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The Isolation Forest (iForest), proposed by Liu, Ting, and Zhou at TKDE 2012, has become a prominent tool for unsupervised anomaly detection. However, recent research by Hariri, Kind, and Brunner, published in TKDE 2021, has revealed issues with iForest. They identified the presence of axis-aligned ghost clusters that can be misidentified as normal clusters, leading to biased anomaly scores and inaccurate predictions. In response, they developed the Extended Isolation Forest (EIF), which effectively solves these issues by eliminating the ghost clusters introduced by iForest. This enhancement results in improved consistency of anomaly scores and superior performance. We reveal a previously overlooked problem in the Extended Isolation Forest (EIF), showing that it is vulnerable to ghost inter-clusters between normal clusters of data points. In this paper, we introduce the Rotated Isolation Forest (RIF) algorithm which effectively addresses both the axis-aligned ghost clusters observed in iForest and the ghost inter-clusters seen in EIF. RIF accomplishes this by randomly rotating the dataset (using random rotation matrices and QR decomposition) before feeding it into the iForest construction, thereby increasing dataset variation and eliminating ghost clusters. Our experiments conclusively demonstrate that the RIF algorithm outperforms iForest and EIF, as evidenced by the results obtained from both synthetic datasets and real-world datasets.

Copper is one of the most extensively studied materials for energy conversion and catalytic systems, with a wide range of other applications from nanophotonics to biotechnology. However, existing synthesis methods are limited with many undesirable by-products and poorly defined morphologies. Here, we report a surfactant-free on-substrate wet synthesis approach that yields monocrystalline metallic Cu microflakes with (111) crystalline exposed surface. By systematically studying the growth mechanism, we achieve unprecedented sizes of more than 130 {\mu}m, which is two orders of magnitude larger than reported in most previous studies, along with higher aspect ratios of over 400. Furthermore, we show distinctly higher stability against oxidation provided by the halide adlayer. Overall, our facile synthesis approach delivers an exciting venue for the emerging fields of catalysis and nanophotonics.

Accurate uncertainty information associated with essential climate variables (ECVs) is crucial for reliable climate modeling and understanding the spatiotemporal evolution of the Earth system. In recent years, geoscience and climate scientists have benefited from rapid progress in deep learning to advance the estimation of ECV products with improved accuracy. However, the quantification of uncertainties associated with the output of such deep learning models has yet to be thoroughly adopted. This survey explores the types of uncertainties associated with ECVs estimated from deep learning and the techniques to quantify them. The focus is on highlighting the importance of quantifying uncertainties inherent in ECV estimates, considering the dynamic and multifaceted nature of climate data. The survey starts by clarifying the definition of aleatoric and epistemic uncertainties and their roles in a typical satellite observation processing workflow, followed by bridging the gap between conventional statistical and deep learning views on uncertainties. Then, we comprehensively review the existing techniques for quantifying uncertainties associated with deep learning algorithms, focusing on their application in ECV studies. The specific need for modification to fit the requirements from both the Earth observation side and the deep learning side in such interdisciplinary tasks is discussed. Finally, we demonstrate our findings with two ECV examples, snow cover and terrestrial water storage, and provide our perspectives for future research.

We investigate the properties of positive definite and positive semi-definite symmetric matrices within the framework of symmetrized tropical algebra, an extension of tropical algebra adapted to ordered valued fields. We focus on the eigenvalues and eigenvectors of these matrices. We prove that the eigenvalues of a positive (semi)-definite matrix in the tropical symmetrized setting coincide with its diagonal entries. Then, we show that the images by the valuation of the eigenvalues of a positive definite matrix over a valued nonarchimedean ordered field coincide with the eigenvalues of an associated matrix in the symmetrized tropical algebra. Moreover, under a genericity condition, we characterize the images of the eigenvectors under the map keeping track both of the nonarchimedean valuation and sign, showing that they coincide with tropical eigenvectors in the symmetrized algebra. These results offer new insights into the spectral theory of matrices over tropical semirings, and provide combinatorial formulas for log-limits of eigenvalues and eigenvectors of parametric families of real positive definite matrices.

Image inpainting, the process of restoring missing or corrupted regions of an image by reconstructing pixel information, has recently seen considerable advancements through deep learning-based approaches. In this paper, we introduce a novel deep learning-based pre-processing methodology for image inpainting utilizing the Vision Transformer (ViT). Our approach involves replacing masked pixel values with those generated by the ViT, leveraging diverse visual patches within the attention matrix to capture discriminative spatial features. To the best of our knowledge, this is the first instance of such a pre-processing model being proposed for image inpainting tasks. Furthermore, we show that our methodology can be effectively applied using the pre-trained ViT model with pre-defined patch size. To evaluate the generalization capability of the proposed methodology, we provide experimental results comparing our approach with four standard models across four public datasets, demonstrating the efficacy of our pre-processing technique in enhancing inpainting performance.

Preparing thermal (Gibbs) states is a common task in physics and computer science. Recent algorithms mimic cooling via system-bath coupling, where the cost is determined by mixing time, akin to classical Metropolis-like algorithms. However, few methods exist to demonstrate slow mixing in quantum systems, unlike the well-established classical tools for systems like the Ising model and constraint satisfaction problems. We present a quantum generalization of these tools through a generic bottleneck lemma that implies slow mixing in quantum systems. This lemma focuses on quantum measures of distance, analogous to the classical Hamming distance but rooted in uniquely quantum principles and quantified either through Bohr spectrum jumps or operator locality. Using our bottleneck lemma, we establish unconditional lower bounds on the mixing times of Gibbs samplers for several families of Hamiltonians at low temperatures. For classical Hamiltonians with mixing time lower bounds $T_\mathrm{mix} = \exp[\Omega(n^\alpha)]$, we prove that quantum Gibbs samplers also have $T_\mathrm{mix} = \exp[\Omega(n^\alpha)]$. This applies to models like random $K$-SAT instances and spin glasses. For stabilizer Hamiltonians, we provide a concise proof of exponential lower bounds $T_\mathrm{mix} = \exp[\Omega(n)]$ on mixing times of good $n$-qubit stabilizer codes at low constant temperature. Finally, we consider constant-degree classical Hamiltonians and show how to lift classical slow mixing results in the presence of a transverse field using Poisson Feynman-Kac techniques. We show generic results for models with linear free energy barriers, and we demonstrate that our techniques extend to models with sublinear free energy barriers by proving $T_\mathrm{mix} = \exp[n^{1/2-o(1)}]$ for the ferromagnetic 2D transverse field Ising model., Comment: 59 pages. Arxiv abstract shortened. Fixed error in v1 for non-commuting results

People with learning disabilities have a higher mortality rate and premature deaths compared to the general public, as reported in published research in the UK and other countries. This study analyses hospitalisations of 9,618 patients identified with learning disabilities and long-term conditions for the population of Wales using electronic health record (EHR) data sources from the SAIL Databank. We describe the demographic characteristics, prevalence of long-term conditions, medication history, hospital visits, and lifestyle history for our study cohort, and apply machine learning models to predict the length of hospital stays for this cohort. The random forest (RF) model achieved an Area Under the Curve (AUC) of 0.759 (males) and 0.756 (females), a false negative rate of 0.224 (males) and 0.229 (females), and a balanced accuracy of 0.690 (males) and 0.689 (females). After examining model performance across ethnic groups, two bias mitigation algorithms (threshold optimization and the reductions algorithm using an exponentiated gradient) were applied to minimise performance discrepancies. The threshold optimizer algorithm outperformed the reductions algorithm, achieving lower ranges in false positive rate and balanced accuracy for the male cohort across the ethnic groups. This study demonstrates the potential of applying machine learning models with effective bias mitigation approaches on EHR data sources to enable equitable prediction of hospital stays by addressing data imbalances across groups., Comment: 13 pages of article with 9 figures; Supplementary material follows after article with 27 pages and 27 figures

Identifying and understanding the co-occurrence of multiple long-term conditions (MLTC) in individuals with intellectual disabilities (ID) is vital for effective healthcare management. These individuals often face earlier onset and higher prevalence of MLTCs, yet specific co-occurrence patterns remain unexplored. This study applies an unsupervised approach to characterise MLTC clusters based on shared disease trajectories using electronic health records (EHRs) from 13069 individuals with ID in Wales (2000-2021). Disease associations and temporal directionality were assessed, followed by spectral clustering to group shared trajectories. The population consisted of 52.3% males and 47.7% females, with an average of 4.5 conditions per patient. Males under 45 formed a single cluster dominated by neurological conditions (32.4%), while males above 45 had three clusters, the largest characterised circulatory (51.8%). Females under 45 formed one cluster with digestive conditions (24.6%) as most prevalent, while those aged 45 and older showed two clusters: one dominated by circulatory (34.1%), and the other by digestive (25.9%) and musculoskeletal (21.9%) system conditions. Mental illness, epilepsy, and reflux were common across groups. These clusters offer insights into disease progression in individuals with ID, informing targeted interventions and personalised healthcare strategies.

Two-dimensional (2D) kagome lattice metals are interesting because they display flat electronic bands, Dirac points, Van Hove singularities, and can have interplay between charge density wave (CDW), magnetic order, and superconductivity. In kagome lattice antiferromagnet FeGe, a short-range CDW order was found deep within an antiferromagnetically ordered state, interacting with the magnetic order. Surprisingly, post-growth annealing of FeGe at 560$^{\circ}$C can suppress the CDW order while annealing at 320$^{\circ}$C induces a long-range CDW order, with the ability to cycle between the states repeatedly by annealing. Here we perform transport, neutron scattering, scanning transmission electron microscopy (STEM), and muon spin rotation ($\mu$SR) experiments to unveil the microscopic mechanism of the annealing process and its impact on magneto-transport, CDW, and magnetic properties of FeGe. We find that 560$^{\circ}$C annealing creates germanium vacancies uniformly distributed throughout the FeGe kagome lattice, which prevent the formation of Ge-Ge dimers necessary for the CDW order. Upon annealing at 320$^{\circ}$C, the system segregates into stoichiometric FeGe regions with long-range CDW order and regions with stacking faults that act as nucleation sites for the CDW. The presence or absence of CDW order greatly affects the anomalous Hall effect, incommensurate magnetic order, and spin-lattice coupling in FeGe, thus placing FeGe as the only known kagome lattice material with a tunable CDW and magnetic order, potentially useful for sensing and information transmission.

Data with geometric structure is ubiquitous in machine learning often arising from fundamental symmetries in a domain, such as permutation-invariance in graphs and translation-invariance in images. Group-convolutional architectures, which encode symmetries as inductive bias, have shown great success in applications, but can suffer from instabilities as their depth increases and often struggle to learn long range dependencies in data. For instance, graph neural networks experience instability due to the convergence of node representations (over-smoothing), which can occur after only a few iterations of message-passing, reducing their effectiveness in downstream tasks. Here, we propose and study unitary group convolutions, which allow for deeper networks that are more stable during training. The main focus of the paper are graph neural networks, where we show that unitary graph convolutions provably avoid over-smoothing. Our experimental results confirm that unitary graph convolutional networks achieve competitive performance on benchmark datasets compared to state-of-the-art graph neural networks. We complement our analysis of the graph domain with the study of general unitary convolutions and analyze their role in enhancing stability in general group convolutional architectures.

Non-sensory thalamic nuclei interact with the cortex through thalamocortical and cortico-basal ganglia-thalamocortical loops. Reciprocal connections between the mediodorsal thalamus (MD) and the prefrontal cortex are particularly important in cognition, while the reciprocal connections of the ventromedial (VM), ventral anterior (VA), and ventrolateral (VL) thalamus with the prefrontal and motor cortex are necessary for sensorimotor information processing. However, limited and often oversimplified understanding of the connectivity of the MD, VA, and VL nuclei in primates have hampered development of accurate models that explain their contribution to cognitive and sensorimotor functions. The current prevalent view suggests that the MD connects with the prefrontal cortex, while the VA and VL primarily connect with the premotor and motor cortices. However, past studies have also reported diverse connections that enable these nuclei to integrate information across a multitude of brain systems. In this review, we provide a comprehensive overview of the anatomical connectivity of the primate MD, VA, and VL with the cortex. By synthesizing recent findings, we aim to offer a valuable resource for students, newcomers to the field, and experts developing new theories or models of thalamic function. Our review highlights the complexity of these connections and underscores the need for further research to fully understand the diverse roles of these thalamic nuclei in primates., Comment: 31 pages, 8 figures, 1 table

Random spin systems at low temperatures are glassy and feature computational hardness in finding low-energy states. We study the random all-to-all interacting fermionic Sachdev--Ye--Kitaev (SYK) model and prove that, in contrast, (I) the low-energy states have polynomial circuit depth, yet (II) the annealed and quenched free energies agree to inverse-polynomially low temperatures, ruling out a glassy phase transition in this sense. These results are derived by showing that fermionic and spin systems significantly differ in their commutation index, which quantifies the non-commutativity of Hamiltonian terms. Our results suggest that low-temperature strongly interacting fermions, unlike spins, belong in a classically nontrivial yet quantumly easy phase., Comment: New result on commutation index of k-local Paulis for k > log(n)

We respond to arguments against our criticism that claim to show a divergence of Assembly Theory from popular compression. We have proven that any implementation of the concept of `copy number' underlying Assembly Theory (AT) and its assembly index (Ai) is equivalent to Shannon Entropy and not fundamentally or methodologically different from algorithms like ZIP compression. We show that the weak empirical correlation between Ai and LZW, which the authors offered as a defense against the proof that the assembly index calculation method is a compression scheme, is based on an incomplete and misleading experiment. When the experiment is completed, the asymptotic convergence to LZ compression and Shannon Entropy is evident and aligned with the mathematical proof previously offered. Therefore, this completes the theoretical and empirical demonstrations that any variation of the copy-number concept underlying AT, which resorts to counting the number of object repetitions `to arrive at a measure for life,' is equivalent to statistical compression and Shannon Entropy. We demonstrate that the authors' `we-are-better-because-we-are-worse' defense argument against compression does not withstand basic scrutiny and that their empirical results separating organic from inorganic compounds have not only been previously reported -- sans claims to unify physics and biology -- but are also driven solely by molecular length, not a particular feature of life captured by their assembly index. Finally, we show that Ai is a particular case of our BDM introduced almost a decade earlier and that arguments attributing special stochastic properties to Ai are misleading, not unique, and exactly the same as those that Shannon Entropy is already not only equipped with but designed for which we have also proven to be equivalent to Ai making AT redundant even in practice when applied to their own experimental data., Comment: 12 figures, 53 pages (minor tweaks and adding new refs of previous relevant work not cited by the authors of AT)

The emergence of mobile robotics, particularly in the automotive industry, introduces a promising era of enriched user experiences and adept handling of complex navigation challenges. The realization of these advancements necessitates a focused technological effort and the successful execution of numerous intricate tasks, particularly in the critical domain of Simultaneous Localization and Mapping (SLAM). Various artificial intelligence (AI) methodologies, such as deep learning and reinforcement learning, present viable solutions to address the challenges in SLAM. This study specifically explores the application of reinforcement learning in the context of SLAM. By enabling the agent (the robot) to iteratively interact with and receive feedback from its environment, reinforcement learning facilitates the acquisition of navigation and mapping skills, thereby enhancing the robot's decision-making capabilities. This approach offers several advantages, including improved navigation proficiency, increased resilience, reduced dependence on sensor precision, and refinement of the decision-making process. The findings of this study, which provide an overview of reinforcement learning's utilization in SLAM, reveal significant advancements in the field. The investigation also highlights the evolution and innovative integration of these techniques.

This paper provides a thorough examination of recent developments in the field of multi-choice Machine Reading Comprehension (MRC). Focused on benchmark datasets, methodologies, challenges, and future trajectories, our goal is to offer researchers a comprehensive overview of the current landscape in multi-choice MRC. The analysis delves into 30 existing cloze-style and multiple-choice MRC benchmark datasets, employing a refined classification method based on attributes such as corpus style, domain, complexity, context style, question style, and answer style. This classification system enhances our understanding of each dataset's diverse attributes and categorizes them based on their complexity. Furthermore, the paper categorizes recent methodologies into Fine-tuned and Prompt-tuned methods. Fine-tuned methods involve adapting pre-trained language models (PLMs) to a specific task through retraining on domain-specific datasets, while prompt-tuned methods use prompts to guide PLM response generation, presenting potential applications in zero-shot or few-shot learning scenarios. By contributing to ongoing discussions, inspiring future research directions, and fostering innovations, this paper aims to propel multi-choice MRC towards new frontiers of achievement.

Exploring nonequilibrium hot carriers from plasmonic metal nanostructures is a dynamic field in optoelectronics, driving photochemical reactions such as solar fuel generation. The hot carrier injection mechanism and the reaction rate are highly impacted by the metal/molecule interaction. However, determining the primary type of the reaction and thus the injection mechanism of the hot carriers has remained elusive. In this work, we reveal an electron injection mechanism deviating from a purely outersphere process for the reduction of ferricyanide redox molecule in a gold/p-type gallium nitride (Au/p- GaN) photocathode system. Combining our experimental approach with ab initio simulations, we discover that the efficient inner-sphere transfer of low-energy electrons leads to a continuous enhancement in the photocathode device performance in the interband regime. These findings provide important mechanistic insights, showing our methodology as a powerful tool for analyzing and engineering hot-carrier-driven processes in plasmonic photocatalytic systems and optoelectronic devices.

This paper studies the usefulness of incorporating path information in predicting chemical properties from molecular graphs, in the domain of QSAR (Quantitative Structure-Activity Relationship). Towards this, we developed a GNN-style model which can be toggled to operate in one of two modes: a non-degenerate mode which incorporates path information, and a degenerate mode which leaves out path information. Thus, by comparing the performance of the non-degenerate mode versus the degenerate mode on relevant QSAR datasets, we were able to directly assess the significance of path information on those datasets. Our results corroborate previous works, by suggesting that the usefulness of path information is datasetdependent. Unlike previous studies however, we took the very first steps towards building a model that could predict upfront whether or not path information would be useful for a given dataset at hand. Moreover, we also found that, albeit its simplicity, the degenerate mode of our model yielded rather surprising results, which outperformed more sophisticated SOTA models in certain cases.

The manifold hypothesis presumes that high-dimensional data lies on or near a low-dimensional manifold. While the utility of encoding geometric structure has been demonstrated empirically, rigorous analysis of its impact on the learnability of neural networks is largely missing. Several recent results have established hardness results for learning feedforward and equivariant neural networks under i.i.d. Gaussian or uniform Boolean data distributions. In this paper, we investigate the hardness of learning under the manifold hypothesis. We ask which minimal assumptions on the curvature and regularity of the manifold, if any, render the learning problem efficiently learnable. We prove that learning is hard under input manifolds of bounded curvature by extending proofs of hardness in the SQ and cryptographic settings for Boolean data inputs to the geometric setting. On the other hand, we show that additional assumptions on the volume of the data manifold alleviate these fundamental limitations and guarantee learnability via a simple interpolation argument. Notable instances of this regime are manifolds which can be reliably reconstructed via manifold learning. Looking forward, we comment on and empirically explore intermediate regimes of manifolds, which have heterogeneous features commonly found in real world data.

Let $G$ be a graph, and let $\lambda(G)$ denote the smallest eigenvalue of $G$. First, we provide an upper bound for $\lambda(G)$ based on induced bipartite subgraphs of $G$. Consequently, we extract two other upper bounds, one relying on the average degrees of induced bipartite subgraphs and a more explicit one in terms of the chromatic number and the independence number of $G$. In particular, motivated by our bounds, we introduce two graph invariants that are of interest on their own. Finally, special attention goes to the investigation of the sharpness of our bounds in various classes of graphs as well as the comparison with an existing well-known upper bound., Comment: 10 pages, to appear in Archiv der Mathematik

We consider the problem of estimating the ground state energy of quantum $p$-local spin glass random Hamiltonians, the quantum analogues of widely studied classical spin glass models. Our main result shows that the maximum energy achievable by product states has a well-defined limit (for even $p$) as $n\to\infty$ and is $E_{\text{product}}^\ast=\sqrt{2 \log p}$ in the limit of large $p$. This value is interpreted as the maximal energy of a much simpler so-called Random Energy Model, widely studied in the setting of classical spin glasses. The proof of the limit existing follows from an extension of Fekete's Lemma after we demonstrate near super-additivity of the (normalized) quenched free energy. The proof of the value follows from a second moment method on the number of states achieving a given energy when restricting to an $\epsilon$-net of product states. Furthermore, we relate the maximal energy achieved over all states to a $p$-dependent constant $\gamma\left(p\right)$, which is defined by the degree of violation of a certain asymptotic independence ansatz over graph matchings. We show that the maximal energy achieved by all states $E^\ast\left(p\right)$ in the limit of large $n$ is at most $\sqrt{\gamma\left(p\right)}E_{\text{product}}^\ast$. We also prove using Lindeberg's interpolation method that the limiting $E^\ast\left(p\right)$ is robust with respect to the choice of the randomness and, for instance, also applies to the case of sparse random Hamiltonians. This robustness in the randomness extends to a wide range of random Hamiltonian models including SYK and random quantum max-cut., Comment: 54 pages, 0 figures. arXiv admin note: substantial text overlap with arXiv:2309.11709

We prove the full equivalence between Assembly Theory (AT) and Shannon Entropy via a method based upon the principles of statistical compression renamed `assembly index' that belongs to the LZ family of popular compression algorithms (ZIP, GZIP, JPEG). Such popular algorithms have been shown to empirically reproduce the results of AT, results that have also been reported before in successful applications to separating organic from non-organic molecules and in the context of the study of selection and evolution. We show that the assembly index value is equivalent to the size of a minimal context-free grammar. The statistical compressibility of such a method is bounded by Shannon Entropy and other equivalent traditional LZ compression schemes, such as LZ77, LZ78, or LZW. In addition, we demonstrate that AT, and the algorithms supporting its pathway complexity, assembly index, and assembly number, define compression schemes and methods that are subsumed into the theory of algorithmic (Kolmogorov-Solomonoff-Chaitin) complexity. Due to AT's current lack of logical consistency in defining causality for non-stochastic processes and the lack of empirical evidence that it outperforms other complexity measures found in the literature capable of explaining the same phenomena, we conclude that the assembly index and the assembly number do not lead to an explanation or quantification of biases in generative (physical or biological) processes, including those brought about by (abiotic or Darwinian) selection and evolution, that could not have been arrived at using Shannon Entropy or that have not been reported before using classical information theory or algorithmic complexity., Comment: 15 pages + appendix, 2 figures