The C-Nail^® system is a novel intramedullary fixation method for displaced intra-articular calcaneal fractures. The aim of this study was to evaluate the biomechanical performance of the C-Nail^® system and compare it with conventional plate fixation for the treatment of displaced intra-articular calcaneal fractures using finite element analysis. The geometry of a Sanders type-IIB fracture was constructed using the computer-aided design software Ansys SpaceClaim. The C-Nail^® system (Medin, Nové Mesto n. Morave, Czech Republic) and the calcaneal locking plate (Auxein Inc., 35 Doral, Florida) and screws were designed according to the manufacturer specifications. Vertical loading of 350 N and 700 N were applied to the subtalar joint surfaces to simulate partial weight bearing and full weight bearing. Construct stiffness, total deformation, and von Mises stress were assessed. The maximum stress on the C-Nail^® system was lower compared with the plate (110 MPa vs. 360 MPa). At the bone level the stress was found to have higher values in the case of the plate compared to the C-Nail^® system. The study suggests that the C-Nail^® system can provide sufficient stability, making it a viable option for the treatment of displaced intra-articular calcaneal fractures.

In this paper we are addressing two main topics, as follows. First, a rigorous qualitative study is elaborated for a second-order parabolic problem, equipped with nonlinear anisotropic diffusion and cubic nonlinear reaction, as well as non-homogeneous Cauchy-Neumann boundary conditions. Under certain assumptions on the input data: $f(t,x)$, $w(t,x)$ and $v_0\left(x\right)$, we prove the well-posedness (the existence, a priori estimates, regularity, uniqueness) of a solution in the Sobolev space $W_p^{1,2}\left(Q\right)$, facilitating for the present model to be a more complete description of certain classes of physical phenomena. The second topic refers to the construction of two numerical schemes in order to approximate the solution of a particular mathematical model (local and nonlocal case). To illustrate the effectiveness of the new mathematical model, we present some numerical experiments by applying the model to image segmentation tasks.

In our current paper we are introducing a new method to enhance semantic image segmentation accuracy of a U-Net neural network model by integrating it with a mathematical model based on reaction-diffusion equations. The methods currently used for semantic image segmentation, including U-Net neural networks, are processing images as blocks of pixels in which the boundaries, the colors and patterns are all mixed together as inputs to the transformations that take place inside the layers of the convolutional neural networks. In our method we are modifying the architecture of a U-Net network and introduce a new data input feed in parallel to the image feed that needs to be segmented. The new input feed is mathematically extracted from the input image and contains the edges (shape) information of the image to be processed. The new input feed it's used during the U-Net decoding phase in order to help shape more precisely the up-scaled output edges, thus leading to improved accuracy performance of the network. Introducing the parallel feed shows an improvement of accuracy metrics up to 4% (if compared to the U-Net model) and has a limited impact on computational resources consumed at training, because we are only adding a small number of new parameters to be calculated.

Innovation ecosystems often face challenges such as inadequate coordination, insufficient protection of intellectual property, limited access to quality expertise, and inefficient matchmaking between innovators and experts. This paper provides an in-depth design analysis of SPARK-IT, a novel business innovation platform specifically addressing these challenges. The platform leverages advanced AI to precisely match innovators with suitable mentors, supported by a distributed web scraper that constructs expert profiles from reliable sources (e.g., LinkedIn and BrainMap). Data privacy and security are prioritized through robust encryption that restricts sensitive content exclusively to innovators and mentors, preventing unauthorized access even by platform administrators. Additionally, documents are stored encrypted on decentralized storage, with their cryptographic hashes anchored on blockchain to ensure transparency, traceability, non-repudiation, and immutability. To incentivize active participation, SPARK-IT utilizes a dual-token approach comprising reward and reputation tokens. The reward tokens, SparkCoins, are wrapped stablecoins with tangible monetary value, enabling seamless internal transactions and external exchanges. Finally, the paper discusses key design challenges and critical architectural trade-offs and evaluates the socio-economic impacts of implementing this innovative solution.

The paper concerns a nonlinear second-order system of coupled PDEs, having the principal part in divergence form and subject to in-homogeneous dynamic boundary conditions, for both $\theta (t,x)$ and $\phi (t,x)$. Two main topics are addressed here, as follows. First, under a certain hypothesis on the input data, $f_1$, $f_2$, $w_1$, $w_2$, $\alpha$, $\xi$, ${\theta }_0$, ${\alpha }_0$, ${\phi }_0$, and ${\xi }_0$, we prove the well-posedness of a solution $\theta ,\alpha ,\phi ,\xi$, which is $\left(\theta (t,x),\alpha (t,x)\right)\in W_p^{1,2}\left(Q\right)\times W_p^{1,2}(\Sigma )$, $\left(\phi (t,x),\xi (t,x)\right)\in W_{\nu }^{1,2}\left(Q\right)\times W_p^{1,2}(\Sigma )$, $\nu =min\{q,\mu \}$. According to the new formulation of the problem, we extend the previous results, allowing the new mathematical model to be even more complete to describe the diversity of physical phenomena to which it can be applied: interface problems, image analysis, epidemics, etc. The main goal of the present paper is to develop an iterative scheme of fractional-step type in order to approximate the unique solution to the nonlinear second-order system. The convergence result is established for the new numerical method, and on the basis of this approach, a conceptual algorithm, alg-frac_sec-ord_ u+varphi _dbc, is elaborated. The benefit brought by such a method consists of simplifying the computations so that the time required to approximate the solutions decreases significantly. Some conclusions are given as well as new research topics for the future.

In this paper we propose and compare two methods to optimize the numerical computations for the diffusion term in a nonlocal formulation for a reaction-diffusion equation. The diffusion term is particularly computationally intensive due to the integral formulation, and thus finding a better way of computing its numerical approximation could be of interest, given that the numerical analysis usually takes place on large input domains having more than one dimension. After introducing the general reaction-diffusion model, we discuss a numerical approximation scheme for the diffusion term, based on a finite difference method. In the next sections we propose two algorithms to solve the numerical approximation scheme, focusing on finding a way to improve the time performance. While the first algorithm (sequential) is used as a baseline for performance measurement, the second algorithm (parallel) is implemented using two different memory-sharing parallelization technologies: Open Multi-Processing (OpenMP) and CUDA. All the results were obtained by using the model in image processing applications such as image restoration and segmentation.