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Osteoarthritis is a degenerative condition affecting bones and cartilage, often leading to osteophyte formation, bone density loss, and joint space narrowing. Treatment options to restore normal joint function vary depending on the severity of the condition. This work introduces an innovative deep-learning framework processing shoulder CT scans. It features the semantic segmentation of the proximal humerus and scapula, the 3D reconstruction of bone surfaces, the identification of the glenohumeral (GH) joint region, and the staging of three common osteoarthritic-related pathologies: osteophyte formation (OS), GH space reduction (JS), and humeroscapular alignment (HSA). The pipeline comprises two cascaded CNN architectures: 3D CEL-UNet for segmentation and 3D Arthro-Net for threefold classification. A retrospective dataset of 571 CT scans featuring patients with various degrees of GH osteoarthritic-related pathologies was used to train, validate, and test the pipeline. Root mean squared error and Hausdorff distance median values for 3D reconstruction were 0.22mm and 1.48mm for the humerus and 0.24mm and 1.48mm for the scapula, outperforming state-of-the-art architectures and making it potentially suitable for a PSI-based shoulder arthroplasty preoperative plan context. The classification accuracy for OS, JS, and HSA consistently reached around 90% across all three categories. The computational time for the inference pipeline was less than 15s, showcasing the framework's efficiency and compatibility with orthopedic radiology practice. The outcomes represent a promising advancement toward the medical translation of artificial intelligence tools. This progress aims to streamline the preoperative planning pipeline delivering high-quality bone surfaces and supporting surgeons in selecting the most suitable surgical approach according to the unique patient joint conditions.

In the most common literature about fractional calculus, we find that $_{a}D_{t}^{\alpha }f\left( t\right) =\,_{a}I_{t}^{-\alpha }f\left( t\right) $ is assumed implicitly in the tables of fractional integrals and derivatives. However, this is not straightforward from the definitions of $_{a}I_{t}^{\alpha }f\left( t\right) $ and $_{a}D_{t}^{\alpha }f\left( t\right) $. In this sense, we prove that $_{0}D_{t}^{\alpha }f\left( t\right) =\,_{0}I_{t}^{-\alpha }f\left( t\right) $ is true for $f\left( t\right) =t^{\nu -1}\log t$, and $f\left( t\right) =e^{\lambda t}$, despite the fact that these derivations are highly non-trivial. Moreover, the corresponding formulas for $_{-\infty }D_{t}^{\alpha }\left\vert t\right\vert ^{-\delta }$ and $_{-\infty }I_{t}^{\alpha }\left\vert t\right\vert ^{-\delta }$ found in the literature are incorrect; thus, we derive the correct ones, proving in turn that $_{-\infty }D_{t}^{\alpha }\left\vert t\right\vert ^{-\delta }=\,_{-\infty }I_{t}^{-\alpha }\left\vert t\right\vert ^{-\delta }$ holds true, Comment: 17 pages

In the framework of the theory of linear viscoelasticity, we derive an analytical expression of the relaxation modulus in the Andrade model $G_{\alpha }\left( t\right) $ for the case of rational parameter \mbox{$\alpha =m/n\in (0,1)$} in terms of Mittag--Leffler functions from its Laplace transform $\tilde{G}_{\alpha }\left( s\right) $. It turns out that the expression obtained can be rewritten in terms of Rabotnov functions. Moreover, for the original parameter $\alpha =1/3$ in the Andrade model, we obtain an expression in terms of Miller-Ross functions. The asymptotic behaviours of $G_{\alpha }\left( t\right) $ for $t\rightarrow 0^{+}$ and $t\rightarrow +\infty $ are also derived applying the Tauberian theorem. The analytical results obtained have been numerically checked by solving the Volterra integral equation satisfied by $G_{\alpha }\left( t\right) $ by using a successive approximation approach, as well as computing the inverse Laplace transform of $\tilde{G}_{\alpha }\left( s\right) $ by using Talbot's method.

The formal term-by-term differentiation with respect to parameters is demonstrated to be legitimate for the Mittag-Leffler type functions. The justification of differentiation formulas is made by using the concept of the uniform convergence. This approach is applied to the Mittag-Leffler function depending on two parameters and, additionally, for the 3-parametric Mittag-Leffler functions (namely, for the Prabhakar function and the Le Roy type functions), as well as for the 4-parametric Mittag-Leffler function (and, in particular, for theWright function). The differentiation with respect to the involved parameters is discussed also in case those special functions which are represented via the Mellin-Barnes integrals., Comment: 15 pages

Pancreas segmentation has been traditionally challenging due to its small size in computed tomography abdominal volumes, high variability of shape and positions among patients, and blurred boundaries due to low contrast between the pancreas and surrounding organs. Many deep learning models for pancreas segmentation have been proposed in the past few years. We present a thorough systematic review based on the Preferred Reporting Items for Systematic Reviews and Meta-analyses (PRISMA) statement. The literature search was conducted on PubMed, Web of Science, Scopus, and IEEE Xplore on original studies published in peer-reviewed journals from 2013 to 2023. Overall, 130 studies were retrieved. We initially provided an overview of the technical background of the most common network architectures and publicly available datasets. Then, the analysis of the studies combining visual presentation in tabular form and text description was reported. The tables grouped the studies specifying the application, dataset size, design (model architecture, learning strategy, and loss function), results, and main contributions. We first analyzed the studies focusing on parenchyma segmentation using coarse-to-fine approaches, multi-organ segmentation, semi-supervised learning, and unsupervised learning, followed by those studies on generalization to other datasets and those concerning the design of new loss functions. Then, we analyzed the studies on segmentation of tumors, cysts, and inflammation reporting multi-stage methods, semi-supervised learning, generalization to other datasets, and design of new loss functions. Finally, we provided a critical discussion on the subject based on the published evidence underlining current issues that need to be addressed before clinical translation.

Modular soft robots have shown higher potential in sophisticated tasks than single-module robots. However, the modular structure incurs the complexity of accurate control and necessitates a control strategy specifically for modular robots. In this paper, we introduce a data collection strategy and a novel and accurate bidirectional LSTM configuration controller for modular soft robots with module number adaptability. Such a controller can control module configurations in robots with different module numbers. Simulation cable-driven robots and real pneumatic robots have been included in experiments to validate the proposed approaches, and we have proven that our controller can be leveraged even with the increase or decrease of module number. This is the first paper that gets inspiration from the physical structure of modular robots and utilizes bidirectional LSTM for module number adaptability. Future work may include a planning method that bridges the task and configuration spaces and the integration of an online controller., Comment: 10 figures, 4 tables

A well-ordering principle is a principle of the form: If $X$ is well-ordered then $F(X)$ is well-ordered, where $F$ is some natural operator transforming linear orders into linear orders. Many important subsystems of Second-order Arithmetic of interest in Reverse Mathematics are known to be equivalent to well-ordering principles. We give a unified treatment for proving lower bounds on the logical strength of various Ramsey-theoretic principles relations using characterizations of the corresponding formal systems in terms of well-ordering principles. Our implications (over $RCA_0$) from combinatorial theorems to $ACA_0$ and $ACA_0^+$ also establish uniform computable reductions of the corresponding well-ordering principles to the corresponding Ramsey-type theorems.

Soft robots have been leveraged in considerable areas like surgery, rehabilitation, and bionics due to their softness, flexibility, and safety. However, it is challenging to produce two same soft robots even with the same mold and manufacturing process owing to the complexity of soft materials. Meanwhile, widespread usage of a system requires the ability to replace inner components without highly affecting system performance, which is interchangeability. Due to the necessity of this property, a hybrid adaptive controller is introduced to achieve interchangeability from the perspective of control approaches. This method utilizes an offline-trained recurrent neural network controller to cope with the nonlinear and delayed response from soft robots. Furthermore, an online optimizing kinematics controller is applied to decrease the error caused by the above neural network controller. Soft pneumatic robots with different deformation properties but the same mold have been included for validation experiments. In the experiments, the systems with different actuation configurations and the different robots follow the desired trajectory with errors of 3.3 +- 2.9% and 4.3 +- 4.1% compared with the working space length, respectively. Such an adaptive controller also shows good performance on different control frequencies and desired velocities. This controller is also compared with a model-based controller in simulation. This controller endows soft robots with the potential for wide application, and future work may include different offline and online controllers. A weight parameter adjusting strategy may also be proposed in the future., Comment: accepted by IEEE Robotics and Automation Letters

The purpose of this note is to propose an application of the Lambert W function in linear viscoelasticity based on the Bernstein and Stieltjes properties of this function. In particular we recognize the role of the main branch W_0(t) in a peculiar model of creep with two spectral functions in frequency that completely characterize the creep model. In order to calculate these spectral functions, it turns out that the conjugate symmetry property of the Lambert W function along its branch cut on the negative real axis is essential. We supplement our analysis by computing the corresponding relaxation function and providing the plots of all computed functions., Comment: 22 pages, 9 figures

A generalization of the canonical coherent states of a quantum harmonic oscillator has been performed by requiring the conditions of normalizability, continuity in the label and resolution of the identity operator with a positive weight function. Relying on this approach, in the present scenario coherent states are generalized over the canonical or finite dimensional Fock space of the harmonic oscillator. A class of generalized coherent states is determined such that the distribution of the number of excitations departs from the Poisson statistics according to combinations of stretched exponential decays, power laws and logarithmic forms. The analysis of the Mandel parameter shows that these generalized coherent states exhibit (non-classical) sub-Poissonian or super-Poissonian statistics of the number of excitations for small values of the label, according to determined properties. The statistics is uniquely sub-Poissonian for large values of the label. As particular cases, truncated Wright generalized coherent states exhibit uniquely non-classical properties, differently from the truncated Mittag-Leffler generalized coherent states., Comment: 18 pages, 8 figures

When the Canonical Ramsey's Theorem by Erd\H{o}s and Rado is applied to regressive functions one obtains the Regressive Ramsey's Theorem by Kanamori and McAloon. Taylor proved a "canonical" version of Hindman's Theorem, analogous to the Canonical Ramsey's Theorem. We introduce the restriction of Taylor's Canonical Hindman's Theorem to a subclass of the regressive functions, the $\lambda$-regressive functions, relative to an adequate version of min-homogeneity and prove some results about the Reverse Mathematics of this Regressive Hindman's Theorem and of natural restrictions of it. In particular we prove that the first non-trivial restriction of the principle is equivalent to Arithmetical Comprehension. We furthermore prove that this same principle strongly computably reduces the well-ordering-preservation principle for base-$\omega$ exponentiation., Comment: Corrected proofs of Proposition 2. Added Theorem 2

The important consequence of the Kramers-Kronig relations (KKrs) is that dissipative behavior in material media inevitably implies the existence of dispersion, i.e., a frequency dependence in the constitutive equations. Basically, the relations are the frequency-domain expression of causality and correspond mathematically to pairs of Hilbert transforms. The relations have many forms and can be obtained with diverse mathematical tools. Here, two different demonstrations are given in the electromagnetic case, illustrating the eclectic mathematical apparatus available for this purpose. Then, we apply the acoustic (mechanical)-electromagnetic analogy to obtain the elastic versions. Finally, we discuss the concepts of stability and passivity and provide a novel algorithm to compute the relations numerically by using the fast Fourier transform., Comment: 13 pages, 1 figure

We consider the time-fractional Cattaneo equation involving the tempered Caputo space-fractional derivative. We find the characteristic function of the related process and we explain the main differences with previous stochastic treatments of the time-fractional Cattaneo equation., Comment: 11 pages

In this paper we consider a modified fractional Maxwell model based on the application of Hadamard-type fractional derivatives. The model is physically motivated by the fact that we can take into account at the same time memory effects and the time-dependence of the viscosity coefficient. We obtain an ultra-slow relaxation response whose explicit analytic form is given by the Mittag-Leffler function with a logarithmic argument. We show graphically the main properties of this relaxation response, also with the asymptotic behaviour., Comment: 10 pages, 3 figures