Abstract

Submodular functions are known to satisfy various forms of fractional subadditivity. This work investigates the conditions for equality to hold exactly or approximately in the fractional subadditivity of submodular functions. We establish that a small gap in the inequality implies that the function is close to being modular, and that the gap is zero if and only if the function is modular. We then present natural implications of these results for special cases of submodular functions, such as entropy, relative entropy, and matroid rank. As a consequence, we characterize the necessary and sufficient conditions for equality to hold in Shearer's lemma, recovering a result of Ellis et al. (2016) as a special case. We leverage our results to propose a new multivariate mutual information, which generalizes Watanabe's total correlation (1960), Han's dual total correlation (1975), and Csiszar and Narayan's shared information (2004), and analyze its properties. Among these properties, we extend Watanabe's characterization of total correlation as the maximum correlation over partitions to fractional partitions. When applied to matrix determinantal inequalities for positive definite matrices, our results recover the equality conditions of the classical determinantal inequalities of Hadamard, Szasz, and Fischer as special cases.

Abstract

The robustness of precast concrete structures is primarily governed by connections between the precast structural components. Joint connections deliver a vital role in load transfer, restraining movement, and providing stability at local and global level. This calls for appropriate connection mechanism for precast elements providing integrity under different loading conditions and ease of construction. The connection details in literature or available in practice have been rarely evaluated. This paper discusses the numerical modelling of precast reinforced concrete structural wall-column with different joint connection systems and evaluates various seismic design parameters, simulated through in-plane lateral loading in a finite element software. The connection systems evaluated are reinforcement bar connection, headed bar connections, U-bar connection and steel wire loop connection, which are subsequently compared with a cast-in-situ reinforced concrete wall-column model having similar material and geometrical properties. The seismic behaviour of connections have been studied with regards to the damage pattern, stresses, lateral load capacity, base shear coefficient, stiffness, deformation characteristics, strength factors, and damage index. Among all the connection systems, U-bar connection and loop connection using steel wire ropes showed stresses within the yield limit, while other connection systems reached their yield capacity, indicating damage. Apparently, steel wire loop connection is found to be effective in transfer of lateral load between the precast reinforced concrete elements, as observed from the numerical analysis; whereas other connection systems yielded prior to the design load. However, all connections except the reinforcement bar connection surpassed design load prior to the peak limit.

Abstract

The Facility Location Problem (FLP) is a well-studied optimization problem with applications in many real-world scenarios. Past literature has explored the solutions from different perspectives to tackle FLPs. These include investigating FLPs under objective functions such as utilitarian, egalitarian, Nash welfare, etc. Also, there is no treatment for asymmetric welfare functions around the facility. We propose a unified framework, FLIGHT, to accommodate a broad class of welfare notions. The framework undergoes rigorous theoretical analysis, and we prove some structural properties of the solution to FLP. Additionally, we provide approximation bounds, which provide insight into an interesting fact: as the number of agents arbitrarily increases, the choice of welfare notion is irrelevant. Furthermore, the paper also includes results around concentration bounds under certain distributional assumptions over the preferred locations of agents.

Abstract

This paper considers the problem of fair probabilistic binary classification with binary protected groups. The classifier assigns scores, and a practitioner predicts labels using a certain cut-off threshold based on the desired trade-off between false positives vs. false negatives. It derives these thresholds from the ROC of the classifier. The resultant classifier may be unfair to one of the two protected groups in the dataset. It is desirable that no matter what threshold the practitioner uses, the classifier should be fair to both the protected groups; that is, the ℒₚ norm between FPRs and TPRs of both the protected groups should be at most ε. We call such fairness on ROCs of both the protected attributes εₚ-Equalized ROC. Given a classifier not satisfying ε₁-Equalized ROC, we aim to design a post-processing method to transform the given (potentially unfair) classifier's output (score) to a suitable randomized yet fair classifier. That is, the resultant classifier must satisfy ε₁-Equalized ROC. First, we introduce a threshold query model on the ROC curves for each protected group. The resulting classifier is bound to face a reduction in AUC. With the proposed query model, we provide a rigorous theoretical analysis of the minimal AUC loss to achieve ε₁-Equalized ROC. To achieve this, we design a linear time algorithm, namely FROC, to transform a given classifier's output to a probabilistic classifier that satisfies ε₁-Equalized ROC. We prove that under certain theoretical conditions, FROC achieves the theoretical optimal guarantees. We also study the performance of our FROC on multiple real-world datasets with many trained classifiers.

Abstract

Abstract— Transgenic crops have become widespread but have associated health concerns. Testing for transgenic corn is slow and lengthy. In this paper, we used UV-Vis spectroscopy in combination with chemometrics and the PCA-SVM classifier to identify different types of corn samples from each other, including transgenic varieties. The presented methodology and the classifier can differentiate very well between the three different varieties of corn considered in this paper. Although there is a slight improvement in prediction accuracies compared to the state-of-the-art methods, our method is considerably more cost-effective and less time-consuming.

Abstract

Graph Neural Network (GNN) research is rapidly advancing due to GNNs’ capacity to learn distributed representations from graph-structured data. However, centralizing large volumes of real-world graph data for GNN training is often impractical due to privacy concerns, regulatory restrictions, and commercial competition. Federated learning (FL), a distributed learning paradigm, offers a solution by preserving data privacy with collaborative model training. Despite progress in training huge vision and language models, federated learning for GNNs remains underexplored. To address this challenge, we present a novel method for federated learning on GNNs based on spectral GNNs equipped with neural ordinary differential equations (ODE) for better information capture, showing promising results across both homophilic and heterophilic graphs. Our approach effectively handles non-Independent and Identically Distributed (non-IID) data, while also achieving performance comparable to existing methods that only operate on IID data. It is designed to be privacy-preserving and bandwidth-optimized, making it suitable for real-world applications such as social network analysis, recommendation systems, and fraud detection, which often involve complex, non-IID, and heterophilic graph structures. Our results in the area of federated learning on non-IID heterophilic graphs demonstrate significant improvements while also achieving better performance on homophilic graphs. This work highlights the potential of federated learning in diverse and challenging graph settings.

Abstract

The fully entangled fraction (FEF) measures the proximity of a quantum state to maximally entangled states. FEF , in systems, is a significant benchmark for various quantum information processing protocols including teleportation. Quantum conditional entropy (QCE) on the other hand is a measure of correlation in quantum systems. Conditional entropies for quantum systems can be negative, marking a departure from conventional classical systems. The negativity of quantum conditional entropies plays a decisive role in tasks like state merging and dense coding. In the present work, we investigate the relation of these two important yardsticks. Our probe is mainly done in the ambit of states with maximally mixed marginals, with a few illustrations from other classes of quantum states. We start our study in two-qubit systems, where for the Werner states, we obtain lower bounds to its FEF when the conditional Rényi entropy is negative. We then obtain relations between FEF and QCE for two-qubit Weyl states. Moving on to two qudit states, we find a necessary and sufficient condition based on FEF, for the isotropic state to have negative conditional entropy. In two qudit systems, the relation between FEF and QCE is probed for the rank-deficient and generalized Bell diagonal states. FEF is intricately linked with k-copy nonlocality and k- copy steerability. The relations between FEF and QCE facilitates to find conditions for k- copy nonlocality and k- copy steerability based on QCE. We obtain such conditions for certain classes of states in two qubits and two qudits. Applications of the relations obtained are provided in the context of work extraction, faithful entanglement and entropic uncertainty relations.

Abstract

Effective decision-making in complex environments with multi-discrete action spaces poses significant challenges for agent architectures, particularly in image-based settings. While Decision Transformers have shown promise in various domains, their performance often suffers in environments where agents must handle multi-discrete actions. Existing enhancements to Decision Transformer architectures have yet to address this critical issue, limiting their ability to support agents in learning robust policies in these environments. To address this gap, we propose Multi-State Action Tokenisation (M-SAT), a novel approach designed to improve agent decision-making by tokenising actions at the individual action level and incorporating auxiliary state information. This disentanglement of actions improves both the performance of agents and the interpretability of individual actions within attention layers, fostering better visibility into agent decision processes. Importantly, M-SAT facilitates the development of more interpretable and transparent agents capable of making complex decisions in dynamic environments involving multi-discrete action spaces. We evaluate M-SAT on the challenging ViZDoom environments, focusing on scenarios with multi-discrete action spaces and image-based observations, such as Deadly Corridor, My Way Home and Death Match. Our approach demonstrates superior performance compared to baseline Decision Transformers, with no additional data or significant computational overheads. Furthermore, we observe that M-SAT does not require positional encoding to achieve high performance, with its removal occasionally leading to further improvements. These findings suggest that M-SAT enables more efficient and interpretable agent-based decision-making in multi-discrete action spaces.

Abstract

The study of information revivals, witnessing the violation of certain data-processing inequalities, has provided an important paradigm in the study of non-Markovian quantum stochastic processes. Although often used interchangeably, we argue here that the notions of “revivals” and “backflows,” i.e., flows of information from the environment back into the system, are distinct: an information revival can occur without any backflow ever taking place. In this paper, we examine in detail the phenomenon of noncausal revivals and relate them to the theory of short Markov chains and squashed non-Markovianity. We also provide an operational condition, in terms of system-only degrees of freedom, to witness the presence of genuine backflow that cannot be explained by noncausal revivals. As a byproduct, we demonstrate that focusing on processes with genuine backflows, while excluding those with only noncausal revivals, resolves the issue of nonconvexity of Markovianity, thus enabling the construction of a convex resource theory of genuine quantum non-Markovianity

Abstract

An influential mathematical model of memory, the temporal context model (TCM), posits that we encode items and their associations with temporal context (Howard & Kahana, 2002). Temporal context is conceived of as a recency-weighted average of past experiences. Critically, the model assumes that when an item is retrieved later, the associated temporal context is also obligatorily retrieved. Existing evidence for the idea of retrieved temporal context primarily comes from free-recall studies. However, free recall introduces some critical confounds that are difficult to resolve (Folkerts et al., 2018) and also encourages memory strategies that may mimic temporal context effects (Hintzman, 2011). Schwartz et al. (2005) showed that temporal context influences image recognition within short experimental lists. We extend this by using the Natural Scenes Dataset (NSD) to demonstrate that reinstating temporal context enhances recognition accuracy even across long timescales. We demonstrate that when the relevant temporal context is successfully reinstated for a reference image, the recognition accuracy of subsequent images increases. Critically, we show that this influence falls off with temporal distance at encoding from the reference image only when the temporal context is successfully retrieved, as predicted by TCM. Furthermore, the slope of this temporal gradient increases as a function of the strength of the influence of the retrieved temporal context. These findings extend our understanding of temporal context effects in episodic memory by showing that temporal context is retrieved even in tasks that do not encourage linking between items as a memory strategy.