Search

We present measurements of $B \to K{}^{*}(892)\gamma$ decays using $365\,{\rm fb}^{-1}$ of data collected from 2019 to 2022 by the Belle~II experiment at the SuperKEKB asymmetric-energy $e^+e^-$ collider. The data sample contains $(387 \pm 6) \times 10^6$ $B\overline{B}$ events. We measure branching fractions ($\mathcal{B}$) and $C\!P$ asymmetries ($\mathcal{A}_{C\!P}$) for both $B^{0}\to K{}^{*0}\gamma$ and $B^{+}\to K{}^{*+}\gamma$ decays. The difference in $C\!P$ asymmetries ($\Delta \mathcal{A}_{C\!P}$) and the isospin asymmetry ($\Delta_{0+}$) between these neutral and charged channels are also measured. We obtain the following branching fractions and $C\!P$ asymmetries: $\mathcal{B} (B^{0} \to K{}^{*0}\gamma) = (4.14 \pm 0.10 \pm 0.11 ) \times 10^{-5}$, $\mathcal{B} (B^{+} \to K{}^{*+}\gamma) = (4.02 \pm 0.13 \pm 0.13 )\times 10^{-5}$, $\mathcal{A}_{C\!P} (B^{0} \to K{}^{*0}\gamma) = (-3.3 \pm 2.3 \pm 0.4 )\%$, and $\mathcal{A}_{C\!P} (B^{+} \to K{}^{*+}\gamma) = (-0.7 \pm 2.9 \pm 0.6 )\%$. The measured difference in $C\!P$ asymmetries is $\Delta \mathcal{A}_{C\!P} = (+2.6 \pm 3.8 \pm 0.7 )\%$, and the measured isospin asymmetry is $\Delta_{0+} = (+5.0 \pm 2.0 \pm 1.5 )\%$. The first uncertainties listed are statistical and the second are systematic. These results are consistent with world-average values and theory predictions.

In this article, we probe the trilinear R-parity violating (RPV) supersymmetric (SUSY) scenarios with specific non-zero interactions in the light of neutrino oscillation, Higgs, and flavor observables. We attempt to fit the set of observables using a state-of-the-art Markov Chain Monte Carlo (MCMC) set-up and study its impact on the model parameter space. Our main objective is to constrain the trilinear couplings individually, along with some other SUSY parameters relevant to the observables. We present the constrained parameter regions in the form of marginalized posterior distributions on different two-dimensional parameter planes. We perform our analyses with two different scenarios characterized by our choices for the lightest SUSY particle (LSP), bino, and stop. Our results indicate that the lepton number violating trilinear couplings $\lambda_{i33}$ ($i$=1,2) and $\lambda_{j33}^{\prime}$ ($j$=1,2,3) can be at most of the order of $10^{-4}$ or even smaller while $\tan\beta$ is restricted to below 15 even when $3\sigma$ allowed regions are considered. We further comment on the possible LHC signatures of these LSPs focusing on and around the best-fit regions., Comment: 41 pages, 9 figures and 8 tables

In inverse reinforcement learning (IRL), an agent seeks to replicate expert demonstrations through interactions with the environment. Traditionally, IRL is treated as an adversarial game, where an adversary searches over reward models, and a learner optimizes the reward through repeated RL procedures. This game-solving approach is both computationally expensive and difficult to stabilize. In this work, we propose a novel approach to IRL by direct policy optimization: exploiting a linear factorization of the return as the inner product of successor features and a reward vector, we design an IRL algorithm by policy gradient descent on the gap between the learner and expert features. Our non-adversarial method does not require learning a reward function and can be solved seamlessly with existing actor-critic RL algorithms. Remarkably, our approach works in state-only settings without expert action labels, a setting which behavior cloning (BC) cannot solve. Empirical results demonstrate that our method learns from as few as a single expert demonstration and achieves improved performance on various control tasks.

[1] investigates advanced connotations of Hardy and Rellich-type inequalities on complete noncompact Riemannian manifolds, delving on deriving inequalities that incorporate poignant weight functions. These inequalities prolongate classical results by providing sharper estimates conforming the geometry and structure of the underlying manifold. We in this paper further extend the inequalities and in due course exhibit them in section [4] in terms of theorems and proofs., Comment: 10 pages

Transformers are slow to train on videos due to extremely large numbers of input tokens, even though many video tokens are repeated over time. Existing methods to remove such uninformative tokens either have significant overhead, negating any speedup, or require tuning for different datasets and examples. We present Run-Length Tokenization (RLT), a simple approach to speed up video transformers inspired by run-length encoding for data compression. RLT efficiently finds and removes runs of patches that are repeated over time prior to model inference, then replaces them with a single patch and a positional encoding to represent the resulting token's new length. Our method is content-aware, requiring no tuning for different datasets, and fast, incurring negligible overhead. RLT yields a large speedup in training, reducing the wall-clock time to fine-tune a video transformer by 30% while matching baseline model performance. RLT also works without any training, increasing model throughput by 35% with only 0.1% drop in accuracy. RLT speeds up training at 30 FPS by more than 100%, and on longer video datasets, can reduce the token count by up to 80%. Our project page is at https://rccchoudhury.github.io/projects/rlt/., Comment: 16 pages, 6 figures. Accepted to NeurIPS 2024 (spotlight)

Recent breakthroughs in large language models (LLMs) have generated both interest and concern about their potential adoption as accessible information sources or communication tools across different domains. In public health -- where stakes are high and impacts extend across populations -- adopting LLMs poses unique challenges that require thorough evaluation. However, structured approaches for assessing potential risks in public health remain under-explored. To address this gap, we conducted focus groups with health professionals and health issue experiencers to unpack their concerns, situated across three distinct and critical public health issues that demand high-quality information: vaccines, opioid use disorder, and intimate partner violence. We synthesize participants' perspectives into a risk taxonomy, distinguishing and contextualizing the potential harms LLMs may introduce when positioned alongside traditional health communication. This taxonomy highlights four dimensions of risk in individual behaviors, human-centered care, information ecosystem, and technology accountability. For each dimension, we discuss specific risks and example reflection questions to help practitioners adopt a risk-reflexive approach. This work offers a shared vocabulary and reflection tool for experts in both computing and public health to collaboratively anticipate, evaluate, and mitigate risks in deciding when to employ LLM capabilities (or not) and how to mitigate harm when they are used.

In this paper, we investigate the evolution of certain functionals involving higher powers of a scalar quantity $F$ under Bernard List's extended Ricci flow on a compact Riemannian manifold. By deriving explicit expressions for the time derivative of integrals of the form $\int_M F^n \cdot \frac{\partial F}{\partial t} \, d\mu$ for various powers $n$, we explore the intricate interplay between geometric quantities and scalar functions without making any assumptions about the manifold, the scalar field $\Phi$, or the function $u$.

Finite state machines (FSMs) regulate sequential circuits, including access to sensitive information and privileged CPU states. Courtesy of contemporary research on laser attacks, laser-based fault injection (LFI) is becoming even more precise where an adversary can thwart chip security by altering individual flip-flop (FF) values. Different laser models, e.g., bit flip, bit set, and bit reset, have been developed to appreciate LFI on practical targets. As traditional approaches may incorporate substantial overhead, state-based SPARSE and transition-based TAMED countermeasures were proposed in our prior work to improve FSM resiliency efficiently. TAMED overcame SPARSE's limitation of being too conservative, and generating multiple LFI resilient encodings for contemporary LFI models on demand. SPARSE, however, incorporated design layout information into its vulnerability estimation which makes its vulnerability estimation metric more accurate. In this paper, we extend TAMED by proposing a transition-based encoding CAD framework (TRANSPOSE), that incorporates spatial transitional vulnerability metrics to quantify design susceptibility of FSMs based on both the bit flip model and the set-reset models. TRANSPOSE also incorporates floorplan optimization into its framework to accommodate secure spatial inter-distance of FF-sensitive regions. All TRANSPOSE approaches are demonstrated on 5 multifarious benchmarks and outperform existing FSM encoding schemes/frameworks in terms of security and overhead., Comment: 14 pages, 11 figures

We measure the time-integrated CP asymmetry in $D^{0} \rightarrow K^{0}_{S}K^{0}_{S}$ decays reconstructed in $e^{+}e^{-} \rightarrow c\overline{c}$ events collected by the Belle and Belle II experiments. The corresponding data samples have integrated luminosities of 980 fb$^{-1}$ and 428 fb$^{-1}$, respectively. The $D^{0}$ decays are required to originate from the $D^{*+} \rightarrow D^{0}\pi^{+}$ decay, which determines the charm flavor at production time. A control sample of $D^{0} \rightarrow K^{+}K^{-}$ decays is used to correct for production and detection asymmetries. The result, $(-1.4\pm1.3{\rm(stat)}\pm0.1{\rm (syst)})\%$, is consistent with previous determinations and with CP symmetry., Comment: 10 pages, 3 figures. arXiv admin note: text overlap with arXiv:2410.22961

We perform a model-independent measurement of the $D^0$-$\overline{D}{}^0$ mixing parameters using samples of $e^+e^-$-collision data collected by the Belle and Belle II experiments that have integrated luminosities of $951\ \text{fb}^{-1}$ and $408\ \text{fb}^{-1}$, respectively. Approximately $2.05\times10^6$ neutral $D$ mesons are reconstructed in the $D^0\rightarrow K^0_{S}\pi^+\pi^-$ channel, with the neutral $D$ flavor tagged by the charge of the pion in the $D^{*+}\rightarrow D^0\pi^+$ decay. Assuming charge-parity symmetry, the mixing parameters are measured to be $ x = (4.0\pm1.7\pm0.4)\times 10^{-3} $ and $ y = (2.9\pm1.4\pm0.3)\times 10^{-3}$, where the first uncertainties are statistical and the second systematic. The results are consistent with previous determinations.

The rapid evolution of Large Language Models (LLMs) offers promising potential to alleviate the global scarcity of mental health professionals. However, LLMs' alignment with essential mental health counseling competencies remains understudied. We introduce CounselingBench, a novel NCMHCE-based benchmark evaluating LLMs across five key mental health counseling competencies. Testing 22 general-purpose and medical-finetuned LLMs, we find frontier models exceed minimum thresholds but fall short of expert-level performance, with significant variations: they excel in Intake, Assessment & Diagnosis yet struggle with Core Counseling Attributes and Professional Practice & Ethics. Medical LLMs surprisingly underperform generalist models accuracy-wise, while at the same time producing slightly higher-quality justifications but making more context-related errors. Our findings highlight the complexities of developing AI systems for mental health counseling, particularly for competencies requiring empathy and contextual understanding. We found that frontier LLMs perform at a level exceeding the minimal required level of aptitude for all key mental health counseling competencies, but fall short of expert-level performance, and that current medical LLMs do not significantly improve upon generalist models in mental health counseling competencies. This underscores the critical need for specialized, mental health counseling-specific fine-tuned LLMs that rigorously aligns with core competencies combined with appropriate human supervision before any responsible real-world deployment can be considered., Comment: 9 Pages, In Submission to NAACL 2025

The disparity in the languages commonly studied in Natural Language Processing (NLP) is typically reflected by referring to languages as low vs high-resourced. However, there is limited consensus on what exactly qualifies as a `low-resource language.' To understand how NLP papers define and study `low resource' languages, we qualitatively analyzed 150 papers from the ACL Anthology and popular speech-processing conferences that mention the keyword `low-resource.' Based on our analysis, we show how several interacting axes contribute to `low-resourcedness' of a language and why that makes it difficult to track progress for each individual language. We hope our work (1) elicits explicit definitions of the terminology when it is used in papers and (2) provides grounding for the different axes to consider when connoting a language as low-resource., Comment: Accepted at EMNLP 2024

Dementia is a neurodegenerative condition that combines several diseases and impacts millions around the world and those around them. Although cognitive impairment is profoundly disabling, it is the noncognitive features of dementia, referred to as Neuropsychiatric Symptoms (NPS), that are most closely associated with a diminished quality of life. Agitation and aggression (AA) in people living with dementia (PwD) contribute to distress and increased healthcare demands. Current assessment methods rely on caregiver intervention and reporting of incidents, introducing subjectivity and bias. Artificial Intelligence (AI) and predictive algorithms offer a potential solution for detecting AA episodes in PwD when utilized in real-time. We present a 5-year study system that integrates a multimodal approach, utilizing the EmbracePlus wristband and a video detection system to predict AA in severe dementia patients. We conducted a pilot study with three participants at the Ontario Shores Mental Health Institute to validate the functionality of the system. The system collects and processes raw and digital biomarkers from the EmbracePlus wristband to accurately predict AA. The system also detected pre-agitation patterns at least six minutes before the AA event, which was not previously discovered from the EmbracePlus wristband. Furthermore, the privacy-preserving video system uses a masking tool to hide the features of the people in frames and employs a deep learning model for AA detection. The video system also helps identify the actual start and end time of the agitation events for labeling. The promising results of the preliminary data analysis underscore the ability of the system to predict AA events. The ability of the proposed system to run autonomously in real-time and identify AA and pre-agitation symptoms without external assistance represents a significant milestone in this research field.

Home robots performing personalized tasks must adeptly balance user preferences with environmental affordances. We focus on organization tasks within constrained spaces, such as arranging items into a refrigerator, where preferences for placement collide with physical limitations. The robot must infer user preferences based on a small set of demonstrations, which is easier for users to provide than extensively defining all their requirements. While recent works use Large Language Models (LLMs) to learn preferences from user demonstrations, they encounter two fundamental challenges. First, there is inherent ambiguity in interpreting user actions, as multiple preferences can often explain a single observed behavior. Second, not all user preferences are practically feasible due to geometric constraints in the environment. To address these challenges, we introduce APRICOT, a novel approach that merges LLM-based Bayesian active preference learning with constraint-aware task planning. APRICOT refines its generated preferences by actively querying the user and dynamically adapts its plan to respect environmental constraints. We evaluate APRICOT on a dataset of diverse organization tasks and demonstrate its effectiveness in real-world scenarios, showing significant improvements in both preference satisfaction and plan feasibility. The project website is at https://portal-cornell.github.io/apricot/, Comment: Conference on Robot Learning (CoRL) 2024

The boundary $\partial X$ of a boundary continuous Gromov hyperbolic space $X$ carries a natural Moebius structure on the boundary. For a proper, geodesically complete, boundary continuous Gromov hyperbolic space $X$, the boundary $\partial X$ equipped with its cross-ratio is a particular kind of quasi-metric space, called a quasi-metric antipodal space. Given a quasi-metric antipodal space $Z$, one may consider the family of all hyperbolic fillings of $Z$. In \cite{biswas2024quasi} it was shown that this family has a unique upper bound $\mathcal{M}(Z)$ (with respect to a natural partial order on hyperbolic fillings of $Z$), which can be described explicitly in terms of the cross-ratio on $Z$. As shown in \cite{biswas2024quasi}, the spaces $\mathcal{M}(Z)$ constitute a natural class of spaces called maximal Gromov hyperbolic spaces. A natural problem is to describe explicitly the maximal Gromov hyperbolic spaces $X$ whose boundary $\partial X$ is finite. We show that for a maximal Gromov hyperbolic space $X$ with boundary $\partial X$ of cardinality $n$, the space $X$ is isometric to a finite polyhedral complex embedded in $(\mathbb{R}^n, ||\cdot||_{\infty})$ with cells of dimension at most $n/2$, given by attaching $n$ half-lines to vertices of a compact polyhedral complex. In particular the geometry at infinity of $X$ is trivial. The combinatorics of the polyhedral complex is determined by certain relations $R \subset \partial X \times \partial X$ on the boundary $\partial X$, called antipodal relations. In \cite{biswas2024quasi} it was shown that maximal Gromov hyperbolic spaces are injective metric spaces. We give a shorter, simpler proof of this fact in the case of spaces with finite boundary. We also consider the space of deformations of a maximal Gromov hyperbolic space with finite boundary, and define an associated Teichmuller space.

Adverse Drug Reactions (ADRs) from psychiatric medications are the leading cause of hospitalizations among mental health patients. With healthcare systems and online communities facing limitations in resolving ADR-related issues, Large Language Models (LLMs) have the potential to fill this gap. Despite the increasing capabilities of LLMs, past research has not explored their capabilities in detecting ADRs related to psychiatric medications or in providing effective harm reduction strategies. To address this, we introduce the Psych-ADR benchmark and the Adverse Drug Reaction Response Assessment (ADRA) framework to systematically evaluate LLM performance in detecting ADR expressions and delivering expert-aligned mitigation strategies. Our analyses show that LLMs struggle with understanding the nuances of ADRs and differentiating between types of ADRs. While LLMs align with experts in terms of expressed emotions and tone of the text, their responses are more complex, harder to read, and only 70.86% aligned with expert strategies. Furthermore, they provide less actionable advice by a margin of 12.32% on average. Our work provides a comprehensive benchmark and evaluation framework for assessing LLMs in strategy-driven tasks within high-risk domains., Comment: 27 pages, 8 figures, 15 tables

The reproducibility of scientific articles is central to the advancement of science. Despite this importance, evaluating reproducibility remains challenging due to the scarcity of ground truth data. Predictive models can address this limitation by streamlining the tedious evaluation process. Typically, a paper's reproducibility is inferred based on the availability of artifacts such as code, data, or supplemental information, often without extensive empirical investigation. To address these issues, we utilized artifacts of papers as fundamental units to develop a novel, dual-spectrum framework that focuses on author-centric and external-agent perspectives. We used the author-centric spectrum, followed by the external-agent spectrum, to guide a structured, model-based approach to quantify and assess reproducibility. We explored the interdependencies between different factors influencing reproducibility and found that linguistic features such as readability and lexical diversity are strongly correlated with papers achieving the highest statuses on both spectrums. Our work provides a model-driven pathway for evaluating the reproducibility of scientific research. The code, methods, and artifacts for our study are publicly available at: https://github.com/reproducibilityproject/NLRR/, Comment: 10 pages, CIKM 2024

In the bottomonium sector, the hindered magnetic dipole (M1) transitions between P-wave states $h_b(2P) \rightarrow \chi_{bJ}(1P) \gamma$, $J=0, \, 1, \, 2$, are expected to be severely suppressed according to the Relativized Quark Model, due to the spin flip of the $b$ quark. Nevertheless, a recent model following the coupled-channel approach predicts the corresponding branching fractions to be enhanced by orders of magnitude. In this Letter, we report the first search for such transitions. We find no significant signals and set upper limits at 90% CL on the corresponding branching fractions: $\mathcal{B}[h_b(2P)\to\gamma\chi_{b0}(1P)] < 2.7 \times 10^{-1}$, $\mathcal{B}[h_b(2P)\to\gamma\chi_{b1}(1P)] < 5.4 \times 10^{-3}$ and $\mathcal{B}[h_b(2P)\to\gamma\chi_{b2}(1P)] < 1.3 \times 10^{-2}$. These values help to constrain the parameters of the coupled-channel models. The results are obtained using a $121.4 \, fb^{-1}$ data sample taken around $\sqrt{s}= 10.860 \, GeV$ with the Belle detector at the KEKB asymmetric-energy $e^+e^-$ collider.

We have designed and commissioned a new readout board to detect photosensor signals from gas-bubbler panels to continuously monitor the gas flow through the resistive plate chambers of the $K_L^0$ and muon detector of Belle II. The gas flow measurements have been integrated into Belle II's alarm system. The bubbler-monitoring system was first employed during the February 2024 to July 2024 Belle II data-taking period., Comment: 4 pages, 5 figures

We discuss the theoretical framework behind reconstruction of a generic class of inflationary potentials for canonical single-field slow-roll inflation in a model-independent fashion. The Non-Bunch Davies (NBD) initial condition is an essential choice to determine the structure of potential and to accommodate the blue-tilted tensor power spectrum feature recently observed in NANOGrav. Using the reconstruction technique we found the favoured parameter space which supports blue tilted tensor power spectrum. The validity of the EFT prescription in inflation is also maintained through the use of a new field excursion formula while keeping the necessary and sufficient conditions on the sub-Planckian field values in check. We find that the reconstructed potential display inflection point behaviour, which has deeper connection with high energy physics., Comment: 31 pages, 2 tables, 6 figures, Comments are welcome, Published in Journal of High Energy Astrophysics

We present a measurement of the branching fraction and time-dependent charge-parity ($CP$) decay-rate asymmetries in $B^0 \to J/\psi \pi^0$ decays. The data sample was collected with the Belle~II detector at the SuperKEKB asymmetric $e^+e^-$ collider in 2019-2022 and contains $(387\pm 6)\times 10^6$ $B\overline{B}$ meson pairs from $\Upsilon(4S)$ decays. We reconstruct $392\pm 24$ signal decays and fit the $CP$ parameters from the distribution of the proper-decay-time difference of the two $B$ mesons. We measure the branching fraction to be $B(B^0 \to J/\psi \pi^0)=(2.02 \pm 0.12 \pm 0.10)\times 10^{-5}$ and the direct and mixing-induced $CP$ asymmetries to be $C_{CP}=0.13 \pm 0.12 \pm 0.03$ and $S_{CP}=-0.88 \pm 0.17 \pm 0.03$, respectively, where the first uncertainties are statistical and the second are systematic. We observe mixing-induced $CP$ violation with a significance of $5.0$ standard deviations for the first time in this mode.

While large language models (LLMs) show impressive decision-making abilities, current methods lack a mechanism for automatic self-improvement from errors during task execution. We propose LEAP, an iterative fine-tuning framework that continually improves LLM agents using feedback from AI expert teachers. Our key insight is to equip the expert teachers with a privileged state -- information that is available during training but hidden at test time. This allows even weak experts to provide precise guidance, significantly improving the student agent's performance without access to privileged information at test time. We evaluate LEAP on diverse decision-making benchmarks, including text-based games (ALFWorld), web navigation (WebShop), and interactive coding (Intercode Bash). Our experiments show that LEAP (1) outperforms behavior cloning and ReAct baselines (2) enables weak student models (e.g., Llama3-8B) to exceed the performance of strong teacher models (GPT4-o), and (3) allows weak models to self-improve using privileged versions of themselves. We also provide a theoretical analysis showing that LEAP's success hinges on balancing privileged information with the student's realizability, which we empirically validate. Our code is available at https://leap-llm.github.io, Comment: 34 pages, 6 figures, 5 tables

The remarkable capabilities of large language models (LLMs) in language understanding and generation have not rendered them immune to hallucinations. LLMs can still generate plausible-sounding but factually incorrect or fabricated information. As LLM-empowered chatbots become popular, laypeople may frequently ask health-related queries and risk falling victim to these LLM hallucinations, resulting in various societal and healthcare implications. In this work, we conduct a pioneering study of hallucinations in LLM-generated responses to real-world healthcare queries from patients. We propose MedHalu, a carefully crafted first-of-its-kind medical hallucination dataset with a diverse range of health-related topics and the corresponding hallucinated responses from LLMs with labeled hallucination types and hallucinated text spans. We also introduce MedHaluDetect framework to evaluate capabilities of various LLMs in detecting hallucinations. We also employ three groups of evaluators -- medical experts, LLMs, and laypeople -- to study who are more vulnerable to these medical hallucinations. We find that LLMs are much worse than the experts. They also perform no better than laypeople and even worse in few cases in detecting hallucinations. To fill this gap, we propose expert-in-the-loop approach to improve hallucination detection through LLMs by infusing expert reasoning. We observe significant performance gains for all the LLMs with an average macro-F1 improvement of 6.3 percentage points for GPT-4., Comment: 14 pages

Controlling the dynamics of quantum many-body systems is crucial for developing quantum technologies. This work demonstrates that counter-diabatic (CD) driving provides a powerful tool for steering collective spin systems along entangled trajectories for a long time. In particular, CD driving leads to approximate stroboscopic freezing and eternal entanglement oscillations for a large class of initial states in the periodically driven Lipkin-Meshkov-Glick model. This is accompanied by a decrease in the average eigenstate entanglement and inverse participation ratio, thereby signalling greater eigenstate localization. Our work opens a new route to evade Floquet heating and control entanglement generation in collective spin systems., Comment: 6+3 pages, 4+1 figures

We perform the first search for $C\!P$ violation in ${D_{(s)}^{+}\to{}K_{S}^{0}K^{-}\pi^{+}\pi^{+}}$ decays. We use a combined data set from the Belle and Belle II experiments, which study $e^+e^-$ collisions at center-of-mass energies at or near the $\Upsilon(4S)$ resonance. We use 980 fb$^{-1}$ of data from Belle and 428 fb$^{-1}$ of data from Belle~II. We measure six $C\!P$-violating asymmetries that are based on triple products and quadruple products of the momenta of final-state particles, and also the particles' helicity angles. We obtain a precision at the level of 0.5% for $D^+\to{}K_{S}^{0}K^{-}\pi^{+}\pi^{+}$ decays, and better than 0.3% for $D^+_{s}\to{}K_{S}^{0}K^{-}\pi^{+}\pi^{+}$ decays. No evidence of $C\!P$ violation is found. Our results for the triple-product asymmetries are the most precise to date for singly-Cabibbo-suppressed $D^+$ decays. Our results for the other asymmetries are the first such measurements performed for charm decays., Comment: 21 pages, 10 figures

The adaptation of foundation models has significantly advanced environmental audio deepfake detection (EADD), a rapidly growing area of research. These models are typically fine-tuned or utilized in their frozen states for downstream tasks. However, the dimensionality of their representations can substantially lead to a high parameter count of downstream models, leading to higher computational demands. So, a general way is to compress these representations by leveraging state-of-the-art (SOTA) unsupervised dimensionality reduction techniques (PCA, SVD, KPCA, GRP) for efficient EADD. However, with the application of such techniques, we observe a drop in performance. So in this paper, we show that representation vectors contain redundant information, and randomly selecting 40-50% of representation values and building downstream models on it preserves or sometimes even improves performance. We show that such random selection preserves more performance than the SOTA dimensionality reduction techniques while reducing model parameters and inference time by almost over half., Comment: Submitted to ICASSP 2025

Due to the non-smoothness of optimization problems in Machine Learning, generalized smoothness assumptions have been gaining a lot of attention in recent years. One of the most popular assumptions of this type is $(L_0,L_1)$-smoothness (Zhang et al., 2020). In this paper, we focus on the class of (strongly) convex $(L_0,L_1)$-smooth functions and derive new convergence guarantees for several existing methods. In particular, we derive improved convergence rates for Gradient Descent with (Smoothed) Gradient Clipping and for Gradient Descent with Polyak Stepsizes. In contrast to the existing results, our rates do not rely on the standard smoothness assumption and do not suffer from the exponential dependency from the initial distance to the solution. We also extend these results to the stochastic case under the over-parameterization assumption, propose a new accelerated method for convex $(L_0,L_1)$-smooth optimization, and derive new convergence rates for Adaptive Gradient Descent (Malitsky and Mishchenko, 2020)., Comment: 51 pages, 1 figure

Recent constraints on neutron star mass and radius have advanced our understanding of the equation of state of cold dense matter. Some of them have been obtained by modeling the pulses of three millisecond X-ray pulsars observed by the Neutron Star Interior Composition Explorer (NICER). Here, we present a Bayesian parameter inference for a fourth pulsar, PSR J1231-1411, using the same technique with NICER and XMM-Newton data. When applying a broad mass-inclination prior from radio timing measurements and the emission region geometry model that can best explain the data, we find likely-converged results only when using a limited radius prior. If limiting the radius to be consistent with the previous observational constraints and equation of state analyses, we infer the radius to be $12.6 \pm 0.3$ km and the mass to be $1.04_{-0.03}^{+0.05}$ $M_\odot$, each reported as the posterior credible interval bounded by the $16\,\%$ and $84\,\%$ quantiles. If using an uninformative prior but limited between $10$ and $14$ km, we find otherwise similar results, but $R_{\mathrm{eq}} = 13.5_{-0.5}^{+0.3}$ km for the radius. In both cases, we find a non-antipodal hot region geometry where one emitting spot is at the equator or slightly above, surrounded by a large colder region, and where a non-circular hot region lies close to southern rotational pole. If using a wider radius prior, we only find solutions that fit the data significantly worse. We discuss the challenges in finding the better fitting solutions, possibly related to the weak interpulse feature in the pulse profile., Comment: 22 pages, 13 figures (2 of which are figure sets), 3 tables, accepted for publication in ApJ

In the case of compute-intensive machine learning, efficient operating system scheduling is crucial for performance and energy efficiency. This paper conducts a comparative study over FIFO(First-In-First-Out) and RR(Round-Robin) scheduling policies with the application of real-time machine learning training processes and data pipelines on Ubuntu-based systems. Knowing a few patterns of CPU usage and energy consumption, we identify which policy (the exclusive or the shared) provides higher performance and/or lower energy consumption for typical modern workloads. Results of this study would help in providing better operating system schedulers for modern systems like Ubuntu, working to improve performance and reducing energy consumption in compute intensive workloads.

We present the updated constraints on cosmological parameters in a 12 parameter cosmology extended with dynamical dark energy parameters ($w_0$, $w_a$), sum of neutrino masses ($\sum m_{\nu}$), effective number of neutrinos ($N_{\rm eff}$), scaling of the lensing amplitude ($A_{\rm lens}$), and running of the scalar spectral index ($\alpha_s$). For 'CMB' data, we use the latest Planck PR4 (2020) HiLLiPoP and LoLLiPoP likelihoods, Planck PR4+ACT DR6 lensing, and Planck 2018 lowl-$l$ TT likelihoods. Also, we use the latest DESI DR1 BAO likelihoods and SNeIa likelihoods from the Pantheon+ and DESY5 samples. We find: i) Contrary to the findings of DESI collaboration, we find that the CMB+BAO+Pantheon+ leads to the inclusion of cosmological constant within $2\sigma$, while CMB+BAO+DESY5 excludes the same at more than 2$\sigma$. Thus, the dynamical nature of dark energy cannot yet be considered a robust cosmological signature. As pointed out in earlier literature, the DESY5 SNe sample might have systematics which are driving the exclusion of cosmological constant. ii) We find that for certain data combinations lead to a 1$\sigma$+ detection of $\sum m_{\nu}$, and we get a posterior peak in all dataset combinations, which is an encouraging trend towards future detection. We also provide a robust bound of $\sum m_{\nu} \lesssim 0.3$ eV (95%). Given the current uncertainty in determining the correct underlying cosmological model, we prescribe this bound for the cosmology and particle physics community. iii) With CMB+BAO+SNe, we find that $A_{\rm lens}=1$ is included at 2$\sigma$ but not at $1\sigma$. This indicates that with Planck PR4 likelihoods, there is currently no lensing anomaly in a dynamical dark energy cosmology. iv) We find that even in this largely extended cosmology, the Hubble tension persists at the level of 3.2-3.9$\sigma$. (truncated), Comment: 17 pages, 10 figures

This paper presents an overview of the Volvo Discovery Challenge, held during the ECML-PKDD 2024 conference. The challenge's goal was to predict the failure risk of an anonymized component in Volvo trucks using a newly published dataset. The test data included observations from two generations (gen1 and gen2) of the component, while the training data was provided only for gen1. The challenge attracted 52 data scientists from around the world who submitted a total of 791 entries. We provide a brief description of the problem definition, challenge setup, and statistics about the submissions. In the section on winning methodologies, the first, second, and third-place winners of the competition briefly describe their proposed methods and provide GitHub links to their implemented code. The shared code can be interesting as an advanced methodology for researchers in the predictive maintenance domain. The competition was hosted on the Codabench platform., Comment: ECML/PKDD 2024, Discovery Challenge

Signal transmission over underwater optical wireless communication (UOWC) experiences the combined effect of oceanic turbulence and pointing errors statistically modeled using the sum of two Meijer-G functions. There is a research gap in the exact statistical analysis of multi-aperture UOWC systems that use selection combining diversity techniques to enhance performance compared to single-aperture systems. In this paper, we develop a general framework for the continued product and positive integer exponent for the sum of Meijer-G functions to analyze the exact statistical performance of the UOWC system in terms of multivariate Fox-H function for both independent and non-identically distributed (i.ni.d.) and independent and identically distributed (i.i.d.) channels. We also approximate the performance of a multi-aperture UOWC system with i.i.d. channels using the single-variate Fox-H function. Using the generalized approach, we present analytical expressions for average bit-error rate (BER) and ergodic capacity for the considered system operating over exponential generalized gamma (EGG) oceanic turbulence combined with zero-boresight pointing errors. We also develop asymptotic expressions for the average BER at a high signal-to-noise (SNR) to capture insights into the system's performance. Our simulation findings confirm the accuracy of our derived expressions and illustrate the impact of turbulence parameters for i.ni.d. and i.i.d. models for the average BER and ergodic capacity, which may provide a better estimate for the efficient deployment of UOWC., Comment: This work has been submitted to IEEE for possible publication

Multiparty Session Types (MPSTs) offer a structured way of specifying communication protocols and guarantee relevant communication properties, such as deadlock-freedom. In this paper, we extend a minimal MPST system with quantum data and operations, enabling the specification of quantum protocols. Quantum MPSTs (QMPSTs) provide a formal notation to describe quantum protocols, both at the abstract level of global types, describing which communications can take place in the system and their dependencies, and at the concrete level of local types and quantum processes, describing the expected behavior of each participant in the protocol. Type-checking relates these two levels formally, ensuring that processes behave as prescribed by the global type. Beyond usual communication properties, QMPSTs also allow us to prove that qubits are owned by a single process at any time, capturing the quantum no-cloning and no-deleting theorems. We use our approach to verify four quantum protocols from the literature, respectively Teleportation, Secret Sharing, Bit-Commitment, and Key Distribution., Comment: To appear at SEFM 2024

We advance the thesis that the simulation of quantum circuits is fundamentally about the efficient management of a large (potentially exponential) number of delimited continuations. The family of Scheme languages, with its efficient implementations of first-class continuations and with its imperative constructs, provides an elegant host for modeling and simulating quantum circuits., Comment: Appeared at Scheme Workshop 2022

Non-Gaussianity in the primordial curvature perturbation is a crucial element of the early universe due to its significant impact on the primordial black hole (PBH) production. In this work, we focus on the effects of negative non-Gaussianity on PBH abundance through the lens of the compaction function criterion for PBH formation. Our setup utilizes an effective field theory of non-singular bounce, including the standard slow-roll inflation with an ultra-slow roll phase for amplifying the curvature perturbations to form PBHs. We investigate with two separate values of the non-Gaussianity parameter, $f_{\rm NL}=(-39.95,-35/8)$, found within the ekpyrotic contraction and the matter bounce scenarios, respectively, and show that a negatively large amount of $f_{\rm NL}$ can provide sizeable abundance, $10^{-3}\leq f_{\rm PBH}\leq 1$, and completely mitigates the PBH overproduction issue. We also highlight that the case with the effective sound speed $c_{s}=1$, coupled with $f_{\rm NL}=-39.95$, provides an agreement under $1\sigma$ for the scalar-induced gravitational wave explanation of the latest PTA (NANOGrav15 and EPTA) signal. Lastly, we extract an upper bound on the most negative value of, $f_{\rm NL}\sim -60$, below which we show breaching of the underlying perturbativity constraints on the power spectrum amplitude., Comment: 51 pages, 6 figures, 2 tables, Comments are welcome, Reference list updated

Photonic topological insulators provide unidirectional, robust, wavelength-selective transport of light at an interface while keeping it insulated at the bulk of the material. The non-trivial topology results in an immunity to backscattering, sharp turns, and fabrication defects. This work leverages these unique properties to design a 2-channel optical demultiplexer based on a lithium niobate photonic topological insulator with piezoelectric switch-off capabilities. A photonic topological insulator design for the demultiplexer allows for good wavelength selectivity, crosstalk as low as $-$54 dB, and better isolation between output channels. The primary operating wavelengths presented are the telecommunication wavelengths of 1310 nm and 1550 nm, but the use of the lithium niobate material allows operation at multiple operating wavelengths. Furthermore, we propose a post-fabrication method to switch off the topological protection and, thus, optical transmittance via an applied voltage utilizing the inverse piezoelectric effect of lithium niobate. This work will contribute to advancing lithium niobate integrated photonics and developing efficient, multi-wavelength, electrically controlled optical communication systems and integrated photonic circuits.

We give a conjectural formula for the characteristic number of rational cuspidal curves in the projective plane by extending the idea of Kontsevich's recursion formula (namely, pulling back the equality of two divisors in the four pointed moduli space). The key geometric input that is needed here is that in the closure of rational cuspidal curves, there are two component rational curves which are tangent to each other at the nodal point. While this fact is geometrically quite believable, we haven't as yet proved it; hence our formula is for the moment conjectural. The answers that we obtain agree with what has been computed earlier Ran, Pandharipande, Zinger and Ernstrom and Kennedy. We extend this technique (modulo another conjecture) to obtain the characteristic number of rational quartics with an E6 singularity., Comment: 19 pages, 8 figures. Comments are welcome

Expressing stressful experiences in words is proven to improve mental and physical health, but individuals often disengage with writing interventions as they struggle to organize their thoughts and emotions. Reflective prompts have been used to provide direction, and large language models (LLMs) have demonstrated the potential to provide tailored guidance. Current systems often limit users' flexibility to direct their reflections. We thus present ExploreSelf, an LLM-driven application designed to empower users to control their reflective journey. ExploreSelf allows users to receive adaptive support through dynamically generated questions. Through an exploratory study with 19 participants, we examine how participants explore and reflect on personal challenges using ExploreSelf. Our findings demonstrate that participants valued the balance between guided support and freedom to control their reflective journey, leading to deeper engagement and insight. Building on our findings, we discuss implications for designing LLM-driven tools that promote user empowerment through effective reflective practices., Comment: 17 pages excluding reference and appendix

Pulse profile modelling (PPM) is a technique for inferring mass, radius and hotspot properties of millisecond pulsars. PPM is now regularly used for analysis of rotation-powered millisecond pulsars (RMPs) with data from the Neutron Star Interior Composition ExploreR (NICER). Extending PPM to accreting millisecond pulsars (AMPs) is attractive, because they are a different source class featuring bright X-ray radiation from hotspots powered by accretion. In this paper, we present a modification of one of the PPM codes, X-PSI, so that it can be used for AMPs. In particular, we implement a model of an accretion disc and atmosphere model appropriate for the hotspots of AMPs, and improve the overall computational efficiency. We then test parameter recovery with synthetic NICER data in two scenarios with reasonable parameters for AMPs. We find in the first scenario, where the hotspot is large, that we are able to tightly and accurately constrain all parameters including mass and radius. In the second scenario, which is a high inclination system with a smaller hotspot, we find degeneracy between a subset of model parameters and a slight bias in the inferred mass and radius. This analysis of synthetic data lays the ground work for future analysis of AMPs with NICER data. Such an analysis could be complemented by future (joint) analysis of polarization data from the Imaging X-ray Polarimetry Explorer (IXPE)., Comment: 14 pages, 5 figures, 3 tables. Paper submitted to MNRAS

Big data analytics is one of the most promising areas of new research and development in computer science, enterprises, e-commerce, and defense. For many organizations, big data is regarded as one of their most important strategic assets. This explosive growth has made it necessary to develop effective techniques for examining and analyzing big data from a mathematical perspective. Among various methods of analyzing big data, topological data analysis (TDA) is now considered one of the useful tools. However, there is no fundamental concept related to topological structure in big data. In this paper, we introduce some fundamental ideas related to the neighborhood structure of words in data searching, which can be extended to form important topological structures of big data in the future. Additionally, we introduce big data primal in big data searching and discuss the application of neighborhood structures in detecting anomalies in data searching using the Jaccard similarity coefficient.

Human demonstrations as prompts are a powerful way to program robots to do long-horizon manipulation tasks. However, translating these demonstrations into robot-executable actions presents significant challenges due to execution mismatches in movement styles and physical capabilities. Existing methods either depend on human-robot paired data, which is infeasible to scale, or rely heavily on frame-level visual similarities that often break down in practice. To address these challenges, we propose RHyME, a novel framework that automatically aligns human and robot task executions using optimal transport costs. Given long-horizon robot demonstrations, RHyME synthesizes semantically equivalent human videos by retrieving and composing short-horizon human clips. This approach facilitates effective policy training without the need for paired data. RHyME successfully imitates a range of cross-embodiment demonstrators, both in simulation and with a real human hand, achieving over 50\% increase in task success compared to previous methods. We release our datasets and graphics at this https://portal.cs.cornell.edu/rhyme/.

Most music generation models directly generate a single music mixture. To allow for more flexible and controllable generation, the Multi-Source Diffusion Model (MSDM) has been proposed to model music as a mixture of multiple instrumental sources (e.g. piano, drums, bass, and guitar). Its goal is to use one single diffusion model to generate mutually-coherent music sources, that are then mixed to form the music. Despite its capabilities, MSDM is unable to generate music with rich melodies and often generates empty sounds. Its waveform diffusion approach also introduces significant Gaussian noise artifacts that compromise audio quality. In response, we introduce a Multi-Source Latent Diffusion Model (MSLDM) that employs Variational Autoencoders (VAEs) to encode each instrumental source into a distinct latent representation. By training a VAE on all music sources, we efficiently capture each source's unique characteristics in a "source latent." The source latents are concatenated and our diffusion model learns this joint latent space. This approach significantly enhances the total and partial generation of music by leveraging the VAE's latent compression and noise-robustness. The compressed source latent also facilitates more efficient generation. Subjective listening tests and Frechet Audio Distance (FAD) scores confirm that our model outperforms MSDM, showcasing its practical and enhanced applicability in music generation systems. We also emphasize that modeling sources is more effective than direct music mixture modeling. Codes and models are available at https://github.com/XZWY/MSLDM. Demos are available at https://xzwy.github.io/MSLDMDemo/., Comment: ICASSP 2025 in Submission

The conventional ultralight QCD axion is typically rendered invisible at collider experiments by its large decay constant. What could also hint at its possible existence is the observation of other (heavy) particles that are characteristically related to the light axion. One such scenario is afforded within the framework of the clockwork mechanism where the axion can have suppressed couplings with the gluons or photons while its companion axion-like particles (ALPs) have relatively unsuppressed couplings. We study a minimal clockwork model for the QCD axion invoking a KSVZ-like setup and examine the visibility of the ALPs $(a_n)$ at the LHC through the process $p p \to a_n \, (+ \,{\rm additional \, jets})$, $a_n \to \gamma \gamma$. The model contains $N$ ALPs with a decay constant $f$ and masses defined by a scale $m$ characteristic of the nearest-neighbour interactions of the scalar fields. For $10\lesssim m \lesssim 100$ GeV, $f \sim 1$ TeV and $N \sim \mathcal{O}(10)$, the full spectrum of ALPs is accessible and the corresponding diphoton invariant mass distribution comprises a unique signature of a wide band of resonances. For the case of light ALPs $(m \sim \mathcal{O}(10 \,{\rm GeV}))$ with the axion being a dark matter candidate, the mass-splittings among the former are so small that the signal profile mimics that of a single broad resonance, or an $\textit{axion iceberg}$. The effect subsides for heavier ALPs, albeit still exhibiting undulating peaks. For light ALPs, the scenario is imminently testable by the end of LHC's Run 3 phase, with the estimated cumulative significance reaching the discovery threshold for an integrated luminosity of $\sim 300 {\rm \,fb^{-1}}$. While the signals for the heavier ALPs in this minimal setup may not be as prominent within the ongoing LHC operation, one could expect to probe a wider parameter space of the model at the forthcoming HL-LHC., Comment: 35 pages, 17 figures

In multiplayer, first-person shooter games like Counter-Strike: Global Offensive (CS:GO), coordinated movement is a critical component of high-level strategic play. However, the complexity of team coordination and the variety of conditions present in popular game maps make it impractical to author hand-crafted movement policies for every scenario. We show that it is possible to take a data-driven approach to creating human-like movement controllers for CS:GO. We curate a team movement dataset comprising 123 hours of professional game play traces, and use this dataset to train a transformer-based movement model that generates human-like team movement for all players in a "Retakes" round of the game. Importantly, the movement prediction model is efficient. Performing inference for all players takes less than 0.5 ms per game step (amortized cost) on a single CPU core, making it plausible for use in commercial games today. Human evaluators assess that our model behaves more like humans than both commercially-available bots and procedural movement controllers scripted by experts (16% to 59% higher by TrueSkill rating of "human-like"). Using experiments involving in-game bot vs. bot self-play, we demonstrate that our model performs simple forms of teamwork, makes fewer common movement mistakes, and yields movement distributions, player lifetimes, and kill locations similar to those observed in professional CS:GO match play., Comment: The project website is at https://davidbdurst.com/mlmove/

The formation of the massive stars, and in particular, the role that the magnetic fields play in their early evolutionary phase is still far from being completely understood. Here, we present Atacama Large Millimeter/Submillimeter Array (ALMA) 1.2 mm full polarized continuum, and H$^{13}$CO$^+$(3$-$2), CS(5$-$4), and HN$^{13}$C(3$-$2) line observations with a high angular resolution ($\sim$0.4$''$ or 1100 au). In the 1.2 mm continuum emission, we reveal a dusty envelope surrounding the massive protostars, IRAS16547-E and IRAS16547-W, with dimensions of $\sim$10,000 au. This envelope has a bi-conical structure likely carved by the powerful thermal radio jet present in region. The magnetic fields vectors follow very-well the bi-conical envelope. The polarization fraction is $\sim$2.0\% in this region. Some of these vectors seem to converge to IRAS 16547-E, and IRAS 16547-W, the most massive protostars. Moreover, the velocity fields revealed from the spectral lines H$^{13}$CO$^+$(3$-$2), and HN$^{13}$C(3$-$2) show velocity gradients with a good correspondence with the magnetic fields, that maybe are tracing the cavities of molecular outflows or maybe in some parts infall. We derived a magnetic field strength in some filamentary regions that goes from 2 to 6.1\,mG. We also find that the CS(5$-$4) molecular line emission reveals multiple outflow cavities or bow-shocks with different orientations, some of which seem to follow the NW-SE radio thermal jet., Comment: Accepted by the Astrophysical Journal, 13 pages

Recent research on learned indexes has created a new perspective for indexes as models that map keys to their respective storage locations. These learned indexes are created to approximate the cumulative distribution function of the key set, where using only a single model may have limited accuracy. To overcome this limitation, a typical method is to use multiple models, arranged in a hierarchical manner, where the query performance depends on two aspects: (i) traversal time to find the correct model and (ii) search time to find the key in the selected model. Such a method may cause some key space regions that are difficult to model to be placed at deeper levels in the hierarchy. To address this issue, we propose an alternative method that modifies the key space as opposed to any structural or model modifications. This is achieved through making the key set more learnable (i.e., smoothing the distribution) by inserting virtual points. Furthermore, we develop an algorithm named CSV to integrate our virtual point insertion method into existing learned indexes, reducing both their traversal and search time. We implement CSV on state-of-the-art learned indexes and evaluate them on real-world datasets. Extensive experimental results show significant query performance improvement for the keys in deeper levels of the index structures at a low storage cost.

Let $M$ be an $n$-dimensional Hadamard manifold of pinched negative curvature $-b^2 \leq K_M \leq -a^2$. The solution of the Dirichlet problem at infinity for $M$ leads to the construction of a family of mutually absolutely continuous probability measures $\{\mu_x\}_{x \in M}$ called the harmonic measures. Fixing a basepoint $o \in M$, the Poisson kernel of $M$ is the function $P : M \times \partial M \to (0, \infty)$ defined by \begin{equation*} P(x, \xi) = \frac{d\mu_x}{d\mu_o}(\xi) \ , \ x \in M, \xi \in \partial M. \end{equation*} We prove the following global upper and lower bounds for the Poisson kernel: \begin{equation*} \frac{1}{C}\: e^{-2K{(o|\xi)}_x}\: e^{a d(x, o)} \le P(x,\xi) \le C\: e^{2K{(x|\xi)}_o}\: e^{-a d(x,o)} \:, \end{equation*} for some positive constants $C \geq 1, K > 0$ depending solely on $a, b$ and $n$. The above estimates may be viewed as a generalization of the well-known formula for the Poisson kernel in terms of Busemann functions for the special case of Gromov hyperbolic harmonic manifolds. These estimates do not follow directly from known estimates on Green's functions or harmonic measures. Instead we use techniques due to Anderson-Schoen for estimating positive harmonic functions in cones. As applications, we obtain quantitative estimates for the convergence $\mu_x \to \delta_{\xi}$ as $x \in M \to \xi \in \partial M$, and for the convergence of harmonic measures on finite spheres to the harmonic measures on the boundary at infinity as the radius of the spheres tends to infinity., Comment: 22 pages, 3 figures

Symmetries play a crucial role in understanding phases of matter and the transitions between them. Theoretical investigations of quantum models with SU($N$) symmetry have provided important insights into many-body phenomena. However, these models have generally remained a theoretical idealization, since it is very difficult to exactly realize the SU($N$) symmetry in conventional quantum materials for large $N$. Intriguingly however, in recent years, ultracold alkaline-earth-atom (AEA) quantum simulators have paved the path to realize SU($N$)-symmetric many-body models, where $N$ is tunable and can be as large as 10. This symmetry emerges due to the closed shell structure of AEAs, thereby leading to a perfect decoupling of the electronic degrees of freedom from the nuclear spin. In this work, we provide a systematic review of recent theoretical and experimental work on the many-body physics of these systems. We first discuss the thermodynamic properties and collective modes of trapped Fermi gases, highlighting the enhanced interaction effects that appear as $N$ increases. We then discuss the properties of the SU($N$) Fermi-Hubbard model, focusing on some of the major experimental achievements in this area. We conclude with a compendium highlighting some of the significant theoretical progress on SU($N$) lattice models and a discussion of some exciting directions for future research., Comment: 42 pages, 17 figures, 1 table