Miracle-dz/UniFAR-FTUs huggingface dataset:
On the Largest Product-free Subsets of the Alternating Groups

A subset $A$ of a group $G$ is called product-free if there is no solution to $a=bc$ with $a,b,c$ all in $A$. It is easy to see that the largest product-free subset of the symmetric group $S_n$ is obtained by taking the set of all odd permutations, i.e. $S_n \setminus A_n$, where $A_n$ is the alternating group. By contrast, it is a long-standing open problem to find the largest product-free subset of $A_n$. We solve this problem for large $n$, showing that the maximum size is achieved by the previously conjectured extremal examples, namely families of the form $\{\pi~|~\pi(x)\in I, \pi(I)\cap I=\emptyset\}$ and their inverses. Moreover, we show that the maximum size is only achieved by these extremal examples, and we have stability: any product-free subset of $A_n$ of nearly maximum size is structurally close to an extremal example. Our proof uses a combination of tools from Combinatorics and Non-abelian Fourier Analysis, including a crucial new ingredient exploiting some recent theory developed by Filmus, Kindler, Liftshitz and Minzer for global hypercontractivity on the symmetric group.
On the External Validity of Average-Case Analyses of Graph Algorithms

The number one criticism of average-case analysis is that we do not actually know the probability distribution of real-world inputs. Thus, analyzing an algorithm on some random model has no implications for practical performance. At its core, this criticism doubts the existence of external validity, i.e., it assumes that algorithmic behavior on the somewhat simple and clean models does not translate beyond the models to practical performance real-world input. With this paper, we provide a first step towards studying the question of external validity systematically. To this end, we evaluate the performance of six graph algorithms on a collection of 2740 sparse real-world networks depending on two properties; the heterogeneity (variance in the degree distribution) and locality (tendency of edges to connect vertices that are already close). We compare this with the performance on generated networks with varying locality and heterogeneity. We find that the performance in the idealized setting of network models translates surprisingly well to real-world networks. Moreover, heterogeneity and locality appear to be the core properties impacting the performance of many graph algorithms.
A Graph and Attentive Multi-Path Convolutional Network for Traffic Prediction

Traffic prediction is an important and yet highly challenging problem due to the complexity and constantly changing nature of traffic systems. To address the challenges, we propose a graph and attentive multi-path convolutional network (GAMCN) model to predict traffic conditions such as traffic speed across a given road network into the future. Our model focuses on the spatial and temporal factors that impact traffic conditions. To model the spatial factors, we propose a variant of the graph convolutional network (GCN) named LPGCN to embed road network graph vertices into a latent space, where vertices with correlated traffic conditions are close to each other. To model the temporal factors, we use a multi-path convolutional neural network (CNN) to learn the joint impact of different combinations of past traffic conditions on the future traffic conditions. Such a joint impact is further modulated by an attention generated from an embedding of the prediction time, which encodes the periodic patterns of traffic conditions. We evaluate our model on real-world road networks and traffic data. The experimental results show that our model outperforms state-of-art traffic prediction models by up to 18.9% in terms of prediction errors and 23.4% in terms of prediction efficiency.
Fluctuation contribution to spin Hall effect in superconductors

We theoretically study the contribution of superconducting ﬂuctuation to extrinsic spin Hall eﬀects in two- and three-dimensional electron gas and intrinsic spin Hall eﬀects in two-dimensional electron gas with Rashba-type spin-orbit interaction. The Aslamazov-Larkin, Density-of-States, Maki-Thompson terms have logarithmic divergence ln (cid:15) in the limit (cid:15) = ( T − T c ) /T c → +0 in two- dimensional systems for both extrinsic and intrinsic spin Hall eﬀects except the Maki-Thompson terms in extrinsic eﬀect, which are proportional to ( (cid:15) − γ ϕ ) − 1 ln (cid:15) with a cutoﬀ γ ϕ in two-dimensional systems. We found that the ﬂuctuation eﬀects on the extrinsic spin Hall eﬀect have an opposite sign to that in the normal state, while those on the intrinsic spin Hall eﬀect have the same sign.
Sampling-free Inference for Ab-Initio Potential Energy Surface Networks

Recently, it has been shown that neural networks not only approximate the ground-state wave functions of a single molecular system well but can also generalize to multiple geometries. While such generalization significantly speeds up training, each energy evaluation still requires Monte Carlo integration which limits the evaluation to a few geometries. In this work, we address the inference shortcomings by proposing the Potential learning from ab-initio Networks (PlaNet) framework, in which we simultaneously train a surrogate model in addition to the neural wave function. At inference time, the surrogate avoids expensive Monte-Carlo integration by directly estimating the energy, accelerating the process from hours to milliseconds. In this way, we can accurately model high-resolution multi-dimensional energy surfaces for larger systems that previously were unobtainable via neural wave functions. Finally, we explore an additional inductive bias by introducing physically-motivated restricted neural wave function models. We implement such a function with several additional improvements in the new PESNet++ model. In our experimental evaluation, PlaNet accelerates inference by 7 orders of magnitude for larger molecules like ethanol while preserving accuracy. Compared to previous energy surface networks, PESNet++ reduces energy errors by up to 74%.
Benchmarking Unsupervised Anomaly Detection and Localization

Unsupervised anomaly detection and localization, as of one the most practical and challenging problems in computer vision, has received great attention in recent years. From the time the MVTec AD dataset was proposed to the present, new research methods that are constantly being proposed push its precision to saturation. It is the time to conduct a comprehensive comparison of existing methods to inspire further research. This paper extensively compares 13 papers in terms of the performance in unsupervised anomaly detection and localization tasks, and adds a comparison of inference efficiency previously ignored by the community. Meanwhile, analysis of the MVTec AD dataset are also given, especially the label ambiguity that affects the model fails to achieve full marks. Moreover, considering the proposal of the new MVTec 3D-AD dataset, this paper also conducts experiments using the existing state-of-the-art 2D methods on this new dataset, and reports the corresponding results with analysis.
Formulation and evaluation of an analytical model for composite box-beams

A direct method for determining the effective elastic stiffnesses and deformation behavior of composite box-beam (BB) structures is developed analytically, validated, and demonstrated. The BB walls are modeled as orthotropic-ply laminated plates, so that the elastic properties vary both through the thickness and around the BB contour; deformation is described in terms of extension, bending, twisting, shearing, and torsion-related out-of-plane warping. Numerical results for several BB configurations are presented in tables and graphs and compared with experimental data and FEM computations (Stemple and Lee, 1989): good general agreement is obtained for cross-ply, antisymmetric, and symmetric layups, except for symmetric layups with ply orientation angles theta greater than 30 deg. Both out-of-plane warping and transverse shear coupling are found to have significant effects on BB elastic response.
Investigations on the flavor-dependent axial charges of the octet baryons

We have investigated the axial charges of the ground octet baryons within the extended chiral constituent quark model, where all the possible compact ﬁve-quark Fock components qqq ( q ¯ q )( q = u, d, s ) in the baryons are considered. The transition couplings between the three- and ﬁve-quark components in the baryons are assumed to be via the 3 P 0 mechanism, which could reproduce the sea asymmetry in proton very well. The numerical results for the ﬂavor-dependent axial charges of the octet baryons are comparable to those predicted by other theoretical approaches. It is shown that the singlet axial charges of the octet baryons, which should indicate total baryons spin arising from the spin of the quarks, fall in the range 0 . 45 − 0 . 75 in present model. This is in consistent with the predictions by lattice QCD and chiral perturbation theory. It’s also very interesting that the light quarks spin ∆ u and ∆ d in the Λ baryon are of small but negative values, which exactly vanish in the traditional three-quark model.
INSTITUTE OF ECONOMIC STUDIES WORKING PAPER SERIES W 05 : 01 July 2005 Does development aid help poor countries catch up ? An analysis of the basic relations

Aid flows are included into the standard cross-country catch-up relation. Robustness of the result is tested by changing time periods and by adding extra variables. The main results are: Absolute convergence and absolute aid effectiveness are both rejected. While conditional convergence is accepted, conditional aid effectiveness is found to be weak. The two relations are largely independent. However, aid has a clear activity effect in the short run. Finally, we try to divide the countries into an A-group where aid is effective and a B-group where it harms. Several criteria of division were explored, but none were very successful – the most satisfactory is the one that divides countries according to their level of development. Jel. : C14, C23, F35, O4
The Missing Invariance Principle Found - the Reciprocal Twin of Invariant Risk Minimization

Machine learning models often generalize poorly to out-of-distribution (OOD) data as a result of relying on features that are spuriously correlated with the label during training. Recently, the technique of Invariant Risk Minimization (IRM) was proposed to learn predictors that only use invariant features by conserving the feature-conditioned label expectation $\mathbb{E}_e[y|f(x)]$ across environments. However, more recent studies have demonstrated that IRM-v1, a practical version of IRM, can fail in various settings. Here, we identify a fundamental flaw of IRM formulation that causes the failure. We then introduce a complementary notion of invariance, MRI, based on conserving the label-conditioned feature expectation $\mathbb{E}_e[f(x)|y]$, which is free of this flaw. Further, we introduce a simplified, practical version of the MRI formulation called MRI-v1. We prove that for general linear problems, MRI-v1 guarantees invariant predictors given sufficient number of environments. We also empirically demonstrate that MRI-v1 strongly out-performs IRM-v1 and consistently achieves near-optimal OOD generalization in image-based nonlinear problems.
Core-set Selection Using Metrics-based Explanations (CSUME) for multiclass ECG

The adoption of deep learning-based healthcare decision support systems such as the detection of irregular cardiac rhythm is hindered by challenges such as lack of access to quality data and the high costs associated with the collection and annotation of data. The collection and processing of large volumes of healthcare data is a continuous process. The performance of data-hungry Deep Learning models (DL) is highly dependent on the quantity and quality of the data. While the need for data quantity has been established through research adequately, we show how a selection of good quality data improves deep learning model performance. In this work, we take Electrocardiogram (ECG) data as a case study and propose a model performance improvement methodology for algorithm developers, that selects the most informative data samples from incoming streams of multi-class ECG data. Our Core-Set selection methodology uses metrics-based explanations to select the most informative ECG data samples. This also provides an understanding (for algorithm developers) as to why a sample was selected as more informative over others for the improvement of deep learning model performance. Our experimental results show a 9.67% and 8.69% precision and recall improvement with a significant training data volume reduction of 50%. Additionally, our proposed methodology asserts the quality and annotation of ECG samples from incoming data streams. It allows automatic detection of individual data samples that do not contribute to model learning thus minimizing possible negative effects on model performance. We further discuss the potential generalizability of our approach by experimenting with a different dataset and deep learning architecture.
Constraints on τ NL from Planck temperature and polarization

We update constraints on the amplitude of the primordial trispectrum, using the final Planck mission temperature and polarization data. In the squeezed limit, a cosmological local trispectrum would be observed as a spatial modulation of small-scale power on the CMB sky. We reconstruct this signal as a source of statistical anisotropy via quadratic estimator techniques. We systematically demonstrate how the estimated power spectrum of a reconstructed modulation field can be translated into a constraint on τ NL via likelihood methods, demonstrating the procedures effectiveness by inferring known τ NL signal(s) from simulations. Our baseline results constrain τ NL < 1700 at the 95% confidence level, providing the most stringent constraints to date.
Federated Neural Bandit

Recent works on neural contextual bandit have achieved compelling performances thanks to their ability to leverage the strong representation power of neural networks (NNs) for reward prediction. Many applications of contextual bandit involve multiple agents who collaborate without sharing raw observations, giving rise to the setting of federated contextual bandit . Existing works on federated contextual bandit rely on linear or kernelized bandit, which may fall short when modeling complicated real-world reward functions. In this regard, we introduce the federated neural-upper conﬁdence bound (FN-UCB) algorithm. To better exploit the federated setting, we adopt a weighted combination of two UCBs: UCB a allows every agent to additionally use the observations from the other agents to accelerate exploration (without sharing raw observations); UCB b uses an NN with aggregated parameters for reward prediction in a similar way as federated averaging for supervised learning. Notably, the weight between the two UCBs required by our theoretical analysis is amenable to an interesting interpretation, which emphasizes UCB a initially for accelerated exploration and relies more on UCB b later after enough observations have been collected to train the NNs for accurate reward prediction (i.e., reliable exploitation ). We prove sub-linear upper bounds on both the cumulative regret and the number of communication rounds of FN-UCB, and use empirical experiments to demonstrate its competitive performances.
Multi-Domain Virtual Network Embedding Algorithm Based on Horizontal Federated Learning

Network Virtualization (NV) is an emerging network dynamic planning technique to overcome network rigidity. As its necessary challenge, Virtual Network Embedding (VNE) enhances the scalability and flexibility of the network by decoupling the resources and services of the underlying physical network. For future multi-domain physical network modeling with the characteristics of dynamics, heterogeneity, privacy, and real-time, the existing related works perform unsatisfactorily. Federated learning (FL) jointly optimizes the network by sharing parameters among multiple parties and is widely used to address data privacy and data silos. Aiming at the NV challenge of multi-domain physical networks, this work is the first to propose using FL to model VNE, and presents a VNE architecture based on Horizontal Federated Learning (HFL) (HFL-VNE). Specifically, combined with the distributed training paradigm of FL, we deploy local servers in each physical domain, which can effectively focus on local features and reduce resource fragmentation. A global server is deployed to aggregate and share training parameters, which enhances local data privacy and significantly improves learning efficiency. Furthermore, we deploy the Deep Reinforcement Learning (DRL) model in each server to dynamically adjust and optimize the resource allocation of the multi-domain physical network. In DRL-assisted FL, HFL-VNE jointly optimizes decision-making through specific local and federated reward mechanisms and loss functions. Finally, the superiority of HFL-VNE is proved by combining simulation experiments and comparing it with related works.
MUSSES2020J: The Earliest Discovery of a Fast Blue Ultraluminous Transient at Redshift 1.063

In this Letter, we report the discovery of an ultraluminous fast-evolving transient in rest-frame UV wavelengths, MUSSES2020J, soon after its occurrence by using the Hyper Suprime-Cam (HSC) mounted on the 8.2 m Subaru telescope. The rise time of about 5 days with an extremely high UV peak luminosity shares similarities to a handful of fast blue optical transients whose peak luminosities are comparable with the most luminous supernovae while their timescales are significantly shorter (hereafter “fast blue ultraluminous transient,” FBUT). In addition, MUSSES2020J is located near the center of a normal low-mass galaxy at a redshift of 1.063, suggesting a possible connection between the energy source of MUSSES2020J and the central part of the host galaxy. Possible physical mechanisms powering this extreme transient such as a wind-driven tidal disruption event and an interaction between supernova and circumstellar material are qualitatively discussed based on the first multiband early-phase light curve of FBUTs, although whether the scenarios can quantitatively explain the early photometric behavior of MUSSES2020J requires systematical theoretical investigations. Thanks to the ultrahigh luminosity in UV and blue optical wavelengths of these extreme transients, a promising number of FBUTs from the local to the high-z universe can be discovered through deep wide-field optical surveys in the near future.
Generalized Stochastic Matching

In this paper, we generalize the recently studied stochastic matching problem to more accurately model a significant medical process, kidney exchange, and several other applications. Up until now the stochastic matching problem that has been studied was as follows: given a graph G= (V,E), each edge is included in the realized sub-graph of G independently with probability pe, and the goal is to find a degree-bounded sub-graph Q of G that has an expected maximum matching that approximates the expected maximum matching of G. This model does not account for possibilities of vertex dropouts, which can be found in several applications, e.g. in kidney exchange when donors or patients opt out of the exchange process as well as in online freelancing and online dating when online profiles are found to be faked. Thus, we will study a more generalized model of stochastic matching in which vertices and edges are both realized independently with some probabilities pv, pe, respectively, which more accurately fits important applications than the previously studied model. We will discuss the first algorithms and analysis for this generalization of the stochastic matching model and prove that they achieve good approximation ratios. In particular, we show that the approximation factor of a natural algorithm for this problem is at least 0.6568 in unweighted graphs, and 1/2+ε in weighted graphs for some constant ε >0. We further improve our result for unweighted graphs to 2/3 using edge degree constrained sub-graphs (EDCS).
Shaping physical properties of galaxy subtypes in the VIPERS survey: Environment matters

Aims. This study aims to explore the relation between the physical properties of di ﬀ erent galaxy sub-classes, from red passive to blue star-forming, and their environment. Our work is based on the analysis of 31631 galaxies from the VIMOS Public Extragalactic Redshift Survey (VIPERS), observed at 0 . 5 < z < 0 . 9. The unprecedented volume of VIPERS and the wealth of auxiliary derived data allow us to associate sub-classes of the main galaxy populations with their possibly di ﬀ erent evolutionary paths. This is the ﬁrst time such a study is performed with such statistical precision. to subclasses of ﬁfth mass assembly appears to be dominated by mergers. When it comes to blue galaxies, the trend of decreasing fraction with denser environments seen for the group as a whole (sub-classes C7–11) is found to be driven mostly by one (the most numerous) group of galaxies; sub-class C10. These are compact low-mass galaxies with high, speciﬁc star formation rates, which are preferentially found in low-density environments. However, the remaining blue galaxies (sub-classes C7–9) are larger and appear in denser environments than galaxies within C10.
Convergence and Sample Complexity of Policy Gradient Methods for Stabilizing Linear Systems

System stabilization via policy gradient (PG) methods has drawn increasing attention in both control and machine learning communities. In this paper, we study their convergence and sample complexity for stabilizing linear time-invariant systems in terms of the number of system rollouts. Our analysis is built upon a discounted linear quadratic regulator (LQR) method which alternatively updates the policy and the discount factor of the LQR problem. Firstly, we propose an explicit rule to adaptively adjust the discount factor by exploring the stability margin of a linear control policy. Then, we establish the sample complexity of PG methods for stabilization, which only adds a coefficient logarithmic in the spectral radius of the state matrix to that for solving the LQR problem with a prior stabilizing policy. Finally, we perform simulations to validate our theoretical findings and demonstrate the effectiveness of our method on a class of nonlinear systems.
Federated X-Armed Bandit

This work establishes the first framework of federated X-armed bandit, where different clients face heterogeneous local objective functions defined on the same domain and are required to collaboratively figure out the global optimum. We propose the first federated algorithm for such problems, named Fed-PNE. By utilizing the topological structure of the global objective inside the hierarchical partitioning and the weak smoothness property, our algorithm achieves sublinear cumulative regret with respect to both the number of clients and the evaluation budget. Meanwhile, it only requires logarithmic communications between the central server and clients, protecting the client privacy. Experimental results on synthetic functions and real datasets validate the advantages of Fed-PNE over various centralized and federated baseline algorithms.