Miracle-dz/UniFAR-FTUs huggingface dataset:
Investigations of the spatial and temporal variations of Sr and Nd isotopes in sediments from two Indian Rivers: Implications to source identification

Radiogenic isotopes of Sr and Nd provide crucial information on chemical and physical erosion processes, therefore used as tracers for fingerprinting the sources of fluvial sediments. Moreover, elemental geochemistry, 87Sr/86Sr and 143Nd/144Nd signatures in silicate fractions of sediments primarily reflect intricate controls of characteristics and provenance of sediment. A suite of sediment samples collected from two rivers of India, Narmada (large) and Netravati (small) were analyzed for elemental concentrations, 87Sr/86Sr and 143Nd/144Nd in silicate as well as acid‐leachable fractions. 87Sr/86Sr in acid‐leachable sediment fractions from both the rivers (0.7094 ± 0.0002 for Narmada and 0.7158 ± 0.003 for Netravati) showed more radiogenic 87Sr/86Sr in Netravati compared to Narmada indicating influence of source rocks in their watersheds. Weak correlation of sedimentary 87Sr/86Sr and 143Nd/144Nd with Al and Chemical Index of Alteration (CIA) in silicate fraction indicates that isotopic compositions are primarily controlled by their sources and not by chemical weathering in both the rivers. Provenance of sediments in Narmada is dominated by their supply from Deccan deposits with secondary supply from mid‐late Proterozoic Vindhyan along with Mesoproterozoic to Mesoarchean TDMNd ages. Sediments from Netravati reflected signatures of peninsular gneisses dominant with gneisses schists and granodiorite along with Paleoarchean TDMNd ages. Based on variability of 87Sr/86Sr and 143Nd/144Nd, present study highlight that sediment supplies from tributaries to the mainstream in Narmada is inadequate as compared to that in Netravati. 87Sr/86Sr and 143Nd/144Nd signatures in Narmada and Netravati are comparable with Global Rivers.
Design and Realization of a Benchmarking Testbed for Evaluating Autonomous Platooning Algorithms

Autonomous vehicle platoons present near- and long-term opportunities to enhance operational efficiencies and save lives. The past 30 years have seen rapid development in the autonomous driving space, enabling new technologies that will alleviate the strain placed on human drivers and reduce vehicle emissions. This paper introduces a testbed for evaluating and benchmarking platooning algorithms on 1/10th scale vehicles with onboard sensors. To demonstrate the testbed's utility, we evaluate three algorithms, linear feedback and two variations of distributed model predictive control, and compare their results on a typical platooning scenario where the lead vehicle tracks a reference trajectory that changes speed multiple times. We validate our algorithms in simulation to analyze the performance as the platoon size increases, and find that the distributed model predictive control algorithms outperform linear feedback on hardware and in simulation.
Towards better Human-Agent Alignment: Assessing Task Utility in LLM-Powered Applications

The rapid development in the field of Large Language Models (LLMs) has led to a surge in applications that facilitate collaboration among multiple agents to assist humans in their daily tasks. However, a significant gap remains in assessing whether LLM-powered applications genuinely enhance user experience and task execution efficiency. This highlights the pressing need for methods to verify utility of LLM-powered applications, particularly by ensuring alignment between the application's functionality and end-user needs. We introduce AgentEval provides an implementation for the math problems, a novel framework designed to simplify the utility verification process by automatically proposing a set of criteria tailored to the unique purpose of any given application. This allows for a comprehensive assessment, quantifying the utility of an application against the suggested criteria. We present a comprehensive analysis of the robustness of quantifier's work.
Representation theory of W-algebras, II: Ramond twisted representations

We study the Ramond twisted representations of the affine W-algebra W^k(g,f) in the case that f admits a good even grading. We establish the vanishing and the almost irreducibility of the corresponding BRST cohomology. This confirms some of the recent conjectures of Kac and Wakimoto. In type A, our results give the characters of all irreducible ordinary Ramond twisted representations of W^k(sl_n,f) for all nilpotent elements f and all non-critical k, and prove the existence of modular invariant representations conjectured by Kac and Wakimoto.
Interface logistic problems: large diffusion and singular perturbation results

In this work we consider an interface logistic problem where two populations live in two different regions, separated by a membrane or interface where it happens an interchange of flux. Thus, the two populations only interact or are coupled through such a membrane where we impose the so-called Kedem-Katchalsky boundary conditions. For this particular scenario we analyze the existence and uniqueness of positive solutions depending on the parameters involve in the system, obtaining interesting results where one can see for the first time the effect of the membrane under such boundary conditions. To do so, we first ascertain the asymptotic behaviour of several linear and nonlinear problems for which we include a diffusion coefficient and analyse the behaviour of the solutions when such a diffusion parameter goes to zero or infinity. Despite their own interest, since these asymptotic results have never been studied before, they will be crucial in analyzing the existence and uniqueness for the main interface logistic problems under analysis. Finally, we apply such an asymptotic analysis to characterize the existence of solutions in terms of the growth rate of the populations, when both populations possess the same growth rate and, also, when they depend on different parameters.
Rationality of Learning Algorithms in Repeated Normal-Form Games

Many learning algorithms are known to converge to an equilibrium for specific classes of games if the same learning algorithm is adopted by all agents. However, when the agents are self-interested, a natural question is whether agents have a strong incentive to adopt an alternative learning algorithm that yields them greater individual utility. We capture such incentives as an algorithm's rationality ratio, which is the ratio of the highest payoff an agent can obtain by deviating from a learning algorithm to its payoff from following it. We define a learning algorithm to be $c$-rational if its rationality ratio is at most $c$ irrespective of the game. We first establish that popular learning algorithms such as fictitious play and regret matching are not $c$-rational for any constant $c\geq 1$. We then propose and analyze two algorithms that are provably $1$-rational under mild assumptions, and have the same properties as (a generalized version of) fictitious play and regret matching, respectively, if all agents follow them. Finally, we show that if an assumption of perfect monitoring is not satisfied, there are games for which $c$-rational algorithms do not exist, and illustrate our results with numerical case studies.
Improved Regret for Bandit Convex Optimization with Delayed Feedback

We investigate bandit convex optimization (BCO) with delayed feedback, where only the loss value of the action is revealed under an arbitrary delay. Previous studies have established a regret bound of $O(T^{3/4}+d^{1/3}T^{2/3})$ for this problem, where $d$ is the maximum delay, by simply feeding delayed loss values to the classical bandit gradient descent (BGD) algorithm. In this paper, we develop a novel algorithm to enhance the regret, which carefully exploits the delayed bandit feedback via a blocking update mechanism. Our analysis first reveals that the proposed algorithm can decouple the joint effect of the delays and bandit feedback on the regret, and improve the regret bound to $O(T^{3/4}+\sqrt{dT})$ for convex functions. Compared with the previous result, our regret matches the $O(T^{3/4})$ regret of BGD in the non-delayed setting for a larger amount of delay, i.e., $d=O(\sqrt{T})$, instead of $d=O(T^{1/4})$. Furthermore, we consider the case with strongly convex functions, and prove that the proposed algorithm can enjoy a better regret bound of $O(T^{2/3}\log^{1/3}T+d\log T)$. Finally, we show that in a special case with unconstrained action sets, it can be simply extended to achieve a regret bound of $O(\sqrt{T\log T}+d\log T)$ for strongly convex and smooth functions.
On generalized Beauville decompositions

Motivated by the Beauville decomposition of an abelian scheme and the"Perverse = Chern"phenomenon for a compactified Jacobian fibration, we study in this paper splittings of the perverse filtration for compactified Jacobian fibrations. On the one hand, we prove for the Beauville-Mukai system associated with an irreducible curve class on a K3 surface the existence of a Fourier-stable multiplicative splitting of the perverse filtration, which extends the Beauville decomposition for the nonsingular fibers. Our approach is to construct a Lefschetz decomposition associated with a Fourier-conjugate $\mathfrak{sl}_2$-triple, which relies heavily on recent work concerning the interaction between derived equivalences and LLV algebras for hyper-K\"ahler varieties. Motivic lifting and connections to the Beauville-Voisin conjectures are also discussed. On the other hand, we construct for any $g\geq 2$ a compactified Jacobian fibration of genus g curves such that each curve is integral with at worst simple nodes and the (multiplicative) perverse filtration does not admit a multiplicative splitting. This shows that in general an extension of the Beauville decomposition cannot exist for compactified Jacobian fibrations even when the simplest singular point appears.
On-the-Fly Syntax Highlighting: Generalisation and Speed-ups

On-the-fly syntax highlighting is the task of rapidly associating visual secondary notation values with each character of a language derivation. Research in this domain is driven by the prevalence of online software development tools, which frequently display source code on screen and heavily rely on syntax highlighting mechanisms. In this context, three contrasting demands confront resolvers in this space: speed, accuracy, and development costs. Speed constraints are essential to ensure tool usability, manifesting as responsiveness for end users accessing online source code and minimising system overhead. Simultaneously, achieving precise highlighting is critical for enhancing code comprehensibility. Nevertheless, obtaining accurate results necessitates the capacity to perform grammatical analysis on the code under consideration, even in cases of varying grammatical correctness. Furthermore, addressing the development costs of such resolvers is imperative, given the multitude of programming language versions. The current state-of-the-art approach in this field leverages the original lexer and parser of programming languages to create syntax highlighting oracles, subsequently used for training base Recurrent Neural Network models. As the question of the generalisation of such a solution persists, this paper addresses this aspect by extending the original work to three additional mainstream programming languages and conducting a comprehensive review of the outcomes. Moreover, the original limitations in evaluation performance and training costs are mitigated through the introduction of a novel Convolutional based Neural Network model. This study examines the performance gains of running models on GPUs, finding that the new CNN implementation is much faster than previous methods while maintaining high accuracy.
Tackling Negative Transfer on Graphs

Transfer learning aims to boost the learning on the target task leveraging knowledge learned from other relevant tasks. However, when the source and target are not closely related, the learning performance may be adversely affected, a phenomenon known as negative transfer. In this paper, we investigate the negative transfer in graph transfer learning, which is important yet underexplored. We reveal that, unlike image or text, negative transfer commonly occurs in graph-structured data, even when source and target graphs share semantic similarities. Specifically, we identify that structural differences significantly amplify the dissimilarities in the node embeddings across graphs. To mitigate this, we bring a new insight: for semantically similar graphs, although structural differences lead to significant distribution shift in node embeddings, their impact on subgraph embeddings could be marginal. Building on this insight, we introduce two effective yet elegant methods, Subgraph Pooling (SP) and Subgraph Pooling++ (SP++), that transfer subgraph-level knowledge across graphs. We theoretically analyze the role of SP in reducing graph discrepancy and conduct extensive experiments to evaluate its superiority under various settings. Our code and datasets are available at: https://github.com/Zehong-Wang/Subgraph-Pooling.
A Survey of Generative AI for De Novo Drug Design: New Frontiers in Molecule and Protein Generation

Artificial intelligence (AI)-driven methods can vastly improve the historically costly drug design process, with various generative models already in widespread use. Generative models for de novo drug design, in particular, focus on the creation of novel biological compounds entirely from scratch, representing a promising future direction. Rapid development in the field, combined with the inherent complexity of the drug design process, creates a difficult landscape for new researchers to enter. In this survey, we organize de novo drug design into two overarching themes: small molecule and protein generation. Within each theme, we identify a variety of subtasks and applications, highlighting important datasets, benchmarks, and model architectures and comparing the performance of top models. We take a broad approach to AI-driven drug design, allowing for both micro-level comparisons of various methods within each subtask and macro-level observations across different fields. We discuss parallel challenges and approaches between the two applications and highlight future directions for AI-driven de novo drug design as a whole. An organized repository of all covered sources is available at https://github.com/gersteinlab/GenAI4Drug.
Stochastic Comparisons of Random Extremes from non-identical Random Variables

We propose some new results on the comparison of the minimum or maximum order statistic from a random number of non-identical random variables. Under the non-identical set-up, with certain conditions, we prove that random minimum (maximum) of one system dominates the other in hazard rate (reversed hazard rate) order. Further, we prove variation diminishing property (Karlin [8]) for all possible restrictions to derive the new results.
Machine Learning, Density Functional Theory, and Experiments to Understand the Photocatalytic Reduction of CO$_2$ by CuPt/TiO$_2$

The photoconversion of CO$_2$ to hydrocarbons is a sustainable route to its transformation into value-added compounds and, thereby, crucial to mitigating the energy and climate crises. CuPt nanoparticles on TiO$_2$ surfaces have been reported to show promising photoconversion efficiency. For further progress, a mechanistic understanding of the catalytic properties of these CuPt/TiO$_2$ systems is vital. Here, we employ $\textit{ab-initio}$ calculations, machine learning, and photocatalysis experiments to explore their configurational space and examine their reactivity and find that the interface plays a key role in stabilizing *CO$_2$, *CO, and other CH-containing intermediates, facilitating higher activity and selectivity for methane. A bias-corrected machine-learning interatomic potential trained on density functional theory data enables efficient exploration of the potential energy surfaces of numerous CO$_2$@CuPt/TiO$_2$ configurations via basin-hopping Monte Carlo simulations, greatly accelerating the study of these photocatalyst systems. Our simulations show that CO$_2$ preferentially adsorbs at the interface, with C atom bonded to a Pt site and one O atom occupying an O-vacancy site. The interface also promotes the formation of *CH and *CH$_2$ intermediates. For confirmation, we synthesize CuPt/TiO$_2$ samples with a variety of compositions and analyze their morphologies and compositions using scanning electron microscopy and energy-dispersive X-ray spectroscopy, and measure their photocatalytic activity. Our computational and experimental findings qualitatively agree and highlight the importance of interface design for selective conversion of CO$_2$ to hydrocarbons.
The photodissociation dynamics and ultrafast electron diffraction image of cyclobutanone from the surface hopping dynamics simulation

The comprehension of nonadiabatic dynamics in polyatomic systems relies heavily on the simultaneous advancements in theoretical and experimental domains. The gas-phase electron diffraction (GUED) technique has attracted widespread attention as a promising tool for observing the photochemical and photophysical features at all-atomic level with high temporal and spatial resolutions. In this work, the GUED spectra were predicted to perform a double-blind test of accuracy in excited-state simulation for cyclobutanone based on the trajectory surface hopping method, with respect to the benchmark data obtained by upcoming MeV-GUED experiments at the Stanfold Linear Accelerator Laboratory. The results show that the ultrafast nonadiabatic dynamics occurs in the photoinduced dynamics, and two C2 and C3 channels play dominant roles in the nonadiabatic reactions of cyclobutanone. The simulated UED signal can be directly interpreted by atomic movements, providing a unique view to monitor the time-dependent evolution of the molecular structure in the femtosecond dynamics.
MUSTARD: Mastering Uniform Synthesis of Theorem and Proof Data

Recent large language models (LLMs) have witnessed significant advancement in various tasks, including mathematical reasoning and theorem proving. As these two tasks require strict and formal multi-step inference, they are appealing domains for exploring the reasoning ability of LLMs but still face important challenges. Previous studies such as Chain-of-Thought (CoT) have revealed the effectiveness of intermediate steps guidance. However, such step-wise annotation requires heavy labor, leading to insufficient training steps for current benchmarks. To fill this gap, this work introduces MUSTARD, a data generation framework that masters uniform synthesis of theorem and proof data of high quality and diversity. MUSTARD synthesizes data in three stages: (1) It samples a few mathematical concept seeds as the problem category. (2) Then, it prompts a generative language model with the sampled concepts to obtain both the problems and their step-wise formal solutions. (3) Lastly, the framework utilizes a proof assistant (e.g., Lean Prover) to filter the valid proofs. With the proposed MUSTARD, we present a theorem-and-proof benchmark MUSTARDSAUCE with 5,866 valid data points. Each data point contains an informal statement, an informal proof, and a translated formal proof that passes the prover validation. We perform extensive analysis and demonstrate that MUSTARD generates validated high-quality step-by-step data. We further apply the MUSTARDSAUCE for fine-tuning smaller language models. The fine-tuned Llama 2-7B achieves a 15.41% average relative performance gain in automated theorem proving, and 8.18% in math word problems. Codes and data are available at https://github.com/Eleanor-H/MUSTARD.
Remarks on MacMahon's $q$-series

In his important 1920 paper on partitions, MacMahon defined the partition generating functions \begin{align*} A_k(q)=\sum_{n=1}^{\infty}\mathfrak{m}(k;n)q^n&:=\sum_{0<s_1<s_2<\cdots<s_k} \frac{q^{s_1+s_2+\cdots+s_k}}{(1-q^{s_1})^2(1-q^{s_2})^2\cdots(1-q^{s_k})^2},\\ C_k(q)=\sum_{n=1}^{\infty} \mathfrak{m}_{odd}(k;n)q^n&:=\sum_{0<s_1<s_2<\cdots<s_k} \frac{q^{2s_1+2s_2+\cdots+2s_k-k}}{(1-q^{2s_1-1})^2(1-q^{2s_2-1})^2\cdots(1-q^{2s_k-1})^2}. \end{align*} These series give infinitely many formulas for two prominent generating functions. For each non-negative $k$, we prove that $A_k(q), A_{k+1}(q), A_{k+2}(q),\dots$ (resp. $C_k(q), C_{k+1}(q), C_{k+2}(q),\dots$) give the generating function for the 3-colored partition function $p_3(n)$ (resp. the overpartition function $\overline{p}(n)$). To be precise, we have \begin{align*}&\sum_{n=0}^{\infty}p_3(n)q^{n}=q^{-\frac{k^2+k}{2}}\sum_{m=k}^\infty \binom{2m+1}{m+k+1}A_{m}(q),\\&\sum_{n=0}^{\infty} \overline{p}(n)q^{n}=q^{-k^2}\sum_{m=k}^\infty \binom{2m}{m+k}C_{m}(q). \end{align*} These formulas systematically give infinitely many formulas for the 3-colored partition function and the overpartition function in terms of MacMahon's $\mathfrak{m}(\bullet;n)$ and $\mathfrak{m}_{odd}(\bullet;n)$ partition functions.
Image sequence analysis for object detection and segmentation

A sequence of images contains more information than a single image. Due to this reason, image sequence analysis has been used in computer vision for quite some time. In particular, using a sequence of images is useful for object detection when the camera moves relative to the object. Due to the relative motion, objects at different distances from the camera have different image motion. Using this property, one can obtain information on structure of the 3-D scene as well as the relative motion between the camera and the scene. Furthermore, the individual images are corrupted by camera noise. Using a sequence of images enables us to suppress this noise and detect low-contrast objects more reliably. In this research, image sequence analysis is used for detection of objects in 3-D space as well as on planar surfaces. The work would be useful for detecting obstacles in the flight path of an aircraft. The research also explores the use of these principles for segmenting scene text objects in video sequences with a relative motion between the camera and the scene.
Black Bear Density in Glacier National Park

We report the first abundance and density estimates for American black bears (Ursus americanus) in Glacier National Park (NP), Montana, USA. We used data from 2 independent and concurrent noninvasive genetic sampling methods—hair traps and bear rubs—collected during 2004 to generate individual black bear encounter histories for use in closed population mark-recapture models. We improved the precision of our abundance estimate by using noninvasive genetic detection events to develop individual-level covariates of sampling effort within the full and one-half mean maximum distance moved (MMDM) from each bear's estimated activity center to explain capture probability heterogeneity and inform our estimate of the effective sampling area. Models including the one-half MMDM covariate received overwhelming Akaike's Information Criterion support suggesting that buffering our study area by this distance would be more appropriate than no buffer or the full MMDM buffer for estimating the effectively sampled area and thereby density. Our model- averaged super-population abundance estimate was 603 (95% CI ¼522-684) black bears for Glacier NP. Our black bear density estimate (11.4 bears/100km 2 ,9 5% CI¼9.9-13.0) was consistent with published estimates for populations that are sympatric with grizzly bears (U. arctos) and without access to spawning salmonids. Published 2013. This article is a U.S. Government work and is in the public domain in the USA