range and g-fusion frame sequences. Also, the canonical dual g-fusion frames are presented and we introduce Parseval g-fusion frames.

G-fusion frames which are obtained from the combination of g-frames and fusion frames were recently introduced for Hilbert spaces. In this paper, we present a new identity for g-frames which was given by Najati in a special case. Also, by using the idea of this identity and their dual frames, some equalities and inequalities will be presented for g-fusion frames.

Controlled frames in Hilbert spaces have been introduced by Balazs, Antoine and Grybos to improve the numerical output of in relation to algorithms for inverting the frame operator. In this paper we have introduced and displayed some new concepts and results on controlled fusion frames for Hilbert spaces. It is shown that controlled fusion frames as a generalization of fusion frames give a generalized way to obtain numerical advantage in the sense of reconditioning to check the fusion frame condition. For this end, we introduce the notion of Q-duality for Controlled fusion frames. Also, we survey the robustness of Controlled fusion frames under some perturbations.

In this paper, we study the problem of finding the Euclidean distance to a convex cone generated by a set of discrete points in $\mathbb{R}^n_+$. In particular, we are interested in problems where the discrete points are the set of feasible solutions of some binary linear programming constraints. This problem has applications in manufacturing, machine learning, clustering, pattern recognition, and statistics. Our problem is a high-dimensional constrained optimization problem. We propose a Frank-Wolfe based algorithm to solve this non-convex optimization problem with a convex-noncompact feasible set. Our approach consists of two major steps: presenting an equivalent convex optimization problem with a non-compact domain, and finding a compact-convex set that includes the iterates of the algorithm. We discuss the convergence property of the proposed approach. Our numerical work shows the effectiveness of this approach., Comment: 9 pages