Class Of Metrics Research Articles

A Model for Automating the Abstraction of Planning Problems in a Narrative Context

Contemporary automated planning research emphasizes the use of domain knowledge abstractions like heuristics to improve search efficiency. Transformative automated abstraction techniques which decompose or otherwise reformulate the problem have a limited presence, owing to poor performance in key metrics like plan length and time efficiency. In this paper, we argue for a reexamination of these transformative techniques in the context of narrative planning, where classical metrics are less appropriate. We propose a model for automating abstraction by decomposing a planning problem into subproblems which serve as abstract features of the problem. We demonstrate the application of this approach on a low-level problem and discuss key features of the resulting abstract problem. Plans in the abstract problem are shorter, representing summaries of low-level plans, but can be directly translated into low-level plans for the original problem.

Latent dynamics of primary sensory cortical population activity structured by fluctuations in the local field potential.

As emerging technologies enable measurement of precise details of the activity within microcircuits at ever-increasing scales, there is a growing need to identify the salient features and patterns within the neural populations that represent physiologically and behaviorally relevant aspects of the network. Accumulating evidence from recordings of large neural populations suggests that neural population activity frequently exhibits relatively low-dimensional structure, with a small number of variables explaining a substantial fraction of the structure of the activity. While such structure has been observed across the brain, it is not known how reduced-dimension representations of neural population activity relate to classical metrics of "brain state," typically described in terms of fluctuations in the local field potential (LFP), single-cell activity, and behavioral metrics. Hidden state models were fit to spontaneous spiking activity of populations of neurons, recorded in the whisker area of primary somatosensory cortex of awake mice. Classic measures of cortical state in S1, including the LFP and whisking activity, were compared to the dynamics of states inferred from spiking activity. A hidden Markov model fit the population spiking data well with a relatively small number of states, and putative inhibitory neurons played an outsize role in determining the latent state dynamics. Spiking states inferred from the model were more informative of the cortical state than a direct readout of the spiking activity of single neurons or of the population. Further, the spiking states predicted both the trial-by-trial variability in sensory responses and one aspect of behavior, whisking activity. Our results show how classical measurements of brain state relate to neural population spiking dynamics at the scale of the microcircuit and provide an approach for quantitative mapping of brain state dynamics across brain areas.

HiCDiffusion - diffusion-enhanced, transformer-based prediction of chromatin interactions from DNA sequences

Prediction of chromatin interactions from DNA sequence has been a significant research challenge in the last couple of years. Several solutions have been proposed, most of which are based on encoder-decoder architecture, where 1D sequence is convoluted, encoded into the latent representation, and then decoded using 2D convolutions into the Hi-C pairwise chromatin spatial proximity matrix. Those methods, while obtaining high correlation scores and improved metrics, produce Hi-C matrices that are artificial - they are blurred due to the deep learning model architecture. In our study, we propose the HiCDiffusion, sequence-only model that addresses this problem. We first train the encoder-decoder neural network and then use it as a component of the diffusion model - where we guide the diffusion using a latent representation of the sequence, as well as the final output from the encoder-decoder. That way, we obtain the high-resolution Hi-C matrices that not only better resemble the experimental results - improving the Fréchet inception distance by an average of 11 times, with the highest improvement of 56 times - but also obtain similar classic metrics to current state-of-the-art encoder-decoder architectures used for the task.

Evaluation of flood metrics across the Mississippi-Atchafalaya River Basin and their relation to flood damages.

Societal risks from flooding are evident at a range of spatial scales and climate change will exacerbate these risks in the future. Assessing flood risks across broad geographical regions is a challenge, and often done using streamflow time-series records or hydrologic models. In this study, we used a national-scale hydrological model to identify, assess, and map 16 different streamflow metrics that could be used to describe flood risks across 34,987 HUC12 subwatersheds within the Mississippi-Atchafalaya River Basin (MARB). A clear spatial difference was observed among two different classes of metrics. Watersheds in the eastern half of the MARB exhibited higher overall flows as characterized by the mean, median, and maximum daily values, whereas western MARB watersheds were associated with flood indicative of high extreme flows such as skewness, standardized streamflow index and top days. Total agricultural and building losses within HUC12 watersheds were related to flood metrics and those focused on higher overall flows were more correlated to expected annual losses (EAL) than extreme value metrics. Results from this study are useful for identifying continental scale patterns of flood risks within the MARB and should be considered a launching point from which to improve the connections between watershed scale risks and the potential use of natural infrastructure practices to reduce these risks.

Comparison of DNA methylation based classification models for precision diagnostics of central nervous system tumors

As part of the advancement in therapeutic decision-making for brain tumor patients at St. Jude Children’s Research Hospital (SJCRH), we developed three robust classifiers, a deep learning neural network (NN), k-nearest neighbor (kNN), and random forest (RF), trained on a reference series DNA-methylation profiles to classify central nervous system (CNS) tumor types. The models’ performance was rigorously validated against 2054 samples from two independent cohorts. In addition to classic metrics of model performance, we compared the robustness of the three models to reduced tumor purity, a critical consideration in the clinical utility of such classifiers. Our findings revealed that the NN model exhibited the highest accuracy and maintained a balance between precision and recall. The NN model was the most resistant to drops in performance associated with a reduction in tumor purity, showing good performance until the purity fell below 50%. Through rigorous validation, our study emphasizes the potential of DNA-methylation-based deep learning methods to improve precision medicine for brain tumor classification in the clinical setting.

B-117 Rapid Classification of Cleanliness Grades of Vaginal Discharge through Computational Analysis of SERS Spectra via Variational Auto-Encoder Model And Long Short-Term Memory Networks

Abstract Background Classification of cleanliness grades of vaginal discharge plays a pivotal role in clinical laboratories, serving as indicators for the presence of various vaginal infections such as bacterial vaginosis and candidal vulvovaginitis, etc. The conventional method for assessing vaginal discharge cleanliness involves manual microscopy, a technique susceptible to variations based on the examiner's expertise and subjective judgment, hindering the attainment of swift and accurate diagnoses. Methods This study introduces a novel approach by integrating Surface-Enhanced Raman Spectroscopy (SERS) with a deep learning algorithm for the rapid classification of vaginal discharge cleanliness grades. The proposed classification method combines the Variational Auto-Encoder (VAE) and Long Short-Term Memory (LSTM) to process SERS spectra. The quality of the training data is assessed using the signal-to-noise ratio (SNR) as a standard indicator. Results The application of the VAE-LSTM algorithm significantly enhances classification performance, providing swift and accurate results while reducing the required time. Comparative analyses with various classical machine learning algorithms and evaluation metrics reveal the superior predictive capability and time efficiency of the VAE-LSTM algorithm, demonstrating 100% accuracy and a fitting time of 2 seconds. Blind testing of SERS spectra collected from unknown patients further validates the reliability of the proposed method. Conclusions This study presents a promising and practical approach for the rapid classification of vaginal discharge cleanliness grades. The integration of the SERS technique with the VAE-LSTM algorithm not only ensures accuracy and efficiency in clinical diagnosis but also lays the foundation for advancements in non-invasive diagnostic technologies in gynecological healthcare.

Generative language models on nucleotide sequences of human genes.

Language models, especially transformer-based ones, have achieved colossal success in natural language processing. To be precise, studies like BERT for natural language understanding and works like GPT-3 for natural language generation are very important. If we consider DNA sequences as a text written with an alphabet of four letters representing the nucleotides, they are similar in structure to natural languages. This similarity has led to the development of discriminative language models such as DNABERT in the field of DNA-related bioinformatics. To our knowledge, however, the generative side of the coin is still largely unexplored. Therefore, we have focused on the development of an autoregressive generative language model such as GPT-3 for DNA sequences. Since working with whole DNA sequences is challenging without extensive computational resources, we decided to conduct our study on a smaller scale and focus on nucleotide sequences of human genes, i.e. unique parts of DNA with specific functions, rather than the whole DNA. This decision has not significantly changed the structure of the problem, as both DNA and genes can be considered as 1D sequences consisting of four different nucleotides without losing much information and without oversimplification. First of all, we systematically studied an almost entirely unexplored problem and observed that recurrent neural networks (RNNs) perform best, while simple techniques such as N-grams are also promising. Another beneficial point was learning how to work with generative models on languages we do not understand, unlike natural languages. The importance of using real-world tasks beyond classical metrics such as perplexity was noted. In addition, we examined whether the data-hungry nature of these models can be altered by selecting a language with minimal vocabulary size, four due to four different types of nucleotides. The reason for reviewing this was that choosing such a language might make the problem easier. However, in this study, we found that this did not change the amount of data required very much.

Discretization and quantification for distributionally robust optimization with decision-dependent ambiguity sets

ABSTRACT In this paper, we investigate the discrete approximation and the quantitative analysis for a class of the distributionally robust optimization problems with decision-dependent ambiguity sets. We establish the local Lipschitz continuity of the decision-dependent ambiguity set, measured by the Hausdorff distance, under a broad class of metrics known as ζ-structure and the Slater condition. Furthermore, we employ Lagrange duality and first-order growth conditions to derive quantitative analysis for the optimal value and optimal solution. We also examine the application of a classical and widely-used ambiguity set within the theoretical framework of this paper. Finally, we conduct experiments to demonstrate the computational times and variations in the optimal value.

Approximation schemes for Min-Sum [formula omitted]-Clustering

We consider the Min-Sum k-Clustering (k-MSC) problem. Given a set of points in a metric which is represented by an edge-weighted graph G=(V,E) and a parameter k, the goal is to partition the points V into k clusters such that the sum of distances between all pairs of the points within the same cluster is minimized.The k-MSC problem is known to be APX-hard on general metrics. The best known approximation algorithms for the problem obtained by Behsaz et al. (2019) achieve an approximation ratio of O(log|V|) in polynomial time for general metrics and an approximation ratio 2+ϵ in quasi-polynomial time for metrics with bounded doubling dimension. No approximation schemes for k-MSC (when k is part of the input) is known for any non-trivial metrics prior to our work. In fact, most of the previous works rely on the simple fact that there is a 2-approximate reduction from k-MSC to the balanced k-median problem and design approximation algorithms for the latter to obtain an approximation for k-MSC.In this paper, we obtain the first Quasi-Polynomial Time Approximation Schemes (QPTAS) for the problem on metrics induced by graphs of bounded treewidth, graphs of bounded highway dimension, graphs of bounded doubling dimensions (including fixed dimensional Euclidean metrics), and planar and minor-free graphs. We bypass the barrier of 2 for k-MSC by introducing a new clustering problem, which we call min-hub clustering, which is a generalization of balanced k-median and is a trade off between center-based clustering problems (such as balanced k-median) and pair-wise clustering (such as Min-Sum k-clustering). We then show how one can find approximation schemes for Min-hub clustering on certain classes of metrics.

A novel profit-driven framework for model evaluation in credit scoring

Credit scoring is a prominent problem in machine learning (ML). ML classifiers used to assess creditworthiness need to be evaluated using appropriate metrics. Common metrics fall into two categories: cost-sensitive and traditional cost-insensitive. Traditional cost-insensitive metrics like accuracy and area under the curve (AUC) have several drawbacks. They can be difficult for managers to understand, potentially misleading in certain scenarios, and often overlook the business realities of credit scoring. Conversely, existing cost-sensitive metrics are imperfect, leading many studies to rely on classic AUC metrics. In this study, we introduce the expected profit ratio (EPR), a novel framework for evaluating classifiers in credit scoring. EPR does not require a base scenario and accurately calculates the profit. Its flexibility makes it suitable for all types of credit-scoring problems, and its simplicity aids in comprehension and explanation. By enabling accurate profit calculation, EPR helps managers, executives, and administrators make informed decisions and investments. This metric lays the foundation for more sophisticated and precise model evaluation and comparison in credit scoring. Additionally, it can be used as a performance measure, alongside fairness and other criteria needed to achieve trustworthy artificial intelligence (AI).

Metric Mean Dimension and Mean Hausdorff Dimension Varying the Metric

Let f:M→M\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$f:\\mathbb {M}\\rightarrow \\mathbb {M}$$\\end{document} be a continuous map on a compact metric space M\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathbb {M}$$\\end{document} equipped with a fixed metric d, and let τ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ au $$\\end{document} be the topology on M\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathbb {M}$$\\end{document} induced by d. We denote by M(τ)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathbb {M}(\ au )$$\\end{document} the set consisting of all metrics on M\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathbb {M}$$\\end{document} that are equivalent to d. Let mdimM(M,d,f)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \ ext {mdim}_{\ ext {M}}(\\mathbb {M},d, f)$$\\end{document} and mdimH(M,d,f)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \ ext {mdim}_{\ ext {H}} (\\mathbb {M},d, f)$$\\end{document} be, respectively, the metric mean dimension and mean Hausdorff dimension of f. First, we will establish some fundamental properties of the mean Hausdorff dimension. Furthermore, it is important to note that mdimM(M,d,f)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \ ext {mdim}_{\ ext {M}}(\\mathbb {M},d, f)$$\\end{document} and mdimH(M,d,f)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \ ext {mdim}_{\ ext {H}} (\\mathbb {M},d, f)$$\\end{document} depend on the metric d chosen for M\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathbb {M}$$\\end{document}. In this work, we will prove that, for a fixed dynamical system f:M→M\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$f:\\mathbb {M}\\rightarrow \\mathbb {M}$$\\end{document}, the functions mdimM(M,f):M(τ)→R∪{∞}\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ ext {mdim}_{\ ext {M}} (\\mathbb {M}, f):\\mathbb {M}(\ au )\\rightarrow \\mathbb {R}\\cup \\{\\infty \\}$$\\end{document} and mdimH(M,f):M(τ)→R∪{∞}\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \ ext {mdim}_{\ ext {H}}(\\mathbb {M}, f): \\mathbb {M}(\ au )\\rightarrow \\mathbb {R}\\cup \\{\\infty \\}$$\\end{document} are not continuous, where mdimM(M,f)(ρ)=mdimM(M,ρ,f)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \ ext {mdim}_{\ ext {M}}(\\mathbb {M}, f) (\\rho )= \ ext {mdim}_{\ ext {M}} (\\mathbb {M},\\rho , f)$$\\end{document} and mdimH(M,f)(ρ)=mdimH(M,ρ,f)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \ ext {mdim}_{\ ext {H}}(\\mathbb {M}, f) (\\rho )= \ ext {mdim}_{\ ext {H}} (\\mathbb {M},\\rho , f)$$\\end{document} for any ρ∈M(τ)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\rho \\in \\mathbb {M}(\ au )$$\\end{document}. Furthermore, we will present examples of certain classes of metrics for which the metric mean dimension is a continuous function.

DES-AS: Dynamic ensemble selection based on algorithm Shapley

Dynamic ensemble selection (DES) effectively improves aggregation performance by dynamically finding the most appropriate subset of classifiers for each query sample. The key component of this strategy is to define an appropriate criterion for evaluating the competence of the candidate classifiers. In this study, we present a new group-based criterion, synergy competence, to comprehensively measure the magnitude of the intricate synergy effect among classifiers. In addition, we introduce the algorithm Shapley, a variant of the Shapley value (SV) in the game theory, to measure the synergy competence of each classifier, which helps in the construction of a synergy-based DES system, called DES-AS. We argue that candidate classifiers with positive algorithm Shapley should be selected as they contribute to the ensemble. After selecting a subset of classifiers, the normalized algorithm Shapley is employed to calculate the voting weights for a cooperative final classification decision. The experimental analyses conducted on forty real-world datasets not only indicate that the synergy competence estimated by the algorithm Shapley is more applicable than classic group-based metrics, but also show that DES-AS is substantially more effective and robust than state-of-the-art models. The statistical test results also indicate that the estimated synergy competence reflects the real competence of each classifier better than the baseline models.

VCC-DiffNet: Visual Conditional Control Diffusion Network for Remote Sensing Image Captioning

Pioneering remote sensing image captioning (RSIC) works use autoregressive decoding for fluent and coherent sentences but suffer from high latency and high computation costs. In contrast, non-autoregressive approaches improve inference speed by predicting multiple tokens simultaneously, though at the cost of performance due to a lack of sequential dependencies. Recently, diffusion model-based non-autoregressive decoding has shown promise in natural image captioning with iterative refinement, but its effectiveness is limited by the intrinsic characteristics of remote sensing images, which complicate robust input construction and affect the description accuracy. To overcome these challenges, we propose an innovative diffusion model for RSIC, named the Visual Conditional Control Diffusion Network (VCC-DiffNet). Specifically, we propose a Refined Multi-scale Feature Extraction (RMFE) module to extract the discernible visual context features of RSIs as input of the diffusion model-based non-autoregressive decoder to conditionally control a multi-step denoising process. Furthermore, we propose an Interactive Enhanced Decoder (IE-Decoder) utilizing dual image–description interactions to generate descriptions finely aligned with the image content. Experiments conducted on four representative RSIC datasets demonstrate that our non-autoregressive VCC-DiffNet performs comparably to, or even better than, popular autoregressive baselines in classic metrics, achieving around an 8.22× speedup in Sydney-Captions, an 11.61× speedup in UCM-Captions, a 15.20× speedup in RSICD, and an 8.13× speedup in NWPU-Captions.

Romberg's test revisited: Changes in classical and advanced sway metrics in patients with pure sensory neuropathy

ObjectivesThe Romberg test, undoubtedly a classical and well-established method in physical neurological assessment of patients with sensory ataxia, has long been suspected to be prone to several limitations. Here, we quantified upright stance before and after visual deprivation in a selected cohort of patients with pure sensory neuropathy. MethodsStatic balance was assessed in sensory neuropathy patients during quiet stance on a force platform under different visual and proprioceptive feedback conditions. Sural nerve neurography was employed to evaluate the severity of peripheral neuropathy. Conventional and advanced postural sway metrics were investigated to draw a quantitative analogy to the clinical Romberg test. ResultsPosturographic analyses showed that patients displayed Romberg and vestibular Romberg quotient values around 2, indicating an approximately twofold increase in body sway in the absence of vision. However, the diagnostic discrimination ability between patients and controls was only modest. Even less impactful were the diagnostic contributions of frequency domain and non-linear sway analyses. This was primarily attributed to the heightened body sway exhibited by patients with sensory neuropathy under 'eyes open' conditions, diminishing the contrast with the 'eyes closed' condition as assessed in the classical Romberg test. ConclusionWe conclude that the Romberg test, even in its quantitative form with the aid of an apparatus, had an unsatisfactory classification value in terms of distinguishing patients from healthy controls. Instead, it should be interpreted within the comprehensive context of the broader neurological examination and the electrodiagnosis of peripheral nerve function.

Octonionic Calabi–Yau Theorem

On a certain class of 16-dimensional manifolds a new class of Riemannian metrics, called octonionic Kähler, is introduced and studied. It is an octonionic analogue of Kähler metrics on complex manifolds and of HKT-metrics of hypercomplex manifolds. Then for this class of metrics an octonionic version of the Monge–Ampère equation is introduced and solved under appropriate assumptions. The latter result is an octonionic version of the Calabi–Yau theorem from Kähler geometry.

Topological AdS black holes surrounded by Chaplygin dark fluid: From stability to geometrothermodynamic analysis

Implementing the concept of Dark Fluid with a Chaplygin-like equation of state within General Relativity, we construct a new higher-dimensional, static, and spherically symmetric anti-de Sitter (AdS) black hole solution. Energy conditions are explored alongside curvature singularity tools. The inspection at the level of the phase structure and P−v critical behavior is carried out in the context of the extended phase space, where the cosmological constant appears as pressure. Our findings disclose non-trivial similarities between the small/large phase transition of AdS black holes surrounded by Chaplygin dark fluid and van der Waals systems’ liquid/gas phase transition. This analysis offers insights into the physical interpretation of the P−v diagram and identifies critical exponents that reveal the scaling behavior of thermodynamic quantities close to criticality in a universal manner. We finally deepen our understanding of the thermodynamic properties and microstructure of AdS black holes by leveraging the geometrothermodynamic formalism. Specifically, we employ tools, including Weinhold, Ruppeiner, Hendi–Panahiyan–Eslam–Momennia (HPEM), and Quevedo classes I and II. We show that each class of metrics predicts either the physical limitation point and/or the phase-transition critical points, with HPEM and Quevedo formulations providing richer information about the phase transitions. Altogether, this study contributes to advancing our knowledge of the role of Chaplygin gas in General Relativity and thoroughly examining the thermodynamic phase structure of high-dimensional AdS black holes under extreme conditions.

Examples of cosmological spacetimes without CMC Cauchy surfaces

CMC (constant mean curvature) Cauchy surfaces play an important role in mathematical relativity as finding solutions to the vacuum Einstein constraint equations is made much simpler by assuming CMC initial data. However, Bartnik (Commun Math Phys 117(4):615–624, 1988) constructed a cosmological spacetime without a CMC Cauchy surface whose spatial topology is the connected sum of two three-dimensional tori. Similarly, Chruściel et al. (Commun Math Phys 257(1):29–42, 2005) constructed a vacuum cosmological spacetime without CMC Cauchy surfaces whose spatial topology is also the connected sum of two tori. In this article, we enlarge the known number of spatial topologies for cosmological spacetimes without CMC Cauchy surfaces by generalizing Bartnik’s construction. Specifically, we show that there are cosmological spacetimes without CMC Cauchy surfaces whose spatial topologies are the connected sum of any compact Euclidean or hyperbolic three-manifold with any another compact Euclidean or hyperbolic three-manifold. Analogous examples in higher spacetime dimensions are also possible. We work with the Tolman–Bondi class of metrics and prove gluing results for variable marginal conditions, which allows for smooth gluing of Schwarzschild to FLRW models.

Evaluation Metrics for Generative Models: An Empirical Study

Generative models such as generative adversarial networks, diffusion models, and variational auto-encoders have become prevalent in recent years. While it is true that these models have shown remarkable results, evaluating their performance is challenging. This issue is of vital importance to push research forward and identify meaningful gains from random noise. Currently, heuristic metrics such as the inception score (IS) and Fréchet inception distance (FID) are the most common evaluation metrics, but what they measure is not entirely clear. Additionally, there are questions regarding how meaningful their score actually is. In this work, we propose a novel evaluation protocol for likelihood-based generative models, based on generating a high-quality synthetic dataset on which we can estimate classical metrics for comparison. This new scheme harnesses the advantages of knowing the underlying likelihood values of the data by measuring the divergence between the model-generated data and the synthetic dataset. Our study shows that while FID and IS correlate with several f-divergences, their ranking of close models can vary considerably, making them problematic when used for fine-grained comparison. We further use this experimental setting to study which evaluation metric best correlates with our probabilistic metrics.

Polynomial Equivalence of Complexity Geometries

This paper proves the polynomial equivalence of a broad class of definitions of quantum computational complexity. We study right-invariant metrics on the unitary group—often called `complexity geometries' following the definition of quantum complexity proposed by Nielsen—and delineate the equivalence class of metrics that have the same computational power as quantum circuits. Within this universality class, any unitary that can be reached in one metric can be approximated in any other metric in the class with a slowdown that is at-worst polynomial in the length and number of qubits and inverse-polynomial in the permitted error. We describe the equivalence classes for two different kinds of error we might tolerate: Killing-distance error, and operator-norm error. All metrics in both equivalence classes are shown to have exponential diameter; all metrics in the operator-norm equivalence class are also shown to give an alternative definition of the quantum complexity class BQP. My results extend those of Nielsen et al., who in 2006 proved that one particular metric is polynomially equivalent to quantum circuits. The Nielsen et al. metric is incredibly highly curved. I show that the greatly enlarged equivalence class established in this paper also includes metrics that have modest curvature. I argue that the modest curvature makes these metrics more amenable to the tools of differential geometry, and therefore makes them more promising starting points for Nielsen's program of using differential geometry to prove complexity lowerbounds. In a previous paper my collaborators and I—inspired by the UV/IR decoupling that happens in the phenomenon of renormalization—conjectured that high- dimensional metrics that look very different at short scales will often nevertheless give rise at long scales to the same emergent effective geometry. The results of this paper provide evidence for those conjectures, since many complexity metrics that have radically different penalty factors and therefore radically different short- distance properties are shown to belong to the same long-distance equivalence class.

Phytochemical drivers of insect herbivory: a functional toolbox to support agroecological diversification.

Plant metabolism is a key feature of biodiversity that remains underexploited in functional frameworks used in agroecology. Here, we study how phytochemical diversity considered at three organizational levels can promote pest control. In a factorial field experiment, we manipulated plant diversity in three monocultures and three mixed crops of oilseed rape to explore how intra- and interspecific phytochemical diversity affects pest infestation. We combined recent progress in metabolomics with classic metrics used in ecology to test a box of hypotheses grounded in plant defence theory. According to the hypothesis of 'phytochemically mediated coevolution', our study stresses the relationships between herbivore infestation and particular classes of specialized metabolites like glucosinolates. Among 178 significant relationships between metabolites and herbivory rates, only 20% were negative. At the plant level, phytochemical abundance and richness had poor predictive power on pest regulation. This challenges the hypothesis of 'synergistic effects'. At the crop cover level, in line with the hypothesis of 'associational resistance', the phytochemical dissimilarity between neighbouring plants limited pest infestation. We discuss the intricate links between associational resistance and bottom-up pest control. Bridging different levels of organization in agroecosystems helps to dissect the multi-scale relationships between phytochemistry and insect herbivory.