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We analyze the stability properties of a very simple holographic model for a confining field theory. The gravity dual consists of an Abelian gauge field, with non-trivial magnetic flux, coupled to six-dimensional gravity with a negative cosmological constant. We construct a one-parameter family of regular solitonic solutions, where the gauge field carries flux along a compact circle that smoothly shrinks at a finite value of the holographic direction, introducing a confinement scale in the dual effective four-dimensional field theory. The free energy of these solitonic backgrounds is compared to that of domain-wall solutions representing a five-dimensional conformal field theory. This reveals a zero-temperature first-order phase transition in the dual field theory, separating confining and conformal phases. We compute the spectrum of bound states by analysing field fluctuations in the gravity background, after dimensional reduction on the circle. The lightest states are a scalar and a vector particle. A tachyonic instability emerges near a turning point in the free energy, where its concavity changes. The phase transition prevents the realisation of this instability. Within the stable portion of parameter space, all bound states, including the lightest scalar, have masses comparable to other dynamical scales. Near the phase transition and beyond, in metastable and unstable regions, we find deviations in the mass of the lightest scalar, suggesting it couples to the trace of the stress-energy tensor in the field theory, consistently with its interpretation as an approximate dilaton., Comment: 20 pages, 4 figures. Reference added to data release

The TraX Engine is an advanced data processing tool developed by ADVACAM in collaboration with the European Space Agency (ESA), specifically designed for analyzing data from Timepix detectors equipped with various sensor materials (Si, CdTe, GaAs, SiC). TraX Engine can process large datasets across various scientific and medical applications, including space radiation monitoring, particle therapy, and imaging. In space applications, the TraX Engine has been used to process data from satellites like OneWeb JoeySat deployed in LEO orbit, where it continuously monitors space radiation environments measuring flux, dose, and dose rate in real-time. In medical applications, particularly in particle therapy, the TraX Engine is used to process data to characterize radiation fields in terms of particle flux, Linear Energy Transfer, and spatial distribution of the radiation dose. The TraX Engine can identify and classify scattered particles, such as secondary protons and electrons, and estimate their contribution to out-of-field doses. In imaging applications, the TraX Engine is integrated into Compton cameras, where it supports photon source localization through directional reconstruction of photons. The system ability to identify gamma radiation source with high precision makes it suitable for medical imaging tasks, such as tracking I-131 used in thyroid cancer treatment or localizing radiation sources. This paper presents the architecture and capabilities of the newly developed software TraX Engine, alongside results from various applications, demonstrating its role in particle tracking, radiation monitoring, imaging, and others. With its modular architecture, the TraX Engine offers multiple interfaces, including a command-line tool, an API, a web portal, and a graphical user interface, ensuring usability across different fields and user expertise levels., Comment: 14 pages, 7 figures

The semi-random hypergraph process is a natural generalisation of the semi-random graph process, which can be thought of as a one player game. For fixed $r < s$, starting with an empty hypergraph on $n$ vertices, in each round a set of $r$ vertices $U$ is presented to the player independently and uniformly at random. The player then selects a set of $s-r$ vertices $V$ and adds the hyperedge $U \cup V$ to the $s$-uniform hypergraph. For a fixed (monotone) increasing graph property, the player's objective is to force the graph to satisfy this property with high probability in as few rounds as possible. We focus on the case where the player's objective is to construct a subgraph isomorphic to an arbitrary, fixed hypergraph $H$. In the case $r=1$ the threshold for the number of rounds required was already known in terms of the degeneracy of $H$. In the case $2 \le r < s$, we give upper and lower bounds on this threshold for general $H$, and find further improved upper bounds for cliques in particular. We identify cases where the upper and lower bounds match. We also demonstrate that the lower bounds are not always tight by finding exact thresholds for various paths and cycles.

Objective: To propose a mathematical model for applying Ionization Detail (ID), the detailed spatial distribution of ionization along a particle track, to proton and ion beam radiotherapy treatment planning (RTP). Approach: Our model provides for selection of preferred ID parameters (I_p) for RTP, that associate closest to biological effects. Cluster dose is proposed to bridge the large gap between nanoscopic I_p and macroscopic RTP. Selection of I_p is demonstrated using published cell survival measurements for protons through argon, comparing results for nineteen Ip: N_k; k = 2,3,...,10, the number of ionizations in clusters of k or more per particle, and F_k; k = 1,2,...,10, the number of clusters of k or more per particle. We then describe application of the model to ID-based RTP and propose a path to clinical translation. Main results: The preferred I_p were N_4 and F_5 for aerobic cells, N_5 and F_7 for hypoxic cells. Signifcant differences were found in cell survival for beams having the same LET or the preferred N_k. Conversely, there was no signi?cant difference for F_5 for aerobic cells and F_7 for hypoxic cells, regardless of ion beam atomic number or energy. Further, cells irradiated with the same cluster dose for these I_p had the same cell survival. Based on these preliminary results and other compelling results in nanodosimetry, it is reasonable to assert that I_p exist that are more closely associated with biological effects than current LET-based approaches and microdosimetric RBE-based models used in particle RTP. However, more biological variables such as cell line and cycle phase, as well as ion beam pulse structure and rate still need investigation. Signifcance: Our model provides a practical means to select preferred I_p from radiobiological data, and to convert I_p to the macroscopic cluster dose for particle RTP., Comment: 31 pages, 12 figures

Plastic scintillator strips are considered as one of the promising solutions for the cost-effective construction of total-body positron emission tomography, (PET) system. The purpose of the performed measurements is to compare the transparency of long plastic scintillators with dimensions 6 mm x 24 mm x 1000 mm and with all surfaces polished. Six different types of commercial, general purpose, blue-emitting plastic scintillators with low attenuation of visible light were tested, namely: polyvinyl toluene-based BC-408, EJ-200, RP-408, and polystyrene-based Epic, SP32 and UPS-923A. For determination of the best type of plastic scintillator for totalbody Jagiellonian positron emission tomograph (TB-J-PET) construction, emission and transmission spectra, and technical attenuation length (TAL) of blue light-emitting by the scintillators were measured and compared. The TAL values were determined with the use of UV lamp as excitation source, and photodiode as light detector. Emission spectra of investigated scintillators have maxima in the range from 420 nm to 429 nm. The BC-408 and EJ-200 have the highest transmittance values of about 90% at the maximum emission wavelength measured through a 6 mm thick scintillator strip and the highest technical attenuation length reaching about 2000 mm, allowing assembly of long detection modules for time-of-flight (TOF) J-PET scanners. Influence of the 6 mm x 6 mm, 12 mm x 6 mm, 24 mm x 6 mm cross-sections of the 1000 mm long EJ-200 plastic scintillator on the TAL and signal intensity was measured. The highest TAL value was determined for samples with 24 mm x 6 mm cross-section., Comment: 10 pages, 5 figures

Prior research has found that economic downturns have positive effects on new teacher quality, but has not been able to determine the extent to which this relationship arises from a supply response (increased quantity or positive selection of teaching candidates) vs. a demand response (selection in hiring enabled by falling demand). In this paper, I use longitudinal data on students and teachers in Massachusetts to describe the effects of higher unemployment rates on both supply and demand for teachers. I show that students who graduate from college when unemployment rates are higher are more likely to take a teacher certification test, and that this effect is stronger among students who were higher achieving while in high school. On the demand side of the market, higher unemployment reduces new teacher hiring and the overall number of teachers employed, but I find no evidence that schools differentially employ higher achieving teaching candidates during economic downturns. While I cannot definitively rule out changes in demand-side selection, I show that much of the positive relationship between unemployment rates and teacher quality can be explained by positively selected supply. My results suggest that economic incentives impact both the quantity and the quality of new teaching candidates, with implications for attracting and retaining high-quality teachers outside of economic downturns.

In Massachusetts, as is true nationally, teachers are less racially diverse than students. As of the 2021-22 school year, 87 percent of teachers in the state were White, compared with only 54 percent of students. In response to this disparity, Massachusetts lawmakers have proposed legislation targeting the shortage of teachers of color. In this report, the author uses data on Massachusetts K-12 public school students and teachers to provide evidence on three leaks in the teacher pipeline that policies could target to support teaching candidates of color. The sample consists of Massachusetts public school students from the high school graduating classes of 2003 to 2013 who indicated an interest in teaching by taking the state's Communications and Literacy Skills Test (CLST), which is required for teacher licensure.

A re-examination of high-resolution spectral monitoring of the W UMa-type binaries AW UMa and Epsilon CrA casts doubt on the widely utilized Lucy (1968a, 1968b) model of contact binaries. The detection of the very faint profile of the secondary component in AW UMa leads to a new spectroscopic determination of the mass ratio, q(sp) = 0.092 +/- 0.007, which is close to the previous, medium-resolution spectroscopic result of Pribulla & Rucinski (2008), q(sp) = 0.101 +/- 0.006, and remains substantially different from a cluster of generally accepted photometric results by several authors, concentrated around q(ph) = 0.080 +/- 0.005. The two approaches are independent, with the spectroscopic technique being more direct yet more demanding on telescope/spectrograph resources, while the photometric determinations are accessible to smaller telescopes but entirely dependent on the Lucy model. A survey of binaries with the best-determined values of the mass ratio shows a common tendency for q(ph) < q(sp). The tendency for systematically smaller values of q(ph) may result from the overfilling of the primary lobe and underfilling of the secondary lobe relative to the Roche model geometry, as predicted by the Stepien (2009) model; the tendency may be variable in time. Despite the observed moderate inter-systemic velocities, the photometric Lucy model may remain useful in providing approximate, though biased, results for the mass ratio. A complicating factor in detailed spectral analysis may be the occurrence of Enhanced Spectral-line Perturbations (ESP) projected over the secondary profiles, appearing in different numbers in the two studied binaries. The ESPs are tentatively identified within the Stepien model as collision fronts or fountains of hot, primary-component gas from the circumbinary, energy-carrying flow., Comment: Accepted by AJ. Minor changes possible

An attempt is made to evaluate progress of the Polish astrophysical research of stars and of the inter-stellar medium (ISM) on the basis of scientific paper citations in the ADS database. Rather modest citation levels were observed in the years before the mid-1950's. In the years 1958 - 1973, thanks to the partly opened foreign contacts and to strong support from astronomers of the older generation, work of a number of young, energetic enthusiasts reached the world science levels and formed a strong basis for the well recognized, international successes of the next generations., Comment: Presented on the 100-year anniversary of the Polish Astronomical Society during the meeting in Torun, Poland, Sept.11-16, 2023

This study explores the potential of fine-tuning foundational English Large Language Models (LLMs) for generating Polish text. The first step involves Language Adaptive Pre-training (LAPT) on a high-quality dataset of 3.11 GB, consisting of 276 million Polish tokens. The LAPT is followed by additional fine-tuning aimed at solving nine KLEJ challenges. Our trained model Curie-7B-v1 not only generates Polish text with the lowest perplexity of 3.02 among decoder-based Polish models but also closely rivals the performance of the best Polish encoder-decoder models with a less than 2% gap on 8 out of 9 tasks. Curie-7B-v1 used approximately 2-3% of a typical dataset size to learn Polish. The LAPT was completed in less than five days using a consumer GPU, highlighting the method's efficiency. The proficiency of the model in Polish was significantly enhanced, demonstrating the viability of this approach for adding new languages to existing LLMs by training just 1.2% of its parameters. To contribute to the community's collaborative progress, the model has been released as open-source., Comment: 10 pages

Let $M$ be an ordered matching of size $n$, that is, a partition of the set $[2n]$ into 2-element subsets. The sock number of $M$ is the maximum size of a sub-matching of $M$ in which all left-ends of the edges precede all the right-ends (such matchings are also called bipartite). The name of this parameter comes from an amusing "real-life" problem posed by Bosek, concerning an on-line pairing of randomly picked socks from a drying machine. Answering one of Bosek's questions we prove that the sock number of a random matching of size $n$ is asymptotically equal to $n/2$. Moreover, we prove that the expected average number of socks waiting for their match during the whole process is equal to $\frac{2n+1}{6}$. Analogous results are obtained if socks come not in pairs, but in sets of size $r\geq 2$, which corresponds to a similar problem for random ordered $r$-matchings. We also attempt to enumerate matchings with a given sock number.

A graph $d$-process starts with an empty graph on $n$ vertices, and adds one edge at each time step, chosen uniformly at random from those pairs which are not yet edges and whose both vertices have current degree less than $d$. If, in the final graph, at most one vertex has degree $d-1$ and all other have degree $d$, we call the process saturated. We present a new approach to analysing this process based on random allocation of balls in bins. This allows us to get improved results on the degree distribution throughout the process and, consequently, to determine the asymptotic probability of non-saturation of the process., Comment: 39 pages

An ordered $r$-matching of size $n$ is an $r$-uniform hypergraph on a linearly ordered set of vertices, consisting of $n$ pairwise disjoint edges. Two ordered $r$-matchings are isomorphic if there is an order-preserving isomorphism between them. A pair of twins in an ordered $r$-matching is formed by two vertex disjoint isomorphic sub-matchings. Let $t^{(r)}(n)$ denote the maximum size of twins one may find in every ordered $r$-matching of size $n$. By relating the problem to that of largest twins in permutations and applying some recent Erd\H{o}s-Szekeres-type results for ordered matchings, we show that $t^{(r)}(n)=\Omega\left(n^{\frac{3}{5\cdot(2^{r-1}-1)}}\right)$ for every fixed $r\geqslant 2$. On the other hand, $t^{(r)}(n)=O\left(n^{\frac{2}{r+1}}\right)$, by a simple probabilistic argument. As our main result, we prove that, for almost all ordered $r$-matchings of size $n$, the size of the largest twins achieves this bound.

Objective: The aim of this work is to investigate the feasibility of the Jagiellonian Positron Emission Tomography (J-PET) scanner for intra-treatment proton beam range monitoring. Approach: The Monte Carlo simulation studies with GATE and PET image reconstruction with CASToR were performed in order to compare six J-PET scanner geometries (three dual-heads and three cylindrical). We simulated proton irradiation of a PMMA phantom with a Single Pencil Beam (SPB) and Spread-Out Bragg Peak (SOBP) of various ranges. The sensitivity and precision of each scanner were calculated, and considering the setup's cost-effectiveness, we indicated potentially optimal geometries for the J-PET scanner prototype dedicated to the proton beam range assessment. Main results: The investigations indicate that the double-layer cylindrical and triple-layer double-head configurations are the most promising for clinical application. We found that the scanner sensitivity is of the order of 10$^{-5}$ coincidences per primary proton, while the precision of the range assessment for both SPB and SOBP irradiation plans was found below 1 mm. Among the scanners with the same number of detector modules, the best results are found for the triple-layer dual-head geometry. Significance: We performed simulation studies demonstrating that the feasibility of the J-PET detector for PET-based proton beam therapy range monitoring is possible with reasonable sensitivity and precision enabling its pre-clinical tests in the clinical proton therapy environment. Considering the sensitivity, precision and cost-effectiveness, the double-layer cylindrical and triple-layer dual-head J-PET geometry configurations seem promising for the future clinical application. Experimental tests are needed to confirm these findings., Comment: 19 pages, 7 pages

We report a study of the original image reconstruction algorithm based on the time-of-flight maximum likelihood expectation maximisation (TOF MLEM), developed for the total-body (TB) Jagiellonian PET (J-PET) scanners. The method is applicable to generic cylindrical or modular multi-layer layouts and is extendable to multi-photon imaging. The system response matrix (SRM) is represented as a set of analytical functions, uniquely defined for each pair of plastic scintillator strips used for the detection. A realistic resolution model (RM) in detector space is derived from fitting the Monte Carlo simulated emissions and detections of annihilation photons on oblique transverse planes. Additional kernels embedded in SRM account for TOF, parallax effect and axial smearing. The algorithm was tested on datasets, simulated in GATE for the NEMA IEC and static XCAT phantoms inside a 24-module 2-layer TB J-PET. Compared to the reference TOF MLEM with none or a shift-invariant RM, an improvement was observed, as evaluated by the analysis of image quality, difference images and ground truth metrics. We also reconstructed the data with additive contributions, pre-filtered geometrically and with non-TOF scatter correction applied. Despite some deterioration, the obtained results still capitalise on the realistic RM with better edge preservation and superior ground truth metrics. The envisioned prospects of the TOF MLEM with analytical SRM include its application in multi-photon imaging and further upgrade to account for the non-collinearity, positron range and other factors.

For $r,n\ge2$, an ordered $r$-uniform matching of size $n$ is an $r$-uniform hypergraph on a linearly ordered vertex set $V$, with $|V|=rn$, consisting of $n$ pairwise disjoint edges. There are $\tfrac12\binom{2r}r$ different ways two edges may intertwine, called here patterns. Among them we identify $3^{r-1}$ collectable patterns $P$, which have the potential of appearing in arbitrarily large quantities called $P$-cliques. We prove an Erd\H{o}s-Szekeres type result guaranteeing in every ordered $r$-uniform matching the presence of a $P$-clique of a prescribed size, for some collectable pattern $P$. In particular, in the diagonal case, one of the $P$-cliques must be of size $\Omega\left( n^{3^{1-r}}\right)$. In addition, for each collectable pattern $P$ we show that the largest size of a $P$-clique in a random ordered $r$-uniform matching of size $n$ is, with high probability, $\Theta\left(n^{1/r}\right)$.

Total-Body PET is one of the most promising medical diagnostics modalities. The high sensitivity provided by Total-Body technology can be advantageous for novel tomography methods like positronium imaging. Several efforts are ongoing to lower the price of the TB-PET systems. Among the alternatives, the Jagiellonian PET (J-PET) technology, based on plastic scintillator strips, offers a low-cost alternative. The work aimed to compare five Total-Body J-PET geometries as a possible next generation J-PET scanner design. We present comparative studies of performance characteristics of the cost-effective Total-Body PET scanners using J-PET technology. We investigated in silico five Total-Body scanner geometries. Monte Carlo simulations of the XCAT phantom, the 2-meter sensitivity line source and positronium sensitivity phantoms were performed. We compared the sensitivity profiles for 2-gamma and 3-gamma tomography, relative cost of the setups and performed quantitative analysis of the reconstructed images. The analysis of the reconstructed XCAT images reveals the superiority of the seven-ring scanners over the three-ring setups. However, the three-ring scanners would be approximately 2-3 times cheaper. The peak sensitivity values for two-gamma vary from 20 to 34 cps/kBq. The sensitivity curves for the positronium tomography have a similar shape to the two-gamma sensitivity profiles. The peak values are lower compared to the two-gamma cases, from about 20-28 times, with a maximum of 1.66 cps/kBq. The results show the feasibility of multi-organ imaging of all the systems to be considered for the next generation of TB J-PET designs. The relative cost for all the scanners is about 10-4 times lower compared to the cost of the uExplorer. These properties coupled together with J-PET cost-effectiveness, make the J-PET technology an attractive solution for broad application in clinics.

An ordered matching of size $n$ is a graph on a linearly ordered vertex set $V$, $|V|=2n$, consisting of $n$ pairwise disjoint edges. There are three different ordered matchings of size two on $V=\{1,2,3,4\}$: an alignment $\{1,2\},\{3,4\}$, a nesting $\{1,4\},\{2,3\}$, and a crossing $\{1,3\},\{2,4\}$. Accordingly, there are three basic homogeneous types of ordered matchings (with all pairs of edges arranged in the same way) which we call, respectively, lines, stacks, and waves. We prove an Erd\H{o}s-Szekeres type result guaranteeing in every ordered matching of size $n$ the presence of one of the three basic sub-structures of a given size. In particular, one of them must be of size at least $n^{1/3}$. We also investigate the size of each of the three sub-structures in a random ordered matching. Additionally, the former result is generalized to $3$-uniform ordered matchings. Another type of unavoidable patterns we study are twins, that is, pairs of order-isomorphic, disjoint sub-matchings. By relating to a similar problem for permutations, we prove that the maximum size of twins that occur in every ordered matching of size $n$ is $O\left(n^{2/3}\right)$ and $\Omega\left(n^{3/5}\right)$. We conjecture that the upper bound is the correct order of magnitude and confirm it for almost all matchings. In fact, our results for twins are proved more generally for $r$-multiple twins, $r\ge2$.

We study the powers of Hamiltonian cycles in randomly augmented Dirac graphs, that is, $n$-vertex graphs $G$ with minimum degree at least $(1/2+\varepsilon)n$ to which some random edges are added. For any Dirac graph and every integer $m\ge2$, we accurately estimate the threshold probability $p=p(n)$ for the event that the random augmentation $G\cup G(n,p)$ contains the $m$-th power of a Hamiltonian cycle.

Twins in a finite word are formed by a pair of identical subwords placed at disjoint sets of positions. We investigate the maximum length of twins in a random word over a $k$-letter alphabet. The obtained lower bounds for small values of $k$ significantly improve the best estimates known in the deterministic case. Bukh and Zhou in 2016 showed that every ternary word of length $n$ contains twins of length at least $0.34n$. Our main result states that in a random ternary word of length $n$, with high probability, one can find twins of length at least $0.41n$. In the general case of alphabets of size $k\geq 3$ we obtain analogous lower bounds of the form $\frac{1.64}{k+1}n$ which are better than the known deterministic bounds for $k\leq 354$. In addition, we present similar results for multiple twins in random words.

In vivo assessment of cancer and precise location of altered tissues at initial stages of molecular disorders are important diagnostic challenges. Positronium is copiously formed in the free molecular spaces in the patient's body during positron emission tomography (PET). The positronium properties vary according to the size of inter- and intramolecular voids and the concentration of molecules in them such as, e.g., molecular oxygen, O2; therefore, positronium imaging may provide information about disease progression during the initial stages of molecular alterations. Current PET systems do not allow acquisition of positronium images. This study presents a new method that enables positronium imaging by simultaneous registration of annihilation photons and deexcitation photons from pharmaceuticals labeled with radionuclides. The first positronium imaging of a phantom built from cardiac myxoma and adipose tissue is demonstrated. It is anticipated that positronium imaging will substantially enhance the specificity of PET diagnostics., Comment: 10 pages, 5 figures

Given $k\ge3$ and $1\leq \ell< k$, an $(\ell,k)$-cycle is one in which consecutive edges, each of size $k$, overlap in exactly $\ell$ vertices. We study the smallest number of edges in $k$-uniform $n$-vertex hypergraphs which do not contain hamiltonian $(\ell,k)$-cycles, but once a new edge is added, such a cycle is promptly created. It has been conjectured that this number is of order $n^\ell$ and confirmed for $\ell\in\{1,k/2,k-1\}$, as well as for the upper range $0.8k\leq \ell\leq k-1$. Here we extend the validity of this conjecture to the lower-middle range $(k-1)/3\le\ell<(k-1)/2$., Comment: This is a revised version (we fill a gap in the proof of Lemma 10)

By an $r$-tuplet in a permutation we mean a family of $r$ pairwise disjoint subsequences with the same relative order. The length of an $r$-tuplet is defined as the length of any single subsequence in the family. Let $t^{(r)}(n)$ denote the largest $k$ such that every permutation of length $n$ contains an $r$-tuplet of length $k$. We prove that $t^{(r)}(n)=O\left(n^{\frac r{2r-1}}\right)$ and $t^{(r)}(n)=\Omega\left( n^{\frac{R}{2R-1}} \right)$, where $R=\binom{2r-1}r$. We conjecture that the upper bound brings the correct order of magnitude of $t^{(r)}(n)$ and support this conjecture by proving that it holds for almost all permutations. Our work generalizes previous studies of the case $r=2$., Comment: Updated grant number

BRITE-Constellation is devoted to high-precision optical photometric monitoring of bright stars, distributed all over the Milky Way, in red and/or blue passbands. Photometry from space avoids the turbulent and absorbing terrestrial atmosphere and allows for very long and continuous observing runs with high time resolution and thus provides the data necessary for understanding various processes inside stars (e.g., asteroseismology) and in their immediate environment. While the first astronomical observations from space focused on the spectral regions not accessible from the ground it soon became obvious around 1970 that avoiding the turbulent terrestrial atmosphere significantly improved the accuracy of photometry and satellites explicitly dedicated to high-quality photometry were launched. A perfect example is BRITE-Constellation, which is the result of a very successful cooperation between Austria, Canada and Poland. Research highlights for targets distributed nearly over the entire HRD are presented, but focus primarily on massive and hot stars., Comment: BRITE-Constellation was designed, built, launched, and is operated and supported by the Austrian Research Promotion Agency, the University of Vienna, the Technical University of Graz, the University of Innsbruck, the Canadian Space Agency, the University of Toronto Institute for Aerospace Studies, the Foundation for Polish Science and Technology and the National Science Centre. 23 figures