arXiv subjects

Ziqiang Feng

Publications and source records attributed to Ziqiang Feng.

9 recordsLinked to original sources

arXiv2025

Transitive partially hyperbolic diffeomorphisms in dimension three

We prove that any $C^{1+\alpha}$ transitive conservative partially hyperbolic diffeomorphism of a closed 3-manifold with virtually solvable fundamental group is ergodic. Consequently, in light of \cite{FP-classify}, this establishes the equivalence between transitivity and ergodicity for $C^{1+\alpha}$ conservative partially hyperbolic diffeomorphisms in \emph{any} closed 3-manifold. Moreover, we provide a characterization of compact accessibility classes under transitivity, thereby giving a precise classification of all accessibility classes for transitive 3-dimensional partially hyperbolic diffeomorphisms.

math.DS↗

arXiv2025

Accessibility and central integrability in the absence of periodic points

We consider a partially hyperbolic diffeomorphism $f: M \to M$ without periodic points on a closed manifold $M$. We prove that $f$ is accessible when $M$ is a 3-manifold with non-virtually-solvable fundamental group $\pi_1(M)$. In the case where $\dim E^c = 1$, we demonstrate that the center bundle $E^c$ is uniquely integrable if $f$ lacks accessibility. Furthermore, we provide a complete characterization of accessibility classes for such systems with one-dimensional center bundles.

math.DS↗

arXiv2025

Gemini 2.5: Pushing the Frontier with Advanced Reasoning, Multimodality, Long Context, and Next Generation Agentic Capabilities

In this report, we introduce the Gemini 2.X model family: Gemini 2.5 Pro and Gemini 2.5 Flash, as well as our earlier Gemini 2.0 Flash and Flash-Lite models. Gemini 2.5 Pro is our most capable model yet, achieving SoTA performance on frontier coding and reasoning benchmarks. In addition to its incredible coding and reasoning skills, Gemini 2.5 Pro is a thinking model that excels at multimodal understanding and it is now able to process up to 3 hours of video content. Its unique combination of long context, multimodal and reasoning capabilities can be combined to unlock new agentic workflows. Gemini 2.5 Flash provides excellent reasoning abilities at a fraction of the compute and latency requirements and Gemini 2.0 Flash and Flash-Lite provide high performance at low latency and cost. Taken together, the Gemini 2.X model generation spans the full Pareto frontier of model capability vs cost, allowing users to explore the boundaries of what is possible with complex agentic problem solving.

cs.CL↗

arXiv2025

Partially hyperbolic diffeomorphisms homotopic to the identity in dimension three

We show that any conservative partially hyperbolic diffeomorphism homotopic to the identity is accessible unless the fundamental group of its ambient 3-manifold is virtually solvable. As a consequence, such diffeomorphisms are ergodic, giving an affirmative answer to the Hertz-Hertz-Ures Ergodicity Conjecture in the homotopy class of identity.

math.DS↗

arXiv2024

Partially Hyperbolic Dynamics with Quasi-isometric Center

We consider the class of partially hyperbolic diffeomorphisms on a closed 3-manifold with quasi-isometric center. Under the non-wandering condition, we prove that the diffeomorphisms are accessible if there is no $su$-torus. As a consequence, volume-preserving diffeomorphisms in this context are ergodic in the absence of $su$-tori, thereby confirming the Hertz-Hertz-Ures Ergodicity Conjecture for this class. We show the existence of transitive Anosov flows on a closed 3-manifold admitting a non-wandering partially hyperbolic diffeomorphism with quasi-isometric center and fundamental group of exponential growth. Furthermore, we provide a complete classification of these diffeomorphisms, showing they fall into two categories: skew products and discretized Anosov flows.

math.DS↗

arXiv2024

Accessibility and Ergodicity of Partially Hyperbolic Diffeomorphisms without Periodic Points

We prove that every $C^2$ conservative partially hyperbolic diffeomorphism of a closed 3-manifold without periodic points is ergodic, which gives an affirmative answer to the Ergodicity Conjecture by Hertz-Hertz-Ures in the absence of periodic points. We also show that a partially hyperbolic diffeomorphism of a closed 3-manifold $M$ with no periodic points is accessible if the non-wandering set is all of $M$ and the fundamental group $\pi_1(M)$ is not virtually solvable.

math.DS↗

arXiv2022

ByteStore: Hybrid Layouts for Main-Memory Column Stores

The performance of main memory column stores highly depends on the scan and lookup operations on the base column layouts. Existing column-stores adopt a homogeneous column layout, leading to sub-optimal performance on real workloads since different columns possess different data characteristics. In this paper, we propose ByteStore, a column store that uses different storage layouts for different columns. We first present a novel data-conscious column layout, PP-VBS (Prefix-Preserving Variable Byte Slice). PP-VBS exploits data skew to accelerate scans without sacrificing lookup performance. Then, we present an experiment-driven column layout advisor to select individual column layouts for a workload. Extensive experiments on real data show that ByteStore outperforms homogeneous storage engines by up to 5.2X.

cs.DB↗

arXiv2018

The Decay Rate of Patterson-Sullivan Measures with Potential Functions and Critical Exponents

Basing upon the recent development of the Patterson-Sullivan measures with a Hölder continuous nonzero potential function, we use tools of both dynamics of geodesic flows and geometric properties of negatively curved manifolds to present a new formula illustrating the relation between the exponential decay rate of Patterson-Sullivan measures with a Hölder continuous potential function and the corresponding critical exponent.

math.DS↗

arXiv2014

SINAP surface preparation processing for 500MHz superconducting cavity

This paper illustrates the design, fabrication and experiment results of surface preparation system for 500MHz superconducting cavity at Shanghai Institute of Applied Physic (SINAP). The SINAP established a set of clean room, buffered chemical polishing equipment, and high pressure ultra-pure water rinsing facility. The whole surface preparation procedure has been operated successfully and verified by the successful vertical tests of 500MHz single cell superconducting cavity.

physics.acc-ph↗