Miracle-dz/UniFAR-FTUs huggingface dataset:
On sample complexity of conditional independence testing with Von Mises estimator with application to causal discovery

Motivated by conditional independence testing, an essential step in constraint-based causal discovery algorithms, we study the nonparametric Von Mises estimator for the entropy of multivariate distributions built on a kernel density estimator. We establish an exponential concentration inequality for this estimator. We design a test for conditional independence (CI) based on our estimator, called VM-CI, which achieves optimal parametric rates under smoothness assumptions. Leveraging the exponential concentration, we prove a tight upper bound for the overall error of VM-CI. This, in turn, allows us to characterize the sample complexity of any constraint-based causal discovery algorithm that uses VM-CI for CI tests. To the best of our knowledge, this is the first sample complexity guarantee for causal discovery for continuous variables. Furthermore, we empirically show that VM-CI outperforms other popular CI tests in terms of either time or sample complexity (or both), which translates to a better performance in structure learning as well.
Studying speed-accuracy trade-offs in best-of-n collective decision-making through heterogeneous mean-field modelling

To succeed in their objectives, groups of individuals must be able to make quick and accurate collective decisions on the best option among a set of alternatives with different qualities. Group-living animals aim to do that all the time. Plants and fungi are thought to do so too. Swarms of autonomous robots can also be programmed to make best-of-n decisions for solving tasks collaboratively. Ultimately, humans critically need it and so many times they should be better at it. Thanks to their mathematical tractability, simple models like the voter model and the local majority rule model have proven useful to describe the dynamics of such collective decision-making processes. To reach a consensus, individuals change their opinion by interacting with neighbors in their social network. At least among animals and robots, options with a better quality are exchanged more often and therefore spread faster than lower-quality options, leading to the collective selection of the best option. With our work, we study the impact of individuals making errors in pooling others' opinions caused, for example, by the need to reduce the cognitive load. Our analysis is grounded on the introduction of a model that generalizes the two existing models (local majority rule and voter model), showing a speed-accuracy trade-off regulated by the cognitive effort of individuals. We also investigate the impact of the interaction network topology on the collective dynamics. To do so, we extend our model and, by using the heterogeneous mean-field approach, we show the presence of another speed-accuracy trade-off regulated by network connectivity. An interesting result is that reduced network connectivity corresponds to an increase in collective decision accuracy.
Maser Investigation toward Off-Plane Stars (MIOPS): Detection of SiO Masers in the Galactic Thick Disk and Halo

Studying stars that are located off the Galactic plane is important for understanding the formation history of the Milky Way. We searched for SiO masers toward off-plane O-rich asymptotic giant branch (AGB) stars from the catalog presented by Mauron et al. in order to shed light on the origins of these objects. A total of 102 stars were observed in the SiO J = 1−0, v = 1 and 2 transitions with the Effelsberg 100 m and Tianma 65 m telescopes. SiO masers were discovered in eight stars, all first detections. The measured maser velocities allow for initial estimates of the host AGB stars’ radial velocities. We find that the radial velocities of three stars (namely G068.881−24.615, G070.384−24.886, and G084.453−21.863) significantly deviate from the values expected from Galactic circular motion. The updated distances and 3D motions indicate that G068.881−24.615 is likely located in the Galactic halo, while G160.648−08.846 is probably located in the Galactic thin disk, and the other six stars are probably part of the Galactic thick disk.
Cyclic covers: Hodge theory and categorical Torelli theorems

Let $Y$ admit a rectangular Lefschetz decomposition of its derived category, and consider a cyclic cover $X\to Y$ ramified over a divisor $Z$. In a setting not considered by Kuznetsov and Perry, we define a subcategory $\mathcal{A}_Z$ of the equivariant derived category of $X$ which contains, rather than is contained in, $\mathrm{D}^{\mathrm{b}}(Z)$. We then show that the equivariant category of the Kuznetsov component of $X$ is decomposed into copies of $\mathcal{A}_Z$. As an application, we relate $\mathcal{A}_Z$ with the cohomology of $Z$ under some numerical assumptions. In particular, we obtain categorical Torelli theorems for the lowest degree prime Fano threefolds of index 1 and 2.
Numerical approximation of McKean-Vlasov SDEs via stochastic gradient descent

We propose a novel approach to numerically approximate McKean-Vlasov stochastic differential equations (MV-SDE) using stochastic gradient descent (SGD) while avoiding the use of interacting particle systems. The technique of SGD is deployed to solve a Euclidean minimization problem, which is obtained by first representing the MV-SDE as a minimization problem over the set of continuous functions of time, and then by approximating the domain with a finite-dimensional subspace. Convergence is established by proving certain intermediate stability and moment estimates of the relevant stochastic processes (including the tangent ones). Numerical experiments illustrate the competitive performance of our SGD based method compared to the IPS benchmarks. This work offers a theoretical foundation for using the SGD method in the context of numerical approximation of MV-SDEs, and provides analytical tools to study its stability and convergence.
Effective-one-body waveforms for extreme-mass-ratio binaries: Consistency with second-order gravitational self-force quasicircular results and extension to nonprecessing spins and eccentricity

We present a first complete implementation of an effective-one-body (EOB) model for extreme-mass-ratio inspirals (EMRIs) that incorporates aligned spins (on both the primary and the secondary) as well as orbital eccentricity. The model extends TEOBResumS-Dal\'i for these binaries by (i) recasting conservative first-order gravitational self-force (1GSF) information in the resummed EOB potentials; (ii) employing a post-Newtonian (PN) $3^{+19}$PN-accurate (3PN comparable-mass terms hybridized with test-particle terms up to 22PN relative order) expression for the gravitational-wave flux at infinity; (iii) using an improved implementation of the horizon flux that better approximates its test-mass representation. With respect to our previous work [Phys. Rev. D 106 (2022) 8, 084062], we demonstrate that the inclusion of the $3^{+19}$PN-accurate $\ell=9$ and $\ell=10$ modes in the flux at infinity significantly improves the model's agreement with second-order accurate GSF (2GSF) circular waveforms. For a standard EMRI with mass ratio $q \equiv m_1/m_2 = 5 \times 10^4$ and $m_2 = 10 M_\odot$, the accumulated EOB/2GSF dephasing is $\lesssim $ rad for $\sim 1$ yr of evolution, which is consistent with the standard accuracy requirements for EMRIs. We also showcase the generation of eccentric and spinning waveforms and discuss future extensions of our EOB towards a physically complete model for EMRIs.
Stochastic Conjugate Frameworks for Nonconvex and Nonsmooth Optimization

We introduce two new stochastic conjugate frameworks for a class of nonconvex and possibly also nonsmooth optimization problems. These frameworks are built upon Stochastic Recursive Gradient Algorithm (SARAH) and we thus refer to them as Acc-Prox-CG-SARAH and Acc-Prox-CG-SARAH-RS, respectively. They are efficiently accelerated, easy to implement, tune free and can be smoothly extended and modified. We devise a deterministic restart scheme for stochastic optimization and apply it in our second stochastic conjugate framework, which serves the key difference between the two approaches. In addition, we apply the ProbAbilistic Gradient Estimator (PAGE) and further develop a practical variant, denoted as Acc-Prox-CG-SARAH-ST, in order to reduce potential computational overhead. We provide comprehensive and rigorous convergence analysis for all three approaches and establish linear convergence rates for unconstrained minimization problem with nonconvex and nonsmooth objective functions. Experiments have demonstrated that Acc-Prox-CG-SARAH and Acc-Prox-CG-SARAH-RS both outperform state-of-art methods consistently and Acc-Prox-CG-SARAH-ST can as well achieve comparable convergence speed. In terms of theory and experiments, we verify the strong computational efficiency of the deterministic restart scheme in stochastic optimization methods.
Lipschitz extension theorems with explicit constants

In this mostly expository article, we give streamlined proofs of several well-known Lipschitz extension theorems. We pay special attention to obtaining statements with explicit expressions for the Lipschitz extension constants. One of our main results is an explicit version of a very general Lipschitz extension theorem of Lang and Schlichenmaier. A special case of the theorem reads as follows. We prove that if $X$ is a metric space and $A\subset X$ satisfies the condition $\text{Nagata}(n, c)$, then any $1$-Lipschitz map $f\colon A \to Y$ to a Banach space $Y$ admits a Lipschitz extension $F\colon X \to Y$ whose Lipschitz constant is at most $1000\cdot (c+1)\cdot \log_2(n+2)$. By specifying to doubling metric spaces, this recovers an extension result of Lee and Naor. We also revisit another theorem of Lee and Naor by showing that if $A\subset X$ consists of $n$ points, then Lipschitz extensions as above exist with a Lipschitz constant of at most $600 \cdot \log n \cdot (\log \log n)^{-1}$.
Magnetization of Flat Superconducting Films on Ferromagnetic Substrates

Ferromagnetic substrate influences the electromagnetic response of a type-II superconducting film to the applied magnetic field. We present a two-dimensional integrodifferential model for the magnetization of a flat superconductor/ferromagnet bilayer of an arbitrary shape using a thin shell quasistatic model for the ferromagnetic substrate and an infinitely thin approximation for the superconducting layer. An efficient numerical method is developed and used to investigate the effect of a ferromagnetic substrate. In particular, we simulate the thin bilayer magnetization in a parallel field and, for a high field, the critical-state distributions of the superconducting current density. These critical-state distributions are different from those known for a normal external field.
The perils and promises of fact-checking with large language models

Automated fact-checking, using machine learning to verify claims, has grown vital as misinformation spreads beyond human fact-checking capacity. Large language models (LLMs) like GPT-4 are increasingly trusted to write academic papers, lawsuits, and news articles and to verify information, emphasizing their role in discerning truth from falsehood and the importance of being able to verify their outputs. Understanding the capacities and limitations of LLMs in fact-checking tasks is therefore essential for ensuring the health of our information ecosystem. Here, we evaluate the use of LLM agents in fact-checking by having them phrase queries, retrieve contextual data, and make decisions. Importantly, in our framework, agents explain their reasoning and cite the relevant sources from the retrieved context. Our results show the enhanced prowess of LLMs when equipped with contextual information. GPT-4 outperforms GPT-3, but accuracy varies based on query language and claim veracity. While LLMs show promise in fact-checking, caution is essential due to inconsistent accuracy. Our investigation calls for further research, fostering a deeper comprehension of when agents succeed and when they fail.
Towards Robust Pruning: An Adaptive Knowledge-Retention Pruning Strategy for Language Models

The pruning objective has recently extended beyond accuracy and sparsity to robustness in language models. Despite this, existing methods struggle to enhance robustness against adversarial attacks when continually increasing model sparsity and require a retraining process. As humans step into the era of large language models, these issues become increasingly prominent. This paper proposes that the robustness of language models is proportional to the extent of pre-trained knowledge they encompass. Accordingly, we introduce a post-training pruning strategy designed to faithfully replicate the embedding space and feature space of dense language models, aiming to conserve more pre-trained knowledge during the pruning process. In this setup, each layer's reconstruction error not only originates from itself but also includes cumulative error from preceding layers, followed by an adaptive rectification. Compared to other state-of-art baselines, our approach demonstrates a superior balance between accuracy, sparsity, robustness, and pruning cost with BERT on datasets SST2, IMDB, and AGNews, marking a significant stride towards robust pruning in language models.
Study of neutrinoless double beta decay in the Standard Model extended with sterile neutrinos

We study a model where the Standard Model is augmented with three sterile neutrino states. For the mixing matrix of active and sterile neutrinos, we adopt a particular parametrization of $(6\times6)$ unitary matrix. In this context, light neutrino masses being generated via type-I seesaw mechanism, we derive, analytically, the masses of the sterile states using exact seesaw relation. The masses of the sterile states being derived in terms of the lightest mass of active neutrinos and active-active and active-sterile mixing angles and phases, they can be all light, all heavy, or a mixture of light and and heavy as compared to the active states. This can be attributed to the interplay of the $CP$ violating (CPV) phases of the $6\times 6$ mixing matrix. As both active and sterile states can mediate the neutrinoless double beta decay ($0\nu\beta\beta$) process, their contributions to the effective mass of electron neutrino, $\lvert m_{ee}\lvert$ become a function of mass of the lightest active state and active-active and active-sterile mixing angles and phases. We explore the parameter space of $\lvert m_{ee}\lvert$, keeping in mind, the present and future sensitivity of $0\nu\beta\beta$ decay searches. By making use of constraints from charged lepton flavour violation (cLFV) processes and non-unitary, we explore the role of additional CPV phases and active-sterile mixing angle values. The numerical values thus obtained for $\lvert m_{ee}\rvert$ can vary from as low as $\mathcal{O}(10^{-4})$ to saturating the present experimental limit. We have also checked the reliability of our result by calculating the branching ratio of $\mu \rightarrow e \gamma$, a prominent cLFV process, and non-unitarity, in this framework.
Helpful elements in a brief work-oriented intervention targeting musculoskeletal and mental health literacy

Abstract Musculoskeletal and mental health complaints are common in the general population and frequent reasons for healthcare utilization and work absence. Illness perceptions, coping expectancies, rumination and self-stigma are important factors in the management of these health complaints and factors closely linked to health literacy (HL). The aims of the study were to identify helpful elements in a brief intervention (BI) targeting HL regarding common musculoskeletal and mental health complaints and to identify patient perceptions of how the intervention was helpful and whether it affected their subsequent coping. Three focus group interviews with 14 patients were conducted. Systematic text condensation was used for the analysis, supported by the health literacy skill (HLS) framework to sharpen the focus on intervention elements related to the acquisition and utilization of HLSs. Results revealed the importance of receiving comprehensible health information and guidance, the use of metaphors to create recognizable narratives and the use of practical examples and exercises. Normalizing the experienced health complaints, together with a safe and accommodating clinical environment, facilitated the change process. The BI initiated processes that contributed to acceptance, resilience and empowerment, aiding work–life balance and return to work. The study presents authentic narratives of value for future focus in BI.
Is there role of adjuvant radiotherapy after complete resection of locally advanced nonsmall cell lung cancer?

Purpose of review This review aims to provide a timely and relevant overview of the role of postoperative radiotherapy (PORT) in completely resected stage IIIA-N2 nonsmall cell lung cancer (NSCLC). Given the controversy surrounding the use of PORT and the emergence of advanced radiation techniques and therapies, this review provides valuable insight into current and potential treatment strategies. Recent findings The Lung ART and PORT-C trials have provided valuable insights into the efficacy of PORT in stage IIIA-N2 NSCLC. While the results have been mixed, studies have shown that advanced radiation techniques, such as intensity-modulated radiotherapy (IMRT) and proton therapy, can reduce cardiopulmonary toxicities associated with PORT. Molecular targeted therapies and immunotherapies have also shown potential in improving NSCLC treatment outcomes. Summary The role of radiotherapy becomes smaller and smaller in new era. However, it is too early to abolish radiotherapy for all the patients after complete resection of locally advanced NSCLC. Nowadays, it is recommended to adopt individualized treatment approaches guided by multidisciplinary team consultations. The integration of IMRT, proton therapy, and emerging therapies offers the potential to enhance treatment efficacy while minimizing toxicity. Further research is needed to optimize the use of PORT and explore the method to identify the patients who can really benefit from PORT.
A randomized clinical trial of a gamified app for the treatment of perfectionism.

OBJECTIVES Perfectionism is a common transdiagnostic problem that may lead to substantial distress and functional impairments. Cognitive behavioural therapy (CBT) is an effective treatment for perfectionism. However, the existing significant barriers to access and utilization of mental health services, including among college students, demand the development of low-intensity accessible interventions. The aim of the present study was to evaluate the effectiveness of a low-intensity CBT-based self-help gamified app developed specifically for perfectionism in a sample of college students. METHODS Participants completed assessments of perfectionism, related symptoms, emotional burden and functional impairments at pretreatment, posttreatment and at one-month follow-up. RESULTS Compared with the waitlist condition (n = 35), the app condition (n = 35) demonstrated a significant and greater reduction in perfectionism, obsessive-compulsive symptoms, functional impairments and subjective ratings of emotional burden. CONCLUSIONS Results suggest that a brief, daily app-based game-like intervention targeting maladaptive perfectionistic beliefs may be a viable, low-cost alternative to traditional CBT treatments for vulnerable populations on college campuses.
The Spatial Effect of China's Haze Pollution and the Impact from Economic Change and Energy Structure

In this article,according to spatial econometrics,we especially focus on studying the interaction between the haze pollution of the province and its neighborhoods' pollution in China's 31 provinces,as well as the impacts from energy structure and economy changes.First,there exists positive global spatial autocorrelation in China's provinces.There also exists a "high-high" "polarization" phenomenon,which emerged in The Beijing Tianjin Hebei region,The Yangtze River Delta region and the middle region which connects the two areas.We account it for industry transfer,which further intensify the economy-pollution spatial linkage among China's provinces.And on this account,the pollution spillover effect is more obvious.Second,the spatial environmental Kuznets Curve econometric model is set up to quantitatively analyze the pollution's spillover effects and its influencing factors,which finds that the change of pollution's level highly associates with energy structure and industrial structure.In addition,the inverse "U" relationship between haze pollution and economic development may not exist at all or not emerge.The level of pollution is rising continuously with the growth of GDP per capital.According to the empirical analysis,we can conclude that it is just short-term for improving haze pollution by transferring industry to neighborhoods to improve environmental quality.Because of the existence of pollution spillover,the strict environmental regulation's region,for instance Beijing,Tianjin,cannot get all the benefits from their regulation.The most effective method is that neighborhoods coordinate their efforts to deal with haze pollution.In the long run,optimizing the energy consumption structure and the industrial structure will play a key role in controlling haze.And reducing the use of inferior coal can solve the problem in a short-term.
Diet and migraine: what is proven?

Purpose of review The purpose of this review is to present the latest research findings about diet and migraine, what can be used in the clinic now, and what needs further investigation. Recent findings Recent findings highlight that dietary triggers exist for migraine, for example, coffee and alcohol, according to a new systematic review. Elimination diets must be personalized to delineate a balanced diet with acceptable quality and pattern. A piece of average-quality evidence shows that the ketogenic diet (KD) and the Dietary Approaches to Stop Hypertension (DASH) are effective in reducing the frequency, duration, and severity of migraine headaches in adult patients. The gut microbiome is altered in patients with migraine, and further research will identify the benefits of pre and probiotic use for migraine. Advanced digital technology in continuous monitoring can provide educational content based on patients’ needs, help patients adhere to dietary plans, and strengthen personalized care. The complex interaction of lifestyle factors, the influence of age and sex, and patients’ needs in various life phases are essential in formulating dietary plans. Summary The diet-migraine interaction is a dynamic bidirectional phenomenon that requires careful monitoring, review, and justification of dietary choices to yield the optimal outcome while minimizing potential risks.