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We give examples of atomic integral domains satisfying each of the eight logically possible combinations of existence or non-existence of the following kinds of elements: 1) primes, 2) absolutely irreducible elements that are not prime, and 3) irreducible elements that are not absolutely irreducible. A non-zero non-unit is called absolutely irreducible (or, a strong atom) if every one of its powers factors uniquely into irreducibles., Comment: 21 pages

Deep generative modeling has emerged as a powerful tool for synthesizing realistic medical images, driving advances in medical image analysis, disease diagnosis, and treatment planning. This chapter explores various deep generative models for 3D medical image synthesis, with a focus on Variational Autoencoders (VAEs), Generative Adversarial Networks (GANs), and Denoising Diffusion Models (DDMs). We discuss the fundamental principles, recent advances, as well as strengths and weaknesses of these models and examine their applications in clinically relevant problems, including unconditional and conditional generation tasks like image-to-image translation and image reconstruction. We additionally review commonly used evaluation metrics for assessing image fidelity, diversity, utility, and privacy and provide an overview of current challenges in the field.

The study of magnetoresistance (MR) phenomena has been pivotal in advancing magnetic sensors and spintronic devices. Helimagnets present an intriguing avenue for spintronics research. Theoretical predictions suggest that MR magnitude in the helimagnetic (HM) regime surpasses that in the ferromagnetic (FM) regime by over an order of magnitude. However, in metallic helimagnets like manganese phosphide, MR in the HM phase remains modest (10%), limiting its application in MR devices. Here, a groundbreaking approach is presented to achieve a giant low field MR effect in nanostructured manganese phosphide films by leveraging confinement and strain effects along with spin helicity. Unlike the modest MR observed in bulk manganese phosphide single crystals and large grain polycrystalline films, which exhibit a small negative MR in the FM region (2%) increasing to 8% in the HM region across 10-300 K, a grain size-dependent giant positive MR (90%) is discovered near FM to HM transition temperature (110 K), followed by a rapid decline to a negative MR below 55 K in manganese phosphide nanocrystalline films. These findings illuminate a novel strain-mediated spin helicity phenomenon in nanostructured helimagnets, presenting a promising pathway for the development of high-performance MR sensors and spintronic devices through the strategic utilization of confinement and strain effects.

We show that if there exists a countable Borel equivalence relation which is hyper-hyperfinite but not hyperfinite then the complexity of hyperfinite countable Borel equivalence relations is as high as possible, namely, $\Sigma^1_2$-complete.

Quantitative mass spectrometry has revolutionized proteomics by enabling simultaneous quantification of thousands of proteins. Pooling patient-derived data from multiple institutions enhances statistical power but raises significant privacy concerns. Here we introduce FedProt, the first privacy-preserving tool for collaborative differential protein abundance analysis of distributed data, which utilizes federated learning and additive secret sharing. In the absence of a multicenter patient-derived dataset for evaluation, we created two, one at five centers from LFQ E.coli experiments and one at three centers from TMT human serum. Evaluations using these datasets confirm that FedProt achieves accuracy equivalent to DEqMS applied to pooled data, with completely negligible absolute differences no greater than $\text{$4 \times 10^{-12}$}$. In contrast, -log10(p-values) computed by the most accurate meta-analysis methods diverged from the centralized analysis results by up to 25-27. FedProt is available as a web tool with detailed documentation as a FeatureCloud App., Comment: 52 pages, 16 figures, 12 tables. Last two authors listed are joint last authors

1 ps timing resolution is the entry point to signature based searches relying on secondary/tertiary vertices and particle identification. We describe a preliminary design for PSEC5, an 8-channel 40 GS/s waveform-sampling ASIC in the TSMC 65 nm process targetting 1 ps resolution at 20 mW power per channel. Each channel consists of four fast and one slow switched capacitor arrays (SCA), allowing ps time resolution combined with a long effective buffer. Each fast SCA is 1.6 ns long and has a nominal sampling rate of 40 GS/s. The slow SCA is 204.8 ns long and samples at 5 GS/s. Recording of the analog data for each channel is triggered by a fast discriminator capable of multiple triggering during the window of the slow SCA. To achieve a large dynamic range, low leakage, and high bandwidth, the SCA sampling switches are implemented as 2.5 V nMOSFETs controlled by 1.2 V shift registers. Stored analog data are digitized by an external ADC at 10 bits or better. Specifications on operational parameters include a 4 GHz analog bandwidth and a dead time of 20 microseconds, corresponding to a 50 kHz readout rate, determined by the choice of the external ADC., Comment: 16th Pisa Meeting on Advanced Detectors

We report room-temperature bulk plasticity mediated by dislocations in single-crystal cubic KTaO3, contrasting the conventional knowledge that single-crystal KTaO3 is susceptible to brittle cleavage. A mechanics-based combinatorial experimental approach using cyclic Brinell indentation, scratching, and uniaxial bulk compression consistently demonstrates room-temperature dislocation plasticity in KTaO3 from the mesoscale to the macroscale. This approach also delivers tunable dislocation densities and plastic zone sizes. Scanning transmission electron microscopy analysis underpins the activated slip system to be <110>{1-10}. Given the growing significance of KTaO3 as an emerging electronic oxide and the increasing interest in dislocations for tuning physical properties of oxides, our findings are expected to trigger synergistic research interest in KTaO3 with dislocations.

Accurate occupancy information helps to improve building energy efficiency and occupant comfort. Occupancy detection methods based on CO2 sensors have received attention due to their low cost and low intrusiveness. In naturally ventilated buildings, the accuracy of CO2-based occupancy detection is generally low in related studies due to the complex ventilation behavior and the difficulty in measuring the actual air exchange through windows. In this study, we present two novel features for occupancy detection based on the spatial distribution of the CO2 concentration. After a quantitative analysis with Support Vector Machine (SVM) as classifier, it was found that the accuracy of occupancy state detection in naturally ventilated rooms could be improved by up to 14.8 percentage points compared to the baseline, reaching 83.2 % (F1 score 0.84) without any ventilation information. With ventilation information, the accuracy reached 87.6 % (F1 score 0.89). The performance of occupancy quantity detection was significantly improved by up to 25.3 percentage points versus baseline, reaching 56 %, with root mean square error (RMSE) of 11.44 occupants, using only CO2-related features. Additional ventilation information further enhanced the performance to 61.8 % (RMSE 9.02 occupants). By incorporating spatial features, the model using only CO2-related features revealed similar performance as the model containing additional ventilation information, resulting in a better low-cost occupancy detection method for naturally ventilated buildings., Comment: Indoor Environments, Volume 1, Issue 3, 2024, 100018, ISSN 2950-3620

While both agent interaction and personalisation are vibrant topics in research on large language models (LLMs), there has been limited focus on the effect of language interaction on the behaviour of persona-conditioned LLM agents. Such an endeavour is important to ensure that agents remain consistent to their assigned traits yet are able to engage in open, naturalistic dialogues. In our experiments, we condition GPT-3.5 on personality profiles through prompting and create a two-group population of LLM agents using a simple variability-inducing sampling algorithm. We then administer personality tests and submit the agents to a collaborative writing task, finding that different profiles exhibit different degrees of personality consistency and linguistic alignment to their conversational partners. Our study seeks to lay the groundwork for better understanding of dialogue-based interaction between LLMs and highlights the need for new approaches to crafting robust, more human-like LLM personas for interactive environments., Comment: To appear in Proceedings of the 1st Personalization of Generative AI Workshop, EACL 2024

We show that content on the web is often translated into many languages, and the low quality of these multi-way translations indicates they were likely created using Machine Translation (MT). Multi-way parallel, machine generated content not only dominates the translations in lower resource languages; it also constitutes a large fraction of the total web content in those languages. We also find evidence of a selection bias in the type of content which is translated into many languages, consistent with low quality English content being translated en masse into many lower resource languages, via MT. Our work raises serious concerns about training models such as multilingual large language models on both monolingual and bilingual data scraped from the web., Comment: Accepted at ACL Findings 2024

Despite considerable success, large Denoising Diffusion Models (DDMs) with UNet backbone pose practical challenges, particularly on limited hardware and in processing gigapixel images. To address these limitations, we introduce two Neural Cellular Automata (NCA)-based DDMs: Diff-NCA and FourierDiff-NCA. Capitalizing on the local communication capabilities of NCA, Diff-NCA significantly reduces the parameter counts of NCA-based DDMs. Integrating Fourier-based diffusion enables global communication early in the diffusion process. This feature is particularly valuable in synthesizing complex images with important global features, such as the CelebA dataset. We demonstrate that even a 331k parameter Diff-NCA can generate 512x512 pathology slices, while FourierDiff-NCA (1.1m parameters) reaches a three times lower FID score of 43.86, compared to the four times bigger UNet (3.94m parameters) with a score of 128.2. Additionally, FourierDiff-NCA can perform diverse tasks such as super-resolution, out-of-distribution image synthesis, and inpainting without explicit training.

We consider 3-manifolds admitting the action of an involution such that its space of orbits is homeomorphic to $S^3.$ Such involutions are called \textit{hyperelliptic} as the manifolds admitting such an action. We prove that the sectional 2-rank of a finite group acting on a 3-manifold and containing a hyperelliptic involution with fixed-point set with two components has sectional 2-rank at most four; this upper bound is sharp. The cases where the hyperelliptic involution has a fixed-point set with a number of components different from 2 have been already considered in literature. Our result completes the analysis and we obtain some general results where the number of the components of the fixed-point set is not fixed. In particular, we obtain that a finite group acting on a 3-manifold and containing a hyperelliptic involution has 2-rank at most four, and four is the best possible upper bound. Finally, we restrict to the basic case of simple groups acting on hyperelliptic 3-manifolds: we use our result about the sectional 2-rank to prove that a simple group containing a hyperelliptic involution is isomorphic to $PSL(2,q)$ for some odd prime power $q$, or to one of four other small simple groups., Comment: 20 pages, 3 figures; a minor change to the title, declarations added

Missing data are frequently observed by practitioners and researchers in the building energy modeling community. In this regard, advanced data-driven solutions, such as Deep Learning methods, are typically required to reflect the non-linear behavior of these anomalies. As an ongoing research question related to Deep Learning, a model's applicability to limited data settings can be explored by introducing prior knowledge in the network. This same strategy can also lead to more interpretable predictions, hence facilitating the field application of the approach. For that purpose, the aim of this paper is to propose the use of Physics-informed Denoising Autoencoders (PI-DAE) for missing data imputation in commercial buildings. In particular, the presented method enforces physics-inspired soft constraints to the loss function of a Denoising Autoencoder (DAE). In order to quantify the benefits of the physical component, an ablation study between different DAE configurations is conducted. First, three univariate DAEs are optimized separately on indoor air temperature, heating, and cooling data. Then, two multivariate DAEs are derived from the previous configurations. Eventually, a building thermal balance equation is coupled to the last multivariate configuration to obtain PI-DAE. Additionally, two commonly used benchmarks are employed to support the findings. It is shown how introducing physical knowledge in a multivariate Denoising Autoencoder can enhance the inherent model interpretability through the optimized physics-based coefficients. While no significant improvement is observed in terms of reconstruction error with the proposed PI-DAE, its enhanced robustness to varying rates of missing data and the valuable insights derived from the physics-based coefficients create opportunities for wider applications within building systems and the built environment., Comment: Accepted for publication in Energy and Buildings

The construction of exact solutions for radiative transfer in a plane-parallel medium has been addressed by Hemsch and Ferziger in 1972 for a partial frequency redistribution model of the formation of spectral lines consisting in a linear combination of frequency coherent and fully incoherent scattering. The method of solution is based on an eigenfunction expansion of the radiation field, leading to two singular integral equations with a Cauchy-type kernel, that have to be solved one after the other. We reconsider this problem, using as starting point the integral formulation of the radiative transfer equation, where the terms involving the coupling between the two scattering mechanisms are clearly displayed, as well as the primary source of photons. With an inverse Laplace transform, we recover the singular integral equations previously established and with Hilbert transforms, as in the previous work, recast them as boundary value problems in the complex plane. Their solutions are presented in detail for an infinite and a semi-infinite medium. The coupling terms are carefully analyzed and consistency with either the coherent or the incoherent limit is systematically checked. We recover the important results of the previous work that an exact solution exists for an infinite medium, whereas for a semi-infinite medium, which requires the introduction of half-space auxiliary functions, the solution is given by a Fredholm integral equation to be solved numerically. The solutions of the singular integral equations are used to construct explicit expressions providing the radiation field for an arbitrary primary source and for the Green function. An explicit expression is given for the radiation field emerging from a semi-infinite medium., Comment: 43 pages, 6 figures, to be published in the Journal of Computational and Theoretical Transport

We give a complete description of the Poisson boundary of wreath products $A\wr B= \bigoplus_{B} A\rtimes B$ of countable groups $A$ and $B$, for probability measures $\mu$ with finite entropy where lamp configurations stabilize almost surely. If, in addition, the projection of $\mu$ to $B$ is Liouville, we prove that the Poisson boundary of $(A\wr B,\mu)$ is equal to the space of limit lamp configurations, endowed with the corresponding hitting measure. In particular, this answers an open question asked by Kaimanovich, and Lyons-Peres, for $B=\mathbb{Z}^d$, $d\ge 3$, and measures $\mu$ with a finite first moment., Comment: 39 pages

Cellular communication technologies such as 5G are deployed on a large scale around the world. Compared to other communication technologies such as WiFi, Bluetooth, or Ultra Wideband, the 5G communication standard describes support for a large variety of use cases, e.g., Internet of Things, vehicular, industrial, and campus-wide communications. An organization can operate a Private 5G network to provide connectivity to devices in their manufacturing environment. Physical Layer Key Generation (PLKG) is a method to generate a symmetric secret on two nodes despite the presence of a potential passive eavesdropper. To the best of our knowledge, this work is one of the first to implement PLKG in a real Private 5G network. Therefore, it highlights the possibility of integrating PLKG in the communication technology highly relevant for industrial applications. This paper exemplifies the establishment of a long-term symmetric key between an aerial vehicle and IT infrastructure both located in a manufacturing environment and communicating via the radio interface of the Private 5G network., Comment: To be published at "2023 IEEE World Forum on Internet of Things (WF-IoT)"

We discuss the synergies between heliospheric and dust science, the open science questions, the technological endeavors and programmatic aspects that are important to maintain or develop in the decade to come. In particular, we illustrate how we can use interstellar dust in the solar system as a tracer for the (dynamic) heliosphere properties, and emphasize the fairly unexplored, but potentially important science question of the role of cosmic dust in heliospheric and astrospheric physics. We show that an Interstellar Probe mission with a dedicated dust suite would bring unprecedented advances to interstellar dust research, and can also contribute-through measuring dust - to heliospheric science. This can, in particular, be done well if we work in synergy with other missions inside the solar system, thereby using multiple vantage points in space to measure the dust as it `rolls' into the heliosphere. Such synergies between missions inside the solar system and far out are crucial for disentangling the spatially and temporally varying dust flow. Finally, we highlight the relevant instrumentation and its suitability for contributing to finding answers to the research questions., Comment: 18 pages, 7 Figures, 5 Tables. Originally submitted as white paper for the National Academies Decadal Survey for Solar and Space Physics 2024-2033

Cataract surgery is a frequently performed procedure that demands automation and advanced assistance systems. However, gathering and annotating data for training such systems is resource intensive. The publicly available data also comprises severe imbalances inherent to the surgical process. Motivated by this, we analyse cataract surgery video data for the worst-performing phases of a pre-trained downstream tool classifier. The analysis demonstrates that imbalances deteriorate the classifier's performance on underrepresented cases. To address this challenge, we utilise a conditional generative model based on Denoising Diffusion Implicit Models (DDIM) and Classifier-Free Guidance (CFG). Our model can synthesise diverse, high-quality examples based on complex multi-class multi-label conditions, such as surgical phases and combinations of surgical tools. We affirm that the synthesised samples display tools that the classifier recognises. These samples are hard to differentiate from real images, even for clinical experts with more than five years of experience. Further, our synthetically extended data can improve the data sparsity problem for the downstream task of tool classification. The evaluations demonstrate that the model can generate valuable unseen examples, allowing the tool classifier to improve by up to 10% for rare cases. Overall, our approach can facilitate the development of automated assistance systems for cataract surgery by providing a reliable source of realistic synthetic data, which we make available for everyone.

We present simulations of whole-body low-dose time-of-flight positron emission tomography (TOF-PET) based on the direct surface production [1] by 511 keV gamma rays of energetic electrons via the Photo-electric and Compton Effects, eliminating the scintillator and photodetector sub-systems in PET scanners. In Ref. [1] we described Microchannel Plates (MCP) constructed from thin dielectric laminae containing heavy nuclei such as lead or tungsten (LMCP$^{\rm{TM}}$). The laminae surfaces are micro-patterned to form channels, which can then be functionalized to support secondary electron emission in the manner of conventional MCPs. We have simulated direct conversion using modifications to the TOPAS Geant4-based tool kit. A 20 $\times$ 20 $\times$ 2.54 cm$^3$ LMCP, composed of 150-micron thick lead-glass laminae, is predicted to have a $\ge 30$% conversion efficiency to a primary electron that penetrates an interior wall of a pore. The subsequent secondary electron shower is largely confined to one pore and can provide high space and time resolutions. In whole-body PET scanners the technique eliminates the scintillator and photodetector subsystems. The consequent absence of a photocathode allows assembly of large arrays at atmospheric pressure and less stringent vacuum requirements, including use of pumped and cycled systems. TOPAS simulations of the Derenzo and XCAT-brain phantoms are presented with dose reductions of factors of 100 and 1000 from a literature benchmark. New applications of PET at a significantly lower radiation dose include routine screening for early detection of pathologies, the use in diagnostics in previously unserved patient populations such as children, and a larger installed facility base in rural and under-served populations, where simpler gamma detectors and lower radiation doses may enable small low-cost portable PET scanners., Comment: Version 10a is the published manuscript in NIM-A. 22 pages, 18 figures

We have used the TOPAS simulation framework to model the direct conversion of 511 keV gamma rays to electrons in a micro-channel plate (MCP) constructed from thin laminae of a heavy-metal-loaded dielectric such as lead-glass, patterned with micro-channels (LMCP). The laminae serve as the converter of the gamma ray to a primary electron within a depth from a channel-forming surface such that the electron penetrates the channel surface (`surface direct conversion'). The channels are coated with a secondary-emitting material to produce electron multiplication in the channels. The laminae are stacked on edge with the channels running from the top of the resulting `slab' to the bottom; after assembly the slab is metalized top and bottom to form the finished LMCP. The shape of the perimeter of a lamina determines the dimensions of the slab at the lamina location in the slab, allowing non-uniform cross-sections in slab thickness, width, and length. The slab also can be non-planar, allowing curved surfaces in both lateral dimensions. The laminar construction allows incorporating structural elements in the LMCP for modular assembly in large-area arrays. The channels can be patterned on the laminae surfaces with internal shapes and structure, texture, and coatings optimized for specific applications and performance. The channels can be non-uniform across the LMCP and need not be parallel in either transverse direction. Surface direct conversion of the gamma ray to an electron eliminates the common two-step conversion of the gamma ray into an optical photon in a scintillator followed by the conversion of the photon into an electron in a photodetector. The simulations predict an efficiency for conversion of 511 keV gamma rays of $\gtrapprox$ 30\% for a 2.54 cm-thick lead-glass LMCP. The elimination of the photocathode allows assembly at atmospheric pressure., Comment: 13 pages, 10 figures, most recent version is of the accepted manuscript

We prove that finite entropy random walks on the torsion-free Baumslag group in dimension $d=2$ have non-trivial Poisson boundary. This is in contrast with the torsion case where the situation for simple random walks on Baumslag groups is the same as for the lamplighter groups of the same dimension. Our proof uses the realization of the Baumslag group as a linear group. We define and study a class of linear groups associated with multivariable polynomials which we denote $G_k(p)$. We show that the groups $G_3(p)$ have non-trivial Poisson boundary for all irreducible finite entropy measures, under a condition on the polynomial $p$ which we call the spaced polynomial property. We show that the Baumslag group has $G_3(1+x-y)$ as a subgroup, and that the polynomial $p = 1+x-y$, satisfies this property. Given any upper-triangle group of characteristic zero, we prove that one of the following must hold: 1) all finite second moment symmetric random walks on $G$ have trivial boundary 2) the group admits a block, which has a $3$ dimensional wreath product as a subgroup, and all non-degenerate random walks on $G$ have non-trivial boundary. 3) $G$ has a group $G_3(p)$ as a subgroup. We give a conjectural characterisation of all polynomials satisfying the spaced polynomial property. If this is confirmed, our result provides a characterisation of linear groups $G$ which admit a finitely supported symmetric random walk with non-trivial boundary., Comment: 19 pages

Two major challenges in time-of-flight positron emission tomography (TOF-PET) are low spatial resolution and high radioactive dose to the patient, both of which result from limitations in detection technology rather than fundamental physics. A new type of TOF-PET detector employing low-atomic number (low-Z) scintillation media and large-area, high-resolution photodetectors to record Compton scattering locations in the detector has been proposed as a promising alternative, but the minimum technical requirements for such a system have not yet been established. Here we present a simulation study evaluating the potential of a proposed low-Z detection medium, linear alkylbenzene (LAB) doped with a switchable molecular recorder, for next-generation TOF-PET detection. We developed a custom Monte Carlo simulation of full-body TOF-PET using the TOPAS Geant4 software package. By quantifying contributions and tradeoffs for energy, spatial, and timing resolution of the detector, we show that at reasonable combination of specifications, our likelihood-based identification of pairs of first interaction locations in the simulated detector identifies 87.1% of pairs with zero or negligible error, and correctly rejects 90% of all in-patient scatters. The same specifications give TOF-PET sensitivity of ~66.7% and PSF width 4.6 mm with clear contrast. A detector with these specifications provides a clear image of a brain phantom simulated at less than 1% of a standard radiotracer dose., Comment: 25 pages, 9 figures

Muons have a similar latency/energy correlation from pion decay as do the neutrinos, and hence in each time-slice in a stroboscopic analysis measurements of their momentum spectra can reduce systematic uncertainties due to flux. There are, however, unique issues for muons: 1) during standard neutrino data-taking muon measurements in the forward direction must be in formidable high-flux high-radiation environments; 2) because of the very high incident hadron flux in the Absorber Hall, muons must be detected after a thick absorber, imposing a range cutoff at a momentum much above the minimum neutrino momentum of interest; 3) the muon velocity, unlike that of neutrinos, differs from $c$, and so the muon detected time will require correction for the muon flight path, requiring measurement of the muon momentum; 4) multiple scattering is significant for low-momentum muons, and so a `good geometry' is essential for precision muon flux measurements; and 5) developments in psec timing allow muon momenta in the momentum region of interest to be measured precisely by time-of-flight over short distances with photodetectors of a few-psec resolution. Here we advocate that a program of extensive precise low-intensity muon momentum spectrum measurements be carried out early in the LBNF program before the Absorber Hall becomes too hot. The low-momentum muon spectra taken in this experiment would be cross-normalized to the high-intensity neutrino data through the currently planned muon monitors which can operate in both the low and high intensity geometries. While beyond the scope of uniquely muon-related issues, the note includes a proposal for an long-base-line oscillation analysis strategy that exploits stroboscopic information for both neutrinos and muons to reduce systematic uncertainties on the neutrino fluxes and event selection in Far and Near detectors.