Miracle-dz/UniFAR-FTUs huggingface dataset:
Correlation matrix of equi-correlated normal population: fluctuation of the largest eigenvalue, scaling of the bulk eigenvalues, and stock market

Given an $N$-dimensional sample of size $T$ and form a sample correlation matrix $\mathbf{C}$. Suppose that $N$ and $T$ tend to infinity with $T/N $ converging to a fixed finite constant $Q>0$. If the population is a factor model, then the eigenvalue distribution of $\mathbf{C}$ almost surely converges weakly to Mar\v{c}enko-Pastur distribution such that the index is $Q$ and the scale parameter is the limiting ratio of the specific variance to the $i$-th variable $(i\to\infty)$. For an $N$-dimensional normal population with equi-correlation coefficient $\rho$, which is a one-factor model, for the largest eigenvalue $\lambda$ of $\mathbf{C}$, we prove that $\lambda/N$ converges to the equi-correlation coefficient $\rho$ almost surely. These results suggest an important role of an equi-correlated normal population and a factor model in (Laloux et al. Random matrix theory and financial correlations, Int. J. Theor. Appl. Finance, 2000): the histogram of the eigenvalue of sample correlation matrix of the returns of stock prices fits the density of Mar\v{c}enko-Pastur distribution of index $T/N $ and scale parameter $1-\lambda/N$. Moreover, we provide the limiting distribution of the largest eigenvalue of a sample covariance matrix of an equi-correlated normal population. We discuss the phase transition as to the decay rate of the equi-correlation coefficient in $N$.
MegaCRN: Meta-Graph Convolutional Recurrent Network for Spatio-Temporal Modeling

Spatio-temporal modeling as a canonical task of multivariate time series forecasting has been a significant research topic in AI community. To address the underlying heterogeneity and non-stationarity implied in the graph streams, in this study, we propose Spatio-Temporal Meta-Graph Learning as a novel Graph Structure Learning mechanism on spatio-temporal data. Specifically, we implement this idea into Meta-Graph Convolutional Recurrent Network (MegaCRN) by plugging the Meta-Graph Learner powered by a Meta-Node Bank into GCRN encoder-decoder. We conduct a comprehensive evaluation on two benchmark datasets (METR-LA and PEMS-BAY) and a large-scale spatio-temporal dataset that contains a variaty of non-stationary phenomena. Our model outperformed the state-of-the-arts to a large degree on all three datasets (over 27% MAE and 34% RMSE). Besides, through a series of qualitative evaluations, we demonstrate that our model can explicitly disentangle locations and time slots with different patterns and be robustly adaptive to different anomalous situations. Codes and datasets are available at https://github.com/deepkashiwa20/MegaCRN.
Gelation and Re-entrance in Mixtures of Soft Colloids and Linear Polymers of Equal Size

Liquid mixtures composed of colloidal particles and much smaller non-adsorbing linear homopolymers can undergo a gelation transition due to polymer-mediated depletion forces. We now show that the addition of linear polymers to suspensions of soft colloids having the same hydrodynamic size yields a liquid-to-gel-to-re-entrant liquid transition. In particular, the dynamic state diagram of 1,4-polybutadiene star–linear polymer mixtures was determined with the help of linear viscoelastic and small-angle X-ray scattering experiments. While keeping the star polymers below their nominal overlap concentration, a gel was formed upon increasing the linear polymer content. Further addition of linear chains yielded a re-entrant liquid. This unexpected behavior was rationalized by the interplay of three possible phenomena: (i) depletion interactions, driven by the size disparity between the stars and the polymer length scale which is the mesh size of its entanglement network; (ii) colloidal deswelling due to the increased osmotic pressure exerted onto the stars; and (iii) a concomitant progressive suppression of the depletion efficiency on increasing the polymer concentration due to reduced mesh size, hence a smaller range of attraction. Our results unveil an exciting new way to tailor the flow of soft colloids and highlight a largely unexplored path to engineer soft colloidal mixtures.
Velocity Offset Between Emission and Absorption Lines Might Be an Effective Indicator of a Dual Core System

This paper presents the detection of a significant velocity offset between the emission and absorption lines of a dual core system in SDSS J155708.82+273518.74 (=SDSS J1557). The photometric image of SDSS J1557 exhibits two clear cores with a projected separation of ∼2. ″2 (4.9 kpc) determined by GALFIT. Based on the applications of the commonly accepted pPXF code with 636 theoretical SSP templates, the host galaxy contribution can be well determined. Then, the emission-line features of SDSS J1557 can be well measured after subtraction of the host starlight. It is found that the velocity offset of emission lines with respect to absorption lines reaches 458 ± 13 km s−1. According to a Baldwin–Phillips–Terlevich diagram, SDSS J1557 is a composite galaxy. In addition, SDSS J1557 can well fit the M BH − σ * relation of bulges, and a galaxy merger would not change this relation. Two reasonable models (an AGN-driven outflow versus a dual core system) are discussed to explain this velocity offset. The model of an AGN-driven outflow fails to interpret the systematic redshift of the emission lines and similar velocity offsets for the various emission lines of SDSS J1557. Instead, the significant velocity offset between the emission and absorption lines might be an effective indicator of a dual core system.
Macroscopic quantum effects of electromagnetic induction in silicon nanostructures

At room temperature, a macroscopic quantum galvanomagnetic effect of Faraday electromagnetic induction was demonstrated under conditions of the capture of single magnetic flux quanta in the edge channels, confined by chains of negative-U centers, in a silicon nanostructure heavily doped with boron, prepared in Hall geometry on an n-type Si (100) substrate. It is shown that this effect leads to the appearance of an induction current when only a constant magnetic field is applied in the absence of an externally applied voltage or a stabilized current. The experimental dependences of xx U , xy U , and pn U on the magnitude of the external magnetic field in its various directions demonstrate both the Hall staircase of conductivity and the Shubnikov–de Haas oscillations.
Changes in Power and Information Flow in Resting-state EEG by Working Memory Process

Many studies have analyzed working memory (WM) from electroencephalogram (EEG). However, little is known about changes in the brain neurodynamics among resting-state (RS) according to the WM process. Here, we identified frequencyspecific power and information flow patterns among three RS EEG before and after WM encoding and WM retrieval. Our results demonstrated the difference in power and information flow among RS EEG in delta (1-3.5 Hz), alpha (8-13.5 Hz), and beta (14-29.5 Hz) bands. In particular, there was a marked increase in the alpha band after WM retrieval. In addition, we calculated the association between significant characteristics of RS EEG and WM performance, and interestingly, correlations were found only in the alpha band. These results suggest that RS EEG according to the WM process has a significant impact on the variability and WM performance of brain mechanisms in relation to cognitive function.
Examples of unicity subspaces in L1-approximation

The purpose of this paper is to study the problem of existence of subspaces G of C(X) where is a compact disconnected subset of the real line or a compact subset of such that G guarantees uniqueness of best L1-approximations for weighted approximation of continuous real-valued functions. Some examples of such subspaces, including subspaces of polynomials and linear spline functions of two variables, are presented.
Change in Kinetics and Kinematics during 1-Footed Drop Landing with an Increase in Upper Body Weight

The purpose of this study was to investigate changes in kinetic and kinematic variables associated with an increase in upper body weight. Eighteen healthy male university students(, ) participated. Eight motion analysis cameras(Qualysis Oqus 500) and 2 force AMTI platforms(Advanced Mechanical Technologies Inc. OR6-7, US) were used to record motion and forces during the drop landing at a frequency of 120 Hz and 1200 Hz, respectively. QTM software(Qualisys Track Manager) was used to record the data, and the variables were analyzed with Visual 3D and Matlab 2009. For the drop landing, a box of was constructed from wood. Knee and ankle maximum flexion angle, knee flexion angle, knee and ankle angle at landing, time for maximum ankle flexion after landing, and time for maximum knee flexion after landing were calculated. There was a significant change in the time for maximum and minimum ground force reaction and the time for maximum dorsal flexion after landing(p
Algorithms Approaching the Threshold for Semi-random Planted Clique

We design new polynomial-time algorithms for recovering planted cliques in the semi-random graph model introduced by Feige and Kilian. The previous best algorithms for this model succeed if the planted clique has size at least n2/3 in a graph with n vertices. Our algorithms work for planted-clique sizes approaching n1/2 — the information-theoretic threshold in the semi-random model and a conjectured computational threshold even in the easier fully-random model. This result comes close to resolving open questions by Feige and Steinhardt. To generate a graph in the semi-random planted-clique model, we first 1) plant a clique of size k in an n-vertex –graph with edge probability 1/2 and then adversarially add or delete an arbitrary number edges not touching the planted clique and delete any subset of edges going out of the planted clique. For every є>0, we give an nO(1/є)-time algorithm that recovers a clique of size k in this model whenever k ≥ n1/2+є. In fact, our algorithm computes, with high probability, a list of about n/k cliques of size k that contains the planted clique. Our algorithms also extend to arbitrary edge probabilities p and improve on the previous best guarantee whenever p ≤ 1−n−0.001. Our algorithms rely on a new conceptual connection that translates certificates of upper bounds on biclique numbers in unbalanced bipartite –random graphs into algorithms for semi-random planted clique. Analogous to the (conjecturally) optimal algorithms for the fully-random model, the previous best guarantees for semi-random planted clique correspond to spectral relaxations of biclique numbers based on eigenvalues of adjacency matrices. We construct an SDP lower bound that shows that the n2/3 threshold in prior works is an inherent limitation of these spectral relaxations. We go beyond this limitation by using higher-order sum-of-squares relaxations for biclique numbers. We also provide some evidence that the information-computation trade-off of our current algorithms may be inherent by proving an average-case lower bound for unbalanced bicliques in the low-degree polynomial model.
The Heisenberg-Wigner formalism for transverse fields

We discuss the Heisenberg-Wigner phase-space formalism in quantum electrodynamics as well as scalar quantum electrodynamics with respect to transverse ﬁelds. In regard to the special characteristics of such ﬁeld types we derive modiﬁed transport equations such that particle momenta perpendicular to the propagation direction of the waves show up as external parameters only. In case of spatially oscillating ﬁelds we further demonstrate how to transform momentum derivative operators of inﬁnite order into simple coupling terms.
Present and future constraints on secluded dark matter in the Galactic Halo with TeV Gamma-ray observatories

The dark matter relic density may be governed by the presence of new mediators that connect the dark matter field with the Standard Model particles. When the dark matter particle mass is larger than the mediator's, the pair production of mediators is kinematically open. This setup is known in the literature as secluded dark matter. Motivated by the appearance of secluded dark matter in several model building endeavours, we investigate the sensitivity of TeV gamma-ray instruments in the Southern Hemisphere namely, H.E. S.S. , CTA, and SWGO to secluded dark matter annihilating in the Galactic Halo. We exploit the complementarity aspects of these detectors to find restrictive bounds on the annihilation cross-section for different annihilation channels. In particular, for a dark matter particle mass of 2 TeV, H.E. S.S. is able to constraint 〈σv〉 ≥ 4 × 10-26 cm3 s-1 at 95% confidence level for the 4q and 4τ channel, while CTA will be sensitive to 〈σv〉 ≥ 7 × 10-27 cm3 s-1 and SWGO 〈σv〉 ≥ 6 × 10-27 cm3 s-1 for the 4τ channel, both well below the thermal relic cross-section. In fact, the combination of CTA and SWGO will be able to probe cross-sections below the thermal relic value for dark matter particles in the whole mass range between 100 GeV and 100 TeV in the 4q and 4τ channels, and between 100 GeV and ∼ 40 TeV in the 4b channel.
Microwave response of type-II superconductors at weak pinning

Theory of linear microwave response of thin films of type-II superconductors in the mixed state is developed taking into account random spatial fluctuations of the parameters of the system, such as the order parameter, diffusion coefficient, or film thickness. In the regime of collective pinning the microwave response of the system exhibits strong frequency dispersion, arising from nonequilibrium vortex core quasiparticles. The corresponding contribution to the ac conductivity is controlled by the inelastic relaxation time, and may exceed the usual Bardeen-Stephen conductivity. It is caused by the Debye-type inelastic relaxation. Debye mechanism of microwave losses may be responsible for strong effects of electromagnetic noise upon dc conductivity in the mixed state at low temperatures.
Large Discourse Treebanks from Scalable Distant Supervision

Discourse parsing is an important upstream task in Natural Language Processing (NLP) with strong implications for many real-world applications, for example sentiment analysis (Bhatia et al., 2015; Nejat et al., 2017; Hogenboom et al., 2015), text classification (Ji and Smith, 2017) and summarization (Gerani et al., 2014), just to name a few. Despite this widely recognized role of discourse parsing in NLP, most recent discourse parsers (and consequently downstream tasks) still rely on small scale human annotated discourse treebanks (such as RSTDT (Carlson et al., 2003), Instr-DT (Subba and Di Eugenio, 2009) or PDTB (Prasad et al., 2008)), trying to infer general-purpose discourse structures from very limited data in a few narrow domains. While in principle diverse and large discourse treebanks could be annotated, the process is expensive, tedious and does not scale. To overcome this dire situation and allow discourse parsers to be trained on larger, more diverse and domain independent datasets, we propose a framework to generate “silver-standard” discourse trees from distant supervision on the auxiliary task of sentiment analysis1. Our approach explicitly models discourse structures, distinguishing it from previous work on implicit discourse modelling, such as Liu et al. (2019), previously criticized in Ferracane et al. (2019).
Temporal broadening of attosecond photoelectron wavepackets from solid surfaces

The response of solids to electromagnetic fields is of crucial importance in many areas of science and technology. Many fundamental questions remain to be answered about the dynamics of the photoexcited electrons that underpin this response, which can evolve on timescales of tens to hundreds of attoseconds. How, for example, is the photoexcited electron affected by the periodic potential as it travels in the solid, and how do the other electrons respond in these strongly correlated systems? Furthermore, control of electronic motion in solids with attosecond precision would pave the way for the development of ultrafast optoelectronics. Attosecond electron dynamics can be traced using streaking, a technique in which a strong near-infrared laser field accelerates an attosecond electron wavepacket photoemitted by an extreme ultraviolet light pulse, imprinting timing information onto it. We present attosecond streaking measurements on the wide-bandgap semiconductor tungsten trioxide, and on gold, a metal used in many nanoplasmonic devices. Information about electronic motion in the solid is encoded on the temporal properties of the photoemitted electron wavepackets, which are consistent with a spread of electron transport times to the surface following photoexcitation.
A scheme for excitation of thorium-229 nuclei based on the electronic bridge excitaion

Thorium-229 possesses the lowest nuclear ﬁrst excited state with an energy of about 8 eV. The extremely narrow linewidth of the nuclear ﬁrst excited state with the uncertainty of 53 THz prevents the direct laser excitation and the realization of the nuclear clock. We present a proposal using the Coulomb crystal of a linear chain formed by the 229 Th 3+ ions, the nuclei of 229 Th 3+ ions in the ion trap are excited by the electronic bridge (EB) process. The 7 P 1 / 2 state of the thorium-229 nuclear ground state is chosen for the EB excitation. Using the two-level optical Bloch equation under experimental conditions, we calculate that 2 out of 36 prepared thorium ions in the Coulomb crystal can be excited to the nuclear ﬁrst excited state, and it takes about 2 hours to scan over the uncertainty of 0.22 eV. Taking the advantage of transition enhancement of the EB and the long stability of the Coulomb crystal, the energy uncertainty of the ﬁrst excited state can be limited to the order of 1 GHz.
Tropicalization of the mirror curve near the large radius limit

The mirror of a toric orbifold is an affine curve called the mirror curve. In this paper, firstly, we recall the basic tools in tropical geometry and give a definition of the mirror curve. Then we calculate the tropical spine of the mirror curve for a smooth toric Calabi-Yau 3-fold near the large radius limit. Finally, we recall a special kind of real algebraic curves called the cyclic-M curve and show that under some special choices of parameters near the large radius limit, the mirror curve is a cyclic-M curve. Applying Mikhalkin's result of cyclic-M curves, we show that the mirror curve is glued from tubes and pairs of pants.
Linear transfers as minimal costs of dilations of measures in balayage order

Linear transfers between probability distributions were introduced in [5,6] in order to extend the theory of optimal mass transportation while preserving the important duality established by Kantorovich. It is shown here that $\{0, +\infty\}$-valued linear transfers can be characterized by balayage of measures with respect to suitable cones of functions \`a la Choquet, while general linear transfers extend balayage theory by requiring the"sweeping out"of measures to optimize certain cost functionals. We study the dual class of Kantorovich operators, which are natural and manageable extensions of Markov operators. It is also an important subclass of capacities, and could be called"convex functional Choquet capacities,"since they play for non-linear maps the same role that convex envelopes do for arbitrary numerical functions. A forthcoming paper [7] will study their ergodic properties and their applications.
Evaluating Model-free Reinforcement Learning toward Safety-critical Tasks

Safety comes first in many real-world applications involving autonomous agents. Despite a large number of reinforcement learning (RL) methods focusing on safety-critical tasks, there is still a lack of high-quality evaluation of those algorithms that adheres to safety constraints at each decision step under complex and unknown dynamics. In this paper, we revisit prior work in this scope from the perspective of state-wise safe RL and categorize them as projection-based, recovery-based, and optimization-based approaches, respectively. Furthermore, we propose Unrolling Safety Layer (USL), a joint method that combines safety optimization and safety projection. This novel technique explicitly enforces hard constraints via the deep unrolling architecture and enjoys structural advantages in navigating the trade-off between reward improvement and constraint satisfaction. To facilitate further research in this area, we reproduce related algorithms in a unified pipeline and incorporate them into SafeRL-Kit, a toolkit that provides off-the-shelf interfaces and evaluation utilities for safety-critical tasks. We then perform a comparative study of the involved algorithms on six benchmarks ranging from robotic control to autonomous driving. The empirical results provide an insight into their applicability and robustness in learning zero-cost-return policies without task-dependent handcrafting. The project page is available at https://sites.google. com/view/saferlkit.
QESK: Quantum-based Entropic Subtree Kernels for Graph Classification

In this paper, we propose a novel graph kernel, namely the Quantum-based Entropic Subtree Kernel (QESK), for Graph Classification. To this end, we commence by computing the Average Mixing Matrix (AMM) of the Continuous-time Quantum Walk (CTQW) evolved on each graph structure. Moreover, we show how this AMM matrix can be employed to compute a series of entropic subtree representations associated with the classical Weisfeiler-Lehman (WL) algorithm. For a pair of graphs, the QESK kernel is defined by computing the exponentiation of the negative Euclidean distance between their entropic subtree representations, theoretically resulting in a positive definite graph kernel. We show that the proposed QESK kernel not only encapsulates complicated intrinsic quantum-based structural characteristics of graph structures through the CTQW, but also theoretically addresses the shortcoming of ignoring the effects of unshared substructures arising in state-of-the-art R-convolution graph kernels. Moreover, unlike the classical R-convolution kernels, the proposed QESK can discriminate the distinctions of isomorphic subtrees in terms of the global graph structures, theoretically explaining the effectiveness. Experiments indicate that the proposed QESK kernel can significantly outperform state-of-the-art graph kernels and graph deep learning methods for graph classification problems.
On the LAMBDA -type doubling in the ground state of SiH.

The (0, 0) band of the 2? -2? transition of SiH has been remeasured from high-dispersion plates and more precise values of the ? -doubling parameters for the 2? state have been determined. From these optical measurements the transition between the two components of the lowest rotational level can be predicted to lie at 2968 ? 6 MHz.