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In this paper we address the problem of performing Bayesian inference for the parameters of a nonlinear multi-output model and the covariance matrix of the different output signals. We propose an adaptive importance sampling (AIS) scheme for multivariate Bayesian inversion problems, which is based in two main ideas: the variables of interest are split in two blocks and the inference takes advantage of known analytical optimization formulas. We estimate both the unknown parameters of the multivariate non-linear model and the covariance matrix of the noise. In the first part of the proposed inference scheme, a novel AIS technique called adaptive target adaptive importance sampling (ATAIS) is designed, which alternates iteratively between an IS technique over the parameters of the non-linear model and a frequentist approach for the covariance matrix of the noise. In the second part of the proposed inference scheme, a prior density over the covariance matrix is considered and the cloud of samples obtained by ATAIS are recycled and re-weighted to obtain a complete Bayesian study over the model parameters and covariance matrix. ATAIS is the main contribution of the work. Additionally, the inverted layered importance sampling (ILIS) is presented as a possible compelling algorithm (but based on a conceptually simpler idea). Different numerical examples show the benefits of the proposed approaches

Vertical motions across the ocean are central to processes, like CO$_2$ fixation, heat removal or pollutant transport, which are essential to the Earth's climate. This work explores 3D conveyor routes {associated with} the Atlantic Meridional Overturning Circulation (AMOC). Our findings show the geometry of mixing structures in the upper and deep ocean layers by means of Lagrangian Coherent Structures. This tool identifies among others, zones linked to vertical transport and characterizes vertical transport time scales. We focus the study in two regions. The first one is the Flemish Cap region, a zone of interaction between the major AMOC components, where our analysis identifies a domain of deep waters that ascend very rapidly to the ocean surface. The second one is the Irminger Sea, where our analysis confirms the existence of a downwelling zone, and reveals a previously unreported upwelling connection between very deep waters and the ocean surface., Comment: 14 pages, 4 figures

We study the online coloring of $\sigma$-interval graphs which are interval graphs where the interval lengths are between 1 and $\sigma$ and 2-count interval graphs which are interval graphs that require at most $2$ distinct interval lengths. For online $\sigma$-interval graph coloring, we focus on online algorithms that do not have knowledge of the interval representation. The Kierstead-Trotter algorithm has competitive ratio 3 for all $\sigma$ and no online algorithm has competitive ratio better than 2, even for $\sigma=1$. In this paper, we show that for every $\epsilon>0$, there is a $\sigma>1$ such that there is no online algorithm for $\sigma$-interval coloring with competitive ratio less than $3-\epsilon$. Our strategy also improves the best known lower bounds for the greedy algorithm First-Fit for many values of $\sigma$. For online 2-count interval graph coloring, we analyze the performance of First-Fit and algorithms under various scenarios. We consider algorithms that receive the interval representation as input and algorithms that do not. We also consider algorithms that have prior knowledge of the interval lengths and algorithms that do not. We provide non-trivial lower bounds for each of the four cases. In particular, we show that there is no online algorithm with competitive ratio less than $2.5$ when the interval lengths are known, there is no online algorithm with competitive ratio less than $2$ when the interval representation is known, and there is no online algorithm with competitive ratio less than $1.75$ when both the interval lengths and interval representation are known.

We define the problem as a two-player game between Algorithm and Builder. The game is played in rounds. Each round, Builder presents an interval that is neither contained in nor contains any previously presented interval. Algorithm immediately and irrevocably assigns the interval a color that has not been assigned to any interval intersecting it. The set of intervals form an interval representation for a unit interval graph and the colors form a proper coloring of that graph. For every positive integer $\omega$, we define the value $R(\omega)$ as the maximum number of colors for which Builder has a strategy that forces Algorithm to use $R(\omega)$ colors with the restriction that the unit interval graph constructed cannot contain a clique of size $\omega$. In 1981, Chrobak and \'{S}lusarek showed that $R(\omega)\leq2\omega -1$. In 2005, Epstein and Levy showed that $R(\omega)\geq\lfloor{3\omega/2\rfloor}$. This problem remained unsolved for $\omega\geq 3$. In 2022, Bir\'o and Curbelo showed that $R(3)=5$. In this paper, we show that $R(4)=7$, Comment: Alternative title: On the on-line chain partitioning of semi-orders with proper interval representation

In recent years, there is a growing interest in combining techniques attributed to the areas of Statistics and Machine Learning in order to obtain the benefits of both approaches. In this article, the statistical technique lasso for variable selection is represented through a neural network. It is observed that, although both the statistical approach and its neural version have the same objective function, they differ due to their optimization. In particular, the neural version is usually optimized in one-step using a single validation set, while the statistical counterpart uses a two-step optimization based on cross-validation. The more elaborated optimization of the statistical method results in more accurate parameter estimation, especially when the training set is small. For this reason, a modification of the standard approach for training neural networks, that mimics the statistical framework, is proposed. During the development of the above modification, a new optimization algorithm for identifying the significant variables emerged. Experimental results, using synthetic and real data sets, show that this new optimization algorithm achieves better performance than any of the three previous optimization approaches.

In the quest to understand the basic universal features of compressible convection, one would like to disentangle genuine consequences of compression from spatial variations of transport properties. In the present work, we consider a very peculiar equation of state, whereby entropy is solely dependent on density, so that a nearly isentropic fluid domain is nearly isochoric. Within this class of equations of state, there is a thermal adiabatic gradient and a key property of compressible convection is still present, namely its capacity to viscously dissipate a large fraction of the thermal energy involved, of the order of the well-named dissipation number. In a series of anelastic approximations, under the assumption of an infinite Prandtl number, the number of governing parameters can be brought down to two, the Rayleigh number and the dissipation number. This framework is proposed as a playground for compressible convection, an opportunity to extend the vast corpus of theoretical analyses on the Oberbeck-Boussinesq equations regarding stability, bifurcations or the determination of upper bounds for the turbulent heat transfer. Here, in a two-dimensional geometry, we concentrate on the structure of upward and downward plumes depending on the dissipation number, on the heat flux dependence on the dissipation number and on the ratio of dissipation to convective heat flux. For dissipation numbers of order unity, in the limit of large Rayleigh numbers, dissipation becomes related to the entropy heat flux at each depth, so that the vertical dissipation profile can be predicted, and consequently so does the total ratio of dissipation to convective heat flux., Comment: 42 pages, 17 figures

The application of Bayesian inference for the purpose of model selection is very popular nowadays. In this framework, models are compared through their marginal likelihoods, or their quotients, called Bayes factors. However, marginal likelihoods depends on the prior choice. For model selection, even diffuse priors can be actually very informative, unlike for the parameter estimation problem. Furthermore, when the prior is improper, the marginal likelihood of the corresponding model is undetermined. In this work, we discuss the issue of prior sensitivity of the marginal likelihood and its role in model selection. We also comment on the use of uninformative priors, which are very common choices in practice. Several practical suggestions are discussed and many possible solutions, proposed in the literature, to design objective priors for model selection are described. Some of them also allow the use of improper priors. The connection between the marginal likelihood approach and the well-known information criteria is also presented. We describe the main issues and possible solutions by illustrative numerical examples, providing also some related code. One of them involving a real-world application on exoplanet detection., Comment: accepted in WIREs Computational Statistics (to appear)

An on-line chain partitioning algorithm receives a poset, one element at a time, and irrevocably assigns the element to one of the chains. Over 30 years ago, Szemer\'edi proved that any on-line algorithm could be forced to use $\binom{w+1}{2}$ chains to partition a poset of width $w$. The maximum number of chains that can be forced on any on-line algorithm remains unknown. In a survey paper by Bosek et al., it is shown that Szemer\'edi's argument could be improved to obtain a lower bound almost twice as good. Variants of the problem were considered where the class is restricted to posets of bounded dimension or where the poset is presented via a realizer of size $d$. In this paper, we prove two results. First, we prove that any on-line algorithm can be forced to use $(2-o(1))\binom{w+1}{2}$ chains to partition a $2$-dimensional poset of width $w$. Second, we prove that any on-line algorithm can be forced to use $(2-\frac{1}{d-1}-o(1))\binom{w+1}{2}$ chains to partition a poset of width $w$ presented via a realizer of size $d$.

An on-line chain partitioning algorithm receives a poset, one element at a time, and irrevocably assigns the element to one of the chains in the partition. The on-line chain partitioning problem involves finding the minimal number of chains needed by an optimal on-line algorithm. Chrobak and \'Slusarek considered variants of the on-line chain partitioning problem in which the elements are presented as intervals and intersecting intervals are incomparable. They constructed an on-line algorithm which uses at most $3w-2$ chains, where $w$ is the width of the interval order, and showed that this algorithm is optimal. They also considered the problem restricted to intervals of unit-length and while they showed that first-fit needs at most $2w-1$ chains, over $30$ years later, it remains unknown whether a more optimal algorithm exists. In this paper, we improve upon previously known bounds and show that any on-line algorithm can be forced to use $\lceil\frac{3}{2}w\rceil$ chains to partition a semi-order presented in the form of its unit-interval representation. As a consequence, we completely solve the problem for $w=3$.

We propose a novel adaptive importance sampling scheme for Bayesian inversion problems where the inference of the variables of interest and the power of the data noise is split. More specifically, we consider a Bayesian analysis for the variables of interest (i.e., the parameters of the model to invert), whereas we employ a maximum likelihood approach for the estimation of the noise power. The whole technique is implemented by means of an iterative procedure, alternating sampling and optimization steps. Moreover, the noise power is also used as a tempered parameter for the posterior distribution of the the variables of interest. Therefore, a sequence of tempered posterior densities is generated, where the tempered parameter is automatically selected according to the actual estimation of the noise power. A complete Bayesian study over the model parameters and the scale parameter can be also performed. Numerical experiments show the benefits of the proposed approach.

Monte Carlo sampling methods are the standard procedure for approximating complicated integrals of multidimensional posterior distributions in Bayesian inference. In this work, we focus on the class of Layered Adaptive Importance Sampling (LAIS) scheme, which is a family of adaptive importance samplers where Markov chain Monte Carlo algorithms are employed to drive an underlying multiple importance sampling scheme. The modular nature of LAIS allows for different possible implementations, yielding a variety of different performance and computational costs. In this work, we propose different enhancements of the classical LAIS setting in order to increase the efficiency and reduce the computational cost, of both upper and lower layers. The different variants address computational challenges arising in real-world applications, for instance with highly concentrated posterior distributions. Furthermore, we introduce different strategies for designing cheaper schemes, for instance, recycling samples generated in the upper layer and using them in the final estimators in the lower layer. Different numerical experiments, considering several challenging scenarios, show the benefits of the proposed schemes comparing with benchmark methods presented in the literature.

The converse of the Borel-Cantelli Lemma states that if $\{A_i\}_{i=1}^\infty$ is a sequence of independent events such that $\sum P(A_i)=\infty$, then almost surely infinitely many of these events will occur. Erd\H os and R\'enyi proved that it is sufficient to weaken the condition of independence to pairwise independence. In this paper we study various conditions of weak independence that imply the conclusion of the converse of the Borel--Cantelli Lemma. We will determine the exact implicational relationship among these conditions.

In this paper, association results from genome-wide association studies (GWAS) are combined with a deep learning framework to test the predictive capacity of statistically significant single nucleotide polymorphism (SNPs) associated with obesity phenotype. Our approach demonstrates the potential of deep learning as a powerful framework for GWAS analysis that can capture information about SNPs and the important interactions between them. Basic statistical methods and techniques for the analysis of genetic SNP data from population-based genome-wide studies have been considered. Statistical association testing between individual SNPs and obesity was conducted under an additive model using logistic regression. Four subsets of loci after quality-control (QC) and association analysis were selected: P-values lower than 1x10-5 (5 SNPs), 1x10-4 (32 SNPs), 1x10-3 (248 SNPs) and 1x10-2 (2465 SNPs). A deep learning classifier is initialised using these sets of SNPs and fine-tuned to classify obese and non-obese observations. Using a deep learning classifier model and genetic variants with P-value < 1x10-2 (2465 SNPs) it was possible to obtain results (SE=0.9604, SP=0.9712, Gini=0.9817, LogLoss=0.1150, AUC=0.9908 and MSE=0.0300). As the P-value increased, an evident deterioration in performance was observed. Results demonstrate that single SNP analysis fails to capture the cumulative effect of less significant variants and their overall contribution to the outcome in disease prediction, which is captured using a deep learning framework., Comment: 8 pages, 2 figures, 4 tables, 9 equations, conference

The QUIJOTE Experiment was developed to study the polarization in the Cosmic Microwave Background (CMB) over the frequency range of 10-50 GHz. Its first instrument, the Multi Frequency Instrument (MFI), measures in the range 10-20 GHz which coincides with one of the naturally transparent windows in the atmosphere. The Tenerife Microwave Spectrometer (TMS) has been designed to investigate the spectrum between 10-20 GHz in more detail. The MFI bands are 2 GHz wide whereas the TMS bands will be 250 MHz wide covering the complete 10-20 GHz range with one receiver chain and Fourier spectral filter bank. It is expected that the relative calibration between frequency bands will be better known than the MFI channels and that the higher resolution will provide essential information on narrow band interference and features such as ozone. The TMS will study the atmospheric spectra as well as provide key information on the viability of ground-based absolute spectral measurements. Here the novel Fourier transform spectrometer design is described showing its suitability to wide band measurement and $\sqrt{N}$ advantage over the usual scanning techniques., Comment: 8 pages, 10 figures. Accepted for publication in TIM

Many different species are adversely affected by poaching. In response to this escalating crisis, efforts to stop poaching using hidden cameras, drones and DNA tracking have been implemented with varying degrees of success. Limited resources, costs and logistical limitations are often the cause of most unsuccessful poaching interventions. The study presented in this paper outlines a flexible and interoperable framework for the automatic detection of animals and poaching activity to facilitate early intervention practices. Using a robust deep learning pipeline, a convolutional neural network is trained and implemented to detect rhinos and cars (considered an important tool in poaching for fast access and artefact transportation in natural habitats) in the study, that are found within live video streamed from drones Transfer learning with the Faster RCNN Resnet 101 is performed to train a custom model with 350 images of rhinos and 350 images of cars. Inference is performed using a frame sampling technique to address the required trade-off control precision and processing speed and maintain synchronisation with the live feed. Inference models are hosted on a web platform using flask web serving, OpenCV and TensorFlow 1.13. Video streams are transmitted from a DJI Mavic Pro 2 drone using the Real-Time Messaging Protocol (RMTP). The best trained Faster RCNN model achieved a mAP of 0.83 @IOU 0.50 and 0.69 @IOU 0.75 respectively. In comparison an SSD-mobilenetmodel trained under the same experimental conditions achieved a mAP of 0.55 @IOU .50 and 0.27 @IOU 0.75.The results demonstrate that using a FRCNN and off-the-shelf drones is a promising and scalable option for a range of conservation projects., Comment: The papaer is 10 pages and contains 11 images and 1 table

One of the most important challenges in the analysis of high-throughput genetic data is the development of efficient computational methods to identify statistically significant Single Nucleotide Polymorphisms (SNPs). Genome-wide association studies (GWAS) use single-locus analysis where each SNP is independently tested for association with phenotypes. The limitation with this approach, however, is its inability to explain genetic variation in complex diseases. Alternative approaches are required to model the intricate relationships between SNPs. Our proposed approach extends GWAS by combining deep learning stacked autoencoders (SAEs) and association rule mining (ARM) to identify epistatic interactions between SNPs. Following traditional GWAS quality control and association analysis, the most significant SNPs are selected and used in the subsequent analysis to investigate epistasis. SAERMA controls the classification results produced in the final fully connected multi-layer feedforward artificial neural network (MLP) by manipulating the interestingness measures, support and confidence, in the rule generation process. The best classification results were achieved with 204 SNPs compressed to 100 units (77% AUC, 77% SE, 68% SP, 53% Gini, logloss=0.58, and MSE=0.20), although it was possible to achieve 73% AUC (77% SE, 63% SP, 45% Gini, logloss=0.62, and MSE=0.21) with 50 hidden units - both supported by close model interpretation., Comment: 12 pages, 6 figures, 12 tables, 9 equations, journal

Gynaecologists and obstetricians visually interpret cardiotocography (CTG) traces using the International Federation of Gynaecology and Obstetrics (FIGO) guidelines to assess the wellbeing of the foetus during antenatal care. This approach has raised concerns among professionals with regards to inter- and intra-variability where clinical diagnosis only has a 30\% positive predictive value when classifying pathological outcomes. Machine learning models, trained with FIGO and other user derived features extracted from CTG traces, have been shown to increase positive predictive capacity and minimise variability. This is only possible however when class distributions are equal which is rarely the case in clinical trials where case-control observations are heavily skewed in favour of normal outcomes. Classes can be balanced using either synthetic data derived from resampled case training data or by decreasing the number of control instances. However, this either introduces bias or removes valuable information. Concerns have also been raised regarding machine learning studies and their reliance on manually handcrafted features. While this has led to some interesting results, deriving an optimal set of features is considered to be an art as well as a science and is often an empirical and time consuming process. In this paper, we address both of these issues and propose a novel CTG analysis methodology that a) splits CTG time-series signals into n-size windows with equal class distributions, and b) automatically extracts features from time-series windows using a one dimensional convolutional neural network (1DCNN) and multilayer perceptron (MLP) ensemble. Collectively, the proposed approach normally distributes classes and removes the need to handcrafted features from CTG traces., Comment: 11 Pages, 12 Figures (excluding profile pictures), accepted for publication in IEEE Transactions in Emerging Topics in Computational Intelligence

Nonequilibrium systems with strong parameter fluctuations are challenging to describe with standard Statistical Mechanics techniques. Superstatistics -- that can be seen as statistics of an underlying family of statistical distributions -- has emerged as a tool able to describe these complex systems. This has been successfully applied, for example, to hydrodynamic turbulence, internal convection, and even DNA architecture, but not to macroscopic biological systems. Here we document the occurrence of Superstatistics in the animal world, and reveal the emergence of Log-normal Superstatistics in a living system, when ants in a confined space are exposed to a threat. We use a data-driven superstatistical model to explain both normal and "panic" dynamics, identifying non-Gaussian velocity distributions, time scale separation, and the Log-normal statistics of a stochastic diffusion coefficient. We also reveal distinct behavioral regimes in the ants' collective panic response and how it relates with the individual ant memory and cluster formation. Furthermore, our findings indicate that optical signals or simple antennation are not significant mechanisms for panic transmission. These discoveries provide a foundation for the understanding of the biological origin of Log-normal type diffusion in confined environments., Comment: 10 pages, 6 figures

The emergence of an ageing population is a significant public health concern. This has led to an increase in the number of people living with progressive neurodegenerative disorders like dementia. Consequently, the strain this is places on health and social care services means providing 24-hour monitoring is not sustainable. Technological intervention is being considered, however no solution exists to non-intrusively monitor the independent living needs of patients with dementia. As a result many patients hit crisis point before intervention and support is provided. In parallel, patient care relies on feedback from informal carers about significant behavioural changes. Yet, not all people have a social support network and early intervention in dementia care is often missed. The smart meter rollout has the potential to change this. Using machine learning and signal processing techniques, a home energy supply can be disaggregated to detect which home appliances are turned on and off. This will allow Activities of Daily Living (ADLs) to be assessed, such as eating and drinking, and observed changes in routine to be detected for early intervention. The primary aim is to help reduce deterioration and enable patients to stay in their homes for longer. A Support Vector Machine (SVM) and Random Decision Forest classifier are modelled using data from three test homes. The trained models are then used to monitor two patients with dementia during a six-month clinical trial undertaken in partnership with Mersey Care NHS Foundation Trust. In the case of load disaggregation for appliance detection, the SVM achieved (AUC=0.86074, Sen=0.756 and Spec=0.92838). While the Decision Forest achieved (AUC=0.9429, Sen=0.9634 and Spec=0.9634). ADLs are also analysed to identify the behavioural patterns of the occupant while detecting alterations in routine.

This two-part paper aims to provide a Lagrangian perspective of the final southern warming in spring of 2002, during which the stratospheric polar vortex (SPV) experienced a unique splitting. We approach the subject from a dynamical systems viewpoint and search for Lagrangian coherent structures using a Lagrangian descriptor that is applied to reanalysis data. Part I presents our methodology and focuses by means of a kinematic model, on the understanding of fundamental processes for filamentation and ultimately for vortex splitting on an isentropic surface in the middle stratosphere. The present Part II discusses the three dimensional (3D) evolution of the flow during the selected event. For this, we apply concepts developed in Part I concerning a definition of the vortex boundary that helps in the selection of trajectories to illuminate the evolving flow structures, and a criterion that allows to justify why at an isentropic level a pinched vortex will split in later times. Lagrangian structures identified include surfaces that are several kilometers deep, and which a particle trajectory analysis confirms as barriers to the flow. The role of Lagrangian structures in determining the fate of particles during the SPV splitting is discussed., Comment: 15 pages, 8 pages

The present two-part paper provides a Lagrangian perspective of the final southern warming in 2002, during which the stratospheric polar vortex (SPV) experienced a unique splitting. Part I focuses on the understanding of fundamental processes for filamentation and ultimately for vortex splitting on a selected isentropic surface in the middle stratosphere. Part II discusses the three-dimensional evolution of the selected sudden warming event. We approach the subject from a dynamical systems viewpoint and search for Lagrangian coherent structures using a Lagrangian descriptor as a tool. In this Part I we work in the idealized framework of a kinematic model that allows for an understanding of the contributing elements of the flow in late September during the splitting. We introduce a definition of kinematic SPV boundary based on a criterion for binning parcels inside and outside the vortex according to their values of the Lagrangian descriptor and associated PDF. This definition is justified by using arguments that go beyond heuristic considerations based on the potential vorticity. Next, we turn to the filamentation proceses along this kinematic boundary, and the role of Lagrangian structures in the SPV splitting. We determine a criterion for splitting based on the structure of the evolving unstable and unstable manifolds., Comment: 25 pages, 11 figures

The aetiology of polygenic obesity is multifactorial, which indicates that life-style and environmental factors may influence multiples genes to aggravate this disorder. Several low-risk single nucleotide polymorphisms (SNPs) have been associated with BMI. However, identified loci only explain a small proportion of the variation ob-served for this phenotype. The linear nature of genome wide association studies (GWAS) used to identify associations between genetic variants and the phenotype have had limited success in explaining the heritability variation of BMI and shown low predictive capacity in classification studies. GWAS ignores the epistatic interactions that less significant variants have on the phenotypic outcome. In this paper we utilise a novel deep learning-based methodology to reduce the high dimensional space in GWAS and find epistatic interactions between SNPs for classification purposes. SNPs were filtered based on the effects associations have with BMI. Since Bonferroni adjustment for multiple testing is highly conservative, an important proportion of SNPs involved in SNP-SNP interactions are ignored. Therefore, only SNPs with p-values < 1x10-2 were considered for subsequent epistasis analysis using stacked auto encoders (SAE). This allows the nonlinearity present in SNP-SNP interactions to be discovered through progressively smaller hidden layer units and to initialise a multi-layer feedforward artificial neural network (ANN) classifier. The classifier is fine-tuned to classify extremely obese and non-obese individuals. The best results were obtained with 2000 compressed units (SE=0.949153, SP=0.933014, Gini=0.949936, Lo-gloss=0.1956, AUC=0.97497 and MSE=0.054057). Using 50 compressed units it was possible to achieve (SE=0.785311, SP=0.799043, Gini=0.703566, Logloss=0.476864, AUC=0.85178 and MSE=0.156315)., Comment: 13 pages, 4 figures, 13 equations, 2 tables, conference

QUIJOTE (Q-U-I JOint TEnerife) is an experiment designed to achieve CMB B-mode polarization detection and sensitive enough to detect a primordial gravitational-wave component if the B-mode amplitude is larger than r = 0.05. It consists in two telescopes and three instruments observing in the frequency range 10-42 GHz installed at the Teide Observatory in the Canary Islands, Spain. The observing strategy includes three raster scan deep integration fields for cosmology, a nominal wide survey covering the Northen Sky and specific raster scan deep integration observations in regions of specific interest. The main goals of the project are presented and the first scientific results obtained with the first instrument are reviewed., Comment: 8 pages, 1 logo, 6 figures

Genome Wide Association Studies (GWAS) are used to identify statistically significant genetic variants in case-control studies. GWAS typically use a p-value threshold of 5 x 10-8 to identify highly ranked single nucleotide polymorphisms (SNPs). However, evidence has shown that many of these are, in fact, false positives. Using lower p-values it is possible to to investigate the joint epistatic interactions between SNPs and provide better insights into phenotype expression. However, computational complexity is increased exponentially as a function of higher-order combinations. In this paper, we propose a novel framework, based on nonlinear transformations of combinatorically large SNP data, using stacked autoencoders, to identify higher-order SNP interactions. We focus on the challenging problem of classifying preterm births. Evidence suggests that this complex condition has a strong genetic component with unexplained heritability reportedly between 20%-40%. This claim is substantiated using a GWAS data set, obtained from dbGap, which contains predominantly urban low-income African-American women who had normal deliveries (between 37 and 42 weeks of gestation) and preterm deliveries (less than 37 weeks of gestation). Latent representations from original SNP sequences are used to initialize a deep learning classifier before it is fine-tuned for classification tasks (term and preterm births). The complete network models the epistatic effects of major and minor SNP perturbations. All models are evaluated using standard binary classifier performance metrics. The findings show that important information pertaining to SNPs and epistasis can be extracted from 4666 raw SNPs generated using logistic regression (p-value=5 x 10-3) and used to fit a deep learning model and obtain results (Sen=0.9289, Spec=0.9591, Gini=0.9651, Logloss=0.3080, AUC=0.9825, MSE=0.0942) using 500 hidden nodes., Comment: 11 pages, 18 equations, four figures, journal paper

We identify and describe the main dynamic regimes occurring during the melting of the PCM n-octadecane in horizontal layers of several sizes heated from below. This configuration allows to cover a wide range of effective Rayleigh numbers on the liquid PCM phase, up to $\sim 10^9$, without changing any external parameter control. We identify four different regimes as time evolves: (i) the conductive regime, (ii) linear regime, (iii) coarsening regime and (iv) turbulent regime. The first two regimes appear at all domain sizes. However the third and fourth regime require a minimum advance of the solid/liquid interface to develop, and we observe them only for large enough domains. The transition to turbulence takes places after a secondary instability that forces the coarsening of the thermal plumes. Each one of the melting regimes creates a distinct solid/liquid front that characterizes the internal state of the melting process. We observe that most of the magnitudes of the melting process are ruled by power laws, although not all of them. Thus the number of plumes, some regimes of the Rayleigh number as a function of time, the number of plumes after the primary and secondary instability, the thermal and kinetic boundary layers follow simple power laws. In particular, we find that the Nusselt number scales with the Rayleigh number as $Nu \sim Ra^{0.29}$ in the turbulent regime, consistent with theories and experiments on Rayleigh-B\'enard convection that show an exponent $2/7$., Comment: 20 pages, 12 figures

This Response is concerned with the recent Comment of Ruiz-Herrera, "Limitations of the Method of Lagrangian Descriptors" [arXiv:1510.04838], criticising the method of Lagrangian Descriptors. In spite of the significant body of literature asserting the contrary, Ruiz-Herrera claims that the method fails to reveal the presence of stable and unstable manifolds of hyperbolic trajectories in incompressible systems and in almost all linear systems. He supports this claim by considering the method of Lagrangian descriptors applied to three specific examples. However in this response we show that Ruiz-Herrera does not understand the proper application and interpretation of the method and, when correctly applied, the method beautifully and unambiguously detects the stable and unstable manifolds of the hyperbolic trajectories in his examples., Comment: 7 pages, 3 figures

QUIJOTE (Q-U-I JOint TEnerife) is a new polarimeter aimed to characterize the polarization of the Cosmic Microwave Background and other Galactic and extragalactic signals at medium and large angular scales in the frequency range 10-40 GHz. The multi-frequency (10-20~GHz) instrument, mounted on the first QUIJOTE telescope, saw first light on November 2012 from the Teide Observatory (2400~m a.s.l). During 2014 the second telescope has been installed at this observatory. A second instrument at 30~GHz will be ready for commissioning at this telescope during summer 2015, and a third additional instrument at 40~GHz is now being developed. These instruments will have nominal sensitivities to detect the B-mode polarization due to the primordial gravitational-wave component if the tensor-to-scalar ratio is larger than r=0.05., Comment: To appear in "Highlights of Spanish Astrophysics VIII", Proceedings of the XI Scientific Meeting of the Spanish Astronomical Society, Teruel, Spain (2014)

The QUIJOTE (Q-U-I JOint Tenerife) CMB Experiment is designed to observe the polarization of the Cosmic Microwave Background and other Galactic and extragalactic signals at medium and large angular scales in the frequency range of 10-40 GHz. The first of the two QUIJOTE telescopes and the multi-frequency (10-20 GHz) instrument have been in operation since November 2012. In 2014 a second telescope and a new instrument at 30GHz will be ready for commissioning, and an additional instrument at 40 GHz is in its final design stages. After three years of effective observations, the data obtained by these telescopes and instruments will have the required sensitivity to detect a primordial gravitational-wave component if the tensor-to-scalar ratio is larger than r = 0.05. At the moment, we have completed half of the wide Galactic survey with the multi-frequency instrument covering 18 000 square degrees of the Northern hemisphere. When we finish this survey in early 2014, we shall have reached approximately 14{\mu}K per one degree beam at 11, 13, 17 and 19 GHz, in both Q and U., Comment: Rencontres du Vietnam 2013: Cosmology in the Planck Era. Conference Proceedings. Typos added