Stochastic path-integral approach for predicting the superconducting temperatures of anharmonic solids

We develop a stochastic path-integral approach for predicting the superconducting transition temperatures of anharmonic solids. By defining generalized Bloch basis, we generalize the formalism of the stochastic path-integral approach, which is originally developed for liquid systems. We implement the formalism for ab initio calculations using the projector augmented-wave method, and apply the implementation to estimate the superconducting transition temperatures of metallic deuterium and hydrogen sulfide. For metallic deuterium, which is approximately harmonic, our result coincides well with that obtained from the standard approach based on the harmonic approximation and the density functional perturbation theory. For hydrogen sulfide, we find that anharmonicity strongly suppresses the predicted superconducting transition temperature. Compared to the self-consistent harmonic approximation approach, our approach yields a transition temperature closer to the experimentally observed one.Comment: 12 pages, 12 figures, 3 table

Phase Retrieval of Quaternion Signal via Wirtinger Flow

The main aim of this paper is to study quaternion phase retrieval (QPR), i.e., the recovery of quaternion signal from the magnitude of quaternion linear measurements. We show that all $d$-dimensional quaternion signals can be reconstructed up to a global right quaternion phase factor from $O(d)$ phaseless measurements. We also develop the scalable algorithm quaternion Wirtinger flow (QWF) for solving QPR, and establish its linear convergence guarantee. Compared with the analysis of complex Wirtinger flow, a series of different treatments are employed to overcome the difficulties of the non-commutativity of quaternion multiplication. Moreover, we develop a variant of QWF that can effectively utilize a pure quaternion priori (e.g., for color images) by incorporating a quaternion phase factor estimate into QWF iterations. The estimate can be computed efficiently as it amounts to finding a singular vector of a $4\times 4$ real matrix. Motivated by the variants of Wirtinger flow in prior work, we further propose quaternion truncated Wirtinger flow (QTWF), quaternion truncated amplitude flow (QTAF) and their pure quaternion versions. Experimental results on synthetic data and color images are presented to validate our theoretical results. In particular, for pure quaternion signal recovery, our quaternion method often succeeds with measurements notably fewer than real methods based on monochromatic model or concatenation model.Comment: 21 pages (paper+supplemental), 6 figure

Uniform Exact Reconstruction of Sparse Signals and Low-rank Matrices from Phase-Only Measurements

In phase-only compressive sensing (PO-CS), our goal is to recover low-complexity signals (e.g., sparse signals, low-rank matrices) from the phase of complex linear measurements. While perfect recovery of signal direction in PO-CS was observed quite early, the exact reconstruction guarantee for a fixed, real signal was recently done by Jacques and Feuillen [IEEE Trans. Inf. Theory, 67 (2021), pp. 4150-4161]. However, two questions remain open: the uniform recovery guarantee and exact recovery of complex signal. In this paper, we almost completely address these two open questions. We prove that, all complex sparse signals or low-rank matrices can be uniformly, exactly recovered from a near optimal number of complex Gaussian measurement phases. By recasting PO-CS as a linear compressive sensing problem, the exact recovery follows from restricted isometry property (RIP). Our approach to uniform recovery guarantee is based on covering arguments that involve a delicate control of the (original linear) measurements with overly small magnitude. To work with complex signal, a different sign-product embedding property and a careful rescaling of the sensing matrix are employed. In addition, we show an extension that the uniform recovery is stable under moderate bounded noise. We also propose to add Gaussian dither before capturing the phases to achieve full reconstruction with norm information. Experimental results are reported to corroborate and demonstrate our theoretical results.Comment: 39 pages, 1 figur

Quantized Low-Rank Multivariate Regression with Random Dithering

Low-rank multivariate regression (LRMR) is an important statistical learning model that combines highly correlated tasks as a multiresponse regression problem with low-rank priori on the coefficient matrix. In this paper, we study quantized LRMR, a practical setting where the responses and/or the covariates are discretized to finite precision. We focus on the estimation of the underlying coefficient matrix. To make consistent estimator that could achieve arbitrarily small error possible, we employ uniform quantization with random dithering, i.e., we add appropriate random noise to the data before quantization. Specifically, uniform dither and triangular dither are used for responses and covariates, respectively. Based on the quantized data, we propose the constrained Lasso and regularized Lasso estimators, and derive the non-asymptotic error bounds. With the aid of dithering, the estimators achieve minimax optimal rate, while quantization only slightly worsens the multiplicative factor in the error rate. Moreover, we extend our results to a low-rank regression model with matrix responses. We corroborate and demonstrate our theoretical results via simulations on synthetic data or image restoration.Comment: 16 pages (Submitted

Reliability Analysis of Memristor Crossbar Routers: Collisions and On/off Ratio Requirement

Memristors are commonly used in crossbar arrays as “in-memory computing” elements to solve the von-Neumann bottleneck problem. However, they can also be used as “in-memory routing” elements to configure on-chip interconnection schemes and route signals among computing elements in configurable multi-core neuromorphic processors. While there has been a significant focus on the use of memristive devices as in-memory computing elements, to date, studies on the fundamental reliability properties of memristors as routing elements are still missing. In this paper, we analyze the reliability issues of using these devices in routing crossbar arrays, caused by sharing routing resources (collisions), and undesired pulses due to the leakage paths (on/off ratio requirement). We show that there is a trade-off between routing collision probability and the degree of connectivity (i.e., fan-in) of the receivers sharing routing channels. We provide specifications and guidelines based on a theoretical analysis for engineering the properties of memristive devices, and for designing routing systems based on memristor crossbars

Solving Quadratic Systems with Full-Rank Matrices Using Sparse or Generative Priors

The problem of recovering a signal $\boldsymbol{x} \in \mathbb{R}^n$ from a quadratic system $\{y_i=\boldsymbol{x}^\top\boldsymbol{A}_i\boldsymbol{x},\ i=1,\ldots,m\}$with full-rank matrices$\boldsymbol{A}_i$frequently arises in applications such as unassigned distance geometry and sub-wavelength imaging. With i.i.d. standard Gaussian matrices$\boldsymbol{A}_i$, this paper addresses the high-dimensional case where$m\ll n$by incorporating prior knowledge of$\boldsymbol{x}$. First, we consider a$k$-sparse$\boldsymbol{x}$and introduce the thresholded Wirtinger flow (TWF) algorithm that does not require the sparsity level$k$. TWF comprises two steps: the spectral initialization that identifies a point sufficiently close to$\boldsymbol{x}$(up to a sign flip) when$m=O(k^2\log n)$, and the thresholded gradient descent (with a good initialization) that produces a sequence linearly converging to$\boldsymbol{x}$with$m=O(k\log n)$measurements. Second, we explore the generative prior, assuming that$\boldsymbol{x}$lies in the range of an$L$-Lipschitz continuous generative model with$k$-dimensional inputs in an$\ell_2$-ball of radius$r$. We develop the projected gradient descent (PGD) algorithm that also comprises two steps: the projected power method that provides an initial vector with$O\big(\sqrt{\frac{k \log L}{m}}\big)$$\ell_2$-error given$m=O(k\log(Lnr))$measurements, and the projected gradient descent that refines the$\ell_2$-error to$O(\delta)$at a geometric rate when$m=O(k\log\frac{Lrn}{\delta^2})$. Experimental results corroborate our theoretical findings and show that: (i) our approach for the sparse case notably outperforms the existing provable algorithm sparse power factorization; (ii) leveraging the generative prior allows for precise image recovery in the MNIST dataset from a small number of quadratic measurements

High Dimensional Statistical Estimation under Uniformly Dithered One-bit Quantization

In this paper, we propose a uniformly dithered 1-bit quantization scheme for high-dimensional statistical estimation. The scheme contains truncation, dithering, and quantization as typical steps. As canonical examples, the quantization scheme is applied to the estimation problems of sparse covariance matrix estimation, sparse linear regression (i.e., compressed sensing), and matrix completion. We study both sub-Gaussian and heavy-tailed regimes, where the underlying distribution of heavy-tailed data is assumed to have bounded moments of some order. We propose new estimators based on 1-bit quantized data. In sub-Gaussian regime, our estimators achieve near minimax rates, indicating that our quantization scheme costs very little. In heavy-tailed regime, while the rates of our estimators become essentially slower, these results are either the first ones in an 1-bit quantized and heavy-tailed setting, or already improve on existing comparable results from some respect. Under the observations in our setting, the rates are almost tight in compressed sensing and matrix completion. Our 1-bit compressed sensing results feature general sensing vector that is sub-Gaussian or even heavy-tailed. We also first investigate a novel setting where both the covariate and response are quantized. In addition, our approach to 1-bit matrix completion does not rely on likelihood and represent the first method robust to pre-quantization noise with unknown distribution. Experimental results on synthetic data are presented to support our theoretical analysis.Comment: We add lower bounds for 1-bit quantization of heavy-tailed data (Theorems 11, 14

Divergent adaptations of leaf functional traits to light intensity across common urban plant species in Lanzhou, northwestern China

Leaves are the most important photosynthetic organs in plants. Understanding the growth strategy of leaves in different habitats is crucial for elucidating the mechanisms underlying plant response and adaptation to the environment change. This study investigated the scaling relationships of the laminar area (LA), leaf fresh mass (LFM), leaf dry mass (LDM), and explored leaf nitrogen (N) and phosphorus (P) content in leaves, and the relative benefits of these pairwise traits in three common urban plants (Yulania denudata, Parthenocissus quinquefolia, and Wisteria sinensis) under different light conditions, including (full-sun and canopy-shade). The results showed that: the scaling exponent of LDM vs LA (> 1, p < 0.05) meant that the LDM increased faster than LA, and supported the hypothesis of diminishing returns. The LFM and LDM had isometric relationships in all the three species, suggesting that the leaf water content of the leaves was nearly unaltered during laminar growth. Y. denudata and W. sinensis had higher relative benefit in full-sun habitats, while the reverse was observed in P. quinquefolia. The N and P content and the N:P ratio in full-sun leaves were generally higher than those of canopy-shade leaves. The leaves of the three urban plants exhibited a shift in strategy during transfer from the canopy shaded to the sunny habitat for adapting to the lower light conditions. The response of plant leaves to the environment shapes the rich variations at the leaf level, and quantification of the relative benefits of plants in different habitats provides novel insights into the response and adaptation strategies of plants

SIRT1 activation by 2,3,5,6-tetramethylpyrazine alleviates neuroinflammation via inhibiting M1 microglia polarization

BackgroundNeuroinflammation has been reported as a potential contributing factor to brain diseases, and is characterized by activated microglia with release of multiple inflammatory mediators. 2,3,5,6-Tetramethylpyrazine (TMP) is an active alkaloid in Ligusticum chuanxiong Hort. and has various biological activities, including anti-inflammatory and neuroprotection properties. However, the anti-neuroinflammatory activity of TMP has been less studied and its potential molecular mechanisms in this field remain unclear. This study aimed to investigate the effects of TMP and its underlying mechanisms in neuroinflammation.MethodsIn vitro, lipopolysaccharide (LPS)-stimulated BV2 microglia were used to assess the effects of TMP on inflammatory cytokines as well as the components of the SIRT1/NF-κB signaling pathway, which were measured by using ELISA, western blotting, qRT-qPCR and immunofluorescence. Moreover, LPS-induced acute neuroinflammation model in mice was performed to detect whether TMP could exert anti-neuroinflammatory effects in vivo, and the EX527, a SIRT1 inhibitor, were given intraperitoneally every two days prior to TMP treatment. Serums and spinal trigeminal nucleus (Sp5) tissues were collected for ELISA assay, and the Sp5 tissues were used for HE staining, Nissl staining, immunofluorescence, qRT-PCR and western blotting.ResultsIn vitro, TMP treatment significantly reduced the secretion of pro-inflammatory cytokines, including TNF-α and IL-6, promoted SIRT1 protein expression and inactivated NF-κB signaling pathway in LPS-induced neuroinflammation. Interestingly, pretreatment with EX527 blocked the therapeutic effects of TMP on neuroinflammation in vitro. Furthermore, TMP reduced the levels of pro-inflammatory cytokines and chemokines, and prevented microglia from polarizing towards a pro-inflammatory state through activating SIRT1 and inhibiting NF-κB activation in LPS-induced neuroinflammation in mice. And EX527 reversed the beneficial effects of TMP against LPS exposure in mice.ConclusionIn summary, this study unravels that TMP could mitigate LPS-induced neuroinflammation via SIRT1/NF-κB signaling pathway