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At the University of Rhode Island (URI), the URI Open Access Fund Committee met in early 2024 to advise the Provost and Executive Vice President for Academic Affairs on the continuation of the URI Open Access Fund. The URI Open Access Fund was created in 2013 to reimburse URI authors for Article Processing Charges when they published in qualifying Open Access journals and had no other funding available. The committee examined the current Open Access publishing landscape and consulted with two other institutions on their practices. The report of the committee offers the following six recommendations: 1) The URI Open Access Fund should be retired; 2) Hire a Scholarly Communications Librarian to educate faculty on options for making their work open access, on article-level metrics, demonstrating and enhancing the impact of their scholarship, etc.; 3) Encourage URI faculty to make their articles open access by depositing their manuscripts in DigitalCommons@URI in compliance with the URI Open Access Policy; 4) Continue to support Diamond OA initiatives and Subscribe to Open options that provide OA with no author-facing charges and offer alternatives to the large, for-profit academic publishers; 5) Consider support for the membership models of fully open access publishers, e.g. PLoS, MDPI, Frontiers; and 6) Consider participating in Transformative Agreements through consortia such as Lyrasis. A short bibliography is included.

Image classification models, including convolutional neural networks (CNNs), perform well on a variety of classification tasks but struggle under conditions of partial occlusion, i.e., conditions in which objects are partially covered from the view of a camera. Methods to improve performance under occlusion, including data augmentation, part-based clustering, and more inherently robust architectures, including Vision Transformer (ViT) models, have, to some extent, been evaluated on their ability to classify objects under partial occlusion. However, evaluations of these methods have largely relied on images containing artificial occlusion, which are typically computer-generated and therefore inexpensive to label. Additionally, methods are rarely compared against each other, and many methods are compared against early, now outdated, deep learning models. We contribute the Image Recognition Under Occlusion (IRUO) dataset, based on the recently developed Occluded Video Instance Segmentation (OVIS) dataset (arXiv:2102.01558). IRUO utilizes real-world and artificially occluded images to test and benchmark leading methods' robustness to partial occlusion in visual recognition tasks. In addition, we contribute the design and results of a human study using images from IRUO that evaluates human classification performance at multiple levels and types of occlusion. We find that modern CNN-based models show improved recognition accuracy on occluded images compared to earlier CNN-based models, and ViT-based models are more accurate than CNN-based models on occluded images, performing only modestly worse than human accuracy. We also find that certain types of occlusion, including diffuse occlusion, where relevant objects are seen through "holes" in occluders such as fences and leaves, can greatly reduce the accuracy of deep recognition models as compared to humans, especially those with CNN backbones.

Generative models unfairly penalize data belonging to minority classes, suffer from model autophagy disorder (MADness), and learn biased estimates of the underlying distribution parameters. Our theoretical and empirical results show that training generative models with intentionally designed hypernetworks leads to models that 1) are more fair when generating datapoints belonging to minority classes 2) are more stable in a self-consumed (i.e., MAD) setting, and 3) learn parameters that are less statistically biased. To further mitigate unfairness, MADness, and bias, we introduce a regularization term that penalizes discrepancies between a generative model's estimated weights when trained on real data versus its own synthetic data. To facilitate training existing deep generative models within our framework, we offer a scalable implementation of hypernetworks that automatically generates a hypernetwork architecture for any given generative model.

The rapid advancement of Generative Adversarial Networks (GANs) necessitates the need to robustly evaluate these models. Among the established evaluation criteria, the Fr\'{e}chetInception Distance (FID) has been widely adopted due to its conceptual simplicity, fast computation time, and strong correlation with human perception. However, FID has inherent limitations, mainly stemming from its assumption that feature embeddings follow a Gaussian distribution, and therefore can be defined by their first two moments. As this does not hold in practice, in this paper we explore the importance of third-moments in image feature data and use this information to define a new measure, which we call the Skew Inception Distance (SID). We prove that SID is a pseudometric on probability distributions, show how it extends FID, and present a practical method for its computation. Our numerical experiments support that SID either tracks with FID or, in some cases, aligns more closely with human perception when evaluating image features of ImageNet data. Our work also shows that principal component analysis can be used to speed up the computation time of both FID and SID. Although we focus on using SID on image features for GAN evaluation, SID is applicable much more generally, including for the evaluation of other generative models.

Seismic advances in generative AI algorithms for imagery, text, and other data types has led to the temptation to use synthetic data to train next-generation models. Repeating this process creates an autophagous (self-consuming) loop whose properties are poorly understood. We conduct a thorough analytical and empirical analysis using state-of-the-art generative image models of three families of autophagous loops that differ in how fixed or fresh real training data is available through the generations of training and in whether the samples from previous generation models have been biased to trade off data quality versus diversity. Our primary conclusion across all scenarios is that without enough fresh real data in each generation of an autophagous loop, future generative models are doomed to have their quality (precision) or diversity (recall) progressively decrease. We term this condition Model Autophagy Disorder (MAD), making analogy to mad cow disease., Comment: 31 pages, 31 figures, pre-print

Recently, the first foundation model developed specifically for image segmentation tasks was developed, termed the "Segment Anything Model" (SAM). SAM can segment objects in input imagery based on cheap input prompts, such as one (or more) points, a bounding box, or a mask. The authors examined the \textit{zero-shot} image segmentation accuracy of SAM on a large number of vision benchmark tasks and found that SAM usually achieved recognition accuracy similar to, or sometimes exceeding, vision models that had been trained on the target tasks. The impressive generalization of SAM for segmentation has major implications for vision researchers working on natural imagery. In this work, we examine whether SAM's performance extends to overhead imagery problems and help guide the community's response to its development. We examine SAM's performance on a set of diverse and widely studied benchmark tasks. We find that SAM does often generalize well to overhead imagery, although it fails in some cases due to the unique characteristics of overhead imagery and its common target objects. We report on these unique systematic failure cases for remote sensing imagery that may comprise useful future research for the community., Comment: Work accepted at WACV 2024, this is only a pre-print, please go to WACV website for the official version

Recent object detection models for infrared (IR) imagery are based upon deep neural networks (DNNs) and require large amounts of labeled training imagery. However, publicly available datasets that can be used for such training are limited in their size and diversity. To address this problem, we explore cross-modal style transfer (CMST) to leverage large and diverse color imagery datasets so that they can be used to train DNN-based IR image-based object detectors. We evaluate six contemporary stylization methods on four publicly-available IR datasets - the first comparison of its kind - and find that CMST is highly effective for DNN-based detectors. Surprisingly, we find that existing data-driven methods are outperformed by a simple grayscale stylization (an average of the color channels). Our analysis reveals that existing data-driven methods are either too simplistic or introduce significant artifacts into the imagery. To overcome these limitations, we propose meta-learning style transfer (MLST), which learns a stylization by composing and tuning well-behaved analytic functions. We find that MLST leads to more complex stylizations without introducing significant image artifacts and achieves the best overall detector performance on our benchmark datasets., Comment: This paper has been accepted to WACV 2025

We study the generalization behavior of transfer learning of deep neural networks (DNNs). We adopt the overparameterization perspective -- featuring interpolation of the training data (i.e., approximately zero train error) and the double descent phenomenon -- to explain the delicate effect of the transfer learning setting on generalization performance. We study how the generalization behavior of transfer learning is affected by the dataset size in the source and target tasks, the number of transferred layers that are kept frozen in the target DNN training, and the similarity between the source and target tasks. We show that the test error evolution during the target DNN training has a more significant double descent effect when the target training dataset is sufficiently large. In addition, a larger source training dataset can yield a slower target DNN training. Moreover, we demonstrate that the number of frozen layers can determine whether the transfer learning is effectively underparameterized or overparameterized and, in turn, this may induce a freezing-wise double descent phenomenon that determines the relative success or failure of learning. Also, we show that the double descent phenomenon may make a transfer from a less related source task better than a transfer from a more related source task. We establish our results using image classification experiments with the ResNet, DenseNet and the vision transformer (ViT) architectures.

We study the interpolation capabilities of implicit neural representations (INRs) of images. In principle, INRs promise a number of advantages, such as continuous derivatives and arbitrary sampling, being freed from the restrictions of a raster grid. However, empirically, INRs have been observed to poorly interpolate between the pixels of the fit image; in other words, they do not inherently possess a suitable prior for natural images. In this paper, we propose to address and improve INRs' interpolation capabilities by explicitly integrating image prior information into the INR architecture via deep decoder, a specific implementation of the deep image prior (DIP). Our method, which we call TITAN, leverages a residual connection from the input which enables integrating the principles of the grid-based DIP into the grid-free INR. Through super-resolution and computed tomography experiments, we demonstrate that our method significantly improves upon classic INRs, thanks to the induced natural image bias. We also find that by constraining the weights to be sparse, image quality and sharpness are enhanced, increasing the Lipschitz constant., Comment: 6 pages, 4 figures

There is evidence that transformers offer state-of-the-art recognition performance on tasks involving overhead imagery (e.g., satellite imagery). However, it is difficult to make unbiased empirical comparisons between competing deep learning models, making it unclear whether, and to what extent, transformer-based models are beneficial. In this paper we systematically compare the impact of adding transformer structures into state-of-the-art segmentation models for overhead imagery. Each model is given a similar budget of free parameters, and their hyperparameters are optimized using Bayesian Optimization with a fixed quantity of data and computation time. We conduct our experiments with a large and diverse dataset comprising two large public benchmarks: Inria and DeepGlobe. We perform additional ablation studies to explore the impact of specific transformer-based modeling choices. Our results suggest that transformers provide consistent, but modest, performance improvements. We only observe this advantage however in hybrid models that combine convolutional and transformer-based structures, while fully transformer-based models achieve relatively poor performance., Comment: This paper has been accepted to WACV 2023, but this is not the final version

The inference stage of diffusion models can be seen as running a reverse-time diffusion stochastic differential equation, where samples from a Gaussian latent distribution are transformed into samples from a target distribution that usually reside on a low-dimensional manifold, e.g., an image manifold. The intermediate values between the initial latent space and the image manifold can be interpreted as noisy images, with the amount of noise determined by the forward diffusion process noise schedule. We utilize this interpretation to present Boomerang, an approach for local sampling of image manifolds. As implied by its name, Boomerang local sampling involves adding noise to an input image, moving it closer to the latent space, and then mapping it back to the image manifold through a partial reverse diffusion process. Thus, Boomerang generates images on the manifold that are ``similar,'' but nonidentical, to the original input image. We can control the proximity of the generated images to the original by adjusting the amount of noise added. Furthermore, due to the stochastic nature of the reverse diffusion process in Boomerang, the generated images display a certain degree of stochasticity, allowing us to obtain local samples from the manifold without encountering any duplicates. Boomerang offers the flexibility to work seamlessly with any pretrained diffusion model, such as Stable Diffusion, without necessitating any adjustments to the reverse diffusion process. We present three applications for Boomerang. First, we provide a framework for constructing privacy-preserving datasets having controllable degrees of anonymity. Second, we show that using Boomerang for data augmentation increases generalization performance and outperforms state-of-the-art synthetic data augmentation. Lastly, we introduce a perceptual image enhancement framework, which enables resolution enhancement., Comment: Published in Transactions on Machine Learning Research

Deep neural networks have become essential for numerous applications due to their strong empirical performance such as vision, RL, and classification. Unfortunately, these networks are quite difficult to interpret, and this limits their applicability in settings where interpretability is important for safety, such as medical imaging. One type of deep neural network is neural tangent kernel that is similar to a kernel machine that provides some aspect of interpretability. To further contribute interpretability with respect to classification and the layers, we develop a new network as a combination of multiple neural tangent kernels, one to model each layer of the deep neural network individually as opposed to past work which attempts to represent the entire network via a single neural tangent kernel. We demonstrate the interpretability of this model on two datasets, showing that the multiple kernels model elucidates the interplay between the layers and predictions.

We develop a measure for evaluating the performance of generative networks given two sets of images. A popular performance measure currently used to do this is the Fr\'echet Inception Distance (FID). FID assumes that images featurized using the penultimate layer of Inception-v3 follow a Gaussian distribution, an assumption which cannot be violated if we wish to use FID as a metric. However, we show that Inception-v3 features of the ImageNet dataset are not Gaussian; in particular, every single marginal is not Gaussian. To remedy this problem, we model the featurized images using Gaussian mixture models (GMMs) and compute the 2-Wasserstein distance restricted to GMMs. We define a performance measure, which we call WaM, on two sets of images by using Inception-v3 (or another classifier) to featurize the images, estimate two GMMs, and use the restricted $2$-Wasserstein distance to compare the GMMs. We experimentally show the advantages of WaM over FID, including how FID is more sensitive than WaM to imperceptible image perturbations. By modelling the non-Gaussian features obtained from Inception-v3 as GMMs and using a GMM metric, we can more accurately evaluate generative network performance.

We study overparameterization in generative adversarial networks (GANs) that can interpolate the training data. We show that overparameterization can improve generalization performance and accelerate the training process. We study the generalization error as a function of latent space dimension and identify two main behaviors, depending on the learning setting. First, we show that overparameterized generative models that learn distributions by minimizing a metric or $f$-divergence do not exhibit double descent in generalization errors; specifically, all the interpolating solutions achieve the same generalization error. Second, we develop a novel pseudo-supervised learning approach for GANs where the training utilizes pairs of fabricated (noise) inputs in conjunction with real output samples. Our pseudo-supervised setting exhibits double descent (and in some cases, triple descent) of generalization errors. We combine pseudo-supervision with overparameterization (i.e., overly large latent space dimension) to accelerate training while matching or even surpassing generalization performance without pseudo-supervision. While our analysis focuses mostly on linear models, we also apply important insights for improving generalization of nonlinear, multilayer GANs.

High dimensionality poses many challenges to the use of data, from visualization and interpretation, to prediction and storage for historical preservation. Techniques abound to reduce the dimensionality of fixed-length sequences, yet these methods rarely generalize to variable-length sequences. To address this gap, we extend existing methods that rely on the use of kernels to variable-length sequences via use of the Recurrent Neural Tangent Kernel (RNTK). Since a deep neural network with ReLu activation is a Max-Affine Spline Operator (MASO), we dub our approach Max-Affine Spline Kernel (MASK). We demonstrate how MASK can be used to extend principal components analysis (PCA) and t-distributed stochastic neighbor embedding (t-SNE) and apply these new algorithms to separate synthetic time series data sampled from second-order differential equations.

Most current computer vision datasets are composed of disconnected sets, such as images from different classes. We prove that distributions of this type of data cannot be represented with a continuous generative network without error. They can be represented in two ways: With an ensemble of networks or with a single network with truncated latent space. We show that ensembles are more desirable than truncated distributions in practice. We construct a regularized optimization problem that establishes the relationship between a single continuous GAN, an ensemble of GANs, conditional GANs, and Gaussian Mixture GANs. This regularization can be computed efficiently, and we show empirically that our framework has a performance sweet spot which can be found with hyperparameter tuning. This ensemble framework allows better performance than a single continuous GAN or cGAN while maintaining fewer total parameters.

We study the linear subspace fitting problem in the overparameterized setting, where the estimated subspace can perfectly interpolate the training examples. Our scope includes the least-squares solutions to subspace fitting tasks with varying levels of supervision in the training data (i.e., the proportion of input-output examples of the desired low-dimensional mapping) and orthonormality of the vectors defining the learned operator. This flexible family of problems connects standard, unsupervised subspace fitting that enforces strict orthonormality with a corresponding regression task that is fully supervised and does not constrain the linear operator structure. This class of problems is defined over a supervision-orthonormality plane, where each coordinate induces a problem instance with a unique pair of supervision level and softness of orthonormality constraints. We explore this plane and show that the generalization errors of the corresponding subspace fitting problems follow double descent trends as the settings become more supervised and less orthonormally constrained.

The effective quantum dynamics of Bianchi I spacetime is addressed within the statistical regularization scheme in Quantum Reduced Loop Gravity. The case of a minimally coupled massless scalar field is studied and compared with the effective $\bar{\mu}-$Loop Quantum Cosmology. The dynamics provided by the two approaches match in the semiclassical limit but differ significantly after the bounces. Analytical and numerical inspections show that energy density, expansion scalar and shear are bounded also in Quantum Reduced Loop Gravity and the classical singularity is resolved for generic initial conditions in all spatial directions., Comment: 19 pages, 23 figures, 1 table

While long short-term memory (LSTM) neural net architectures are designed to capture sequence information, human language is generally composed of hierarchical structures. This raises the question as to whether LSTMs can learn hierarchical structures. We explore this question with a well-formed bracket prediction task using two types of brackets modeled by an LSTM. Demonstrating that such a system is learnable by an LSTM is the first step in demonstrating that the entire class of CFLs is also learnable. We observe that the model requires exponential memory in terms of the number of characters and embedded depth, where a sub-linear memory should suffice. Still, the model does more than memorize the training input. It learns how to distinguish between relevant and irrelevant information. On the other hand, we also observe that the model does not generalize well. We conclude that LSTMs do not learn the relevant underlying context-free rules, suggesting the good overall performance is attained rather by an efficient way of evaluating nuisance variables. LSTMs are a way to quickly reach good results for many natural language tasks, but to understand and generate natural language one has to investigate other concepts that can make more direct use of natural language's structural nature.

The finite volume correction for a mean-field monomer-dimer system with an attractive interaction are computed for the pressure density, the monomer density and the susceptibility. The results are obtained by introducing a two-dimensional integral representation for the partition function decoupling both the hard-core interaction and the attractive one. The next-to-leading terms for each of the mentioned quantities is explicitly derived as well as the value of their sign that is related to their monotonic convergence in the thermodynamic limit., Comment: 14 pages

The inverse problem method is tested for a class of monomer-dimer statistical mechanics models that contain also an attractive potential and display a mean-field critical point at a boundary of a coexistence line. The inversion is obtained by analytically identifying the parameters in terms of the correlation functions and via the maximum-likelihood method. The precision is tested in the whole phase space and, when close to the coexistence line, the algorithm is used together with a clustering method to take care of the underlying possible ambiguity of the inversion., Comment: 29 pages, 2 appendices, 13 figures

This study analyzes rates and ways of data sharing regarding mitochondrial, Y chromosomal and autosomal polymorphisms in a total of 162 papers on human ancient DNA published between 1988 and 2013. For the most part, data are available in such a way as to make their scrutiny and reuse possible. The estimated sharing rate is not far from totality (97.6% +/- 2.1%) and substantially higher than observed in other fields of genetic research (Evolutionary, Medical and Forensic Genetics). A questionnaire-based survey suggests that the authors awareness of the importance of openness and transparency for scientific progress is a fundamental factor for the achievement of such a high sharing rate. Most data were made available through body text, but the use of primary databases increased with the application of complete mitochondrial and next generation sequencing methods. Our study highlights three important aspects. First, we provide evidence that researchers motivations are as necessary as stakeholders policies and norms to achieve very high sharing rates. Second, careful analyses of the ways in which data are made available are an important first step to maximize data findability, accessibility, useability and preservation. Third and finally, the case of human ancient DNA studies demonstrates how Open Science can foster scientific advancements, showing that openness and transparency can help build rigorous and reliable scientific practices even in the presence of complex experimental challenges., Comment: 26 pages, 7 figures (1 supplementary), 6 Tables (5 supplementary of which 2 are available only upon request)

The demand of transparency of clinical research results, the need of accelerating the process of transferring innovation in the daily medical practice as well as assuring patient safety and product efficacy make it necessary to extend the functionality of traditional trial registries. These new systems should combine different functionalities to track the information exchange, support collaborative work, manage regulatory documents and monitor the entire clinical investigation (CIV) lifecycle. This is the approach used to develop MEDIS, a Medical Device Information System, described in this paper under the perspective of the business process, and the underlining architecture. Moreover, MEDIS was designed on the basis of Health Level 7 (HL7) v.3 standards and methodology to make it interoperable with similar registries, but also to facilitate information exchange between different health information systems., Comment: 16 pages, 1 table, 5 figures; International Journal of Computer Science & Information Technology (IJCSIT) Vol 4, No 6, December 2012

In this work a transformation acoustics scheme for generic elastic media is developed. Our approach starts form the decomposition of the elasticity tensor in terms of its eigentensors, an idea previously used by Norris. While Norris' transformation acoustics is restricted to the special class of so-called pentamode materials, we show that a similar scheme can be defined for the most general elasticity tensor. As in case of Norris' model (and in sharp contrast to transformation optics), the compatibility equations of the transformation medium are not purely algebraic and it is not guaranteed that solutions to these equations exist for any choice of material parameters and coordinate transformation. Nonetheless, it is shown that our scheme yields new cloaking solutions for certain classes of materials. In particular, we present the first application of a transformation based device for a non-scalar wave equation outside of the field of electromagnetics., Comment: 14 pages, LaTeX

The concept of transformation optics is extended to nonlinear electrodynamics. It is shown that transformation optics favors implicit constitutive relations in terms of energy densities D.E and B.H rather than E^2 and H^2. The Kerr nonlinearity is studied in detail and the transformation optics based engineering of self-interaction effects is discussed. As a specific example we introduce transformation optics applied on a self-focusing field configuration., Comment: 9 pages, 6 figures, REVTeX; v2: typo in affiliation corrected; v3: final version

The well-known TE/TM decomposition of time-harmonic electromagnetic fields in uniaxial anisotropic media is generalized in terms of four-dimensional differential-form formalism by requiring that the field two-form satisfies an orthogonality condition with respect to two given bivectors. Conditions for the electromagnetic medium in which such a decomposition is possible are derived and found to define three subclasses of media. It is shown that the previously known classes of generalized Q-media and generalized P-media are particular cases of the proposed decomposable media (DCM) associated to a quadratic equation for the medium dyadic. As a novel solution, another class of special decomposable media (SDCM) is defined by a linear dyadic equation. The paper further discusses the properties of medium dyadics and plane-wave propagation in all the identified cases of DCM and SDCM.

Based on a recent work by Schuller et al., a geometric representation of all skewonless, non-birefringent, linear media is obtained. The derived constitutive law is based on a "core", encoding the optical metric up to a constant. All further corrections are provided by two (anti-)selfdual bivectors, and an "axion". The bivectors are found to vanish if the optical metric has signature (3,1) - that is, if the Fresnel equation is hyperbolic. We propose applications of this result in the context of transformation optics and premetric electrodynamics., Comment: 12 pages, REVTeX; v2: typos; v3: relevant changes in text, reorganization of manuscript; v4: new section added, final version, to appear in Annalen der Physik

In this paper we show that a negative index of refraction is not a direct implication of transformation optics with orientation-reversing diffeomorphisms. Rather a negative index appears due to a specific choice of sign freedom. Furthermore, we point out that the transformation designed lens, which relies on the concept of spacetime folding, does not amplify evanescent modes, in contrast to the Pendry-Veselago lens. Instead, evanescent modes at the image point are produced by a duplicated source and thus no imaging of the near field (perfect lensing) takes place., Comment: 13 pages, 3 figures, LaTeX

Wolfgang Kummer was well known for his passion for axial gauges and for the formulation of gravity in terms of Cartan variables. The combination of the two applied to two dimensional dilaton gravity is the basis of the "Vienna School", which provided numerous significant results over the last seventeen years. In this review we trace the history of this success with particular emphasis on dilaton supergravity. We also present some previously unpublished results on the structure of non-local vertices in quantum dilaton supergravity with non-minimally coupled matter., Comment: 33 pages, Contribution to "Fundamental Interactions - A Memorial Volume for Wolfgang Kummer", to appear in World Scientific (v2: references added, v3: typos corrected)

Using the recently found first order formulation of two-dimensional dilaton gravity with boundary, we perform a Hamiltonian analysis and subsequent path integral quantization. The importance of the boundary terms to obtain the correct quantum result are outlined and the quantum triviality of the theory is shown to hold with this modification as well. We compare with recent classical results and comment on further applications., Comment: 8 p., no figures; to appear in the proceedings of the 4th workshop "Gravity, Astrophysics, and Strings at the Black Sea", Primorsko, June 10-16, 2007

We review the construction of the universal Hamilton-Jacobi counterterm for dilaton gravity in two dimensions, derive the corresponding result in the Cartan formulation and elaborate further upon black hole thermodynamics and semi-classical corrections. Applications include spherically symmetric black holes in arbitrary dimensions with Minkowski- or AdS-asymptotics, the BTZ black hole and black holes in two-dimensional string theory., Comment: 9 pages, proceedings contribution to QFEXT07 submitted to IJMPA, v2: added Ref

It is shown that the same essentially non-semiclassical mechanism, which generates in the nonsupersymmetric pure Yang-Mills theory the binary condensate of gauge field strengths, is responsible for the spontaneous breaking of the two supersymmetries in N=2 super Yang-Mills systems. A detailed discussion is presented in ref. \cite{LBPM}, Comment: 2 pages, no figures, contribution to the XXXth International Conference on High Energy Physics, (ICHEP2000), July-August 2000, Osaka, Japan