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We explicitly define the notions of (bona fide, approximate or asymptotic) compound p-values and e-values, which have been implicitly presented and used in the recent multiple testing literature. While it is known that the e-BH procedure with compound e-values controls the FDR, we show the converse: every FDR controlling procedure can be recovered by instantiating the e-BH procedure with certain compound e-values. Since compound e-values are closed under averaging, this allows for combination and derandomization of arbitrary FDR procedures. We then connect compound e-values to empirical Bayes. In particular, we use the fundamental theorem of compound decision theory to derive the log-optimal simple separable compound e-value for testing a set of point nulls against point alternatives: it is a ratio of mixture likelihoods. As one example, we construct asymptotic compound e-values for multiple t-tests, where the (nuisance) variances may be different across hypotheses. Our construction may be interpreted as a data-driven instantiation of the optimal discovery procedure, and our results provide the first type-I error guarantees for the same, along with significant power gains.

We study the problem of determining a matrix whose $k$th multiplicative compound, with $k > 1$, is a prescribed matrix $M$. The cardinality of the set of matrices whose $k$th multiplicative compound equals $M$ is characterized in terms of $\rank(M)$. On the one hand, if $\rank(M)\le 1$, it is shown that there exist infinitely many such matrices for which a complete characterization is determined. On the other hand, if $\rank(M)>1$, then there exists a unique matrix -- up to an overall sign -- whose compound is $M$. An algorithm for finding a matrix whose compound equals $M$ is detailed, and its time complexity is analyzed.

The statistical model for the calculation of the compound nucleus formation cross section and the probability of compound nucleus formation in heavy-ion collisions is discussed in detail. The light, heavy, and super-heavy nucleus-nucleus systems are considered in this model in the framework of one approach. It is shown that the compound nucleus is formed in competition between passing through the compound-nucleus formation barrier and the quasi-elastic barrier. The compound-nucleus formation barrier is the barrier separating the system of contacting incident nuclei and the spherical or near-spherical ground state of the compound nucleus. The quasi-elastic barrier is the barrier between the contacting and well-separated deformed ions. It is shown that the compound nucleus formation cross-section is suppressed when the quasi-elastic barrier is lower than the compound nucleus formation barrier. The critical value of angular momentum, which limits the compound nucleus formation cross-section values for light and medium ion-ion systems at over-barrier collision energies, is discussed in the model. The suppression of the compound nucleus formation cross-section even at small partial wave

We report on the magnetic, transport, and thermal properties of the hexagonal ZrNiAl-type compound CeMgIn with Ce atoms forming a distorted kagome network. This compound exhibits successive antiferromagnetic transition at $T_\text{N1} =$ 2.1 K, $T_\text{N2} =$ 1.7 K, and possibly $T_\text{N3} =$ 1.3 K. The electrical resistivity exhibits a minimum at 11 K and a nonlogarithmic increase with decreasing temperature down to $T_\text{N2}$. We found that CeMgIn is the first ZrNiAl-type compound whose resistivity increase can be well explained by considering a model in which the electron-spin scattering is enhanced by the magnetic frustration and the Ruderman-Kittel-Kasuya-Yosida interaction. These results suggest that CeMgIn is a notable compound whose physical properties are strongly affected by geometrical frustration. Since the Sommerfeld coefficient is 97 mJ/mol K$^2$, CeMgIn is classified as a moderate heavy-fermion compound.

Large language models (LLMs) demonstrate remarkable performance across various tasks, prompting researchers to develop diverse evaluation benchmarks. However, most benchmarks typically measure the ability of LLMs to respond to individual questions, neglecting the complex interactions in real-world applications. We introduce Compound Question Synthesis (CQ-Syn) to build Compound-QA, a benchmark targeting questions composed of multiple interrelated sub-questions. This benchmark is derived from existing QA datasets, annotated with proprietary LLMs, and verified by humans for accuracy. It encompasses five categories: Factual-Statement, Cause-and-Effect, Hypothetical-Analysis, Comparison-and-Selection, and Evaluation-and-Suggestion. It evaluates the LLM capability in terms of three dimensions, including understanding, reasoning, and knowledge. Evaluating nine open-source LLMs on Compound-QA reveals that their performance on compound questions is notably lower than on non-compound questions. We further explore strategies to enhance LLMs' handling of compound questions, and our results show that these methods substantially improve models' comprehension and reasoning abilities.

Compound flooding, where the combination or successive occurrence of two or more flood drivers leads to an extreme impact, can greatly exacerbate the adverse consequences associated with flooding in coastal regions. This paper reviews the practices and trends in coastal compound flood research methodologies and applications, as well as synthesizes key findings at regional and global scales. Systematic review is employed to construct a literature database of 271 studies relevant to compound flood hazards in a coastal context. This review explores the types of compound flood events, their mechanistic processes, and synthesizes the definitions and terms exhibited throughout the literature. Considered in the review are six flood drivers (fluvial, pluvial, coastal, groundwater, damming/dam failure, and tsunami) and five precursor events and environmental conditions (soil moisture, snow, temp/heat, fire, and drought). Furthermore, this review summarizes the trends in research methodology, examines the wide range of study applications, and considers the influences of climate change and urban environments. Finally, this review highlights the knowledge gaps in compound flood research and di

Early discovery projects often face a budgeted prioritization problem: many structures can be enumerated or purchased, but only a small fraction can be tested, reviewed, or synthesized first. I formulate this setting as risk-aware compound-library compression. Given a molecular library and a fixed Top-k budget, the goal is to return an enriched candidate subset while preserving uncertainty, applicability-domain evidence, ADMET/structural alerts, and audit fields needed for human review. The framework intentionally uses a transparent 2D activity proxy rather than a complex representation model, combining Morgan fingerprints, RDKit descriptors, a multilayer perceptron, split-conformal uncertainty intervals, leakage auditing, and auditable export. On ChEMBL 36, the model achieved Spearman 0.7674 and EF@1% 2.7331 on internal validation, and Spearman 0.5171 with EF@1% 2.4359 on a temporal holdout. After fold-0 training-overlap control, a scaffold-disjoint BACE subset retained ROC AUC 0.7626 and EF@1% 2.0253. In a strict 100-molecule BACE decision-layer replay, risk-aware ordering kept Hit@10 at 0.9000 while exposing review evidence that pure activity sorting omits. An EGFR/CHEMBL203 lab

Hypothesis: Immiscible liquids are commonly used to achieve unique functions in many applications, where the breakup of compound droplets in airflow is an important process. Due to the existence of the liquid-liquid interface, compound droplets are expected to form different deformation and breakup morphologies compared with single-component droplets. Experiments: We investigate experimentally the deformation and breakup of compound droplets in airflow. The deformation characteristics of compound droplets are quantitatively analyzed and compared with single-component droplets. Theoretical models are proposed to analyze the transition between breakup morphologies. Findings: The breakup modes of compound droplets are classified into shell retraction, shell breakup, and core-shell breakup based on the location where the breakup occurs. The comparison with single-component droplets reveals that the compound droplet is stretched more in the flow direction and expands less in the cross-flow direction, and these differences occur when the core of the compound droplet protrudes into the airflow. The transition conditions between different breakup modes are obtained theoretically. In additi

Open compound domain adaptation (OCDA) aims to transfer knowledge from a labeled source domain to a mix of unlabeled homogeneous compound target domains while generalizing to open unseen domains. Existing OCDA methods solve the intra-domain gaps by a divide-and-conquer strategy, which divides the problem into several individual and parallel domain adaptation (DA) tasks. Such approaches often contain multiple sub-networks or stages, which may constrain the model's performance. In this work, starting from the general DA theory, we establish the generalization bound for the setting of OCDA. Built upon this, we argue that conventional OCDA approaches may substantially underestimate the inherent variance inside the compound target domains for model generalization. We subsequently present Stochastic Compound Mixing (SCMix), an augmentation strategy with the primary objective of mitigating the divergence between source and mixed target distributions. We provide theoretical analysis to substantiate the superiority of SCMix and prove that the previous methods are sub-groups of our methods. Extensive experiments show that our method attains a lower empirical risk on OCDA semantic segmentatio

This work studies the semantic representations learned by BERT for compounds, that is, expressions such as sunlight or bodyguard. We build on recent studies that explore semantic information in Transformers at the word level and test whether BERT aligns with human semantic intuitions when dealing with expressions (e.g., sunlight) whose overall meaning depends -- to a various extent -- on the semantics of the constituent words (sun, light). We leverage a dataset that includes human judgments on two psycholinguistic measures of compound semantic analysis: lexeme meaning dominance (LMD; quantifying the weight of each constituent toward the compound meaning) and semantic transparency (ST; evaluating the extent to which the compound meaning is recoverable from the constituents' semantics). We show that BERT-based measures moderately align with human intuitions, especially when using contextualized representations, and that LMD is overall more predictable than ST. Contrary to the results reported for 'standard' words, higher, more contextualized layers are the best at representing compound meaning. These findings shed new light on the abilities of BERT in dealing with fine-grained semant

Translation, rotation, and scaling are three commonly used geometric manipulation operations in image processing. Besides, some of them are successfully used in developing effective knowledge graph embedding (KGE) models such as TransE and RotatE. Inspired by the synergy, we propose a new KGE model by leveraging all three operations in this work. Since translation, rotation, and scaling operations are cascaded to form a compound one, the new model is named CompoundE. By casting CompoundE in the framework of group theory, we show that quite a few scoring-function-based KGE models are special cases of CompoundE. CompoundE extends the simple distance-based relation to relation-dependent compound operations on head and/or tail entities. To demonstrate the effectiveness of CompoundE, we conduct experiments on three popular KG completion datasets. Experimental results show that CompoundE consistently achieves the state of-the-art performance.

This work introduces a multi-output classification (MOC) framework designed for domain adaptation in fault diagnosis, particularly under partially labeled (PL) target domain scenarios and compound fault conditions in rotating machinery. Unlike traditional multi-class classification (MCC) methods that treat each fault combination as a distinct class, the proposed approach independently estimates the severity of each fault type, improving both interpretability and diagnostic accuracy. The model incorporates multi-kernel maximum mean discrepancy (MK-MMD) and entropy minimization (EM) losses to facilitate feature transfer from the source to the target domain. In addition, frequency layer normalization (FLN) is applied to preserve structural properties in the frequency domain, which are strongly influenced by system dynamics and are often stationary with respect to changes in rpm. Evaluations across six domain adaptation cases with PL data demonstrate that MOC outperforms baseline models in macro F1 score. Moreover, MOC consistently achieves better classification performance for individual fault types, and FLN shows superior adaptability compared to other normalization techniques.

Conventional approaches to facial expression recognition primarily focus on the classification of six basic facial expressions. Nevertheless, real-world situations present a wider range of complex compound expressions that consist of combinations of these basics ones due to limited availability of comprehensive training datasets. The 6th Workshop and Competition on Affective Behavior Analysis in-the-wild (ABAW) offered unlabeled datasets containing compound expressions. In this study, we propose a zero-shot approach for recognizing compound expressions by leveraging a pretrained visual language model integrated with some traditional CNN networks.

Large Language Models (LLMs) have showcased remarkable capabilities surpassing conventional NLP challenges, creating opportunities for use in production use cases. Towards this goal, there is a notable shift to building compound AI systems, wherein LLMs are integrated into an expansive software infrastructure with many components like models, retrievers, databases and tools. In this paper, we introduce a blueprint architecture for compound AI systems to operate in enterprise settings cost-effectively and feasibly. Our proposed architecture aims for seamless integration with existing compute and data infrastructure, with ``stream'' serving as the key orchestration concept to coordinate data and instructions among agents and other components. Task and data planners, respectively, break down, map, and optimize tasks and data to available agents and data sources defined in respective registries, given production constraints such as accuracy and latency.

The semi-tensor product (STP) of matrices is extended to the STP of hypermatrices. Some basic properties of the STP of matrices are extended to the STP of hypermatrices. The hyperdeterminant of hypersquares is introduced. Some algebraic and geometric structures of matrices are extended to hypermatrices. Then the compound hypermatrix is proposed. The STP of hypermatrix is used to compound hypermatrix. Basic properties are proved to be available for compound hypermatrix.

Content-based analysis and retrieval of digital images found in scientific articles is often hindered by images consisting of multiple subfigures (compound figures). We address this problem by proposing a method to automatically classify and separate compound figures, which consists of two main steps: (i) a supervised compound figure classifier (CFC) discriminates between compound and non-compound figures using task-specific image features; and (ii) an image processing algorithm is applied to predicted compound images to perform compound figure separation (CFS). Our CFC approach is shown to achieve state-of-the-art classification performance on a published dataset. Our CFS algorithm shows superior separation accuracy on two different datasets compared to other known automatic approaches. Finally, we propose a method to evaluate the effectiveness of the CFC-CFS process chain and use it to optimize the misclassification loss of CFC for maximal effectiveness in the process chain.

In distributional semantic accounts of the meaning of noun-noun compounds (e.g. starfish, bank account, houseboat) the important role of constituent polysemy remains largely unaddressed(cf. the meaning of star in starfish vs. star cluster vs. star athlete). Instead of semantic vectors that average over the different meanings of a constituent, disambiguated vectors of the constituents would be needed in order to see what these more specific constituent meanings contribute to the meaning of the compound as a whole. This paper presents a novel approach to this specific problem of word sense disambiguation: set expansion. We build on the approach developed by Mahabal et al. (2018) which was originally designed to solve the analogy problem. We modified their method in such a way that it can address the problem of sense disambiguation of compound constituents. The results of experiments with a data set of almost 9000 compounds (LADEC, Gagné et al. 2019) suggest that this approach is successful, yet the success is sensitive to the frequency with which the compounds are attested.

We numerically investigate the hydrodynamics of a compound drop in a plane Poiseuille flow under Stokes regime. A neutrally buoyant, initially concentric compound drop is released into a fully developed flow, where it migrates to its equilibrium position. Based on the results, we find that the core-shell interaction affects the dynamics of both the core and the compound drop. During the initial transient period, the core revolves about the center of the compound drop due to the internal circulation inside the shell. At equilibrium, depending upon the nature of the flow field inside the shell, we identify two distinct core behaviors: stable state and limit-cycle state. In the stable state, the core stops revolving and moves outward very slowly. The core in the limit-cycle state continues to revolve in a nearly fixed orbit with no further inward motion. We also find that the migration of the compound drop affects the eccentricity of the core significantly. A comparison with the simple drop reveals that the core enhances the deformation of the compound drop. The outward moving core in stable state pushes the compound drop towards the walls, and the revolving core in limit-cycle state

Schema evolution is critical in managing database systems to ensure compatibility across different data versions. A schema registry typically addresses the challenges of schema evolution in real-time data streaming by managing, validating, and ensuring schema compatibility. However, current schema registries struggle with complex syntactic alterations like field renaming or type changes, which often require significant manual intervention and can disrupt service. To enhance the flexibility of schema evolution, we propose the use of generalized schema evolution (GSE) facilitated by a compound AI system. This system employs Large Language Models (LLMs) to interpret the semantics of schema changes, supporting a broader range of syntactic modifications without interrupting data streams. Our approach includes developing a task-specific language, Schema Transformation Language (STL), to generate schema mappings as an intermediate representation (IR), simplifying the integration of schema changes across different data processing platforms. Initial results indicate that this approach can improve schema mapping accuracy and efficiency, demonstrating the potential of GSE in practical applica