arXiv subjects
Publications and source records attributed to Zihao Qi.
In this paper, we prove that for every non-degenerate $C^3$ compact star-shaped hypersurface $Σ$ in $\mathbf{R}^{6}$ which carries no prime closed characteristic of Maslov-type index $0$ or no prime closed characteristic of Maslov-type index $-1$, there exist at least three prime closed characteristics on $Σ$.
Unlike video coding for professional content, the delivery pipeline of User Generated Content (UGC) involves transcoding where unpristine reference content needs to be compressed repeatedly. In this work, we observe that existing full-/no-reference quality metrics fail to accurately predict the perceptual quality difference between transcoded UGC content and the corresponding unpristine references. Therefore, they are unsuited for guiding the rate-distortion optimisation process in the transcoding process. In this context, we propose a bespoke full-reference deep video quality metric for UGC transcoding. The proposed method features a transcoding-specific weakly supervised training strategy employing a quality ranking-based Siamese structure. The proposed method is evaluated on the YouTube-UGC VP9 subset and the LIVE-Wild database, demonstrating state-of-the-art performance compared to existing VQA methods.
The quantum dynamics of spin systems with uniform all-to-all interaction are often studied in the totally symmetric space (TSS) of maximal total spin. However the TSS states are atypical in the full many-body Hilbert space. In this work, we explore several aspects of the all-to-all quantum dynamics away from the TSS, and reveal surprising features of the "deep Hilbert space" (DHS). We study the out-of-time order correlator (OTOC) in the infinite-temperature ensemble of the full Hilbert space. We derive a phase-space representation of the DHS OTOC and show that the OTOC can grow super-exponentially in the large $N$ limit, due to the fast dynamics in an unbounded phase space (in finite systems, we observe numerically that the super-exponential growth ends precociously and gives way to a power-law one until saturation). By a similar mechanism, the Krylov complexity grows explosively. We also study the entanglement growth in a quantum quench from a DHS product state, i.e., one of non-aligned spins that resemble the DHS infinite-temperature ensemble with respect to the statistics of the collective spins. Using a field-theoretical method, We exactly calculate the entanglement entropy in the large $N$ limit. We show that, in the DHS, fast OTOC growth does not imply fast entanglement growth, in contrast to the Zurek-Paz relation derived in the TSS.
The paper concerns the Gelfand-Kirillov dimension and the generating series of nonsymmetric operads. An analogue of Bergman's gap theorem is proved, namely, no finitely generated locally finite nonsymmetric operad has Gelfand-Kirillov dimension strictly between $1$ and $2$. For every $r\in \{0\}\cup \{1\}\cup [2,\infty)$ or $r=\infty$, we construct a single-element generated nonsymmetric operad with Gelfand-Kirillov dimension $r$. We also provide counterexamples to two expectations of Khoroshkin and Piontkovski about the generating series of operads.
Quite much recent studies has been attracted to the operated algebra since it unifies various notions such as the differential algebra and the Rota-Baxter algebra. An $Ω$-operated algebra is a an (associative) algebra equipped with a set $Ω$ of linear operators which might satisfy certain operator identities such as the Leibniz rule. A free $Ω$-operated algebra $B$ can be generated on an algebra $A$ similar to a free algebra generated on a set. If $A$ has a Gröbner-Shirshov basis $G$ and if the linear operators $Ω$ satisfy a set $Φ$ of operator identities, it is natural to ask when the union $G\cup Φ$ is a Gröbner-Shirshov basis of $B$. A previous work answers this question affirmatively under a mild condition, and thereby obtains a canonical linear basis of $B$. In this paper, we answer this question in the general case of multiple linear operators. As applications we get operated Gröbner-Shirshov bases for free differential Rota-Baxter algebras and free integro-differential algebras over algebras as well as their linear bases. One of the key technical difficulties is to introduce new monomial orders for the case of two operators, which might be of independent interest.
It is well known that high dynamic range (HDR) video can provide more immersive visual experiences compared to conventional standard dynamic range content. However, HDR content is typically more challenging to encode due to the increased detail associated with the wider dynamic range. In this paper, we improve HDR compression performance using the effective bit depth adaptation approach (EBDA). This method reduces the effective bit depth of the original video content before encoding and reconstructs the full bit depth using a CNN-based up-sampling method at the decoder. In this work, we modify the MFRNet network architecture to enable multiple frame processing, and the new network, multi-frame MFRNet, has been integrated into the EBDA framework using two Versatile Video Coding (VVC) host codecs: VTM 16.2 and the Fraunhofer Versatile Video Encoder (VVenC 1.4.0). The proposed approach was evaluated under the JVET HDR Common Test Conditions using the Random Access configuration. The results show coding gains over both the original VVC VTM 16.2 and VVenC 1.4.0 (w/o EBDA) on JVET HDR tested sequences, with average bitrate savings of 2.9% (over VTM) and 4.8% (against VVenC) based on the Bjontegaard Delta measurement. The source code of multi-frame MFRNet has been released at https://github.com/fan-aaron-zhang/MF-MFRNet.
We study a question which can be roughly stated as follows: Given a (unital or nonunital) algebra $A$ together with a Gröbner-Shirshov basis $G$, consider the free operated algebra $B$ over $A$, such that the operator satisfies some polynomial identities $Φ$ which are Gröbner-Shirshov in the sense of Guo et al., when doesthe union $Φ\cup G$ will be an operated Gröbner-Shirshov basis for $B$? We answer this question in the affirmative under a mild condition in our previous work with Wang. When this condition is satisfied, $Φ\cup G$ is an operated Gröbner-Shirshov basis for $ B$ and as a consequence, we also get a linear basis of $B$. However, the condition could not be applied directly to differential type algebras introduced by Guo, Sit and Zhang, including usual differential algebras. This paper solves completely this problem for differential type algebras.Some new monomial orders are introduced which, together with some known ones, permit the application of the previous result to most of differential type algebras, thus providing new operated GS bases and linear bases for these differential type algebras.Versions are presented both for unital and nonunital algebras. However, a class of examples are also presented, for which the natural expectation in the question is wrong and these examples are dealt with by direct inspection.
The paradigm of Floquet engineering of topological states of matter can be generalized into the time-quasiperiodic scenario, where a lower dimensional time-dependent system maps into a higher dimensional one by combining the physical dimensions with additional synthetic dimensions generated by multiple incommensurate driving frequencies. Different than most previous works in which gapped topological phases were considered, we propose an experimentally realizable, one dimensional chain driven by two frequencies, which maps into a gapless Weyl semimetal in synthetic dimension. Based on analytical reasoning and numerical simulations, we found the nonadiabatic quantum dynamics of this system exhibit energy pumping behaviors characterized by universal functions. We also numerically found such behaviors are robust against a considerable amount of spatial disorder.
Temporal Action Detection (TAD) is an essential and challenging topic in video understanding, aiming to localize the temporal segments containing human action instances and predict the action categories. The previous works greatly rely upon dense candidates either by designing varying anchors or enumerating all the combinations of boundaries on video sequences; therefore, they are related to complicated pipelines and sensitive hand-crafted designs. Recently, with the resurgence of Transformer, query-based methods have tended to become the rising solutions for their simplicity and flexibility. However, there still exists a performance gap between query-based methods and well-established methods. In this paper, we identify the main challenge lies in the large variants of action duration and the ambiguous boundaries for short action instances; nevertheless, quadratic-computational global attention prevents query-based methods to build multi-scale feature maps. Towards high-quality temporal action detection, we introduce Sparse Proposals to interact with the hierarchical features. In our method, named SP-TAD, each proposal attends to a local segment feature in the temporal feature pyramid. The local interaction enables utilization of high-resolution features to preserve action instances details. Extensive experiments demonstrate the effectiveness of our method, especially under high tIoU thresholds. E.g., we achieve the state-of-the-art performance on THUMOS14 (45.7% on mAP@0.6, 33.4% on mAP@0.7 and 53.5% on mAP@Avg) and competitive results on ActivityNet-1.3 (32.99% on mAP@Avg). Code will be made available at https://github.com/wjn922/SP-TAD.
This paper investigates algebraic objects equipped with an operator, such as operated monoids, operated algebras etc. Various free object functors in these operated contexts are explicitly constructed. For operated algebras whose operator satisfies a set $Φ$ of relations (usually called operated polynomial identities (aka. OPIs)), Guo defined free objects, called free $Φ$-algebras, via universal algebra. Free $Φ$-algebras over algebras are studied in details. A mild sufficient condition is found such that $Φ$ together with a Gröbner-Shirshov basis of an algebra $A$ form a Gröbner-Shirshov basis of the free $Φ$-algebra over algebra $A$ in the sense of Guo et al.. Ample examples for which this condition holds are provided, such as all Rota-Baxter type OPIs, a class of differential type OPIs, averaging OPIs and Reynolds OPI.
Continuing a work of Ph.~Monnier, we determine the Gerstenhaber algebra structure over the Poisson cohomology groups for a large class of Poisson structures with isolated singularities over the plane. It reveals that there exists a GAGA type phenomenon. We give an explicit description via generators and relations for the case of simple singularities.
Flat bands in lattice models have provided useful platforms for studying strong correlation and topological physics. Recently, honeycomb superlattices have been shown to host flat bands that persist in the presence of local perturbations respecting lattice symmetries. We analytically derive the flat band energies in the presence of longer range hopping and find that the energies of flat bands are tunable by these perturbations. In real space, the wave function is constructed from standing waves on each honeycomb edge, allowing the construction of plaquette and loop eigenstates due to destructive interference in real space that give rise to the flat bands robust against long range hoppings.
With more encrypted network traffic gets involved in the Internet, how to effectively identify network traffic has become a top priority in the field. Accurate identification of the network traffic is the footstone of basic network services, say QoE, bandwidth allocation, and IDS. Previous identification methods either cannot deal with encrypted traffics or require experts to select tons of features to attain a relatively decent accuracy.In this paper, we present a Deep Learning based end-to-end network traffic identification framework, termed TEST, to avoid the aforementioned problems. CNN and LSTM are combined and implemented to help the machine automatically extract features from both special and time-related features of the raw traffic. The presented framework has two layers of structure, which made it possible to attain a remarkable accuracy on both encrypted traffic classification and intrusion detection tasks. The experimental results demonstrate that our model can outperform previous methods with a state-of-the-art accuracy of 99.98%.