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In this paper, we study the well-posedness of state-dependent and state-independent sweeping processes driven by prox-regular sets and perturbed by a history-dependent operator. Our approach, based on an enhanced version of Gronwall's lemma and fixed-point arguments, provides an efficient framework for analyzing sweeping processes. In particular, our findings recover all existing results for the class of Volterra sweeping processes and provide new insights into history-dependent sweeping processes. Finally, we apply our theoretical results to establish the well-posedness of a viscoelastic model with long memory.

In this paper we analyzed the exclusive photoproduction of $\eta_{c}\gamma$ pairs in the Color Glass Condensate framework. We found that the cross-section of this process is sensitive only to the forward dipole scattering amplitude, and thus could be used as a new tool for analysis of this fundamental nonperturbative object. Using the phenomenological parametrizations of this object, we estimated numerically the production cross-section and counting rates in the kinematics of the ongoing and forthcoming experiments at LHC and future Electron Ion Collider. We found that the cross-section is sufficiently large for dedicated experimental study. We also estimated the role of this process as a potential background to $\eta_{c}$ photoproduction, which is conventionally considered as a gateway for studies of odderons. We found that the contribution of $\eta_{c}\gamma$ (with undetected photon) is on par with expected contributions of odderons in the kinematics of small momentum transfer $|t|\lesssim1$ GeV$^{2}$, though decreases rapidly at larger $|t|$. Finally, we also calculated the feed-down contribution (from radiative decays of other charmonia) and found that a sizable correction comes from $J/\psi\to\eta_{c}\gamma$ decays. This contribution remains pronounced even at relatively large $|t|$ and potentially can impose constraint on detectability of odderons via $\eta_{c}$ photoproduction., Comment: 28 pages, 12 figures. This study complements our previous analysis arXiv:2408.01822, which was done in collinear factorization framework

Segmentation of medical images is a fundamental task with numerous applications. While MRI, CT, and PET modalities have significantly benefited from deep learning segmentation techniques, more recent modalities, like functional ultrasound (fUS), have seen limited progress. fUS is a non invasive imaging method that measures changes in cerebral blood volume (CBV) with high spatio-temporal resolution. However, distinguishing arterioles from venules in fUS is challenging due to opposing blood flow directions within the same pixel. Ultrasound localization microscopy (ULM) can enhance resolution by tracking microbubble contrast agents but is invasive, and lacks dynamic CBV quantification. In this paper, we introduce the first deep learning-based segmentation tool for fUS images, capable of differentiating signals from different vascular compartments, based on ULM automatic annotation and enabling dynamic CBV quantification. We evaluate various UNet architectures on fUS images of rat brains, achieving competitive segmentation performance, with 90% accuracy, a 71% F1 score, and an IoU of 0.59, using only 100 temporal frames from a fUS stack. These results are comparable to those from tubular structure segmentation in other imaging modalities. Additionally, models trained on resting-state data generalize well to images captured during visual stimulation, highlighting robustness. This work offers a non-invasive, cost-effective alternative to ULM, enhancing fUS data interpretation and improving understanding of vessel function. Our pipeline shows high linear correlation coefficients between signals from predicted and actual compartments in both cortical and deeperregions, showcasing its ability to accurately capture blood flow dynamics.

Estimation of the response probability distributions of computer simulators in the presence of randomness is a crucial task in many fields. However, achieving this task with guaranteed accuracy remains an open computational challenge, especially for expensive-to-evaluate computer simulators. In this work, a Bayesian active learning perspective is presented to address the challenge, which is based on the use of the Gaussian process (GP) regression. First, estimation of the response probability distributions is conceptually interpreted as a Bayesian inference problem, as opposed to frequentist inference. This interpretation provides several important benefits: (1) it quantifies and propagates discretization error probabilistically; (2) it incorporates prior knowledge of the computer simulator, and (3) it enables the effective reduction of numerical uncertainty in the solution to a prescribed level. The conceptual Bayesian idea is then realized by using the GP regression, where we derive the posterior statistics of the response probability distributions in semi-analytical form and also provide a numerical solution scheme. Based on the practical Bayesian approach, a Bayesian active learning (BAL) method is further proposed for estimating the response probability distributions. In this context, the key contribution lies in the development of two crucial components for active learning, i.e., stopping criterion and learning function, by taking advantage of posterior statistics. It is empirically demonstrated by five numerical examples that the proposed BAL method can efficiently estimate the response probability distributions with desired accuracy.

Areas of computational mechanics such as uncertainty quantification and optimization usually involve repeated evaluation of numerical models that represent the behavior of engineering systems. In the case of complex nonlinear systems however, these models tend to be expensive to evaluate, making surrogate models quite valuable. Artificial neural networks approximate systems very well by taking advantage of the inherent information of its given training data. In this context, this paper investigates the improvement of the training process by including sensitivity information, which are partial derivatives w.r.t. inputs, as outlined by Sobolev training. In computational mechanics, sensitivities can be applied to neural networks by expanding the training loss function with additional loss terms, thereby improving training convergence resulting in lower generalisation error. This improvement is shown in two examples of linear and non-linear material behavior. More specifically, the Sobolev designed loss function is expanded with residual weights adjusting the effect of each loss on the training step. Residual weighting is the given scaling to the different training data, which in this case are response and sensitivities. These residual weights are optimized by an adaptive scheme, whereby varying objective functions are explored, with some showing improvements in accuracy and precision of the general training convergence., Comment: Submitted to IEEE Access, 40 pages, 18 figures

Fractional statistical moments are utilized for various tasks of uncertainty quantification, including the estimation of probability distributions. However, an estimation of fractional statistical moments of costly mathematical models by statistical sampling is challenging since it is typically not possible to create a large experimental design due to limitations in computing capacity. This paper presents a novel approach for the analytical estimation of fractional moments, directly from polynomial chaos expansions. Specifically, the first four statistical moments obtained from the deterministic PCE coefficients are used for an estimation of arbitrary fractional moments via H\"{o}lder's inequality. The proposed approach is utilized for an estimation of statistical moments and probability distributions in three numerical examples of increasing complexity. Obtained results show that the proposed approach achieves a superior performance in estimating the distribution of the response, in comparison to a standard Latin hypercube sampling in the presented examples.

In this paper, we develop the Galerkin-like method to address first-order integro-differential inclusions. Under compactness or monotonicity conditions, we obtain new results for the existence of solutions for this class of problems, which generalize existing results in the literature and provide new insights for differential inclusions with an unbounded right-hand side. The effectiveness of the proposed approach is illustrated by presenting new existence results for nonconvex state-dependent Volterra sweeping processes, where the right-hand side is unbounded, and the classical theory of differential inclusions is not applicable. This is the first result of its kind. The paper concludes with an application to the existence of an optimal control problem governed by nonconvex state-dependent Volterra sweeping processes in finite dimensions., Comment: 37 pages

First-passage probability estimation of high-dimensional nonlinear stochastic systems is a significant task to be solved in many science and engineering fields, but remains still an open challenge. The present paper develops a novel approach, termed 'fractional moments-based mixture distribution', to address such challenge. This approach is implemented by capturing the extreme value distribution (EVD) of the system response with the concepts of fractional moments and mixture distribution. In our context, the fractional moment itself is by definition a high-dimensional integral with a complicated integrand. To efficiently compute the fractional moments, a parallel adaptive sampling scheme that allows for sample size extension is developed using the refined Latinized stratified sampling (RLSS). In this manner, both variance reduction and parallel computing are possible for evaluating the fractional moments. From the knowledge of low-order fractional moments, the EVD of interest is then expected to be reconstructed. Based on introducing an extended inverse Gaussian distribution and a log extended skew-normal distribution, one flexible mixture distribution model is proposed, where its fractional moments are derived in analytic form. By fitting a set of fractional moments, the EVD can be recovered via the proposed mixture model. Accordingly, the first-passage probabilities under different thresholds can be obtained from the recovered EVD straightforwardly. The performance of the proposed method is verified by three examples consisting of two test examples and one engineering problem.

Constructed facilities should be robust with respect to the loss of load-bearing elements due to abnormal events. Yet, strengthening structures to withstand such damage has a significant impact on construction costs. Strengthening costs should be justified by the threat and should result in smaller expected costs of progressive collapse. In regular frame structures, beams and columns compete for the strengthening budget. In this paper, we present a risk-based formulation to address the optimal design of regular plane frames under element loss conditions. We address the threat probabilities for which strengthening has better cost-benefit than usual design, for different frame configurations, and study the impacts of strengthening extent and cost. The risk-based optimization reveals optimum points of compromise between competing failure modes: local bending of beams, local crushing of columns, and global pancake collapse, for frames of different aspect ratios. The conceptual study is based on a simple analytical model for progressive collapse, but it provides relevant insight for the design and strengthening of real structures., Comment: 36 pages 12 figures

Let $\mathbb{F}$ be a division ring. In this paper, we extent some of the main well-known results about the resultant of two univariate polynomials to the more general context of an Ore extension $\mathbb{F}[x;\sigma,\delta]$. Finally, some algorithms and Magma programs are given as a numerical application of the main theoretical results of this paper., Comment: 38 pages; the presentation of the main results has been improved and many typos have been corrected

The purpose of this study was to explore the response of the central library of the University of Playa Ancha during the COVID-19 pandemic, more specifically, during the mandatory closure and quarantine, with respect to the digital library services offered to undergraduate students. of librarianship of the same house of studies. Through this research, the perception of these students was known about how their needs to obtain reliable and quality information extracted from the library web were satisfied. Consequently, the pandemic was not the same for some users as it was for others, making the digital divide more noticeable, of which there was already some kind of knowledge, but which increased as a result of this context. In this way, the preferences of these students regarding the library digital materials that they used during the closure and mandatory quarantine were known. A quantitative study was carried out, with the application of a structured survey and the results showed that a vast majority of the users surveyed believed that the COVID-19 pandemic made this central library innovate and break with the old paradigm that the Academic library is a physical place without movement.

We consider the equation $\Delta_x u+u_{yy}+f(u)=0,\ x=(x_1,\dots,x_N)\in\mathbb{R}^N,\ y\in \mathbb{R},$ where $N\geq 2$ and $f$ is a sufficiently smooth function satisfying $f(0)=0$, $f'(0)<0$, and some natural additional conditions. We prove that the equation possesses uncountably many positive solutions (disregarding translations) which are radially symmetric in $x'=(x_1,\dots,x_{N-1})$ and decaying as $|x'|\to\infty$, periodic in $x_N$, and quasiperiodic in $y$. Related theorems for more general equations are included in our analysis as well. Our method is based on center manifold and KAM-type results.

This paper describes the inversion procedure being used operationally at the Norwegian Meteorological Institute for estimating ash emission rates from retrieved satellite ash column amounts and a priori knowledge. The overall procedure consists of five stages: (1) generate a priori emission estimates; (2) run forward simulations with unit emissions; (3) collocate/match observations with emission simulations; (4) build system of linear equations; and (5) solve overdetermined system. We go through the mathematical foundations for the inversion procedure, performance for synthetic cases, and performance for real-world cases. The novelties of this paper includes pruning of the linear system of equations used in the inversion and inclusion of observations of ash cloud top altitude. The source code used in this work is freely available under an open source license, and is possible to use for other similar applications., Comment: 17 pages, 11 figures. First public draft

Let $\mathbb{F}_q$ be a field with $q$ elements. In this note, we study some generalized arcs, that is, sets of $\mathbb{F}_q$-points in the projective plane $\mathbb{P}^2(\mathbb{F}_q)$ such that no six of them are on a conic. First, we consider the geometric configurations of such generalized arcs for small values of $q$ and then we give some upper and lower bounds for the cardinality of complete generalized arcs, i.e. generalized arcs which are not contained in a bigger one., Comment: 17 pages, 1 figure, 6 tables

This Campbell systematic review examines the impact of interventions to reduce exclusion from school. School exclusion, also known as suspension in some countries, is a disciplinary sanction imposed by a responsible school authority, in reaction to students' misbehaviour. Exclusion entails the removal of pupils from regular teaching for a period during which they are not allowed to be present in the classroom (in-school) or on school premises (out-of-school). In some extreme cases the student is not allowed to come back to the same school (expulsion). The review summarises findings from 37 reports covering nine different types of intervention. Most studies were from the USA, and the remainder from the UK. The evidence suggests that school-based interventions are effective at reducing school exclusion immediately after, and for a few months after, the intervention. Some specific types of interventions show more promising and stable results than others, namely those involving mentoring/monitoring and those targeting skills training for teachers. Implications for policy, research, and practice arising from the results of this study are discussed. [A list of references to studies included in the study, studies that were excluded, journal articles, studies awaiting classification, and additional studies is provided.]

Let $\mathbb{F}_q$ be a finite field with $q$ elements and denote by $\theta : \mathbb{F}_q\to\mathbb{F}_q$ an automorphism of $\mathbb{F}_q$. In this paper, we deal with skew constacyclic codes, that is, linear codes of $\mathbb{F}_q^n$ which are invariant under the action of a semi-linear map $\Phi_{\alpha,\theta}:\mathbb{F}_q^n\to\mathbb{F}_q^n$, defined by $\Phi_{\alpha,\theta}(a_0,...,a_{n-2}, a_{n-1}):=(\alpha \theta(a_{n-1}),\theta(a_0),...,\theta(a_{n-2}))$ for some $\alpha\in\mathbb{F}_q\setminus\{0\}$ and $n\geq 2$. In particular, we study some algebraic and geometric properties of their dual codes and we give some consequences and research results on $1$-generator skew quasi-twisted codes and on MDS skew constacyclic codes., Comment: 31 pages, 3 tables; this is a revised version that includes improvements to the presentation of the main results, a new subsection and an appendix which is an extension of Section 2 of the previous version