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We generalize the seminal polynomial partitioning theorems of Guth and Katz to a set of semi-Pfaffian sets. Specifically, given a set $\Gamma \subseteq \mathbb{R}^n$ of $k$-dimensional semi-Pfaffian sets, where each $\gamma \in \Gamma$ is defined by a fixed number of Pfaffian functions, and each Pfaffian function is in turn defined with respect to a Pfaffian chain $\vec{q}$ of length $r$, for any $D \ge 1$, we prove the existence of a polynomial $P \in \mathbb{R}[X_1, \ldots, X_n]$ of degree at most $D$ such that each connected component of $\mathbb{R}^n \setminus Z(P)$ intersects at most $\sim \frac{|\Gamma|}{D^{n - k - r}}$ elements of $\Gamma$. Also, for any $D \ge 1$, we prove the existence of a Pfaffian function $P'$ of degree at most $D$ defined with respect to $\vec{q}$, such that each connected component of $\mathbb{R}^n \setminus Z(P')$ intersects at most $\sim \frac{|\Gamma|}{D^{n-k}}$ elements of $\Gamma$. To do so, given a $k$-dimensional semi-Pfaffian set $\mathcal{X} \subseteq \mathbb{R}^n$, and a polynomial $P \in \mathbb{R}[X_1, \ldots, X_n]$ of degree at most $D$, we establish a uniform bound on the number of connected components of $\mathbb{R}^n \setminus Z(P)$ that $\mathcal{X}$ intersects; i.e. we prove that the number of connected components of $(\mathbb{R}^n \setminus Z(P)) \cap \mathcal{X}$ is at most $\sim D^{k+r}$. Finally as applications, we derive Pfaffian versions of Szemer\'edi-Trotter type theorems, and also prove bounds on the number of joints between Pfaffian curves., Comment: 27 pages, 0 figures

We investigate the coevolution of metals and dust for 173 galaxies at 4.010 by JWST. Besides, we observe that the metallicity of galaxies at z>8 presents a metal-to-stellar mass ratio larger than a few 10^-3, above a floor. This suggests a very fast rise of metals at high redshift, impacting the tentative detections of population III objects., Comment: This paper is submitted. It contains a main paper with 5 figures and 2 tables, plus supplementary materials

We use JWST/NIRISS slitless spectroscopy from the Next Generation Deep Extragalactic Exploratory Public (NGDEEP) Survey to investigate the physical condition of star-forming galaxies at $1.7 < z < 3.4$. At these redshifts, the deep NGDEEP NIRISS slitless spectroscopy covers the [O II]$\lambda\lambda$3726,3729, [O III]$\lambda\lambda$4959,5007, H$\beta$ and H$\alpha$ emission features for galaxies with stellar masses $\log(\mathrm{M_\ast/M_\odot}) \gtrsim 7$, nearly a factor of a hundred lower than previous studies. We focus on the [O III]/[O II] (O$_{32}$) ratio which is primarily sensitive to the ionization state and with a secondary dependence on the gas-phase metallicity of the interstellar medium. We find significant ($\gtrsim5\sigma$) correlations between the O$_{32}$ ratio and galaxy properties as O$_{32}$ increases with decreasing stellar mass, decreasing star formation rate (SFR), increasing specific SFR (sSFR$\equiv \mathrm{SFR}/M_*$), and increasing equivalent width (EW) of H$\beta$ and H$\alpha$. These trends suggest a tight connection between the ionization parameter and these galaxy properties. Galaxies at $z\sim2-3$ exhibit a higher O$_{32}$ than local normal galaxies with the same stellar masses and SFRs, indicating that they have a higher ionization parameter and lower metallicity than local normal galaxies. In addition, we observe an evolutionary trend in the O$_{32}$ -- EW(H$\beta$) relation from $z\sim0$ and $z\gtrsim5$, such that higher redshift galaxies have higher EW(H$\beta$) and higher O$_{32}$ at fixed EW. We argue that both the enhanced recent star formation activity and the higher star formation surface density may contribute to the increase in O$_{32}$ and the ionization parameter., Comment: 27 pages, 14 figures

The geo-effectiveness of Coronal Mass Ejections (CMEs) is a critical area of study in space weather, particularly in the lesser-explored domain of CME-CME interactions and their geomagnetic consequences. This study leverages the SWASTi framework to perform 3D MHD simulation of a range of CME-CME interaction scenarios within realistic solar wind conditions. The focus is on the dynamics of the initial magnetic flux, speed, density, and tilt of CMEs, and their individual and combined impacts on the disturbance storm time (Dst) index. Additionally, the kinematic, magnetic, and structural impacts on the leading CME, as well as the mixing of both CMEs, are analyzed. Time series in-situ studies are conducted through virtual spacecraft positioned along three different longitudes at 1 AU. Our findings reveal that CME-CME interactions are non-uniform along different longitudes due to the inhomogeneous ambient solar wind conditions. A significant increase in the momentum and kinetic energy of the leading CME is observed due to collisions with the trailing CME, along with the formation of reverse shocks in cases of strong interaction. These reverse shocks lead to complex wave patterns inside CME2, which can prolong the storm recovery phase. Furthermore, we observed that the minimum Dst value decreases with an increase in the initial density, tilt, and speed of the trailing CME., Comment: Accepted for publication in The Astrophysical Journal

Due to the increasing workload of pathologists, the need for automation to support diagnostic tasks and quantitative biomarker evaluation is becoming more and more apparent. Foundation models have the potential to improve generalizability within and across centers and serve as starting points for data efficient development of specialized yet robust AI models. However, the training foundation models themselves is usually very expensive in terms of data, computation, and time. This paper proposes a supervised training method that drastically reduces these expenses. The proposed method is based on multi-task learning to train a joint encoder, by combining 16 different classification, segmentation, and detection tasks on a total of 912,000 patches. Since the encoder is capable of capturing the properties of the samples, we term it the Tissue Concepts encoder. To evaluate the performance and generalizability of the Tissue Concepts encoder across centers, classification of whole slide images from four of the most prevalent solid cancers - breast, colon, lung, and prostate - was used. The experiments show that the Tissue Concepts model achieve comparable performance to models trained with self-supervision, while requiring only 6% of the amount of training patches. Furthermore, the Tissue Concepts encoder outperforms an ImageNet pre-trained encoder on both in-domain and out-of-domain data., Comment: 22 Pages, 3 Figures, submitted to and under revision at Computers in Biology and Medicine

The INTENTAS project aims to develop an atomic sensor utilizing entangled Bose-Einstein condensates (BECs) in a microgravity environment. This key achievement is necessary to advance the capability for measurements that benefit from both entanglement-enhanced sensitivities and extended interrogation times. The project addresses significant challenges related to size, weight, and power management (SWaP) specific to the experimental platform at the Einstein-Elevator in Hannover. The design ensures a low-noise environment essential for the creation and detection of entanglement. Additionally, the apparatus features an innovative approach to the all-optical creation of BECs, providing a flexible system for various configurations and meeting the requirements for rapid turnaround times. Successful demonstration of this technology in the Einstein-Elevator will pave the way for a future deployment in space, where its potential applications will unlock high-precision quantum sensing.

We present a set of photometric catalogs primarily aimed at providing the community with a comprehensive database for the study of galaxy populations in the high redshift Universe. The set gathers data from eight JWST NIRCam observational programs, targeting the Abell 2744 (GLASS-JWST, UNCOVER, DDT2756 and GO3990), EGS (CEERS), COSMOS and UDS (PRIMER), and GOODS North and South (JADES and NGDEEP) deep fields, for a total area of $\sim$0.2 sq. degrees. Photometric estimates are obtained by means of well-established techniques, including tailored improvements designed to enhance the performance on the specific dataset. We also include new measurements from HST archival data, thus collecting 16 bands spanning from 0.44 to 4.44 $\mu$m. A grand total of $\sim$530 thousand sources is detected on stacks of NIRCam 3.56 and 4.44 $\mu$m mosaics. We assess the photometric accuracy by comparing fluxes and colors against archival catalogs. We also provide photometric redshift estimates, statistically validated against a large set of robust spectroscopic data. The catalogs are publicly available on the Astrodeep website., Comment: 28 pages, 16 figures; accepted for publication on Astronomy & Astrophysics

The normalized stress metric measures how closely distances between vertices in a graph drawing match the graph-theoretic distances between those vertices. It is one of the most widely employed quality metrics for graph drawing, and is even the optimization goal of several popular graph layout algorithms. However, normalized stress can be misleading when used to compare the outputs of two or more algorithms, as it is sensitive to the size of the drawing compared to the graph-theoretic distances used. Uniformly scaling a layout will change the value of stress despite not meaningfully changing the drawing. In fact, the change in stress values can be so significant that a clearly better layout can appear to have a worse stress score than a random layout. In this paper, we study different variants for calculating stress used in the literature (raw stress, normalized stress, etc.) and show that many of them are affected by this problem, which threatens the validity of experiments that compare the quality of one algorithm to that of another. We then experimentally justify one of the stress calculation variants, scale-normalized stress, as one that fairly compares drawing outputs regardless of their size. We also describe an efficient computation for scale-normalized stress and provide an open source implementation.

A crucial yet challenging task in galaxy evolution studies is the identification of distant merging galaxies, a task which suffers from a variety of issues ranging from telescope sensitivities and limitations to the inherently chaotic morphologies of young galaxies. In this paper, we use random forests and convolutional neural networks to identify high-redshift JWST CEERS galaxy mergers. We train these algorithms on simulated $3

We present the results of an investigation of a highly variable CIV broad absorption-line feature in the quasar SBS 1408+544 (z=2.337) that shows a significant shift in velocity over time. This source was observed as a part of the Sloan Digital Sky Survey Reverberation Mapping Project and the SDSS-V Black Hole Mapper Reverberation Mapping Project, and has been included in two previous studies, both of which identified significant variability in a high-velocity CIV broad absorption line (BAL) on timescales of just a few days in the quasar rest frame. Using ~130 spectra acquired over eight years of spectroscopic monitoring with SDSS, we have determined that this BAL is not only varying in strength, but is also systematically shifting to higher velocities. Using cross-correlation methods, we measure the velocity shifts (and corresponding acceleration) of the BAL on a wide range of timescales, measuring an overall velocity shift of delta v = -683 (+89, -84) km s-1 over the 8-year monitoring period. This corresponds to an average rest-frame acceleration of a=1.04 (+0.14, -0.13) cm s-2, though the magnitude of the acceleration on shorter timescales is not constant throughout. We place our measurements in the context of BAL-acceleration models and examine various possible causes of the observed velocity shift., Comment: Published in the Astrophysical Journal

For Coxeter groups with sufficiently large braid relations, we prove that the sequence of powers of a Coxeter element has unbounded reflection length. We establish a connection between the reflection length functions on arbitrary Coxeter groups and the reflection length functions on universal Coxeter groups of the same rank through the solution to the word problem for Coxeter groups. For Coxeter groups corresponding to a Coxeter matrix with the same entry everywhere except the diagonal, upper bounds for the reflection length of the powers of Coxeter elements are established., Comment: 21 pages. Comments are welcome!

Multivariate Hawkes processes (MHP) are a class of point processes in which events at different coordinates interact through mutual excitation. The weighted adjacency matrix of the MHP encodes the strength of the relations, and shares its support with the causal graph of interactions of the process. We consider the problem of testing for causal relationships across the dimensions of a marked MHP. The null hypothesis is that a joint group of adjacency coefficients are null, corresponding to the absence of interactions. The alternative is that they are positive, and the associated interactions do exist. To this end, we introduce a novel estimation procedure in the context of a large sample of independent event sequences. We construct the associated likelihood ratio test and derive the asymptotic distribution of the test statistic as a mixture of chi squared laws. We offer two applications on financial datasets to illustrate the performance of our method. In the first one, our test reveals a deviation from a static equilibrium in bidders' strategies on retail online auctions. In the second one, we uncover some factors at play in the dynamics of German intraday power prices.

In a series of precedent papers, we have presented a comprehensive methodology, termed Field Economics, for translating a standard economic model into a statistical field-formalism framework. This formalism requires a large number of heterogeneous agents, possibly of different types. It reveals the emergence of collective states among these agents or type of agents while preserving the interactions and microeconomic features of the system at the individual level. In two prior papers, we applied this formalism to analyze the dynamics of capital allocation and accumulation in a simple microeconomic framework of investors and firms.Building upon our prior work, the present paper refines the initial model by expanding its scope. Instead of considering financial firms investing solely in real sectors, we now suppose that financial agents may also invest in other financial firms. We also introduce banks in the system that act as investors with a credit multiplier. Two types of interaction are now considered within the financial sector: financial agents can lend capital to, or choose to buy shares of, other financial firms. Capital now flows between financial agents and is only partly invested in real sectors, depending on their relative returns. We translate this framework into our formalism and study the diffusion of capital and possible defaults in the system, both at the macro and micro level.At the macro level, we find that several collective states may emerge, each characterized by a distinct level of average capital and investors per sector. These collective states depend on external parameters such as level of connections between investors or firms' productivity.The multiplicity of possible collective states is the consequence of the nature of the system composed of interconnected heterogeneous agents. Several equivalent patterns of returns and portfolio allocation may emerge. The multiple collective states induce the unstable nature of financial markets, and some of them include defaults may emerge. At the micro level, we study the propagation of returns and defaults within a given collective state. Our findings highlight the significant role of banks, which can either stabilize the system through lending activities or propagate instability through loans to investors.