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Symplectic and Poisson geometry emerged as a tool to understand the mathematical structure behind classical mechanics. However, due to its huge development over the past century, it has become an independent field of research in differential geometry. In this lecture notes, we will introduce the essential objects and techniques in symplectic geometry (e.g Darboux coordinates, Lagrangian submanifolds, cotangent bundles) and Poisson geometry (e.g symplectic foliations, some examples of Poisson structures). This geometric approach will be motivated by examples from classical physics, and at the end we will explore applications of symplectic and Poisson geometry to Lie theory and other fields of mathematical physics., Comment: 30 pages, 3 figures

This article investigates and compares three approaches to link prediction in colaboration networks, namely, an ERGM (Exponential Random Graph Model; Robins et al. 2007), a GCN (Graph Convolutional Network; Kipf and Welling 2017), and a Word2Vec+MLP model (Word2Vec model combined with a multilayer neural network; Mikolov et al. 2013a and Goodfellow et al. 2016). The ERGM, grounded in statistical methods, is employed to capture general structural patterns within the network, while the GCN and Word2Vec+MLP models leverage deep learning techniques to learn adaptive structural representations of nodes and their relationships. The predictive performance of the models is assessed through extensive simulation exercises using cross-validation, with metrics based on the receiver operating characteristic curve. The results clearly show the superiority of machine learning approaches in link prediction, particularly in large networks, where traditional models such as ERGM exhibit limitations in scalability and the ability to capture inherent complexities. These findings highlight the potential benefits of integrating statistical modeling techniques with deep learning methods to analyze complex networks, providing a more robust and effective framework for future research in this field., Comment: 17 pages, 5 figures, 1 table

Effective hospital capacity management is pivotal for enhancing patient care quality, operational efficiency, and healthcare system resilience, notably during demand spikes like those seen in the COVID-19 pandemic. However, devising optimal capacity strategies is complicated by fluctuating demand, conflicting objectives, and multifaceted practical constraints. This study presents a data-driven framework to optimize capacity management decisions within hospital systems during surge events. Two key decisions are optimized over a tactical planning horizon: allocating dedicated capacity to surge patients and transferring incoming patients between emergency departments (EDs) of hospitals to better distribute demand. The optimization models are formulated as robust mixed-integer linear programs, enabling efficient computation of optimal decisions that are robust against demand uncertainty. The models incorporate practical constraints and costs, including setup times and costs for adding surge capacity, restrictions on ED patient transfers, and relative costs of different decisions that reflect impacts on care quality and operational efficiency. The methodology is evaluated retrospectively in a hospital system during the height of the COVID-19 pandemic to demonstrate the potential impact of the recommended decisions. The results show that optimally allocating beds and transferring just 32 patients over a 63 day period around the peak, about one transfer every two days, could have reduced the need for surge capacity in the hospital system by nearly 90%. Overall, this work introduces a practical tool to transform capacity management decision-making, enabling proactive planning and the use of data-driven recommendations to improve outcomes.

Data-driven optimization models have the potential to significantly improve hospital capacity management, particularly during demand surges, when effective allocation of capacity is most critical and challenging. However, integrating models into existing processes in a way that provides value requires recognizing that hospital administrators are ultimately responsible for making capacity management decisions, and carefully building trustworthy and accessible tools for them. In this study, we develop an interactive, user-friendly, electronic dashboard for informing hospital capacity management decisions during surge periods. The dashboard integrates real-time hospital data, predictive analytics, and optimization models. It allows hospital administrators to interactively customize parameters, enabling them to explore a range of scenarios, and provides real-time updates on recommended optimal decisions. The dashboard was created through a participatory design process, involving hospital administrators in the development team to ensure practical utility, trustworthiness, transparency, explainability, and usability. We successfully deployed our dashboard within the Johns Hopkins Health System during the height of the COVID-19 pandemic, addressing the increased need for tools to inform hospital capacity management. It was used on a daily basis, with results regularly communicated to hospital leadership. This study demonstrates the practical application of a prospective, data-driven, interactive decision-support tool for hospital system capacity management., Comment: 25 pages, 11 figures

We give a complete solution to the problem of C*-rigidity for (extended) locally compact metric spaces. Namely, we show that (stable) isomorphisms among Roe algebras always give rise to coarse equivalences. To do so, we develop a framework to study rigidity problems for Roe-like C*-algebras of countably generated coarse spaces. This allows us to provide a unified proof of C*-rigidity for Roe algebras, algebras of operators of controlled propagation, and algebras of quasi-local operators. As further applications, we prove that the outer automorphism groups of all of these algebras are isomorphic to the group of coarse equivalences of the starting coarse space., Comment: 82 pages. Minor correction: "locally compact" changed to "proper" throughout the introduction

We provide a construction of Roe (C*-)algebras of general coarse spaces in terms of coarse geometric modules. This extends the classical theory of Roe algebras of metric spaces and gives a unified framework to deal with either uniform or non-uniform Roe algebras, algebras of operators of controlled propagation, and algebras of quasi-local operators; both in the metric and general coarse geometric setting. The key new definitions are that of coarse geometric module and coarse support of operators between coarse geometric modules. These let us construct natural bridges between coarse geometry and operator algebras. We then study the general structure of Roe-like algebras, and investigate several structural properties, such as admitting Cartan subalgebras or computing their intersection with the compact operators. Lastly, we prove that assigning to a coarse space the K-theory groups of its Roe algebra(s) is a natural functorial operation., Comment: Minor improvements and corrected typos throughout the paper, slightly changed the abstract

In this paper we study the nuclearity and weak containment property of reduced cross-sectional C*-algebras of Fell bundles over inverse semigroups. In order to develop the theory, we first prove an analogue of Fell's absorption trick in the context of Fell bundles over inverse semigroups. In parallel, the approximation property of Exel can be reformulated in this context, and Fell's absorption trick can be used to prove that the approximation property, as defined here, implies that the full and reduced cross-sectional C*-algebras are isomorphic via the left regular representation, i.e., the Fell bundle has the weak containment property. We then use this machinery to prove that a Fell bundle with the approximation property and nuclear unit fiber has a nuclear cross-sectional \cstar{}algebra. This result gives nuclearity of a large class of C*-algebras, as, remarkably, all the machinery in this paper works for \'{e}tale non-Hausdorff groupoids just as well., Comment: Minor typos, version accepted for publication in Adv. Math

Feature preprocessing, which transforms raw input features into numerical representations, is a crucial step in automated machine learning (AutoML) systems. However, the existing systems often have a very small search space for feature preprocessing with the same preprocessing pipeline applied to all the numerical features. This may result in sub-optimal performance since different datasets often have various feature characteristics, and features within a dataset may also have their own preprocessing preferences. To bridge this gap, we explore personalized preprocessing pipeline search, where the search algorithm is allowed to adopt a different preprocessing pipeline for each feature. This is a challenging task because the search space grows exponentially with more features. To tackle this challenge, we propose ClusterP3S, a novel framework for Personalized Preprocessing Pipeline Search via Clustering. The key idea is to learn feature clusters such that the search space can be significantly reduced by using the same preprocessing pipeline for the features within a cluster. To this end, we propose a hierarchical search strategy to jointly learn the clusters and search for the optimal pipelines, where the upper-level search optimizes the feature clustering to enable better pipelines built upon the clusters, and the lower-level search optimizes the pipeline given a specific cluster assignment. We instantiate this idea with a deep clustering network that is trained with reinforcement learning at the upper level, and random search at the lower level. Experiments on benchmark classification datasets demonstrate the effectiveness of enabling feature-wise preprocessing pipeline search.

In this work, we propose a new diffractive trifocal intraocular lens design with focus extension, conceived to provide a high visual performance at intermediate distances. This design is based on a fractal structure known as the "Devil's staircase". To assess its optical performance, numerical simulations have been performed with a ray tracing program using the Liou-Brennan model eye under polychromatic illumination. The simulated through the focus visual acuity was the merit function employed to test its pupil-dependence and its behavior against decentering. A qualitative assessment of the multifocal intraocular lens (MIOL) was also performed experimentally with an adaptive optics visual simulator. The experimental results confirm our numerical predictions. We found that our MIOL design has a trifocal profile, which is very robust to decentration and has low degree of pupil dependence. It performs better at intermediate distances than at near distances and, for a pupil diameter of 3 mm, it works like an EDoF lens over almost the entire defocus range.

Given any quasi-countable, in particular any countable inverse semigroup $S$, we introduce a way to equip $S$ with a proper and right subinvariant extended metric. This generalizes the notion of proper, right invariant metrics for discrete countable groups. Such a metric is shown to be unique up to bijective coarse equivalence of the semigroup, and hence depends essentially only on $S$. This allows us to unambiguously define the uniform Roe algebra of $S$, which we prove can be realized as a canonical crossed product of $\ell^\infty(S)$ and $S$. We relate these metrics to the analogous metrics on Hausdorff \'{e}tale groupoids. Using this setting, we study those inverse semigroups with asymptotic dimension $0$. Generalizing results known for groups, we show that these are precisely the locally finite inverse semigroups, and are further characterized by having strongly quasi-diagonal uniform Roe algebras. We show that, unlike in the group case, having a finite uniform Roe algebra is strictly weaker and is characterized by $S$ being locally $\mathcal L$-finite, and equivalently sparse as a metric space.

Autonomous navigation in dynamic environments is a complex but essential task for autonomous robots. Recent deep reinforcement learning approaches show promising results to solve the problem, but it is not solved yet, as they typically assume no robot kinodynamic restrictions, holonomic movement or perfect environment knowledge. Moreover, most algorithms fail in the real world due to the inability to generate real-world training data for the huge variability of possible scenarios. In this work, we present a novel planner, DQN-DOVS, that uses deep reinforcement learning on a descriptive robocentric velocity space model to navigate in highly dynamic environments. It is trained using a smart curriculum learning approach on a simulator that faithfully reproduces the real world, reducing the gap between the reality and simulation. We test the resulting algorithm in scenarios with different number of obstacles and compare it with many state-of-the-art approaches, obtaining a better performance. Finally, we try the algorithm in a ground robot, using the same setup as in the simulation experiments., Comment: Perception and Navigation for Autonomous Robotics in Unstructured and Dynamic Environments (PNARUDE) workshop in IROS 2022

Eight experiments were conducted to test an oregano-essential-oil-based product (PRO) on performance, gut health, and nutrient absorption capacity in broilers. The first three, up to 14d and without specific challenges, tested the effects on intestinal histology, skeletal integrity, and growth. Other two experiments, up to 28d birds were challenged to induce feed passage syndrome (STR) and test the effect on the antioxidant status and performance, contrasting later the results under a natural challenge in commercial conditions. Finally, in two other experiments, up to 21 d, birds challenged with coccidia were tested to determine the effects on coccidiosis, nutrient digestibility, and feed efficiency (FCR). Corn-soybean-fish meal diets were used. Under healthy conditions, PRO effects were observed on intestinal villus height and surface area, mucosa density and structure, villus to crypt ratio, goblet cells density, mucus production, body weight gain, and FCR (P<0.04), and carcass yield and bone density (P<0.08). Birds affected by STR showed effects (P<0.05) on superoxide dismutase activity, bodyweight gain, FCRE, non-normal feces frequency, bursal diameter, and dysbacteriosis. Birds affected by coccidia showed effects on cocci-positive ratio, cocci microscopic score, oocysts count, bursal diameter, body weight gain, FCR, apparent digestibility of dry matter and crude protein, protein and energy efficiencies (P<0.01), and nitrogen apparent retention (P<0.07). Results showed PRO added value to the diet favoring feed efficiency and performance.

The objective of this study was to determine the effect of feeding an antimicrobial association to males broiler chickens from 0 to 14 days of age on the performance and clinical signs of bacterial processes. Two treatments were tested: a control treatment without Respirend-M, and a treatment with the antimicrobial (300 g/t Respirend-M, 0-14 d). 398 male Cobb 500 chicks were randomly assigned to two treatments and four replications per treatment. Body weight at 14 d, body weight gain, feed intake, feed conversion ratio, and health status were evaluated. The results showed feeding 300 g/t Respirend-M significantly (P<0.05) improved the final body weight, the body weight gain and the feed intake. No statistically significant (P>0.05) effect was detected on the feed conversion ratio., Comment: in Spanish

An experiment was conducted to evaluate the effect of feeding post-weaned piglets different levels of a commercial amoxicillin plus norfloxacin formula (Respirend) on the performance, clinical evidence of sickness, and the cost:benefit ratio. 454 PIC x Camborough female and castrated male, weaned at 21 d of age, with an average initial weight of 6.19 kg, were used in this experiment. Treatment 1 consisted in feeding a basal diet supplemented with 1000 g of a commercial tilmicosin product (Pulmotil) per metric tonne of feed (control group, from 21 to 35 d of age) and Treatments 2), 3) and 4) consisted in feeding the basal diet supplement with 500, 300 y 100 g of Respirend per metric tonne of feed, respectively, from 21 to 42 d of age. The results did not show significant differences (P<0.05) in mortality nor in parenteral medicine administration cost in none of the periods. Nevertheless, 500 g of Respirend per metric tonne of feed improved significantly (P<0.05) the general health status in the period between 21 and 35 d of age. For the whole evaluation period (21 to 42 d of age), this level improved significantly (P<0.05) the final body weight, the average daily weight gain, the average daily feed intake, the feed:gain ratio and optimized the cost:benefit ratio., Comment: in Spanish

Environmental temperature (ET) often changes the nutrient intake/output for layers. Changing feed formulations based on ET may need to be utilized to obtain optimum performance, shell quality and bone status. This study was conducted to investigate the effects of temperature, Ca intake, non-phytate P (NPP) intake and in vitro limestone solubility (LS) on egg-shell quality and bone status in commercial White Leghorn hens. Egg mass and shell weight per unit surface area (SWUSA) decreased with increasing ET (p lower than 0.05), especially when ET was 29.7 C (cycling mean ET)or a constant ET was 32.2 C. Feeding layers a low soluble larger particle size limestone instead of a highly soluble limestone produced beneficial effects for SWUSA at the thermoneutral ET (21.1 C) but the beneficial effect was less or disappeared when ET was higher than 26.6 C in EXP 1 and 2. Feeding layers 245 and 353 mg NPP/h/d supported satisfactory bone status at 21.1 C, however layers housed at higher than 30 C needed an additional intake of 50 mg NPP/h/d to support bone integrity. Results of EXP 1 and 2 indicates that 48 week old layers housed in thermoneutral or warmer ET require a minimum of 4.2 g Ca/h/d for maintaining optimum shell quality and bone integrity. Feeding low LS (34.1% in vitro solubility) improved egg shell quality only for hens housed in thermoneutral ET (21.1 C) and did not improve egg shell quality at higher ET (constant or cycling). Daily NPP intake of 245 and 353 mg/h/d supported optimum egg production and bone status at 21.1 C, respectively. A higher NPP and Ca intake may be required for bone status compared to egg production, especially in older hens.

Background and Objective: In the current study, we sought to determine the value of a meta-analysis to improve decision-making processes related to nutrition in the poultry industry. To this end, nine commercial size experiments were conducted to test the effect of a phytogenic feed additive and three approaches were applied to the data. Materials and Methods: In all experiments, 1-day-old male Cobb 500 chicks were used and fed corn-soybean meal diets. Two dietary treatments were tested: T1, control diet and T2, control diet + feed additive at a 0.05% inclusion rate. The experimental units were broiler houses (7 experiments), floor pens (1 experiment) and cages (1 experiment). The response variables were final body weight, feed intake, feed conversion ratio, mortality and production efficiency. Analyses of variance of data from each and all the experiments were performed using SAS under completely randomized non-blocked or blocked designs, respectively. The meta-analyses were performed in R programming language. Results: No statistically significant effects were found in the evaluated variables in any of the independent experiments (p>0.12), nor following the application of a block design (p>0.08). The meta-analyses showed no statistically significant global effects in terms of final body weight (p>0.19), feed intake (p>0.23), mortality (p>0.09), or European Production Efficiency Factor (p>0.08); however, a positive global effect was found with respect to feed conversion ratio (p<0.046). Conclusion: This meta-analysis demonstrated that the phytogenic feed additive improved the efficiency of birds to convert feed to body weight (35 g less feed per 1 kg of body weight obtained). Thus, the use of meta-analyses in commercial-scale poultry trials can increase statistical power and as a result, help to detect statistical differences if they exist.

In this article we show that the main C*-algebras describing the canonical commutation relations of quantum physics, i.e., the Weyl and resolvent algebras, are in the class of F{\o}lner C*-algebras, a class of C*-algebras admitting a kind of finite approximations of F{\o}lner type. In particular, we show that the tracial states of the resolvent algebra are uniform locally finite dimensional., Comment: 11 pages, minor revision, accepted for publication in Expo. Math

In this note we start the study of whether the reduced C*-algebra of an inverse semigroup is quasi-diagonal, making explicit use of the inner structure of this class of semigroups in order to produce quasi-diagonal approximations. Given a discrete inverse semigroup, we detail the relationship between its isolated subgroups and the quasi-diagonality of its reduced C*-algebra, and prove that such subgroups must be amenable. Moreover, we give a direct characterization of the quasi-diagonality of inverse semigroup whose universal groupoid is minimal. Lastly, we also study the relevance of Green's $\mathcal{D}$-relation when considering quasi-diagonality questions, and give a sufficient condition for the quasi-diagonality of a general inverse semigroup., Comment: 11 pages; minor revision, accepted for publication in J. Op. Th

Polyphenols are natural molecules of crucial importance in many applications, of which tannic acid (TA) is one of the most abundant and established. Most high-value applications require precise control of TA interactions with the system of interest. However, the molecular structure of TA is still not comprehended at the atomic level, of which all electronic and reactivity properties depend. Here, we combine an enhanced sampling global optimization method with density functional theory (DFT)-based calculations to explore the conformational space of TA assisted by unsupervised machine learning visualization, and then investigate its lowest energy conformers. We study the external environment's effect on the TA structure and properties. We find that vacuum favors compact structures by stabilizing peripheral atoms' weak interactions, while in water, the molecule adopts more open conformations. The frontier molecular orbitals of the conformers with lowest harmonic vibrational free energy have a HOMO-LUMO energy gap of 2.21 (3.27) eV, increasing to 2.82 (3.88) eV in water, at the DFT generalized gradient approximation (and hybrid) level of theory. Structural differences also change the distribution of potential reactive sites. We establish the fundamental importance of accurate structural consideration in determining TA and related polyphenols interactions in relevant technological applications.

We present TODS, an automated Time Series Outlier Detection System for research and industrial applications. TODS is a highly modular system that supports easy pipeline construction. The basic building block of TODS is primitive, which is an implementation of a function with hyperparameters. TODS currently supports 70 primitives, including data processing, time series processing, feature analysis, detection algorithms, and a reinforcement module. Users can freely construct a pipeline using these primitives and perform end- to-end outlier detection with the constructed pipeline. TODS provides a Graphical User Interface (GUI), where users can flexibly design a pipeline with drag-and-drop. Moreover, a data-driven searcher is provided to automatically discover the most suitable pipelines given a dataset. TODS is released under Apache 2.0 license at https://github.com/datamllab/tods., Comment: Accepted by AAAI'21 demo track

In this work we present the numerical evaluation of a new design of fractal intraocular lens studied through a ray-tracing program. To determine the monochromatic and polychromatic performance of these lenses in different theoretical model eyes the Modulation Transfer Function (MTF) and the area above the MTF (AMTF) have been used. These merit functions show the same behavior for different values of asphericity (Q), independently from the theoretical model eye, even though there are differences due to the Spherical Aberration (SA) considered in each model., Comment: in Spanish, To be published in Revista Mexicana de Fisica

Corneal inlays (CIs) are the most recent surgical procedure for the treatment of presbyopia in patients who want complete independence from the use of glasses or contact lenses. Although refractive surgery in presbyopic patients is mostly performed in combination with cataract surgery, when the implantation of an intraocular lens is not necessary, the option of CIs has the advantage of being minimally invasive. Current designs of CIs are, either: small aperture devices, or refractive devices, however, both methods do not have good performance simultaneously at intermediate and near distances in eyes that are unable to accommodate. In the present study, we propose the first design of a trifocal CI, allowing good vision, at the same time, at far, intermediate and near vision in presbyopic eyes. We first demonstrate the good performance of the new inlay in comparison with a commercially available CI by using optical design software. We next confirm experimentally the image forming capabilities of our proposal employing an adaptive optics based optical simulator. This new design also has a number of parameters that can be varied to make personalized trifocal CI, opening up a new avenue for the treatment of presbyopia.

Given a discrete and countable inverse semigroup $S$ one can study, in analogy to the group case, its geometric aspects. In particular, we can equip $S$ with a natural metric, given by the path metric in the disjoint union of its Sch\"{u}tzenberger graphs. This graph, which we denote by $\Lambda_S$, inherits much of the structure of $S$. In this article we compare the C*-algebra $\mathcal{R}_S$, generated by the left regular representation of $S$ on $\ell^2(S)$ and $\ell^\infty(S)$, with the uniform Roe algebra over the metric space, namely $C^*_u(\Lambda_S)$. This yields a chacterization of when $\mathcal{R}_S = C^*_u(\Lambda_S)$, which generalizes finite generation of $S$. We have termed this by finite labeability (FL), since it holds when the $\Lambda_S$ can be labeled in a finitary manner. The graph $\Lambda_S$, and the FL condition above, also allow to analyze large scale properties of $\Lambda_S$ and relate them with C*-properties of the uniform Roe algebra. In particular, we show that domain measurability of $S$ (a notion generalizing Day's definition of amenability of a semigroup, cf., [5]) is a quasi-isometric invariant of $\Lambda_S$. Moreover, we characterize property A of $\Lambda_S$ (or of its components) in terms of the nuclearity and exactness of the corresponding C*-algebras. We also treat the special classes of F-inverse and E-unitary inverse semigroups from this large scale point of view., Comment: Accepted version for publication; minor changes