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Chi Li

Publications and source records attributed to Chi Li.

90 records · Page 5Linked to original sources
arXiv2017

Understanding and Auto-Adjusting Performance-Related Configurations

Modern software systems are often equipped with hundreds to thousands of configuration options, many of which greatly affect performance. Unfortunately, properly setting these configurations is challenging for developers due to the complex and dynamic nature of system workload and environment. In this paper, we first conduct an empirical study to understand performance-related configurations and the challenges of setting them in the real-world. Guided by our study, we design a systematic and general control-theoretic framework, SmartConf, to automatically set and dynamically adjust performance-related configurations to meet required operating constraints while optimizing other performance metrics. Evaluation shows that SmartConf is effective in solving real-world configuration problems, often providing better performance than even the best static configuration developers can choose under existing configuration systems.

cs.DC↗
arXiv2017

Minimizing normalized volumes of valuations

For any $\mathbb{Q}$-Gorenstein klt singularity $(X,o)$, we introduce a normalized volume function $\widehat{\rm vol}$ that is defined on the space of real valuations centered at $o$ and consider the problem of minimizing $\widehat{\rm vol}$. We prove that the normalized volume has a uniform positive lower bound by proving an Izumi type estimate for any $\mathbb{Q}$-Gorenstein klt singularity. Furthermore, by proving a properness estimate, we show that the set of real valuations with uniformly bounded normalized volumes is compact, and hence reduce the existence of minimizers for the normalized volume functional $\widehat{\rm vol}$ to a conjectural lower semicontinuity property. We calculate candidate minimizers in several examples to show that this is an interesting and nontrivial problem. In particular, by using an inequality of de-Fernex-Ein-Mustaţă, we show that the divisorial valuation associated to the exceptional divisor of the standard blow up is a minimizer of $\widehat{\rm vol}$ for a smooth point. Finally the relation to Fujita's work on divisorial stability is also pointed out.

math.AG↗
arXiv2017

Kähler-Einstein metrics and volume minimization

We prove that if a $\mathbb{Q}$-Fano variety $V$ specially degenerates to a Kähler-Einstein $\mathbb{Q}$-Fano variety $V$, then for any ample Cartier divisor $H=-r^{-1} K_V$ with $r\in \mathbb{Q}_{>0}$, the normalized volume $\widehat{\rm vol}(v)=A_{\mathcal{C}}^n(v)\cdot {\rm vol}(v)$ is globally minimized at the canonical valuation ${\rm ord}_V$ among all real valuations which are centered at the vertex of the affine cone $\mathcal{C}:=C(V,H)$. This is also generalized to the logarithmic and the orbifold setting. As a consequence, we complete the confirmation of a conjecture in [arXiv:1511.08164] on an equivalent characterization of K-semistability for any smooth Fano manifold. We also prove that the valuation associated to the Reeb vector field of a smooth Sasaki-Einstein metric minimizes $\widehat{\rm vol}$ over the corresponding Kähler cone. These results strengthen the minimization result of Martelli-Sparks-Yau [Martelli et al 08].

math.AG↗
arXiv2017

K-semistability is equivariant volume minimization

This is a continuation to the paper [arXiv:1511.08164] in which a problem of minimizing normalized volumes over $\mathbb{Q}$-Gorenstein klt singularities was proposed. Here we consider its relation with K-semistability, which is an important concept in the study of Kähler-Einstein metrics on Fano varieties. In particular, we prove that for a $\mathbb{Q}$-Fano variety $V$, the K-semistability of $(V, -K_V)$ is equivalent to the condition that the normalized volume is minimized at the canonical valuation ${\rm ord}_V$ among all $\mathbb{C}^*$-invariant valuations on the cone associated to any positive Cartier multiple of $-K_V$. In this case, it's shown that ${\rm ord}_V$ is the unique minimizer among all $\mathbb{C}^*$-invariant quasi-monomial valuations. These results allow us to give characterizations of K-semistability by using equivariant volume minimization, and also by using inequalities involving divisorial valuations over $V$.

math.AG↗
arXiv2017

Deep Supervision with Shape Concepts for Occlusion-Aware 3D Object Parsing

Monocular 3D object parsing is highly desirable in various scenarios including occlusion reasoning and holistic scene interpretation. We present a deep convolutional neural network (CNN) architecture to localize semantic parts in 2D image and 3D space while inferring their visibility states, given a single RGB image. Our key insight is to exploit domain knowledge to regularize the network by deeply supervising its hidden layers, in order to sequentially infer intermediate concepts associated with the final task. To acquire training data in desired quantities with ground truth 3D shape and relevant concepts, we render 3D object CAD models to generate large-scale synthetic data and simulate challenging occlusion configurations between objects. We train the network only on synthetic data and demonstrate state-of-the-art performances on real image benchmarks including an extended version of KITTI, PASCAL VOC, PASCAL3D+ and IKEA for 2D and 3D keypoint localization and instance segmentation. The empirical results substantiate the utility of our deep supervision scheme by demonstrating effective transfer of knowledge from synthetic data to real images, resulting in less overfitting compared to standard end-to-end training.

cs.CV↗
arXiv2017

Ultrafast field-driven monochromatic photoemission from carbon nanotubes

Ultrafast electron pulses, combined with laser-pump and electron-probe technologies, allow for various forms of ultrafast microscopy and spectroscopy to elucidate otherwise challenging to observe physical and chemical transitions. However, the pursuit of simultaneous ultimate spatial and temporal resolution has been largely subdued by the low monochromaticity of the electron pulses and their poor phase synchronization to the optical excitation pulses. State-of-the-art photon-driven sources have good monochromaticity but poor phase synchronization. In contrast, field-driven photoemission has much higher light phase synchronization, due to the intrinsic sub-cycle emission dynamics, but poor monochromaticity. Such sources suffer from larger electron energy spreads (3 - 100 eV) attributed to the relatively low field enhancement of the conventional metal tips which necessitates long pump wavelengths (> 800 nm) in order to gain sufficient ponderomotive potential to access the field-driven regime. In this work, field-driven photoemission from ~1 nm radius carbon nanotubes excited by a femtosecond laser at a short wavelength of 410 nm has been realized. The energy spread of field-driven electrons is effectively compressed to 0.25 eV outperforming all conventional ultrafast electron sources. Our new nanotube-based ultrafast electron source opens exciting prospects for attosecond imaging and emerging light-wave electronics.

physics.optics↗
arXiv2015

Quasi-projectivity of the moduli space of smooth Kahler-Einstein Fano manifolds

In this note, we prove that there is a canonical continuous Hermitian metric on the CM line bundle over the proper moduli space $\bar{\mathcal{M}}$ of smoothable Kahler-Einstein Fano varieties. The curvature of this metric is the Weil-Petersson current, which exists as a positive (1,1)-current on $\bar{\mathcal{M}}$ and extends the canonical Weil-Petersson current on the moduli space parametrizing smooth Kahler-Einstein Fano manifolds $\mathcal{M}$. As a consequence, we show that the CM line bundle is nef and big on $\bar{\mathcal{M}}$ and its restriction on $\mathcal{M}$ is ample.

math.DG↗
arXiv2013

Special test configurations and $K$-stability of Fano varieties

For any flat projective family $(\mX,\mL)\rightarrow C$ such that the generic fibre $\mX_η$ is a klt Q-Fano variety and $\mL|_{\mX_η}\sim_{Q}-K_{X_η}$, we use the techniques from the minimal model program (MMP) to modify the total family. The end product is a family such that every fiber is a klt Q-Fano variety. Moreover, we can prove that the Donaldson-Futaki invariants of the appearing models decrease. When the family is a test configuration of a fixed Fano variety $(X,-K_X)$, this implies Tian's conjecture: given $X$ a Fano manifold, to test its K-(semi, poly)stability, we only need to test on the special test configurations.

math.AG↗
arXiv2013

A Pohozaev identity and critical exponents of some complex Hessian equations

In this note, we prove some non-existence results for Dirichlet problems of complex Hessian equations. The non-existence results are proved using the Pohozaev method. We also prove existence results for radially symmetric solutions. The main difference of the complex case with the real case is that we don't know if a priori radially symmetric property holds in the complex case.

math.AP↗
arXiv2012

Conical Kahler-Einstein metric revisited

In this paper we introduce the "interpolation-degneration" strategy to study Kahler-Einstein metrics on a smooth Fano manifold with cone singularities along a smooth divisor that is proportional to the anti-canonical divisor. By "interpolation" we show the angles in $(0, 2π]$ that admit a conical Kahler-Einstein metric form an interval; and by "degeneration" we figure out the boundary of the interval. As a first application, we show that there exists a Kahler-Einstein metric on $P^2$ with cone singularity along a smooth conic (degree 2) curve if and only if the angle is in $(π/2, 2π]$. When the angle is $2π/3$ this proves the existence of a Sasaki-Einstein metric on the link of a three dimensional $A_2$ singularity, and thus answers a problem posed by Gauntlett-Martelli-Sparks-Yau. As a second application we prove a version of Donaldson's conjecture about conical Kahler-Einstein metrics in the toric case using Song-Wang's recent existence result of toric invariant conical Kahler-Einstein metrics.

math.DG↗
arXiv2011

On the limit behavior of metrics in continuity method to Kahler-Einstein problem in toric Fano case

This is a continuation of paper \cite{Li}. On any toric Fano manifold, we discuss the behavior of limit metric of a sequence of metrics, which are solutions to a continuity family of complex Monge-Ampere equations in Kahler-Einstein problem. We show that the limit metric satisfies a singular complex Monge-Ampere equation. This shows the conic type singularity for the limit metric. The information of conic type singularities can be read from the geometry of the moment polytope.

math.DG↗
arXiv2011

On rotationally symmetric Kahler-Ricci solitons

In this note, using Calabi's method, we construct rotationally symmetric Kahler-Ricci solitons on the total space of direct sum of fixed hermitian line bundle and its projective compactification, where the curvature of hermitian line bundle is Kahler-Einstein. These examples generalize the construction of Koiso, Cao and Feldman-Ilmanen-Knopf.

math.DG↗
arXiv2009

Constant scalar curvature Kahler metric and K-energy

Based on Donaldson's method, we prove that, for an integral Kahler class, when there is a Kahler metric of constant scalar curvature, then it minimizes the K-energy. We do not assume that the automorphism group is discrete.

math.DG↗