Miracle-dz/UniFAR-FTUs huggingface dataset:
Book Embeddings of Regular Graphs

In the influential paper in which he proved that every graph with $m$ edges can be embedded in a book with $O({m}^{1/2})$ pages, Malitz proved the existence of $d$-regular $n$-vertex graphs that require $\Omega(\sqrt{d}n^{\frac{1}{2}-\frac{1}{d}})$ pages. In view of the $O({m}^{1/2})$ bound, this last bound is tight when $d > \log{n}$, and Malitz asked if it is also tight when $d< \log{n}$. We answer negatively to this question by showing that there exist $d$-regular graphs that require $\Omega(n^{\frac{1}{2}-\frac{1}{2(d-1)}})$ pages. In addition, we show that the bound $O({m}^{1/2})$ is not tight either for most $d$-regular graphs by proving that for each fixed $d$, with high probability the random $d$-regular graph can be embedded in $o({m}^{1/2})$ pages. We also give a simpler proof of Malitz's $O({m}^{1/2})$ bound and improve the proportionality constant.
On the Convergence of Primal-Dual Hybrid Gradient Algorithm

The primal-dual hybrid gradient algorithm (PDHG) has been widely used, especially for some basic image processing models. In the literature, PDHG's convergence was established only under some restrictive conditions on its step sizes. In this paper, we revisit PDHG's convergence in the context of a saddle-point problem and try to better understand how to choose its step sizes. More specifically, we show by an extremely simple example that PDHG is not necessarily convergent even when the step sizes are fixed as tiny constants. We then show that PDHG with constant step sizes is indeed convergent if one of the functions of the saddle-point problem is strongly convex, a condition that does hold for some variational models in imaging. With this additional condition, we also establish a worst-case convergence rate measured by the iteration complexity for PDHG with constant step sizes.
A GLM‐based latent variable ordination method for microbiome samples

Distance‐based ordination methods, such as principal coordinates analysis (PCoA), are widely used in the analysis of microbiome data. However, these methods are prone to pose a potential risk of misinterpretation about the compositional difference in samples across different populations if there is a difference in dispersion effects. Accounting for high sparsity and overdispersion of microbiome data, we propose a GLM‐based Ordination Method for Microbiome Samples (GOMMS) in this article. This method uses a zero‐inflated quasi–Poisson (ZIQP) latent factor model. An EM algorithm based on the quasi‐likelihood is developed to estimate parameters. It performs comparatively to the distance‐based approach when dispersion effects are negligible and consistently better when dispersion effects are strong, where the distance‐based approach sometimes yields undesirable results. The estimated latent factors from GOMMS can be used to associate the microbiome community with covariates or outcomes using the standard multivariate tests, which can be investigated in future confirmatory experiments. We illustrate the method in simulations and an analysis of microbiome samples from nasopharynx and oropharynx.
Covariate‐adjusted Spearman's rank correlation with probability‐scale residuals

It is desirable to adjust Spearman's rank correlation for covariates, yet existing approaches have limitations. For example, the traditionally defined partial Spearman's correlation does not have a sensible population parameter, and the conditional Spearman's correlation defined with copulas cannot be easily generalized to discrete variables. We define population parameters for both partial and conditional Spearman's correlation through concordance–discordance probabilities. The definitions are natural extensions of Spearman's rank correlation in the presence of covariates and are general for any orderable random variables. We show that they can be neatly expressed using probability‐scale residuals (PSRs). This connection allows us to derive simple estimators. Our partial estimator for Spearman's correlation between X and Y adjusted for Z is the correlation of PSRs from models of X on Z and of Y on Z, which is analogous to the partial Pearson's correlation derived as the correlation of observed‐minus‐expected residuals. Our conditional estimator is the conditional correlation of PSRs. We describe estimation and inference, and highlight the use of semiparametric cumulative probability models, which allow preservation of the rank‐based nature of Spearman's correlation. We conduct simulations to evaluate the performance of our estimators and compare them with other popular measures of association, demonstrating their robustness and efficiency. We illustrate our method in two applications, a biomarker study and a large survey.
Kernel Methods for the Approximation of Nonlinear Systems

We introduce a data-driven order reduction method for nonlinear control systems, drawing on recent progress in machine learning and statistical dimensionality reduction. The method rests on the assumption that the nonlinear system behaves linearly when lifted into a high (or infinite) dimensional feature space where balanced truncation may be carried out implicitly. This leads to a nonlinear reduction map which can be combined with a representation of the system belonging to a reproducing kernel Hilbert space to give a closed, reduced order dynamical system which captures the essential input-output characteristics of the original model. Empirical simulations illustrating the approach are also provided.
Polynomial Preconditioned GMRES and GMRES-DR

We look at solving large nonsymmetric systems of linear equations using polynomial preconditioned Krylov methods. We give a simple way to find the polynomial. It is shown that polynomial preconditioning can significantly improve restarted GMRES for difficult problems, and the reasons for this are examined. Stability is discussed, and algorithms are given for increased stability. Next, we apply polynomial preconditioning to GMRES with deflated restarting. It is shown that this is worthwhile for sparse matrices and for problems with many small eigenvalues. Multiple right-hand sides are also considered.
Characteristics of primiparous women of advanced age and their partners: a homogenous or heterogenous group?

BACKGROUND Recent studies have reported that primiparous women of advanced maternal age (AMA) appear to constitute a heterogeneous group, emphasizing the need to revise stereotyped views. The aims of this study were the following: 1) to describe the sociodemographic and marital characteristics of Portuguese couples who experienced first childbirth at advanced maternal age (the AMA group) compared with their younger counterparts (the comparison group); 2) to compare the reproductive characteristics of both groups and identify distinct reproductive trajectories within the AMA group; and 3) to distinguish among different subgroups of couples within the AMA group, depending on distinct patterns of sociodemographic, marital, and reproductive characteristics. METHODS The sample consisted of 250 couples. Both partners completed sociodemographic, marital, and reproductive health forms during pregnancy. RESULTS Despite being more highly educated, having a higher socioeconomic status, and having been employed longer, the AMA group displayed diverse conjugal configurations and reproductive trajectories over time. Within the AMA group, two subgroups were distinguished: couples who experienced infertility problems and couples who did not. CONCLUSIONS Couples who experience first childbirth at AMA constitute a heterogeneous group, which includes distinct subgroups with different psychosocial needs during the transition to parenthood. To revise stereotyped views of these couples, protective social policies should be improved, and health professionals should assume nonjudgmental attitudes and promote informed reproductive decisions. Psychoeducative programs concerning the transition to parenthood should take into account the distinct subgroups of couples who experience first childbirth at AMA.
Parallel Triangular Mesh Refinement by Longest Edge Bisection

Longest edge bisection based refinement, which is also known as Rivara refinement, is a well-known technique for adaptive refinement of unstructured triangular meshes. Our work contributes a fine grain parallel adaptive refinement algorithm. Refinements can propagate in an irregular fashion to neighboring triangles. Once propagations are done, refinement templates can be applied. Since elements are created and deleted in an irregular fashion, dynamic data structures need to be designed and concurrency issues need to be resolved. Unlike the previous approaches that solved an independent set problem to resolve concurrent updates, our algorithm instead makes use of prefix computations. Tests carried out on an NVIDIA Tesla M2070 GPU show that running time on a 32 million element mesh is overall roughly 25 times faster than the sequential run on an Intel Xeon system. Our refinement code is available at http://code.google. com/p/gpu-mesh-refine.
Adjoint Sensitivity Analysis for Nonsmooth Differential-Algebraic Equation Systems

An adjoint sensitivity method is presented for nonsmooth semiexplicit differential-algebraic equation systems (NDAEs) of index 1. The adjoint sensitivity system is derived for a generalization of Mayer-type functionals subject to NDAE constraints. Opposed to classical Mayer-type functionals that depend on the differential and algebraic variables evaluated only at the initial and final times, the generalization depends additionally on the evaluation at multiple interior time points. The derived adjoint sensitivity method extends and builds on the method for smooth DAEs by Cao et al. [SIAM J. Sci. Comput. , 24 (2003), pp. 1076--1089] and on the method for nonsmooth ODEs by Ruban [J. Comput. Systems Sci. Internat. , 36 (1997), pp. 536--542].
Artifacts in Incomplete Data Tomography with Applications to Photoacoustic Tomography and Sonar

We develop a paradigm using microlocal analysis that allows one to characterize the visible and added singularities in a broad range of incomplete data tomography problems. We give precise characterizations for photoacoustic and thermoacoustic tomography and sonar, and provide artifact reduction strategies. In particular, our theorems show that it is better to arrange sonar detectors so that the boundary of the set of detectors does not have corners and is smooth. To illustrate our results, we provide reconstructions from synthetic spherical mean data as well as from experimental photoacoustic data.
Rank-1 Tensor Properties with Applications to a Class of Tensor Optimization Problems

This paper studies models and algorithms for a class of tensor optimization problems, based on a rank-1 equivalence property between a tensor and certain unfoldings. It is first shown that in $d$th order tensor space, the set of rank-1 tensors is the same as the intersection of $\lceil \log_2(d) \rceil$ tensor sets, of which tensors have a specific rank-1 balanced unfolding matrix. Moreover, the number $\lceil \log_2(d) \rceil$ is proved to be optimal in some sense. Based on the above equivalence property, three relaxation approaches for solving the best rank-1 tensor approximation problems are proposed, including two convex relaxations and a nonconvex one. The two convex relaxations utilize the matrix nuclear norm regularization/constraints. They have the advantage of identifying whether the solution is a global optimizer of the original problem, by computing the nuclear norm or the Frobenius norm of a certain matrix. Under certain assumptions, the optimal solution of the original problem is characterize.
Analysis of Transition State Theory Rates upon Spatial Coarse-Graining

Spatial multiscale methods have established themselves as useful tools for extending the length scales accessible by conventional statics (i.e., zero temperature molecular dynamics). Recently, extensions of these methods, such as the finite-temperature quasicontinuum (hot-QC) or coarse-grained molecular dynamics (CGMD) methods, have allowed for multiscale molecular dynamics simulations at finite temperature. Here, we assess the quality of the long-time dynamics these methods generate by considering canonical transition rates. Specifically, we analyze the harmonic transition state theory (HTST) rates in CGMD and compare them to the corresponding HTST rate of the fully atomistic system. The ability of such an approach to reliably reproduce the HTST rate is verified through a relative error analysis, which is then used to highlight the major contributions to the error and guide the choice of degrees of freedom. We focus on the error resulting from coarse-graining, which dominates in systems with low temperature and constitutes a lower bound on the error associated with any method that employs coarse-graining. Finally, our analytical results are compared with numerical simulations for the case of a 1-D chain.
Impaired intuition in patients with major depressive disorder.

OBJECTIVES In daily life, many decisions of minor and major importance have to be made. Thereby, intuitive judgments serve as useful guides and help us to adapt to our environment. People with major depressive disorder (MDD) often have difficulties to come to decisions. Is their intuition impaired? Since this question has not been addressed until now, the present study explored intuition in MDD. METHODS Depressed patients (n = 29) and healthy control participants (n = 27) completed the Judgment of Semantic Coherence Task, a well-established paradigm used in basic cognitive research to measure intuition. Furthermore, participants' severity of depressive symptoms (BDI-II), negative affect (PANAS), and rumination (RSQ) were assessed. All participants were interviewed with the SCID. RESULTS Depressed patients showed impaired intuition compared to healthy control participants. In the depressed sample, negative affect accounts for the association between rumination and impaired intuition. Results further reveal that negative affect overall mediates the depression-intuition relationship. Patients with diminished ability to concentrate or indecisiveness had lower intuition indices compared to patients who did not fulfil this diagnostic criterion of MDD. CONCLUSIONS The study introduces the phenomenon of intuition into depression research. Additionally, these results extent findings from basic research showing that induced negative mood as well difficulties to down-regulate negative affect impair intuitive coherence judgments. Current results indicate that the negative affectivity of patients is the crucial mediator in the association between depression and impaired intuition. Limitations of the study as well as the potential etiological role of intuition in MDD are discussed. PRACTITIONER POINTS The finding that intuition is impaired in depressed patients extends our knowledge as to the cognitive profile of patients with MDD. Patients who suffer from indecisiveness have lower intuition indices compared to patients who do not fulfill this diagnostic criterion of MDD. Due to the cross-sectional design, final conclusions as to the etiological role of intuition in MDD cannot be drawn. The question remains open whether impaired intuition is specific to MDD.
A Time Dependent Variational Approach to Image Restoration

In this paper we introduce a purely variational approach to the gradient flows, naturally arising in image denoising models, yielding the existence of global parabolic minimizers, in the sense that $ \int_0^{T}\big[\int_\Omega u \partial_t\varphi\, dx + F(u)\big] \,dt \le \int_0^{T}F(u+\varphi) \,dt, $ whenever $T>0$ and $\varphi\in C_0^\infty(\Omega\times(0,T))$. Our method applies to a wide class of nonparametric regression models in image restoration analysis, such as quantile, robust, and logistic regression. A prototype functional $F$ is the by now classical ${\rm TV}(L^2)$-functional (i.e., the pure ${\rm TV}$-denoising case in image reconstruction) introduced by Rudin, Osher and Fatemi [Phys. D, 268 (1992), pp. 259--268]: $ \boldsymbol F(u):= \mathbf{TV}(u)+\frac{\kappa}{2}\int_\Omega |u-u_o|^2\, dx, $ where $u_o\colon\Omega\to [0,1]$ is a noisy, monochromatic image and $\kappa\gg 1$ a large penalization parameter. The evolutionary variational solutions are obtained as limits of maps, minimizing a .
Quasi-Polynomial Time Approximation Scheme for Weighted Geometric Set Cover on Pseudodisks and Halfspaces

Weighted geometric set-cover problems arise naturally in several geometric and nongeometric settings (e.g., the breakthrough of Bansal and Pruhs [Proceedings of FOCS, 2010, pp. 407--414] reduces a wide class of machine scheduling problems to weighted geometric set cover). More than two decades of research has succeeded in settling the $(1+\epsilon)$-approximability status for most geometric set-cover problems, except for some basic scenarios which are still lacking. One is that of weighted disks in the plane for which, after a series of papers, Varadarajan [Proceedings of STOC'10, 2010, pp. 641--648] presented a clever quasi-sampling technique, which together with improvements by Chan et al. [Proceedings of SODA, 2012, pp. 1576--1585], yielded an $O(1)$-approximation algorithm. Even for the unweighted case, a polynomial time approximation scheme (PTAS) for a fundamental class of objects called pseudodisks (which includes halfspaces, disks, unit-height rectangles, translates of convex sets, etc.) is curren.
Compassion focused therapy: Exploring the effectiveness with a transdiagnostic group and potential processes of change

OBJECTIVES This study aimed to examine the effectiveness of a compassion focused therapy (CFT) group with a transdiagnostic population, as compared to treatment as usual (TAU). A secondary aim was to explore the potential processes of change within the treatment. DESIGN A non-randomized control trial was used. METHOD Fifty-eight participants who engaged in group CFT were compared to 29 participants receiving TAU. Group CFT consisted of 14 sessions twice weekly for 5 weeks and once weekly for 4 weeks. Participants completed measures of psychopathology, shame, self-criticism, fears of self-compassion, and social safeness, at pre-treatment, post-treatment, and 2-month follow-up. Potential processes of change were examined using correlations and regression analysis. RESULTS Significantly greater improvements were found for levels of psychopathology, fears of self-compassion and social safeness for CFT, compared to TAU. Additionally, analyses showed improvements in shame and self-criticism within the CFT group but not the TAU group. All improvements were maintained at 2-month follow-up. Improvements in psychopathology were predicted by changes in self-criticism and fears of self-compassion. CONCLUSION Compassion focused therapy appears to be an effective group intervention for a range of mental health difficulties. The positive impact of the CFT model with a transdiagnostic group emphasizes the value of addressing underlying psychological process, rather than symptoms alone. PRACTITIONER POINTS Compassion focused therapy is a multimodal therapy designed to target high levels of shame and self-criticism. Compassion focused therapy has been shown previously to have positive results within a range of diagnostic-specific populations. While there is an emerging research base, limited studies assessing effectiveness with transdiagnostic populations have been published. CFT was shown to have a significant effect in reducing levels of psychopathology, compared to TAU. A number of potential processes of change were identified: Changes in psychopathology were significantly correlated with changes in self-criticism and fears of self-compassion.
Central Nervous System GLP-1 Receptors Regulate Islet Hormone Secretion and Glucose Homeostasis in Male Rats

The glucagon-like peptide 1 (GLP-1) system plays an important role in blood glucose regulation, in great part through coordinate control of insulin and glucagon secretion. These effects are generally attributed to GLP-1 produced in peripheral sites, principally the intestine. GLP-1 is also produced in hindbrain neurons that signal through GLP-1 receptors (GLP-1rs) expressed in brain regions involved in metabolic regulation. GLP-1 in the central nervous system (CNS) induces satiety, visceral illness, and stress responses. However, recent evidence suggests CNS GLP-1 is also involved in glucose regulation. To test the hypothesis that central GLP-1 regulates islet hormone secretion, conscious rats were given intracerebroventricular (ICV) GLP-1, GLP-1r antagonist exendin-[9-39] (Ex-9), or saline during fasting or hyperglycemia from intravenous glucose. Administration of CNS GLP-1 increased fasting glucose, glucagon, corticosterone, and epinephrine and blunted insulin secretion in response to hyperglycemia. Paradoxically, GLP-1r blockade with ICV Ex-9 also reduced glucose-stimulated insulin secretion, and administration of ICV Ex-9 to freely feeding rats caused mild glucose intolerance. Thus, direct administration of CNS GLP-1 affected islet hormone secretion counter to what is seen with peripherally administered GLP-1, an effect likely due to stimulation of sympathetic nervous system activity. In contrast, blockade of brain GLP-1r supports a role for CNS GLP-1 on glucose-stimulated insulin secretion and glucose control after a meal. These findings suggest a model in which activation of CNS GLP-1r by endogenous peptide promotes glucose tolerance, an effect that can be overridden by stress responses stimulated by exogenous GLP-1.
Efficient Blind Compressed Sensing Using Sparsifying Transforms with Convergence Guarantees and Application to Magnetic Resonance Imaging

Natural signals and images are well-known to be approximately sparse in transform domains such as Wavelets and DCT. This property has been heavily exploited in various applications in image processing and medical imaging. Compressed sensing exploits the sparsity of images or image patches in a transform domain or synthesis dictionary to reconstruct images from undersampled measurements. In this work, we focus on blind compressed sensing, where the underlying sparsifying transform is a priori unknown, and propose a framework to simultaneously reconstruct the underlying image as well as the sparsifying transform from highly undersampled measurements. The proposed block coordinate descent type algorithms involve highly efficient optimal updates. Importantly, we prove that although the proposed blind compressed sensing formulations are highly nonconvex, our algorithms are globally convergent (i.e., they converge from any initialization) to the set of critical points of the objectives defining the formulations. These critical points are guaranteed to be at least partial global and partial local minimizers. The exact point(s) of convergence may depend on initialization. We illustrate the usefulness of the proposed framework for magnetic resonance image reconstruction from highly undersampled k-space measurements. As compared to previous methods involving the synthesis dictionary model, our approach is much faster, while also providing promising reconstruction quality.