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Mixture-of-Experts (MoE) language models can reduce computational costs by 2-4$\times$ compared to dense models without sacrificing performance, making them more efficient in computation-bounded scenarios. However, MoE models generally require 2-4$\times$ times more parameters to achieve comparable performance to a dense model, which incurs larger GPU memory requirements and makes MoE models less efficient in I/O-bounded scenarios like autoregressive generation. In this work, we propose a hybrid dense training and sparse inference framework for MoE models (DS-MoE) which achieves strong computation and parameter efficiency by employing dense computation across all experts during training and sparse computation during inference. Our experiments on training LLMs demonstrate that our DS-MoE models are more parameter-efficient than standard sparse MoEs and are on par with dense models in terms of total parameter size and performance while being computationally cheaper (activating 30-40% of the model's parameters). Performance tests using vLLM show that our DS-MoE-6B model runs up to $1.86\times$ faster than similar dense models like Mistral-7B, and between $1.50\times$ and $1.71\times$ faster than comparable MoEs, such as DeepSeekMoE-16B and Qwen1.5-MoE-A2.7B.

Session types are a typing discipline used to formally describe communication-driven applications with the aim of fewer errors and easier debugging later into the life cycle of the software. Protocols at the transport layer such as TCP, UDP, and QUIC underpin most of the communication on the modern Internet and affect billions of end-users. The transport layer has different requirements and constraints compared to the application layer resulting in different requirements for verification. Despite this, to our best knowledge, no work shows the application of session types at the transport layer. In this work, we discuss how multiparty session types (MPST) can be applied to implement the TCP protocol. We develop an MPST-based implementation of a subset of a TCP server in Rust and test its interoperability against the Linux TCP stack. Our results highlight the differences in assumptions between session type theory and the way transport layer protocols are usually implemented. This work is the first step towards bringing session types into the transport layer., Comment: In Proceedings PLACES 2024, arXiv:2404.03712

We extend the notion of ascent-compatibility from symmetric groups to all Coxeter groups, thereby providing a type-independent framework for constructing families of modules of $0$-Hecke algebras. We apply this framework in type $B$ to give representation-theoretic interpretations of a number of noteworthy families of type-$B$ quasisymmetric functions. Next, we construct modules of the type-$B$ $0$-Hecke algebra corresponding to type-$B$ analogues of Schur functions and introduce a type-$B$ analogue of Schur $Q$-functions; we prove that these shifted domino functions expand positively in the type-$B$ peak functions. We define a type-$B$ analogue of the $0$-Hecke--Clifford algebra, and we use this to provide representation-theoretic interpretations for both the type-$B$ peak functions and the shifted domino functions. We consider the modules of this algebra induced from type-$B$ $0$-Hecke modules constructed via ascent-compatibility and prove a general formula, in terms of type-$B$ peak functions, for the type-$B$ quasisymmetric characteristics of the restrictions of these modules., Comment: 25 pages, 3 figures

Inspired by recent work on refraction billiards in dynamics, we introduce a notion of refraction for combinatorial billiards. This allows us to define a generalization of toric promotion that we call toric promotion with reflections and refractions, which is a dynamical system defined via a graph $G$ whose edges are partitioned into a set of reflection edges and a set of refraction edges. This system is a discretization of a billiards system in which a beam of light can pass through, reflect off of, or refract through each toric hyperplane in a toric arrangement. Vastly generalizing the main theorem known about toric promotion, we give a simple formula for the orbit structure of toric promotion with reflections and refractions when $G$ is a forest. We also completely describe the orbit sizes when $G$ is a cycle with an even number of refraction edges; this result is new even for ordinary toric promotion (i.e., when there are no refraction edges). When $G$ is a cycle of even size with no reflection edges, we obtain an interesting instance of the cyclic sieving phenomenon., Comment: 21 pages, 7 figures

Analysis of microwave sky signals, such as the cosmic microwave background, often requires component separation with multi-frequency methods, where different signals are isolated by their frequency behaviors. Many so-called "blind" methods, such as the internal linear combination (ILC), make minimal assumptions about the spatial distribution of the signal or contaminants, and only assume knowledge of the frequency dependence of the signal. The ILC is a minimum-variance linear combination of the measured frequency maps. In the case of Gaussian, statistically isotropic fields, this is the optimal linear combination, as the variance is the only statistic of interest. However, in many cases the signal we wish to isolate, or the foregrounds we wish to remove, are non-Gaussian and/or statistically anisotropic (in particular for Galactic foregrounds). In such cases, it is possible that machine learning (ML) techniques can be used to exploit the non-Gaussian features of the foregrounds and thereby improve component separation. However, many ML techniques require the use of complex, difficult-to-interpret operations on the data. We propose a hybrid method whereby we train an ML model using only combinations of the data that $\textit{do not contain the signal}$, and combine the resulting ML-predicted foreground estimate with the ILC solution to reduce the error from the ILC. We demonstrate our methods on simulations of extragalactic temperature and Galactic polarization foregrounds, and show that our ML model can exploit non-Gaussian features, such as point sources and spatially-varying spectral indices, to produce lower-variance maps than ILC - eg, reducing the variance of the B-mode residual by factors of up to 5 - while preserving the signal of interest in an unbiased manner. Moreover, we often find improved performance when applying our model to foreground models on which it was not trained., Comment: 22 pages, 13 figures. v2 has some updated references

In this short note, we prove that the set of elementary tensors is weakly closed in the projective tensor product of two Banach spaces. As a result, we are able to answer a question from the literature proving that if $(x_n) \subset X$ and $(y_n) \subset Y$ are two weakly null sequences such that $(x_n \otimes y_n)$ converges weakly in $X \widehat{\otimes}_\pi Y$, then $(x_n \otimes y_n)$ is also weakly null.

Quantum heat engines and quantum refrigerators are proposed in three-terminal quantum Hall (QH) and quantum spin Hall (QSH) setups with a voltage-temperature probe in linear and nonlinear transport regimes. In the linear response regime, we find that efficiency at maximum power approaches the Curzon-Ahlborn limit in both QH and QSH setups. Similarly, in nonlinear response, we find that efficiency at maximum power reaches the Whitney bounds. This is for the first time, we see that in the same setup and using quantum point contacts, the thermoelectric efficiency limits in linear and nonlinear response being achieved., Comment: 36 pages (6 pages main and 30 pages supplementary material) with 21 figures

Solute-intercalation-induced phase separation creates spatial heterogeneities in host materials, a phenomenon ubiquitous in batteries, hydrogen storage, and other energy devices. Despite many efforts, probing intercalation processes at the atomic scale has been a significant challenge. We study hydrogen (de)intercalation in palladium nanocrystals as a model system and achieve atomic-resolution imaging of hydrogen intercalation wave dynamics by utilizing liquid-phase transmission electron microscopy. Our observations reveal that intercalation wave mechanisms, instead of shrinking-core mechanisms, prevail at ambient temperature for palladium nanocubes ranging from ~60 nm down to ~10 nm. We uncover the atomic evolution of hydrogen intercalation wave transitioning from non-planar and inclined boundaries to those closely aligned with {100} planes. Our kinetic Monte Carlo simulations demonstrate the observed intercalation wave dynamics correspond to sorption pathways minimizing the lattice mismatch strain at the phase boundary. Unveiling the atomic intercalation pathways holds profound implications for engineering intercalation-mediated devices and advancements in energy sciences., Comment: 5 pages, 4 figures, plus Methods, Extended Data, and Supplementary Notes

What happens when an infinite number of players play a quantum game? In this paper, we will answer this question by looking at the emergence of cooperation in the presence of noise in a one-shot quantum Prisoner's dilemma (QuPD). We will use the numerical Agent-based model (ABM) and compare it with the analytical Nash equilibrium mapping (NEM) technique. To measure cooperation, we consider five indicators, i.e., game magnetization, entanglement susceptibility, correlation, player's payoff average, and payoff capacity, respectively. In quantum social dilemmas, entanglement plays a non-trivial role in determining the players' behavior in the thermodynamic limit, and we consider the existence of bipartite entanglement between neighboring players. For the five indicators in question, we observe \textit{first}-order phase transitions at two entanglement values, and these phase transition points depend on the payoffs associated with the QuPD game. We numerically analyze and study the properties of both the \textit{Quantum} and the \textit{Defect} phases of the QuPD via the five indicators. The results of this paper demonstrate that both ABM and NEM, in conjunction with the chosen five indicators, provide insightful information on cooperative behavior in the thermodynamic limit of the one-shot quantum Prisoner's dilemma., Comment: 16 pages, 7 figures

MindScape aims to study the benefits of integrating time series behavioral patterns (e.g., conversational engagement, sleep, location) with Large Language Models (LLMs) to create a new form of contextual AI journaling, promoting self-reflection and well-being. We argue that integrating behavioral sensing in LLMs will likely lead to a new frontier in AI. In this Late-Breaking Work paper, we discuss the MindScape contextual journal App design that uses LLMs and behavioral sensing to generate contextual and personalized journaling prompts crafted to encourage self-reflection and emotional development. We also discuss the MindScape study of college students based on a preliminary user study and our upcoming study to assess the effectiveness of contextual AI journaling in promoting better well-being on college campuses. MindScape represents a new application class that embeds behavioral intelligence in AI.

Alzheimer's disease is a progressive, debilitating neurodegenerative disease that affects 50 million people globally. Despite this substantial health burden, available treatments for the disease are limited and its fundamental causes remain poorly understood. Previous work has suggested the existence of clinically-meaningful sub-types, which it is suggested may correspond to distinct etiologies, disease courses, and ultimately appropriate treatments. Here, we use unsupervised learning techniques on electronic health records (EHRs) from a cohort of memory disorder patients to characterise heterogeneity in this disease population. Pre-trained embeddings for medical codes as well as transformer-derived Clinical BERT embeddings of free text are used to encode patient EHRs. We identify the existence of sub-populations on the basis of comorbidities and shared textual features, and discuss their clinical significance., Comment: 14 pages, 5 figures in main text

Prior research has established associations between individuals' language usage and their personal traits; our linguistic patterns reveal information about our personalities, emotional states, and beliefs. However, with the increasing adoption of Large Language Models (LLMs) as writing assistants in everyday writing, a critical question emerges: are authors' linguistic patterns still predictive of their personal traits when LLMs are involved in the writing process? We investigate the impact of LLMs on the linguistic markers of demographic and psychological traits, specifically examining three LLMs - GPT3.5, Llama 2, and Gemini - across six different traits: gender, age, political affiliation, personality, empathy, and morality. Our findings indicate that although the use of LLMs slightly reduces the predictive power of linguistic patterns over authors' personal traits, the significant changes are infrequent, and the use of LLMs does not fully diminish the predictive power of authors' linguistic patterns over their personal traits. We also note that some theoretically established lexical-based linguistic markers lose their reliability as predictors when LLMs are used in the writing process. Our findings have important implications for the study of linguistic markers of personal traits in the age of LLMs.

Visual SLAM with thermal imagery, and other low contrast visually degraded environments such as underwater, or in areas dominated by snow and ice, remain a difficult problem for many state of the art (SOTA) algorithms. In addition to challenging front-end data association, thermal imagery presents an additional difficulty for long term relocalization and map reuse. The relative temperatures of objects in thermal imagery change dramatically from day to night. Feature descriptors typically used for relocalization in SLAM are unable to maintain consistency over these diurnal changes. We show that learned feature descriptors can be used within existing Bag of Word based localization schemes to dramatically improve place recognition across large temporal gaps in thermal imagery. In order to demonstrate the effectiveness of our trained vocabulary, we have developed a baseline SLAM system, integrating learned features and matching into a classical SLAM algorithm. Our system demonstrates good local tracking on challenging thermal imagery, and relocalization that overcomes dramatic day to night thermal appearance changes. Our code and datasets are available here: https://github.com/neufieldrobotics/IRSLAM_Baseline, Comment: 8 pages, 7 figures, Submitted to IROS 2024

We prove the equivalence of the sutured versions of Heegaard Floer homology, monopole Floer homology, and embedded contact homology. As applications we show that the knot versions of Heegaard Floer homology and embedded contact homology are equivalent and that product sutured 3-manifolds are characterized by the fact that they carry an adapted Reeb vector field without periodic orbits.

We study the problem of determining an effective exploration strategy in static and non-linear optimization problems, which depend on an unknown scalar parameter to be learned from online collected noisy data. An optimal trade-off between exploration and exploitation is crucial for effective optimization under uncertainties, and to achieve this we consider a cumulative regret minimization approach over a finite horizon, with each time instant in the horizon characterized by a stochastic exploration signal, whose variance is to be designed. We aim to extend the well-established concepts of regret minimization from linear to non-linear systems, with a focus on the subsequent conceptual differences and challenges. Thus, under an idealized assumption on an appropriately defined information function associated with the excitation, we are able to show that an optimal exploration strategy is either to use no exploration at all (called lazy exploration) or adding an exploration excitation only at the first time instant of the horizon (called immediate exploration). A quadratic numerical example is presented to demonstrate the effectiveness of the proposed strategy., Comment: Extended version of a paper accepted for IEEE Conference on Decision and Control (CDC 2024)

Assurance cases are used to communicate and assess confidence in critical system properties such as safety and security. Historically, assurance cases have been manually created documents, which are evaluated by system stakeholders through lengthy and complicated processes. In recent years, model-based system assurance approaches have gained popularity to improve the efficiency and quality of system assurance activities. This becomes increasingly important, as systems becomes more complex, it is a challenge to manage their development life-cycles, including coordination of development, verification and validation activities, and change impact analysis in inter-connected system assurance artifacts. Moreover, there is a need for assurance cases that support evolution during the operational life of the system, to enable continuous assurance in the face of an uncertain environment, as Robotics and Autonomous Systems (RAS) are adopted into society. In this paper, we contribute ACCESS - Assurance Case Centric Engineering of Safety-critical Systems, an engineering methodology, together with its tool support, for the development of safety critical systems around evolving model-based assurance cases. We show how model-based system assurance cases can trace to heterogeneous engineering artifacts (e.g. system architectural models, system safety analysis, system behaviour models, etc.), and how formal methods can be integrated during the development process. We demonstrate how assurance cases can be automatically evaluated both at development and runtime. We apply our approach to a case study based on an Autonomous Underwater Vehicle (AUV).

We show that for the regular n-simplex, the 1-codimensional central slice that's parallel to a facet will achieve the minimum area (up to a 1-o(1) factor) among all 1-codimensional central slices, thus improving the previous best known lower bound (Brzezinski 2013) by a factor of $\frac{2\sqrt{3}}{e} \approx 1.27$. In addition to the standard technique of interpreting geometric problems as problems about probability distributions and standard Fourier-analytic techniques, we rely on a new idea, mainly \emph{changing the contour of integration} of a meromorphic function.

Optical atomic clocks have demonstrated revolutionary advances in precision timekeeping, but their applicability to the real world is critically dependent on whether such clocks can operate outside a laboratory setting. The challenge to clock portability stems from the many obstacles not only in miniaturizing the underlying components of the clock $-$ namely the ultrastable laser, the frequency comb, and the atomic reference itself $-$ but also in making the clock resilient to environmental fluctuations. Photonic integration offers one compelling solution to simultaneously address the problems of miniaturization and ruggedization, but brings with it a new set of challenges in recreating the functionality of an optical clock using chip-scale building blocks. The clock laser used for atom interrogation is one particular point of uncertainty, as the performance of the meticulously-engineered bulk-cavity stabilized lasers would be exceptionally difficult to transfer to chip. Here we demonstrate that a chip-integrated ultrahigh quality factor (Q) spiral cavity, when interfaced with a 1348 nm seed laser, reaches a fractional frequency instability of $7.5 \times 10^{-14}$, meeting the stability requirements for interrogating the narrow-linewidth transition of $^{88}$Sr$^+$ upon frequency doubling to 674 nm. In addition to achieving the record for laser stability on chip, we use this laser to showcase the operation of a Sr-ion clock with short-term instability averaging down as $3.9 \times 10^{-14} / \sqrt{\tau}$, where $\tau$ is the averaging time. Our demonstration of an optical atomic clock interrogated by an integrated spiral cavity laser opens the door for future advanced clock systems to be entirely constructed using lightweight, portable, and mass-manufacturable integrated optics and electronics.

In the paper, we review the recent construction of the Liouville conformal field theory (CFT) from probabilistic methods, and the formalization of the conformal bootstrap. This model has offered a fruitful playground to unify the probabilistic construction of the path integral, the geometric axiomatics of CFT by Segal and the representation theoretical content of the conformal bootstrap. We explain and extract the main steps and ideas behind the construction and resolution of this non-compact CFT.

Existing neural operator architectures face challenges when solving multiphysics problems with coupled partial differential equations (PDEs) due to complex geometries, interactions between physical variables, and the limited amounts of high-resolution training data. To address these issues, we propose Codomain Attention Neural Operator (CoDA-NO), which tokenizes functions along the codomain or channel space, enabling self-supervised learning or pretraining of multiple PDE systems. Specifically, we extend positional encoding, self-attention, and normalization layers to function spaces. CoDA-NO can learn representations of different PDE systems with a single model. We evaluate CoDA-NO's potential as a backbone for learning multiphysics PDEs over multiple systems by considering few-shot learning settings. On complex downstream tasks with limited data, such as fluid flow simulations, fluid-structure interactions, and Rayleigh-B\'enard convection, we found CoDA-NO to outperform existing methods by over 36%.

We establish dimension-free stability of Webb's sharp simplex slicing (1996). Incidentally, we investigate Lipschitzness of volume of hyperplane central sections of arbitrary convex bodies.

We initiate the study of computing shortest non-separating simple closed curves with some given topological properties on non-orientable surfaces. While, for orientable surfaces, any two non-separating simple closed curves are related by a self-homeomorphism of the surface, and computing shortest such curves has been vastly studied, for non-orientable ones the classification of non-separating simple closed curves up to ambient homeomorphism is subtler, depending on whether the curve is one-sided or two-sided, and whether it is orienting or not (whether it cuts the surface into an orientable one). We prove that computing a shortest orienting (weakly) simple closed curve on a non-orientable combinatorial surface is NP-hard but fixed-parameter tractable in the genus of the surface. In contrast, we can compute a shortest non-separating non-orienting (weakly) simple closed curve with given sidedness in $g^{O(1)}.n\log n$ time, where $g$ is the genus and $n$ the size of the surface. For these algorithms, we develop tools that can be of independent interest, to compute a variation on canonical systems of loops for non-orientable surfaces based on the computation of an orienting curve, and some covering spaces that are essentially quotients of homology covers., Comment: To appear at SoCG 2024

Quantum noise has been extensively utilized to investigate various aspects of quantum transport, such as current-current correlations and wave-particle duality. A recent focus in this field is on $\Delta_T$ quantum noise, which arises because of a finite temperature difference at vanishing charge current. This paper explores the characterization of $\Delta_T$ noise auto-correlation alongside the shot noise and thermal-noise contributions in a 1D metal/insulator/superconductor junction. We consider a finite temperature gradient with zero applied bias for reservoirs at comparable temperatures. Andreev reflection enhances the $\Delta_T$ noise in a metal-insulator-superconductor junction in contrast to a metal-insulator-metal junction in the transparent limit. Unlike quantum noise for which shot-noise dominates thermal-noise at large bias voltages and finite barrier strength, $\Delta_T$ thermal-noise is always higher than $\Delta_T$ shot-noise. Thus, a general bound that is independent of barrier strength is established. This investigation sheds light on the distinct behavior of $\Delta_T$ noise, alongside the ratio of shot-noise to thermal-noise contributions, offering valuable insights into the intricate interplay between finite temperature gradient, barrier strength, and Andreev reflection., Comment: 13 pages, 5 figures

In conformal field theory, the semigroup of annuli with boundary parametrization plays a special role, in that it generates the whole algebra of local conformal symmetries, the so-called Virasoro algebra. The subgroup of elements $\mathbb{A}_f=\mathbb{D}\setminus f(\mathbb{D}^\circ)$ for contracting biholomorphisms $f:\mathbb{D}\to f(\mathbb{D})\subset \mathbb{D}^\circ$ with $f(0)=0$ is called the holomorphic semigroup of annuli. In this article, we construct a differentiable representation of the holomorphic semigroup into the space of bounded operators on the Hilbert space $\mathcal{H}$ of Liouville Conformal Field Theory and show it generates under differentiation the positive Virasoro elements ${\bf L}_n,\tilde{{\bf L}}_n$ for $n\geq 0$. We also construct a projective representation of the semigroup of annuli in the space of bounded operators on $\mathcal{H}$ in terms of Segal amplitudes and show that all Virasoro elements ${\bf L}_n,\tilde{{\bf L}}_n$ for $n\in \mathbb{Z}$ are generated by differentiation of these annuli amplitudes. Finally, we use this to show that the Segal amplitudes for Liouville theory are differentiable with respetc to their boundary parametrizations, and the differential is computed in terms of Virasoro generators. This paper will serve, in a forthcoming work, as a fundamental tool in the construction of the conformal blocks as globally defined holomorphic sections of a holomorphic line bundle on Teichmuller space and satisfying the Ward identities.

Spherical tokamaks (STs) have many desirable features that make them a suitable choice for fusion power plants. To understand their confinement properties, accurate calculation of turbulent micro-instabilities is necessary for tokamak design. Presented is a novel surrogate model for Micro-tearing modes (MTMs), the micro-instability thought to be dominant in high beta STs. Direct numerical calculation of micro-instabilities is computationally expensive and is a significant bottleneck in integrated plasma modelling. The considerable number of geometric and thermodynamic parameters, the interactions that influence these coefficients and the resolutions needed to accurately resolve these modes, makes direct numerical simulation for parameter space exploration computationally extremely challenging. However, this and the dearth of accurate reduced physics models for MTMs makes it suitable for surrogate modelling using Gaussian Process Regression, a modern machine learning technique. This paper outlines the further development of a data-driven reduced-order model across a spherical tokamak reactor-relevant parameter space utilising Gaussian Process Regression (GPR) and classification; techniques from machine learning. To build the original simple GP model these two components were used in an active learning loop to maximise the efficiency of data acquisition thus minimising computational cost. The `simple' GP was seen to show a plateau of fidelity with more data and to be under-confident, particular in areas of parameter space close to marginal stability. It is postulated that the presence of multiple sub-types of MTM could be the root cause, with the underlying function being less smooth than expected. An expansion of the model using clustering algorithms to find optimal sub models using a mixture of experts approach is shown to greatly improve the variances in the outputs of the GP model., Comment: Submitted to the IAEA FEC 2023 conference

We present the Citizen Science program Active Asteroids and describe discoveries stemming from our ongoing project. Our NASA Partner program is hosted on the Zooniverse online platform and launched on 2021 August 31, with the goal of engaging the community in the search for active asteroids -- asteroids with comet-like tails or comae. We also set out to identify other unusual active solar system objects, such as active Centaurs, active quasi-Hilda asteroids, and Jupiter-family comets (JFCs). Active objects are rare in large part because they are difficult to identify, so we ask volunteers to assist us in searching for active bodies in our collection of millions of images of known minor planets. We produced these cutout images with our project pipeline that makes use of publicly available Dark Energy Camera (DECam) data. Since the project launch, roughly 8,300 volunteers have scrutinized some 430,000 images to great effect, which we describe in this work. In total we have identified previously unknown activity on 15 asteroids, plus one Centaur, that were thought to be asteroidal (i.e., inactive). Of the asteroids, we classify four as active quasi-Hilda asteroids, seven as JFCs, and four as active asteroids, consisting of one Main-belt comet (MBC) and three MBC candidates. We also include our findings concerning known active objects that our program facilitated, an unanticipated avenue of scientific discovery. These include discovering activity occurring during an orbital epoch for which objects were not known to be active, and the reclassification of objects based on our dynamical analyses., Comment: 35 pages, 5 figures, 3 tables

This article primarily aims to unify the various formalisms of multivariate coefficients of variation, leveraging advanced concepts of generalized means, whether weighted or not, applied to the eigenvalues of covariance matrices. We highlight the existence of an infinite number of these coefficients and demonstrate that they are bounded. Moreover, we link the various coefficients of variation identified in the literature to specific instances within our unified formalism. We illustrate the utility of our method by applying it to a time series of polarimetric radar imagery. In this context, the coefficient of variation emerges as a key tool for detecting changes or identifying permanent scatterers, which are characterized by their remarkable temporal stability. The multidimensionality arises from the diversity of polarizations. The introduction of the various possible coefficients demonstrates how their selection impacts the detection of samples exhibiting specific temporal behaviors and underscores the contribution of polarimetry to dynamic speckle analysis.

Defant, Li, Propp, and Young recently resolved two enumerative conjectures of Propp concerning the tilings of regions in the hexagonal grid called benzels using two types of prototiles called stones and bones (with varying constraints on allowed orientations of the tiles). Their primary tool, a bijection called compression that converts certain $k$-ribbon tilings to $(k-1)$-ribbon tilings, allowed them to reduce their problems to the enumeration of dimers (i.e., perfect matchings) of certain graphs. We present a generalized version of compression that no longer relies on the perspective of partitions and skew shapes. Using this strengthened tool, we resolve three more of Propp's conjectures and recast several others as problems about perfect matchings., Comment: 16 pages, 19 figures

Spatiotemporal datasets, which consist of spatially-referenced time series, are ubiquitous in many scientific and business-intelligence applications, such as air pollution monitoring, disease tracking, and cloud-demand forecasting. As modern datasets continue to increase in size and complexity, there is a growing need for new statistical methods that are flexible enough to capture complex spatiotemporal dynamics and scalable enough to handle large prediction problems. This work presents the Bayesian Neural Field (BayesNF), a domain-general statistical model for inferring rich probability distributions over a spatiotemporal domain, which can be used for data-analysis tasks including forecasting, interpolation, and variography. BayesNF integrates a novel deep neural network architecture for high-capacity function estimation with hierarchical Bayesian inference for robust uncertainty quantification. By defining the prior through a sequence of smooth differentiable transforms, posterior inference is conducted on large-scale data using variationally learned surrogates trained via stochastic gradient descent. We evaluate BayesNF against prominent statistical and machine-learning baselines, showing considerable improvements on diverse prediction problems from climate and public health datasets that contain tens to hundreds of thousands of measurements. The paper is accompanied with an open-source software package (https://github.com/google/bayesnf) that is easy-to-use and compatible with modern GPU and TPU accelerators on the JAX machine learning platform., Comment: 27 pages, 7 figures, 3 tables, 2 listings

This paper proposes a method for the automatic creation of variables (in the case of regression) that complement the information contained in the initial input vector. The method works as a pre-processing step in which the continuous values of the variable to be regressed are discretized into a set of intervals which are then used to define value thresholds. Then classifiers are trained to predict whether the value to be regressed is less than or equal to each of these thresholds. The different outputs of the classifiers are then concatenated in the form of an additional vector of variables that enriches the initial vector of the regression problem. The implemented system can thus be considered as a generic pre-processing tool. We tested the proposed enrichment method with 5 types of regressors and evaluated it in 33 regression datasets. Our experimental results confirm the interest of the approach.

The use of computer simulations to study the properties of aqueous systems is, today more than ever, an active area of research. In this context, during the last decade there has been a tremendous growth in the use of data-driven approaches to develop more accurate potentials for water as well as to characterize its complexity in chemical and biological contexts. We highlight the progress, giving a historical context, on the path to the development of many-body and reactive potentials to model aqueous chemistry, including the role of machine learning strategies. We focus specifically on conceptual and methodological challenges along the way in performing simulations that seek to tackle problems in modeling the chemistry of aqueous solutions. In conclusion, we summarize our perspectives on the use and integration of advanced data-science techniques to provide chemical insights in physical chemistry and how this will influence computer simulations of aqueous systems in the future., Comment: 37 Pages. 7 Figures. Submitted to Chemical Physics Reviews

In this report, we introduce the Gemini 1.5 family of models, representing the next generation of highly compute-efficient multimodal models capable of recalling and reasoning over fine-grained information from millions of tokens of context, including multiple long documents and hours of video and audio. The family includes two new models: (1) an updated Gemini 1.5 Pro, which exceeds the February version on the great majority of capabilities and benchmarks; (2) Gemini 1.5 Flash, a more lightweight variant designed for efficiency with minimal regression in quality. Gemini 1.5 models achieve near-perfect recall on long-context retrieval tasks across modalities, improve the state-of-the-art in long-document QA, long-video QA and long-context ASR, and match or surpass Gemini 1.0 Ultra's state-of-the-art performance across a broad set of benchmarks. Studying the limits of Gemini 1.5's long-context ability, we find continued improvement in next-token prediction and near-perfect retrieval (>99%) up to at least 10M tokens, a generational leap over existing models such as Claude 3.0 (200k) and GPT-4 Turbo (128k). Finally, we highlight real-world use cases, such as Gemini 1.5 collaborating with professionals on completing their tasks achieving 26 to 75% time savings across 10 different job categories, as well as surprising new capabilities of large language models at the frontier; when given a grammar manual for Kalamang, a language with fewer than 200 speakers worldwide, the model learns to translate English to Kalamang at a similar level to a person who learned from the same content.

We report the identification of 89 new systems containing ultracool dwarf companions to main sequence stars and white dwarfs, using the citizen science project Backyard Worlds: Planet 9 and cross-reference between Gaia and CatWISE2020. Thirty-two of these companions and thirty-three host stars were followed up with spectroscopic observations, with companion spectral types ranging from M7-T9 and host spectral types ranging from G2-M9. These systems exhibit diverse characteristics, from young to old ages, blue to very red spectral morphologies, potential membership to known young moving groups, and evidence of spectral binarity in 9 companions. Twenty of the host stars in our sample show evidence for higher order multiplicity, with an additional 11 host stars being resolved binaries themselves. We compare this sample's characteristics with those of the known stellar binary and exoplanet populations, and find our sample begins to fill in the gap between directly imaged exoplanets and stellary binaries on mass ratio-binding energy plots. With this study, we increase the population of ultracool dwarf companions to FGK stars by $\sim$42\%, and more than triple the known population of ultracool dwarf companions with separations larger than 1,000 au, providing excellent targets for future atmospheric retrievals., Comment: 61 pages, 11 figures, 11 tables. Accepted for publication in AJ

We provide an analysis of a convolutional neural network's ability to identify the lensing signal of single dark matter subhalos in strong galaxy-galaxy lenses in the presence of increasingly complex source light morphology. We simulate a balanced dataset of 800,000 strong lens images both perturbed and unperturbed by a single subhalo ranging in virial mass between $10^{7.5} M_{\odot} - 10^{11}M_{\odot}$ and characterise the source complexity by the number of Sersic clumps present in the source plane ranging from 1 to 5. Using the ResNet50 architecture we train the network to classify images as either perturbed or unperturbed. We find that the network is able to detect subhalos at low enough masses to distinguish between dark matter models even with complex sources and that source complexity has little impact on the accuracy beyond 3 clumps. The model was more confident in its classification when the clumps in the source were compact, but cared little about their spatial distribution. We also tested for the resolution of the data, finding that even in conditions akin to natural seeing the model was still able to achieve an accuracy of 74% in our highest peak signal-to-noise datasets, though this is heavily dominated by the high mass subhalos. It's robustness against resolution is attributed to the model learning the flux ratio anomalies in the perturbed lenses which are conserved in the lower resolution data., Comment: 13 pages, 13 figures, submitted for publication in MNRAS

Switchable order parameters in ferroic materials are essential for functional electronic devices, yet disruptions of the ordering can take the form of planar boundaries or defects that exhibit distinct properties. Characterizing the structure of these boundaries is challenging due to their confined size and three-dimensional nature. Here, a chemical anti-phase boundary in the highly ordered double perovskite \ce{Pb2MgWO6} is investigated using multislice electron ptychography. The boundary is revealed to be inclined along the electron beam direction with a finite width of chemical intermixing. Additionally, regions at and near the boundary exhibit antiferroelectric-like displacements, contrasting with the predominantly paraelectric matrix. Spatial statistics and density functional theory calculations further indicate that despite their higher energy, chemical anti-phase boundaries form due to kinetic constraints during growth, with extended antiferroelectric-like distortions induced by the chemically frustrated environment in the proximity of the boundary. The three-dimensional imaging provides critical insights into the interplay between local chemistry and the polar environment, elucidating the role of anti-phase boundaries and their associated confined structural distortions and offering new opportunities for engineering ferroic thin films.

This paper introduces a new conservative fusion method to exploit the correlated components within the estimation errors. Fusion is the process of combining multiple estimates of a given state to produce a new estimate with a smaller MSE. To perform the optimal linear fusion, the (centralized) covariance associated with the errors of all estimates is required. If it is partially unknown, the optimal fusion cannot be computed. Instead, a solution is to perform a conservative fusion. A conservative fusion provides a gain and a bound on the resulting MSE matrix which guarantees that the error is not underestimated. A well-known conservative fusion is the Covariance Intersection fusion. It has been modified to exploit the uncorrelated components within the errors. In this paper, it is further extended to exploit the correlated components as well. The resulting fusion is integrated into standard distributed algorithms where it allows exploiting the process noise observed by all agents. The improvement is confirmed by simulations.

The global mean surface temperature is widely studied to monitor climate change. A current debate centers around whether there has been a recent (post-1970s) surge/acceleration in the warming rate. This paper addresses whether an acceleration in the warming rate is detectable from a statistical perspective. We use changepoint models, which are statistical techniques specifically designed for identifying structural changes in time series. Four global mean surface temperature records over 1850-2023 are scrutinized within. Our results show limited evidence for a warming surge; in most surface temperature time series, no change in the warming rate beyond the 1970s is detected. As such, we estimate minimum changes in the warming trend for a surge to be detectable in the near future.

The internal linear combination (ILC) method is a popular approach for constructing component-separated maps in cosmic microwave background (CMB) analyses. It optimally combines observed maps at different frequencies to produce an unbiased minimum-variance map of a component. When performed in harmonic space, it is straightforward to analytically compute the contributions of individual sky components to the power spectrum of the resulting ILC map. ILC can also be performed on a basis of needlets, spherical wavelets that have compact support in both pixel and harmonic space, capturing both scale-dependent and spatially varying information. However, an analytic understanding of the power spectra of needlet ILC (NILC) component-separated maps, as needed to enable their use in cosmological parameter inference, has remained an outstanding problem. In this paper, we derive the first analytic expression for the power spectra of NILC maps, as well as an expression for the cross-spectrum of a NILC map with an arbitrary second map, in terms of contributions from individual sky components. We validate our result using simulations, finding that it is exact. These results contain useful insights: we explicitly see how NILC power spectra contain information from contaminant fields beyond the two-point level, and we obtain a formalism with which to parameterize NILC power spectra. However, because this parameter dependence is complicated by correlations and higher-point functions of the component maps and weight maps, we find that it is intractable to perform parameter inference using these analytic expressions. Instead, numerical techniques are needed to estimate parameters using NILC maps -- we explore the use of likelihood-free inference with neural posterior estimation in a companion paper. Our code to produce the results in this paper is available in https://github.com/kmsurrao/NILC-PS-Model., Comment: 19 pages, 3 figures; code available at https://github.com/kmsurrao/NILC-PS-Model

We propose a method to represent bipartite networks using graph embeddings tailored to tackle the challenges of studying ecological networks, such as the ones linking plants and pollinators, where many covariates need to be accounted for, in particular to control for sampling bias. We adapt the variational graph auto-encoder approach to the bipartite case, which enables us to generate embeddings in a latent space where the two sets of nodes are positioned based on their probability of connection. We translate the fairness framework commonly considered in sociology in order to address sampling bias in ecology. By incorporating the Hilbert-Schmidt independence criterion (HSIC) as an additional penalty term in the loss we optimize, we ensure that the structure of the latent space is independent of continuous variables, which are related to the sampling process. Finally, we show how our approach can change our understanding of ecological networks when applied to the Spipoll data set, a citizen science monitoring program of plant-pollinator interactions to which many observers contribute, making it prone to sampling bias.

Grading short answer questions automatically with interpretable reasoning behind the grading decision is a challenging goal for current transformer approaches. Justification cue detection, in combination with logical reasoners, has shown a promising direction for neuro-symbolic architectures in ASAG. But, one of the main challenges is the requirement of annotated justification cues in the students' responses, which only exist for a few ASAG datasets. To overcome this challenge, we contribute (1) a weakly supervised annotation procedure for justification cues in ASAG datasets, and (2) a neuro-symbolic model for explainable ASAG based on justification cues. Our approach improves upon the RMSE by 0.24 to 0.3 compared to the state-of-the-art on the Short Answer Feedback dataset in a bilingual, multi-domain, and multi-question training setup. This result shows that our approach provides a promising direction for generating high-quality grades and accompanying explanations for future research in ASAG and educational NLP.

We present an estimate of the Atacama Cosmology Telescope (ACT) detector polarization angle systematic uncertainty from optics perturbation analysis using polarization-sensitive ray tracing in CODE V optical design software. Uncertainties in polarization angle calibration in CMB measurements can limit constraints on cosmic birefringence and other cosmological parameters sensitive to polarization leakage. Our framework estimates the angle calibration systematic uncertainties from possible displacements in lens positions and orientations, and anti-reflection coating (ARC) thicknesses and refractive indices. With millimeter displacements in lens positions and percent-level perturbations in ARC thicknesses and indices from design, we find the total systematic uncertainty for three ACT detector arrays operating between 90--220 GHz to be at the tenth of degree scale. Reduced lens position and orientation uncertainties from physical measurements could lead to a reduction in the systematic uncertainty estimated with the framework presented here. This optical modeling may inform polarization angle systematic uncertainties for current and future microwave polarimeters, such as the CCAT Observatory, Simons Observatory, and CMB-S4., Comment: 14 pages, 8 figures, version accepted for publication in Applied Optics

The low-lying energy spectrum of the static-colour-source-anti-source system in a vacuum containing light and strange quarks is computed using lattice QCD for a range of different light quark masses. The resulting levels are described using a simple model Hamiltonian and the parameters in this model are extrapolated to the physical light-quark masses. In this framework, the QCD string tension is found to be $\sqrt{\sigma}=445(3)_{\rm stat}(6)_{\rm sys}$ MeV., Comment: 10 pages, 9 figures, small changes to match published version

This report introduces a new family of multimodal models, Gemini, that exhibit remarkable capabilities across image, audio, video, and text understanding. The Gemini family consists of Ultra, Pro, and Nano sizes, suitable for applications ranging from complex reasoning tasks to on-device memory-constrained use-cases. Evaluation on a broad range of benchmarks shows that our most-capable Gemini Ultra model advances the state of the art in 30 of 32 of these benchmarks - notably being the first model to achieve human-expert performance on the well-studied exam benchmark MMLU, and improving the state of the art in every one of the 20 multimodal benchmarks we examined. We believe that the new capabilities of the Gemini family in cross-modal reasoning and language understanding will enable a wide variety of use cases. We discuss our approach toward post-training and deploying Gemini models responsibly to users through services including Gemini, Gemini Advanced, Google AI Studio, and Cloud Vertex AI.

The CTE CoLab, an Urban-led coalition of six national partners, guided 12 community and career and technical education (CTE) colleges through a two-and-a-half year, multistep equity action planning process focused on improving outcomes and advancing racial equity in online and hybrid CTE programs. College teams worked to understand gaps in outcomes for students of color and develop and implement strategies to address barriers to success stemming from historical, systemic, and institutional factors. This report documents the equity action planning process, strategies the colleges implemented to support students, and recommendations informed by lessons learned along the way. Strategies focused on increasing student supports, centering equity in online instruction delivery, and engaging with employers. Larger institutional changes sometimes required starting small, with a committed team bringing diverse expertise, roles, and experience to advance equity. Although the initiative's two-year timeframe proved challenging, colleges laid the groundwork to inform deeper and broader implementation of these strategies moving forward. [This report was produced with The National Council for Workforce Education.]

ACT is a nonprofit organization whose mission is to help people achieve education and workplace success. To help fulfill that mission, ACT offers school-day testing programs that provide all students with state- or district-funded access to its college readiness and admissions assessment, removing barriers to testing and opening doors to postsecondary opportunities. During the 2021-2022 academic year, over 1.3 million students, across all 50 states and the District of Columbia, participated in ACT school-day testing through state or district testing programs. Of these 1.3 million students, it is estimated that 59% could be considered members of underserved student populations according to at least one criterion. In this brief, the authors describe six evidence-backed benefits of school-day ACT testing: (1) Removes Barriers to Testing; (2) Increases the Number of Students Identified as College Ready; (3) Increases the Number of Students Who Are Contacted by Colleges; (4) Provides a Complete Picture for Research; (5) Leads to Improvement in College Enrollment; and (6) Provides Valuable Information to Students Navigating Different Paths.