arXiv subjects

Xiaoyu Zhu

Publications and source records attributed to Xiaoyu Zhu.

At least 37 records · Page 2Linked to original sources

arXiv2023

Unveiling nontrivial fusion rule of Majorana zero mode using a fermionic mode

Fusing Majorana zero modes leads to multiple outcomes, a property being unique to non-Abelian anyons. Successful demonstration of this nontrivial fusion rule would be a hallmark for the development of topological quantum computation.Here we show that this can be done by simply attaching a fermionic mode to a single Majorana zero mode. Through modulation of the energy level of this fermionic mode as well as its coupling with the Majorana mode in different sequences, we show that a zero or integer charge pumping can be realized when different fusion loops are chosen. Such fusion loops are intimately related with the nontrivial fusion rule of Majorana modes and are solely determined by the crossings at zero energy in the parameter space. Finally we demonstrate our proposal in a nanowire-based topological superconductor coupled to a quantum dot. We show that the charge pumping is robust for MZMs in the real system irrespective of the initial condition of FM state, contrary to the case for trivial Andreev bound states. This provides a feasible way to distinguish Majorana modes from trivial Andreev bound states.

cond-mat.mes-hall↗

arXiv2023

Higher-order topological superconductors characterized by Fermi level crossings

We demonstrate that level crossings at the Fermi energy serve as robust indicators for higher-order topology in two-dimensional superconductors of symmetry class D. These crossings occur when the boundary condition in one direction is continuously varied from periodic to open, revealing the topological distinction between opposite edges. The associated Majorana numbers acquire nontrivial values whenever the system supports two Majorana zero modes distributed at its corners. Owing to their immunity to perturbations that break crystalline symmetries, Fermi level crossings are able to characterize a wide range of higher-order topological superconductors. By directly identifying the level-crossing points from the bulk Hamiltonian, we establish the correspondence between gapped bulk and Majorana corner states in higher-order phases. In the end, we illustrate this correspondence using two toy models. Our findings suggest that Fermi level crossings offer a possible avenue for characterizing higher-order topological superconductors in a unifying framework.

cond-mat.mes-hall↗

arXiv2023

Superfast and sub-wavelength orbital rotation of plasmonic particles in focused Gaussian beams

The use of nanophotonics for optical manipulation has continuously attracted interest in both fundamental research and practical applications, due to its significantly enhanced capabilities at the nanoscale. In this work, we showed that plasmonic particles can be trapped at off-axis location in Gaussian beams assisted by surface plasmon resonance. The off-axis displacement can be tuned at the sub-wavelength scale by the incident light beams. Based on these, we propose that a superfast orbital rotation of particles in continuous-wave laser beam can be realized in tightly focused circularly polarized Gaussian beams. The rotation has a tunable orbital radius at the sub-wavelength scale and a superfast rotation speed (more than 10^4 r/s in water under common laboratory conditions). Our work will aid in the development of optically driven nanomachines, and find applications in micro/nano-rheology, micro-fluid mechanics, and biological research at the nanoscale.

physics.optics↗

arXiv2022

Simple modules over the Takiff Lie algebra for $\mathfrak{sl}_{2}$

In this paper, we construct, investigate and, in some cases, classify several new classes of (simple) modules over the Takiff $\mathfrak{sl}_{2}$. More precisely, we first explicitly construct and classify, up to isomorphism, all modules over the Takiff $\mathfrak{sl}_{2}$ that are $U\left(\overline{\mathfrak{h}}\right)$-free of rank one. These split into three general families of modules. The sufficient and necessary conditions for simplicity of these modules are presented, and their isomorphism classes are determined. Using the vector space duality and Mathieu's twisting functors, these three classes of modules are used to construct new families of weight modules over the Takiff $\mathfrak{sl}_{2}$. We give necessary and sufficient conditions for these weight modules to be simple and, in some cases, completely determine their submodule structure.

math.RT↗

arXiv2022

Finite quotients of singular Artin monoids and categorification of the desingularization map

We study various aspects of the structure and representation theory of singular Artin monoids. This includes a number of generalizations of the desingularization map and explicit presentations for certain finite quotient monoids of diagrammatic nature. The main result is a categorification of the classical desingularization map for singular Artin monoids associated to finite Weyl groups using BGG category $\mathcal{O}$.

math.RT↗

arXiv2021

Graph Intention Network for Click-through Rate Prediction in Sponsored Search

Estimating click-through rate (CTR) accurately has an essential impact on improving user experience and revenue in sponsored search. For CTR prediction model, it is necessary to make out user real-time search intention. Most of the current work is to mine their intentions based on user real-time behaviors. However, it is difficult to capture the intention when user behaviors are sparse, causing the behavior sparsity problem. Moreover, it is difficult for user to jump out of their specific historical behaviors for possible interest exploration, namely weak generalization problem. We propose a new approach Graph Intention Network (GIN) based on co-occurrence commodity graph to mine user intention. By adopting multi-layered graph diffusion, GIN enriches user behaviors to solve the behavior sparsity problem. By introducing co-occurrence relationship of commodities to explore the potential preferences, the weak generalization problem is also alleviated. To the best of our knowledge, the GIN method is the first to introduce graph learning for user intention mining in CTR prediction and propose end-to-end joint training of graph learning and CTR prediction tasks in sponsored search. At present, GIN has achieved excellent offline results on the real-world data of the e-commerce platform outperforming existing deep learning models, and has been running stable tests online and achieved significant CTR improvements.

cs.LG↗

arXiv2021

Simple non-weight modules over Lie superalgebras of Block type

In this paper, a family of non-weight modules over Lie superalgebras $S(q)$ of Block type are studied. Free $U(η)$-modules of rank $1$ over Ramond-Block algebras and free $U(\mathfrak{h})$-modules of rank $2$ over Neveu-Schwarz-Block algebras are constructed and classified. Moreover, the sufficient and necessary conditions for such modules to be simple are presented, and their isomorphism classes are also determined. The results cover some existing results.

math.RT↗

arXiv2020

MSNet: A Multilevel Instance Segmentation Network for Natural Disaster Damage Assessment in Aerial Videos

In this paper, we study the problem of efficiently assessing building damage after natural disasters like hurricanes, floods or fires, through aerial video analysis. We make two main contributions. The first contribution is a new dataset, consisting of user-generated aerial videos from social media with annotations of instance-level building damage masks. This provides the first benchmark for quantitative evaluation of models to assess building damage using aerial videos. The second contribution is a new model, namely MSNet, which contains novel region proposal network designs and an unsupervised score refinement network for confidence score calibration in both bounding box and mask branches. We show that our model achieves state-of-the-art results compared to previous methods in our dataset. We will release our data, models and code.

cs.CV↗

arXiv2020

Feature Selection based on Principal Component Analysis for Underwater Source Localization by Deep Learning

In this paper, we propose an interpretable feature selection method based on principal component analysis (PCA) and principal component regression (PCR), which can extract important features for underwater source localization by only introducing the source location without other prior information. This feature selection method is combined with a two-step framework for underwater source localization based on the semi-supervised learning scheme. In the framework, the first step utilizes a convolutional autoencoder to extract the latent features from the whole available dataset. The second step performs source localization via an encoder multi-layer perceptron (MLP) trained on a limited labeled portion of the dataset. The proposed approach has been validated on the public dataset SwllEx-96 Event S5. The result shows the framework has appealing accuracy and robustness on the unseen data, especially when the number of data used to train gradually decreases. After feature selection, not only the training stage has a 95\% acceleration but the performance of the framework becomes more robust on the depth and more accurate when the number of labeled data used to train is extremely limited.

cs.SD↗

arXiv2019

Second-order Topological Superconductors with Mixed Pairing

We show that a two-dimensional semiconductor with Rashba spin-orbit coupling could be driven into the second-order topological superconducting phase when a mixed-pairing state is introduced. The superconducting order we consider involves only even-parity components and meanwhile breaks time-reversal symmetry. As a result, each corner of a square-shaped Rashba semiconductor would host one single Majorana zero mode in the second-order nontrivial phase. Starting from edge physics, we are able to determine the phase boundaries accurately. A simple criterion for the second-order phase is further established, which concerns the relative position between Fermi surfaces and nodal points of the superconducting order parameter. In the end, we propose two setups that may bring this mixed-pairing state into the Rashba semiconductor, followed by a brief discussion on the experimental feasibility of the two platforms.

cond-mat.mes-hall↗

arXiv2019

Conflict-free (vertex)-connection numbers of graphs with small diameters

A path in an(a) edge(vertex)-colored graph is called a conflict-free path if there exists a color used on only one of its edges(vertices). An(A) edge(vertex)-colored graph is called conflict-free (vertex-)connected if for each pair of distinct vertices, there is a conflict-free path connecting them. For a connected graph $G$, the conflict-free (vertex-)connection number of $G$, denoted by $cfc(G)(\text{or}~vcfc(G))$, is defined as the smallest number of colors that are required to make $G$ conflict-free (vertex-)connected. In this paper, we first give the exact value $cfc(T)$ for any tree $T$ with diameters $2,3$ and $4$. Based on this result, the conflict-free connection number is determined for any graph $G$ with $diam(G)\leq 4$ except for those graphs $G$ with diameter $4$ and $h(G)=2$. In this case, we give some graphs with conflict-free connection number $2$ and $3$, respectively. For the conflict-free vertex-connection number, the exact value $vcfc(G)$ is determined for any graph $G$ with $diam(G)\leq 4$.

math.CO↗

arXiv2018

EENMF: An End-to-End Neural Matching Framework for E-Commerce Sponsored Search

E-commerce sponsored search contributes an important part of revenue for the e-commerce company. In consideration of effectiveness and efficiency, a large-scale sponsored search system commonly adopts a multi-stage architecture. We name these stages as ad retrieval, ad pre-ranking and ad ranking. Ad retrieval and ad pre-ranking are collectively referred to as ad matching in this paper. We propose an end-to-end neural matching framework (EENMF) to model two tasks---vector-based ad retrieval and neural networks based ad pre-ranking. Under the deep matching framework, vector-based ad retrieval harnesses user recent behavior sequence to retrieve relevant ad candidates without the constraint of keyword bidding. Simultaneously, the deep model is employed to perform the global pre-ranking of ad candidates from multiple retrieval paths effectively and efficiently. Besides, the proposed model tries to optimize the pointwise cross-entropy loss which is consistent with the objective of predict models in the ranking stage. We conduct extensive evaluation to validate the performance of the proposed framework. In the real traffic of a large-scale e-commerce sponsored search, the proposed approach significantly outperforms the baseline.

cs.IR↗

arXiv2018

Conflict-free connections: algorithm and complexity

A path in an(a) edge(vertex)-colored graph is called \emph{a conflict-free path} if there exists a color used on only one of its edges(vertices). An(A) edge(vertex)-colored graph is called \emph{conflict-free (vertex-)connected} if there is a conflict-free path between each pair of distinct vertices. We call the graph $G$ \emph{strongly conflict-free connected }if there exists a conflict-free path of length $d_G(u,v)$ for every two vertices $u,v\in V(G)$. And the \emph{strong conflict-free connection number} of a connected graph $G$, denoted by $scfc(G)$, is defined as the smallest number of colors that are required to make $G$ strongly conflict-free connected. In this paper, we first investigate the question: Given a connected graph $G$ and a coloring $c: E(or\ V)\rightarrow \{1,2,\cdots,k\} \ (k\geq 1)$ of the graph, determine whether or not $G$ is, respectively, conflict-free connected, vertex-conflict-free connected, strongly conflict-free connected under coloring $c$. We solve this question by providing polynomial-time algorithms. We then show that it is NP-complete to decide whether there is a k-edge-coloring $(k\geq 2)$ of $G$ such that all pairs $(u,v)\in P \ (P\subset V\times V)$ are strongly conflict-free connected. Finally, we prove that the problem of deciding whether $scfc(G)\leq k$ $(k\geq 2)$ for a given graph $G$ is NP-complete.

math.CO↗

arXiv2018

Tunable Majorana corner states in a two-dimensional second-order topological superconductor induced by magnetic fields

A two-dimensional second-order topological superconductor exhibits a finite gap in both bulk and edges, with the nontrivial topology manifesting itself through Majorana zero modes localized at the corners, i.e., Majorana corner states. We investigate a time-reversal-invariant topological superconductor in two dimension and demonstrate that an in-plane magnetic field could transform it into a second-order topological superconductor. A detailed analysis reveals that the magnetic field gives rise to mass terms which take distinct values among the edges, and Majorana corner states naturally emerge at the intersection of two adjacent edges with opposite masses. With the rotation of the magnetic field, Majorana corner states localized around the boundary may hop from one corner to a neighboring one and eventually make a full circle around the system when the field rotates by $2π$. In the end we briefly discuss physical realizations of this system.

cond-mat.mes-hall↗

arXiv2017

Conflict-free vertex-connections of graphs

A path in a vertex-colored graph is called \emph{conflict free} if there is a color used on exactly one of its vertices. A vertex-colored graph is said to be \emph{conflict-free vertex-connected} if any two vertices of the graph are connected by a conflict-free path. This paper investigates the question: For a connected graph $G$, what is the smallest number of colors needed in a vertex-coloring of $G$ in order to make $G$ conflict-free vertex-connected. As a result, we get that the answer is easy for $2$-connected graphs, and very difficult for connected graphs with more cut-vertices, including trees.

math.CO↗

arXiv2017

Proper vertex connection and graph operations

A path in a vertex-colored graph is a {\it vertex-proper path} if any two internal adjacent vertices differ in color. A vertex-colored graph is {\it proper vertex $k$-connected} if any two vertices of the graph are connected by $k$ disjoint vertex-proper paths of the graph. For a $k$-connected graph $G$, the {\it proper vertex $k$-connection number} of $G$, denoted by $pvc_{k}(G)$, is defined as the smallest number of colors required to make $G$ proper vertex $k$-connected. A vertex-colored graph is {\it strong proper vertex-connected}, if for any two vertices $u,v$ of the graph, there exists a vertex-proper $u$-$v$ geodesic. For a connected graph $G$, the {\it strong proper vertex-connection number} of $G$, denoted by $spvc(G)$, is the smallest number of colors required to make $G$ strong proper vertex-connected. In this paper, we study the proper vertex $k$-connection number and the strong proper vertex-connection number on the join of two graphs, the Cartesian, lexicographic, strong and direct product, and present exact values or upper bounds for these operations of graphs.

math.CO↗

arXiv2017

Total proper connection and graph operations

A graph is said to be {\it total-colored} if all the edges and vertices of the graph are colored. A path in a total-colored graph is a {\it total proper path} if $(i)$ any two adjacent edges on the path differ in color, $(ii)$ any two internal adjacent vertices on the path differ in color, and $(iii)$ any internal vertex of the path differs in color from its incident edges on the path. A total-colored graph is called {\it total-proper connected} if any two vertices of the graph are connected by a total proper path of the graph. For a connected graph $G$, the {\it total proper connection number} of $G$, denoted by $tpc(G)$, is defined as the smallest number of colors required to make $G$ total-proper connected. In this paper, we study the total proper connection number for the graph operations. We find that $3$ is the total proper connection number for the join, the lexicographic product and the strong product of nearly all graphs. Besides, we study three kinds of graphs with one factor to be traceable for the Cartesian product as well as the permutation graphs of the star and traceable graphs. The values of the total proper connection number for these graphs are all $3$.

math.CO↗

arXiv2016

Solutions for two conjectures on kaleidoscopic edge-colorings

For an $r$-regular graph $G$, we define an edge-coloring $c$ with colors from $\{1,2,\cdots,$ $k\}$, in such a way that any vertex of $G$ is incident to at least one edge of each color. The multiset-color $c_m(v)$ of a vertex $v$ is defined as the ordered tuple $(a_1,a_2,\cdots ,a_k)$, where $a_i \ (1\leq i\leq k)$ denotes the number of edges with color $i$ which are incident with $v$ in $G$. Then this edge-coloring $c$ is called a {\it $k$-kaleidoscopic coloring} of $G$ if every two distinct vertices in $G$ have different multiset-colors and in this way the graph $G$ is defined as a {\it $k$-kaleidoscope}. In this paper, we determine the integer $k$ for a complete graph $K_n$ to be a $k$-kaleidoscope, and hence solve a conjecture in [P. Zhang, A Kaleidoscopic View of Graph Colorings, Springer, New York, 2016] that for any integers $n$ and $k$ with $n\geq k+3 \geq 6$, the complete graph $K_n$ is a $k$-kaleidoscope. Then, we construct an $r$-regular $3$-kaleidoscope of order $\binom{r-1}{2}-1$ for each integer $r\geq 7$, where $r\equiv 3\ (\text{mod}\ 4)$, which solves another conjecture in the same book on the maximum order for $r$-regular $3$-kaleidoscopes.

math.CO↗