arXiv subjects

Jiang Qian

Publications and source records attributed to Jiang Qian.

18 recordsLinked to original sources

arXiv2024

An Integer Programming Formulation for the Maximally Diverse Grouping Problem

The Maximally Diverse Grouping Problem (MDGP) is the problem of assigning a set of elements to mutually disjoint groups in order to maximise the overall diversity between the elements. Because the MDGP is NP-complete, most studies have focused on heuristic solution approaches, as compared to exact solution approaches, to the problem. On the one hand, heuristic solution approaches, although common in practice, do not guarantee a global optimal solution. On the other hand, studies that have reformulated the problem as an integer linear programme, which can be solved using exact solution approaches, are either restricted to groups of equal size or restricted to the use of the Manhattan distance. The present paper presents a new integer linear programming formulation that is not subjected to either of these restrictions, and can therefore be used to establish useful benchmarks for the performance of heuristics in a broader range of applications moving forward.

math.OC↗

arXiv2024

Deep Brain Ultrasound Ablation Thermal Dose Modeling with in Vivo Experimental Validation

Intracorporeal needle-based therapeutic ultrasound (NBTU) is a minimally invasive option for intervening in malignant brain tumors, commonly used in thermal ablation procedures. This technique is suitable for both primary and metastatic cancers, utilizing a high-frequency alternating electric field (up to 10 MHz) to excite a piezoelectric transducer. The resulting rapid deformation of the transducer produces an acoustic wave that propagates through tissue, leading to localized high-temperature heating at the target tumor site and inducing rapid cell death. To optimize the design of NBTU transducers for thermal dose delivery during treatment, numerical modeling of the acoustic pressure field generated by the deforming piezoelectric transducer is frequently employed. The bioheat transfer process generated by the input pressure field is used to track the thermal propagation of the applicator over time. Magnetic resonance thermal imaging (MRTI) can be used to experimentally validate these models. Validation results using MRTI demonstrated the feasibility of this model, showing a consistent thermal propagation pattern. However, a thermal damage isodose map is more advantageous for evaluating therapeutic efficacy. To achieve a more accurate simulation based on the actual brain tissue environment, a new finite element method (FEM) simulation with enhanced damage evaluation capabilities was conducted. The results showed that the highest temperature and ablated volume differed between experimental and simulation results by 2.1884°C (3.71%) and 0.0631 cm$^3$ (5.74%), respectively. The lowest Pearson correlation coefficient (PCC) for peak temperature was 0.7117, and the lowest Dice coefficient for the ablated area was 0.7021, indicating a good agreement in accuracy between simulation and experiment.

physics.med-ph↗

arXiv2024

Confidence Intervals for the F1 Score: A Comparison of Four Methods

In Natural Language Processing (NLP), binary classification algorithms are often evaluated using the F1 score. Because the sample F1 score is an estimate of the population F1 score, it is not sufficient to report the sample F1 score without an indication of how accurate it is. Confidence intervals are an indication of how accurate the sample F1 score is. However, most studies either do not report them or report them using methods that demonstrate poor statistical properties. In the present study, I review current analytical methods (i.e., Clopper-Pearson method and Wald method) to construct confidence intervals for the population F1 score, propose two new analytical methods (i.e., Wilson direct method and Wilson indirect method) to do so, and compare these methods based on their coverage probabilities and interval lengths, as well as whether these methods suffer from overshoot and degeneracy. Theoretical results demonstrate that both proposed methods do not suffer from overshoot and degeneracy. Experimental results suggest that both proposed methods perform better, as compared to current methods, in terms of coverage probabilities and interval lengths. I illustrate both current and proposed methods on two suggestion mining tasks. I discuss the practical implications of these results, and suggest areas for future research.

stat.ME↗

arXiv2024

Couler: Unified Machine Learning Workflow Optimization in Cloud

Machine Learning (ML) has become ubiquitous, fueling data-driven applications across various organizations. Contrary to the traditional perception of ML in research, ML workflows can be complex, resource-intensive, and time-consuming. Expanding an ML workflow to encompass a wider range of data infrastructure and data types may lead to larger workloads and increased deployment costs. Currently, numerous workflow engines are available (with over ten being widely recognized). This variety poses a challenge for end-users in terms of mastering different engine APIs. While efforts have primarily focused on optimizing ML Operations (MLOps) for a specific workflow engine, current methods largely overlook workflow optimization across different engines. In this work, we design and implement Couler, a system designed for unified ML workflow optimization in the cloud. Our main insight lies in the ability to generate an ML workflow using natural language (NL) descriptions. We integrate Large Language Models (LLMs) into workflow generation, and provide a unified programming interface for various workflow engines. This approach alleviates the need to understand various workflow engines' APIs. Moreover, Couler enhances workflow computation efficiency by introducing automated caching at multiple stages, enabling large workflow auto-parallelization and automatic hyperparameters tuning. These enhancements minimize redundant computational costs and improve fault tolerance during deep learning workflow training. Couler is extensively deployed in real-world production scenarios at Ant Group, handling approximately 22k workflows daily, and has successfully improved the CPU/Memory utilization by more than 15% and the workflow completion rate by around 17%.

cs.DB↗

arXiv2022

TranSHER: Translating Knowledge Graph Embedding with Hyper-Ellipsoidal Restriction

Knowledge graph embedding methods are important for the knowledge graph completion (or link prediction) task. One existing efficient method, PairRE, leverages two separate vectors to model complex relations (i.e., 1-to-N, N-to-1, and N-to-N) in knowledge graphs. However, such a method strictly restricts entities on the hyper-ellipsoid surfaces which limits the optimization of entity distribution, leading to suboptimal performance of knowledge graph completion. To address this issue, we propose a novel score function TranSHER, which leverages relation-specific translations between head and tail entities to relax the constraint of hyper-ellipsoid restrictions. By introducing an intuitive and simple relation-specific translation, TranSHER can provide more direct guidance on optimization and capture more semantic characteristics of entities with complex relations. Experimental results show that TranSHER achieves significant performance improvements on link prediction and generalizes well to datasets in different domains and scales. Our codes are public available at https://github.com/yizhilll/TranSHER.

cs.AI↗

arXiv2020

BS-NAS: Broadening-and-Shrinking One-Shot NAS with Searchable Numbers of Channels

One-Shot methods have evolved into one of the most popular methods in Neural Architecture Search (NAS) due to weight sharing and single training of a supernet. However, existing methods generally suffer from two issues: predetermined number of channels in each layer which is suboptimal; and model averaging effects and poor ranking correlation caused by weight coupling and continuously expanding search space. To explicitly address these issues, in this paper, a Broadening-and-Shrinking One-Shot NAS (BS-NAS) framework is proposed, in which `broadening' refers to broadening the search space with a spring block enabling search for numbers of channels during training of the supernet; while `shrinking' refers to a novel shrinking strategy gradually turning off those underperforming operations. The above innovations broaden the search space for wider representation and then shrink it by gradually removing underperforming operations, followed by an evolutionary algorithm to efficiently search for the optimal architecture. Extensive experiments on ImageNet illustrate the effectiveness of the proposed BS-NAS as well as the state-of-the-art performance.

cs.LG↗

arXiv2018

Low-frequency dielectric response of a periodic array of charged spheres in an electrolyte solution: The simple cubic lattice

We study the low-frequency dielectric response of highly charged spheres arranged in a cubic lattice and immersed in an electrolyte solution. We focus on the influence of the out-of-phase current in the regime where the ionic charge is neutral. We consider the case where the charged spheres have no surface conductance and no frequency-dependent surface capacitance. Hence, the frequency dispersion of the dielectric constant is dominated by the effect of neutral currents outside the electric double layer. In the thin double-layer limit, we use Fixman's boundary condition at the outer surface of the double layer to capture interaction between the electric field and the flow of the ions. For periodic conditions, we combine the methods developed by Lord Rayleigh for understanding the electric conduction across rectangularly arranged obstacles and by Korringa, Kohn and Rostoker for the electronic band structure computation. When the charged spheres occupy a very small volume fraction, smaller than one percent, our solution becomes consistent with the Maxwell Garnett mixing formula together with the single-particle polarization response, as expected, because inter-particle interactions become less prominent in the dilute limit. By contrast, the inter-particle interaction greatly alters the dielectric response even when charged spheres occupy only two percent of the volume. We found that the characteristic frequency shifts to a higher value compared to that derived from the single-particle polarization response. At the same time, the low-frequency dielectric enhancement, a signature of charged spheres immersed in an electrolyte, becomes less prominent for the periodic array of charged spheres. Our results imply that the signature of the dielectric response of a system consisting of densely packed charged spheres immersed in an electrolyte can differ drastically from a dilute suspension.

cond-mat.soft↗

arXiv2016

Dielectric Enhancement from Non-Insulating Particles with Ideally Polarized Interfaces and Zero $ζ$-Potential I: Exact Solution

We solve exactly the dielectric response of a non-insulating sphere of radius $a$ suspended in symmetric, univalent electrolyte solution, with ideally-polarizable interface but without significant $ζ$-potential. We then use this solution to derive the dielectric response of a dilute random suspension of such spheres, with volume fraction $f\ll1$, within the Maxwell-Garnett Effective Medium Approximation. Surprisingly, we discover a huge dielectric enhancement in this bare essential model of dielectric responses of solids in electrolyte solution: at low frequency $ωτ_D \ll (λ/a) / (σ_w / σ_s+1/2)$, the real part of the effective dielectric constant of the mixture is $1-(3f/2)+(9f/4)(a/λ)$. Here $σ_{w/s}$ is the conductivity of the electrolyte solution/solids, $λ$ is the Debye screening length in the solution, $τ_D=λ^2/D$ is the standard time scale of diffusion and $D$ is the ion diffusion coefficient. As $λ$ is of the order nm even for dilute electrolyte solution, even for sub-mm spheres and low volume fraction $f=0.05$ the huge geometric factor $a/λ$ implies an over $10^4$-fold enhancement. Furthermore, we show that this enhancement produces a significant low frequency ($ωτ_D\ll1$) phase shift $\tanθ= \mathrm{Re}~ ε(ω) / \mathrm{Im} ~ε(ω)$ in a simple impedance measurement of the mixture, which is usually negligible in pure electrolyte solution. The phase shift has a scale-invariant maximum $\tanθ_{\mathrm{max}}=(9/4)f/(2σ_w/σ_s+1)$ at $ω_{\mathrm{max}}=(2D/λa)/(2σ_w/σ_s+1)$. We provide a physical picture of the enhancement from an accumulation of charges in a thin Externally Induced Double Layer (EIDL) due to the blocking boundary conditions on interfaces.

physics.class-ph↗

arXiv2016

On Some Inverse Eigenvalue Problems of Quadratic Palindromic Systems

This paper concerns some inverse eigenvalue problems of the quadratic $\star$-(anti)-palindromic system $Q(\lambda)=\lambda^2 A_1^{\star}+\lambda A_0 + \epsilon A_1$, where $\epsilon=\pm 1$, $A_1, A_0 \in \mathbb{C}^{n\times n}$, $A_0^{\star}=\epsilon A_0$, $A_1$ is nonsingular, and the symbol $\star$ is used as an abbreviation for transpose for real matrices and either transpose or conjugate transpose for complex matrices. By using the spectral decomposition of the quadratic $\star$-(anti)-palindromic system, the inverse eigenvalue problems with entire/partial eigenpairs given, and the model updating problems with no-spillover are considered. Some conditions on the solvabilities of these problems are given, and algorithms are proposed to find these solutions. These algorithms are illustrated by some numerical examples.

math.NA↗

arXiv2016

Universal Dielectric Enhancement from Externally Induced Double Layer Without $ζ$-Potential

Motivated by recent experiments showing over $10^4$-fold increase in induced polarization from electrochemically inert, conducting materials in dilute saline solutions, we theoretically demonstrate a new mechanism for dielectric enhancement, in the absence of $ζ-$potentials at interfaces between non-insulating particles and an electrolyte solution. We further show that the magnitude of such enhancement obeys universal scaling laws, independent of the particle's electrical properties and valid across particle shapes: for a dilute suspension of identical, but arbitrarily shaped particles of a linear dimension $a$ and volume fraction $f$, as $ω\to0$ the effective real dielectric constant of the mixture is enhanced from that of water by a factor $1+f~(P_r+(a/λ)P_i)$, and the frequency-dependent phase shift of its impedance has a scale-invariant maximum $f\,\mathsfΘ$ if particles are much more conductive than the solution. Here $λ$ is the solution's Debye length and $P_r$, $P_i$, $\mathsfΘ$ are dimensionless numbers determined solely by the particles' shape. Even for a very dilute electrolyte solution (e.g. $10^{-3}$ molar), sub-mm sized particles, at volume fraction $f=0.1$, can give a $10^4$-fold dielectric enhancement, producing an easily observable phase shift maximum in a simple impedance measurement.We also derive frequency cutoffs as conditions for observing these enhancements, showing that insulating particles produce no enhancement without $ζ$-potential.To prove these results for particles of arbitrary shapes, we develop a physical picture where an externally induced double layer (EIDL), in contrast to the Guoy-Chapman double layer on interfaces with significant $ζ$-potentials, dominates the low-frequency dynamics and produces dielectric enhancement.

physics.class-ph↗

arXiv2016

Refined Schur Method for Robust Pole Assignment with Repeated Poles

Schur-type methods in \cite{Chu2} and \cite{GCQX} solve the robust pole assignment problem by employing the departure from normality of the closed-loop system matrix as the measure of robustness. They work well generally when all poles to be assigned are simple. However, when some poles are close or even repeated, the eigenvalues of the computed closed-loop system matrix might be inaccurate. In this paper, we present a refined Schur method, which is able to deal with the case when some or all of the poles to be assigned are repeated. More importantly, the refined Schur method can still be applied when \verb|place| \cite{KNV} and \verb|robpole| \cite{Tits} fail to output a solution when the multiplicity of some repeated poles is greater than the input freedom.

math.NA↗

arXiv2014

Laser Theory for Optomechanics: Limit Cycles in the Quantum Regime

Optomechanical systems can exhibit self-sustained limit cycles where the quantum state of the mechanical resonator possesses nonclassical characteristics such as a strongly negative Wigner density, as was shown recently in a numerical study by Qian et al. [Physical Review Letters, 109, 253601 (2012)]. Here we derive a Fokker-Planck equation describing mechanical limit cycles in the quantum regime which correctly reproduces the numerically observed nonclassical features. The derivation starts from the standard optomechanical master equation, and is based on techniques borrowed from the laser theory due to Haake's and Lewenstein. We compare our analytical model with numerical solutions of the master equation based on Monte-Carlo simulations, and find very good agreement over a wide and so far unexplored regime of system parameters. As one main conclusion, we predict negative Wigner functions to be observable even for surprisingly classical parameters, i.e. outside the single-photon strong coupling regime, for strong cavity drive, and rather large limit cycle amplitudes. The general approach taken here provides a natural starting point for further studies of quantum effects in optomechanics.

quant-ph↗

arXiv2012

Quantum Signatures of the Optomechanical Instability

In the past few years, coupling strengths between light and mechanical motion in optomechanical setups have improved by orders of magnitude. Here we show that, in the standard setup under continuous laser illumination, the steady state of the mechanical oscillator can develop a non-classical, strongly negative Wigner density if the optomechanical coupling is large at the single-photon level. Because of its robustness, such a Wigner density can be mapped using optical homodyne tomography. These features are observed near the onset of the instability towards self-induced oscillations. We show that there are also distinct signatures in the photon-photon correlation function $g^{(2)}(t)$ in that regime, including oscillations decaying on a time scale not only much longer than the optical cavity decay time, but even longer than the \emph{mechanical} decay time.

cond-mat.mes-hall↗

arXiv2010

Collective dynamics in optomechanical arrays

The emerging field of optomechanics seeks to explore the interaction between nanomechanics and light. Recently, the exciting concept of optomechanical crystals has been introduced, where defects in photonic crystal structures are used to generate both localized optical and mechanical modes that interact with each other. Here we start exploring the collective dynamics of arrays consisting of many coupled optomechanical cells. We show that such "optomechanical arrays" can display synchronization and that they can be described by a modified Kuramoto model that allows to explain and predict most of the features that will be observable in future experiments.

cond-mat.mes-hall↗

arXiv2010

Imaging and manipulating electrons in a 1D quantum dot with Coulomb blockade microscopy

Motivated by the recent experiments by the Westervelt group using a mobile tip to probe the electronic state of quantum dots formed on a segmented nanowire, we study the shifts in Coulomb blockade peak positions as a function of the spatial variation of the tip potential, which can be termed "Coulomb blockade microscopy". We show that if the tip can be brought sufficiently close to the nanowire, one can distinguish a high density electronic liquid state from a Wigner crystal state by microscopy with a weak tip potential. In the opposite limit of a strongly negative tip potential, the potential depletes the electronic density under it and divides the quantum wire into two partitions. There the tip can push individual electrons from one partition to the other, and the Coulomb blockade micrograph can clearly track such transitions. We show that this phenomenon can be used to qualitatively estimate the relative importance of the electron interaction compared to one particle potential and kinetic energies. Finally, we propose that a weak tip Coulomb blockade micrograph focusing on the transition between electron number N=0 and N=1 states may be used to experimentally map the one-particle potential landscape produced by impurities and inhomogeneities.

cond-mat.mes-hall↗

arXiv2008

Hartree-Fock calculations of a finite inhomogeneous quantum wire

We use the Hartree-Fock method to study an interacting one-dimensional electron system on a finite wire, partially depleted at the center by a smooth potential barrier. A uniform one-Tesla Zeeman field is applied throughout the system. We find that with the increase in the potential barrier, the low density electrons under it go from a non-magnetic state to an antiferromagnetic state, and then to a state with a well-localized spin-aligned region isolated by two antiferromagnetic regions from the high density leads. At this final stage, in response to a continuously increasing barrier potential, the system undergoes a series of abrupt density changes, corresponding to the successive expulsion of a single electron from the spin-aligned region under the barrier. Motivated by the recent momentum-resolved tunneling experiments in a parallel wire geometry, we also compute the momentum resolved tunneling matrix elements. Our calculations suggest that the eigenstates being expelled are spatially localized, consistent with the experimental observations. However, additional mechanisms are needed to account for the experimentally observed large spectral weight at near $k=0$ in the tunneling matrix elements.

cond-mat.mes-hall↗

arXiv2007

Time dependent diffusion in a disordered medium with partially absorbing walls: A perturbative approach

We present an analytical study of the time dependent diffusion coefficient in a dilute suspension of spheres with partially absorbing boundary condition. Following Kirkpatrick (J. Chem. Phys. 76, 4255) we obtain a perturbative expansion for the time dependent particle density using volume fraction $f$ of spheres as an expansion parameter. The exact single particle $t$-operator for partially absorbing boundary condition is used to obtain a closed form time-dependent diffusion coefficient $D(t)$ accurate to first order in the volume fraction $f$. Short and long time limits of $D(t)$ are checked against the known short-time results for partially or fully absorbing boundary conditions and long-time results for reflecting boundary conditions. For fully absorbing boundary condition the long time diffusion coefficient is found to be $D(t)=5 a^2/(12 f D_{0} t) +O((D_0t/a^2)^{-2})$, to the first order of perturbation theory. Here $f$ is small but non-zero, $D_0$ the diffusion coefficient in the absence of spheres, and $a$ the radius of the spheres. The validity of this perturbative result is discussed.

cond-mat.stat-mech↗

arXiv2005

Theory of momentum resolved tunneling into a short quantum wire

Motivated by recent tunneling experiments in the parallel wire geometry, we calculate results for momentum resolved tunneling into a short one-dimensional wire, containing a small number of electrons. We derive some general theorems about the momentum dependence, and we carry out exact calculations for up to N=4 electrons in the final state, for a system with screened Coulomb interactions that models the situation of the experiments. We also investigate the limit of large $N$ using a Luttinger-liquid type analysis. We consider the low-density regime, where the system is close to the Wigner crystal limit, and where the energy scale for spin excitations can be much lower than for charge excitations, and we consider temperatures intermediate between the relevant spin energies and charge excitations, as well as temperatures below both energy scales.

cond-mat.mes-hall↗