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The growing interest in eXplainable Artificial Intelligence (XAI) has prompted research into models with built-in interpretability, the most prominent of which are part-prototype models. Part-Prototype Models (PPMs) make decisions by comparing an input image to a set of learned prototypes, providing human-understandable explanations in the form of ``this looks like that''. Despite their inherent interpretability, PPMS are not yet considered a valuable alternative to post-hoc models. In this survey, we investigate the reasons for this and provide directions for future research. We analyze papers from 2019 to 2024, and derive a taxonomy of the challenges that current PPMS face. Our analysis shows that the open challenges are quite diverse. The main concern is the quality and quantity of prototypes. Other concerns are the lack of generalization to a variety of tasks and contexts, and general methodological issues, including non-standardized evaluation. We provide ideas for future research in five broad directions: improving predictive performance, developing novel architectures grounded in theory, establishing frameworks for human-AI collaboration, aligning models with humans, and establishing metrics and benchmarks for evaluation. We hope that this survey will stimulate research and promote intrinsically interpretable models for application domains. Our list of surveyed papers is available at https://github.com/aix-group/ppm-survey.

The Pandora Software Development Kit and algorithm libraries perform reconstruction of neutrino interactions in liquid argon time projection chamber detectors. Pandora is the primary event reconstruction software used at the Deep Underground Neutrino Experiment, which will operate four large-scale liquid argon time projection chambers at the far detector site in South Dakota, producing high-resolution images of charged particles emerging from neutrino interactions. While these high-resolution images provide excellent opportunities for physics, the complex topologies require sophisticated pattern recognition capabilities to interpret signals from the detectors as physically meaningful objects that form the inputs to physics analyses. A critical component is the identification of the neutrino interaction vertex. Subsequent reconstruction algorithms use this location to identify the individual primary particles and ensure they each result in a separate reconstructed particle. A new vertex-finding procedure described in this article integrates a U-ResNet neural network performing hit-level classification into the multi-algorithm approach used by Pandora to identify the neutrino interaction vertex. The machine learning solution is seamlessly integrated into a chain of pattern-recognition algorithms. The technique substantially outperforms the previous BDT-based solution, with a more than 20\% increase in the efficiency of sub-1\,cm vertex reconstruction across all neutrino flavours., Comment: 32 pages, 18 figures

High refractive index (4.4 at 1100 nm), negligibly small absorption in near-infrared spectral range, and ease of processing make MoSe$_2$ a perfect material for applications in near-infrared photonics. So far, implementation of MoSe$_2$-based photonic structures has been hindered by the lack of large surface MoSe$_2$ substrates. The use of molecular beam epitaxy allows the production of homogeneous layers of MoSe$_2$ with a few-inch surface and a thickness controlled at the sub-nm level. In the present work, we design by theoretical calculations and fabricate by a simple lithography process an ultrathin subwavelength grating out of 42-nm thick, epitaxially-grown MoSe$_2$ layer. Our polarization-resolved reflectivity measurements confirm that the gratings host a peculiar type of a confined optical mode that is a bound state in the continuum. Moreover, the fabricated structures enhance the efficiency of the third harmonic generation by over three orders of magnitude as compared to the unstructured MoSe$_2$ layer. The presented results are promising for the realization of flat, ultra-compact devices for lasing, wavefront control, and higher-order topological states of the light.

In retail warehouses, returned products are typically placed in an intermediate storage until a decision regarding further shipment to stores is made. The longer products are held in storage, the higher the inefficiency and costs of the returns management process, since enough storage area has to be provided and maintained while the products are not placed for sale. To reduce the average product storage time, we consider an alternative solution where reallocation decisions for products can be made instantly upon their arrival in the warehouse allowing only a limited number of products to still be stored simultaneously. We transfer the problem to an online multiple knapsack problem and propose a novel reinforcement learning approach to pack the items (products) into the knapsacks (stores) such that the overall value (expected revenue) is maximized. Empirical evaluations on simulated data demonstrate that, compared to the usual offline decision procedure, our approach comes with a performance gap of only 3% while significantly reducing the average storage time of a product by 96%.

The advent of both multi-messenger and time-domain astrophysics over the last decade has seen a large interest in the development of small-scale, cheap, and robust gamma-ray detectors. This has been further encouraged by the availability of CubeSat platforms. Of particular interest are detectors capable of producing spectral and localization measurements of X and gamma-ray transients to allow for accurate follow-up measurements at different wavelengths. A vast number of the instruments developed for such purposes in the last years use a combination of scintillators and Silicon Photomultipliers (SiPMs) for photon detection. Here, we present the design, performance, and space qualification of a readout system capable of reading out 64 SiPM channels. This low-power and low-cost system was originally designed for the POLAR-2 mission, a large scale gamma-ray polarimeter. However, its flexible design makes it equally suitable for use on various CubeSat missions. The system was found to perform well when reading out both plastic and high Z scintillators using a total of 1.8~W. The space qualified design furthermore relies on commercial off-the-shelf components, thereby also removing most international export issues. In this paper, we will present the overall design, the performance of the electronics, its performance when reading out various scintillators and the successful space-qualification of this design., Comment: Submitted for publication in JINST

Interatomic potentials play a vital role in revealing microscopic details and structure-property relations, which are fundamental for multiscale simulations and to assist high-throughput experiments. For metallic glasses, developing these potentials is challenging due to the complexity of their unique disordered structure. As a result, chemistry-specific interaction potentials for this important class of materials are often missing. Here, we solve this gap by implementing an efficient methodology for designing machine learning interatomic potentials (MLIPs) for metallic glasses, and we benchmark it with the widely studied CuZrAl system. By combining a Lennard-Jones surrogate model with swap-Monte Carlo sampling and Density Functional Theory (DFT) corrections, we capture diverse amorphous structures from 14 decades of supercooling. These distinct structures provide robust and efficient training of the model and applicability to the wider spectrum of energies. This approach reduces the need for extensive DFT and ab initio optimization datasets, while maintaining high accuracy. Our MLIP shows results comparable to the classical Embedded Atom Method (EAM) available for CuZrAl, in predicting structural, energetic, and mechanical properties. This work paves the way for the development of new MLIPs for complex metallic glasses, including emerging multicomponent and high entropy metallic glasses., Comment: 9 pages, 5 figures

Development of fabrication protocols for large-area plasmonic nanostructures with sub-10 nm gaps with a spatially controlled distribution is critical for their real-world applications. In this work, we develop a simple, cleanroom-free protocol for the fabrication of macroscopic-sized plasmonic substrates (>6 cm^2), featuring a tunable multi-resonance optical response and light concentration in sub-10 nm gaps. Critically, these gaps are free to interact with the surrounding medium. This architecture consists of non-periodically distributed dielectric nanospheres coated with a metal multilayer, forming semi-spherical core-shell-like nanostructures (CSLNs) surrounded by a planar film. The sub-10 nm gaps formed between metal caps and the planar film are easily tuned by adjusting fabrication parameters such as multimetal layer thickness, composition, or nanosphere size and density. The excellent structural homogeneity, wide optical tunability, and extreme light confinement in the spatially controlled subwavelength nanogaps make CSLN-based substrates an ideal platform for comprehensive surface-enhanced Raman scattering (SERS) spectroscopy. This is proven through a combination of numerical modeling and iterative fabrication/characterization, leading to the optimized substrates showing cutting-edge spatial uniformity down to 1.9% determined as the relative standard deviation (RSD) of the SERS signal of p-mercaptobenzoic acid for 225 spectra over 3600 {\mu}m^2 area. High sensitivity is evidenced by an enhancement factor of ~10^6. The proposed substrates also meet all other demanding criteria, including sufficient signal temporal stability (RSD <4%), high substrate-to-substrate reproducibility (<15%), and SERS activity towards three various analytes. The unique geometry and wide spectral tunability of the CSLN substrates will also be of great value for other plasmon-driven applications., Comment: Main manuscript: 47 pages, 7 figures; Supporting information: 13 pages, 10 figures

Tungsten-based low-activation high-entropy alloys are possible candidates for next-generation fusion reactors due to their exceptional tolerance to irradiation, thermal loads, and stress. We develop an accurate and efficient machine-learned interatomic potential for the W-Ta-Cr-V system and use it in hybrid Monte Carlo molecular dynamics simulations of ordering and segregation to all common types of defects in WTaCrV. The predictions are compared to atom probe tomography analysis of segregation and precipitation in WTaCrV thin films. By also considering two other alloys, WTaV and MoNbTaVW, we are able to draw general conclusions about preferred segregation in refractory alloys and the reasons behind it, guiding future alloy design and elucidating experimental observations. We show that the experimentally observed CrV precipitates in WTaCrV form semicoherent bcc-to-bcc interfaces with the surrounding matrix, as coherent precipitates are not thermodynamically stable due to excessive lattice mismatch. The predictions from simulations align well with our atom probe tomography analysis as well as previous experimental observations.

Spatial summary statistics based on point process theory are widely used to quantify the spatial organization of cell populations in single-cell spatial proteomics data. Among these, Ripley's $K$ is a popular metric for assessing whether cells are spatially clustered or are randomly dispersed. However, the key assumption of spatial homogeneity is frequently violated in spatial proteomics data, leading to overestimates of cell clustering and colocalization. To address this, we propose a novel $K$-based method, termed \textit{KAMP} (\textbf{K} adjustment by \textbf{A}nalytical \textbf{M}oments of the \textbf{P}ermutation distribution), for quantifying the spatial organization of cells in spatial proteomics samples. \textit{KAMP} leverages background cells in each sample along with a new closed-form representation of the first and second moments of the permutation distribution of Ripley's $K$ to estimate an empirical null model. Our method is robust to inhomogeneity, computationally efficient even in large datasets, and provides approximate $p$-values for testing spatial clustering and colocalization. Methodological developments are motivated by a spatial proteomics study of 103 women with ovarian cancer, where our analysis using \textit{KAMP} shows a positive association between immune cell clustering and overall patient survival. Notably, we also find evidence that using $K$ without correcting for sample inhomogeneity may bias hazard ratio estimates in downstream analyses. \textit{KAMP} completes this analysis in just 5 minutes, compared to 538 minutes for the only competing method that adequately addresses inhomogeneity.

Let ${{\bf R}_{\mathbb S^{d-1}}}(p\to q)$ denote the best constant for the $L^p(\mathbb{R}^d)\to L^q(\mathbb S^{d-1})$ Fourier restriction inequality to the unit sphere $\mathbb S^{d-1}$, and let ${\bf R}_{\mathbb S^{d-1}} (p\to q;\textrm{rad})$ denote the corresponding constant for radial functions. We investigate the asymptotic behavior of the operator norms ${{\bf R}_{\mathbb S^{d-1}}}(p\to q)$ and ${\bf R}_{\mathbb S^{d-1}} (p\to q;\textrm{rad})$ as the dimension $d$ tends to infinity. We further establish a dimension-free endpoint Stein-Tomas inequality for radial functions, together with the corresponding estimate for general functions which we prove with an $O(d^{1/2})$ dependence. Our methods rely on a uniform two-sided refinement of Stempak's asymptotic $L^p$ estimate of Bessel functions., Comment: 16 pages, 2 figures

Deep Learning (DL) models are often black boxes, making their decision-making processes difficult to interpret. This lack of transparency has driven advancements in eXplainable Artificial Intelligence (XAI), a field dedicated to clarifying the reasoning behind DL model predictions. Among these, attribution-based methods such as LRP and GradCAM are widely used, though they rely on approximations that can be imprecise. To address these limitations, we introduce One Matrix to Explain Neural Networks (OMENN), a novel post-hoc method that represents a neural network as a single, interpretable matrix for each specific input. This matrix is constructed through a series of linear transformations that represent the processing of the input by each successive layer in the neural network. As a result, OMENN provides locally precise, attribution-based explanations of the input across various modern models, including ViTs and CNNs. We present a theoretical analysis of OMENN based on dynamic linearity property and validate its effectiveness with extensive tests on two XAI benchmarks, demonstrating that OMENN is competitive with state-of-the-art methods., Comment: Under review, code will be released after acceptance

We introduce the space of infinite volume ends of a locally compact second countable (lcsc) space that admits a Radon measure. In certain cases, this coincides with the classical space of ends. Consider a discrete subgroup $\Gamma$ of a unimodular lcsc group $G$ that is not coamenable. Assume that $G$ has property (T) and the associated homogeneous space $G/\Gamma$ is equipped with the Haar measure. We demonstrate that if $G$ is path connected, then $G/\Gamma$ has exactly one infinite volume end. In a related vein, if $G$ acts transitively on a locally finite connected graph $X$ with compact open vertex stabilizers and the action of the subgroup $\Gamma$ is free, we show that $X/\Gamma$ has exactly one end. We also obtain identical results for certain discrete subgroups $\Gamma$ of nonamenable product groups $G$. These results can be applied to understand ends of Schreier graphs and infinite volume ends of quotients of symmetric spaces of noncompact type., Comment: 12 pages

We propose generalized conditional functional principal components analysis (GC-FPCA) for the joint modeling of the fixed and random effects of non-Gaussian functional outcomes. The method scales up to very large functional data sets by estimating the principal components of the covariance matrix on the linear predictor scale conditional on the fixed effects. This is achieved by combining three modeling innovations: (1) fit local generalized linear mixed models (GLMMs) conditional on covariates in windows along the functional domain; (2) conduct a functional principal component analysis (FPCA) on the person-specific functional effects obtained by assembling the estimated random effects from the local GLMMs; and (3) fit a joint functional mixed effects model conditional on covariates and the estimated principal components from the previous step. GC-FPCA was motivated by modeling the minute-level active/inactive profiles over the day ($1{,}440$ 0/1 measurements per person) for $8{,}700$ study participants in the National Health and Nutrition Examination Survey (NHANES) 2011-2014. We show that state-of-the-art approaches cannot handle data of this size and complexity, while GC-FPCA can., Comment: 38 pages with supplementary material, 5 figures for the main article and 4 supplementary figures, 3 tables for the main article and 10 supplementary tables, submitted to Journal of Computational and Graphical Statistics (JCGS)

We introduce Bielik 7B v0.1, a 7-billion-parameter generative text model for Polish language processing. Trained on curated Polish corpora, this model addresses key challenges in language model development through innovative techniques. These include Weighted Instruction Cross-Entropy Loss, which balances the learning of different instruction types, and Adaptive Learning Rate, which dynamically adjusts the learning rate based on training progress. To evaluate performance, we created the Open PL LLM Leaderboard and Polish MT-Bench, novel frameworks assessing various NLP tasks and conversational abilities. Bielik 7B v0.1 demonstrates significant improvements, achieving a 9 percentage point increase in average score compared to Mistral-7B-v0.1 on the RAG Reader task. It also excels in the Polish MT-Bench, particularly in Reasoning (6.15/10) and Role-playing (7.83/10) categories. This model represents a substantial advancement in Polish language AI, offering a powerful tool for diverse linguistic applications and setting new benchmarks in the field.

Let $\Gamma$ be a countable group that admits an essential measurable splitting (for instance, any group measure equivalent to a free product of nontrivial groups). We show: (1) for any two nontrivial countable groups $B$ and $C$ that are measure equivalent, the wreath product groups $B\wr\Gamma$ and $C\wr\Gamma$ are measure equivalent (in fact, orbit equivalent) -- this is interesting even in the case when the groups $B$ and $C$ are finite; and (2) the groups $B\wr \Gamma$ and $(B\times\mathbf{Z})\wr\Gamma$ are measure equivalent (in fact, orbit equivalent) for every nontrivial countable group $B$. On the other hand, we show that certain wreath product actions are not even stably orbit equivalent if $\Gamma$ is instead assumed to be a sofic icc group that is Bernoulli superrigid, and $B$ and $C$ have different cardinalities., Comment: 37 pages, 1 figure, minor revisions and corrections

The NOvA collaboration reports cross-section measurements for $\nu_{\mu}$ charged-current interactions with low hadronic energy (maximum kinetic energy of 250 MeV for protons and 175 MeV for pions) in the NOvA Near Detector. The results are presented as a double-differential cross section as a function of the direct observables of the final-state muon kinematics. Results are also presented as a single-differential cross section as a function of the derived square of the four-momentum transfer, $Q^{2}$, and as a function of the derived neutrino energy. The data correspond to an accumulated 8.09$\times10^{20}$ protons-on-target (POT) in the neutrino mode of the NuMI beam, with a narrow band of neutrino energies peaked at 1.8 GeV. The analysis provides a sample of neutrino-nucleus interactions with an enhanced fraction of quasi-elastic and two-particle-two-hole (2p2h) interactions. This enhancement allows quantitative comparisons with various nuclear models. We find strong disagreement between data and theory-based models in various regions of the muon kinematic phase space, especially in the forward muon direction., Comment: 20 pages, 12 figures. The second version includes an additional citation and adds four previously missing authors

Double- and single-differential cross sections for inclusive charged-current neutrino-nucleus scattering are reported for the kinematic domain 0 to 2 GeV/c in three-momentum transfer and 0 to 2 GeV in available energy, at a mean muon-neutrino energy of 1.86 GeV. The measurements are based on an estimated 995,760 muon-neutrino CC interactions in the scintillator medium of the NOvA Near Detector. The subdomain populated by 2-particle-2-hole reactions is identified by the cross-section excess relative to predictions for neutrino-nucleus scattering that are constrained by a data control sample. Models for 2-particle-2- hole processes are rated by chi-square comparisons of the predicted-versus-measured muon-neutrino CC inclusive cross section over the full phase space and in the restricted subdomain. Shortfalls are observed in neutrino generator predictions obtained using the theory-based Val`encia and SuSAv2 2p2h models., Comment: 20 pages, 14 figures

The anticanonical complex is a combinatorial tool that was invented to extend the features of the Fano polytope from toric geometry to wider classes of varieties. In this note we show that the Gorenstein index of Fano varieties with torus action of complexity one (and even more general of the so-called general arrangement varieties) can be read off its anticanonical complex in terms of lattice distances in full analogy to the toric Fano polytope. As an application we give concrete bounds on the defining data of almost homogeneous Fano threefolds of Picard number one having a reductive automorphism group with two-dimensional maximal torus depending on their Gorenstein index., Comment: 20 pages

This study introduces the eFontes models for automatic linguistic annotation of Medieval Latin texts, focusing on lemmatization, part-of-speech tagging, and morphological feature determination. Using the Transformers library, these models were trained on Universal Dependencies (UD) corpora and the newly developed eFontes corpus of Polish Medieval Latin. The research evaluates the models' performance, addressing challenges such as orthographic variations and the integration of Latinized vernacular terms. The models achieved high accuracy rates: lemmatization at 92.60%, part-of-speech tagging at 83.29%, and morphological feature determination at 88.57%. The findings underscore the importance of high-quality annotated corpora and propose future enhancements, including extending the models to Named Entity Recognition.

We are motivated by a study that seeks to better understand the dynamic relationship between muscle activation and paw position during locomotion. For each gait cycle in this experiment, activation in the biceps and triceps is measured continuously and in parallel with paw position as a mouse trotted on a treadmill. We propose an innovative general regression method that draws from both ordinary differential equations and functional data analysis to model the relationship between these functional inputs and responses as a dynamical system that evolves over time. Specifically, our model addresses gaps in both literatures and borrows strength across curves estimating ODE parameters across all curves simultaneously rather than separately modeling each functional observation. Our approach compares favorably to related functional data methods in simulations and in cross-validated predictive accuracy of paw position in the gait data. In the analysis of the gait cycles, we find that paw speed and position are dynamically influenced by inputs from the biceps and triceps muscles, and that the effect of muscle activation persists beyond the activation itself.

Refractory High-Entropy Alloys (RHEAs) hold promising potential to be used as structural materials in future nuclear fusion reactors, where W and its alloys are currently leading candidates. Fusion materials must be able to withstand extreme conditions, such as (i) severe radiation-damage arising from highly-energetic neutrons, (ii) embrittlement caused by implantation of H and He ions, and (iii) exposure to extreme high-temperatures and thermal gradients. Recent research demonstrated that two RHEAs - the WTaCrV and WTaCrVHf - can outperform both coarse-grained and nanocrystalline W in terms of its radiation response and microstructural stability. Chemical complexity and nanocrystallinity enhance the radiation tolerance of these new RHEAs, but their multi-element nature, including low-melting Cr, complicates bulk fabrication and limits practical applications. We demonstrate that reducing the number of alloying elements and yet retain high-radiation tolerance is possible within the ternary system W-Ta-V via synthesis of two novel nanocrystalline refractory medium-entropy alloys (RMEAs): the W$_{53}$Ta$_{44}$V$_{3}$ and W$_{53}$Ta$_{42}$V$_{5}$ (in at.\%). We experimentally show that the radiation response of the W-Ta-V system can be tailored by small additions of V, and such experimental result was validated with theoretical analysis of chemical short-range orders (CSRO) from combined ab-initio atomistic Monte-Carlo modeling. It is predicted from computational analysis that a small change in V concentration has a significant effect on the Ta-V CRSO between W$_{53}$Ta$_{44}$V$_{3}$ and W$_{53}$Ta$_{42}$V$_{5}$ leading to radiation-resistant microstructures in these RMEAs from chemistry stand-point of views. We deviate from the original high-entropy alloy concept to show that high radiation resistance can be achieved in systems with simplified chemical complexity.

The Guided Imagery technique is reported to be used by therapists all over the world in order to increase the comfort of patients suffering from a variety of disorders from mental to oncology ones and proved to be successful in numerous of ways. Possible support for the therapists can be estimation of the time at which subject goes into deep relaxation. This paper presents the results of the investigations of a cohort of 26 students exposed to Guided Imagery relaxation technique and mental task workloads conducted with the use of dense array electroencephalographic amplifier. The research reported herein aimed at verification whether it is possible to detect differences between those two states and to classify them using deep learning methods and recurrent neural networks such as EEGNet, Long Short-Term Memory-based classifier, 1D Convolutional Neural Network and hybrid model of 1D Convolutional Neural Network and Long Short-Term Memory. The data processing pipeline was presented from the data acquisition, through the initial data cleaning, preprocessing and postprocessing. The classification was based on two datasets: one of them using 26 so-called cognitive electrodes and the other one using signal collected from 256 channels. So far there have not been such comparisons in the application being discussed. The classification results are presented by the validation metrics such as: accuracy, recall, precision, F1-score and loss for each case. It turned out that it is not necessary to collect signals from all electrodes as classification of the cognitive ones gives the results similar to those obtained for the full signal and extending input to 256 channels does not add much value. In Disscussion there were proposed an optimal classifier as well as some suggestions concerning the prospective development of the project., Comment: In review

Complementing results of Hacking and Prokhorov, we determine in an explicit manner all normal degenerations of the projective plane that allow a non-trivial torus action., Comment: updated title, abstract and introduction

This work generalizes the binary search problem to a $d$-dimensional domain $S_1\times\cdots\times S_d$, where $S_i=\{0, 1, \ldots,n_i-1\}$ and $d\geq 1$, in the following way. Given $(t_1,\ldots,t_d)$, the target element to be found, the result of a comparison of a selected element $(x_1,\ldots,x_d)$ is the sequence of inequalities each stating that either $t_i < x_i$ or $t_i>x_i$, for $i\in\{1,\ldots,d\}$, for which at least one is correct, and the algorithm does not know the coordinate $i$ on which the correct direction to the target is given. Among other cases, we show asymptotically almost matching lower and upper bounds of the query complexity to be in $\Omega(n^{d-1}/d)$ and $O(n^d)$ for the case of $n_i=n$. In particular, for fixed $d$ these bounds asymptotically do match. This problem is equivalent to the classical binary search in case of one dimension and shows interesting differences for higher dimensions. For example, if one would impose that each of the $d$ inequalities is correct, then the search can be completed in $\log_2\max\{n_1,\ldots,n_d\}$ queries. In an intermediate model when the algorithm knows which one of the inequalities is correct the sufficient number of queries is $\log_2(n_1\cdot\ldots\cdot n_d)$. The latter follows from a graph search model proposed by Emamjomeh-Zadeh et al. [STOC 2016].

This Letter reports a search for charge-parity ($CP$) symmetry violating nonstandard interactions (NSI) of neutrinos with matter using the NOvA Experiment, and examines their effects on the determination of the standard oscillation parameters. Data from $\nu_{\mu}(\bar{\nu}_{\mu})\rightarrow\nu_{\mu}(\bar{\nu}_{\mu})$ and $\nu_{\mu}(\bar{\nu}_{\mu})\rightarrow\nu_{e}(\bar{\nu}_{e})$ oscillation channels are used to measure the effect of the NSI parameters $\varepsilon_{e\mu}$ and $\varepsilon_{e\tau}$. With 90% CL the magnitudes of the NSI couplings are constrained to be $|\varepsilon_{e\mu}| \, \lesssim 0.3$ and $|\varepsilon_{e\tau}| \, \lesssim 0.4$. A degeneracy at $|\varepsilon_{e\tau}| \, \approx 1.8$ is reported, and we observe that the presence of NSI limits sensitivity to the standard $CP$ phase $\delta_{\tiny\text{CP}}$.

The main result of this paper are dimension-free $L^p$ inequalities, $12,$ $\varepsilon>0,$ and $\theta=\theta(\varepsilon,p)\in (0,1)$ satisfying \[ \frac{1}{p}=\frac{\theta}{p+\varepsilon}+\frac{1-\theta}{2} \] we obtain, for any function $f:\{-1,1\}^n\to \mathbb{C}$ whose spectrum is bounded from above by $d,$ the Bernstein-Markov type inequalities \[\|\Delta^k f\|_{p} \le C(p,\varepsilon)^k \,d^k\, \|f\|_{2}^{1-\theta}\|f\|_{p+\varepsilon}^{\theta},\qquad k\in \mathbb{N}.\] Analogous inequalities are also proved for $p\in (1,2)$ with $p-\varepsilon$ replacing $p+\varepsilon.$ As a corollary, if $f$ is Boolean-valued or $f\colon \{-1,1\}^n\to \{-1,0,1\},$ we obtain the bounds \[\|\Delta^k f\|_{p} \le C(p)^k \,d^k\, \|f\|_p,\qquad k\in \mathbb{N}.\] At the endpoint $p=\infty$ we provide counterexamples for which a linear growth in $d$ does not suffice when $k=1$. We also obtain a counterpart of this result on tail spaces. Namely, for $p>2$ we prove that any function $f:\{-1,1\}^n\to \mathbb{C}$ whose spectrum is bounded from below by $d$ satisfies the upper bound on the decay of the heat semigroup $$ \|e^{-t\Delta}f\|_{p} \le \exp(-c(p,\varepsilon) td) \|f\|_{2}^{1-\theta}\|f\|_{p+\varepsilon}^{\theta},\qquad t>0,$$ and an analogous estimate for $p\in (1,2).$ The constants $c(p,\varepsilon)$ and $C(p,\varepsilon)$ depend only on $p$ and $\varepsilon$; crucially, they are independent of the dimension $n$., Comment: 10 pages, incporporating suggestions from referees reports, accepted for publication in Studia Mathematica

It is increasingly common to collect pre-post data with pseudonyms or self-constructed identifiers. On survey responses from sensitive populations, identifiers may be made optional to encourage higher response rates. The ability to match responses between pre- and post-intervention phases for every participant may be impossible in such applications, leaving practitioners with a choice between the paired t-test on the matched samples and the two-sample t-test on all samples for evaluating mean differences. We demonstrate the inadequacies with both approaches, as the former test requires discarding unmatched data, while the latter test ignores correlation and assumes independence. In cases with a subset of matched samples, an opportunity to achieve limited inference about the correlation exists. We propose a novel technique for such `partially matched' data, which we refer to as the Quantile-based t-test for correlated samples, to assess mean differences using a conservative estimate of the correlation between responses based on the matched subset. Critically, our approach does not discard unmatched samples, nor does it assume independence. Our results demonstrate that the proposed method yields nominal Type I error probability while affording more power than existing approaches. Practitioners can readily adopt our approach with basic statistical programming software., Comment: 17 pages, 3 figures

Between 2011 and 2014 NHANES collected objectively measured physical activity data using wrist-worn accelerometers for tens of thousands of individuals for up to seven days. Here we analyze the minute-level indicators of being active, which can be viewed as binary (because there is an active indicator at every minute), multilevel (because there are multiple days of data for each study participant), functional (because within-day data can be viewed as a function of time) data. To extract within- and between-participant directions of variation in the data, we introduce Generalized Multilevel Functional Principal Component Analysis (GM-FPCA), an approach based on the dimension reduction of the linear predictor. Scores associated with specific patterns of activity are shown to be strongly associated with time to death. Extensive simulation studies indicate that GM-FPCA provides accurate estimation of model parameters, is computationally stable, and is scalable in the number of study participants, visits, and observations within visits. R code for implementing the method is provided.

NOvA is a long-baseline neutrino oscillation experiment that measures oscillations in charged-current $\nu_{\mu} \rightarrow \nu_{\mu}$ (disappearance) and $\nu_{\mu} \rightarrow \nu_{e}$ (appearance) channels, and their antineutrino counterparts, using neutrinos of energies around 2 GeV over a distance of 810 km. In this work we reanalyze the dataset first examined in our previous paper [Phys. Rev. D 106, 032004 (2022)] using an alternative statistical approach based on Bayesian Markov Chain Monte Carlo. We measure oscillation parameters consistent with the previous results. We also extend our inferences to include the first NOvA measurements of the reactor mixing angle $\theta_{13}$ and the Jarlskog invariant. We use these results to quantify the strength of our inferences about CP violation, as well as to examine the effects of constraints from short-baseline measurements of $\theta_{13}$ using antineutrinos from nuclear reactors when making NOvA measurements of $\theta_{23}$. Our long-baseline measurement of $\theta_{13}$ is also shown to be consistent with the reactor measurements, supporting the general applicability and robustness of the PMNS framework for neutrino oscillations., Comment: 20 pages, 17 figures; version accepted by Phys. Rev. D. Data associated with this paper is available at https://doi.org/10.15484/2349444

Cutting and packing problems are present in many, at first glance unconnected, areas, therefore it's beneficial to have a good understanding of their underlying structure, to select proper techniques for finding solutions. Cutting and packing problems are a class of combinatorial problems in which there are specified two classes of objects: big and small items and the task is to place the small items within big items. Even in the 1-dimensional case, bin-packing is strongly NP-hard (Garey 1978), which suggests, that exact solutions may not be found in a reasonable time for bigger instances. In the literature, there are presented many various approaches to packing problems, e.g. mixed-integer programming, approximation algorithms, heuristic solutions, and local search algorithms, including metaheuristic approaches like Tabu Search or Simulated Annealing. The main goal of this work is to review existing solutions, survey the variants arising from the industry applications, present a solution based on constraint programming and compare its performance with the results in the literature. Optimization with constraint programming is a method searching for the global optima, hence it may require a higher workload compared to the heuristic and local search approaches, which may finish in a local optimum. The performance of the presented model will be measured on test data used in the literature, which were used in many articles presenting a variety of approaches to three-dimensional container packing, which will allow us to compare the efficiency of the constraint programming model with other methods used in the operational research.

As child-robot interactions become more and more common in daily life environment, it is important to examine how robot's errors influence children's behavior. We explored how a robot's unexpected behaviors affect child-robot interactions during two workshops on active reading: one in a modern art museum and one in a school. We observed the behavior and attitudes of 42 children from three age groups: 6-7 years, 8-10 years, and 10-12 years. Through our observations, we identified six different types of surprising robot behaviors: personality, movement malfunctions, inconsistent behavior, mispronunciation, delays, and freezing. Using a qualitative analysis, we examined how children responded to each type of behavior, and we observed similarities and differences between the age groups. Based on our findings, we propose guidelines for designing age-appropriate learning interactions with social robots., Comment: 8 pages

Refractory metal nitrides have recently gained attention in various fields of modern photonics due to their cheap and robust production technology, silicon-technology compatibility, high thermal and mechanical resistance, and competitive optical characteristics in comparison to typical plasmonic materials like gold and silver. In this work, we demonstrate that by varying the stoichiometry of sputtered nitride films, both static and ultrafast optical responses of refractory metal nitrides can efficiently be controlled. We further prove that the spectral changes in ultrafast transient response are directly related to the position of the epsilon-near-zero region. At the same time, the analysis of the temporal dynamics allows us to identify three time components - the "fast" femtosecond one, the "moderate" picosecond one, and the "slow" at the nanosecond time scale. We also find out that the non-stoichiometry does not significantly decrease the recovery time of the reflectance value. Our results show the strong electron-phonon coupling and reveal the importance of both the electron and lattice temperature-induced changes in the permittivity near the ENZ region and the thermal origin of the long tail in the transient optical response of refractory nitrides.

Multiplex immunofluorescence (mIF) imaging technology facilitates the study of the tumour microenvironment in cancer patients. Due to the capabilities of this emerging bioimaging technique, it is possible to statistically analyse, for example, the co-varying location and functions of multiple different types of immune cells. Complex spatial relationships between different immune cells have been shown to correlate with patient outcomes and may reveal new pathways for targeted immunotherapy treatments. This tutorial reviews methods and procedures relating to spatial point patterns for complex data analysis. We consider tissue cells as a realisation of a spatial point process for each patient. We focus on proper functional descriptors for each observation and techniques that allow us to obtain information about inter-patient variation. Ovarian cancer is the deadliest gynaecological malignancy and can resist chemotherapy treatment effective in cancers. We use a dataset of high-grade serous ovarian cancer samples from 51 patients. We examine the immune cell composition (T cells, B cells, macrophages) within tumours and additional information such as cell classification (tumour or stroma) and other patient clinical characteristics. Our analyses, supported by reproducible software, apply to other digital pathology datasets.

POLAR-2, a plastic scintillator based Compton polarimeter, is currently under development and planned for a launch to the China Space Station in 2025. It is intended to shed a new light on our understanding of Gamma-Ray Bursts by performing high precision polarization measurements of their prompt emission. The instrument will be orbiting at an average altitude of 383 km with an inclination of 42{\deg} and will be subject to background radiation from cosmic rays and solar events. In this work, we tested the performance of plastic scintillation bars, EJ-200 and EJ-248M from Eljen Technology, under space-like conditions, that were chosen as possible candidates for POLAR-2. Both scintillator types were irradiated with 58 MeV protons at several doses from 1.89 Gy (corresponding to about 13 years in space for POLAR-2) up to 18.7 Gy, that goes far beyond the expected POLAR-2 life time. Their respective properties, expressed in terms of light yield, emission and absorption spectra, and activation analysis due to proton irradiation are discussed. Scintillators activation analyses showed a dominant contribution of $\beta^+$ decay with a typical for this process gamma-ray energy line of 511 keV., Comment: 19 pages, 14 figures