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We consider the three-dimensional time-harmonic electromagnetic (EM) wave scattering transmission problem involving heterogeneous scatterers. The fields are approximated using the local multiple traces formulation (MTF), originally introduced for acoustic scattering. This scheme assigns independent boundary unknowns to each subdomain and weakly enforces Calder\'on identities along with interface transmission conditions. As a result, the MTF effectively handles shared points or edges among multiple subdomains, while supporting various preconditioning and parallelization strategies. Nevertheless, implementing standard solvers presents significant challenges, particularly in managing the degrees of freedom associated with subdomains and their interfaces. To address these difficulties, we propose a novel framework that suitably defines approximation spaces and enables the efficient exchange of normal vectors across subdomain boundaries. This framework leverages the skeleton mesh, representing the union of all interfaces, as the computational backbone, and constitutes the first scalable implementation of the EM MTF. Furthermore, we conduct several numerical experiments, exploring the effects of increasing subdomains and block On-Surface-Raditation-Condition (OSRC) preconditioning, to validate our approach and provide insights for future developments.

Given a group \( G \), a field \( \kappa \), and a factor set \( \sigma \) arising from a partial projective \( \kappa \)-representation of \( G \). This leads to the construction of a topological partial dynamical system \( (\Omega_\sigma, G, \hat{\theta}) \), where \( \Omega_\sigma \) is a compact, totally disconnected Hausdorff space, and \( \sigma \) acts as a twist for \( \hat{\theta} \). We show that the twisted partial group algebra \( \kappa_{par}^{\sigma} G \) can be realized as a crossed product \( {\mathscr L}(\Omega_\sigma) \rtimes_{(\hat{\theta}, \sigma)} G \), with \( {\mathscr L}(\Omega_\sigma) \) denoting the \( \kappa \)-algebra of locally constant functions \( \Omega_\sigma \to \kappa \). The space \( \Omega_\sigma \) corresponds to the spectrum of a unital commutative subalgebra in \( \kappa_{par}^{\sigma} G \), generated by idempotents. By describing \( \Omega_\sigma \) as a subspace of the Bernoulli space \( 2^G \), we examine conditions under which the spectral partial action \( \hat{\theta} \) is topologically free, impacting the ideal structure of \( \kappa_{par}^{\sigma} G \). We further explore generating idempotent factor sets of \( G \) and present conditions on them to ensure the topological freeness of \( \hat{\theta} \). Inspired by Exel's semigroup \( \mathcal{S}(G) \), which governs partial actions and representations of \( G \) and relates to \( \kappa_{par}G \), we characterize the twisted partial group algebra \( \kappa_{par}^{\sigma}G \) as generated by a \( \kappa \)-cancellative inverse semigroup constructed from elements of \( \Omega_\sigma \). When \( \Omega_\sigma \) is discrete, we demonstrate that \( \kappa_{par}^{\sigma} G \) decomposes into a product of matrix algebras over twisted subgroup algebras, generalizing known results for finite \( G \).

Background Advancements in Large Language Models (LLMs) hold transformative potential in healthcare, however, recent work has raised concern about the tendency of these models to produce outputs that display racial or gender biases. Although training data is a likely source of such biases, exploration of disease and demographic associations in text data at scale has been limited. Methods We conducted a large-scale textual analysis using a dataset comprising diverse web sources, including Arxiv, Wikipedia, and Common Crawl. The study analyzed the context in which various diseases are discussed alongside markers of race and gender. Given that LLMs are pre-trained on similar datasets, this approach allowed us to examine the potential biases that LLMs may learn and internalize. We compared these findings with actual demographic disease prevalence as well as GPT-4 outputs in order to evaluate the extent of bias representation. Results Our findings indicate that demographic terms are disproportionately associated with specific disease concepts in online texts. gender terms are prominently associated with disease concepts, while racial terms are much less frequently associated. We find widespread disparities in the associations of specific racial and gender terms with the 18 diseases analyzed. Most prominently, we see an overall significant overrepresentation of Black race mentions in comparison to population proportions. Conclusions Our results highlight the need for critical examination and transparent reporting of biases in LLM pretraining datasets. Our study suggests the need to develop mitigation strategies to counteract the influence of biased training data in LLMs, particularly in sensitive domains such as healthcare.

We study the partial group (co)homology of partial group actions using simplicial methods. We introduce the concept of universal globalization of a partial group action on a $K$-module and prove that, given a partial representation of $G$ on $M$, the partial group homology $H^{par}_{\bullet}(G, M)$ is naturally isomorphic to the usual group homology $H_{\bullet}(G, KG \otimes_{G_{par}} M)$, where $KG \otimes_{G_{par}} M$ is the universal globalization of the partial group action associated to $M$. We dualize this result into a cohomological spectral sequence converging to $H^{\bullet}_{par}(G,M)$.

We simulate the electrical response of multiple disjoint biological 3D cells undergoing an electropermeabilization process. Instead of solving the boundary value problem in the unbounded volume, we reduce it to a system of boundary integrals equations--the local Multiple Traces Formulation--coupled with nonlinear dynamics on the cell membranes. Though in time the model is highly non-linear and poorly regular, the smooth geometry allows for boundary unknowns to be spatially approximated by spherical harmonics. This leads to spectral convergence rates in space. In time, we use a multistep semi-implicit scheme. To ensure stability, the time step needs to be bounded by the smallest characteristic time of the system. Numerical results are provided to validate our claims and future enhancements are pointed out.

Colorectal cancer is the third most aggressive cancer worldwide. Polyps, as the main biomarker of the disease, are detected, localized, and characterized through colonoscopy procedures. Nonetheless, during the examination, up to 25% of polyps are missed, because of challenging conditions (camera movements, lighting changes), and the close similarity of polyps and intestinal folds. Besides, there is a remarked subjectivity and expert dependency to observe and detect abnormal regions along the intestinal tract. Currently, publicly available polyp datasets have allowed significant advances in computational strategies dedicated to characterizing non-parametric polyp shapes. These computational strategies have achieved remarkable scores of up to 90% in segmentation tasks. Nonetheless, these strategies operate on cropped and expert-selected frames that always observe polyps. In consequence, these computational approximations are far from clinical scenarios and real applications, where colonoscopies are redundant on intestinal background with high textural variability. In fact, the polyps typically represent less than 1% of total observations in a complete colonoscopy record. This work introduces COLON: the largest COlonoscopy LONg sequence dataset with around of 30 thousand polyp labeled frames and 400 thousand background frames. The dataset was collected from a total of 30 complete colonoscopies with polyps at different stages, variations in preparation procedures, and some cases the observation of surgical instrumentation. Additionally, 10 full intestinal background video control colonoscopies were integrated in order to achieve a robust polyp-background frame differentiation. The COLON dataset is open to the scientific community to bring new scenarios to propose computational tools dedicated to polyp detection and segmentation over long sequences, being closer to real colonoscopy scenarios., Comment: 7 pages, 3 figures, 3 tables

The first experimental campaigns of Wendelstein 7-X (W7-X) have shown that turbulence plays a decisive role in the performance of neoclassically optimized stellarators. This stresses the importance of understanding microturbulence from the theoretical and experimental points of view. To this end, this paper addresses a comprehensive characterization of the turbulent fluctuations by means of nonlinear gyrokinetic simulations performed with the code stella in two W7-X scenarios. In the first part of the paper, the amplitude of the density fluctuations is calculated and compared with measurements obtained by Doppler reflectometry (DR) in the OP1 experimental campaigns. It is found that the trend of the fluctuations along the radius is explained by the access of the DR system to different regions of the turbulence wavenumber spectrum. In the second part of the article, frequency spectra of the density fluctuations and the zonal component of the turbulent flow are numerically characterized for comparisons against future experimental analyses. Both quantities feature broad frequency spectra with dominant frequencies of O(1)-O(10) kHz., Comment: 27 pages, 16 figures

Scale-free networks play a fundamental role in the study of complex networks and various applied fields due to their ability to model a wide range of real-world systems. A key characteristic of these networks is their degree distribution, which often follows a power-law distribution, where the probability mass function is proportional to $x^{-\alpha}$, with $\alpha$ typically ranging between $2 < \alpha < 3$. In this paper, we introduce Bayesian inference methods to obtain more accurate estimates than those obtained using traditional methods, which often yield biased estimates, and precise credible intervals. Through a simulation study, we demonstrate that our approach provides nearly unbiased estimates for the scaling parameter, enhancing the reliability of inferences. We also evaluate new goodness-of-fit tests to improve the effectiveness of the Kolmogorov-Smirnov test, commonly used for this purpose. Our findings show that the Watson test offers superior power while maintaining a controlled type I error rate, enabling us to better determine whether data adheres to a power-law distribution. Finally, we propose a piecewise extension of this model to provide greater flexibility, evaluating the estimation and its goodness-of-fit features as well. In the complex networks field, this extension allows us to model the full degree distribution, instead of just focusing on the tail, as is commonly done. We demonstrate the utility of these novel methods through applications to two real-world datasets, showcasing their practical relevance and potential to advance the analysis of power-law behavior., Comment: 33 pages, 11 figures

We consider the category of partial actions, where the group and the set upon which the group acts can vary. Within this framework, we develop a theory of quotient partial actions and prove that this category is both (co)complete and encompasses the category of groupoids as a full subcategory. In particular, we establish the existence of a pair of adjoint functors, denoted as $\Phi : \textbf{Grpd} \to \textbf{PA}$ and $\Psi : \textbf{PA} \to \textbf{Grpd}$, with the property that $\Psi \Phi \cong 1_{\textbf{Grpd} }$. Next, for a given groupoid $\Gamma$, we provide a characterization of all partial actions that allow the recovery of the groupoid $\Gamma$ through $\Psi$. This characterization is expressed in terms of certain normal subgroups of a universal group constructed from $\Gamma.$, Comment: The previous version was an incorrect file that was uploaded. I have corrected some typographical errors and improved the proof of Proposition 2.18

Extreme precision radial velocity (EPRV) measurements contend with internal noise (instrumental systematics) and external noise (intrinsic stellar variability) on the road to 10 cm/s "exo-Earth" sensitivity. Both of these noise sources are well-probed using "Sun-as-a-star" RVs and cross-instrument comparisons. We built the Solar Calibrator (SoCal), an autonomous system that feeds stable, disc-integrated sunlight to the recently commissioned Keck Planet Finder (KPF) at the W. M. Keck Observatory. With SoCal, KPF acquires signal-to-noise ~1200, R = ~98,000 optical (445--870 nm) spectra of the Sun in 5~sec exposures at unprecedented cadence for an EPRV facility using KPF's fast readout mode (<16 sec between exposures). Daily autonomous operation is achieved by defining an operations loop using state machine logic. Data affected by clouds are automatically flagged using a reliable quality control metric derived from simultaneous irradiance measurements. Comparing solar data across the growing global network of EPRV spectrographs with solar feeds will allow EPRV teams to disentangle internal and external noise sources and benchmark spectrograph performance. To facilitate this, all SoCal data products are immediately available to the public on the Keck Observatory Archive. We compared SoCal RVs to contemporaneous RVs from NEID, the only other immediately public EPRV solar dataset. We find agreement at the 30-40 cm/s level on timescales of several hours, which is comparable to the combined photon-limited precision. Data from SoCal were also used to assess a detector problem and wavelength calibration inaccuracies associated with KPF during early operations. Long-term SoCal operations will collect upwards of 1,000 solar spectra per six-hour day using KPF's fast readout mode, enabling stellar activity studies at high signal-to-noise on our nearest solar-type star., Comment: 22 pages, 11 figures, accepted to Publications of the Astronomical Society of the Pacific

Stroke is the second leading cause of mortality worldwide. Immediate attention and diagnosis play a crucial role regarding patient prognosis. The key to diagnosis consists in localizing and delineating brain lesions. Standard stroke examination protocols include the initial evaluation from a non-contrast CT scan to discriminate between hemorrhage and ischemia. However, non-contrast CTs may lack sensitivity in detecting subtle ischemic changes in the acute phase. As a result, complementary diffusion-weighted MRI studies are captured to provide valuable insights, allowing to recover and quantify stroke lesions. This work introduced APIS, the first paired public dataset with NCCT and ADC studies of acute ischemic stroke patients. APIS was presented as a challenge at the 20th IEEE International Symposium on Biomedical Imaging 2023, where researchers were invited to propose new computational strategies that leverage paired data and deal with lesion segmentation over CT sequences. Despite all the teams employing specialized deep learning tools, the results suggest that the ischemic stroke segmentation task from NCCT remains challenging. The annotated dataset remains accessible to the public upon registration, inviting the scientific community to deal with stroke characterization from NCCT but guided with paired DWI information.

Quantifying the effects on electromagnetic waves scattered by objects of uncertain shape is key for robust design, particularly in high precision applications. Assuming small random perturbations departing from a nominal domain, the first-order sparse boundary element method (FOSB) has been proven to directly compute statistical moments with poly-logarithmic complexity for a prescribed accuracy, without resorting to computationally intense Monte Carlo simulations. However, implementing the FOSB is not straightforward. To this end, we introduce an easy-to-use with open-source framework to directly apply the technique when dealing with complex objects. Exhaustive computational experiments confirm our claims and demonstrate the technique's applicability as well as provide pathways for further improvement.

The recently introduced independent fluctuating two-ray (IFTR) fading model, consisting of two specular components fluctuating independently plus a diffuse component, has proven to provide an excellent fit to different wireless environments, including the millimeter-wave band. However, the original formulations of the probability density function (PDF) and cumulative distribution function (CDF) of this model are not applicable to all possible values of its defining parameters, and are given in terms of multifold generalized hypergeometric functions, which prevents their widespread use for the derivation of performance metric expressions. In this paper we present a new formulation of the IFTR model as a countable mixture of Gamma distributions which greatly facilitates the performance evaluation for this model in terms of the metrics already known for the much simpler and widely used Nakagami-m fading. Additionally, a closed-form expression is presented for the generalized moment generating function (GMGF), which permits to readily obtain all the moments of the distribution of the model, as well as several relevant performance metrics. Based on these new derivations, the IFTR model is evaluated for the average channel capacity, the outage probability with and without co-channel interference, and the bit error rate (BER), which are verified by Monte Carlo simulations., Comment: This work was submitted to the IEEE for publication