arXiv subjects
Publications and source records attributed to Yu Ye.
We study various invariants, such as cohomology groups, derivations, automorphisms and infinitesimal deformations, of algebraic operads and show that $\mathcal{A}ss$, $\mathcal{C}com$, $\mathcal{L}ie$ and $\mathcal{P}ois$ are rigid or semirigid.
Contact interface properties are important in determining the performances of devices based on atomically thin two-dimensional (2D) materials, especially those with short channels. Understanding the contact interface is therefore quite important to design better devices. Herein, we use scanning transmission electron microscopy, electron energy loss spectroscopy, and first-principles calculations to reveal the electronic structures within the metallic (1T')-semiconducting (2H) MoTe2 coplanar phase boundary across a wide spectral range and correlate its properties and atomic structure. We find that the 2H-MoTe2 excitonic peaks cross the phase boundary into the 1T' phase within a range of approximately 150 nm. The 1T'-MoTe2 crystal field can penetrate the boundary and extend into the 2H phase by approximately two unit cells. The plasmonic oscillations exhibit strong angle dependence, i.e., a red-shift (approximately 0.3 eV-1.2 eV) occurs within 4 nm at 1T'/2H-MoTe2 boundaries with large tilt angles, but there is no shift at zero-tilted boundaries. These atomic-scale measurements reveal the structure-property relationships of 1T'/2H-MoTe2 boundary, providing useful information for phase boundary engineering and device development based on 2D materials.
The alternating direction method of multipliers (ADMM) has recently been recognized as a promising approach for large-scale machine learning models. However, very few results study ADMM from the aspect of communication costs, especially jointly with running time. In this letter, we investigate the communication efficiency and running time of ADMM in solving the consensus optimization problem over decentralized networks. We first review the effort of random walk ADMM (W-ADMM), which reduces communication costs at the expense of running time. To accelerate the convergence speed of W-ADMM, we propose the parallel random walk ADMM (PW-ADMM) algorithm, where multiple random walks are active at the same time. Moreover, to further reduce the running time of PW-ADMM, the intelligent parallel random walk ADMM (IPW-ADMM) algorithm is proposed through integrating the \textit{Random Walk with Choice} with PW-ADMM. By numerical results from simulations, we demonstrate that the proposed algorithms can be both communication efficient and fast in running speed compared with state-of-the-art methods.
Quantum interference gives rise to the asymmetric Fano resonance line shape when the final states of an electronic transition follows within a continuum of states and a discrete state, which has significant applications in optical switching and sensing. The resonant optical phenomena associated with Fano resonance have been observed by absorption spectra, Raman spectra, transmission spectra, etc., but have rarely been reported in photoluminescence (PL) spectroscopy. In this work, we performed spectroscopic studies on layered chromium thiophosphate (CrPS4), a promising ternary antiferromagnetic semiconductor with PL in near-infrared wavelength region and observed Fano resonance when CrPS4 experiences phase transition into the antiferromagnetic state below Néel temperature (38 K). The photoluminescence of the continuum states results from the d band transitions localized at Cr3+ ions, while the discrete state reaches saturation at high excitation power and can be enhanced by the external magnetic field, suggesting it is formed by an impurity level from extra atomic phosphorus. Our findings provide insights into the electronic transitions of CrPS4 and their connection to its intrinsic magnetic properties.
Due to the drastic increase of mobile traffic, wireless caching is proposed to serve repeated requests for content download. To determine the caching scheme for decentralized caching networks, the content preference learning problem based on mobility prediction is studied. We first formulate preference prediction as a decentralized regularized multi-task learning (DRMTL) problem without considering the mobility of mobile terminals (MTs). The problem is solved by a hybrid Jacobian and Gauss-Seidel proximal multi-block alternating direction method (ADMM) based algorithm, which is proven to conditionally converge to the optimal solution with a rate $O(1/k)$. Then we use the tool of \textit{Markov renewal process} to predict the moving path and sojourn time for MTs, and integrate the mobility pattern with the DRMTL model by reweighting the training samples and introducing a transfer penalty in the objective. We solve the problem and prove that the developed algorithm has the same convergence property but with different conditions. Through simulation we show the convergence analysis on proposed algorithms. Our real trace driven experiments illustrate that the mobility-aware DRMTL model can provide a more accurate prediction on geography preference than DRMTL model. Besides, the hit ratio achieved by most popular proactive caching (MPC) policy with preference predicted by mobility-aware DRMTL outperforms the MPC with preference from DRMTL and random caching (RC) schemes.
Privacy concerns with sensitive data are receiving increasing attention. In this paper, we study local differential privacy (LDP) in interactive decentralized optimization. By constructing random local aggregators, we propose a framework to amplify LDP by a constant. We take Alternating Direction Method of Multipliers (ADMM), and decentralized gradient descent as two concrete examples, where experiments support our theory. In an asymptotic view, we address the following question: Under LDP, is it possible to design a distributed private minimizer for arbitrary closed convex constraints with utility loss not explicitly dependent on dimensionality? As an affiliated result, we also show that with merely linear secret sharing, information theoretic privacy is achievable for bounded colluding agents.
In multi-task learning (MTL), related tasks learn jointly to improve generalization performance. To exploit the high learning speed of extreme learning machines (ELMs), we apply the ELM framework to the MTL problem, where the output weights of ELMs for all the tasks are learned collaboratively. We first present the ELM based MTL problem in the centralized setting, which is solved by the proposed MTL-ELM algorithm. Due to the fact that many data sets of different tasks are geo-distributed, decentralized machine learning is studied. We formulate the decentralized MTL problem based on ELM as majorized multi-block optimization with coupled bi-convex objective functions. To solve the problem, we propose the DMTL-ELM algorithm, which is a hybrid Jacobian and Gauss-Seidel Proximal multi-block alternating direction method of multipliers (ADMM). Further, to reduce the computation load of DMTL-ELM, DMTL-ELM with first-order approximation (FO-DMTL-ELM) is presented. Theoretical analysis shows that the convergence to the stationary point of DMTL-ELM and FO-DMTL-ELM can be guaranteed conditionally. Through simulations, we demonstrate the convergence of proposed MTL-ELM, DMTL-ELM, and FO-DMTL-ELM algorithms, and also show that they can outperform existing MTL methods. Moreover, by adjusting the dimension of hidden feature space, there exists a trade-off between communication load and learning accuracy for DMTL-ELM.
Two-dimensional (2D) layered semiconductors, with their ultimate atomic thickness, have shown promise to scale down transistors for modern integrated circuitry. However, the electrical contacts that connect these materials with external bulky metals are usually unsatisfactory, which limits the transistor performance. Recently, contacting 2D semiconductors using coplanar 2D conductors has shown promise in reducing the problematic high resistance contacts. However, many of these methods are not ideal for scaled production. Here, we report on the large-scale, spatially controlled chemical assembly of the integrated 2H-MoTe2 field-effect transistors (FETs) with coplanar metallic 1T' MoTe2 contacts via phase engineered approaches. We demonstrate that the heterophase FETs exhibit ohmic contact behavior with low contact resistance, resulting from the coplanar seamless contact between 2H and 1T' MoTe2 confirmed by transmission electron microscopy characterizations. The average mobility of the heterophase FETs was measured to be as high as 23 cm2 V-1 s-1 (comparable with those of exfoliated single crystals), due to the large 2H MoTe2 single-crystalline domain (486μm). By developing a patterned growth method, we realize the 1T' MoTe2 gated heterophase FET array whose components of channel, gate, and contacts are all 2D materials. Finally, we transfer the heterophase device array onto a flexible substrate and demonstrate the near-infrared photoresponse with high photoresponsivity (~1.02 A/W). Our study provides a basis for the large-scale application of phase-engineered coplanar MoTe2 semiconductors-meter structure in advanced electronics and optoelectronics.
Multiferroic materials are potential to be applied in novel magnetoelectric devices, for example, high-density non-volatile storage. Last decades, research on multiferroic materials was focused on three-dimensional (3D) materials. However, 3D materials suffer from the dangling bonds and quantum tunneling in the nano-scale thin films. Two-dimensional (2D) materials might provide an elegant solution to these problems, and thus are highly on demand. Using first-principles calculations, we predict ferromagnetism and driven ferroelectricity in the monolayer and even a few-layers of CuCrP2S6. Although the total energy of the ferroelectric phase of monolayer is higher than that of the antiferroelectric phase, the ferroelectric phases can be realized by applying a large electric field. Besides the degrees of freedoms in the common multiferroic materials, the valley degree of freedom is also polarized according to our calculations. The spins, electric dipoles and valleys are coupled with each other as shown in the computational results. In experiment, we observe the out-of-plane ferroelectricity in a few-layer CuCrP2S6 (approximately 13 nm thick) at room temperature. 2D ferromagnetism of few-layers is inferred from magnetic hysteresis loops of the massively stacked nanosheets at 10 K. The experimental observations support our calculation very well. Our findings may provide a series of 2D materials for further device applications.
In crystals, the duplication of atoms often follows different periodicity along different directions. It thus gives rise to the so called anisotropy, which is usually even more pronounced in two dimensional (2D) materials due to the absence of $\textbf{z}$ dimension. Indeed, in the emerging 2D materials, electrical anisotropy has been one of the focuses in recent experimental efforts. However, key understandings of the in-plane anisotropic resistance in low-symmetry 2D materials, as well as demonstrations of model devices taking advantage of it, have proven difficult. Here, we show that, in few-layered semiconducting GaTe, electrical conductivity along $\textbf{x}$ and $\textbf{y}$ directions of the 2D crystal can be gate tuned from a ratio of less than one order to as large as 10$^{3}$. This effect is further demonstrated to yield an anisotropic memory resistor behaviour in ultra-thin GaTe, when equipped with an architecture of van der Waals floating gate. Our findings of gate tunable giant anisotropic resistance (GAR) effect pave the way for potential applications in nano-electronics such as multifunctional directional memories in the 2D limit.
We give a combinatorial characterization of upward planar graphs in terms of upward planar orders, which are special linear extensions of edge posets.
We introduce truncation ideals of a $\Bbbk$-linear unitary symmetric operad and use them to study ideal structure, growth property and to classify operads of low Gelfand-Kirillov dimension.
Around the year 1988, Joyal and Street established a graphical calculus for monoidal categories, which provides a firm foundation for many explorations of graphical notations in mathematics and physics. For a deeper understanding of their work, we consider a similar graphical calculus for semi-groupal categories. We introduce two frameworks to formalize this graphical calculus, a topological one based on the notion of a processive plane graph and a combinatorial one based on the notion of a planarly ordered processive graph, which serves as a combinatorial counterpart of a deformation class of processive plane graphs. We demonstrate the equivalence of Joyal and Street's graphical calculus and the theory of upward planar drawings. We introduce the category of semi-tensor schemes, and give a construction of a free monoidal category on a semi-tensor scheme. We deduce the unit convention as a kind of quotient construction, and show an idea to generalize the unit convention. Finally, we clarify the relation of the unit convention and Joyal and Street's construction of a free monoidal category on a tensor scheme.
Van der Waals (vdW) heterostructures constructed with two-dimensional (2D) materials have attracted great interests, due to their fascinating properties and potential for novel applications. While earlier efforts have advanced the understanding of the ultrafast cross-layer charge transfer process in 2D heterostructures, mechanisms for the interfacial photocarrier recombination remain, to a large extent, unclear. Here, we investigate a heterostructure comprised of black phosphorus (BP) and molybdenum disulfide (MoS2), with a type-II band alignment. Interestingly, it is found that the photo-generated electrons in MoS2 (transferred from BP) exhibit an ultrafast lifetime of about 5 ps, significantly shorter than those of the constituent materials. By corroborating with the relaxation of photo-excited holes in BP, it is revealed that the ultrafast time constant is as a result of efficient Langevin recombination, where the high hole mobility of BP facilitates a large recombination coefficient (approximately 2x10^-10 m^2/s). In addition, broadband transient absorption spectroscopy confirms that the hot electrons transferred to MoS2 distribute over a broad energy range following an ultrafast thermalization. The rate of the interlayer Langevin recombination is found to exhibit no energy level dependence. Our findings provide essential insights into the fundamental photo-physics in type-II 2D heterostructures, and also provide useful guidelines for customizing photocarrier lifetimes of BP for high-speed photo-sensitive devices.
We introduce for any Poisson algebra a bicomplex of free Poisson modules, and use it to show that the Poisson cohomology theory introduced in the paper "[M. Flato, M. Gerstenhaber and A. A. Voronov, Cohomology and Deformation of Leibniz Pairs, Lett. Math. Phys. 34 (1995) 77--90]" is given by certain derived functor. Moreover, by constructing a long exact sequence connecting Poisson cohomology groups and Yoneda-extension groups of certain quasi-Poisson modules, we provide a way to compute this Poisson cohomology via the Lie algebra cohomology and the Hochschild cohomology.
We provide explicit and unified formulas for the cocycles of all degrees on the normalized bar resolutions of finite abelian groups. This is achieved by constructing a chain map from the normalized bar resolution to a Koszul-like resolution for any given finite abelian group. With a help of the obtained cocycle formulas, we determine all the braided linear Gr-categories and compute the Dijkgraaf-Witten Invariants of the $n$-torus for all $n$.
We introduce the notions of a $\mathbf{D}$-standard abelian category and a $\mathbf{K}$-standard additive category. We prove that for a finite dimensional algebra $A$, its module category is $\mathbf{D}$-standard if and only if any derived autoequivalence on $A$ is standard, that is, given by a two-sided tilting complex. We prove that if the subcategory of projective $A$-modules is $\mathbf{K}$-standard, then the module category is $\mathbf{D}$-standard. We provide new examples of $\mathbf{D}$-standard module categories.
Chinese Remainder Theorem (CRT) has been widely studied with its applications in frequency estimation, phase unwrapping, coding theory and distributed data storage. Since traditional CRT is greatly sensitive to the errors in residues due to noises, the problem of robustly reconstructing integers via the erroneous residues has been intensively studied in the literature. In order to robustly reconstruct integers, there are two kinds of traditional methods: the one is to introduce common divisors in the moduli and the other is to directly decrease the dynamic range. In this paper, we take further insight into the geometry property of the linear space associated with CRT. Echoing both ways to introduce redundancy, we propose a pseudo metric to analyze the trade-off between the error bound and the dynamic range for robust CRT in general. Furthermore, we present the first robust CRT for multiple numbers to solve the problem of the CRT-based undersampling frequency estimation in general cases. Based on symmetric polynomials, we proved that in most cases, the problem can be solved in polynomial time efficiently. The work in this paper is towards a complete theoretical solution to the open problem over 20 years.