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The Seidov limit is a bound on the maximum latent heat that a presumed first-order phase transition of neutron-star matter can have before its excess energy density, not compensated by additional pressure, results in gravitational collapse. Because latent heat forces an apparent nonanalytic behaviour in plots correlating physical quantities (kinks in two-dimensional, ridges in three-dimensional ones), it can be constrained by data. As the onset of collapse depends on the intensity of gravity, testing for sudden derivative changes and, if they are large, breaching the Seidov limit would reward with two successive discoveries: such a phase transition (which could stem from hadron matter but also from a gravitational phase transition), and a modification of General Relativity (thus breaking the matter/gravity degeneracy). We illustrate the point with $f(R)=R+\alpha R^2$ metric gravity., Comment: 27 pages, 11 figures

Nanoparticles (NPs) based on the polymer poly (lactide-co-glycolide) acid (PLGA) have been widely studied in developing delivery systems for drugs and therapeutic biomolecules, due to the biocompatible and biodegradable properties of the PLGA. In this work, a synthesis method for bone morphogenetic protein (BMP-2)-loaded PLGA NPs was developed and optimized, in order to carry out and control the release of BMP-2, based on the double-emulsion (water/oil/water,W/O/W) solvent evaporation technique. The polymeric surfactant Pluronic F68 was used in the synthesis procedure, as it is known to have an effect on the reduction of the size of the NPs, the enhancement of their stability, and the protection of the encapsulated biomolecule. Spherical solid polymeric NPs were synthesized, showing a reproducible multimodal size distribution, with diameters between 100 and 500 nm. This size range appears to allow the protein to act on the cell surface and at the cytoplasm level. The effect of carrying BMP-2 co-adsorbed with bovine serum albumin on the NP surface was analyzed. The colloidal properties of these systems (morphology by SEM, hydrodynamic size, electrophoretic mobility, temporal stability, protein encapsulation, and short-term release profile) were studied. The effect of both BMP2-loaded NPs on the proliferation, migration, and osteogenic differentiation of mesenchymal stromal cells from human alveolar bone (ABSC) was also analyzed in vitro., Comment: 18 pages, 8 figures

We present some examples that refute two recent results in the literature concerning the equality of the domination and matching numbers for power and generalized power hypergraphs. In this note we pinpoint the flaws in the proofs and suggest how they may be mended., Comment: 7 pages, 1 figure, XIII Encuentro Andaluz de Matem\'atica Discreta, (C\'adiz) Spain, july, 2023

We identify combinations of observables for rotating neutron stars that can one day bear on the question of whether there can be first order phase transitions in the neutron matter therein. We employ the Hartle-Thorne theory for stationary, rotating neutron stars at conventional angular velocities (in the pulsar and millisecond pulsar ranges) and extract three-dimensional sections of the ellipticity or the dynamical angular momentum as function of the star's mass and angular velocity. An eventual first order phase transition in the equation of state (EoS) leaves a clear ridge (nonanalyticity) in these observables, akin to the sudden kink in popular mass-radius diagrams for static stars. Finally, we observe that static neutron stars in General Relativity (GR) will fail to be compact enough for the light ring's position at r=3M to be outside the star, except for the most extreme equations of state. The outer light ring of a rotating star might however be formed unless the EoS softens too much, and its eventual detection can then be used to constrain the EoS (or the gravity theory)., Comment: 17 pages, 26 plots, thoroughly revised following refereeing

Accurate and timely detection of plant stress is essential for yield protection, allowing better-targeted intervention strategies. Recent advances in remote sensing and deep learning have shown great potential for rapid non-invasive detection of plant stress in a fully automated and reproducible manner. However, the existing models always face several challenges: 1) computational inefficiency and the misclassifications between the different stresses with similar symptoms; and 2) the poor interpretability of the host-stress interaction. In this work, we propose a novel fast Fourier Convolutional Neural Network (FFDNN) for accurate and explainable detection of two plant stresses with similar symptoms (i.e. Wheat Yellow Rust And Nitrogen Deficiency). Specifically, unlike the existing CNN models, the main components of the proposed model include: 1) a fast Fourier convolutional block, a newly fast Fourier transformation kernel as the basic perception unit, to substitute the traditional convolutional kernel to capture both local and global responses to plant stress in various time-scale and improve computing efficiency with reduced learning parameters in Fourier domain; 2) Capsule Feature Encoder to encapsulate the extracted features into a series of vector features to represent part-to-whole relationship with the hierarchical structure of the host-stress interactions of the specific stress. In addition, in order to alleviate over-fitting, a photochemical vegetation indices-based filter is placed as pre-processing operator to remove the non-photochemical noises from the input Sentinel-2 time series., Comment: 24 pages

The inductive biases of trained neural networks are difficult to understand and, consequently, to adapt to new settings. We study the inductive biases of linearizations of neural networks, which we show to be surprisingly good summaries of the full network functions. Inspired by this finding, we propose a technique for embedding these inductive biases into Gaussian processes through a kernel designed from the Jacobian of the network. In this setting, domain adaptation takes the form of interpretable posterior inference, with accompanying uncertainty estimation. This inference is analytic and free of local optima issues found in standard techniques such as fine-tuning neural network weights to a new task. We develop significant computational speed-ups based on matrix multiplies, including a novel implementation for scalable Fisher vector products. Our experiments on both image classification and regression demonstrate the promise and convenience of this framework for transfer learning, compared to neural network fine-tuning. Code is available at https://github.com/amzn/xfer/tree/master/finite_ntk., Comment: AISTATS 2021

Anomaly detection at scale is an extremely challenging problem of great practicality. When data is large and high-dimensional, it can be difficult to detect which observations do not fit the expected behaviour. Recent work has coalesced on variations of (random) $k$\emph{d-trees} to summarise data for anomaly detection. However, these methods rely on ad-hoc score functions that are not easy to interpret, making it difficult to asses the severity of the detected anomalies or select a reasonable threshold in the absence of labelled anomalies. To solve these issues, we contextualise these methods in a probabilistic framework which we call the Mondrian \Polya{} Forest for estimating the underlying probability density function generating the data and enabling greater interpretability than prior work. In addition, we develop a memory efficient variant able to operate in the modern streaming environments. Our experiments show that these methods achieves state-of-the-art performance while providing statistically interpretable anomaly scores.

We propose a new probabilistic method for unsupervised recovery of corrupted data. Given a large ensemble of degraded samples, our method recovers accurate posteriors of clean values, allowing the exploration of the manifold of possible reconstructed data and hence characterising the underlying uncertainty. In this setting, direct application of classical variational methods often gives rise to collapsed densities that do not adequately explore the solution space. Instead, we derive our novel reduced entropy condition approximate inference method that results in rich posteriors. We test our model in a data recovery task under the common setting of missing values and noise, demonstrating superior performance to existing variational methods for imputation and de-noising with different real data sets. We further show higher classification accuracy after imputation, proving the advantage of propagating uncertainty to downstream tasks with our model., Comment: 8+12 pages

We propose a meta-learning approach that learns from multiple tasks in a transductive setting, by leveraging the unlabeled query set in addition to the support set to generate a more powerful model for each task. To develop our framework, we revisit the empirical Bayes formulation for multi-task learning. The evidence lower bound of the marginal log-likelihood of empirical Bayes decomposes as a sum of local KL divergences between the variational posterior and the true posterior on the query set of each task. We derive a novel amortized variational inference that couples all the variational posteriors via a meta-model, which consists of a synthetic gradient network and an initialization network. Each variational posterior is derived from synthetic gradient descent to approximate the true posterior on the query set, although where we do not have access to the true gradient. Our results on the Mini-ImageNet and CIFAR-FS benchmarks for episodic few-shot classification outperform previous state-of-the-art methods. Besides, we conduct two zero-shot learning experiments to further explore the potential of the synthetic gradient., Comment: ICLR 2020

We present a novel method for automated identification of putative cell types from single-cell RNA-seq (scRNA-seq) data. By iteratively applying a machine learning approach to an initial clustering of gene expression profiles of a given set of cells, we simultaneously identify distinct cell groups and a weighted list of feature genes for each group. The feature genes, which are differentially expressed in the particular cell group, jointly discriminate the given cell group from other cells. Each such group of cells corresponds to a putative cell type or state, characterised by the feature genes as markers. To benchmark this approach, we use expert-annotated scRNA-seq datasets from a range of experiments, as well as comparing to existing cell annotation methods, which are all based on a pre-existing reference. We show that our method automatically identifies the 'ground truth' cell assignments with high accuracy. Moreover, our method, Single Cell Clustering Assessment Framework (SCCAF) predicts new putative biologically meaningful cell-states in published data on haematopoiesis and the human cortex. SCCAF is available as an open-source software package on GitHub (https://github.com/SCCAF/sccaf) and as a Python package index and has also been implemented as a Galaxy tool in the Human Cell Atlas.

Most research in Bayesian optimization (BO) has focused on \emph{direct feedback} scenarios, where one has access to exact values of some expensive-to-evaluate objective. This direction has been mainly driven by the use of BO in machine learning hyper-parameter configuration problems. However, in domains such as modelling human preferences, A/B tests, or recommender systems, there is a need for methods that can replace direct feedback with \emph{preferential feedback}, obtained via rankings or pairwise comparisons. In this work, we present preferential batch Bayesian optimization (PBBO), a new framework that allows finding the optimum of a latent function of interest, given any type of parallel preferential feedback for a group of two or more points. We do so by using a Gaussian process model with a likelihood specially designed to enable parallel and efficient data collection mechanisms, which are key in modern machine learning. We show how the acquisitions developed under this framework generalize and augment previous approaches in Bayesian optimization, expanding the use of these techniques to a wider range of domains. An extensive simulation study shows the benefits of this approach, both with simulated functions and four real data sets., Comment: 6 pages + 7 pages in supplementary material

We explain some key features of quantum computing via three heuristics and apply them to argue that a deep understanding of quantum computing is unlikely to be helpful to address current bottlenecks in Artificial Intelligence Alignment. Our argument relies on the claims that Quantum Computing leads to compute overhang instead of algorithmic overhang, and that the difficulties associated with the measurement of quantum states do not invalidate any major assumptions of current Artificial Intelligence Alignment research agendas. We also discuss tripwiring, adversarial blinding, informed oversight and side effects as possible exceptions., Comment: 10 pages

Deep neural networks have achieved remarkable success in various challenging tasks. However, the black-box nature of such networks is not acceptable to critical applications, such as healthcare. In particular, the existence of adversarial examples and their overgeneralization to irrelevant, out-of-distribution inputs with high confidence makes it difficult, if not impossible, to explain decisions by such networks. In this paper, we analyze the underlying mechanism of generalization of deep neural networks and propose an ($n$, $k$) consensus algorithm which is insensitive to adversarial examples and can reliably reject out-of-distribution samples. Furthermore, the consensus algorithm is able to improve classification accuracy by using multiple trained deep neural networks. To handle the complexity of deep neural networks, we cluster linear approximations of individual models and identify highly correlated clusters among different models to capture feature importance robustly, resulting in improved interpretability. Motivated by the importance of building accurate and interpretable prediction models for healthcare, our experimental results on an ICU dataset show the effectiveness of our algorithm in enhancing both the prediction accuracy and the interpretability of deep neural network models on one-year patient mortality prediction. In particular, while the proposed method maintains similar interpretability as conventional shallow models such as logistic regression, it improves the prediction accuracy significantly., Comment: 8 pages, 6 figures

Background: Metabolomics datasets are becoming increasingly large and complex, with multiple types of algorithms and workflows needed to process and analyse the data. A cloud infrastructure with portable software tools can provide much needed resources enabling faster processing of much larger datasets than would be possible at any individual lab. The PhenoMeNal project has developed such an infrastructure, allowing users to run analyses on local or commercial cloud platforms. We have examined the computational scaling behaviour of the PhenoMeNal platform using four different implementations across 1-1000 virtual CPUs using two common metabolomics tools. Results: Our results show that data which takes up to 4 days to process on a standard desktop computer can be processed in just 10 min on the largest cluster. Improved runtimes come at the cost of decreased efficiency, with all platforms falling below 80% efficiency above approximately 1/3 of the maximum number of vCPUs. An economic analysis revealed that running on large scale cloud platforms is cost effective compared to traditional desktop systems. Conclusions: Overall, cloud implementations of PhenoMeNal show excellent scalability for standard metabolomics computing tasks on a range of platforms, making them a compelling choice for research computing in metabolomics., Comment: 25 pages, 5 figures

We analyse the most general connection allowed by Einstein-Hilbert theory in Palatini formalism. We also consider a matter lagrangian independent of the affine connection. We show that any solution of the equation of the connection is essentially Levi-Civita up to a term that contains an undetermined 1-form. Finally, it is proved that these connections and Levi-Civita describe a completely equivalent physics., Comment: 8 pages, 2 figures. Talk given by A.J.C. at the workshop Frontiers of Fundamental Physics 15 (Orihuela, Spain, November 2017)

In complex transfer learning scenarios new tasks might not be tightly linked to previous tasks. Approaches that transfer information contained only in the final parameters of a source model will therefore struggle. Instead, transfer learning at a higher level of abstraction is needed. We propose Leap, a framework that achieves this by transferring knowledge across learning processes. We associate each task with a manifold on which the training process travels from initialization to final parameters and construct a meta-learning objective that minimizes the expected length of this path. Our framework leverages only information obtained during training and can be computed on the fly at negligible cost. We demonstrate that our framework outperforms competing methods, both in meta-learning and transfer learning, on a set of computer vision tasks. Finally, we demonstrate that Leap can transfer knowledge across learning processes in demanding reinforcement learning environments (Atari) that involve millions of gradient steps., Comment: Published as a conference paper at ICLR 2019; 23 pages, 8 figures, 6 tables

In this work the one-parameter Fisher-R\'enyi measure of complexity for general $d$-dimensional probability distributions is introduced and its main analytic properties are discussed. Then, this quantity is determined for the hydrogenic systems in terms of the quantum numbers of the quantum states and the nuclear charge.

We study the most general solution for affine connections that are compatible with the variational principle in the Palatini formalism for the Einstein-Hilbert action (with possible minimally coupled matter terms). We find that there is a family of solutions generalising the Levi-Civita connection, characterised by an arbitrary, non-dynamical vector field ${\cal A}_\mu$. We discuss the mathematical properties and the physical implications of this family and argue that, although there is a clear mathematical difference between these new Palatini connections and the Levi-Civita one, both unparametrised geodesics and the Einstein equation are shared by all of them. Moreover, the Palatini connections are characterised precisely by these two properties, as well as by other properties of its parallel transport. Based on this, we conclude that physical effects associated to the choice of one or the other will not be distinguishable, at least not at the level of solutions or test particle dynamics. We propose a geometrical interpretation for the existence and unobservability of the new solutions., Comment: 12 pages, no figures. v2: Minor changes, references added. v3: New references and discussions taken into account. v4: Mayor changes, new references and discussions taken into account. v5: Minor changes, version to published in Phys. Lett. B

We introduce and discuss the notion of monotonicity for the complexity measures of general probability distributions, patterned after the resource theory of quantum entanglement. Then, we explore whether this property is satisfied by the three main intrinsic measures of complexity (Cramer-Rao, Fisher-Shannon, LMC) and some of their generalizations., Comment: Version accepted in Physics Letters A

Crowdsourcing has been proven to be an effective and efficient tool to annotate large datasets. User annotations are often noisy, so methods to combine the annotations to produce reliable estimates of the ground truth are necessary. We claim that considering the existence of clusters of users in this combination step can improve the performance. This is especially important in early stages of crowdsourcing implementations, where the number of annotations is low. At this stage there is not enough information to accurately estimate the bias introduced by each annotator separately, so we have to resort to models that consider the statistical links among them. In addition, finding these clusters is interesting in itself as knowing the behavior of the pool of annotators allows implementing efficient active learning strategies. Based on this, we propose in this paper two new fully unsupervised models based on a Chinese Restaurant Process (CRP) prior and a hierarchical structure that allows inferring these groups jointly with the ground truth and the properties of the users. Efficient inference algorithms based on Gibbs sampling with auxiliary variables are proposed. Finally, we perform experiments, both on synthetic and real databases, to show the advantages of our models over state-of-the-art algorithms.

The R\'enyi and Shannon entropies are information-theoretic measures which have enabled to formulate the position-momentum uncertainty principle in a much more adequate and stringent way than the (variance-based) Heisenberg-like relation. Moreover, they are closely related to various energetic density-functionals of quantum systems. Here we find sharp upper bounds to these quantities in terms of the second order moment $\langle r^2\rangle$ for general spherically symmetric potentials, which substantially improve previous results of this type, by means of the R\'enyi maximization procedure with a covariance constraint due to Costa, Hero and Vignat \cite{CosHer03}. The contributions to these bounds coming from the radial and angular parts of the physical wavefunctions are explicitly given., Comment: 8 pages

The momentum entropic moments and R\'enyi entropies of a one-dimensional particle in an infinite well potential are found by means of explicit calculations of some Dirichlet-like trigonometric integrals. The associated spreading lengths and quantum uncertainty-like sums are also provided., Comment: 14 pages

The analytic information theory of discrete distributions was initiated in 1998 by C. Knessl, P. Jacquet and S. Szpankowski who addressed the precise evaluation of the Renyi and Shannon entropies of the Poisson, Pascal (or negative binomial) and binomial distributions. They were able to derive various asymptotic approximations and, at times, lower and upper bounds for these quantities. Here we extend these investigations in a twofold way. First, we consider a much larger class of distributions, the Rakhmanov distributions $\rho_n(x)=\omega(x)y_n^2(x)$, where $\{y_n(x)\}$ denote the sequences of discrete hypergeometric-type polynomials which are orthogonal with respect to the weight function $\omega(x)$ of Poisson, Pascal, binomial and hypergeometric types; that is the polynomials of Charlier, Meixner, Kravchuk and Hahn. Second, we obtain the explicit expressions for the relative Fisher information of these four families of Rakhmanov distributions with respect to their respective weight functions., Comment: 18 pages, 10 figures

The Cram\'er-Rao, Fisher-Shannon and LMC shape complexity measures have been recently shown to play a relevant role to study the internal disorder of finite many-body systems (e.g., atoms, molecules, nuclei). They highlight amongst the bunch of complexities appeared in the literature by their mathematical simplicity and transparent physical interpretation. They are composed by two spreading measures (variance, Fisher information and Shannon entropies) of the single-particle probability density of the systems. Here we discuss the physico-mathematical knowledge of these two-component complexities for hydrogenic systems with standard ($D = 3$) and non-standard dimensionalities. These systems include not only the hydrogen atom and its isoelectronic series but also a large diversity of quantum systems such as, e.g. exotic atoms, antimatter atoms, some qubits systems and Rydberg atoms, ions and molecules., Comment: 13 pages, 1 figure

The macroscopic properties of a quantum system strongly depend on the spreading of the physical eigenfunctions (wavefunctions) of its Hamiltonian operador over its confined domain. The wavefunctions are often controlled by classical or hypergeometric-type orthogonal polynomials (Hermite, Laguerre and Jacobi). Here we discuss the spreading of these polynomials over its orthogonality interval by means of various information-theoretic quantities which grasp some facets of the polynomial distribution not yet analyzed. We consider the information-theoretic lengths closely related to the Fisher information and R\'enyi and Shannon entropies, which quantify the polynomial spreading far beyond the celebrated standard deviation., Comment: 17 pages

The asymptotics of the weighted $L_{p}$-norms of Hermite polynomials, which describes the R\'enyi entropy of order $p$ of the associated quantum oscillator probability density, is determined for $n\to\infty$ and $p>0$. Then, it is applied to the calculation of the R\'enyi entropy of the quantum-mechanical probability density of the highly-excited (Rydberg) states of the isotropic oscillator., Comment: 11 pages

The uncertainty relation based on the Shannon entropies of the probability densities in position and momentum spaces is improved for quantum systems in arbitrary $D$-dimensional spherically symmetric potentials. To find it, we have used the $L^p$ -- $L^q$ norm inequality of L. De Carli and the logarithmic uncertainty relation for the Hankel transform of S. Omri. Applications to some relevant three-dimensional central potentials are shown., Comment: 13 pages, 3 figures

The position-momentum uncertainty-like inequality based on moments of arbitrary order for d-dimensional quantum systems, which is a generalization of the celebrated Heisenberg formulation of the uncertainty principle, is improved here by use of the Renyi-entropy-based uncertainty relation. The accuracy of the resulting lower bound is physico-computationally analyzed for the two main prototypes in d-dimensional physics: the hydrogenic and oscillator-like systems., Comment: 31 pages, 9 figures