Miracle-dz/UniFAR-FTUs huggingface dataset:
Probing sterile neutrino dark matter in the PTOLEMY-like experiment

We study the prospect to detect the cosmic background of sterile neutrinos in the tritium β-decay, such as the PTOLEMY-like experiments. The sterile neutrino with mass between 1 eV–10 keV may contribute to the local density as warm or cold dark matter component. In this study, we investigate the possibility for searching them in the models with different production in the early Universe, without assuming sterile neutrino as full dark matter component. In these models, especially with low-reheating temperature and late-time phase transition, the capture rate per year can be greatly enhanced to be 𝒪(10) around the mass range 10–100 eV without violating other astrophysical and cosmological observations.
HARDY INEQUALITIES ON RIEMANNIAN MANIFOLDS WITH NEGATIVE CURVATURE

Let M be a complete, simply connected Riemannian manifold with negative curvature. We obtain the sharp constants of Hardy and Rellich inequalities related to the geodesic distance on M. Furthermore, if M is with strictly negative curvature, we show that the Lp Hardy inequalities can be globally refined by adding remainder terms like the Brezis–Vazquez improvement in case p ≥ 2, which is contrary to the case of Euclidean spaces.
Uncertainty quantification for sparse Fourier recovery

One of the most prominent methods for uncertainty quantification in high-dimen-sional statistics is the desparsified LASSO that relies on unconstrained $\ell_1$-minimization. The majority of initial works focused on real (sub-)Gaussian designs. However, in many applications, such as magnetic resonance imaging (MRI), the measurement process possesses a certain structure due to the nature of the problem. The measurement operator in MRI can be described by a subsampled Fourier matrix. The purpose of this work is to extend the uncertainty quantification process using the desparsified LASSO to design matrices originating from a bounded orthonormal system, which naturally generalizes the subsampled Fourier case and also allows for the treatment of the case where the sparsity basis is not the standard basis. In particular we construct honest confidence intervals for every pixel of an MR image that is sparse in the standard basis provided the number of measurements satisfies $n \gtrsim\max\{ s\log^2 s\log p, s \log^2 p \}$ or that is sparse with respect to the Haar Wavelet basis provided a slightly larger number of measurements.
Bayesian interpolation with deep linear networks

Significance Understanding the interplay between network architecture, dataset statistics, and learning algorithms is a key challenge in deep learning. We overcome this challenge analytically for zero-noise Bayesian inference in neural networks with linear activations and output dimension one but arbitrary depth, width, and training data. Our results provide the first rigorous solutions to learning with neural networks in which depth, width, and dataset can vary freely. We identify an emergent notion of effective depth, which combines depth, width, and dataset size, that must be large for networks to compute optimal posteriors from universal priors. Our results both present novel examples of models admitting exact solutions to Bayesian inference and give the first principled Bayesian justification for preferring deeper networks.
Offline Policy Optimization in RL with Variance Regularizaton

Learning policies from fixed offline datasets is a key challenge to scale up reinforcement learning (RL) algorithms towards practical applications. This is often because off-policy RL algorithms suffer from distributional shift, due to mismatch between dataset and the target policy, leading to high variance and over-estimation of value functions. In this work, we propose variance regularization for offline RL algorithms, using stationary distribution corrections. We show that by using Fenchel duality, we can avoid double sampling issues for computing the gradient of the variance regularizer. The proposed algorithm for offline variance regularization (OVAR) can be used to augment any existing offline policy optimization algorithms. We show that the regularizer leads to a lower bound to the offline policy optimization objective, which can help avoid over-estimation errors, and explains the benefits of our approach across a range of continuous control domains when compared to existing state-of-the-art algorithms.
Node-Element Hypergraph Message Passing for Fluid Dynamics Simulations

A recent trend in deep learning research features the application of graph neural networks for mesh-based continuum mechanics simulations. Most of these frameworks operate on graphs in which each edge connects two nodes. Inspired by the data connectivity in the ﬁnite element method, we connect the nodes by elements rather than edges, effectively forming a hypergraph. We implement a message-passing network on such a node-element hypergraph and explore the capability of the network for the modeling of ﬂuid ﬂow. The network is tested on two common benchmark problems, namely the ﬂuid ﬂow around a circular cylinder and airfoil conﬁgurations. The results show that such a message-passing network deﬁned on the node-element hypergraph is able to generate more stable and accurate temporal roll-out predictions compared to the baseline generalized message-passing network deﬁned on a normal graph. Along with adjustments in activation function and training loss, we expect this work to set a new strong baseline for future explorations of mesh-based ﬂuid simulations with graph neural networks.
Progress on the QCD Deconfinement Critical Point for $N_\text{f}=2$ Staggered Fermions

The global center symmetry of quenched QCD at zero baryonic chemical potential is broken spontaneously at a critical temperature $T_c$ leading to a first-order phase transition. Including heavy dynamical quarks breaks the center symmetry explicitly and weakens the first-order phase transition for decreasing quark masses until it turns into a smooth crossover at a $Z(2)$-critical point. We investigate the $Z(2)$-critical quark mass value towards the continuum limit for $N_\text{f}=2$ flavors using lattice QCD in the staggered formulation. As part of a continued study, we present results from Monte-Carlo simulations on $N_\tau=8,10$ lattices. Several aspect ratios and quark mass values were simulated in order to obtain the critical mass from a fit of the Polyakov loop to a kurtosis finite size scaling formula. Moreover, the possibility to develop a Ginzburg-Landau effective theory around the $Z(2)$-critical point is explored.
WaveFormer: transformer-based denoising method for gravitational-wave data

With the advent of gravitational-wave astronomy and the discovery of more compact binary coalescences, data quality improvement techniques are desired to handle the complex and overwhelming noise in gravitational wave (GW) observational data. Though recent machine learning-based studies have shown promising results for data denoising, they are unable to precisely recover both the GW signal amplitude and phase. To address such an issue, we develop a deep neural network centered workflow, WaveFormer, for significant noise suppression and signal recovery on observational data from the Laser Interferometer Gravitational-Wave Observatory (LIGO). The WaveFormer has a science-driven architecture design with hierarchical feature extraction across a broad frequency spectrum. As a result, the overall noise and glitch are decreased by more than one order of magnitude and the signal recovery error is roughly 1% and 7% for the phase and amplitude, respectively. Moreover, on 75 reported binary black hole (BBH) events of LIGO we obtain a significant improvement in inverse false alarm rate. Our work highlights the potential of large neural networks in gravitational wave data analysis and, while primarily demonstrated on LIGO data, its adaptable design indicates promise for broader application within the International Gravitational-Wave Observatories Network (IGWN) in future observational runs.
Probability transport on the Fock space of a disordered quantum spin chain

Within the broad theme of understanding the dynamics of disordered quantum many-body systems, one of the simplest questions one can ask is: given an initial state, how does it evolve in time on the associated Fock-space graph, in terms of the distribution of probabilities thereon? A detailed quantitative description of the temporal evolution of out-of-equilibrium disordered quantum states and probability transport on the Fock space, is our central aim here. We investigate it in the context of a disordered quantum spin chain which hosts a disorder-driven many-body localisation transition. Real-time dynamics/probability transport is shown to exhibit a rich phenomenology, which is markedly different between the ergodic and many-body localised phases. The dynamics is for example found to be strongly inhomogeneous at intermediate times in both phases, but while it gives way to homogeneity at long times in the ergodic phase, the dynamics remain inhomogeneous and multifractal in nature for arbitrarily long times in the localised phase. Similarly, we show that an appropriately defined dynamical lengthscale on the Fock-space graph is directly related to the local spin-autocorrelation, and as such sheds light on the (anomalous) decay of the autocorrelation in the ergodic phase, and lack of it in the localised phase.
Shared Cache Coded Caching Schemes Using Designs and Circuits of Matrices

In this paper, we study shared cache coded caching (SC-CC): a set of caches serves a larger set of users; each user access one cache, and a cache may serve many users. For this problem, under uncoded placement, Parrinello, \"Unsal, and Elia showed an optimal SC-CC scheme, in which the subpacketization level depends upon the number of caches. We show an SC-CC scheme where the subpacketization level does not directly depend upon the number of users or caches; any number of caches and users can be accommodated for a fixed subpacketization level. Furthermore, new caches can be added without re-doing the placement of the existing caches. We show that given an upper limit on the allowable subpacketization level, our SC-CC scheme may achieve a lesser rate than other relevant SC-CC schemes. Our scheme is constructed using matrices and designs. A matroid can be obtained from a matrix over a finite field; the placement of our scheme is decided by a design constructed from a matrix; the circuits of a matroid obtained from the matrix and the design is used to decide the delivery.
Transformer in Transformer as Backbone for Deep Reinforcement Learning

Designing better deep networks and better reinforcement learning (RL) algorithms are both important for deep RL. This work focuses on the former. Previous methods build the network with several modules like CNN, LSTM and Attention. Recent methods combine the Transformer with these modules for better performance. However, it requires tedious optimization skills to train a network composed of mixed modules, making these methods inconvenient to be used in practice. In this paper, we propose to design \emph{pure Transformer-based networks} for deep RL, aiming at providing off-the-shelf backbones for both the online and offline settings. Specifically, the Transformer in Transformer (TIT) backbone is proposed, which cascades two Transformers in a very natural way: the inner one is used to process a single observation, while the outer one is responsible for processing the observation history; combining both is expected to extract spatial-temporal representations for good decision-making. Experiments show that TIT can achieve satisfactory performance in different settings consistently.
Differentiable Search of Accurate and Robust Architectures

Deep neural networks (DNNs) are found to be vulnerable to adversarial attacks, and various methods have been proposed for the defense. Among these methods, adversarial training has been drawing increasing attention because of its simplicity and effectiveness. However, the performance of the adversarial training is greatly limited by the architectures of target DNNs, which often makes the resulting DNNs with poor accuracy and unsatisfactory robustness. To address this problem, we propose DSARA to automatically search for the neural architectures that are accurate and robust after adversarial training. In particular, we design a novel cell-based search space specially for adversarial training, which improves the accuracy and the robustness upper bound of the searched architectures by carefully designing the placement of the cells and the proportional relationship of the filter numbers. Then we propose a two-stage search strategy to search for both accurate and robust neural architectures. At the first stage, the architecture parameters are optimized to minimize the adversarial loss, which makes full use of the effectiveness of the adversarial training in enhancing the robustness. At the second stage, the architecture parameters are optimized to minimize both the natural loss and the adversarial loss utilizing the proposed multi-objective adversarial training method, so that the searched neural architectures are both accurate and robust. We evaluate the proposed algorithm under natural data and various adversarial attacks, which reveals the superiority of the proposed method in terms of both accurate and robust architectures. We also conclude that accurate and robust neural architectures tend to deploy very different structures near the input and the output, which has great practical significance on both hand-crafting and automatically designing of accurate and robust neural architectures.
POMRL: No-Regret Learning-to-Plan with Increasing Horizons

We study the problem of planning under model uncertainty in an online meta-reinforcement learning (RL) setting where an agent is presented with a sequence of related tasks with limited interactions per task. The agent can use its experience in each task and across tasks to estimate both the transition model and the distribution over tasks. We propose an algorithm to meta-learn the underlying structure across tasks, utilize it to plan in each task, and upper-bound the regret of the planning loss. Our bound suggests that the average regret over tasks decreases as the number of tasks increases and as the tasks are more similar. In the classical single-task setting, it is known that the planning horizon should depend on the estimated model's accuracy, that is, on the number of samples within task. We generalize this finding to meta-RL and study this dependence of planning horizons on the number of tasks. Based on our theoretical findings, we derive heuristics for selecting slowly increasing discount factors, and we validate its significance empirically.
Decoupled Self-supervised Learning for Non-Homophilous Graphs

This paper studies the problem of conducting self-supervised learning for node representation learning on graphs. Most existing self-supervised learning methods assume the graph is homophilous, where linked nodes often belong to the same class or have similar features. However, such assumptions of homophily do not always hold in real-world graphs. We address this problem by developing a decoupled self-supervised learning (DSSL) framework for graph neural networks. DSSL imitates a generative process of nodes and links from latent variable modeling of the semantic structure, which decouples different underlying semantics between different neighborhoods into the self-supervised learning process. Our DSSL framework is agnostic to the encoders and does not need prefabricated augmentations, thus is flexible to different graphs. To effectively optimize the framework, we derive the evidence lower bound of the self-supervised objective and develop a scalable training algorithm with variational inference. We provide a theoretical analysis to justify that DSSL enjoys the better downstream performance. Extensive experiments on various types of graph benchmarks demonstrate that our proposed framework can achieve better performance compared with competitive baselines.
Entanglement dynamics of multi-parametric random states: a single parametric formulation

A non-ergodic quantum state of a complex system is in general random as well as multi-parametric, former due to a lack of exact information due to complexity and latter reflecting its varied behavior in different parts of the Hilbert space. An appropriate representation for the reduced density matrix of such a state is a generalized, multi-parametric Wishart ensemble with unit trace. Our theoretical analysis of these ensembles not only resolves the controversy about the growth rates of the average information entropies of the generic states but also leads to new insights in their entanglement dynamics. While the state itself is multi-parametric, we find that the growth of the average measures can be described in terms of an information-theoretic function, referred as the complexity parameter. The latter in turn leads to a common mathematical formulation of the measures for a wide range of states; it could also act as a possible tool for hierarchical arrangement of the entangled states of different systems.
Reiterated Homogenization of nonlinear degenerate elliptic operators with nonstandard growth

It is shown by means of reiterated two-scale convergence in the Sobolev-Orlicz setting, that the sequence of solutions of a class of highly oscillatory problems involving nonlinear elliptic operators with nonstandard growth, converges to a solution of a suitable homogeneous nonlinear elliptic equation associated to an operator with nonstandard growth.
Transonic shocks for 2D steady exothermically reacting Euler flows in a finite nozzle

This paper concerns the existence of transonic shocks for steady exothermically reacting Euler flows in an almost flat nozzle with the small rate of the exothermic reaction. One of the key points is to quantitatively determine the position of the shock front in the nozzle. We focus on contributions of the perturbation of the flat nozzle and the exothermic reaction in determining the position of the shock front by comparing the orders of σ and κ, where σ represents the scale of the perturbation of the flat nozzle and κ represents the rate of the exothermic reaction. To this end, a free boundary problem for the linearized reacting Euler system is proposed to catch an approximating position of the shock front and the associated approximating shock solution, with which the existence of a shock solution close to it can be established via a nonlinear iteration scheme. One of the key steps is to solve the nonlinear equation derived from the solvability condition for the elliptic sub-problem in the domain of the subsonic flow behind the shock front, which determines the free boundary of the proposed problem. Four typical cases are analyzed, which describe possible interactions between the geometry of the nozzle boundary and the exothermic reaction. The results also manifest that the exothermic reaction has a stabilization effect on transonic shocks in the nozzles.
Energy backscatter in large-eddy simulations of three-dimensional incompressible isotropic turbulence

The issue of energy backscatter in decaying three-dimensional incompressible isotropic turbulence is studied by means of large-eddy simulations (LES). For each set of initial parameters, multiple realizations are performed to improve the statistical convergence of the infrared modes. For an initial energy spectrum E(k, 0) ∝ k s 0 as k → 0 with s 0 = 4, LES display a non-negligible k 4 energy backscatter at subsequent times: E(k,t) ∝ t γ4 k 4. The value of γ4, superior to the 0.16 eddy-damped quasi-normal Markovian(EDQNM) value, depends upon the resolution of the simulation and the integration time. In the LES initialized with s 0 = 3.5, a weak energy growth is observed at small wavenumbers. However, the infrared energy spectrum does not develop the k 4 component predicted by Eyink and Thomson (2000 Phys. Fluids 12 477–9). With s 0 = 3, on the other hand, an almost perfect invariance of the infrared energy spectrum is observed. Attention is also paid to the energy decay laws. For s 0 = 4, energy decays as .
Characteristics of constrained turbulent transport in flux-driven toroidal plasmas

We study the dynamics of turbulence transport subject to a constraint on the profile formation and relaxation, dominated by the ion temperature gradient modes, within the framework of adiabatic electron response using a flux-driven global gyro-kinetic toroidal code, GKNET. We observe exponentially constrained profiles, with two different scale lengths, that are spatially constant in each region in higher input power regimes. The profiles are smoothly connected in the knee region located at 1/2−2/3 of the minor radius, outside which the gradient is steepened and shows a weak confinement improvement. Based on the probability density function analysis of heat flux eddies, the power law demonstrates a dependence on the eddy size S, as P∼S−α, which distinguishes events into diffusive and non-diffusive parts including the validation of quasi-linear hypotheses. Radially localized avalanches and global bursts, which exhibit different spatial scales, play central roles in giving rise to constrained profiles on an equal footing. It is also found that the E×B shear layers are initiated by the global bursts, which evolve downward on a slow time scale across the knee region and play a role in adjusting the profile by increasing the gradient. This article is part of a discussion meeting issue ‘H-mode transition and pedestal studies in fusion plasmas’.
Lower Bounds on Implementing Mediators in Asynchronous Systems with Rational and Malicious Agents

Abraham, Dolev, Geffner, and Halpern [1] proved that, in asynchronous systems, a (k, t)-robust equilibrium for n players and a trusted mediator can be implemented without the mediator as long as n > 4(k+t), where an equilibrium is (k, t)-robust if, roughly speaking, no coalition of t players can decrease the payoff of any of the other players, and no coalition of k players can increase their payoff by deviating. We prove that this bound is tight, in the sense that if n ≤ 4(k+t) there exist (k, t)-robust equilibria with a mediator that cannot be implemented by the players alone. Even though implementing (k, t)-robust mediators seems closely related to implementing asynchronous multiparty (k+t)-secure computation [6], to the best of our knowledge there is no known straightforward reduction from one problem to another. Nevertheless, we show that there is a non-trivial reduction from a slightly weaker notion of (k+t)-secure computation, which we call (k+t)-strict secure computation, to implementing (k, t)-robust mediators. We prove the desired lower bound by showing that there are functions on n variables that cannot be (k+t)-strictly securely computed if n ≤ 4(k+t). This also provides a simple alternative proof for the well-known lower bound of 4t+1 on asynchronous secure computation in the presence of up to t malicious agents [4, 8, 10].
Numerical Simulation of Bubble Merger Process on a Single Nucleation Site During Pool Nucleate Boiling

A bubble merger process on a single nucleation site has been investigated by numerically solving the equations governing conservation of mass, momentum and energy in the vapor and liquid phases. The vapor-liquid interface is captured by a level set method which can easily handle breaking and merging of the interface. The level set method is modified to include the effects of phase change at the interface and contact angle at the wall. Also, the evaporative heat flux from the thin liquid film that forms underneath a growing bubble attached to the wall is incorporated in the analysis. Based on the numerical simulations, the effect of bubble merger on vapor removal rate, flow field and heat transfer has been quantified