Miracle-dz/UniFAR-FTUs huggingface dataset:
Online Dominating Set and Independent Set

Finding minimum dominating set and maximum independent set for graphs in the classical online setup are notorious due to their disastrous $\Omega(n)$ lower bound of the competitive ratio that even holds for interval graphs, where $n$ is the number of vertices. In this paper, inspired by Newton number, first, we introduce the independent kissing number $\zeta$ of a graph. We prove that the well known online greedy algorithm for dominating set achieves optimal competitive ratio $\zeta$ for any graph. We show that the same greedy algorithm achieves optimal competitive ratio $\zeta$ for online maximum independent set of a class of graphs with independent kissing number $\zeta$. For minimum connected dominating set problem, we prove that online greedy algorithm achieves an asymptotic competitive ratio of $2(\zeta-1)$, whereas for a family of translated convex objects the lower bound is $\frac{2\zeta-1}{3}$. Finally, we study the value of $\zeta$ for some specific families of geometric objects: fixed and arbitrary oriented unit hyper-cubes in $I\! \! R^d$, congruent balls in $I\! \! R^3$, fixed oriented unit triangles, fixed and arbitrary oriented regular polygons in $I\! \! R^2$. For each of these families, we also present lower bounds of the minimum connected dominating set problem.
Effect of flexoelectricity on electrostatic potential in a bent piezoelectric nanowire

Flexoelectricity presents a strong size effect, and should not be ignored for nanodevices. By taking the flexoelectricity into account, an analytical solution is deduced for the piezoelectric potential generated in a bent ZnO nanowire (NW) cantilever. It is shown that the electric potential in the NW is not independent of z-coordinate, which is different from the results based on the classical piezoelectric theory. The results also show that the effect of flexoelectricity on the voltage is significant in a bent ZnO NW even though the flexoelectric coefficients are set to be the minimum. Moreover, we find that the flexoelectricity plays an important role in filling the gap between the results from the classical piezoelectric theory and experimental results. It is indicated that one can use the flexoelectricity to modify the transfer efficiency from mechanical energy to electrical energy through strain engineering.
A discrete complement of Lyapunov's inequality and its information theoretic consequences

We establish a reversal of Lyapunov's inequality for monotone log-concave sequences, settling a conjecture of Havrilla-Tkocz and Melbourne-Tkocz. A strengthened version of the same conjecture is disproved through counter example. We also derive several information theoretic inequalities as consequences. In particular sharp bounds are derived for the varentropy, R\'enyi entropies, and the concentration of information of monotone log-concave random variables. Moreover, the majorization approach utilized in the proof of the main theorem, is applied to derive analogous information theoretic results in the symmetric setting, where the Lyapunov reversal is known to fail.
Characterization of an Instrument Model for Exoplanet Transit Spectrum Estimation through Wide-scale Analysis on HST Data

Instrument models (IMs) enable the reduction of systematic error in transit spectroscopy light-curve data, but, since the model formulation can influence the estimation of science model parameters, characterization of the instrument model effects is crucial to the interpretation of the reduced data. We analyze a simple instrument model and assess its validity and performance across Hubble WFC3 and STIS instruments. Over a large, n = 63, sample of observed targets, a Markov chain Monte Carlo sampler computes the parent distribution of each instrument model parameter. Possible parent distribution functions are then fit and tested against the empirical IM distribution. Correlation and other analyses are then performed to find IM relationships. The model is shown to perform well across the two instruments and three filters analyzed and, further, the Student’s t distribution is shown to closely fit the empirical parent distribution of IM parameters and the Gaussian distribution is shown to poorly model the observed distribution. This parent distribution can be used in the MCMC prior fitting and demonstrates IM consistency for wide-scale atmospheric analysis using this model. Finally, we propose a simple metric based on light-curve residuals to determine model performance, and we demonstrate its ability to determine whether a derived spectrum under this IM is high quality and robust.
Recognizing Series-Parallel Matrices in Linear Time

A series-parallel matrix is a binary matrix that can be obtained from an empty matrix by successively adjoining rows or columns that are copies of an existing row/column or have at most one one-entry. Equivalently, series-parallel matrices are representation matrices of graphic matroids of series-parallel graphs, which can be recognized in linear time. We propose an algorithm that, for an m-by-n matrix A with k nonzeros, determines in expected time whether A is series-parallel or returns a minimal non–series-parallel submatrix of A. We complement the developed algorithm by an efficient [Formula: see text]implementation and report about computational results. History: Accepted by Andrea Lodi, Area Editor for Design & Analysis of Algorithms–Discrete. Funding: This work was supported by Nederlandse Organisatie voor Wetenschappelijk Onderzoek [Grant OCENW.M20. 151]. Supplemental Material: The software that supports the findings of this study is available at the GitHub software repository ( https://github.com/discopt/cmr-series-parallel ).
The Three Stages of Learning Dynamics in High-Dimensional Kernel Methods

To understand how deep learning works, it is crucial to understand the training dynamics of neural networks. Several interesting hypotheses about these dynamics have been made based on empirically observed phenomena, but there exists a limited theoretical understanding of when and why such phenomena occur. In this paper, we consider the training dynamics of gradient flow on kernel least-squares objectives, which is a limiting dynamics of SGD trained neural networks. Using precise highdimensional asymptotics, we characterize the dynamics of the fitted model in two “worlds”: in the Oracle World the model is trained on the population distribution and in the Empirical World the model is trained on a sampled dataset. We show that under mild conditions on the kernel and L target regression function the training dynamics undergo three stages characterized by the behaviors of the models in the two worlds. Our theoretical results also mathematically formalize some interesting deep learning phenomena. Specifically, in our setting we show that SGD progressively learns more complex functions and that there is a “deep bootstrap” phenomenon: during the second stage, the test error of both worlds remain close despite the empirical training error being much smaller. Finally, we give a concrete example comparing the dynamics of two different kernels which shows that faster training is not necessary for better generalization.
Joint Synthesis of Safety Certificate and Safe Control Policy using Constrained Reinforcement Learning

Safety is the major consideration in controlling complex dynamical systems using reinforcement learning (RL), where the safety certificate can provide provable safety guarantee. A valid safety certificate is an energy function indicating that safe states are with low energy, and there exists a corresponding safe control policy that allows the energy function to always dissipate. The safety certificate and the safe control policy are closely related to each other and both challenging to synthesize. Therefore, existing learning-based studies treat either of them as prior knowledge to learn the other, which limits their applicability with general unknown dynamics. This paper proposes a novel approach that simultaneously synthesizes the energy-function-based safety certificate and learns the safe control policy with CRL. We do not rely on prior knowledge about either an available model-based controller or a perfect safety certificate. In particular, we formulate a loss function to optimize the safety certificate parameters by minimizing the occurrence of energy increases. By adding this optimization procedure as an outer loop to the Lagrangian-based constrained reinforcement learning (CRL), we jointly update the policy and safety certificate parameters and prove that they will converge to their respective local optima, the optimal safe policy and a valid safety certificate. We evaluate our algorithms on multiple safety-critical benchmark environments. The results show that the proposed algorithm learns provably safe policies with no constraint violation. The validity or feasibility of synthesized safety certificate is also verified numerically.
Constraints on interacting dark energy models from time-delay cosmography with seven lensed quasars

Measurements of time-delay cosmography of lensed quasars can provide an independent probe to explore the expansion history of the late-time universe. In this paper, we employ the time-delay cosmography measurements from seven lenses (here abbreviated as the TD data) to constrain interacting dark energy (IDE) models. We mainly focus on the scenario of vacuum energy (with w = −1) interacting with cold dark matter, and consider four typical cases of the interaction form Q. When the TD data alone is employed, we find that the IDE models with Q∝ρde seem to have an advantage in relieving the H0 tension between the cosmic microwave background (CMB) and TD data. When the TD data is added to the CMB+BAO+SN+H0 data, we find that: (i) the coupling parameter β in all the considered IDE models is positive within 1σ range, implying a mild preference for the case of cold dark matter decaying into dark energy; (ii) the IDE model with Q = βH0ρc slightly relieves the S8 tension, but the other considered IDE models further aggravate this tension; (iii) the Akaike information criteria of the IDE models with Q∝ρc are lower than that of the ΛCDM model, indicating that these IDE models are more preferred by the current mainstream data. We conclude that the considered IDE models have their own different advantages when the TD data is employed, and none of them can achieve good scores in all aspects.
Big bang as a topological quantum phase transition

It has been argued that a particular type of quantum-vacuum variable $q$ can provide a solution to the main cosmological constant problem and possibly also give a cold-dark-matter component. We now show that the same $q$-field may suggest a new interpretation of the big bang, namely as a quantum phase transition between topologically inequivalent vacua. These two vacua are characterized by the equilibrium values $q=\pm \, q_{0}$ and there is a kink-type solution $q(t)$ interpolating between $q=- q_{0}$ for $t\to -\infty$ and $q= +q_{0}$ for $t\to \infty$, with conformal symmetry for $q=0$ at $t=0$.
Analytic Solution to the Dynamical Friction Acting on Circularly Moving Perturbers

We present an analytic approach to the dynamical friction (DF) acting on a circularly moving point mass perturber in a gaseous medium. We demonstrate that, when the perturber is turned on at t = 0, steady state (infinite time perturbation) is achieved after exactly one sound-crossing time. At low Mach numbers ≪1 , the circular-motion steady-state DF converges to the linear-motion, finite time perturbation expression. The analytic results describe both the radial and tangential forces on the perturbers caused by the backreaction of the wake propagating in the medium. The radial force is directed inward, toward the motion center, and is dominant at large Mach numbers. For subsonic motion, this component is negligible. For moderate and low Mach numbers, the tangential force is stronger and opposes the motion of the perturber. The analytic solution to the circular-orbit DF suffers from a logarithmic divergence in the supersonic regime. This divergence appears at short distances from the perturber solely (unlike the linear-motion result, which is also divergent at large distances) and can be encoded in a maximum multipole. This is helpful to assess the resolution dependence of numerical simulations implementing DF at the level of Liénard–Wiechert potentials. We also show how our approach can be generalized to calculate the DF acting on a compact circular binary.
Impact of Airways Geometry on Transport of Gases to Blood

Topological structure of bronchial trees affects transport of gases and aerosols in the respiratory system. We start by providing a quantitative assessment of the ability of the alternative tree representations to predict observable geometric and mechanistic characteristics, such as network resistance, dead space volume, and path length. Then we present a model of dynamic transport of oxygen and carbon dioxide along the airways, in the alveoli, across the alveolar membrane, and along the pulmonary blood capillaries. The model also accounts for the exchange of these two gases with blood in the capillaries, as well as for age, gender and other in-species characteristics. Our model's predictions are compared with corresponding observations, providing an additional venue to assess the validity of the existing representations of the lung's bronchial tree.
Joint Far- and Near-End Speech Intelligibility Enhancement Based on the Approximated Speech Intelligibility Index

This paper considers speech enhancement of signals picked up in one noisy environment which must be presented to a listener in another noisy environment. Recently, it has been shown that an optimal solution to this problem requires the consideration of the noise sources in both environments jointly. However, the existing optimal mutual information based method requires a complicated system model that includes natural speech variations, and relies on approximations and assumptions of the underlying signal distributions. In this paper, we propose to use a simpler signal model and optimize speech intelligibility based on the Approximated Speech Intelligibility Index (ASII). We derive a closed-form solution to the joint far- and near-end speech enhancement problem that is independent of the marginal distribution of signal coefficients, and that achieves similar performance to existing work. In addition, we do not need to model or optimize for natural speech variations.
Advanced Chemical Propulsion Study

A study was performed of advanced chemical propulsion technology application to space science (Code S) missions. The purpose was to begin the process of selecting chemical propulsion technology advancement activities that would provide greatest benefits to Code S missions. Several missions were selected from Code S planning data, and a range of advanced chemical propulsion options was analyzed to assess capabilities and benefits re these missions. Selected beneficial applications were found for higher-performing bipropellants, gelled propellants, and cryogenic propellants. Technology advancement recommendations included cryocoolers and small turbopump engines for cryogenic propellants; space storable propellants such as LOX-hydrazine; and advanced monopropellants. It was noted that fluorine-bearing oxidizers offer performance gains over more benign oxidizers. Potential benefits were observed for gelled propellants that could be allowed to freeze, then thawed for use.
A Fast Convergent Ordered-Subsets Algorithm With Subiteration-Dependent Preconditioners for PET Image Reconstruction

We investigated the imaging performance of a fast convergent ordered-subsets algorithm with subiteration-dependent preconditioners (SDPs) for positron emission tomography (PET) image reconstruction. In particular, we considered the use of SDP with the block sequential regularized expectation maximization (BSREM) approach with the relative difference prior (RDP) regularizer due to its prior clinical adaptation by vendors. Because the RDP regularization promotes smoothness in the reconstructed image, the directions of the gradients in smooth areas more accurately point toward the objective function’s minimizer than those in variable areas. Motivated by this observation, two SDPs have been designed to increase iteration step-sizes in the smooth areas and reduce iteration step-sizes in the variable areas relative to a conventional expectation maximization preconditioner. The momentum technique used for convergence acceleration can be viewed as a special case of SDP. We have proved the global convergence of SDP-BSREM algorithms by assuming certain characteristics of the preconditioner. By means of numerical experiments using both simulated and clinical PET data, we have shown that the SDP-BSREM algorithms substantially improve the convergence rate, as compared to conventional BSREM and a vendor’s implementation as Q.Clear. Specifically, SDP-BSREM algorithms converge 35%-50% faster in reaching the same objective function value than conventional BSREM and commercial Q.Clear algorithms. Moreover, we showed in phantoms with hot, cold and background regions that the SDP-BSREM algorithms approached the values of a highly converged reference image faster than conventional BSREM and commercial Q.Clear algorithms.
Interpretable ECG classification via a query-based latent space traversal (qLST)

Electrocardiography (ECG) is an effective and non-invasive diagnostic tool that measures the electrical activity of the heart. Interpretation of ECG signals to detect various abnormalities is a challenging task that requires expertise. Recently, the use of deep neural networks for ECG classification to aid medical practitioners has become popular, but their black box nature hampers clinical implementation. Several saliency-based interpretability techniques have been proposed, but they only indicate the location of important features and not the actual features. We present a novel interpretability technique called qLST, a query-based latent space traversal technique that is able to provide explanations for any ECG classification model. With qLST, we train a neural network that learns to traverse in the latent space of a variational autoencoder trained on a large university hospital dataset with over 800,000 ECGs annotated for 28 diseases. We demonstrate through experiments that we can explain different black box classifiers by generating ECGs through these traversals.
Fractional resonances and prethermal states in Floquet systems

In periodically-driven quantum systems, resonances can induce exotic nonequilibrium behavior and new phases of matter without static analog. We report on the emergence of fractional and integer resonances in a broad class of many-body Hamiltonians with a modulated hopping with a frequency that is either a fraction or an integer of the on-site interaction. We contend that there is a fundamental difference between these resonances when interactions bring the system to a Floquet prethermal state. Second-order processes dominate the dynamics in the fractional resonance case, leading to less entanglement and more localized quantum states than in the integer resonance case dominated by first-order processes. We demonstrate the dominating emergence of fractional resonances using the Magnus expansion of the effective Hamiltonian and quantify their effects on the many-body dynamics via quantum states' von Neumann entropy and Loschmidt echo. Our findings reveal novel features of the nonequilibrium quantum many-body system, such as the coexistence of Floquet prethermalization and localization, that may allow to development of quantum memories for quantum technologies and quantum information processing.
A Self-Sensing Piezoelectric Actuator for Collocated Control

A technique has been developed which allows a single piece of piezoelec tric material to concurrently sense and actuate in a closed loop system. The motivation behind the technique is that such a self-sensing actuator will be truly collocated and has applications in active and intelligent structures, such as vibration suppression. A theoreti cal basis for the self-sensing actuator is given in terms of the electromechanical consti tutive equations for a piezoelectric material. In a practical implementation of the self- sensing actuator an electrical bridge circuit is used to measure strain. The bridge circuit is capable of measuring either strain or time rate of strain in the actuator. The usefulness of the proposed device was experimentally verified by actively damping the vibration in a cantilever beam. A single piezoceramic element bonded to the base of the beam functioned both as a distributed moment actuator and strain sensor. Using a rate feedback control law, the first mode of vibration was suppressed, reducing the settling from 35 seconds to 2.5 seconds. Using a positive position feedback law the first two modes of vibration were suppressed; the first mode settling time was reduced from 35 to 0.3 sec onds and the second mode settling time was reduced from 7 seconds to 0.9 seconds.
FILIP: Fine-grained Interactive Language-Image Pre-Training

Unsupervised large-scale vision-language pre-training has shown promising advances on various downstream tasks. Existing methods often model the cross-modal interaction either via the similarity of the global feature of each modality which misses sufficient information, or finer-grained interactions using cross/self-attention upon visual and textual tokens. However, cross/self-attention suffers from inferior efficiency in both training and inference. In this paper, we introduce a large-scale Fine-grained Interactive Language-Image Pre-training (FILIP) to achieve finer-level alignment through a cross-modal late interaction mechanism, which uses a token-wise maximum similarity between visual and textual tokens to guide the contrastive objective. FILIP successfully leverages the finer-grained expressiveness between image patches and textual words by modifying only contrastive loss, while simultaneously gaining the ability to pre-compute image and text representations offline at inference, keeping both large-scale training and inference efficient. Furthermore, we construct a new large-scale image-text pair dataset called FILIP300M for pre-training. Experiments show that FILIP achieves state-of-the-art performance on multiple downstream vision-language tasks including zero-shot image classification and image-text retrieval. The visualization on word-patch alignment further shows that FILIP can learn meaningful fine-grained features with promising localization ability.
Fast high-fidelity geometric gates for singlet-triplet qubits

Mei-Ya Chen,1 Chengxian Zhang,2, ∗ and Zheng-Yuan Xue1, 3, † Guangdong Provincial Key Laboratory of Quantum Engineering and Quantum Materials, and School of Physics and Telecommunication Engineering, South China Normal University, Guangzhou 510006, China 2 School of Physical Science and Technology, Guangxi University, Nanning 530004, China Guangdong-Hong Kong Joint Laboratory of Quantum Matter and Frontier Research Institute for Physics, South China Normal University, Guangzhou 510006, China (Dated: November 16, 2021)