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Teng Zhang

Teng Zhang appears in the imported research catalog. Authorship, coauthor and topic links are available while profile ownership is still unclaimed.

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Machine Learningcond-mat.mtrl-sciComputer Visiongr-qccond-mat.softcond-mat.mes-hallquant-phArtificial Intelligenceastro-ph.IMComputation and Languagemath.FAmath.STStatistics TheoryLogic in Computer ScienceMethodologyphysics.chem-phphysics.ins-detSoftware Engineeringastro-ph.GABiomoleculesComputationcond-mat.str-elcond-mat.supr-conInformation Theorymath.CAmath.DSmath.ITmath.NAmath.OCmath.RTNumerical Analysisphysics.opticsProgramming Languages

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Published work

53 published item(s)

preprint2026arXiv

Combining Mechanical and Agentic Specification Inference for Move

In this paper, we describe early work on a specification inference tool for the Move Prover that combines a weakest-precondition (WP) analysis over Move bytecode with an agentic coding CLI such as Claude Code. Specification inference reduces the boilerplate of writing specifications in Move: in order to verify a high-level property such as a global state invariant, pre- and post-conditions for the supporting functions typically have to be written by hand, which is tedious. In our setting, a Model Context Protocol (MCP) service exposes the WP analysis and the prover itself to the coding agent. The WP analysis provides a sound, mechanical baseline for inference; the AI is used precisely where WP is weakest -- for loop invariants and high-level idiomatic specifications such as monotonicity, conservation, and structural invariants. The Move Prover serves as the oracle that decides whether the generated specs are valid, and the agent is equipped to generate proof hints and to refine the inferred specification until verification succeeds. The tool has been applied to a corpus of canonical Move code, including code that uses higher-order functions, dynamic dispatch, global state, references, and various forms of loops.

0 citations0 reviewsNo code linkedOpen access
preprint2026arXiv

Dynamic Skill Lifecycle Management for Agentic Reinforcement Learning

Large language model agents increasingly rely on external skills to solve complex tasks, where skills act as modular units that extend their capabilities beyond what parametric memory alone supports. Existing methods assume external skills either accumulate as persistent guidance or internalized into the policy, eventually leading to zero-skill inference. We argue this assumption is overly restrictive, since with limited parametric capacity and uneven marginal contribution across skills, the optimal active skill set is non-monotonic, task- and stage-dependent. In this work, we propose SLIM, a framework of dynamic Skill LIfecycle Management for agentic reinforcement learning (RL), which treats the active external skill set as a dynamic optimization variable jointly updated with policy learning. Specifically, SLIM estimates each active skill's marginal external contribution through leave-one-skill-out validation, then applies three lifecycle operations: retaining high-value skills, retiring skills whose contribution becomes negligible after sufficient exposure, and expanding the skill bank when persistent failures reveal missing capability coverage. Experiments show that SLIM outperforms the best baselines by an average of 7.1% points across ALFWorld and SearchQA. Results further indicate that policy learning and external skill retention are not mutually exclusive: some skills are absorbed into the policy, while others continue to provide external value, supporting SLIM as a more general paradigm for skill-based agentic RL.

0 citations0 reviewsNo code linkedOpen access
preprint2026arXiv

Schur--Horn type inequalities for hyperbolic polynomials

We establish a Schur--Horn type inequality for symmetric hyperbolic polynomials. As an immediate consequence, we resolve a conjecture of Nam Q. Le on Hadamard-type inequalities for hyperbolic polynomials. Our argument is based on the Schur--Horn theorem, the Birkhoff theorem, and Gårding's concavity theorem for hyperbolicity cones. Beyond the eigenvalue level, we develop a symmetrization principle on hyperbolicity cones: if a hyperbolic polynomial is invariant under a finite group action, then its value increases under the associated Reynolds operator (group averaging). Applied to the sign-flip symmetries of linear principal minor polynomials introduced by Blekherman et al., this yields a short proof of the hyperbolic Fischer--Hadamard inequalities for PSD-stable lpm polynomials.

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preprint2026arXiv

Weak majorization inequalities for the cubic and quartic coefficients of $e^{(A+B)t}$ versus $e^{At}e^{Bt}$

Let $A,B\in\mathbb{H}_n$ and set $H=A+B$. For each integer $k\ge 1$ define $$ Q_k:=\sum_{p=0}^k \binom{k}{p} A^pB^{k-p}, R_k:=\Re\,Q_k=\frac{Q_k+Q_k^*}{2}. $$ Then $H^k=\left.\frac{d^k}{dt^k}e^{Ht}\right|_{t=0}$ and $Q_k=\left.\frac{d^k}{dt^k}(e^{At}e^{Bt})\right|_{t=0}$. We prove that, for $k=3,4,$ $$ λ(H^k)\prec_w σ(Q_k). $$ Equivalently, the eigenvalues of the cubic and quartic Taylor coefficients of $e^{(A+B)t}$ are weakly majorized by the singular values of the corresponding coefficients of the Golden--Thompson product $e^{At}e^{Bt}$. Our argument combines Ky Fan variational principles with explicit commutator identitiesfor $R_k-H^k$ at orders $k=3,4$, reducing the problem to the positivity of certain double-commutator trace forms tested against Ky Fan maximizing projections. We also record a general sufficient condition for higher orders based on commutator decompositions.

0 citations0 reviewsNo code linkedOpen access
preprint2025arXiv

Beijing Normal University 12-meter Interferometric kHz GW Detector Prototype: Design and Scientific Prospects

Current gravitational-wave detectors have achieved remarkable sensitivity around 100 Hz, enabling ground-breaking discoveries. Enhancing sensitivity at higher frequencies in the kilohertz (kHz) range promises access to rich physics, particularly the extreme conditions during the merger stage of binary neutron stars. However, the high-frequency sensitivity of Michelson-based interferometers is fundamentally limited by their linear optical cavities, which are optimized for low-frequency signal enhancement. In [Phys. Rev. X 13, 021019 (2023)], a new configuration employing an L-shaped optical resonator was proposed to overcome this limitation, offering exceptional sensitivity in the kHz band. As a pathfinder, the 12-meter prototype at Beijing Normal University is designed to demonstrate the sensing and control schemes of this new kHz detector configuration and to explore its performance in the high-power regime with suspended optics. Beyond its primary scientific goal, the prototype also offers potential sensitivity in the megahertz (MHz) range, potentially enabling constraints on exotic sources. This paper presents an overview of the prototype, including its optical design and current development status of key components.

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preprint2024arXiv

When $D$-companion matrix meets incomplete polynomials

In this paper, we provide a simple proof of a generalization of the Gauss-Lucas theorem. By using methods of D-companion matrix, we get the majorization relationship between the zeros of convex combinations of incomplete polynomials and an origin polynomial. Moreover, we prove that the set of all zeros of all convex combinations of incomplete polynomials coincides with the closed convex hull of zeros of the original polynomial. The location of zeros of convex combinations of incomplete polynomials is determined.

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preprint2022arXiv

3D Morphology of Open Clusters in the Solar Neighborhood with Gaia EDR3 II: Hierarchical Star Formation Revealed by Spatial and Kinematic Substructures

We identify members of 65 open clusters in the solar neighborhood using the machine-learning algorithm StarGO based on Gaia EDR3 data. After adding members of twenty clusters from previous studies (Pang et al. 2021a,b; Li et al. 2021) we obtain 85 clusters, and study their morphology and kinematics. We classify the substructures outside the tidal radius into four categories: filamentary (f1) and fractal (f2) for clusters $<100$ Myr, and halo (h) and tidal-tail (t) for clusters $>100$ Myr. The kinematical substructures of f1-type clusters are elongated; these resemble the disrupted cluster Group X. Kinematic tails are distinct in t-type clusters, especially Pleiades. We identify 29 hierarchical groups in four young regions (Alessi 20, IC 348, LP 2373, LP 2442); ten among these are new. The hierarchical groups form filament networks. Two regions (Alessi 20, LP 2373) exhibit global "orthogonal" expansion (stellar motion perpendicular to the filament), which might cause complete dispersal. Infalling-like flows (stellar motion along the filament) are found in UBC 31 and related hierarchical groups in the IC 348 region. Stellar groups in the LP 2442 region (LP 2442 gp 1-5) are spatially well-mixed but kinematically coherent. A merging process might be ongoing in the LP 2442 subgroups. For younger systems ($\lesssim30$ Myr), the mean axis ratio, cluster mass and half-mass radius tend to increase with age values. These correlations between structural parameters may imply two dynamical processes occurring in the hierarchical formation scenario in young stellar groups: (1) filament dissolution and (2) sub-group mergers.

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

Atomic-Scale Visualization of Chiral Charge Density Wave States and Their Reversible Transition

Chirality is essential for various amazing phenomena in life and matter. However,chirality and its switching in electronic superlattices, such as charge density wave(CDW) arrays, remain elusive. In this study, we characterize the chirality transition with atom-resolution imaging in a single-layer NbSe2 CDW pattern by technique of scanning tunneling microscopy. The atomic lattice of the CDW array is found continuous and intact although its chirality is switched. Several intermediate states are tracked by time-resolved imaging, revealing the fast and dynamic chirality transition. Importantly, the switching is reversibly realized with an external electric-field. Our findings unveil the delicate transition process of chiral CDW array in a 2D crystal down to the atomic scale and may be applicable for future nanoscale devices.

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

Element-wise Estimation Error of Generalized Fused Lasso

The main result of this article is that we obtain an elementwise error bound for the Fused Lasso estimator for any general convex loss function $ρ$. We then focus on the special cases when either $ρ$ is the square loss function (for mean regression) or is the quantile loss function (for quantile regression) for which we derive new pointwise error bounds. Even though error bounds for the usual Fused Lasso estimator and its quantile version have been studied before; our bound appears to be new. This is because all previous works bound a global loss function like the sum of squared error, or a sum of Huber losses in the case of quantile regression in Padilla and Chatterjee (2021). Clearly, element wise bounds are stronger than global loss error bounds as it reveals how the loss behaves locally at each point. Our element wise error bound also has a clean and explicit dependence on the tuning parameter $λ$ which informs the user of a good choice of $λ$. In addition, our bound is nonasymptotic with explicit constants and is able to recover almost all the known results for Fused Lasso (both mean and quantile regression) with additional improvements in some cases.

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

Layer-by-layer growth of bilayer graphene single-crystals enabled by self-transmitting catalytic activity

Direct growth of large-area vertically stacked two-dimensional (2D) van der Waal (vdW) materials is a prerequisite for their high-end applications in integrated electronics, optoelectronics and photovoltaics. Currently, centimetre- to even metre-scale monolayers of single-crystal graphene (MLG) and hexagonal boron nitride (h-BN) have been achieved by epitaxial growth on various single-crystalline substrates. However, in principle, this success in monolayer epitaxy seems extremely difficult to be replicated to bi- or few-layer growth, as the full coverage of the first layer was believed to terminate the reactivity of those adopting catalytic metal surfaces. Here, we report an exceptional layer-by-layer chemical vapour deposition (CVD) growth of large size bi-layer graphene single-crystals, enabled by self-transmitting catalytic activity from platinum (Pt) surfaces to the outermost graphene layers. In-situ growth and real-time surveillance experiments, under well-controlled environments, unambiguously verify that the growth does follow the layer-by-layer mode on open surfaces of MLG/Pt(111). First-principles calculations indicate that the transmittal of catalytic activity is allowed by an appreciable electronic hybridisation between graphene overlayers and Pt surfaces, enabling catalytic dissociation of hydrocarbons and subsequently direct graphitisation of their radicals on the outermost sp2 carbon surface. This self-transmitting catalytic activity is also proven to be robust for tube-furnace CVD in fabricating single-crystalline graphene bi-, tri- and tetra-layers, as well as h-BN few-layers. Our findings offer an exceptional strategy for potential controllable, layer-by-layer and wafer-scale growth of vertically stacked few-layered 2D single crystals.

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preprint2022arXiv

On the Optimization of Margin Distribution

Margin has played an important role on the design and analysis of learning algorithms during the past years, mostly working with the maximization of the minimum margin. Recent years have witnessed the increasing empirical studies on the optimization of margin distribution according to different statistics such as medium margin, average margin, margin variance, etc., whereas there is a relative paucity of theoretical understanding. In this work, we take one step on this direction by providing a new generalization error bound, which is heavily relevant to margin distribution by incorporating ingredients such as average margin and semi-variance, a new margin statistics for the characterization of margin distribution. Inspired by the theoretical findings, we propose the MSVMAv, an efficient approach to achieve better performance by optimizing margin distribution in terms of its empirical average margin and semi-variance. We finally conduct extensive experiments to show the superiority of the proposed MSVMAv approach.

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

Robust Regularized Low-Rank Matrix Models for Regression and Classification

While matrix variate regression models have been studied in many existing works, classical statistical and computational methods for the analysis of the regression coefficient estimation are highly affected by high dimensional and noisy matrix-valued predictors. To address these issues, this paper proposes a framework of matrix variate regression models based on a rank constraint, vector regularization (e.g., sparsity), and a general loss function with three special cases considered: ordinary matrix regression, robust matrix regression, and matrix logistic regression. We also propose an alternating projected gradient descent algorithm. Based on analyzing our objective functions on manifolds with bounded curvature, we show that the algorithm is guaranteed to converge, all accumulation points of the iterates have estimation errors in the order of $O(1/\sqrt{n})$ asymptotically and substantially attaining the minimax rate. Our theoretical analysis can be applied to general optimization problems on manifolds with bounded curvature and can be considered an important technical contribution to this work. We validate the proposed method through simulation studies and real image data examples.

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

The Design and Implementation of a Broadly Applicable Algorithm for Optimizing Intra-Day Surgical Scheduling

Surgical scheduling optimization is an active area of research. However, few algorithms to optimize surgical scheduling are implemented and see sustained use. An algorithm is more likely to be implemented, if it allows for surgeon autonomy, i.e., requires only limited scheduling centralization, and functions in the limited technical infrastructure of widely used electronic medical records (EMRs). In order for an algorithm to see sustained use, it must be compatible with changes to hospital capacity, patient volumes, and scheduling practices. To meet these objectives, we developed the BEDS (better elective day of surgery) algorithm, a greedy heuristic for smoothing unit-specific surgical admissions across days. We implemented BEDS in the EMR of a large pediatric academic medical center. The use of BEDS was associated with a reduction in the variability in the number of admissions. BEDS is freely available as a dashboard in Tableau, a commercial software used by numerous hospitals. BEDS is readily implementable with the limited tools available to most hospitals, does not require reductions to surgeon autonomy or centralized scheduling, and is compatible with changes to hospital capacity or patient volumes. We present a general algorithmic framework from which BEDS is derived based on a particular choice of objectives and constraints. We argue that algorithms generated by this framework retain many of the desirable characteristics of BEDS while being compatible with a wide range of objectives and constraints.

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preprint2021arXiv

A Broadband Signal Recycling Scheme for Approaching the Quantum Limit from Optical Losses

Quantum noise limits the sensitivity of laser interferometric gravitational-wave detectors. Given the state-of-the-art optics, the optical losses define the lower bound of the best possible quantum-limited detector sensitivity. In this work, we come up with a broadband signal recycling scheme which gives potential solution to approaching this lower bound by converting the signal recycling cavity to be a broadband signal amplifier using an active optomechanical filter. We will show the difference and advantage of such a scheme compared with the previous white light cavity scheme using the optomechanical filter in [Phys.Rev.Lett.115.211104 (2015)]. The drawback is that the new scheme is more susceptible to the thermal noise of the mechanical oscillator.

0 citations0 reviewsNo code linkedOpen access
preprint2021arXiv

Enhancing high frequency sensitivity of gravitational wave detectors with sloshing-Sagnac interferometer

Sensitivity of gravitational-wave detectors is limited in the high-frequency band by quantum shot noise and eventually limited by the optical loss in signal recycling cavity. This limit is the main obstacle on the way to detect gravitational waves from the binary neutron star mergers in the current and the future generation detectors, as it does not depend on either the arm length, or the injected squeezing level. In this paper, we come up with the sloshing Sagnac interferometer topology, which can be obtained from the Michelson interferometer by optically connecting the end mirrors into an additional optical cavity. This transforms the interferometer into a triply-coupled cavity system capable of beating the loss-induced high-frequency limit of the signal-recycled Michelson interferometer. With advanced LIGO+ comparable parameters, a sloshing-Sagnac scheme can achieve 7 times better sensitivity at 2.5\,kHz or 4 times better signal to noise ratio for a typical waveform of binary neutron post merge. Being an evolution of Michelson interferometer, the sloshing-Sagnac interferometer can possibly be used as a topology for the future generation detectors and upgrade of current detectors.

0 citations0 reviewsNo code linkedOpen access
preprint2021arXiv

Study of acceleration measurement in gravitational wave detection

Position-meter and speed-meter interferometers have been analysed for detecting gravitational waves. We introduce the concept of acceleration measurement in comparison with position and speed measurement. In this paper, we describe a general acceleration measurement and derive its standard quantum limit. We provide an example of an acceleration-meter interferometer configuration. We show that shot noise dominates at low frequency following a frequency dependence of $1/Ω^2$, while radiation pressure noise is constant. The acceleration-meter has even a stronger radiation pressure noise suppression than speed-meter.

0 citations0 reviewsNo code linkedOpen access
preprint2021arXiv

Understanding and controlling hexagonal patterns of wrinkles in neo-Hookean elastic bilayer structures

A controlled surface wrinkling pattern has been widely used in diverse applications, such as stretchable electronics, smart windows, and haptics. Here, we focus on hexagonal wrinkling patterns because of their great potentials in realizing anisotropic and tunable friction and serving as a dynamical template for making non-flat thin films through self-assembling processes. We employ large-scale finite element simulations of a bilayer neo-Hookean solid (e.g., a film bonded on a substrate) to explore mechanical principles that govern the formation of hexagonal wrinkling patterns and strategies for making nearly perfect hexagonal patterns. In our model, the wrinkling instabilities are driven by the confined film expansion. Our results indicate robust hexagonal patterns exist at a relatively small modulus mismatch (on the order of 10) between the film and substrate. Besides, the film expansion should not exceed the onset of wrinkling value too much to avoid post-buckling patterns. By harnessing the imperfection insensitivity of one-dimension sinusoidal wrinkles, we apply a sequential loading to the bilayer structure to produce the nearly perfect hexagonal patterns. Lastly, we discuss the connection between the simple bilayer model and the gradient structures commonly existed in experiments.

0 citations0 reviewsNo code linkedOpen access
preprint2020arXiv

Applications of BERT Based Sequence Tagging Models on Chinese Medical Text Attributes Extraction

We convert the Chinese medical text attributes extraction task into a sequence tagging or machine reading comprehension task. Based on BERT pre-trained models, we have not only tried the widely used LSTM-CRF sequence tagging model, but also other sequence models, such as CNN, UCNN, WaveNet, SelfAttention, etc, which reaches similar performance as LSTM+CRF. This sheds a light on the traditional sequence tagging models. Since the aspect of emphasis for different sequence tagging models varies substantially, ensembling these models adds diversity to the final system. By doing so, our system achieves good performance on the task of Chinese medical text attributes extraction (subtask 2 of CCKS 2019 task 1).

0 citations0 reviewsNo code linkedOpen access
preprint2020arXiv

Faces à la Carte: Text-to-Face Generation via Attribute Disentanglement

Text-to-Face (TTF) synthesis is a challenging task with great potential for diverse computer vision applications. Compared to Text-to-Image (TTI) synthesis tasks, the textual description of faces can be much more complicated and detailed due to the variety of facial attributes and the parsing of high dimensional abstract natural language. In this paper, we propose a Text-to-Face model that not only produces images in high resolution (1024x1024) with text-to-image consistency, but also outputs multiple diverse faces to cover a wide range of unspecified facial features in a natural way. By fine-tuning the multi-label classifier and image encoder, our model obtains the vectors and image embeddings which are used to transform the input noise vector sampled from the normal distribution. Afterwards, the transformed noise vector is fed into a pre-trained high-resolution image generator to produce a set of faces with the desired facial attributes. We refer to our model as TTF-HD. Experimental results show that TTF-HD generates high-quality faces with state-of-the-art performance.

0 citations0 reviewsNo code linkedOpen access
preprint2020arXiv

Feasibility study of beam-expanding telescopes in the interferometer arms for the Einstein Telescope

The optical design of the Einstein Telescope (ET) is based on a dual-recycled Michelson interferometer with Fabry-Perot cavities in the arms. ET will be constructed in a new infrastructure, allowing us to consider different technical implementations beyond the constraints of the current facilities. In this paper we investigate the feasibility of using beam-expander telescopes in the interferometer arms. We provide an example implementation that matches the optical layout as presented in the ET design update 2020. We further show that the beam-expander telescopes can be tuned to compensate for mode mismatches between the arm cavities and the rest of the interferometer.

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preprint2020arXiv

Geometry underlies the mechanical stiffening and softening of an indented floating film

A basic paradigm underlying the Hookean mechanics of amorphous, isotropic solids is that small deformations are proportional to the magnitude of external forces. However, slender bodies may undergo large deformations even under minute forces, leading to nonlinear responses rooted in purely geometric effects. Here we study the indentation of a polymer film on a liquid bath. Our experiments and simulations support a recently-predicted stiffening response [Vella & Davidovitch, Phys. Rev. E 98, 013003 (2018)], and we show that the system softens at large slopes, in agreement with our theory that addresses small and large deflections. We show how stiffening and softening emanate from nontrivial yet generic features of the stress and displacement fields.

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preprint2020arXiv

Implications of the Quantum Noise Target for the Einstein Telescope Infrastructure Design

The design of a complex instrument such as Einstein Telescope (ET) is based on a target sensitivity derived from an elaborate case for scientific exploration. At the same time it incorporates many trade-off decisions to maximise the scientific value by balancing the performance of the various subsystems against the cost of the installation and operation. In this paper we discuss the impact of a long signal recycling cavity (SRC) on the quantum noise performance. We show the reduction in sensitivity due to a long SRC for an ET high-frequency interferometer, provide details on possible compensations schemes and suggest a reduction of the SRC length. We also recall details of the trade-off between the length and optical losses for filter cavities, and show the strict requirements for an ET low-frequency interferometer. Finally, we present an alternative filter cavity design for an ET low-frequency interferometer making use of a coupled cavity, and discuss the advantages of the design in this context.

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preprint2020arXiv

Memory Augmented Generative Adversarial Networks for Anomaly Detection

In this paper, we present a memory-augmented algorithm for anomaly detection. Classical anomaly detection algorithms focus on learning to model and generate normal data, but typically guarantees for detecting anomalous data are weak. The proposed Memory Augmented Generative Adversarial Networks (MEMGAN) interacts with a memory module for both the encoding and generation processes. Our algorithm is such that most of the \textit{encoded} normal data are inside the convex hull of the memory units, while the abnormal data are isolated outside. Such a remarkable property leads to good (resp.\ poor) reconstruction for normal (resp.\ abnormal) data and therefore provides a strong guarantee for anomaly detection. Decoded memory units in MEMGAN are more interpretable and disentangled than previous methods, which further demonstrates the effectiveness of the memory mechanism. Experimental results on twenty anomaly detection datasets of CIFAR-10 and MNIST show that MEMGAN demonstrates significant improvements over previous anomaly detection methods.

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preprint2020arXiv

Mesoscale structure of wrinkle patterns and defect-proliferated liquid crystalline phases

Thin solids often develop elastic instabilities and subsequently complex, multiscale deformation patterns. Revealing the organizing principles of this spatial complexity has ramifications for our understanding of morphogenetic processes in plant leaves and animal epithelia, and perhaps even the formation of human fingerprints. We elucidate a primary source of this morphological complexity - an incompatibility between an elastically-favored "micro-structure" of uniformly spaced wrinkles and a "macro-structure" imparted through the wrinkle director and dictated by confinement forces. Our theory is borne out of experiments and simulations of floating sheets subjected to radial stretching. By analyzing patterns of grossly radial wrinkles we find two sharply distinct morphologies: defect-free patterns with a fixed number of wrinkles and non-uniform spacing, and patterns of uniformly spaced wrinkles separated by defect-rich buffer zones. We show how these morphological types reflect distinct minima of a Ginzburg-Landau functional - a coarse-grained version of the elastic energy, which penalizes nonuniform wrinkle spacing and amplitude, as well as deviations of their actual director from the axis imposed by confinement. Our results extend the effective description of wrinkle patterns as liquid crystals (H. Aharoni et al., Nat. Commun. 8:15809, 2017), and we highlight a fascinating analogy between the geometry-energy interplay that underlies the proliferation of defects in the mechanical equilibrium of confined sheets and in thermodynamic phases of superconductors and chiral liquid crystals.

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preprint2020arXiv

Quantum Squeezing Schemes for Heterodyne Readout

Advanced gravitational-wave detectors are limited by quantum noise in their most sensitive frequency band. Quantum noise suppression techniques, such as the application of the quantum squeezed state of light, have been actively studied in the context of homodyne readouts. In this paper, we consider quantum squeezing schemes for the heterodyne readouts. This is motivated by a successful suppression of the higher-order-mode content by stable recycling cavities in advanced detectors. The heterodyne readout scheme requires precise tuning of the interferometer parameters and a broadband squeezing source, but is conceptually simple and elegant. We further show that it is compatible with the frequency-dependent squeezing, which reduces both the shot noise and the radiation-pressure noise. We propose a test of the heterodyne readout with squeezing in Advanced LIGO. This can serve as a pathfinder not only for the implementation in future detectors, such as Einstein Telescope and Cosmic Explorer, but also for general high-precision optical measurements.

0 citations0 reviewsNo code linkedOpen access
preprint2020arXiv

Review: Progress on 2D topological insulators and potential ap-plications in electronic devices

Two-dimensional topological insulators (2DTI) have attracted increasing attention during the past few years. New 2DTI with increasing larger spin-orbit coupling (SOC) gaps have been predicted by theoretical calculations and some of them have been synthesized experimentally. In this review, the 2DTI, ranging from single element graphene-like materials to bi-elemental TMDs and to multi-elemental materials, with different thicknesses, structures and phases, have been summarized and discussed. The topological properties (especially the quantum spin Hall effect and Dirac fermion feature) and potential applications have been summarized. This review also points out the challenge and opportuni-ties for future 2DTI study, especially on the device applications based on the topological properties.

0 citations0 reviewsNo code linkedOpen access
preprint2020arXiv

Towards observing the neutron star collapse with gravitational wave detectors

Gravitational waves from binary neutron star inspirals have been detected along with the electromagnetic transients coming from the aftermath of the merger in GW170817. However, much is still unknown about the post-merger dynamics that connects these two sets of observables. This includes if, and when, the post-merger remnant star collapses to a black hole, and what are the necessary conditions to power a short gamma-ray burst, and other observed electromagnetic counterparts. Observing the collapse of the post-merger neutron star would shed led on these questions, constraining models for the short gamma-ray burst engine and the hot neutron star equation of state. In this work, we explore the scope of using gravitational wave detectors to measure the timing of the collapse either indirectly, by establishing the shut-off of the post-merger gravitational emission, or---more challengingly---directly, by detecting the collapse signal. For the indirect approach, we consider a kilohertz high-frequency detector design that utilises a previously studied coupled arm cavity and signal recycling cavity resonance. This design would give a signal-to-noise ratio of 0.5\,-\,8.6 (depending on the variation of waveform parameters) for a collapse gravitational wave signal occurring at 10\,ms post-merger of a binary at 50\,Mpc and with total mass $2.7 M_\odot$. For the direct approach, we propose a narrow-band detector design, utilising the sensitivity around the frequency of the arm cavity free spectral range. The proposed detector achieves a signal-to-noise ratio of 0.3\,-\,1.9, independent of the collapse time. This detector is limited by both the fundamental classical and quantum noise with the arm cavity power chosen as 10\,MW.

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preprint2019arXiv

CORAL8: Concurrent Object Regression for Area Localization in Medical Image Panels

This work tackles the problem of generating a medical report for multi-image panels. We apply our solution to the Renal Direct Immunofluorescence (RDIF) assay which requires a pathologist to generate a report based on observations across the eight different WSI in concert with existing clinical features. To this end, we propose a novel attention-based multi-modal generative recurrent neural network (RNN) architecture capable of dynamically sampling image data concurrently across the RDIF panel. The proposed methodology incorporates text from the clinical notes of the requesting physician to regulate the output of the network to align with the overall clinical context. In addition, we found the importance of regularizing the attention weights for word generation processes. This is because the system can ignore the attention mechanism by assigning equal weights for all members. Thus, we propose two regularizations which force the system to utilize the attention mechanism. Experiments on our novel collection of RDIF WSIs provided by a large clinical laboratory demonstrate that our framework offers significant improvements over existing methods.

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preprint2019arXiv

Non-uniform Curvature and Anisotropic Deformation Control Wrinkling Patterns on Tori

We investigate wrinkling patterns in a tri-layer torus consisting of an expanding thin outer layer, an intermediate soft layer and an inner core with a tunable shear modulus, inspired by pattern formation in developmental biologies, such as follicle pattern formation during the development of chicken embryos. We show from large-scale finite element simulations that hexagonal wrinkling patterns form for stiff cores whereas stripe wrinkling patterns develop for soft cores. Hexagons and stripes co-exist to form hybrid patterns for cores with intermediate stiffness. The governing mechanism for the pattern transition is that the stiffness of the inner core controls the degree to which the major radius of the torus expands this has a greater effect on deformation in the long direction as compared to the short direction of the torus. This anisotropic deformation alters stress states in the outer layer which change from biaxial (preferred hexagons) to uniaxial (preferred stripes) compression as the core stiffness is reduced. As the outer layer continues to expand, stripe and hexagon patterns will evolve into Zigzag and segmented labyrinth, respectively. Stripe wrinkles are observed to initiate at the inner surface of the torus while hexagon wrinkles start from the outer surface as a result of curvature-dependent stresses in the torus. We further discuss the effects of elasticities and geometries of the torus on the wrinkling patterns.

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preprint2016arXiv

A Review on Mechanics and Mechanical Properties of 2D Materials - Graphene and Beyond

Since the first successful synthesis of graphene just over a decade ago, a variety of two-dimensional (2D) materials (e.g., transition metal-dichalcogenides, hexagonal boron-nitride, etc.) have been discovered. Among the many unique and attractive properties of 2D materials, mechanical properties play important roles in manufacturing, integration and performance for their potential applications. Mechanics is indispensable in the study of mechanical properties, both experimentally and theoretically. The coupling between the mechanical and other physical properties (thermal, electronic, optical) is also of great interest in exploring novel applications, where mechanics has to be combined with condensed matter physics to establish a scalable theoretical framework. Moreover, mechanical interactions between 2D materials and various substrate materials are essential for integrated device applications of 2D materials, for which the mechanics of interfaces (adhesion and friction) has to be developed for the 2D materials. Here we review recent theoretical and experimental works related to mechanics and mechanical properties of 2D materials. While graphene is the most studied 2D material to date, we expect continual growth of interest in the mechanics of other 2D materials beyond graphene.

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preprint2016arXiv

Denoising and Covariance Estimation of Single Particle Cryo-EM Images

The problem of image restoration in cryo-EM entails correcting for the effects of the Contrast Transfer Function (CTF) and noise. Popular methods for image restoration include `phase flipping', which corrects only for the Fourier phases but not amplitudes, and Wiener filtering, which requires the spectral signal to noise ratio. We propose a new image restoration method which we call `Covariance Wiener Filtering' (CWF). In CWF, the covariance matrix of the projection images is used within the classical Wiener filtering framework for solving the image restoration deconvolution problem. Our estimation procedure for the covariance matrix is new and successfully corrects for the CTF. We demonstrate the efficacy of CWF by applying it to restore both simulated and experimental cryo-EM images. Results with experimental datasets demonstrate that CWF provides a good way to evaluate the particle images and to see what the dataset contains even without 2D classification and averaging.

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preprint2016arXiv

Hydrogenation of Penta-Graphene Leads to Unexpected Large Improvement in Thermal Conductivity

Penta-graphene (PG) has been identified as a novel 2D material with an intrinsic bandgap, which makes it especially promising for electronics applications. In this work, we use first-principles lattice dynamics and iterative solution of the phonon Boltzmann transport equation (BTE) to determine the thermal conductivity of PG and its more stable derivative - hydrogenated penta-graphene (HPG). As a comparison, we also studied the effect of hydrogenation on graphene thermal conductivity. In contrast to hydrogenation of graphene, which leads to a dramatic decrease in thermal conductivity (from 3590 to 1328 W/mK - a 63% reduction), HPG shows a notable increase in thermal conductivity (615 W/mK), which is 76% higher than that of PG (350 W/mK). The high thermal conductivity of HPG makes it more thermally conductive than most other semi-conducting 2D materials, such as the transition metal chalcogenides. Our detailed analyses show that the primary reason for the counter-intuitive hydrogenation-induced thermal conductivity enhancement is the weaker bond anharmonicity in HPG than PG. This leads to weaker phonon scattering after hydrogenation, despite the increase in the phonon scattering phase space. The high thermal conductivity of HPG may inspire intensive research around HPG and other derivatives of PG as potential materials for future nanoelectronic devices. The fundamental physics understood from this study may open up a new strategy to engineer thermal transport properties of other 2D materials by controlling bond anharmonicity via functionalization.

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preprint2016arXiv

Marchenko-Pastur Law for Tyler's M-estimator

This paper studies the limiting behavior of Tyler's M-estimator for the scatter matrix, in the regime that the number of samples $n$ and their dimension $p$ both go to infinity, and $p/n$ converges to a constant $y$ with $0<y<1$. We prove that when the data samples $x_1, \ldots, x_n$ are identically and independently generated from the Gaussian distribution $\mathcal{N}(0, I)$, the operator norm of the difference between a properly scaled Tyler's M-estimator and $\sum_{i=1}^n x_i x_i^\top/n$ tends to zero. As a result, the spectral distribution of Tyler's M-estimator converges weakly to the Marčenko-Pastur distribution.

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preprint2016arXiv

Monitoring Assumptions in Assume-Guarantee Contracts

Pre-deployment verification of software components with respect to behavioral specifications in the assume-guarantee form does not, in general, guarantee absence of errors at run time. This is because assumptions about the environment cannot be discharged until the environment is fixed. An intuitive approach is to complement pre-deployment verification of guarantees, up to the assumptions, with post-deployment monitoring of environment behavior to check that the assumptions are satisfied at run time. Such a monitor is typically implemented by instrumenting the application code of the component. An additional challenge for the monitoring step is that environment behaviors are typically obtained through an I/O library, which may alter the component's view of the input format. This transformation requires us to introduce a second pre-deployment verification step to ensure that alarms raised by the monitor would indeed correspond to violations of the environment assumptions. In this paper, we describe an approach for constructing monitors and verifying them against the component assumption. We also discuss limitations of instrumentation-based monitoring and potential ways to overcome it.

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preprint2016arXiv

Optimal Margin Distribution Machine

Support vector machine (SVM) has been one of the most popular learning algorithms, with the central idea of maximizing the minimum margin, i.e., the smallest distance from the instances to the classification boundary. Recent theoretical results, however, disclosed that maximizing the minimum margin does not necessarily lead to better generalization performances, and instead, the margin distribution has been proven to be more crucial. Based on this idea, we propose a new method, named Optimal margin Distribution Machine (ODM), which tries to achieve a better generalization performance by optimizing the margin distribution. We characterize the margin distribution by the first- and second-order statistics, i.e., the margin mean and variance. The proposed method is a general learning approach which can be used in any place where SVM can be applied, and their superiority is verified both theoretically and empirically in this paper.

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preprint2015arXiv

Discovery of a Weyl Semimetal in non-Centrosymmetric Compound TaAs

Three-dimensional (3D) topological Weyl semimetals (TWSs) represent a novel state of quantum matter with unusual electronic structures that resemble both a "3D graphene" and a topological insulator by possessing pairs of Weyl points (through which the electronic bands disperse linearly along all three momentum directions) connected by topological surface states, forming the unique "Fermi-arc" type Fermi-surface (FS). Each Weyl point is chiral and contains half of the degrees of freedom of a Dirac point, and can be viewed as a magnetic monopole in the momentum space. Here, by performing angle-resolved photoemission spectroscopy on non-centrosymmetric compound TaAs, we observed its complete band structures including the unique "Fermi-arc" FS and linear bulk band dispersion across the Weyl points, in excellent agreement with the theoretical calculations. This discovery not only confirms TaAs as the first 3D TWS, but also provides an ideal platform for realizing exotic physical phenomena (e.g. negative magnetoresistance, chiral magnetic effects and quantum anomalous Hall effect) which may also lead to novel future applications.

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preprint2015arXiv

Flexible Expectile Regression in Reproducing Kernel Hilbert Space

Expectile, first introduced by Newey and Powell (1987) in the econometrics literature, has recently become increasingly popular in risk management and capital allocation for financial institutions due to its desirable properties such as coherence and elicitability. The current standard tool for expectile regression analysis is the multiple linear expectile regression proposed by Newey and Powell in 1987. The growing applications of expectile regression motivate us to develop a much more flexible nonparametric multiple expectile regression in a reproducing kernel Hilbert space. The resulting estimator is called KERE which has multiple advantages over the classical multiple linear expectile regression by incorporating non-linearity, non-additivity and complex interactions in the final estimator. The kernel learning theory of KERE is established. We develop an efficient algorithm inspired by majorization-minimization principle for solving the entire solution path of KERE. It is shown that the algorithm converges at least at a linear rate. Extensive simulations are conducted to show the very competitive finite sample performance of KERE. We further demonstrate the application of KERE by using personal computer price data.

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preprint2015arXiv

Giant Thermal Rectification from Polyethylene Nanofiber Thermal Diodes

The realization of phononic computing is held hostage by the lack of high performance thermal devices. Here we show through theoretical analysis and molecular dynamics simulations that unprecedented thermal rectification factors (as large as 1.20) can be achieved utilizing the phase dependent thermal conductivity of polyethylene nanofibers. More importantly, such high thermal rectifications only need very small temperature differences (< 20 oC) across the device, which is a significant advantage over other thermal diodes which need temperature biases on the order of the operating temperature. Taking this into consideration, we show that the dimensionless temperature-scaled rectification factors of the polymer nanofiber diodes range from 12 to 25 - much larger than other thermal diodes (< 8). The polymer nanofiber thermal diode consists of a crystalline portion whose thermal conductivity is highly phase-sensitive and a cross-linked portion which has a stable phase. Nanoscale size effect can be utilized to tune the phase transition temperature of the crystalline portion, enabling thermal diodes capable of operating at different temperatures. This work will be instrumental to the design of high performance, inexpensive and easily processible thermal devices, based on which thermal circuits can be built to ultimately enable phononic computing.

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preprint2015arXiv

Molecular Beam Epitaxy Growth of Superconducting LiFeAs Film on SrTiO3(001) Substrate

The stoichiometric "111" iron-based superconductor, LiFeAs, has attacted great research interest in recent years. For the first time, we have successfully grown LiFeAs thin film by molecular beam epitaxy (MBE) on SrTiO3(001) substrate, and studied the interfacial growth behavior by reflection high energy electron diffraction (RHEED) and low-temperature scanning tunneling microscope (LT-STM). The effects of substrate temperature and Li/Fe flux ratio were investigated. Uniform LiFeAs film as thin as 3 quintuple-layer (QL) is formed. Superconducting gap appears in LiFeAs films thicker than 4 QL at 4.7 K. When the film is thicker than 13 QL, the superconducting gap determined by the distance between coherence peaks is about 7 meV, close to the value of bulk material. The ex situ transport measurement of thick LiFeAs film shows a sharp superconducting transition around 16 K. The upper critical field, Hc2(0)=13.0 T, is estimated from the temperature dependent magnetoresistance. The precise thickness and quality control of LiFeAs film paves the road of growing similar ultrathin iron arsenide films.

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preprint2015arXiv

Orthogonal Matrix Retrieval in Cryo-Electron Microscopy

In single particle reconstruction (SPR) from cryo-electron microscopy (cryo-EM), the 3D structure of a molecule needs to be determined from its 2D projection images taken at unknown viewing directions. Zvi Kam showed already in 1980 that the autocorrelation function of the 3D molecule over the rotation group SO(3) can be estimated from 2D projection images whose viewing directions are uniformly distributed over the sphere. The autocorrelation function determines the expansion coefficients of the 3D molecule in spherical harmonics up to an orthogonal matrix of size $(2l+1)\times (2l+1)$ for each $l=0,1,2,...$. In this paper we show how techniques for solving the phase retrieval problem in X-ray crystallography can be modified for the cryo-EM setup for retrieving the missing orthogonal matrices. Specifically, we present two new approaches that we term Orthogonal Extension and Orthogonal Replacement, in which the main algorithmic components are the singular value decomposition and semidefinite programming. We demonstrate the utility of these approaches through numerical experiments on simulated data.

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preprint2015arXiv

Predicting Fracture Energies and Crack-Tip Fields of Soft Tough Materials

Soft materials including elastomers and gels are pervasive in biological systems and technological applications. Whereas it is known that intrinsic fracture energies of soft materials are relatively low, how the intrinsic fracture energy cooperates with mechanical dissipation in process zone to give high fracture toughness of soft materials is not well understood. In addition, it is still challenging to predict fracture energies and crack-tip strain fields of soft tough materials. Here, we report a scaling theory that accounts for synergistic effects of intrinsic fracture energies and dissipation on the toughening of soft materials. We then develop a coupled cohesive-zone and Mullins-effect model capable of quantitatively predicting fracture energies of soft tough materials and strain fields around crack tips in soft materials under large deformation. The theory and model are quantitatively validated by experiments on fracture of soft tough materials under large deformations. We further provide a general toughening diagram that can guide the design of new soft tough materials.

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preprint2014arXiv

A Novel M-Estimator for Robust PCA

We study the basic problem of robust subspace recovery. That is, we assume a data set that some of its points are sampled around a fixed subspace and the rest of them are spread in the whole ambient space, and we aim to recover the fixed underlying subspace. We first estimate "robust inverse sample covariance" by solving a convex minimization procedure; we then recover the subspace by the bottom eigenvectors of this matrix (their number correspond to the number of eigenvalues close to 0). We guarantee exact subspace recovery under some conditions on the underlying data. Furthermore, we propose a fast iterative algorithm, which linearly converges to the matrix minimizing the convex problem. We also quantify the effect of noise and regularization and discuss many other practical and theoretical issues for improving the subspace recovery in various settings. When replacing the sum of terms in the convex energy function (that we minimize) with the sum of squares of terms, we obtain that the new minimizer is a scaled version of the inverse sample covariance (when exists). We thus interpret our minimizer and its subspace (spanned by its bottom eigenvectors) as robust versions of the empirical inverse covariance and the PCA subspace respectively. We compare our method with many other algorithms for robust PCA on synthetic and real data sets and demonstrate state-of-the-art speed and accuracy.

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preprint2014arXiv

A study of a debt-influenced equilibrium of the Keen model

The Keen model is a mathematical model that describes the dynamic evolution of wages, employment, and debt based on the known Minsky's Financial Instability Hypothesis. It consists of three first order nonlinear ordinary differential equations. There exists an equilibrium state that corresponds to a collapse of both wage and employment but certain debts remain. In this paper, we construct an example in which this equilibrium appears to be stable. More interestingly, the debt becomes negative, which indicates some source of income without laboring.

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preprint2014arXiv

Large Margin Distribution Machine

Support vector machine (SVM) has been one of the most popular learning algorithms, with the central idea of maximizing the minimum margin, i.e., the smallest distance from the instances to the classification boundary. Recent theoretical results, however, disclosed that maximizing the minimum margin does not necessarily lead to better generalization performances, and instead, the margin distribution has been proven to be more crucial. In this paper, we propose the Large margin Distribution Machine (LDM), which tries to achieve a better generalization performance by optimizing the margin distribution. We characterize the margin distribution by the first- and second-order statistics, i.e., the margin mean and variance. The LDM is a general learning approach which can be used in any place where SVM can be applied, and its superiority is verified both theoretically and empirically in this paper.

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preprint2014arXiv

lp-Recovery of the Most Significant Subspace among Multiple Subspaces with Outliers

We assume data sampled from a mixture of d-dimensional linear subspaces with spherically symmetric distributions within each subspace and an additional outlier component with spherically symmetric distribution within the ambient space (for simplicity we may assume that all distributions are uniform on their corresponding unit spheres). We also assume mixture weights for the different components. We say that one of the underlying subspaces of the model is most significant if its mixture weight is higher than the sum of the mixture weights of all other subspaces. We study the recovery of the most significant subspace by minimizing the lp-averaged distances of data points from d-dimensional subspaces, where p>0. Unlike other lp minimization problems, this minimization is non-convex for all p>0 and thus requires different methods for its analysis. We show that if 0<p<=1, then for any fraction of outliers the most significant subspace can be recovered by lp minimization with overwhelming probability (which depends on the generating distribution and its parameters). We show that when adding small noise around the underlying subspaces the most significant subspace can be nearly recovered by lp minimization for any 0<p<=1 with an error proportional to the noise level. On the other hand, if p>1 and there is more than one underlying subspace, then with overwhelming probability the most significant subspace cannot be recovered or nearly recovered. This last result does not require spherically symmetric outliers.

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preprint2014arXiv

Polymer Nanofibers with Outstanding Thermal Conductivity and Thermal Stability: Fundamental Linkage between Molecular Characteristics and Macroscopic Thermal Properties

Polymer nanofibers with high thermal conductivities and outstanding thermal stabilities are highly desirable in heat transfer-critical applications such as thermal management, heat exchangers and energy storage. In this work, we unlock the fundamental relations between the thermal conductivity and thermal stability of polymer nanofibers and their molecular characteristics by studying the temperature-induced phase transitions and thermal transport of a series of polymer nanofibers. Ten different polymer nanofibers with systematically chosen molecular structures are studied using large scale molecular dynamics simulations. We found that high thermal conductivity and good thermal stability can be achieved in polymers with rigid backbones, exemplified by π-conjugated polymers, due to suppressed segmental rotations and large phonon group velocities. The low probability of segmental rotation does not only prevent temperature-induced phase transition but also enables long phonon mean free paths due to reduced disorder scattering. Although stronger inter-chain interactions can also improve the thermal stability, polymers with such a feature usually have heavier atoms, weaker backbone bonds, and segments vulnerable to random rotations, which lead to low thermal conductivities. This work elucidates the underlying linkage between the molecular nature and macroscopic thermal properties of polymer nanofibers, which is instrumental to the design of thermally conductive polymer nanofibers with high temperature stabilities.

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preprint2014arXiv

Robust computation of linear models by convex relaxation

Consider a dataset of vector-valued observations that consists of noisy inliers, which are explained well by a low-dimensional subspace, along with some number of outliers. This work describes a convex optimization problem, called REAPER, that can reliably fit a low-dimensional model to this type of data. This approach parameterizes linear subspaces using orthogonal projectors, and it uses a relaxation of the set of orthogonal projectors to reach the convex formulation. The paper provides an efficient algorithm for solving the REAPER problem, and it documents numerical experiments which confirm that REAPER can dependably find linear structure in synthetic and natural data. In addition, when the inliers lie near a low-dimensional subspace, there is a rigorous theory that describes when REAPER can approximate this subspace.

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preprint2013arXiv

Multivariate Generalized Gaussian Distribution: Convexity and Graphical Models

We consider covariance estimation in the multivariate generalized Gaussian distribution (MGGD) and elliptically symmetric (ES) distribution. The maximum likelihood optimization associated with this problem is non-convex, yet it has been proved that its global solution can be often computed via simple fixed point iterations. Our first contribution is a new analysis of this likelihood based on geodesic convexity that requires weaker assumptions. Our second contribution is a generalized framework for structured covariance estimation under sparsity constraints. We show that the optimizations can be formulated as convex minimization as long the MGGD shape parameter is larger than half and the sparsity pattern is chordal. These include, for example, maximum likelihood estimation of banded inverse covariances in multivariate Laplace distributions, which are associated with time varying autoregressive processes.

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preprint2012arXiv

Hybrid Linear Modeling via Local Best-fit Flats

We present a simple and fast geometric method for modeling data by a union of affine subspaces. The method begins by forming a collection of local best-fit affine subspaces, i.e., subspaces approximating the data in local neighborhoods. The correct sizes of the local neighborhoods are determined automatically by the Jones' $β_2$ numbers (we prove under certain geometric conditions that our method finds the optimal local neighborhoods). The collection of subspaces is further processed by a greedy selection procedure or a spectral method to generate the final model. We discuss applications to tracking-based motion segmentation and clustering of faces under different illuminating conditions. We give extensive experimental evidence demonstrating the state of the art accuracy and speed of the suggested algorithms on these problems and also on synthetic hybrid linear data as well as the MNIST handwritten digits data; and we demonstrate how to use our algorithms for fast determination of the number of affine subspaces.

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preprint2012arXiv

Probabilistic Recovery of Multiple Subspaces in Point Clouds by Geometric lp Minimization

We assume data independently sampled from a mixture distribution on the unit ball of the D-dimensional Euclidean space with K+1 components: the first component is a uniform distribution on that ball representing outliers and the other K components are uniform distributions along K d-dimensional linear subspaces restricted to that ball. We study both the simultaneous recovery of all K underlying subspaces and the recovery of the best l0 subspace (i.e., with largest number of points) by minimizing the lp-averaged distances of data points from d-dimensional subspaces of the D-dimensional space. Unlike other lp minimization problems, this minimization is non-convex for all p>0 and thus requires different methods for its analysis. We show that if 0<p <= 1, then both all underlying subspaces and the best l0 subspace can be precisely recovered by lp minimization with overwhelming probability. This result extends to additive homoscedastic uniform noise around the subspaces (i.e., uniform distribution in a strip around them) and near recovery with an error proportional to the noise level. On the other hand, if K>1 and p>1, then we show that both all underlying subspaces and the best l0 subspace cannot be recovered and even nearly recovered. Further relaxations are also discussed. We use the results of this paper for partially justifying recent effective algorithms for modeling data by mixtures of multiple subspaces as well as for discussing the effect of using variants of lp minimizations in RANSAC-type strategies for single subspace recovery.

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preprint2012arXiv

Robust recovery of multiple subspaces by geometric l_p minimization

We assume i.i.d. data sampled from a mixture distribution with K components along fixed d-dimensional linear subspaces and an additional outlier component. For p>0, we study the simultaneous recovery of the K fixed subspaces by minimizing the l_p-averaged distances of the sampled data points from any K subspaces. Under some conditions, we show that if $0<p\leq1$, then all underlying subspaces can be precisely recovered by l_p minimization with overwhelming probability. On the other hand, if K>1 and p>1, then the underlying subspaces cannot be recovered or even nearly recovered by l_p minimization. The results of this paper partially explain the successes and failures of the basic approach of l_p energy minimization for modeling data by multiple subspaces.

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preprint2010arXiv

Randomized hybrid linear modeling by local best-fit flats

The hybrid linear modeling problem is to identify a set of d-dimensional affine sets in a D-dimensional Euclidean space. It arises, for example, in object tracking and structure from motion. The hybrid linear model can be considered as the second simplest (behind linear) manifold model of data. In this paper we will present a very simple geometric method for hybrid linear modeling based on selecting a set of local best fit flats that minimize a global l1 error measure. The size of the local neighborhoods is determined automatically by the Jones' l2 beta numbers; it is proven under certain geometric conditions that good local neighborhoods exist and are found by our method. We also demonstrate how to use this algorithm for fast determination of the number of affine subspaces. We give extensive experimental evidence demonstrating the state of the art accuracy and speed of the algorithm on synthetic and real hybrid linear data.

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preprint2009arXiv

Median K-flats for hybrid linear modeling with many outliers

We describe the Median K-Flats (MKF) algorithm, a simple online method for hybrid linear modeling, i.e., for approximating data by a mixture of flats. This algorithm simultaneously partitions the data into clusters while finding their corresponding best approximating l1 d-flats, so that the cumulative l1 error is minimized. The current implementation restricts d-flats to be d-dimensional linear subspaces. It requires a negligible amount of storage, and its complexity, when modeling data consisting of N points in D-dimensional Euclidean space with K d-dimensional linear subspaces, is of order O(n K d D+n d^2 D), where n is the number of iterations required for convergence (empirically on the order of 10^4). Since it is an online algorithm, data can be supplied to it incrementally and it can incrementally produce the corresponding output. The performance of the algorithm is carefully evaluated using synthetic and real data.

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