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We construct a hydrodynamic theory of active smectics A in two-dimensional space, including the creation/annihilation and motility of dislocations with Burgers' number $\pm1$. We derive analytical criteria on the set of parameters that lead to flows. We show that the motility of dislocations can lead to flow transitions with distinct features from the previously reported active Helfrich--Hurault shear instability with, notably, a first-order transition in the velocity from quiescence to turbulence., Comment: 5 pages, 5 figures

We introduce a class of neural controlled differential equation inspired by quantum mechanics. Neural quantum controlled differential equations (NQDEs) model the dynamics by analogue of the Schr\"{o}dinger equation. Specifically, the hidden state represents the wave function, and its collapse leads to an interpretation of the classification probability. We implement and compare the results of four variants of NQDEs on a toy spiral classification problem., Comment: Code available at: https://github.com/lingyiyang/NQDE

Quantum state discrimination plays an essential role in quantum technology, crucial for quantum error correction, metrology, and sensing. While conventional methods rely on integrating readout signals or classifying raw signals, we developed a method to extract information about state transitions during readout, based on the path signature method, a tool for analyzing stochastic time series. The hardware experiments demonstrate an improvement in transmon qutrit state readout fidelity from 85.9 $\pm$ 1.0% to 91.0 $\pm$ 0.5%, without the need for additional hardware. This method has the potential to become a foundational tool for quantum technology.

Cell adhesion proteins typically form stable clusters that anchor the cell membrane to its environment. Several works have suggested that cell membrane protein clusters can emerge from a local feedback between the membrane curvature and the density of proteins. Here, we investigate the effect of such curvature-sensing mechanism in the context of cell adhesion proteins. We show how clustering emerges in an intermediate range of adhesion and curvature-sensing strengths. We identify key differences with the tilt-induced gradient sensing mechanism we previously proposed (Lin et al., arXiv:2307.03670, 2023)., Comment: 13 pages, 7 figures

Cell adhesion proteins are transmembrane proteins that bind cells to their environment. These proteins typically cluster into disk-shaped or linear structures. Here we show that such clustering patterns spontaneously emerge when the protein sense the membrane deformation gradient, for example by reaching a lower-energy conformation when the membrane is tilted relative to the underlying binding substrate. Increasing the strength of the membrane gradient-sensing mechanism first yields isolated disk-shaped clusters and then long linear structures. Our theory is coherent with experimental estimates, suggesting that a tilt-induced clustering mechanism is relevant in the context of cell adhesion proteins., Comment: 6 pages, 3 figures, with SI (ancillary files)

We propose a general random subspace framework for unconstrained nonconvex optimization problems that requires a weak probabilistic assumption on the subspace gradient, which we show to be satisfied by various random matrix ensembles, such as Gaussian and sparse sketching, using Johnson-Lindenstrauss embedding properties. We show that, when safeguarded with trust region or quadratic regularization, this random subspace approach satisfies, with high probability, a complexity bound of order $\mathcal{O}(\epsilon^{-2})$ to drive the (full) gradient below $\epsilon$; matching in the accuracy order, deterministic counterparts of these methods and securing almost sure convergence. Furthermore, no problem dimension dependence appears explicitly in the projection size of the sketching matrix, allowing the choice of low-dimensional subspaces. We particularise this framework to Random Subspace Gauss-Newton (RS-GN) methods for nonlinear least squares problems, that only require the calculation of the Jacobian in the subspace; with similar complexity guarantees. Numerical experiments with RS-GN on CUTEst nonlinear least squares are also presented, with some encouraging results., Comment: arXiv admin note: substantial text overlap with arXiv:2206.03371

We propose a Randomised Subspace Gauss-Newton (R-SGN) algorithm for solving nonlinear least-squares optimization problems, that uses a sketched Jacobian of the residual in the variable domain and solves a reduced linear least-squares on each iteration. A sublinear global rate of convergence result is presented for a trust-region variant of R-SGN, with high probability, which matches deterministic counterpart results in the order of the accuracy tolerance. Promising preliminary numerical results are presented for R-SGN on logistic regression and on nonlinear regression problems from the CUTEst collection., Comment: This work first appears in Thirty-seventh International Conference on Machine Learning, 2020, in Workshop on Beyond First Order Methods in ML Systems. https://sites.google.com/view/optml-icml2020/accepted-papers?authuser=0. arXiv admin note: text overlap with arXiv:2206.03371

This paper investigates theoretical properties of subsampling and hashing as tools for approximate Euclidean norm-preserving embeddings for vectors with (unknown) additive Gaussian noises. Such embeddings are sometimes called Johnson-lindenstrauss embeddings due to their celebrated lemma. Previous work shows that as sparse embeddings, the success of subsampling and hashing closely depends on the $l_\infty$ to $l_2$ ratios of the vector to be mapped. This paper shows that the presence of noise removes such constrain in high-dimensions, in other words, sparse embeddings such as subsampling and hashing with comparable embedding dimensions to dense embeddings have similar approximate norm-preserving dimensionality-reduction properties. The key is that the noise should be treated as an information to be exploited, not simply something to be removed. Theoretical bounds for subsampling and hashing to recover the approximate norm of a high dimension vector in the presence of noise are derived, with numerical illustrations showing better performances are achieved in the presence of noise., Comment: 10 pages

Random embeddings project high-dimensional spaces to low-dimensional ones; they are careful constructions which allow the approximate preservation of key properties, such as the pair-wise distances between points. Often in the field of optimisation, one needs to explore high-dimensional spaces representing the problem data or its parameters and thus the computational cost of solving an optimisation problem is connected to the size of the data/variables. This thesis studies the theoretical properties of norm-preserving random embeddings, and their application to several classes of optimisation problems., Comment: arXiv admin note: text overlap with arXiv:2105.11815

Biological cells can actively tune their intracellular architecture according to their overall shape. Here we explore the rheological implication of such coupling in a minimal model of a dense cellular material where each cell exerts an active mechanical stress along its axis of elongation. Increasing the active stress amplitude leads to several transitions. An initially hexagonal crystal motif is first destabilized into a solid with anisotropic cells. Increasing activity further, we find a re-entrant transition to a regime with finite hexatic order and finite shear modulus, in which cells arrange according to a rhombile pattern with periodically arranged rosette structures. The shear modulus vanishes again at a third threshold beyond which spontaneous tissue flows arise. In this last regime, we observe the emergence of cell shape patterns called topological defects, with flow and stress fields around defects agreeing with those observed in epithelial tissue experiments. We further provide a testable prediction of cell-cell rearrangement hotspots near topological defects. Overall, our work connects seemingly distinct features - e.g. rosettes and topological defects - observed across various types of epithelial tissues., Comment: 27 pages; 21 figures

Cell monolayers are a central model system to tissue biophysics. In vivo, epithelial tissues are curved on the scale of microns, and curvature's role in the onset of spontaneous tissue flows is still not well-understood. Here, we present a hydrodynamic theory for an apical-basal asymmetric active nematic gel on a curved strip. We show that surface curvature qualitatively changes monolayer motion compared to flat space: the resulting flows can be thresholdless, and the transition to motion may change from continuous to discontinuous. Surface curvature, friction and active tractions are all shown to control the flow pattern selected: from simple shear to vortex chains., Comment: 5 pages, 3 figures, 20 supplemental pages, 11 supplemental figures, 2 supplemental movies

The aim of this paper is two-fold: firstly, to present subspace embedding properties for $s$-hashing sketching matrices, with $s\geq 1$, that are optimal in the projection dimension $m$ of the sketch, namely, $m=\mathcal{O}(d)$, where $d$ is the dimension of the subspace. A diverse set of results are presented that address the case when the input matrix has sufficiently low coherence (thus removing the $\log^2 d$ factor dependence in $m$, in the low-coherence result of Bourgain et al (2015) at the expense of a smaller coherence requirement); how this coherence changes with the number $s$ of column nonzeros (allowing a scaling of $\sqrt{s}$ of the coherence bound), or is reduced through suitable transformations (when considering hashed -- instead of subsampled -- coherence reducing transformations such as randomised Hadamard). Secondly, we apply these general hashing sketching results to the special case of Linear Least Squares (LLS), and develop Ski-LLS, a generic software package for these problems, that builds upon and improves the Blendenpik solver on dense input and the (sequential) LSRN performance on sparse problems. In addition to the hashing sketching improvements, we add suitable linear algebra tools for rank-deficient and for sparse problems that lead Ski-LLS to outperform not only sketching-based routines on randomly generated input, but also state of the art direct solver SPQR and iterative code HSL on certain subsets of the sparse Florida matrix collection; namely, on least squares problems that are significantly overdetermined, or moderately sparse, or difficult.

In this paper, we propose a dimensionless anomaly detection method for multivariate streams. Our method is independent of the unit of measurement for the different stream channels, therefore dimensionless. We first propose the variance norm, a generalisation of Mahalanobis distance to handle infinite-dimensional feature space and singular empirical covariance matrix rigorously. We then combine the variance norm with the path signature, an infinite collection of iterated integrals that provide global features of streams, to propose SigMahaKNN, a method for anomaly detection on (multivariate) streams. We show that SigMahaKNN is invariant to stream reparametrisation, stream concatenation and has a graded discrimination power depending on the truncation level of the path signature. We implement SigMahaKNN as an open-source software, and perform extensive numerical experiments, showing significantly improved anomaly detection on streams compared to isolation forest and local outlier factors in applications ranging from language analysis, hand-writing analysis, ship movement paths analysis and univariate time-series analysis.

The Medium Energy X-ray Telescope (ME) is one of the main payloads of the Hard X-ray Modulation Telescope (dubbed as Insight-HXMT). The background of Insight-HXMT/ME is mainly caused by the environmental charged particles and the background intensity is modulated remarkably by the geomagnetic field, as well as the geographical location. At the same geographical location, the background spectral shape is stable but the intensity varies with the level of the environmental charged particles. In this paper, we develop a model to estimate the ME background based on the ME database that is established with the two-year blank sky observations of the high Galactic latitude. In this model, the entire geographical area covered by Insight-HXMT is divided into grids of $5^{\circ}\times5^{\circ}$ in geographical coordinate system. For each grid, the background spectral shape can be obtained from the background database and the intensity can be corrected by the contemporary count rate of the blind FOV detectors. Thus the background spectrum can be obtained by accumulating the background of all the grids passed by Insight-HXMT during the effective observational time. The model test with the blank sky observations shows that the systematic error of the background estimation in $8.9-44.0$ keV is $\sim1.3\%$ for a pointing observation with an average exposure $\sim5.5$ ks. We also find that the systematic error is anti-correlated with the exposure, which indicates the systematic error is partly contributed by the statistical error of count rate measured by the blind FOV detectors., Comment: to be published in Journal of High Energy Astrophysics