Searcharxiv⌕ Search

arXiv subjects

Bin Qian

Publications and source records attributed to Bin Qian.

At least 37 records · Page 2Linked to original sources
arXiv2024

Gradient bounds and Liouville property for a class of hypoelliptic diffusion via coupling

In this paper, we obtain the reverse Bakry-Émery type estimates for a class of hypoelliptic diffusion operator by coupling method. The (right and reverse) Poincaré inequalities and the (right and reverse) logarithmic Sobolev inequalities are presented as consequences of such estimates. Wang-Harnack inequality, Hamilton's gradient estimate and Liouville property are also presented by reverse logarithmic Sobolev inequality.

math.PR↗
arXiv2024

FLMarket: Enabling Privacy-preserved Pre-training Data Pricing for Federated Learning

Federated Learning (FL), as a mainstream privacy-preserving machine learning paradigm, offers promising solutions for privacy-critical domains such as healthcare and finance. Although extensive efforts have been dedicated from both academia and industry to improve the vanilla FL, little work focuses on the data pricing mechanism. In contrast to the straightforward in/post-training pricing techniques, we study a more difficult problem of pre-training pricing without direct information from the learning process. We propose FLMarket that integrates a two-stage, auction-based pricing mechanism with a security protocol to address the utility-privacy conflict. Through comprehensive experiments, we show that the client selection according to FLMarket can achieve more than 10% higher accuracy in subsequent FL training compared to state-of-the-art methods. In addition, it outperforms the in-training baseline with more than 2% accuracy increase and 3x run-time speedup.

cs.LG↗
arXiv2024

Generalized and high-efficiency arbitrary-positioned buffer for smoothed particle hydrodynamics

This paper develops an arbitrary-positioned buffer for the smoothed particle hydrodynamics (SPH) method, whose generality and high efficiency are achieved through two techniques. First, with the local coordinate system established at each arbitrary-positioned in-/outlet, particle positions in the global coordinate system are transformed into those in it via coordinate transformation. Since one local axis is located perpendicular to the in-/outlet boundary, the position comparison between particles and the threshold line or surface can be simplified to just this coordinate dimension. Second, particle candidates subjected to position comparison at one specific in-/outlet are restricted to those within the local cell-linked lists nearby the defined buffer zone, which significantly enhances computational efficiency due to a small portion of particles being checked. With this developed buffer, particle generation and deletion at arbitrary-positioned in- and outlets of complex flows can be handled efficiently and straightforwardly. We validate the effectiveness and versatility of the developed buffer through 2-D and 3-D non-/orthogonal uni-/bidirectional flows with arbitrary-positioned in- and outlets, driven by either pressure or velocity boundary conditions.

cs.CE↗
arXiv2023

Sharp Li--Yau Inequalities for Dunkl Harmonic Oscillators

We study the Li--Yau inequality for the heat equation corresponding to the Dunkl harmonic oscillator, which is a non-local Schrödinger operator parameterized by reflections and multiplicity functions. In the particular case when the reflection group is isomorphic to $\mathbb{Z}_2^d$, the result is sharp in the sense that equality is achieved by the heat kernel of the classic harmonic oscillator. We also provide the application on parabolic Harnack inequalities.

math.AP↗
arXiv2021

Li--Yau Inequalities for Dunkl Heat Equations

Motivated by recent works due to Yu--Zhao [J. Geom. Anal. 2020] and Weber--Zacher [arXiv:2012.12974], we study Li--Yau inequalities for the heat equation corresponding to the Dunkl Laplacian, which is a non-local operator parameterized by reflection groups and multiplicity functions. The results are sharp in the particular case when the reflection group is isometric to $\mathbb{Z}_2^d$.

math.AP↗
arXiv2021

Revisiting Li-Yau type inequalities on Riemannian manifolds

Inspired Yau's work (Comm. Anal. Geom., 1994), in this short note we provide a new version of Li-Yau gradient estimate for the linear heat equation, which generalizes some known results and gives new gradient estimates. Also we explain the different known results as different cases here.

math.DG↗
arXiv2021

Topological quantum phase transition in the magnetic semimetal HoSb

Magnetic topological semimetals, a novel state of quantum matter with nontrivial band topology, have emerged as a new frontier in physics and materials science. An external stimulus like temperature or magnetic field could be expected to alter their spin states and thus the Fermi surface anisotropies and topological features. Here, we perform the angular magnetoresistance measurements and electronic band structure calculations to reveal the evolution of HoSb's Fermi surface anisotropies and topological nature in different magnetic states. The angular magnetoresistance results manifest that its Fermi surface anisotropy is robust in the paramagnetic state but is significantly modulated in the antiferromagnetic and ferromagnetic states. More interestingly, a transition from the trivial (nontrivial) to nontrivial (trivial) topological electronic phase is observed when HoSb undergoes a magnetic transition from the paramagnetic (antiferromagnetic) to antiferromagnetic (ferromagnetic) state induced by temperature (applied magnetic field). Our studying suggests that HoSb provides an archetype platform to study the correlations between magnetism and topological states of matter.

cond-mat.mtrl-sci↗
arXiv2020

Pressure Engineering of the Dirac Fermions in Quasi-One-Dimensional Tl$_2$Mo$_6$Se$_6$

Topological band dispersions other than the standard Dirac or Weyl fermions have garnered the increasing interest in materials science. Among them, the cubic Dirac fermions were recently proposed in the family of quasi-one-dimensional conductors A$_2$Mo$_6$X$_6$ (A= Na, K, In, Tl; X= S, Se, Te), where the band crossing is characterized by a linear dispersion in one $k$-space direction but the cubic dispersion in the plane perpendicular to it. It is not yet clear, however, how the external perturbations can alter these nontrivial carriers and ultimately induce a new distinct quantum phase. Here we study the evolution of Dirac fermions, in particular the cubic Dirac crossing, under external pressure in the representative quasi-one-dimensional Tl$_2$Mo$_6$Se$_6$ via the first-principles calculations. Specifically, it is found that the topological properties, including the bulk Dirac crossings and the topological surface states, change progressively under pressure up to 50 GPa where it undergoes a structural transition from the hexagonal phase to body-centered tetragonal phase. Above 50 GPa, the system is more likely to be topologically trivial. Further, we also investigate its phonon spectra, which reveals a gradual depletion of the negative phonon modes with pressure, consistent with the more three-dimensional Fermi surface in the high-pressure phase. Our work may provide a useful guideline for further experimental search and the band engineering of the topologically nontrivial fermions in this intriguing state of matter.

cond-mat.mtrl-sci↗
arXiv2020

Orchestrating the Development Lifecycle of Machine Learning-Based IoT Applications: A Taxonomy and Survey

Machine Learning (ML) and Internet of Things (IoT) are complementary advances: ML techniques unlock complete potentials of IoT with intelligence, and IoT applications increasingly feed data collected by sensors into ML models, thereby employing results to improve their business processes and services. Hence, orchestrating ML pipelines that encompasses model training and implication involved in holistic development lifecycle of an IoT application often leads to complex system integration. This paper provides a comprehensive and systematic survey on the development lifecycle of ML-based IoT application. We outline core roadmap and taxonomy, and subsequently assess and compare existing standard techniques used in individual stage.

cs.DC↗
arXiv2018

Topological Type-II Dirac Fermions Approaching the Fermi Level in a Transition Metal Dichalcogenide NiTe2

Type-II Dirac/Weyl semimetals are characterized by strongly tilted Dirac cones such that the Dirac/Weyl node emerges at the boundary of electron and hole pockets as a new state of quantum matter, distinct from the standard Dirac/Weyl points with a point-like Fermi surface which are referred to as type-I nodes. The type-II Dirac fermions were recently predicted by theory and have since been confirmed in experiments in the PtSe2-class of transition metal dichal-cogenides. However, the Dirac nodes observed in PtSe2, PdTe2 and PtTe2 candidates are quite far away from the Fermi level, making the signature of topological fermions obscure as the physical properties are still dominated by the non-Dirac quasiparticles. Here we report the synthesis of a new type-II Dirac semimetal NiTe2 in which a pair of type-II Dirac nodes are located very close to the Fermi level. The quantum oscillations in this material reveal a nontrivial Berry's phase associated with these Dirac fermions. Our first principles calculations further unveil a topological Dirac cone in its surface states. Therefore, NiTe2 may not only represent an improved system to formulate the theoretical understanding of the exotic consequences of type-II Dirac fermions, it also facilitates possible applications based on these topological carriers.

cond-mat.str-el↗
arXiv2015

Magnetoelectricity coupled exchange bias in BaMnF$_4$

Multiferroic BaMnF$_4$ powder were prepared by hydrothermal method. Hysteretic field dependent magnetization curve at 5 K confirms the weak ferromagnetism aroused from the canted antiferromagnetic spins by magnetoelectric coupling. The blocking temperature of 65 K for exchange bias coincides well with the peak at 65 K in the zero-field cooled temperature-dependent magnetization curve, which has been assigned to the onset temperature of two-dimensional antiferromagnetism. An upturn kink of exchange field and coercivity with decreasing temperature was observed from 40 K to 20 K, which is consistent with the two-dimensional to three-dimensional antiferromagnetic transition at Néel temperature (~26 K). In contrast to the conventional mechanism of magnetization pinned by interfacial exchange coupling in multiphases, the exchange bias in BaMnF$_4$ is argued to be a bulk effect in single phase, due to the magnetization pinned by the polarization through magnetoelectric coupling.

cond-mat.mtrl-sci↗
arXiv2013

Remarks on Li-Yau inequality on graphs

In this paper, we study Li-Yau gradient estimates for the solutions $u$ to the heat equation $\partial_tu=Δu$ on graphs under the curvature condition $CD(n,-K)$ introduced by Bauer et al. in \cite{BHLLMY}. As applications, we derive Harnack inequalities and heat kernel estimates on graphs. Also we present a type of Hamilton gradient estimates.

math.DG↗
arXiv2013

Possible nodal superconducting gap in Fe$_{1+y}$(Te$_{1-x}$Se$_{x}$) single crystals from ultra-low temperature penetration depth measurements

Using a radio frequency tunnel diode oscillator technique, we measured the temperature dependence of the in-plane London penetration depth $Δλ_{ab}(T)$ in Fe$_{1+y}$(Te$_{1-x}$Se$_{x})$ single crystals, down to temperatures as low as 50 mK. A significant number of samples, with nominal Se concentration $x$=0.36, 0.40, 0.43 and 0.45 respectively, were studied and in many cases we found that $Δλ_{ab}(T)$ shows an upturn below 0.7 K, indicative of a paramagnetic type contribution. After subtracting the magnetic background, the low temperature behavior of penetration depth is best described by a power law with exponent $n\approx2$ and with no systematic dependence on the Se concentration. Most importantly, in the limit of T$\rightarrow$0, in some samples we observed a narrow region of linear temperature dependence of penetration depth, suggestive of nodes in the superconducting gap of Fe$_{1+y}$(Te$_{1-x}$Se$_{x})$.

cond-mat.supr-con↗
arXiv2013

$L^1$-Uniqueness of the Fokker-Planck equation on a Riemannian manifold

In this paper, we obtain a necessary and sufficient condition for $L^{\infty}$-uniqueness of Sturm-Liouville operator $a(x)\frac{d^2}{dx^2} + b(x) \frac d{dx} -V$ on an open interval of $\rr$, which is equivalent to the $L^1$-uniqueness of the associated Fokker-Planck equation. For a general elliptic operator $\LL^V:=Δ+b \cdot\nabla -V$ on a Riemannian manifold, we obtain sharp sufficient conditions for the $L^1$-uniqueness of the Fokker-Planck equation associated with $\LL^V$, via comparison with a one-dimensional Sturm-Liouville operator. Furthermore the $L^1$-Liouville property is derived as a direct consequence of the $L^\infty$-uniqueness of $\LL^V$.

math.CA↗
arXiv2013

Differential Harnack inequalities and Perelman type entropy formulae for subelliptic operators

In this paper, under the generalized curvature-dimension inequality recently introduced by F. Baudoin and N. Garofalo, we obtain differential Harnack inequalities for the positive solutions to the Schödinger equation associated to subelliptic operator with potential. As applications of the differential Harnack inequality, we derive the corresponding parabolic Harnack inequality. Also we define the Perelman type entropy associated to subelliptic operators and derive its monotonicity.

math.DG↗
arXiv2011

Positive curvature property for sub-Laplace on nilpotent Lie group of rank two

In this note, we concentrate on the sub-Laplace on the nilpotent Lie group of rank two, which is the infinitesimal generator of the diffusion generated by $n$ Brownian motions and their $\frac{n(n-1)}2$ Lévy area processes, which is the simple extension of the sub-Laplace on the Heisenberg group $\mathbb{H}$. In order to study contraction properties of the heat kernel, we show that, as in the cases of the Heisenberg group and the three Brownian motion model, the restriction of the sub-Laplace acting on radial functions (see Definition \ref{radial fun}) satisfies a positive Ricci curvature condition (more precisely a $CD(0, \infty)$ inequality, see Theorem \ref{positive}, whereas the operator itself does not satisfy any $CD(r,\infty)$ inequality. From this we may deduce some useful, sharp gradient bounds for the associated heat kernel. It can be seen a generalization of the paper \cite{Qian2}.

math.PR↗
arXiv2011

Asymptotic estimates on the time derivative of $Φ$-entropy on Riemannian manifolds

In this note, we obtain the asymptotic estimate for the time derivative of the $Φ$-entropy in terms of the lower bound on the Bakry-Emery $Γ_2$ curvature. In the cases of Hyperbolic space and Heisenberg group, we show that the time derivative of the $Φ$-entropy is non-increasing, and we also get sharp asymptotic bound for the time derivative of the entropy in the Heisenberg group.

math.DG↗