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Energy dispersive X-ray (EDX) spectrum imaging yields compositional information with a spatial resolution down to the atomic level. However, experimental limitations often produce extremely sparse and noisy EDX spectra. Under such conditions, every detected X-ray must be leveraged to obtain the maximum possible amount of information about the sample. To this end, we introduce a robust multiscale Bayesian approach that accounts for the Poisson statistics in the EDX data and leverages their underlying spatial correlations. This is combined with EDX spectral simulation (elemental contributions and Bremsstrahlung background) into a Bayesian estimation strategy. When tested using simulated datasets, the chemical maps obtained with this approach are more accurate and preserve a higher spatial resolution than those obtained by standard methods. These properties translate to experimental datasets, where the method enhances the atomic resolution chemical maps of a canonical tetragonal ferroelectric PbTiO3 sample, such that ferroelectric domains are mapped with unit-cell resolution.

We discuss C$^*$-algebras associated with several different natural shifts on the Hilbert space of the $s$-adic tree, continuing the analysis from \cite{HKMP3} and in particular we describe their structure and compute the $K$-Theory groups., Comment: arXiv admin note: text overlap with arXiv:2412.00854

We design an algorithm that generates an $n$-vertex unlabeled chordal graph uniformly at random in expected polynomial time. Along the way, we develop the following two results: (1) an $\mathsf{FPT}$ algorithm for counting and sampling labeled chordal graphs with a given automorphism $\pi$, parameterized by the number of moved points of $\pi$, and (2) a proof that the probability that a random $n$-vertex labeled chordal graph has a given automorphism $\pi\in S_n$ is at most $1/2^{c\max\{\mu^2,n\}}$, where $\mu$ is the number of moved points of $\pi$ and $c$ is a constant. Our algorithm for sampling unlabeled chordal graphs calls the aforementioned $\mathsf{FPT}$ algorithm as a black box with potentially large values of the parameter $\mu$, but the probability of calling this algorithm with a large value of $\mu$ is exponentially small., Comment: Accepted for publication at STACS 2025 (International Symposium on Theoretical Aspects of Computer Science); 41 pages

Motivated by the change-making problem, we extend the notion of greediness to sets of positive integers not containing the element $1$, and from there to numerical semigroups. We provide an algorithm to determine if a given set (not necessarily containing the number $1$) is greedy. We also give specific conditions for sets of cardinality three, and we prove that numerical semigroups generated by three consecutive integers are greedy., Comment: Accepted for publication in Communications in Algebra, Taylor and Francis group. Contains 23 pages, 2 tables, 4 algorithms

Democratic governments comprise a subset of a population whose goal is to produce coherent decisions that solve societal challenges while respecting the will of the people they represent. New governance frameworks represent this problem as a social network rather than as a hierarchical pyramid with centralized authority. But how should this network be structured? To investigate this question, we model the set of decisions a population must make as a satisfiability problem and the structure of information flow involved in decision-making as a social hypergraph. This allows us to consider the benefits of different governance structures, from dictatorships to direct democracy. In between these extremes, we find a regime of effective governance where decision groups are formed as needed by key stakeholders to discuss and make specific decisions. This regime of effective governance allows even incoherent or polarized populations to make coherent decisions at low coordination costs. More broadly, we present not just simulation results, but a modeling framework that can be used to explore the costs and benefits of a wide range of governance strategies using bottom-up approaches and their ability to tackle decision problems that challenge standard governments.

We discuss C$^*$-algebras associated with several different natural shifts on the Hilbert space of the $s$-adic tree, that is, the tree of balls in the space of $s$-adic integers.

Let $\A$ be a finite dimensional vector space and $\Phi$ be a finite root system in $\A$. To this data is associated an affine poly-simplicial complex. Motivated by a forthcoming construction of connectified higher buildings, we study "affine weight polytopes" associated to these data. We prove that these polytopes tesselate $\A$. We also prove a kind of "mixed" tessellation, involving the affine weight polytopes and the poly-simplical structure on $\A$.

Beyond high-fidelity image synthesis, diffusion models have recently exhibited promising results in dense visual perception tasks. However, most existing work treats diffusion models as a standalone component for perception tasks, employing them either solely for off-the-shelf data augmentation or as mere feature extractors. In contrast to these isolated and thus sub-optimal efforts, we introduce a unified, versatile, diffusion-based framework, Diff-2-in-1, that can simultaneously handle both multi-modal data generation and dense visual perception, through a unique exploitation of the diffusion-denoising process. Within this framework, we further enhance discriminative visual perception via multi-modal generation, by utilizing the denoising network to create multi-modal data that mirror the distribution of the original training set. Importantly, Diff-2-in-1 optimizes the utilization of the created diverse and faithful data by leveraging a novel self-improving learning mechanism. Comprehensive experimental evaluations validate the effectiveness of our framework, showcasing consistent performance improvements across various discriminative backbones and high-quality multi-modal data generation characterized by both realism and usefulness., Comment: 26 pages, 14 figures

The Legacy Survey of Space and Time (LSST) at Vera C. Rubin Observatory is planned to begin in the Fall of 2025. The LSST survey cadence has been designed via a community-driven process regulated by the Survey Cadence Optimization Committee (SCOC), which recommended up to 3% of the observing time to carry out Target of Opportunity (ToO) observations. Experts from the scientific community, Rubin Observatory personnel, and members of the SCOC were brought together to deliver a recommendation for the implementation of the ToO program during a workshop held in March 2024. Four main science cases were identified: gravitational wave multi-messenger astronomy, high energy neutrinos, Galactic supernovae, and small potentially hazardous asteroids possible impactors. Additional science cases were identified and briefly addressed in the documents, including lensed or poorly localized gamma-ray bursts and twilight discoveries. Trigger prioritization, automated response, and detailed strategies were discussed for each science case. This document represents the outcome of the Rubin ToO 2024 workshop, with additional contributions from members of the Rubin Science Collaborations. The implementation of the selection criteria and strategies presented in this document has been endorsed in the SCOC Phase 3 Recommendations document (PSTN-056). Although the ToO program is still to be finalized, this document serves as a baseline plan for ToO observations with the Rubin Observatory.

Models of how things spread often assume that transmission mechanisms are fixed over time. However, social contagions--the spread of ideas, beliefs, innovations--can lose or gain in momentum as they spread: ideas can get reinforced, beliefs strengthened, products refined. We study the impacts of such self-reinforcement mechanisms in cascade dynamics. We use different mathematical modeling techniques to capture the recursive, yet changing nature of the process. We find a critical regime with a range of power-law cascade size distributions with varying scaling exponents. This regime clashes with classic models, where criticality requires fine tuning at a precise critical point. Self-reinforced cascades produce critical-like behavior over a wide range of parameters, which may help explain the ubiquity of power-law distributions in empirical social data.

We present REM, a framework for segmenting a wide range of concepts in video that can be described through natural language. Our method capitalizes on visual-language representations learned by video diffusion models on Internet-scale datasets. A key insight of our approach is preserving as much of the generative model's original representation as possible, while fine-tuning it on narrow-domain Referral Object Segmentation datasets. As a result, our framework can accurately segment and track rare and unseen objects, despite being trained on object masks from a limited set of categories. Additionally, it can generalize to non-object dynamic concepts, such as waves crashing in the ocean, as demonstrated in our newly introduced benchmark for Referral Video Process Segmentation (Ref-VPS). Our experiments show that REM performs on par with state-of-the-art approaches on in-domain datasets, like Ref-DAVIS, while outperforming them by up to twelve points in terms of region similarity on out-of-domain data, leveraging the power of Internet-scale pre-training., Comment: Project page at https://miccooper9.github.io/projects/ReferEverything/

The recent advances in Large Language Model's generation and reasoning capabilities present an opportunity to develop truly conversational recommendation systems. However, effectively integrating recommender system knowledge into LLMs for natural language generation which is tailored towards recommendation tasks remains a challenge. This paper addresses this challenge by making two key contributions. First, we introduce a new dataset (REGEN) for natural language generation tasks in conversational recommendations. REGEN (Reviews Enhanced with GEnerative Narratives) extends the Amazon Product Reviews dataset with rich user narratives, including personalized explanations of product preferences, product endorsements for recommended items, and summaries of user purchase history. REGEN is made publicly available to facilitate further research. Furthermore, we establish benchmarks using well-known generative metrics, and perform an automated evaluation of the new dataset using a rater LLM. Second, the paper introduces a fusion architecture (CF model with an LLM) which serves as a baseline for REGEN. And to the best of our knowledge, represents the first attempt to analyze the capabilities of LLMs in understanding recommender signals and generating rich narratives. We demonstrate that LLMs can effectively learn from simple fusion architectures utilizing interaction-based CF embeddings, and this can be further enhanced using the metadata and personalization data associated with items. Our experiments show that combining CF and content embeddings leads to improvements of 4-12% in key language metrics compared to using either type of embedding individually. We also provide an analysis to interpret how CF and content embeddings contribute to this new generative task.

Rubidium two-photon frequency standards are emerging as powerful contenders for compact, durable devices with exceptional stability. The field has focused on single-color excitation to date. Here we demonstrate the key advantages of a two-color excitation of a two-photon optical frequency standard based on the $5S_{1/2}\,{\rightarrow}\,5D_{5/2}$ transition of rubidium-87 utilising driving fields at 780 nm and 776 nm. We show that utilising the $5P_{3/2}$ intermediate state to resonantly enhance the transition, we can for the first time attain frequency stabilities comparable to the rubidium single-color two-photon frequency standards, notably with approximately ten-fold less optical power and ten-fold lower rubidium vapor density. Optimisation of the detuning from the $5P_{3/2}$ intermediate state, and optical powers of driving lasers, has a dramatic effect on the frequency stability, achieving the best short-term stability of any two-photon rubidium frequency standard to date, of $6{\times}10^{-14}$ at $\tau$ = 1 s. We demonstrate this level of performance is compatible with a compact geometry, by fully self-referencing the frequency standard using an integrated fiber frequency comb to simultaneously stabilize the 780 nm laser's detuning from the $5P_{3/2}$ intermediate state, and produce a frequency-stable microwave output. A comprehensive noise characterization underpins our observations of this two-color frequency standard which explains the measured stability, showing this frequency standard is shot-noise limited initially before becoming limited by light shifts in the long-term. This work represents a major advance towards a low size, weight, and power frequency standard based on this two-color excitation method., Comment: 13 pages, 7 figures

In 2019, D. Muthiah proposed a strategy to define affine Kazhdan-Lusztig $R$-polynomials for Kac-Moody groups. Since then, Bardy-Panse, the first author and Rousseau have introduced the formalism of twin masures and the authors have extended combinatorial results from affine root systems to general Kac-Moody root systems in a previous article. In this paper, we use these results to explicitly define affine $R$-Kazhdan-Lusztig polynomials for Kac-Moody groups. The construction is based on a path model lifting to twin masures. Conjecturally, these polynomials count the cardinality of intersections of opposite affine Schubert cells, as in the case of reductive groups., Comment: 54 pages, comments welcome

An exciting recent development for deep-tissue imaging with cellular resolution is three-photon fluorescence microscopy (3PM) with excitation at long wavelengths (1300 and 1700 nm). In the last few years, long-wavelength 3PM has driven rapid progress in deep-tissue imaging beyond the depth limit of two-photon microscopy, with impacts in neuroscience, immunology, and cancer biology. However, wide adoption of 3PM faces challenges. Three-photon excitation (3PE) is naturally weaker than two-photon excitation, which places a premium on ultrashort pulses with high peak power. The inefficiency, complexity, and cost of current sources of these pulses present major barriers to the use of 3PM in typical biomedical research labs. Here, we describe a fiber-based source of femtosecond pulses with multi-megawatt peak power, tunable from 850 nm to 1700 nm. Compressed pulses from a fiber amplifier at 1030~nm are launched into an antiresonant hollow-core fiber filled with argon. By varying only the gas pressure, pulses with hundreds of nanojoules of energy and sub-100 fs duration are obtained at wavelengths between 850 and 1700 nm. This approach is a new route to an efficient, robust, and potentially low-cost source for multiphoton deep-tissue imaging. In particular, 960-nJ and 50-fs pulses are generated at 1300 nm with a conversion efficiency of 10\%. The nearly 20-MW peak power is an order of magnitude higher than the previous best from femtosecond fiber source at 1300~nm. As an example of the capabilities of the source, these pulses are used to image structure and neuronal activity in mouse brain as deep as 1.1 mm below the dura., Comment: Supplement appended at end

The Onion Decomposition has recently been shown to provide principled models of complex graphs that better reproduce the sparse networks found in nature, but at the cost of complicated connection rules. We propose a k-edge swapping MCMC algorithm to efficiently obtain a uniform sample from the ensemble of simple graphs with a fixed Onion Decomposition and degree sequence. We prove the non-connectivity of the 2-edge swap algorithm for some small graphs, but then provide numerical experiments to show that this non-connectivity is not a problem for 2-edge swap in many practical cases, and likely irrelevant when using k-edge swaps with k>2. We finish by comparing our null model to other well-known models in the literature, and show that keeping constraints on the meso-scale structures of the Onion Decomposition greatly increases both the structural and functional realism of random graph null model.

Hybrid recommender systems, combining item IDs and textual descriptions, offer potential for improved accuracy. However, previous work has largely focused on smaller datasets and model architectures. This paper introduces Flare (Fusing Language models and collaborative Architectures for Recommender Enhancement), a novel hybrid recommender that integrates a language model (mT5) with a collaborative filtering model (Bert4Rec) using a Perceiver network. This architecture allows Flare to effectively combine collaborative and content information for enhanced recommendations. We conduct a two-stage evaluation, first assessing Flare's performance against established baselines on smaller datasets, where it demonstrates competitive accuracy. Subsequently, we evaluate Flare on a larger, more realistic dataset with a significantly larger item vocabulary, introducing new baselines for this setting. Finally, we showcase Flare's inherent ability to support critiquing, enabling users to provide feedback and refine recommendations. We further leverage critiquing as an evaluation method to assess the model's language understanding and its transferability to the recommendation task.

Complex 3D scene understanding has gained increasing attention, with scene encoding strategies playing a crucial role in this success. However, the optimal scene encoding strategies for various scenarios remain unclear, particularly compared to their image-based counterparts. To address this issue, we present a comprehensive study that probes various visual encoding models for 3D scene understanding, identifying the strengths and limitations of each model across different scenarios. Our evaluation spans seven vision foundation encoders, including image-based, video-based, and 3D foundation models. We evaluate these models in four tasks: Vision-Language Scene Reasoning, Visual Grounding, Segmentation, and Registration, each focusing on different aspects of scene understanding. Our evaluations yield key findings: DINOv2 demonstrates superior performance, video models excel in object-level tasks, diffusion models benefit geometric tasks, and language-pretrained models show unexpected limitations in language-related tasks. These insights challenge some conventional understandings, provide novel perspectives on leveraging visual foundation models, and highlight the need for more flexible encoder selection in future vision-language and scene-understanding tasks. Code: https://github.com/YunzeMan/Lexicon3D, Comment: NeurIPS 2024. Project page: https://yunzeman.github.io/lexicon3d Github: https://github.com/YunzeMan/Lexicon3D

Stochastic diffusion is the noisy and uncertain process through which dynamics like epidemics, or agents like animal species, disperse over a larger area. Understanding these processes is becoming increasingly important as we attempt to better prepare for potential pandemics and as species ranges shift in response to climate change. Unfortunately, modeling of stochastic diffusion is mostly done through inaccurate deterministic tools that fail to capture the random nature of dispersal or else through expensive computational simulations. In particular, standard tools fail to fully capture the heterogeneity of the area over which this diffusion occurs. Rural areas with low population density require different epidemic models than urban areas; likewise, the edges of a species range require us to explicitly track low integer numbers of individuals rather than vague averages. In this work, we introduce a series of new tools called "mean-FLAME" models that track stochastic dispersion using approximate master equations that explicitly follow the probability distribution of an area of interest over all of its possible states, up to states that are active enough to be approximated using a mean-field model. In one limit, this approach is locally exact if we explicitly track enough states, and in the other limit collapses back to traditional deterministic models if we track no state explicitly. Applying this approach, we show how deterministic tools fail to capture the uncertainty around the speed of nonlinear dynamical processes. This is especially true for marginal areas that are close to unsuitable for diffusion, like the edge of a species range or epidemics in small populations. Capturing the uncertainty in such areas is key to producing accurate forecasts and guiding potential interventions., Comment: For supplemental appendix, see "Ancillary files" under "Access paper" on the right

Master equations provide researchers with the ability to track the distribution over possible states of a system. From these equations, we can summarize the temporal dynamics through a method of moments. These distributions and their moments capture the stochastic nature of a system, which is essential to study infectious diseases. In this paper, we define the states of the system to be the number of infected cells of a given type in the epithelium, the hollow organ tissue in the human body. Epithelium found in the cervix provides a location for viral infections to live and persist, such as human papillomavirus (HPV). HPV is a highly transmissible disease which most commonly affects biological females and has the potential to progress into cervical cancer. By defining a master equation model which tracks the infected cell layer dynamics, information on disease extinction, progression, and viral output can be derived from the method of moments. From this methodology and the outcomes we glean from it, we aim to inform differing states of HPV infected cells, and assess the effects of structural information for each outcome., Comment: 15 pages, 8 figures

Additive manufacturing (AM) technologies have undergone significant advancements through the integration of cooperative robotics additive manufacturing (C-RAM) platforms. By deploying AM processes on the end effectors of multiple robotic arms, not only are traditional constraints such as limited build volumes circumvented, but systems also achieve accelerated fabrication speeds, cooperative sensing capabilities, and in-situ multi-material deposition. Despite advancements, challenges remain, particularly regarding defect generation including voids, cracks, and residual stress. Various factors contribute to these issues, including toolpath planning (i.e., slicing strategies), part decomposition for cooperative printing, and motion planning (i.e., path and trajectory planning). This review first examines the critical aspects of system control for C-RAM systems comprised of slicing and motion planning. The methods for the mitigation of defects through the adjustment of these aspects and the process parameters of AM methods are then described in the context of how they modify the AM process: pre-process, inter-layer (i.e., during layer pauses), and mid-layer (i.e., during material deposition). The application of advanced sensing technologies, including high-resolution cameras, laser scanners, and thermal imaging, to facilitate the capture of micro, meso, and macro-scale defects is explored. The role of digital twins is analyzed, emphasizing their capability to simulate and predict manufacturing outcomes, enabling preemptive adjustments to prevent defects. Finally, the outlook and future opportunities for developing next-generation C-RAM systems are outlined., Comment: 28 pages, 17 figures

AI assistants are being increasingly used by students enrolled in higher education institutions. While these tools provide opportunities for improved teaching and education, they also pose significant challenges for assessment and learning outcomes. We conceptualize these challenges through the lens of vulnerability, the potential for university assessments and learning outcomes to be impacted by student use of generative AI. We investigate the potential scale of this vulnerability by measuring the degree to which AI assistants can complete assessment questions in standard university-level STEM courses. Specifically, we compile a novel dataset of textual assessment questions from 50 courses at EPFL and evaluate whether two AI assistants, GPT-3.5 and GPT-4 can adequately answer these questions. We use eight prompting strategies to produce responses and find that GPT-4 answers an average of 65.8% of questions correctly, and can even produce the correct answer across at least one prompting strategy for 85.1% of questions. When grouping courses in our dataset by degree program, these systems already pass non-project assessments of large numbers of core courses in various degree programs, posing risks to higher education accreditation that will be amplified as these models improve. Our results call for revising program-level assessment design in higher education in light of advances in generative AI., Comment: 20 pages, 8 figures

Understanding the nuances of a user's extensive interaction history is key to building accurate and personalized natural language systems that can adapt to evolving user preferences. To address this, we introduce PERSOMA, Personalized Soft Prompt Adapter architecture. Unlike previous personalized prompting methods for large language models, PERSOMA offers a novel approach to efficiently capture user history. It achieves this by resampling and compressing interactions as free form text into expressive soft prompt embeddings, building upon recent research utilizing embedding representations as input for LLMs. We rigorously validate our approach by evaluating various adapter architectures, first-stage sampling strategies, parameter-efficient tuning techniques like LoRA, and other personalization methods. Our results demonstrate PERSOMA's superior ability to handle large and complex user histories compared to existing embedding-based and text-prompt-based techniques.

In many applications, synchronizing audio with visuals is crucial, such as in creating graphic animations for films or games, translating movie audio into different languages, and developing metaverse applications. This review explores various methodologies for achieving realistic facial animations from audio inputs, highlighting generative and adaptive models. Addressing challenges like model training costs, dataset availability, and silent moment distributions in audio data, it presents innovative solutions to enhance performance and realism. The research also introduces a new taxonomy to categorize audio-visual synchronization methods based on logistical aspects, advancing the capabilities of virtual assistants, gaming, and interactive digital media.

Most novel view synthesis methods such as NeRF are unable to capture the true high dynamic range (HDR) radiance of scenes since they are typically trained on photos captured with standard low dynamic range (LDR) cameras. While the traditional exposure bracketing approach which captures several images at different exposures has recently been adapted to the multi-view case, we find such methods to fall short of capturing the full dynamic range of indoor scenes, which includes very bright light sources. In this paper, we present PanDORA: a PANoramic Dual-Observer Radiance Acquisition system for the casual capture of indoor scenes in high dynamic range. Our proposed system comprises two 360{\deg} cameras rigidly attached to a portable tripod. The cameras simultaneously acquire two 360{\deg} videos: one at a regular exposure and the other at a very fast exposure, allowing a user to simply wave the apparatus casually around the scene in a matter of minutes. The resulting images are fed to a NeRF-based algorithm that reconstructs the scene's full high dynamic range. Compared to HDR baselines from previous work, our approach reconstructs the full HDR radiance of indoor scenes without sacrificing the visual quality while retaining the ease of capture from recent NeRF-like approaches., Comment: 10 pages, 8 figures

The lack of fluency in sign language remains a barrier to seamless communication for hearing and speech-impaired communities. In this work, we propose a low-cost, real-time ASL-to-speech translation glove and an exhaustive training dataset of sign language patterns. We then benchmarked this dataset with supervised learning models, such as LSTMs, GRUs and Transformers, where our best model achieved 92% accuracy. The SignSpeak dataset has 7200 samples encompassing 36 classes (A-Z, 1-10) and aims to capture realistic signing patterns by using five low-cost flex sensors to measure finger positions at each time step at 36 Hz. Our open-source dataset, models and glove designs, provide an accurate and efficient ASL translator while maintaining cost-effectiveness, establishing a framework for future work to build on., Comment: 6 pages, 2 figures, NeurIPS

We present a discontinuous Galerkin-finite difference hybrid scheme that allows high-order shock capturing with the discontinuous Galerkin method for general relativistic magnetohydrodynamics in dynamical spacetimes. We present several optimizations and stability improvements to our algorithm that allow the hybrid method to successfully simulate single, rotating, and binary neutron stars. The hybrid method achieves the efficiency of discontinuous Galerkin methods throughout almost the entire spacetime during the inspiral phase, while being able to robustly capture shocks and resolve the stellar surfaces. We also use Cauchy-Characteristic evolution to compute the first gravitational waveforms at future null infinity from binary neutron star mergers. The simulations presented here are the first successful binary neutron star inspiral and merger simulations using discontinuous Galerkin methods., Comment: 31 pages, 8 figures, minor wording updates

Recently, a new characterization of Lyndon words that are also perfectly clustering was proposed by Lapointe and Reutenauer (2024). A word over a ternary alphabet {a,b,c} is called perfectly clustering Lyndon if and only if it is the product of two palindromes and it can be written as apbqc where p and q are palindromes. We study the properties of palindromes appearing as factors p and q and their links with iterated palindromes over a ternary alphabet., Comment: In Proceedings GASCom 2024, arXiv:2406.14588

We present electrical and thermal transport measurements in single crystals of the metallic oxide RuO$_2$. The resistivity and Seebeck coefficient measured up to 970K confirm the metallic nature of transport. Magnetoresistance and Hall effect measurements as a function of orientation can be most easily described by a multiband transport model. We find that the ordinary Hall effect dominates any anomalous Hall signal in single crystals.

Atomic clocks are at the leading edge of accuracy and precision and are essential for synchronization of distributed critical infrastructure, position, navigation and timing, and scientific applications. There has been a breakthrough in the performance of atomic clocks with the shift from microwave to optical frequency transitions. However, this performance increase has come at the cost of size, complexity and fragility, which has confined optical clocks to laboratories. Here we report on a recent international collaboration where three emerging optical clocks, each based on different operating principles, were trialled at sea. Over weeks of unsupervised naval operation, these clocks demonstrated exceptional reliability and provided frequency stability outputs in optical, microwave and radio-frequency domains. The performance of all three devices was orders of magnitude superior to existing best-in-class commercial solutions over short and medium timescales, marking a significant step toward deploying optical clocks in real-world environments.

The change-making problem consists of representing a certain amount of money with the least possible number of coins, from a given, pre-established set of denominations. The greedy algorithm works by choosing the coins of largest possible denomination first. This greedy strategy does not always produce the least number of coins, except when the set of denominations obeys certain properties. We call a set of denominations with these properties a greedy set. If the set of denominations is an infinite sequence, we call it totally greedy if every prefix subset is greedy. In this paper we investigate some totally greedy sequences arising from second-order linear recurrences with constant coefficients, as well as their subsequences, and we prove sufficient conditions under which these sequences are totally greedy., Comment: 15 pages, no figures

Energy dispersive X-ray (EDX) spectroscopy in the transmission electron microscope is a key tool for nanomaterials analysis, providing a direct link between spatial and chemical information. However, using it for precisely determining chemical compositions presents challenges of noisy data from low X-ray yields and mixed signals from phases that overlap along the electron beam trajectory. Here, we introduce a novel method, non-negative matrix factorisation based pan-sharpening (PSNMF), to address these limitations. Leveraging the Poisson nature of EDX spectral noise and binning operations, PSNMF retrieves high quality phase spectral and spatial signatures via consecutive factorisations. After validating PSNMF with synthetic datasets of different noise levels, we illustrate its effectiveness on two distinct experimental cases: a nano-mineralogical lamella, and supported catalytic nanoparticles. Not only does PSNMF obtain accurate phase signatures, datasets reconstructed from the outputs have demonstrably lower noise and better fidelity than from the benchmark denoising method of principle component analysis.

Let $G$ be a split Kac-Moody group over a local field. In their study of the Iwahori-Hecke algebra of $G$, A.Braverman, D. Kazhdan and M. Patnaik defined a partial order - called the affine Bruhat order - on the extended affine Weyl semi-group $W^+$ of $G$. In this paper, we study finiteness questions for covers and co-covers of $W^+$, generalizing results of A. Welch. In particular we prove that the intervals for this order are finite. Our results rely on the finiteness of the set of quantum roots of arbitrary Kac-Moody root systems, which we prove. We also obtain a classification of quantum roots.