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Offline reinforcement learning (RL) learns policies from a fixed dataset, but often requires large amounts of data. The challenge arises when labeled datasets are expensive, especially when rewards have to be provided by human labelers for large datasets. In contrast, unlabelled data tends to be less expensive. This situation highlights the importance of finding effective ways to use unlabelled data in offline RL, especially when labelled data is limited or expensive to obtain. In this paper, we present the algorithm to utilize the unlabeled data in the offline RL method with kernel function approximation and give the theoretical guarantee. We present various eigenvalue decay conditions of $\mathcal{H}_k$ which determine the complexity of the algorithm. In summary, our work provides a promising approach for exploiting the advantages offered by unlabeled data in offline RL, whilst maintaining theoretical assurances.

This study uses CAPM (Convex Adversarial Polytope for Maxpool-based CNN) to improve the verified bound for general purpose maxpool-based convolutional neural networks (CNNs) under bounded norm adversarial perturbations. The maxpool function is decomposed as a series of ReLU functions to extend the convex relaxation technique to maxpool functions, by which the verified bound can be efficiently computed through a dual network. The experimental results demonstrate that this technique allows the state-of-the-art verification precision for maxpool-based CNNs and involves a much lower computational cost than current verification methods, such as DeepZ, DeepPoly and PRIMA. This method is also applicable to large-scale CNNs, which previous studies show to be often computationally prohibitively expensive. Under certain circumstances, CAPM is 40-times, 20-times or twice as fast and give a significantly higher verification bound (CAPM 98% vs. PRIMA 76%/DeepPoly 73%/DeepZ 8%) as compared to PRIMA/DeepPoly/DeepZ. Furthermore, we additionally present the time complexity of our algorithm as $O(W^2NK)$, where $W$ is the maximum width of the neural network, $N$ is the number of neurons, and $K$ is the size of the maxpool layer's kernel.

In the presence of system-environment coupling, classical complex systems undergo stochastic dynamics, where rich phenomena can emerge at large spatio-temporal scales. To investigate these phenomena, numerical approaches for simulating stochastic dynamics are indispensable and can be computationally expensive. In light of the recent fast development in machine learning techniques, here, we establish a generic machine learning approach to simulate the stochastic dynamics, dubbed the noise-aware neural network (NANN). One key feature of this approach is its ability to generate the long-time stochastic dynamics of complex large-scale systems by just training NANN with the one-step dynamics of smaller-scale systems, thus reducing the computational cost. Furthermore, this NANN based approach is quite generic. Case-by-case special design of the architecture of NANN is not necessary when it is employed to investigate different stochastic complex systems. Using the noisy Kuramoto model and the Vicsek model as concrete examples, we demonstrate its capability in simulating stochastic dynamics. We believe that this novel machine learning approach can be a useful tool in investigating the large spatio-temporal scaling behavior of complex systems subjected to the influences of the environmental noise., Comment: 7 pages, 3 figures

In this paper, we study the rigidity problem for compact minimal Legendrian submanifolds in the unit Euclidean spheres via eigenvalues of fundamental matrices, which measure the squared norms of the second fundamental form on all normal directions. By using Lu's inequality on the upper bound of the squared norm of Lie brackets of symmetric matrices, we establish an optimal pinching theorem for such submanifolds of all dimensions, giving a new characterization for the Calabi tori. This pinching condition can also be described by the eigenvalues of the Ricci curvature tensor. Moreover, when the third large eigenvalue of the fundamental matrix vanishes everywhere, we get an optimal rigidity theorem under a weaker pinching condition., Comment: 19 pages

Quantum entanglement is a fundamental property of quantum mechanics and plays a crucial role in quantum computation and information. We study entanglement via the lens of computational complexity by considering quantum generalizations of the class NP with multiple unentangled quantum proofs, the so-called QMA(2) and its variants. The complexity of QMA(2) is a longstanding open problem, and only the trivial bounds QMA $\subseteq$ QMA(2) $\subseteq$ NEXP are known. In this work, we study the power of unentangled quantum proofs with non-negative amplitudes, a class which we denote $\text{QMA}^+(2)$. In this setting, we are able to design proof verification protocols for problems both using logarithmic size quantum proofs and having a constant probability gap in distinguishing yes from no instances. In particular, we design global protocols for small set expansion, unique games, and PCP verification. As a consequence, we obtain NP $\subseteq \text{QMA}^+_{\log}(2)$ with a constant gap. By virtue of the new constant gap, we are able to ``scale up'' this result to $\text{QMA}^+(2)$, obtaining the full characterization $\text{QMA}^+(2)$=NEXP by establishing stronger explicitness properties of the PCP for NEXP. One key novelty of these protocols is the manipulation of quantum proofs in a global and coherent way yielding constant gaps. Previous protocols (only available for general amplitudes) are either local having vanishingly small gaps or treat the quantum proofs as classical probability distributions requiring polynomially many proofs thereby not implying non-trivial bounds on QMA(2). Finally, we show that QMA(2) is equal to $\text{QMA}^+(2)$ provided the gap of the latter is a sufficiently large constant. In particular, if $\text{QMA}^+(2)$ admits gap amplification, then QMA(2)=NEXP., Comment: 64 pages

Quantum entanglement is a key enabling ingredient in diverse applications. However, the presence of unwanted adversarial entanglement also poses challenges in many applications. In this paper, we explore methods to "break" quantum entanglement. Specifically, we construct a dimension-independent k-partite disentangler (like) channel from bipartite unentangled input. We show: For every $d,\ell\ge k$, there is an efficient channel $\Lambda: \mathbb{C}^{d\ell} \otimes \mathbb{C}^{d\ell} \to \mathbb{C}^{dk}$ such that for every bipartite separable state $\rho_1\otimes \rho_2$, the output $\Lambda(\rho_1\otimes\rho_2)$ is close to a k-partite separable state. Concretely, for some distribution $\mu$ on states from $\mathbb{C}^d$, $$ \left\|\Lambda(\rho_1 \otimes \rho_2) - \int | \psi \rangle \langle \psi |^{\otimes k} d\mu(\psi)\right\|_1 \le \tilde O \left(\left(\frac{k^{3}}{\ell}\right)^{1/4}\right). $$ Moreover, $\Lambda(| \psi \rangle \langle \psi |^{\otimes \ell}\otimes | \psi \rangle \langle \psi |^{\otimes \ell}) = | \psi \rangle \langle \psi |^{\otimes k}$. Without the bipartite unentanglement assumption, the above bound is conjectured to be impossible. Leveraging our disentanglers, we show that unentangled quantum proofs of almost general real amplitudes capture NEXP, greatly relaxing the nonnegative amplitudes assumption in the recent work of QMA^+(2)=NEXP. Specifically, our findings show that to capture NEXP, it suffices to have unentangled proofs of the form $| \psi \rangle = \sqrt{a} | \psi_+ \rangle + \sqrt{1-a} | \psi_- \rangle$ where $| \psi_+ \rangle$ has non-negative amplitudes, $| \psi_- \rangle$ only has negative amplitudes and $| a-(1-a) | \ge 1/poly(n)$ with $a \in [0,1]$. Additionally, we present a protocol achieving an almost largest possible gap before obtaining QMA^R(k)=NEXP$, namely, a 1/poly(n) additive improvement to the gap results in this equality., Comment: 28 pages

In this paper, we fix the complex structure and explore the moduli space of the heterotic system by considering two different yet "dual" deformation paths starting from a K\"ahler solution. They correspond to deformation along the Bott-Chern cohomology class and the Aeppli cohomology class respectively. Using the implicit function theorem, we prove the local existence of heterotic solutions along these two paths and hence establish an initial step to construct local moduli coordinates around a K\"ahler solution., Comment: 35 pages

Pseudorandom states (PRS) are an important primitive in quantum cryptography. In this paper, we show that subset states can be used to construct PRSs. A subset state with respect to $S$, a subset of the computational basis, is \[ \frac{1}{\sqrt{|S|}}\sum_{i\in S} |i\rangle. \] As a technical centerpiece, we show that for any fixed subset size $|S|=s$ such that $s = 2^n/\omega(\mathrm{poly}(n))$ and $s=\omega(\mathrm{poly}(n))$, where $n$ is the number of qubits, a random subset state is information-theoretically indistinguishable from a Haar random state even provided with polynomially many copies. This range of parameter is tight. Our work resolves a conjecture by Ji, Liu and Song. Since subset states of small size have small entanglement across all cuts, this construction also illustrates a pseudoentanglement phenomenon., Comment: 9 pages; add a minimum background on pseudoentanglement

Spectrum sensing in cognitive radio necessitates effective monitoring of wide bandwidths, which requires high-rate sampling. Traditional spectrum sensing methods employing high-precision analog-to-digital converters (ADCs) result in increased power consumption and expensive hardware costs. In this paper, we explore blind spectrum sensing utilizing one-bit ADCs. We derive a closed-form detector based on Rao's test and demonstrate its equivalence with the second-order eigenvalue-moment-ratio test. Furthermore, a near-exact distribution based on the moment-based method, and an approximate distribution in the low signal-to-noise ratio (SNR) regime with the use of the central limit theorem, are obtained. Theoretical analysis is then performed and our results show that the performance loss of the proposed detector is approximately $2$ dB ($\pi/2$) compared to detectors employing $\infty$-bit ADCs when SNR is low. This loss can be compensated for by using approximately $2.47$ ($\pi^2/4$) times more samples. In addition, we unveil that the efficiency of incoherent accumulation in one-bit detection is the square root of that of coherent accumulation. Simulation results corroborate the correctness of our theoretical calculations.

Modern reinforcement learning (RL) often faces an enormous state-action space. Existing analytical results are typically for settings with a small number of state-actions, or simple models such as linearly modeled Q-functions. To derive statistically efficient RL policies handling large state-action spaces, with more general Q-functions, some recent works have considered nonlinear function approximation using kernel ridge regression. In this work, we derive sample complexities for kernel based Q-learning when a generative model exists. We propose a nonparametric Q-learning algorithm which finds an $\epsilon$-optimal policy in an arbitrarily large scale discounted MDP. The sample complexity of the proposed algorithm is order optimal with respect to $\epsilon$ and the complexity of the kernel (in terms of its information gain). To the best of our knowledge, this is the first result showing a finite sample complexity under such a general model.

Non-relativistic quantum chromodynamics (NRQCD) factorization formulism is an important approach to investigate the production of the heavy quarkonium. In this paper, we study the production of the $\Omega_{ccc}$ and $\Omega_{bbb}$ at the $e^+e^-$ collider, using the NRQCD factorization formulism. We calculate the total and differential cross sections exactly of the processes, $e^+e^-\rightarrow \gamma^*/Z^*\rightarrow \Omega_{ccc}\bar{c}\bar{c}\bar{c}$ and $e^+e^-\rightarrow \gamma^*/Z^*\rightarrow \Omega_{bbb}\bar{b}\bar{b}\bar{b}$, in the leading order at the $e^+e^-$ colliders with different energies. The results show that it is hard to observe them at the $e^+e^-$ collider directly.

Deep space explorations require transferring huge amounts of data quickly from very distant targets. Laser communication is a promising technology that can offer a data rate of magnitude faster than conventional microwave communication due to the fundamentally narrow divergence of light. This study demonstrated a photon-sensitive receiver prototype with over Gigabit data rate, immunity to strong background photon noise, and simultaneous tracking ability. The advantages are inherited from a joint-optimized superconducting nanowire single-photon detector (SNSPD) array, designed into a four-quadrant structure with each quadrant capable of resolving six photons. Installed in a free-space coupled and low-vibration cryostat, the system detection efficiency reached 72.7%, the detector efficiency was 97.5%, and the total photon counting rate was 1.6 Gcps. Additionally, communication performance was tested for pulse position modulation (PPM) format. A series of signal processing methods were introduced to maximize the performance of the forward error correction (FEC) code. Consequently, the receiver exhibits a faster data rate and better sensitivity by about twofold (1.76 photons/bit at 800 Mbps and 3.40 photons/bit at 1.2 Gbps) compared to previously reported results (3.18 photon/bit at 622 Mbps for the Lunar Laser Communication Demonstration). Furthermore, communications in strong background noise and with simultaneous tracking ability were demonstrated aimed at the challenges of daylight operation and accurate tracking of dim beacon light in deep space scenarios.

Inference on the minimum clinically important difference, or MCID, is an important practical problem in medicine. The basic idea is that a treatment being statistically significant may not lead to an improvement in the patients' well-being. The MCID is defined as a threshold such that, if a diagnostic measure exceeds this threshold, then the patients are more likely to notice an improvement. Typical formulations use an underspecified model, which makes a genuine Bayesian solution out of reach. Here, for a challenging personalized MCID problem, where the practically-significant threshold depends on patients' profiles, we develop a novel generalized posterior distribution, based on a working binary quantile regression model, that can be used for estimation and inference. The advantage of this formulation is two-fold: we can theoretically control the bias of the misspecified model and it has a latent variable representation which we can leverage for efficient Gibbs sampling. To ensure that the generalized Bayes inferences achieve a level of frequentist reliability, we propose a variation on the so-called generalized posterior calibration algorithm to suitably tune the spread of our proposed posterior., Comment: Feedback welcome at https://researchers.one/articles/22.08.00008

We study the probability of Boolean functions with small max influence to become constant under random restrictions. Let $f$ be a Boolean function such that the variance of $f$ is $\Omega(1)$ and all its individual influences are bounded by $\tau$. We show that when restricting all but a $\rho=\tilde{\Omega}((\log(1/\tau))^{-1})$ fraction of the coordinates, the restricted function remains nonconstant with overwhelming probability. This bound is essentially optimal, as witnessed by the tribes function $\mathrm{TRIBES}=\mathrm{AND}_{n/C\log n}\circ\mathrm{OR}_{C\log n}$. We extend it to an anti-concentration result, showing that the restricted function has nontrivial variance with probability $1-o(1)$. This gives a sharp version of the "it ain't over till it's over" theorem due to Mossel, O'Donnell, and Oleszkiewicz. Our proof is discrete, and avoids the use of the invariance principle. We also show two consequences of our above result: (i) As a corollary, we prove that for a uniformly random input $x$, the block sensitivity of $f$ at $x$ is $\tilde{\Omega}(\log(1/\tau))$ with probability $1-o(1)$. This should be compared with the implication of Kahn, Kalai, and Linial's result, which implies that the average block sensitivity of $f$ is $\Omega(\log(1/\tau))$. (ii) Combining our proof with a well-known result due to O'Donnell, Saks, Schramm, and Servedio, one can also conclude that: Restricting all but a $\rho=\tilde\Omega(1/\sqrt{\log (1/\tau) })$ fraction of the coordinates of a monotone function $f$, then the restricted function has decision tree complexity $\Omega(\tau^{-\Theta(\rho)})$ with probability $\Omega(1)$., Comment: 31 pages

We investigate the steady-state and dynamical properties of a reciprocal many-body system consisting of self-propelled active particles with local alignment interactions that exists within a fan-shaped neighborhood of each particle. We find that the nonreciprocity can emerge in this reciprocal system once the spontaneous symmetry breaking is present, and the effective description of the system assumes a non-Hermitian structure that directly originates from the emergent nonreciprocity. This emergent nonreciprocity can impose strong influences on the properties the system. In particular, it can even drive a real-space condensation of active particles. Our findings pave the way for identifying a new class of physics in reciprocal systems that is driven by the emergent nonreciprocity., Comment: 6+1 pages, 3+1 figures

Energy carrier evolution is crucial for material performance. Ultrafast microscopy has been widely applied to visualize the spatiotemporal evolution of energy carriers. However, direct imaging of small amounts of energy carriers on nanoscale remains difficult due to extremely weak transient signals. Here we present a method for ultrasensitive and high-throughput imaging of energy carrier evolution in space and time. This method combines femtosecond pump-probe techniques with interferometric scattering microscopy (iSCAT), named Femto-iSCAT. The interferometric principle and unique spatially-modulated contrast enhancement increase the transient image contrast by >2 orders of magnitude and enable the exploration of new science. We address three important and challenging problems: transport of different energy carriers at various interfaces, heterogeneous hot electron distribution and relaxation in single plasmonic resonators, and distinct structure-dependent edge state dynamics of carriers and excitons in optoelectronic semiconductors. Femto-iSCAT holds great potential as a universal tool for ultrasensitive imaging of energy carrier evolution in space and time.

Nonequilibrium many-body transient dynamics play an important role in the adaptation of active matter systems environment changes. However, the generic universal behavior of such dynamics is usually elusive and left as open questions. Here, we investigate the transient dynamics of vortex-like states in a two-dimensional active matter system that consists of self-propelled particles with alignment interactions subjected to extrinsic environmental noise. We identify a universal power-law scaling for the average lifetime of vortex-like states with respect to the speed of the self-propelled particles. This universal scaling behavior manifests strong robustness against the noise, up to the level where influences from environmental fluctuations are large enough to directly randomize the moving directions of particles. Direct experimental observations can be readily performed by related experimental setups operated at a decently low noise level., Comment: 5 pages, 3 figures

Photon number resolving (PNR) is an important capacity for detectors working in quantum and classical applications. Although a conventional superconducting nanowire single-photon detector (SNSPD) is not a PNR detector, by arranging nanowires in a series array and multiplexing photons over space, such series PNR-SNSPD can gain quasi-PNR capacity. However, the accuracy and maximum resolved photon number are both limited by the signal-to-noise (SNR) ratio of the output pulses. Here, we introduce a matched filter, which is an optimal filter in terms of SNR for SNSPD pulses. Experimentally, compared to conventional readout using a room-temperature amplifier, the normalized spacing between pulse amplitudes from adjacent photon number detections increased by a maximum factor of 2.1 after the matched filter. Combining with a cryogenic amplifier to increase SNR further, such spacing increased by a maximum factor of 5.3. In contrast to a low pass filter, the matched filter gave better SNRs while maintaining good timing jitters. Minimum timing jitter of 55 ps was obtained experimentally. Our results suggest that the matched filter is a useful tool for improving the performance of the series PNR-SNSPD and the maximum resolved photon number can be expected to reach 65 or even large.

In prediction problems, it is common to model the data-generating process and then use a model-based procedure, such as a Bayesian predictive distribution, to quantify uncertainty about the next observation. However, if the posited model is misspecified, then its predictions may not be calibrated -- that is, the predictive distribution's quantiles may not be nominal frequentist prediction upper limits, even asymptotically. Rather than abandoning the comfort of a model-based formulation for a more complicated non-model-based approach, here we propose a strategy in which the data itself helps determine if the assumed model-based solution should be adjusted to account for model misspecification. This is achieved through a generalized Bayes formulation where a learning rate parameter is tuned, via the proposed generalized predictive calibration (GPrC) algorithm, to make the predictive distribution calibrated, even under model misspecification. Extensive numerical experiments are presented, under a variety of settings, demonstrating the proposed GPrC algorithm's validity, efficiency, and robustness., Comment: 33 pages, 5 figures, 6 tables

Camera scene detection is among the most popular computer vision problem on smartphones. While many custom solutions were developed for this task by phone vendors, none of the designed models were available publicly up until now. To address this problem, we introduce the first Mobile AI challenge, where the target is to develop quantized deep learning-based camera scene classification solutions that can demonstrate a real-time performance on smartphones and IoT platforms. For this, the participants were provided with a large-scale CamSDD dataset consisting of more than 11K images belonging to the 30 most important scene categories. The runtime of all models was evaluated on the popular Apple Bionic A11 platform that can be found in many iOS devices. The proposed solutions are fully compatible with all major mobile AI accelerators and can demonstrate more than 100-200 FPS on the majority of recent smartphone platforms while achieving a top-3 accuracy of more than 98%. A detailed description of all models developed in the challenge is provided in this paper., Comment: Mobile AI 2021 Workshop and Challenges: https://ai-benchmark.com/workshops/mai/2021/. arXiv admin note: substantial text overlap with arXiv:2105.08630; text overlap with arXiv:2105.07825, arXiv:2105.07809, arXiv:2105.08629

Depth estimation is an important computer vision problem with many practical applications to mobile devices. While many solutions have been proposed for this task, they are usually very computationally expensive and thus are not applicable for on-device inference. To address this problem, we introduce the first Mobile AI challenge, where the target is to develop an end-to-end deep learning-based depth estimation solutions that can demonstrate a nearly real-time performance on smartphones and IoT platforms. For this, the participants were provided with a new large-scale dataset containing RGB-depth image pairs obtained with a dedicated stereo ZED camera producing high-resolution depth maps for objects located at up to 50 meters. The runtime of all models was evaluated on the popular Raspberry Pi 4 platform with a mobile ARM-based Broadcom chipset. The proposed solutions can generate VGA resolution depth maps at up to 10 FPS on the Raspberry Pi 4 while achieving high fidelity results, and are compatible with any Android or Linux-based mobile devices. A detailed description of all models developed in the challenge is provided in this paper., Comment: Mobile AI 2021 Workshop and Challenges: https://ai-benchmark.com/workshops/mai/2021/. arXiv admin note: text overlap with arXiv:2105.07809

The three-dimensional ternary LiFeO2 compound presents various unusual essential properties. The main features are thoroughly explored by the density functional and many-body perturbation theory. The concise physical/chemical picture, the critical spin-polarizations and orbital hybridizations in the Li-O and Fe-O bonds, are clearly examined through geometric optimization, quasi-particle energy spectra, spin-polarized density of states, the spatial charge densities, the spin-density distributions, and the strong optical responses. The unusual optical transitions cover various frequency-dependent absorption structures, and the most prominent plasmon modes are identified by the dielectric functions, energy loss functions, reflectance spectra, and absorption coefficients. Optical excitations are anisotropic and strongly affected by excitonic effects. The close combinations of electronic, magnetic and optical properties allow us to identify the significant spin-polarizations and orbital hybridizations for each available excitation channel. The lithium ferrite compound can be used for spintronic and photo-catalysis applications.

Generalized Bayes posterior distributions are formed by putting a fractional power on the likelihood before combining with the prior via Bayes's formula. This fractional power, which is often viewed as a remedy for potential model misspecification bias, is called the learning rate, and a number of data-driven learning rate selection methods have been proposed in the recent literature. Each of these proposals has a different focus, a different target they aim to achieve, which makes them difficult to compare. In this paper, we provide a direct head-to-head comparison of these learning rate selection methods in various misspecified model scenarios, in terms of several relevant metrics, in particular, coverage probability of the generalized Bayes credible regions. In some examples all the methods perform well, while in others the misspecification is too severe to be overcome, but we find that the so-called generalized posterior calibration algorithm tends to outperform the others in terms of credible region coverage probability., Comment: 22 pages, 2 figures, 4 tables

Optical spectrometers are the central instruments for exploring the interaction between light and matter. The current pursuit of the field is to design a spectrometer without the need for wavelength multiplexing optics to effectively reduce the complexity and physical size of the hardware. Based on computational spectroscopic results and combining a broadband-responsive dynamic detector, we successfully demonstrate an optics-free single-detector spectrometer that maps the tunable quantum efficiency of a superconducting nanowire into an ill-conditioned matrix to build a solvable inverse mathematical equation. Such a spectrometer can realize a broadband spectral responsivity ranging from 660 to 1900 nm. The spectral resolution at the telecom is 6 nm, exceeding the energy resolving capacity of existing infrared single-photon detectors. Meanwhile, benefiting from the optics-free setup, precise time-of-flight measurements can be simultaneously achieved. We have demonstrated a spectral LiDAR with 8 spectral channels. This work provides a concise method for building multifunctional spectrometers and paves the way for applying superconducting nanowire detectors in spectroscopy.

We prove that for every decision tree, the absolute values of the Fourier coefficients of a given order $\ell\geq1$ sum to at most $c^{\ell}\sqrt{\binom{d}{\ell}(1+\log n)^{\ell-1}},$ where $n$ is the number of variables, $d$ is the tree depth, and $c>0$ is an absolute constant. This bound is essentially tight and settles a conjecture due to Tal (arxiv 2019; FOCS 2020). The bounds prior to our work degraded rapidly with $\ell,$ becoming trivial already at $\ell=\sqrt{d}.$ As an application, we obtain, for every integer $k\geq1,$ a partial Boolean function on $n$ bits that has bounded-error quantum query complexity at most $k$ and randomized query complexity $\tilde{\Omega}(n^{1-\frac{1}{2k}}).$ This separation of bounded-error quantum versus randomized query complexity is best possible, by the results of Aaronson and Ambainis (STOC 2015) and Bravyi, Gosset, Grier, and Schaeffer (2021). Prior to our work, the best known separation was polynomially weaker: $O(1)$ versus $\Omega(n^{2/3-\epsilon})$ for any $\epsilon>0$ (Tal, FOCS 2020). As another application, we obtain an essentially optimal separation of $O(\log n)$ versus $\Omega(n^{1-\epsilon})$ for bounded-error quantum versus randomized communication complexity, for any $\epsilon>0.$ The best previous separation was polynomially weaker: $O(\log n)$ versus $\Omega(n^{2/3-\epsilon})$ (implicit in Tal, FOCS 2020)., Comment: Journal version (SIAM Journal on Computing)

This paper reviews the NTIRE 2020 Challenge on NonHomogeneous Dehazing of images (restoration of rich details in hazy image). We focus on the proposed solutions and their results evaluated on NH-Haze, a novel dataset consisting of 55 pairs of real haze free and nonhomogeneous hazy images recorded outdoor. NH-Haze is the first realistic nonhomogeneous haze dataset that provides ground truth images. The nonhomogeneous haze has been produced using a professional haze generator that imitates the real conditions of haze scenes. 168 participants registered in the challenge and 27 teams competed in the final testing phase. The proposed solutions gauge the state-of-the-art in image dehazing., Comment: CVPR Workshops Proceedings 2020

Lithium metasilicate (Li2SiO3) has attracted considerable interest as a promising electrolyte material for potential use in lithium batteries. However, its electronic properties are still not thoroughly understood. In this work, density functional theory calculations were adopted, our calculations find out that Li2SiO3 exhibits unique lattice symmetry (orthorhombic crystal), valence and conduction bands, charge density distribution, and van Hove singularities. Delicate analyses, the critical multi-orbital hybridizations in Li-O and Si-O bonds 2s- (2s, 2px, 2py, 2pz) and (3s, 3px, 3py, 3pz)- (2s, 2px, 2py, 2pz), respectively was identified. In particular, this system shows a huge indirect-gap of 5.077 eV. Therefore, there exist many strong covalent bonds, with obvious anisotropy and non-uniformity. On the other hand, the spin-dependent magnetic configurations are thoroughly absent. The theoretical framework could be generalized to explore the essential properties of cathode and anode materials of oxide compounds., Comment: 18 pages, 7 figures

The magneto-transport properties of phosphorene are investigated by employing the generalized tight-binding model to calculate the energy bands. For bilayer phosphorene, a composite magnetic and electric field is shown to induce a feature-rich Landau level (LL) spectrum which includes two subgroups of low-lying LLs. The two subgroups possess distinct features in level spacings, quantum numbers, as well as field dependencies. These together lead to anomalous quantum Hall (QH) conductivities which include a well-shape, staircase and composite quantum structures with steps having varying heights and widths. The Fermi energy-magnetic field-Hall conductivity ($E_{F}-B_{z}-\sigma_{xy}$) and Fermi energy-electric field-Hall conductivity ($E_{F}-E_{z}-\sigma_{xy}$) phase diagrams clearly exhibit oscillatory behaviors and cross-over from integer to half-integer QH effect. The predicted results should be verifiable by magneto-transport measurements in a dual-gated system.

We fabricate a microscale electromechanical system, in which a suspended superconducting membrane, treated as a mechanical oscillator, capacitively couples to a superconducting microwave resonator. As the microwave driving power increases, nonmonotonic dependence of the resonance frequency of the mechanical oscillator on the driving power has been observed. We also demonstrate the optical switching of the resonance frequency of the mechanical oscillator. Theoretical models for qualitative understanding of our experimental observations are presented. Our experiment may pave the way for the application of a mechanical oscillator with its resonance frequency controlled by the electromagnetic and/or optical fields, such as a microwave-optical interface and a controllable element in a superqubit-mechanical oscillator hybrid system., Comment: 8 pages,4 figures

Protecting sensitive information against data exploiting attacks is an emerging research area in data mining. Over the past, several different methods have been introduced to protect individual privacy from such attacks while maximizing data-utility of the application. However, these existing techniques are not sufficient to effectively protect data owner privacy, especially in the scenarios that utilize visualizable data (e.g. images, videos) or the applications that require heavy computations for implementation. To address these problems, we propose a new dimension reduction-based method for privacy preservation. Our method generates dimension-reduced data for performing machine learning tasks and prevents a strong adversary from reconstructing the original data. We first introduce a theoretical approach to evaluate dimension reduction-based privacy preserving mechanisms, then propose a non-linear dimension reduction framework motivated by state-of-the-art neural network structures for privacy preservation. We conducted experiments over three different face image datasets (AT&T, YaleB, and CelebA), and the results show that when the number of dimensions is reduced to seven, we can achieve the accuracies of 79%, 80%, and 73% respectively and the reconstructed images are not recognizable to naked human eyes.

The threshold degree of a Boolean function $f\colon\{0,1\}^n\to\{0,1\}$ is the minimum degree of a real polynomial $p$ that represents $f$ in sign: $\mathrm{sgn}\; p(x)=(-1)^{f(x)}.$ A related notion is sign-rank, defined for a Boolean matrix $F=[F_{ij}]$ as the minimum rank of a real matrix $M$ with $\mathrm{sgn}\; M_{ij}=(-1)^{F_{ij}}$. Determining the maximum threshold degree and sign-rank achievable by constant-depth circuits ($\text{AC}^{0}$) is a well-known and extensively studied open problem, with complexity-theoretic and algorithmic applications. We give an essentially optimal solution to this problem. For any $\epsilon>0,$ we construct an $\text{AC}^{0}$ circuit in $n$ variables that has threshold degree $\Omega(n^{1-\epsilon})$ and sign-rank $\exp(\Omega(n^{1-\epsilon})),$ improving on the previous best lower bounds of $\Omega(\sqrt{n})$ and $\exp(\tilde{\Omega}(\sqrt{n}))$, respectively. Our results subsume all previous lower bounds on the threshold degree and sign-rank of $\text{AC}^{0}$ circuits of any given depth, with a strict improvement starting at depth $4$. As a corollary, we also obtain near-optimal bounds on the discrepancy, threshold weight, and threshold density of $\text{AC}^{0}$, strictly subsuming previous work on these quantities. Our work gives some of the strongest lower bounds to date on the communication complexity of $\text{AC}^{0}$., Comment: 99 pages

The degeneration of articular cartilage (AC) occurs in osteoarthritis (OA), which is a leading cause of pain and disability in middle-aged and older people. The early disease related changes in cartilage extra-cellular matrix (ECM) start with depletion of proteoglycan(PG), leading to an increase in tissue hydration and permeability. These early compositional changes are small (<10%) and hence difficult to register with conventional non-invasive imaging technologies (magnetic resonance and ultrasound imaging). Here we apply Brillouin microscopy for detecting changes in the mechanical properties and composition of porcine AC. OA-like degradation is mimicked by enzymatic tissue digestion, and we compare Brillouin microscopy measurements against histological staining of PG depletion over varying digestion times and enzyme concentrations. The non-destructive nature of Brillouin imaging technology opens new avenues for creating minimally invasive arthroscopic devices for OA diagnostics and therapeutic monitoring., Comment: 10 pages, 5 figures

Diversities are a generalization of metric spaces in which a non-negative value is assigned to all finite subsets of a set, rather than just to pairs of points. Here we provide an analogue of the theory of negative type metrics for diversities. We introduce negative type diversities, and show that, as in the metric space case, they are a generalization of $L_1$-embeddable diversities. We provide a number of characterizations of negative type diversities, including a geometric characterisation. Much of the recent interest in negative type metrics stems from the connections between metric embeddings and approximation algorithms. We extend some of this work into the diversity setting, showing that lower bounds for embeddings of negative type metrics into $L_1$ can be extended to diversities by using recently established extremal results on hypergraphs.

In laboratories, ultrahigh magnetic fields are usually produced with very large currents through superconducting, resistive or hybrid magnets, which require extreme conditions, such as low temperature, huge cooling water or tens of megawatts of power. In this work we report that when single walled carbon nanotubes (SWNTs) are cut, there are magnetic moments at the shearing end of SWNTs. The average magnetic moment is found to be 41.5+-9.8uB per carbon atom in the end states with a width of 1 nm at temperature of 300.0K, suggesting ultrahigh magnetic fields can be produced. The dangling sigma and pi bonds of the carbon atoms at the shearing ends play important roles for this unexpectedly high magnetic moments because the oxidation temperature of cut SWNTs is found to be as low as 312 in dry air. Producing ultrahigh magnetic field with SWNTs has the advantage of working at higher working temperature and with low energy consumption, suggesting great potentials of applications.

The Las Vergnas' strong map conjecture, states that any strong map of oriented matroids $f:\mathcal{M}_1\rightarrow\mathcal{M}_2$ can be factored into extensions and contractions. The conjecture is known to be false due to a construction by Richter-Gebert, he find a non-factorizable strong map $f:\mathcal{M}_1\rightarrow\mathcal{M}_2$, however in his example $\mathcal{M}_1$ is not realizable. The problem that whether there exists a non-factorizable strong map between realizable oriented matroids still remains open. In this paper we provide a counterexample to the strong map conjecture on realizable oriented matroids, which is a strong map $f:\mathcal{M}_1\rightarrow\mathcal{M}_2$, $\mathcal{M}_1$ is an alternating oriented matroid of rank $4$ and $f$ has corank $2$. We prove it is not factorizable by showing that there is no uniform oriented matroid $\mathcal{M}^{\prime}$ of rank $3$ such that $\mathcal{M}_1\rightarrow\mathcal{M}^{\prime}\rightarrow\mathcal{M}_2$., Comment: 7 pages, update a proof that do not need linear integer programming

The magneto-optical properties of bilayer phosphorene is investigated by the generalized tight-binding model and the gradient approximation. The vertical inter-Landau-level transitions, being sensitive to the polarization directions, are mainly determined by the spatial symmetries of sub-envelope functions on the distinct sublattices. The anisotropic excitations strongly depend on the electric and magnetic fields. A perpendicular uniform electric field could greatly diversify the selection rule, frequency, intensity, number and form of symmetric absorption peaks. Specifically, the unusual magneto-optical properties appear beyond the critical field as a result of two subgroups of Landau levels with the main and side modes. The rich and unique magneto-absorption spectra arise from the very close relations among the geometric structures, multiple intralayer and interlayer hopping integrals, and composite external fields.

Nematic order often breaks the tetragonal symmetry of iron-based superconductors. It arises from regular structural transition or electronic instability in the normal phase. Here, we report the observation of a nematic superconducting state, by measuring the angular dependence of the in-plane and out-of-plane magnetoresistivity of Ba0.5K0.5Fe2As2 single crystals. We find large twofold oscillations in the vicinity of the superconducting transition, when the direction of applied magnetic field is rotated within the basal plane. To avoid the influences from sample geometry or current flow direction, the sample was designed as Corbino-shape for in-plane and mesa-shape for out-of-plane measurements. Theoretical analysis shows that the nematic superconductivity arises from the weak mixture of the quasi-degenerate s-wave and d-wave components of the superconducting condensate, most probably induced by a weak anisotropy of stresses inherent to single crystals., Comment: 15 pages, 4 figures, and Supplementary Information for 38 pages. Accepted to be published in Nature Communications

Brillouin microscopy measures compressibility, but is being increasingly used to assess stiffness of cells and tissues. Using hydrogels with tunable properties, we demonstrate that Brillouin microscopy is insensitive to stiffness of hydrated materials, but depends strongly on water content, consistent with a theoretical model of biphasic compressibility. Empirical correlations between Brillouin measurements and stiffness arise due to their mutual dependence on water content, but correlations vanish once hydration is controlled., Comment: Updated version with expanded discussion, additional data and a mathematical model to relate Brillouin measurements to water content

The electronic nematic phase is characterized as an ordered state of matter with rotational symmetry breaking, and has been well studied in the quantum Hall system and the high-$T_c$ superconductors, regardless of cuprate or pnictide family. The nematic state in high-$T_c$ systems often relates to the structural transition or electronic instability in the normal phase. Nevertheless, the electronic states below the superconducting transition temperature is still an open question. With high-resolution scanning tunneling microscope measurements, direct observation of vortex core in FeSe thin films revealed the nematic superconducting state by Song \emph{et al}. Here, motivated by the experiment, we construct the extended Ginzburg-Landau free energy to describe the elliptical vortex, where a mixed \emph{s}-wave and \emph{d}-wave superconducting order is coupled to the nematic order. The nematic order induces the mixture of two superconducting orders and enhances the anisotropic interaction between the two superconducting orders, resulting in a symmetry breaking from $C_4$ to $C_2$. Consequently, the vortex cores are stretched into an elliptical shape. In the equilibrium state, the elliptical vortices assemble a lozenge-like vortex lattice, being well consistent with experimental results., Comment: accepted by npj Quantum Materials

Nanogap engineering of low-dimensional nanomaterials, has received considerable interest in a variety of fields, ranging from molecular electronics to memories. Creating nanogaps at a certain position is of vital importance for the repeatable fabrication of the devices. In this work, we report a rational design of non-volatile memories based on sub-5 nm nanogaped single-walled carbon nanotubes (SWNTs) via the electromechanical motion. The nanogaps are readily realized by electroburning in a partially suspended SWNTs device with nanoscale region. The SWNT memory devices are applicable for both metallic and semiconducting SWNTs, resolving the challenge of separation of semiconducting SWNTs from metallic ones. Meanwhile, the memory devices exhibit excellent performance: ultra-low writing energy (4.1*10-19 J per bit), ON/OFF ratio of 105, stable switching ON operations and over 30 hours retention time in ambient conditions, which are of great potential for applications.

The electronic properties of aluminum-doped graphenes enriched by multi-orbital hybridizations are investigated using first-principles calculations. The feature-rich electronic structures exhibit the quasi-rigid red shifts of the carbon-created energy bands, the Al-dominated valence and conduction bands, and many free electrons in the conduction Dirac cone. These are directly reflected in the special structures of density of states (DOS). The Al- and alkali-induced high free carrier densities are almost the same. There exist certain important differences among the Al-, alkali- and halogen-doped grapehenes, such as, the buckled or planar graphene, the preserved or seriously distorted Dirac cone, the existence of the adatom-dominated valence bands, the free electrons or holes, the degenerate or splitting spin-related states, and the simple or complicated peaks in DOS. The similarities and differences mainly come from the diverse orbital hybridizations in adatom-C bonds, as indicated from the atom-dominated bands, the spatial charge distributions and the orbital-projected DOS.

Plasmonic metasurfaces enable simultaneous control of the phase, momentum, amplitude and polarisation of light and hence promise great utility in realisation of compact photonic devices. In this paper, we demonstrate a novel chip-scale device suitable for simultaneous polarisation and spectral measurements through use of six integrated plasmonic metasurfaces (IPMs), which diffract light with a given polarisation state and spectral component into well-defined spatial domains. Full calibration and characterisation of our device is presented, whereby good spectral resolution and polarisation accuracy over a wavelength range of 500-700~nm is shown. Functionality of our device in a M\"uller matrix modality is demonstrated through determination of the polarisation properties of a commercially available variable waveplate. Our proposed IPM is robust, compact and can be fabricated with a single photolithography step, promising many applications in polarisation imaging, quantum communication and quantitative sensing.

We review the progress of nonmagnetic impurity doping study on the Fe-based superconductors. On the theoretical side, two highly potential candidates for the pairing symmetry order parameter, i.e. the multi-gap s++ and s+- wave models, have been proposed but continuously debated. The debate arises because of the complex gap structure, exceptive magnetic and metallic behaviors of Fe-based superconductors which may make the influences of nonmagnetic defects varied in chemical potential, impurity disorder, inter- and intra-band scattering strength, and electron localization, and hence difficulty in directly obtaining the most important information for understanding the symmetry order parameter. Experimentally, the nonmagnetic impurity substitution study has been widely carried out, which has provided very useful insights. We review herein the various nonmagnetic impurity doping experiments, including the controlled defects within the superconducting Fe2X2 planes through samples quality improvement, a single impurity effects on the electronic state and local moment, the magnetic response of the Fe2X2 planes both on macroscopic scale as antiferromagnetic state and local scale of moment, as well as the significant effect in modifying the transport properties. The experiments enable us to qualitatively analyze the nonmagnetic impurities effects on the superconducting state for many Fe-based superconductors. We also propose herein some strategies for the nonmagnetic impurity doping study. As an important model for explaining the nonmagnetic impurities doping effects, the pair-breaking model is compared with various theoretical approaches via analyzing the pair-breaking rates of various Fe-superconductors., Comment: 82 pages, 44 figures, topical review article to be published in Superconductor Science and Technology

For any $n$-by-$n$ matrix $A$ of the form \[[\begin{array}{cccc} 0 & A_1 & & \\ & 0 & \ddots & \\ & & \ddots & A_{k-1} \\ & & & 0\end{array}],\] we consider two $k$-by-$k$ matrices \[A'=[\begin{array}{cccc} 0 & \|A_1\| & & \\ & 0 & \ddots & \\ & & \ddots & \|A_{k-1}\| \\ & & & 0\end{array}] \ {and} \ A''=[\begin{array}{cccc} 0 & m(A_1) & & \\ & 0 & \ddots & \\ & & \ddots & m(A_{k-1}) \\ & & & 0\end{array}],\] where $\|\cdot\|$ and $m(\cdot)$ denote the operator norm and minimum modulus of a matrix, respectively. It is shown that the numerical radii $w(\cdot)$ of $A$, $A'$ and $A''$ are related by the inequalities $w(A'')\le w(A)\le w(A')$. We also determine exactly when either of the inequalities becomes an equality., Comment: 12 pages

We give a complete characterization of nonnegative integers $j$ and $k$ and a positive integer $n$ for which there is an $n$-by-$n$ matrix with its power partial isometry index equal to $j$ and its ascent equal to $k$. Recall that the power partial isometry index $p(A)$ of a matrix $A$ is the supremum, possibly infinity, of nonnegative integers $j$ such that $I, A, A^2, \ldots, A^j$ are all partial isometries while the ascent $a(A)$ of $A$ is the smallest integer $k\ge 0$ for which $\ker A^k$ equals $\ker A^{k+1}$. It was known before that, for any matrix $A$, either $p(A)\le\min\{a(A), n-1\}$ or $p(A)=\infty$. In this paper, we prove more precisely that there is an $n$-by-$n$ matrix $A$ such that $p(A)=j$ and $a(A)=k$ if and only if one of the following conditions holds: (a) $j=k\le n-1$, (b) $j\le k-1$ and $j+k\le n-1$, and (c) $j\le k-2$ and $j+k=n$. This answers a question we asked in a previous paper., Comment: 11 pages

We derive a matrix model, under unitary similarity, of an $n$-by-$n$ matrix $A$ such that $A, A^2, \ldots, A^k$ ($k\ge 1$) are all partial isometries, which generalizes the known fact that if $A$ is a partial isometry, then it is unitarily similar to a matrix of the form ${\scriptsize\left[\begin{array}{cc} 0 & B 0 & C\end{array}\right]}$ with $B^*B+C^*C=I$. Using this model, we show that if $A$ has ascent $k$ and $A, A^2, \ldots, A^{k-1}$ are partial isometries, then the numerical range $W(A)$ of $A$ is a circular disc centered at the origin if and only if $A$ is unitarily similar to a direct sum of Jordan blocks whose largest size is $k$. As an application, this yields that, for any $S_n$-matrix $A$, $W(A)$ (resp., $W(A\otimes A)$) is a circular disc centered at the origin if and only if $A$ is unitarily similar to the Jordan block $J_n$. Finally, examples are given to show that the conditions that $W(A)$ and $W(A\otimes A)$ are circular discs at 0 are independent of each other for a general matrix $A$., Comment: 28 pages

For $n$-by-$n$ and $m$-by-$m$ complex matrices $A$ and $B$, it is known that the inequality $w(A\otimes B)\le\|A\|w(B)$ holds, where $w(\cdot)$ and $\|\cdot\|$ denote, respectively, the numerical radius and the operator norm of a matrix. In this paper, we consider when this becomes an equality. We show that (1) if $\|A\|=1$ and $w(A\otimes B)=w(B)$, then either $A$ has a unitary part or $A$ is completely nonunitary and the numerical range $W(B)$ of $B$ is a circular disc centered at the origin, (2) if $\|A\|=\|A^k\|=1$ for some $k$, $1\le k<\infty$, then $w(A)\ge\cos(\pi/(k+2))$, and, moreover, the equality holds if and only if $A$ is unitarily similar to the direct sum of the $(k+1)$-by-$(k+1)$ Jordan block $J_{k+1}$ and a matrix $B$ with $w(B)\le\cos(\pi/(k+2))$, and (3) if $B$ is a nonnegative matrix with its real part (permutationally) irreducible, then $w(A\otimes B)=\|A\|w(B)$ if and only if either $p_A=\infty$ or $n_B\le p_A<\infty$ and $B$ is permutationally similar to a block-shift matrix \[[ {array}{cccc} 0 & B_1 & & & 0 & \ddots & & & \ddots & B_k & & & 0 {array} ]\] with $k=n_B$, where $p_A=\sup\{\ell\ge 1: \|A^{\ell}\|=\|A\|^{\ell}\}$ and $n_B=\sup\{\ell\ge 1 : B^{\ell}\neq 0\}$.

We calculate the lifetime of both the o-Ps and the p-Ps positronium annihilation decay $ Ps\to\gamma\gamma$ in the strong circular polarized laser field. We take a strategy of the factorization to separate the effects caused by the Coulomb interaction and the strong laser field interaction. It is factorized in the time direction but not in the space direction. Our results show that in the laser with long wavelength and high intensity, the lifetimes of those Ps states are dramatically increased. For $\rm CO_2$ laser with $10\, \mu m$ wavelength and $10^{13} W/cm^2$ intensity, lifetime of the spin-single positronium is increased by $10^8$ times. Our result is consistent with those obtained by solving the Sch{\"{o}}dinger equation. This effect may be useful for the high harmonic generation(HHG) effects provided with the Ps\cite{keitel2004}., Comment: submitted to Communications in Theoretical Physics

For an $n$-by-$n$ complex matrix $A$, we define its zero-dilation index $d(A)$ as the largest size of a zero matrix which can be dilated to $A$. This is the same as the maximum $k$ ($\ge 1$) for which 0 is in the rank-$k$ numerical range of $A$. Using a result of Li and Sze, we show that if $d(A) > \lfloor 2n/3\rfloor$, then, under unitary similarity, $A$ has the zero matrix of size $3d(A)-2n$ as a direct summand. It complements the known fact that if $d(A)>\lfloor n/2\rfloor$, then 0 is an eigenvalue of $A$. We then use it to give a complete characterization of $n$-by-$n$ matrices $A$ with $d(A)=n-1$, namely, $A$ satisfies this condition if and only if it is unitarily similar to $B\oplus 0_{n-3}$, where $B$ is a 3-by-3 matrix whose numerical range $W(B)$ is an elliptic disc and whose eigenvalue other than the two foci of $\partial W(B)$ is 0. We also determine the value of $d(A)$ for any normal matrix and any weighted permutation matrix $A$., Comment: 26 pages

A KMS matrix is one of the form $$J_n(a)=[{array}{ccccc} 0 & a & a^2 &... & a^{n-1} & 0 & a & \ddots & \vdots & & \ddots & \ddots & a^2 & & & \ddots & a 0 & & & & 0{array}]$$ for $n\ge 1$ and $a$ in $\mathbb{C}$. Among other things, we prove the following properties of its numerical range: (1) $W(J_n(a))$ is a circular disc if and only if $n=2$ and $a\neq 0$, (2) its boundary $\partial W(J_n(a))$ contains a line segment if and only if $n\ge 3$ and $|a|=1$, and (3) the intersection of the boundaries $\partial W(J_n(a))$ and $\partial W(J_n(a)[j])$ is either the singleton $\{\min\sigma(\re J_n(a))\}$ if $n$ is odd, $j=(n+1)/2$ and $|a|>1$, or the empty set $\emptyset$ if otherwise, where, for any $n$-by-$n$ matrix $A$, $A[j]$ denotes its $j$th principal submatrix obtained by deleting its $j$th row and $j$th column ($1\le j\le n$), $\re A$ its real part $(A+A^*)/2$, and $\sigma(A)$ its spectrum., Comment: 35 pages