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Li Wu

Publications and source records attributed to Li Wu.

At least 37 records · Page 2Linked to original sources

Failure Identification from Unstable Log Data using Deep Learning

The reliability of cloud platforms is of significant relevance because society increasingly relies on complex software systems running on the cloud. To improve it, cloud providers are automating various maintenance tasks, with failure identification frequently being considered. The precondition for automation is the availability of observability tools, with system logs commonly being used. The focus of this paper is log-based failure identification. This problem is challenging because of the instability of the log data and the incompleteness of the explicit logging failure coverage within the code. To address the two challenges, we present CLog as a method for failure identification. The key idea presented herein based is on our observation that by representing the log data as sequences of subprocesses instead of sequences of log events, the effect of the unstable log data is reduced. CLog introduces a novel subprocess extraction method that uses context-aware neural network and clustering methods to extract meaningful subprocesses. The direct modeling of log event contexts allows the identification of failures with respect to the abrupt context changes, addressing the challenge of insufficient logging failure coverage. Our experimental results demonstrate that the learned subprocesses representations reduce the instability in the input, allowing CLog to outperform the baselines on the failure identification subproblems - 1) failure detection by 9-24% on F1 score and 2) failure type identification by 7% on the macro averaged F1 score. Further analysis shows the existent negative correlation between the instability in the input event sequences and the detection performance in a model-agnostic manner.

cs.SE↗

Linear instability of periodic orbits of free period Lagrangian systems

In this paper we provide a sufficient condition for the linear instability of a periodic orbit for a free period Lagrangian system on a Riemannian manifold. The main result establish a general criterion for the linear instability of a maybe degenerate) periodic orbit admitting a orbit cylinder in terms to the parity of a suitable spectral index encoding the functional and symplectic property of the problem.

math.DS↗

Spectral stability, spectral flow and circular relative equilibria for the Newtonian $n$-body problem

For the Newtonian (gravitational) $n$-body problem in the Euclidean $d$-dimensional space, $d\ge 2$, the simplest possible periodic solutions are provided by circular relative equilibria, (RE) for short, namely solutions in which each body rigidly rotates about the center of mass and the configuration of the whole system is constant in time and central (or, more generally, balanced) configuration. For $d\le 3$, the only possible (RE) are planar, but in dimension four it is possible to get truly four dimensional (RE). A classical problem in celestial mechanics aims at relating the (in-)stability properties of a (RE) to the index properties of the central (or, more generally, balanced) configuration generating it. In this paper, we provide sufficient conditions that imply the spectral instability of planar and non-planar (RE) in $\mathbb R^4$ generated by a central configuration, thus answering some of the questions raised in \cite[Page 63]{Moe14}. As a corollary, we retrieve a classical result of Hu and Sun \cite{HS09} on the linear instability of planar (RE) whose generating central configuration is non-degenerate and has odd Morse index, and fix a gap in the statement of \cite[Theorem 1]{BJP14} about the spectral instability of planar (RE) whose (possibly degenerate) generating central configuration has odd Morse index. The key ingredients are a new formula of independent interest that allows to compute the spectral flow of a path of symmetric matrices having degenerate starting point, and a symplectic decomposition of the phase space of the linearized Hamiltonian system along a given (RE) which is inspired by Meyer and Schmidt's planar decomposition \cite{MS05} and which allows us to rule out the uninteresting part of the dynamics corresponding to the translational and (partially) to the rotational symmetry of the problem.

math.DS↗

Mean index for non-periodic orbits in Hamiltonian systems

In this paper, we define mean index for non-periodic orbits in Hamiltonian systems and study its properties. In general, the mean index is an interval in R which is uniformly continuous on the systems. We show that the index interval is a point for a quasi-periodic orbit. The mean index can be considered as a generalization of rotation number which defined by Johnson and Moser in the study of almost periodic Schrodinger operators. Motivated by their works, we study the relation of Fredholm property of the linear operator and the mean index at the end of the paper.

math.DS↗

Weil-Petersson Teichmüller space III: dependence of Riemann mappings for Weil-Petersson curves

The primary purpose of the paper is to study how a Riemann mapping depends on the corresponding Jordan curve. We are mainly concerned with those Jordan curves in the Weil-Petersson class, namely, the corresponding Riemann mappings can be quasiconformally extended to the whole plane with Beltrami coefficients being square integrable under the Poincaré metric. We endow the space of all normalized Weil-Petersson curves with a new real Hilbert manifold structure and show that it is topologically equivalent to the standard complex Hilbert manifold structure.

math.CV↗

Spectral flow, Brouwer degree and Hill's determinant formula

In 2005 a new topological invariant defined in terms of the Brouwer degree of a determinant map, was introduced by Musso, Pejsachowicz and the first name author for counting the conjugate points along a semi-Riemannian geodesic. This invariant was defined in terms of a suspension of a complexified family of linear second order Dirichlet boundary value problems. In this paper, starting from this result, we generalize this invariant to a general self-adjoint Morse-Sturm system and we prove a new spectral flow formula. Finally we discuss the relation between this spectral flow formula and the Hill's determinant formula and we apply this invariant for detecting instability of periodic orbits of a Hamiltonian system.

math.CA↗

Sturm theory with applications in geometry and classical mechanics

Classical Sturm non-oscillation and comparison theorems as well as the Sturm theorem on zeros for solutions of second order differential equations have a natural symplectic version, since they describe the rotation of a line in the phase plane of the equation. In the higher dimensional symplectic version of these theorems, lines are replaced by Lagrangian subspaces and intersections with a given line are replaced by non-transversality instants with a distinguished Lagrangian subspace. Thus the symplectic Sturm theorems describe some properties of the Maslov index. Starting from the celebrated paper of Arnol'd on symplectic Sturm theory for optical Hamiltonians, we provide a generalization of his results to general Hamiltonians. We finally apply these results for detecting some geometrical information about the distribution of conjugate and focal points on semi-Riemannian manifolds and for studying the geometrical properties of the solutions space of singular Lagrangian systems arising in Celestial Mechanics.

math.DG↗

Fog Computing Applications: Taxonomy and Requirements

Fog computing was designed to support the specific needs of latency-critical applications such as augmented reality, and IoT applications which produce massive volumes of data that are impractical to send to faraway cloud data centers for analysis. However this also created new opportunities for a wider range of applications which in turn impose their own requirements on future fog computing platforms. This article presents a study of a representative set of 30 fog computing applications and the requirements that a general-purpose fog computing platform should support.

cs.DC↗

Linear instability for periodic orbits of non-autonomous Lagrangian systems

Inspired by the classical Poincaré criterion about the instability of orientation preserving minimizing closed geodesics on surfaces, we investigate the relation intertwining the instability and the variational properties of periodic solutions of a non-autonomous Lagrangian on a finite dimensional Riemannian manifold. We establish a general criterion for a priori detecting the linear instability of a periodic orbit on a Riemannian manifold for a (maybe not Legendre convex) non-autonomous Lagrangian simply by looking at the parity of the spectral index, which is the right substitute of the Morse index in the framework of strongly indefinite variational problems and defined in terms of the spectral flow of a path of Fredholm quadratic forms on a Hilbert bundle.

math.DS↗

Multiplicity of closed characteristics on $P$-symmetric compact convex hypersurfaces in $\mathbb{R}^{2n}$

There is a long standing conjecture that there are at least $n$ closed characteristics for any compact convex hypersurface $Σ$ in $\mathbb{R}^{2n}$, and the symmetric case, i.e. $Σ=-Σ$, has already been proved by C. Liu, Y. Long and C. Zhu in [Math. Ann., 323(2002), pp. 201-215]. In this paper, we extend the result in that paper to the $P$-symmetric case $Σ=PΣ$ for a certain class of symplectic matrix $P$, and prove that there are at least $[\frac{3n}{4}]$ closed characteristics on $Σ$ for any positive integer $n$, where $[a]:=\sup\{l\in\mathbb{Z},l\leq a\}$. To obtain our result, the key problem is to estimate (3.13) in which the method is based on the theorem called Common Index Jump Theorem. By using the Bott-type iteration formulas of Maslov index and Maslov-type index for a certain kind of iteration symplectic path, we provide the some new estimations (4.9-4.11), which are not considered in other papers.

math.DS↗

On the $j$-th Eigenvalue of Sturm-Liouville Problem and the Maslov Index

In the previous papers \cite{HLWZ,KWZ}, the jump phenomena of the $j$-th eigenvalue were completely characterized for Sturm-Liouville problems. In this paper, we show that the jump number of these eigenvalue branches is exactly the Maslov index for the path of corresponding boundary conditions. Then we determine the sharp range of the $j$-th eigenvalue on each layer of the space of boundary conditions. Finally, we prove that the graph of monodromy matrix tends to the Dirichlet boundary condition as the spectral parameter goes to $-\infty$.

math.FA↗

Decomposition of Spectral flow and Bott-type Iteration Formula

Let $A(t)$ be a continuous path of Fredhom operators, we first prove that the spectral flow $sf(A(t))$ is cogredient invariant. Based on this property, we give a decomposition formula of spectral flow if the path is invariant under a matrix-like cogredient. As applications, we give the generalized Bott-type iteration formula for linear Hamiltonian systems.

math.FA↗

Singularity of the $n$-th eigenvalue of high dimensional Sturm-Liouville problems

It is natural to consider continuous dependence of the $n$-th eigenvalue on $d$-dimensional ($d\geq2$) Sturm-Liouville problems after the results on $1$-dimensional case by Kong, Wu and Zettl [14]. In this paper, we find all the boundary conditions such that the $n$-th eigenvalue is not continuous, and give complete characterization of asymptotic behavior of the $n$-th eigenvalue. This renders a precise description of the jump phenomena of the $n$-th eigenvalue near such a boundary condition. Furthermore, we divide the space of boundary conditions into $2d+1$ layers and show that the $n$-th eigenvalue is continuously dependent on Sturm-Liouville equations and on boundary conditions when restricted into each layer. In addition, we prove that the analytic and geometric multiplicities of an eigenvalue are equal. Finally, we obtain derivative formula and positive direction of eigenvalues with respect to boundary conditions.

math.SP↗

The Hörmander index in the finite-dimensional case

In this paper, we calculate Hörmander index in the finite-dimensional case. Then we use the result to give some iteration inequalities, and prove almost existence of mean indices for given complete autonomous Hamiltonian system on compact symplectic manifold with symplectic trivial tangent bundle and given autonomous Hamiltonian system on regular compact energy hypersurface of symplectic manifold with symplectic trivial tangent bundle.

math.SG↗

Morse Index Theorem of Lagrangian Systems and Stability of Brake Orbit

In this paper, we prove Morse index theorem of Lagrangian system with any self-adjoint boundary conditions. Based on it, we give some nontrivial estimation on the difference of Morse indices. As an application, we get a new criterion for the stability problem of brake periodic orbit.

math.DS↗

Interfaces of high efficient kesterite Cu2ZnSnS(e)4 thin film solar cells

Cu2ZnSnS(e)4 (CZTS(e)) solar cells have attracted much attention due to the elemental abundance and the non-toxicity. However, the record efficiency of 12.6% for Cu2ZnSn(S,Se)4 (CZTSSe) solar cells is much lower than that of Cu(In,Ga)Se2 (CIGS) solar cells. One crucial reason is the recombination at interfaces. In recent years, large amount investigations have been done to analyze the interfacial problems and improve the interfacial properties via a variety of methods. This paper gives a review of progresses on interfaces of CZTS(e) solar cells, including: (1) the band alignment optimization at buffer/CZTS(e) interface, (2) tailoring the thickness of MoS(e)2 interfacial layers between CZTS(e) absorber and Mo back contact, (3) the passivation of rear interface, (4) the passivation of front interface, and (5) the etching of secondary phases.

physics.app-ph↗

On $S$-matrix, and fusion rules for irreducible $V^G$-modules

Let $V$ be a simple vertex operator algebra, and $G$ a finite automorphism group of $V$ such that $V^G$ is regular. The definition of entries in $S$-matrix on $V^G$ is discussed, and then is extended. The set of $V^G$-modules can be considered as a unitary space. In this paper, we obtain some connections between $V$-modules and $V^G$-modules over that unitary space. As an application, we determine the fusion rules for irreducible $V^G$-modules which occur as submodules of irreducible $V$-modules by the fusion rules for irreducible $V$-modules and by the structure of $G$.

math-ph↗

Deciphering chemical order/disorder and material properties at the single-atom level

Correlating 3D arrangements of atoms and defects with material properties and functionality forms the core of several scientific disciplines. Here, we determined the 3D coordinates of 6,569 iron and 16,627 platinum atoms in a model iron-platinum nanoparticle system to correlate 3D atomic arrangements and chemical order/disorder with material properties at the single-atom level. We identified rich structural variety and chemical order/disorder including 3D atomic composition, grain boundaries, anti-phase boundaries, anti-site point defects and swap defects. We show for the first time that experimentally measured 3D atomic coordinates and chemical species with 22 pm precision can be used as direct input for first-principles calculations of material properties such as atomic magnetic moments and local magnetocrystalline anisotropy. This work not only opens the door to determining 3D atomic arrangements and chemical order/disorder of a wide range of nanostructured materials with high precision, but also will transform our understanding of structure-property relationships at the most fundamental level.

cond-mat.mtrl-sci↗