arXiv subjects
Publications and source records attributed to Min Huang.
Using the Markov distance and Ptolemy inequality introduced by Lee-Li-Rabideau-Schiffler \cite{LLRS}, we completely determine the monotonicity of the generalized Markov numbers along the lines of a given slope.
Inverse design of nanoparticles for desired scattering spectra and dynamic switching between the two opposite scattering anomalies, i.e. superscattering and invisibility, is important in realizing cloaking, sensing and functional devices. However, traditionally the design process is quite complicated, which involves complex structures with many choices of synthetic constituents and dispersions. Here, we demonstrate that a well-trained deep-learning neural network can handle these issues efficiently, which can not only forwardly predict scattering spectra of multilayer nanoparticles with high precision, but also inversely design the required structural and material parameters efficiently. Moreover, we show that the neural network is capable of finding out multi-wavelength invisibility-to-superscattering switching points at the desired wavelengths in multilayer nanoparticles composed of metals and phase-change materials. Our work provides a useful solution of deep learning for inverse design of nanoparticles with dynamic scattering spectra by using phase-change materials.
Daytime radiative cooling has attracted considerable attention recently due to its tremendous potential for passively exploiting the coldness of deep-sky as clean and renewable energy. Many advanced materials with novel photonic micro-nanostructures have already been developed to enable highly efficient daytime radiative coolers, among which the flexible hierarchical porous coatings (HPCs) are a more distinguished category. However, it is still hard to precisely control the size distribution of the randomized pores within the HPCs, usually resulting in a deficient solar reflection at the near-infrared optical regime under diverse fabrication conditions of the coatings. We report here a three-phase (i.e., air pore-phase, microsphere-phase and polymer-phase) self-assembled hybrid porous composite coating which dramatically increases the average solar reflectance and yields a remarkable temperature drop of ~10 degC and 30 degC compared to the ambient circumstance and black paint, respectively, according to the rooftop measurements. Mie theory and Monte Carlo simulations reveal the origin of the low reflectivity of as-prepared two-phase porous HPCs, and the optical cooling improvement of the three-phase porous composite coatings is attributed to the newly generated interfaces possessing the high scattering efficiency between the hierarchical pores and silica microspheres hybridized with appropriate mass fractions. As a result, the hybrid porous composite approach enhances the whole performance of the coatings, which provides a promising alternative to the flexible daytime radiative cooler.
A bias-free source-independent quantum random number generator scheme based on the measurement of vacuum fluctuation is proposed to realize the effective elimination of system bias and common mode noise introduced by the local oscillator. Optimal parameter settings are derived to avoid the system recording two canonically conjugate quadratures simultaneously in each measurement. In particular, it provides a new approach to investigate the performance difference between measuring two quadratures of equal and unequal intensity. It is experimentally demonstrated that the system supports 4.2 Gbps bias-free source-independent random number generation, where its common mode rejection ratio reaches 61.17 dB. Furthermore, the scheme offers an all-optical method facilitating the integration of source-independent quantum random number generators into compact chips.
Nowadays, collaborative filtering recommender systems have been widely deployed in many commercial companies to make profit. Neighbourhood-based collaborative filtering is common and effective. To date, despite its effectiveness, there has been little effort to explore their robustness and the impact of data poisoning attacks on their performance. Can the neighbourhood-based recommender systems be easily fooled? To this end, we shed light on the robustness of neighbourhood-based recommender systems and propose a novel data poisoning attack framework encoding the purpose of attack and constraint against them. We firstly illustrate how to calculate the optimal data poisoning attack, namely UNAttack. We inject a few well-designed fake users into the recommender systems such that target items will be recommended to as many normal users as possible. Extensive experiments are conducted on three real-world datasets to validate the effectiveness and the transferability of our proposed method. Besides, some interesting phenomenons can be found. For example, 1) neighbourhood-based recommender systems with Euclidean Distance-based similarity have strong robustness. 2) the fake users can be transferred to attack the state-of-the-art collaborative filtering recommender systems such as Neural Collaborative Filtering and Bayesian Personalized Ranking Matrix Factorization.
We are concerned with relating derived categories of all modules of two dual Koszul algebras defined by a locally bounded quiver. We first generalize the well known Acyclic Assembly Lemma and formalize an old method of extending a functor from an additive category into a complex category to its complex category. Applying this to the Koszul functor associated with a Koszul algebra defined by a gradable quiver, we obtain a Koszul complex functor, that descends to an equivalence of a continuous family of pairs of triangulated subcategories of doubly unbounded complexes of the respective derived categories of all modules of the Koszul algebra and its Koszul dual. Under this special setting, this extends Beilinson, Ginzburg and Soegel's Koszul duality. In case the Koszul algebra is right or left locally bounded and its Koszul dual is left or right locally bounded respectively (for instance, the quiver has no right infinite path or no left infinite path), our Koszul duality restricts to an equivalence of the bounded derived categories of finitely supported modules, and an equivalence of the bounded derived categories of finite dimensional modules.
We present a simple, fast, and accurate method for pricing a variety of discretely monitored options in the Black-Scholes framework, including autocallable structured products, single and double barrier options, and Bermudan options. The method is based on a quadrature technique, and it employs only elementary calculations and a fixed one-dimensional uniform grid. The convergence rate is $O(1/N^4)$ and the complexity is $O(MN\log N)$, where $N$ is the number of grid points and $M$ is the number of observation dates.
We study quantum cluster algebras from unpunctured surfaces with arbitrary coefficients and quantization. We first give a new proof of the Laurent expansion formulas for commutative cluster algebras from unpunctured surfaces, we then give the quantum Laurent expansion formulas for the quantum cluster algebras. Particularly, this gives a combinatorial proof of the positivity for such class of quantum cluster algebras.
A wavelength-degenerate pump-probe spectroscopy is used to study the ultrafast dynamics of strong-field ionization in femtosecond-laser subwavelength-structured fused silica. The comparative spectra demonstrate that femtosecond-laser subwavelength structuring always give rise to great enhancement for strong-field ionization as well as third-order nonlinear optical effects, which is the direct evidence of great local field enhancement in subwavelength apertures of fs-laser highly-excited surface. In short, the study shows the prominent subwavelength spatial effect of strong-field ionization in femtosecond-laser ablation of dielectrics, which greatly contributes to the well-known "incubation effect".
For fused silica irradiated by near-100-fs, 795-nm laser pulses with fluence approaching the damage threshold, the transient transmission spectroscopy based on a wavelength-degenerate pump-probe technique clearly presents two dynamic processes corresponding to the instantaneous effects of laser optical field and the delayed effects of free electron dynamics, respectively. The reversible, instantaneous process originates in third-order nonlinear optical responses (in particular the optical Kerr effect) ascribed to virtual optical-field ionization (VOFI) that significantly contributes to the nonlinear optical polarization with energy exchange recoverability. Whereas, the irreversible, delayed process originates in the effects of free electron plasma generated by initial real optical-field ionization (ROFI) and subsequent impact ionization (II), being responsible for the energy dissipation and optical breakdown. In general, the femtosecond wavelength-degenerate pump-probe spectroscopy can detect VOFI, ROFI, and II simultaneously in strong-field nonlinear polarization and ionization of fused silica, and offer flexible ways to distinguish the different mechanisms. For the near-100-fs pulses, our results confirm that II provided with a typical delay time about 300 fs is responsible for the optical breakdown of fused silica.
We give the quantum Laurent expansion formula for the quantum cluster algebras from unpunctured orbifolds with arbitrary coefficients and quantization. As an application, positivity for such class of quantum cluster algebras is given. For technical reasons, it will always be assumed that the weights of the orbifold points are 2.
For a skew-symmetrizable cluster algebra $\mathcal A_{t_0}$ with principal coefficients at $t_0$, we prove that each seed $Σ_t$ of $\mathcal A_{t_0}$ is uniquely determined by its {\bf C-matrix}, which was proposed by Fomin and Zelevinsky in \cite{FZ3} as a conjecture. Our proof is based on the fact that the positivity of cluster variables and sign-coherence of $c$-vectors hold for $\mathcal A_{t_0}$, which was actually verified in \cite{GHKK}. More discussion is given in the sign-skew-symmetric case so as to obtain a conclusion as weak version of the conjecture in this general case.
Using the unfolding method given in \cite{HL}, we prove the conjectures on sign-coherence and a recurrence formula respectively of ${\bf g}$-vectors for acyclic sign-skew-symmetric cluster algebras. As a following consequence, the conjecture is affirmed in the same case which states that the ${\bf g}$-vectors of any cluster form a basis of $\mathbb Z^n$. Also, the additive categorification of an acyclic sign-skew-symmetric cluster algebra $\mathcal A(Σ)$ is given, which is realized as $(\mathcal C^{\widetilde Q},Γ)$ for a Frobenius $2$-Calabi-Yau category $\mathcal C^{\widetilde Q}$ constructed from an unfolding $(Q,Γ)$ of the acyclic exchange matrix $B$ of $\mathcal A(Σ)$.
In this paper, we build the unfolding approach from acyclic sign-skew-symmetric matrices of finite rank to skew-symmetric matrices of infinite rank, which can be regard as an improvement of that in the skew-symmetrizable case. Using this approach, we give a positive answer to the problem by Berenstein, Fomin and Zelevinsky in \cite{fz3} which asks whether an acyclic sign-skew-symmetric matrix is always totally sign-skew-symmetric. As applications, the positivity for cluster algebras in acyclic sign-skew-symmetric case is given; further, the $F$-polynomials of cluster algebras are proved to have constant term 1 in acyclic sign-skew-symmetric case.
Our motivation is to build a systematic method in order to investigate the structure of cluster algebras of geometric type. The method is given through the notion of mixing-type sub-seeds, the theory of seed homomorphisms and the view-point of gluing of seeds. As an application, for (rooted) cluster algebras, we completely classify rooted cluster subalgebras and characterize rooted cluster quotient algebras in detail. Also, we build the relationship between the categorification of a rooted cluster algebra and that of its rooted cluster subalgebras. Note that cluster algebras of geometric type studied here are of the sign-skew-symmetric case.
Following our previous work [18], we introduce the notions of partial seed homomorphisms and partial ideal rooted cluster morphisms. Related to the theory of Green's equivalences, the isomorphism classes of sub-rooted cluster algebras of a rooted cluster algebra are corresponded one-by-one to the regular $\mathcal D$-classes of the semigroup consisting of partial seed endomorphisms of the initial seed. Moreover, for a rooted cluster algebra from a Riemannian surface, they are also corresponded to the isomorphism classes of the so-called paunched surfaces.
We introduce a new rigorous method, based on Borel summability and asymptotic constants of motion generalizing \cite{invent} and \cite{ode1}, to analyze singular behavior of nonlinear ODEs in a neighborhood of infinity and provide global information about their solutions. In equations with the Painlevé-Kowalevski (P-K) property (stating that movable singularities are not branched) it allows for solving connection problems. The analysis in carried in detail for P$_1$, $y"=6y^2+z$, for which we find the Stokes multipliers in closed form and global asymptotics for solutions having power-like behavior in some direction in $\CC$, in particular for the tritronquées. Calculating the Stokes multipliers solely relies on the P-K property and does not use linearization techniques such as Riemann-Hilbert or isomonodromic reformulations. We discuss how the approach would work to calculate connection constants for a larger class of P-K integrable equations. We develop methods for finding asymptotic expansions in sectors where solutions have infinitely many singularities. These techniques do not rely on integrability and apply to more general second order ODEs which, after normalization, are asymptotically close to autonomous Hamiltonian systems.
Beam-line equipment was upgraded for experiment E08-027 (g2p) in Hall A at Jefferson Lab. Two beam position monitors (BPMs) were necessary to measure the beam position and angle at the target. A new BPM receiver was designed and built to handle the low beam currents (50-100 nA) used for this experiment. Two new super-harps were installed for calibrating the BPMs. In addition to the existing fast raster system, a slow raster system was installed. Before and during the experiment, these new devices were tested and debugged, and their performance was also evaluated. In order to achieve the required accuracy (1-2 mm in position and 1-2 mrad in angle at the target location), the data of the BPMs and harps were carefully analyzed, as well as reconstructing the beam position and angle event by event at the target location. The calculated beam position will be used in the data analysis to accurately determine the kinematics for each event.