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The 2D projective nature of X-ray radiography presents significant limitations in fluoroscopy-guided interventions, particularly the loss of depth perception and prolonged radiation exposure. Integrating magnetic trackers into these workflows is promising; however, it remains challenging and under-explored in current research and practice. To address this, we employed a radiolucent magnetic field generator (FG) prototype as a foundational step towards seamless magnetic tracking (MT) integration. A two-layer FG mounting frame was designed for compatibility with various C-arm X-ray systems, ensuring smooth installation and optimal tracking accuracy. To overcome technical challenges, including accurate C-arm pose estimation, robust fluoro-CT registration, and 3D navigation, we proposed the incorporation of external aluminum fiducials without disrupting conventional workflows. Experimental evaluation showed no clinically significant impact of the aluminum fiducials and the C-arm on MT accuracy. Our fluoro-CT registration demonstrated high accuracy (mean projection distance approxiamtely 0.7 mm, robustness (wide capture range), and generalizability across local and public datasets. In a phantom targeting experiment, needle insertion error was between 2 mm and 3 mm, with real-time guidance using enhanced 2D and 3D navigation. Overall, our results demonstrated the efficacy and clinical applicability of the MT-assisted approach. To the best of our knowledge, this is the first study to integrate a radiolucent FG into a fluoroscopy-guided workflow., Comment: 11 pages

We aim at characterizing the X-ray-to-optical/near-infrared broad-band emission of luminous QSOs in the first Gyr of cosmic evolution to understand whether they exhibit differences compared to the lower-\textit{z} QSO population. Our goal is also to provide for these objects a reliable and uniform catalog of SED fitting derivable properties such as bolometric and monochromatic luminosities, Eddington ratios, dust extinction, strength of the hot dust emission. We characterize the X-ray/UV emission of each QSO using average SEDs from luminous Type 1 sources and calculate bolometric and monochromatic luminosities. Finally we construct a mean SED extending from the X-rays to the NIR bands. We find that the UV-optical emission of these QSOs can be modelled with templates of $z\sim$2 luminous QSOs. We observe that the bolometric luminosities derived adopting some bolometric corrections at 3000 \AA\ ($BC_{3000\text{\AA}}$) largely used in the literature are slightly overestimated by 0.13 dex as they also include reprocessed IR emission. We estimate a revised value, i.e. $BC_{3000\text{\AA}}=3.3 $ which can be used for deriving $L_\text{bol}$ in \textit{z} $\geq$ 6 QSOs. A sub-sample of 11 QSOs is provided with rest-frame NIR photometry, showing a broad range of hot dust emission strength, with two sources exhibiting low levels of emission. Despite potential observational biases arising from non-uniform photometric coverage and selection biases, we produce a X-ray-to-NIR mean SED for QSOs at \textit{z} $\gtrsim$ 6, revealing a good match with templates of lower-redshift, luminous QSOs up to the UV-optical range, with a slightly enhanced contribution from hot dust in the NIR.

We present a detailed imaging analysis of 260 ks of sub-arcsecond resolution Chandra Advanced CCD Imaging Spectrometer (ACIS-S) observations of the nearby Seyfert 2 galaxy NGC 5728. Our study focuses on the bright and diffuse soft X-ray emission within the galaxy's inner ~1 kpc. By comparing the X-ray emission across different energy bands, we identify localized variations in the absorbing column and emission processes. We observe more X-ray absorption in the direction perpendicular to the bicone, which is co-located with an inner warped CO disk in the galaxy. The innermost region, which shows the strongest excess of hard X-ray emission, is spatially coincident with the CO(2-1) emission from ALMA and dusty spirals observed in a Hubble Space Telescope V-H color map. We detect soft extended emission associated with the circumnuclear star-forming ring at ~1 kpc, suggestive of hot gas with kT=0.44 keV. We derive measurements for the hot gas mass, M=7.9x10^5 solar masses, pressure, p=2.0x10^-10 dyne per square cm, and cooling times, t=193.2 Myr. In the vicinity of the star-forming ring, we detect two X-ray point sources with soft X-ray spectra and 0.3-7 keV luminosities L~8x10^38 erg per second. These properties suggest X-ray binaries., Comment: Accepted for publication on ApJ

Optimization plays an important role in tackling public health problems. Animal instincts can be used effectively to solve complex public health management issues by providing optimal or approximately optimal solutions to complicated optimization problems common in public health. BAT algorithm is an exemplary member of a class of nature-inspired metaheuristic optimization algorithms and designed to outperform existing metaheuristic algorithms in terms of efficiency and accuracy. It's inspiration comes from the foraging behavior of group of microbats that use echolocation to find their target in the surrounding environment. In recent years, BAT algorithm has been extensively used by researchers in the area of optimization, and various variants of BAT algorithm have been developed to improve its performance and extend its application to diverse disciplines. This paper first reviews the basic BAT algorithm and its variants, including their applications in various fields. As a specific application, we apply the BAT algorithm to a biostatistical estimation problem and show it has some clear advantages over existing algorithms., Comment: 31 pages, 2 figures

We use the Hubble Space Telescope to analyse the extended [O III] 5007A emission in seven bright radio-quiet type 1 quasars (QSO1s), focusing on the morphology and physical conditions of their extended Narrow-Line Regions (NLRs). We find NLRs extending 3-9 kpc, with four quasars showing roughly symmetrical structures (b/a=1.2-1.5) and three displaying asymmetric NLRs (b/a=2.4-5.6). When included with type 1 and type 2 AGNs from previous studies, the sizes of the extended [O III] regions scale with luminosity as $R[O III] \sim L[O III]^{0.5}$, consistent with photoionisation. However, when analysed separately, type 1s exhibit a steeper slope ($\gamma=0.57\pm0.05$) compared to type 2 AGNs ($\gamma=0.48\pm0.02$). We use photoionisation modeling to estimate the maximum NLRs sizes, assuming a minimum ionisation parameter of $\log(U) = -3$, an ionising luminosity based on the $L[O III]$-derived bolometric luminosity, and a minimum gas number density $n_H \sim 100\,\text{cm}^{-3}$, assuming that molecular clouds provide a reservoir for the ionised gas. The derived sizes agree well with direct measurements for a sample of type 2 quasars, but are underestimated for the current sample of QSO1s. A better agreement is obtained for the QSO1s using bolometric luminosities derived from the 5100A continuum luminosity. Radial mass profiles for the QSO1s show significant extended mass in all cases, but with less [O III]-emitting gas near the central AGN compared to QSO2s. This may suggest that the QSO1s are in a later evolutionary stage than QSO2s, further past the blow-out stage., Comment: Accepted for publication on MNRAS

One of the main open questions in the field of luminous ($L_{\rm bol}>10^{47}\,\rm erg\,s^{-1}$) quasars (QSOs) at $z \gtrsim 6$ is the rapid formation ($< 1\,$Gyr) of their supermassive black holes (SMBHs). For this work we analysed the relation between the X-ray properties and other properties describing the physics and growth of both the accretion disc and the SMBH in QSOs at the Epoch of Reionization (EoR). The sample consists of 21 $z>6$ QSOs, which includes 16 sources from the rapidly grown QSOs from the HYPERION sample and five other luminous QSOs with available high-quality archival X-ray data. We discovered a strong and statistically significant ($>3\sigma$) relation between the X-ray continuum photon index ($\Gamma$) and the $\rm C\,IV$ disc wind velocity ($v_{\rm C\,IV}$) in $z>6$ luminous QSOs, whereby the higher the $v_{\rm C\,IV}$, the steeper the $\Gamma$. This relation suggests a link between the disc-corona configuration and the kinematics of disc winds. Furthermore, we find evidence at $>2-3\sigma$ level that $\Gamma$ and $v_{\rm C\,IV}$ are correlated to the growth rate history of the SMBH. Although additional data are needed to confirm it, this result may suggest that, in luminous $z>6$ QSOs, the SMBH predominantly grows via fast accretion rather than via initial high seed BH mass., Comment: Accepted for publication in Astronomy & Astrophysics

Machine learning models may capture and amplify biases present in data, leading to disparate test performance across social groups. To better understand, evaluate, and mitigate these possible biases, a deeper theoretical understanding of how model design choices and data distribution properties could contribute to bias is needed. In this work, we contribute a precise analytical theory in the context of ridge regression, both with and without random projections, where the former models neural networks in a simplified regime. Our theory offers a unified and rigorous explanation of machine learning bias, providing insights into phenomena such as bias amplification and minority-group bias in various feature and parameter regimes. For example, we demonstrate that there may be an optimal regularization penalty or training time to avoid bias amplification, and there can be fundamental differences in test error between groups that do not vanish with increased parameterization. Importantly, our theoretical predictions align with several empirical observations reported in the literature. We extensively empirically validate our theory on diverse synthetic and semi-synthetic datasets.

Within the scaling laws paradigm, which underpins the training of large neural networks like ChatGPT and Llama, we consider a supervised regression setting and establish the existance of a strong form of the model collapse phenomenon, a critical performance degradation due to synthetic data in the training corpus. Our results show that even the smallest fraction of synthetic data (e.g., as little as 1\% of the total training dataset) can still lead to model collapse: larger and larger training sets do not enhance performance. We further investigate whether increasing model size, an approach aligned with current trends in training large language models, exacerbates or mitigates model collapse. In a simplified regime where neural networks are approximated via random projections of tunable size, we both theoretically and empirically show that larger models can amplify model collapse. Interestingly, our theory also indicates that, beyond the interpolation threshold (which can be extremely high for very large datasets), larger models may mitigate the collapse, although they do not entirely prevent it. Our theoretical findings are empirically verified through experiments on language models and feed-forward neural networks for images.

In the realm of competitive gaming, 3D first-person shooter (FPS) games have gained immense popularity, prompting the development of game AI systems to enhance gameplay. However, deploying game AI in practical scenarios still poses challenges, particularly in large-scale and complex FPS games. In this paper, we focus on the practical deployment of game AI in the online multiplayer competitive 3D FPS game called Arena Breakout, developed by Tencent Games. We propose a novel gaming AI system named Private Military Company Agent (PMCA), which is interactable within a large game map and engages in combat with players while utilizing tactical advantages provided by the surrounding terrain. To address the challenges of navigation and combat in modern 3D FPS games, we introduce a method that combines navigation mesh (Navmesh) and shooting-rule with deep reinforcement learning (NSRL). The integration of Navmesh enhances the agent's global navigation capabilities while shooting behavior is controlled using rule-based methods to ensure controllability. NSRL employs a DRL model to predict when to enable the navigation mesh, resulting in a diverse range of behaviors for the game AI. Customized rewards for human-like behaviors are also employed to align PMCA's behavior with that of human players.

Exploring SMBH population in protoclusters offers valuable insights into how environment affects SMBH growth. However, research on AGN within these areas is still limited by the small number of protoclusters known at high redshift and by the availability of associated deep X-ray observations. To understand how different environments affect AGN triggering and growth at high redshift, we investigated the X-ray AGN population in the field of the MUSE Quasar Nebula 01 (MQN01) protocluster at z ~3.25. This field is known for hosting the largest Lya nebula in the Borisova+16 sample, and one of the largest overdensities of UV-continuum selected and sub-mm galaxies found so far at this redshift. We conducted a ultra deep Chandra X-ray survey (634 ks) observation of the MQN01 field and produced a comparative analyses of the properties of the X-ray AGNs detected in MQN01 against those observed in other selected protoclusters, such as Spiderweb and SSA22. By combining the X-ray, deep MUSE and ALMA data of the same field, we identified six X-ray AGNs within a volume of 16 cMpc^2 and \pm 1000 km/s, corresponding to an X-ray AGN overdensity of ~1000. This overdensity increases at the bright end, exceeding what was observed in the Spiderweb and SSA22 within similar volumes. The AGN fraction measured in MQN01 is significantly higher (f_AGN > 20%) than in the field and increases with stellar masses, reaching a value of 100% for log(M*/Msun) > 10.5. Lastly, we observe that the average specific accretion rate (\lambda_sBHAR) for SMBH populations in MQN01 is higher than in the field and other protoclusters, generally increasing as one moves toward the center of the overdensity. Our results, especially the large fraction of highly accreting SMBHs in the inner regions of the MQN01 overdensity, suggest that protocluster environments offer ideal physical conditions for SMBH triggering and growth., Comment: 19 pages, 13 figures, submitted on the A&A on September 9, 2024

Liver tumor ablation procedures require accurate placement of the needle applicator at the tumor centroid. The lower-cost and real-time nature of ultrasound (US) has advantages over computed tomography (CT) for applicator guidance, however, in some patients, liver tumors may be occult on US and tumor mimics can make lesion identification challenging. Image registration techniques can aid in interpreting anatomical details and identifying tumors, but their clinical application has been hindered by the tradeoff between alignment accuracy and runtime performance, particularly when compensating for liver motion due to patient breathing or movement. Therefore, we propose a 2D-3D US registration approach to enable intra-procedural alignment that mitigates errors caused by liver motion. Specifically, our approach can correlate imbalanced 2D and 3D US image features and use continuous 6D rotation representations to enhance the model's training stability. The dataset was divided into 2388, 196 and 193 image pairs for training, validation and testing, respectively. Our approach achieved a mean Euclidean distance error of 2.28 mm $\pm$ 1.81 mm and a mean geodesic angular error of 2.99$^{\circ}$ $\pm$ 1.95$^{\circ}$, with a runtime of 0.22 seconds per 2D-3D US image pair. These results demonstrate that our approach can achieve accurate alignment and clinically acceptable runtime, indicating potential for clinical translation., Comment: 15 pagers, 9 figures

In multi-agent learning, the predominant approach focuses on generalization, often neglecting the optimization of individual agents. This emphasis on generalization limits the ability of agents to utilize their unique strengths, resulting in inefficiencies. This paper introduces Comparative Advantage Maximization (CAM), a method designed to enhance individual agent specialization in multiagent systems. CAM employs a two-phase process, combining centralized population training with individual specialization through comparative advantage maximization. CAM achieved a 13.2% improvement in individual agent performance and a 14.9% increase in behavioral diversity compared to state-of-the-art systems. The success of CAM highlights the importance of individual agent specialization, suggesting new directions for multi-agent system development., Comment: 19 pages

We present a multi-wavelength analysis of MCG+11-11-032, a nearby AGN with the unique classification of both a binary and a dual AGN candidate. With new Chandra observations we aim to resolve any dual AGN system via imaging data, and search for signs of a binary AGN via analysis of the X-ray spectrum. Analyzing the Chandra spectrum, we find no evidence of previously suggested double-peaked Fe K$\alpha$ lines; the spectrum is instead best fit by an absorbed powerlaw with a single Fe K$\alpha$ line, as well as an additional line centered at $\approx$7.5 keV. The Chandra observation reveals faint, soft, and extended X-ray emission, possibly linked to low-level nuclear outflows. Further analysis shows evidence for a compact, hard source -- MCG+11-11-032 X2 -- located 3.27'' from the primary AGN. Modeling MCG+11-11-032 X2 as a compact source, we find that it is relatively luminous ($L_{\text{2$-$10 keV}} = 1.52_{-0.48}^{+0.96}\times 10^{41}$ erg s$^{-1}$), and the location is coincident with an compact and off-nuclear source resolved in Hubble Space Telescope infrared (F105W) and ultraviolet (F621M, F547M) bands. Pairing our X-ray results with a 144 MHz radio detection at the host galaxy location, we observe X-ray and radio properties similar to those of ESO 243-49 HLX-1, suggesting that MCG+11-11-032 X2 may be a hyper-luminous X-ray source. This detection with Chandra highlights the importance of a high-resolution X-ray imager, and how previous binary AGN candidates detected with large-aperture instruments benefit from high-resolution follow-up. Future spatially resolved optical spectra, and deeper X-ray observations, can better constrain the origin of MCG+11-11-032 X2., Comment: 16 pages, 7 figures, submitted to ApJ

Language models (LMs) trained on web-scale datasets are largely successful due to their ability to memorize large amounts of training data, even if only present in a few examples. These capabilities are often desirable in evaluation on tasks such as question answering but raise questions about whether these models can exhibit genuine reasoning or succeed only at mimicking patterns from the training data. This distinction is particularly salient in forecasting tasks, where the answer is not present in the training data, and the model must reason to make logical deductions. We present Reasoning and Tools for Forecasting (RTF), a framework of reasoning-and-acting (ReAct) agents that can dynamically retrieve updated information and run numerical simulation with equipped tools. We evaluate our model with questions from competitive forecasting platforms and demonstrate that our method is competitive with and can outperform human predictions. This suggests that LMs, with the right tools, can indeed think and adapt like humans, offering valuable insights for real-world decision-making.

This manuscript provides an in-depth exploration of Brownian Motion, a fundamental stochastic process in probability theory for Biostatisticians. It begins with foundational definitions and properties, including the construction of Brownian motion and its Markovian characteristics. The document delves into advanced topics such as the Karhunen-Loeve expansion, reflection principles, and Levy's modulus of continuity. Through rigorous proofs and theorems, the manuscript examines the non-differentiability of Brownian paths, the behavior of zero sets, and the significance of local time. The notes also cover important results like Donsker's theorem and Blumenthal's 0-1 law, emphasizing their implications in the study of stochastic processes.

In this article we study the first, the second and the third homology groups of the elementary group $\textrm{E}_2(A)$, where $A$ is a commutative ring. In particular, we prove a refined Bloch-Wigner type exact sequence over a semilocal ring (with some mild restriction on its residue fields) such that $-1\in (A^{\times})^2$ or $|A^{\times}/(A^{\times})^2|\leq 4$.

The latest trends in the adoption of cloud, edge, and distributed computing, as well as a rise in applying AI/ML workloads, have created a need to measure, monitor, and reduce the carbon emissions of these compute-intensive workloads and the associated communication costs. The data movement over networks has considerable carbon emission that has been neglected due to the difficulty in measuring the carbon footprint of a given end-to-end network path. We present a novel network carbon footprint measuring mechanism and propose three ways in which users can optimize scheduling network-intensive tasks to enable carbon savings through shifting tasks in time, space, and overlay networks based on the geographic carbon intensity.

Large Language Models (LLM) are increasingly trained on data generated by other LLM, either because generated text and images become part of the pre-training corpus, or because synthetized data is used as a replacement for expensive human-annotation. This raises concerns about \emph{model collapse}, a drop in model performance when their training sets include generated data. Considering that it is easier for both humans and machines to tell between good and bad examples than to generate high-quality samples, we investigate the use of verification on synthesized data to prevent model collapse. We provide a theoretical characterization using Gaussian mixtures, linear classifiers, and linear verifiers to derive conditions with measurable proxies to assess whether the verifier can effectively select synthesized data that leads to optimal performance. We experiment with two practical tasks -- computing matrix eigenvalues with transformers and news summarization with LLMs -- which both exhibit model collapse when trained on generated data, and show that verifiers, even imperfect ones, can indeed be harnessed to prevent model collapse and that our proposed proxy measure strongly correlates with performance.

Deep Reinforcement Learning (DRL) agents have demonstrated impressive success in a wide range of game genres. However, existing research primarily focuses on optimizing DRL competence rather than addressing the challenge of prolonged player interaction. In this paper, we propose a practical DRL agent system for fighting games named Sh\=ukai, which has been successfully deployed to Naruto Mobile, a popular fighting game with over 100 million registered users. Sh\=ukai quantifies the state to enhance generalizability, introducing Heterogeneous League Training (HELT) to achieve balanced competence, generalizability, and training efficiency. Furthermore, Sh\=ukai implements specific rewards to align the agent's behavior with human expectations. Sh\=ukai's ability to generalize is demonstrated by its consistent competence across all characters, even though it was trained on only 13% of them. Additionally, HELT exhibits a remarkable 22% improvement in sample efficiency. Sh\=ukai serves as a valuable training partner for players in Naruto Mobile, enabling them to enhance their abilities and skills., Comment: Accept at ICML 2024

Principal curve is a well-known statistical method oriented in manifold learning using concepts from differential geometry. In this paper, we propose a novel metric-based principal curve (MPC) method that learns one-dimensional manifold of spatial data. Synthetic datasets Real applications using MNIST dataset show that our method can learn the one-dimensional manifold well in terms of the shape.

The advent of Internet of Things (IoT) technology has generated massive interest in voice-controlled smart homes. While many voice-controlled smart home systems are designed to understand and support widely spoken languages like English, speakers of low-resource languages like Luganda may need more support. This research project aimed to develop a Luganda speech intent classification system for IoT applications to integrate local languages into smart home environments. The project uses hardware components such as Raspberry Pi, Wio Terminal, and ESP32 nodes as microcontrollers. The Raspberry Pi processes Luganda voice commands, the Wio Terminal is a display device, and the ESP32 nodes control the IoT devices. The ultimate objective of this work was to enable voice control using Luganda, which was accomplished through a natural language processing (NLP) model deployed on the Raspberry Pi. The NLP model utilized Mel Frequency Cepstral Coefficients (MFCCs) as acoustic features and a Convolutional Neural Network (Conv2D) architecture for speech intent classification. A dataset of Luganda voice commands was curated for this purpose and this has been made open-source. This work addresses the localization challenges and linguistic diversity in IoT applications by incorporating Luganda voice commands, enabling users to interact with smart home devices without English proficiency, especially in regions where local languages are predominant., Comment: Presented as a conference paper at ICLR 2024/AfricaNLP

In this article we study the low dimensional homology of the projective linear group $\textrm{PGL}_2(A)$ over a commutative ring $A$. In particular, we prove a Bloch-Wigner type exact sequence over local domains. As applications we prove that $H_2(\textrm{PGL}_2(A),\mathbb{Z}\left[\frac{1}{2}\right])\simeq K_2(A)\left[\frac{1}{2}\right]$ and $H_3(\textrm{PGL}_2(A),\mathbb{Z}\left[\frac{1}{2}\right])\simeq K_3^{\textrm{ind}}(A)\left[\frac{1}{2}\right]$ provided $|A/\mathcal{m}_A|\neq 2,3,4,8$.

This paper presents a discriminative classifier for compositional data. This classifier is based on the posterior distribution of the Generalized Dirichlet which is the discriminative counterpart of Generalized Dirichlet mixture model. Moreover, following the mixture of experts paradigm, we proposed a hierarchical mixture of this classifier. In order to learn the models parameters, we use a variational approximation by deriving an upper-bound for the Generalized Dirichlet mixture. To the best of our knownledge, this is the first time this bound is proposed in the literature. Experimental results are presented for spam detection and color space identification.

We propose TRAC, a tool for the specification and verification of coordinated multiparty distributed systems. Relying on finite-state machines (FSMs) where transition labels look like Hoare triples, \thetool can specify the coordination of the participants of a distributed protocol for instance an execution model akin blockchain smart contracts (SCs). In fact, the transitions of our FSMs yield guards, and assignments over data variables, and with participants binders. The latter allow us to model scenarios with an unbounded number of participants which can vary at run-time. We introduce a notion of well-formedness to rule out meaningless or problematic specifications. This notion is verified with TRAC and demonstrated on several case studies borrowed from the smart contracts domain. Then, we evaluate the performance of TRAC using a set of randomised examples, studying the correlations between the features supported and the time taken to decide well-formedness.

We report the identification of a quasar overdensity in the BOSSJ0210 field, dubbed Cosmic Himalayas, consisting of 11 quasars at $z=2.16-2.20$, the densest overdensity of quasars ($17\sigma$) in the $\sim$10,000 deg$^2$ of the Sloan Digital Sky Survey. We present the spatial distributions of galaxies and quasars and an HI absorption map of the intergalactic medium (IGM). On the map of 465 galaxies selected from the MAMMOTH-Subaru survey, we find two galaxy density peaks that do not fall on the quasar overdensity but instead exist at the northwest and southeast sides, approximately 25 $h^{-1}$ comoving-Mpc apart from the quasar overdensity. With a spatial resolution of 15 $h^{-1}$ comoving Mpc in projection, we produce a three-dimensional HI tomography map by the IGM Ly$\alpha$ forest in the spectra of 23 SDSS/eBOSS quasars behind the quasar overdensity. Surprisingly, the quasar overdensity coincides with neither an absorption peak nor a transmission peak of IGM HI but lies near the border separating opaque and transparent volumes, with the more luminous quasars located in an environment with lesser IGM HI. Hence remarkably, the overdensity region traced by the 11 quasars, albeit all in coherently active states, has no clear coincidence with peaks of galaxies or HI absorption densities. Current physical scenarios with mixtures of HI overdensities and quasar photoionization cannot fully interpret the emergence of Cosmic Himalayas, suggesting this peculiar structure is an excellent laboratory to unveil the interplay between galaxies, quasars, and the IGM., Comment: 19 pages, 11 figures, submitted to ApJ, comments are welcome

The formation and structure of the Milky Way has a fundamental role in our understanding of the universe and its evolution, and thanks to the Gaia mission and large spectroscopic surveys, we live an exceptional moment of data availability, allowing us to trace the building blocks of the Galactic disk and their relations. In this sense, we propose here the exploration of a large dataset in a top-down fashion, elaborating a similarity map of the local Galactic volume in order to segregate and characterise its main components, searching for hints about their relations. We have used the t-SNE algorithm with chemical, orbital and kinematic properties of the stars to produce 2D manifolds and dissect their structure by isolating populations to further analyse their behaviour. The young thin disk could be clearly separated from the older thick disk, also showing a puzzling transition zone with hints about the aftermath of the Gaia-Sausage-Enceladus merger. Moving groups and resonant features also appear prominently in the maps, splitting the disk into inner and outer portions as consequence of the resonances produced by the Galactic bar. The dynamical halo appears as an extreme end related to the heated portion of the thick disk, showing sub-structures corresponding to known accreted populations. Open and globular clusters also appear in their chemical/evolutionary context. We present details of the developed strategy, an overview of the different populations and their relations, as well as a discussion and insights of our results in the scenario of Galactic evolution., Comment: 21 pages, 30 figures

In cancer research, leveraging patient-derived xenografts (PDXs) in pre-clinical experiments is a crucial approach for assessing innovative therapeutic strategies. Addressing the inherent variability in treatment response among and within individual PDX lines is essential. However, the current literature lacks a user-friendly statistical power analysis tool capable of concurrently determining the required number of PDX lines and animals per line per treatment group in this context. In this paper, we present a simulation-based R package for sample size determination, named `\textbf{PDXpower}', which is publicly available at The Comprehensive R Archive Network \url{https://CRAN.R-project.org/package=PDXpower}. The package is designed to estimate the necessary number of both PDX lines and animals per line per treatment group for the design of a PDX experiment, whether for an uncensored outcome, or a censored time-to-event outcome. Our sample size considerations rely on two widely used analytical frameworks: the mixed effects ANOVA model for uncensored outcomes and Cox's frailty model for censored data outcomes, which effectively account for both inter-PDX variability and intra-PDX correlation in treatment response. Step-by-step illustrations for utilizing the developed package are provided, catering to scenarios with or without preliminary data.