arXiv subjects

Fei Qi

Publications and source records attributed to Fei Qi.

At least 19 recordsLinked to original sources

arXiv2026

Boson-fermion meromorphic open-string vertex algebras and their canonically twisted modules

We construct a $\frac{\mathbb{Z}}{2}$-graded meromorphic open-string vertex algebra from a finite-dimensional vector space with a nondegenerate symmetric bilinear form, together with its canonically twisted module. This algebra is generated by suitable noncommutative generalizations of bosonic and fermionic fields and is a noncommutative generalization of the free boson-fermion vertex operator superalgebra. Similarly to the purely bosonic and purely fermionic cases in the early works by the second author in [H1], by Fiordalisi and the third author in [FQ], and by the third author in [Q3], the usual super-commutatitive relations between creation and annihilation operators still hold while no relations exist among creation operators. In particular, normal-ordering remains well-defined. As in [H1], [FQ], and [Q3], we prove a generalized Wick's theorem in this case, which gives a formula for a product of two normal ordered products of bosonic and fermionic generating fields. Using this generalized Wick's theorem, we construct the $\frac{\mathbb{Z}}{2}$-graded meromorphic open-string vertex algebra and its canonically twisted module in this case. The construction in this paper is the algebraic part of our construction of suitable Dirac-like operators from spin manifolds.

math.QA↗

arXiv2026

Deformation rigidity of some simple affine VOAs

In this paper, we prove that simple affine vertex operator algebras with positive integral levels admit only trivial first-order deformations. Therefore, the deformation rigidity conjecture of strongly rational vertex operator algebras holds for these cases. We also show that the same holds simple affine vertex operator algebra of $\mathfrak{sl}_2$ at the non-integral admissible level $-4/3$. Therefore, neither $C_2$-cofiniteness nor rationality is a necessary condition for deformation rigidity of VOAs. We conjecture that the same should hold for every simple affine VOA that does not coincide with the corresponding universal affine VOA.

math.QA↗

arXiv2025

A cohomology theory of supercommutative algebras and grading-restricted vertex superalgebras

This paper constructs the cohomology theory for grading-restricted vertex superalgebras, generalizing Yi-Zhi Huang's cohomology theory of grading-restricted vertex algebras. To simplify the discussion, motivate the construction, and make it easier for the reader to understand the technical points, we also include the construction of the cohomology theory of supercommutative associative algebras, a generalization of the Harrison cohomology theory of a commutative algebra that has not been explicitly written down. The paper will serve as the foundation for many subsequent studies, especially, the deformation theory of vertex superalgebras.

math.QA↗

arXiv2025

FunduSAM: A Specialized Deep Learning Model for Enhanced Optic Disc and Cup Segmentation in Fundus Images

The Segment Anything Model (SAM) has gained popularity as a versatile image segmentation method, thanks to its strong generalization capabilities across various domains. However, when applied to optic disc (OD) and optic cup (OC) segmentation tasks, SAM encounters challenges due to the complex structures, low contrast, and blurred boundaries typical of fundus images, leading to suboptimal performance. To overcome these challenges, we introduce a novel model, FunduSAM, which incorporates several Adapters into SAM to create a deep network specifically designed for OD and OC segmentation. The FunduSAM utilizes Adapter into each transformer block after encoder for parameter fine-tuning (PEFT). It enhances SAM's feature extraction capabilities by designing a Convolutional Block Attention Module (CBAM), addressing issues related to blurred boundaries and low contrast. Given the unique requirements of OD and OC segmentation, polar transformation is used to convert the original fundus OD images into a format better suited for training and evaluating FunduSAM. A joint loss is used to achieve structure preservation between the OD and OC, while accurate segmentation. Extensive experiments on the REFUGE dataset, comprising 1,200 fundus images, demonstrate the superior performance of FunduSAM compared to five mainstream approaches.

cs.CV↗

arXiv2024

First-order deformations of freely generated vertex algebras

We solve the problem of how to classify the first-order vertex-algebraic deformations for any grading-restricted vertex algebra $V$ that is freely generated by homogeneous elements of positive weights. We approach by computing the second cohomology $H^2_{1/2}(V, V)$ constructed by Yi-Zhi Huang. We start with the cocycle on two generators and show that its cohomology class is completely determined by its singular part. To extend the cocycle to any pair of elements in $V$, we take a generating function approach, formulate the cocycle equation, and show that all the complementary solutions are coboundaries. Then we use a very general procedure to construct a particular solution. The procedure applies to vertex algebras that are not freely generated. As a by-product, we show that $H^2_{1/2}(V, V) = H^2_\infty(V, V)$. Using these results, we explicitly determine the first-order deformations of the universal Virasoro VOA $Vir_c$, universal affine VOA $V^l(\mathfrak{g})$, Heisenberg VOA $V^l(\mathfrak{h})$, and the universal Zamolodchikov VOA $W_3^c$.

math.QA↗

arXiv2023

The First Verification Test of Space-Ground Collaborative Intelligence via Cloud-Native Satellites

Recent advancements in satellite technologies and the declining cost of access to space have led to the emergence of large satellite constellations in Low Earth Orbit. However, these constellations often rely on bent-pipe architecture, resulting in high communication costs. Existing onboard inference architectures suffer from limitations in terms of low accuracy and inflexibility in the deployment and management of in-orbit applications. To address these challenges, we propose a cloud-native-based satellite design specifically tailored for Earth Observation tasks, enabling diverse computing paradigms. In this work, we present a case study of a satellite-ground collaborative inference system deployed in the Tiansuan constellation, demonstrating a remarkable 50\% accuracy improvement and a substantial 90\% data reduction. Our work sheds light on in-orbit energy, where in-orbit computing accounts for 17\% of the total onboard energy consumption. Our approach represents a significant advancement of cloud-native satellite, aiming to enhance the accuracy of in-orbit computing while simultaneously reducing communication cost.

cs.DC↗

arXiv2023

Fermionic construction of the $\frac{\mathbb{Z}}{2}$-graded meromorphic open-string vertex algebra and its $\mathbb{Z}_2$-twisted module, I

We define the $\frac{\mathbb{Z}}{2}$-graded meromorphic open-string vertex algebra that is an appropriate noncommutative generalization of the vertex operator superalgebra. We also illustrate an example that can be viewed as a noncommutative generalization of the free fermion vertex operator superalgebra. The example is bulit upon a universal half-integer-graded non-anti-commutative Fock space where a creation operator and an annihilation operator satisfy the fermionic anti-commutativity relation, while no relations exist among the creation operators. The former feature allows us to define the normal ordering, while the latter feature allows us to describe interactions among the fermions. With respect to the normal ordering, Wick's theorem holds and leads to a proof of weak associativity and a closed formula of correlation functions.

math.QA↗

arXiv2023

Fermionic construction of the $\frac{\mathbb{Z}}{2}$-graded meromorphic open-string vertex algebra and its $\mathbb{Z}_2$-twisted module, II

This paper continues with Part I. We define the module for a $\frac{\mathbb{Z}}{2}$-graded meromorphic open-string vertex algebra that is twisted by an involution and show that the axioms are sufficient to guarantee the convergence of products and iterates of any number of vertex operators. A module twisted by the parity involution is called a canonically $\mathbb{Z}_2$-twisted module. As an example, we give a fermionic construction of the canonically $\mathbb{Z}_2$-twisted module for the $\frac{\mathbb{Z}}{2}$-graded meromorphic open-string vertex algebra constructed in Part I. Similar to the situation in Part I, the example is also built on a universal $\mathbb{Z}$-graded non-anti-commutative Fock space where a creation operator and an annihilation operator satisfy the fermionic anti-commutativity relation, while no relations exist among the creation operators or among the zero modes. The Wick's theorem still holds, though the actual vertex operator needs to be corrected from the na\"ive definition by normal ordering using the $\exp(\Delta(x))$-operator in Part I.

math.QA↗

arXiv2023

Uniform tensor clustering by jointly exploring sample affinities of various orders

Conventional clustering methods based on pairwise affinity usually suffer from the concentration effect while processing huge dimensional features yet low sample sizes data, resulting in inaccuracy to encode the sample proximity and suboptimal performance in clustering. To address this issue, we propose a unified tensor clustering method (UTC) that characterizes sample proximity using multiple samples' affinity, thereby supplementing rich spatial sample distributions to boost clustering. Specifically, we find that the triadic tensor affinity can be constructed via the Khari-Rao product of two affinity matrices. Furthermore, our early work shows that the fourth-order tensor affinity is defined by the Kronecker product. Therefore, we utilize arithmetical products, Khatri-Rao and Kronecker products, to mathematically integrate different orders of affinity into a unified tensor clustering framework. Thus, the UTC jointly learns a joint low-dimensional embedding to combine various orders. Finally, a numerical scheme is designed to solve the problem. Experiments on synthetic datasets and real-world datasets demonstrate that 1) the usage of high-order tensor affinity could provide a supplementary characterization of sample proximity to the popular affinity matrix; 2) the proposed method of UTC is affirmed to enhance clustering by exploiting different order affinities when processing high-dimensional data.

cs.LG↗

arXiv2022

Central recirculation zone in a V-shaped premixed swirling flame

This paper presents an experimental study on the emergence of the central recirculation zone (CRZ) in a V-shaped premixed swirling flame, using simultaneous measurement of particle image velocimetry (PIV) and CH* chemiluminescence. The results show that either increasing the Reynolds number (Re) or decreasing the equivalence ratio ({\Phi}) would facilitate the emergence of CRZ. Further analysis demonstrates that the CRZ characteristics and its emergence are strongly influenced by the inner shear layer (ISL) surrounding the CRZ, while the swirl intensity remains unchanged. Dimensional analysis is performed to understand the underlying mechanism, suggesting the CRZ emergence is controlled by a non-dimensional parameter, Re_s=|{\gamma}|_max D/{\nu}_s, defined based on the maximum ISL intensity (|{\gamma}|_max), the exit diameter (D), and the kinematic viscosity ({\nu}_s) of the burnt gas. By estimating the temperature and viscosity with a simple heat-loss model, we show in the |{\gamma}|_max D-{\nu}_s regime diagram that the cases with and without CRZ are separated by a single boundary line, corresponding to a critical Re_s of about 424. This verifies the applicability of the proposed Re_s criterion to lean-premixed V-shaped swirling flames under various conditions. Unlike most previous works that attribute the CRZ of swirling flames to vortex breakdown, the present work reveals the non-negligible effect of the ISL, especially the CRZ suppression when the ISL is weakened by flame heating.

physics.flu-dyn↗

arXiv2022

On the extensions of the left modules for a meromorphic open-string vertex algebra, I

We study the extensions of two left modules $W_1, W_2$ for a meromorphic open-string vertex algebra $V$. We show that the extensions satisfying some technical but natural convergence conditions are in bijective correspondence to the first cohomology classes associated to the $V$-bimodule $\mathcal{H}_N(W_1, W_2)$ constructed in \cite{HQ-Red}. When $V$ is grading-restricted and contains a nice vertex subalgebra $V_0$, those convergence conditions hold automatically. In addition, we show that the dimension of $\text{Ext}^1(W_1, W_2)$ is bounded above by the fusion rule $N\binom{W_2}{VW_1}$ in the category of $V_0$-modules. In particular, if the fusion rule is finite, then $\text{Ext}^1(W_1, W_2)$ is finite-dimensional. We also give an example of an abelian category consisting of certain modules of the Virasoro VOA that does not contain any nice subalgebras, while the convergence conditions hold for every object.

math.QA↗

arXiv2022

Emergence of Self-dual Patterns in Active Colloids with Periodical Feedback to Local Density

The central task in the study of self-organization is to explore the general mechanism of emergences. However, this is inhibited by the missing of a full knowledge of the microscopic dynamics of emergence. Here, in this study, the microscopic dynamics of self-organization for patterns is investigated and quantified in a periodically propelled Quincke system. The periodical coupling between propulsion and repulsion at the particle level leads to local directed oscillating particle flows and promises a loop of positive feedback to density fluctuations. Nevertheless, the global evolution of the resulting cluster phase is dominated by a global dual transformation. As stable attractors of the dual transformation, self-dual patterns including stripe patterns and square lattices can be achieved by tuning the strength and the frequency of propelling. However, stripes are possible only at strong propelling where boundary particle flows can form. The findings in this study show that the dynamics of emergence on different length scales are controlled by different mechanisms. The competition and the interplay between different microscopic dynamic processes play the central role in determining the product of emergence. Moreover, the periodically oscillating self-dual patterns demonstrate a classical approach to time crystals.

cond-mat.soft↗

arXiv2021

First cohomologies of affine, Virasoro and lattice vertex operator algebras

In this paper we study the first cohomologies for the following three examples of vertex operator algebras: (i) the simple affine VOA associated to a simple Lie algebra with positive integral level; (ii) the Virasoro VOA corresponding to minimal models; (iii) the lattice VOA associated to a positive definite even lattice. We prove that in all these cases, the first cohomology $H^1(V, W)$ are given by the zero-mode derivations when $W$ is any $V$-module with an $\N$-grading (not necessarily by the operator $L(0)$). This agrees with the conjecture made by Yi-Zhi Huang and the author in 2018. For negative energy representations of Virasoro VOA, the same conclusion holds when $W$ is $L(0)$-graded with lowest weight greater or equal to $-3$. Relationship between the first cohomology of the VOA and that of the associated Zhu's algebra is also discussed.

math.QA↗

arXiv2021

Meromorphic open-string vertex algebras and modules over two-dimensional orientable space forms

We study the meromorphic open-string vertex algebras and their modules over the two-dimensional Riemannian manifolds that are complete, connected, orientable, and of constant sectional curvature $K\neq 0$. Using the parallel tensors, we explicitly determine a basis for the meromorphic open-string vertex algebra, its modules generated by eigenfunctions of the Laplace-Beltrami operator, and their irreducible quotients. We also study the modules generated by lowest weight subspace satisfying a geometrically interesting condition. It is showed that every irreducible module of this type is generated by some (local) eigenfunction on the manifold. A classification is given for modules of this type admitting a composition series of finite length. In particular and remarkably, if every composition factor is generated by eigenfunctions of eigenvalue $p(p-1)K$ for some $p\in \mathbb{Z}_+$, then the module is completely reducible.

math.QA↗

arXiv2021

Single camera high repetition rate two-color formaldehyde planar laser-induced fluorescence thermometry with a wavelength-switching burst mode laser

We consider a two-color formaldehyde PLIF thermometry scheme using a wavelength-switching injection seeding Nd:YAG laser at 355 nm. The 28183.5 cm-1 and 28184.5 cm-1 peaks of formaldehyde are used to measure low temperature combustion zone. Using a burst mode amplifier and a high speed camera, high-repetition rate (20 kHz) temperature field measurement is validated on a laminar coflow diffusion flame and demonstrated on a turbulent confined jet in hot crossflow flame.

physics.optics↗

arXiv2021

PGNet: Real-time Arbitrarily-Shaped Text Spotting with Point Gathering Network

The reading of arbitrarily-shaped text has received increasing research attention. However, existing text spotters are mostly built on two-stage frameworks or character-based methods, which suffer from either Non-Maximum Suppression (NMS), Region-of-Interest (RoI) operations, or character-level annotations. In this paper, to address the above problems, we propose a novel fully convolutional Point Gathering Network (PGNet) for reading arbitrarily-shaped text in real-time. The PGNet is a single-shot text spotter, where the pixel-level character classification map is learned with proposed PG-CTC loss avoiding the usage of character-level annotations. With a PG-CTC decoder, we gather high-level character classification vectors from two-dimensional space and decode them into text symbols without NMS and RoI operations involved, which guarantees high efficiency. Additionally, reasoning the relations between each character and its neighbors, a graph refinement module (GRM) is proposed to optimize the coarse recognition and improve the end-to-end performance. Experiments prove that the proposed method achieves competitive accuracy, meanwhile significantly improving the running speed. In particular, in Total-Text, it runs at 46.7 FPS, surpassing the previous spotters with a large margin.

cs.CV↗

arXiv2020

Calibrated Intervention and Containment of the COVID-19 Pandemic

Within a short period of time, COVID-19 grew into a world-wide pandemic. Transmission by pre-symptomatic and asymptomatic viral carriers rendered intervention and containment of the disease extremely challenging. Based on reported infection case studies, we construct an epidemiological model that focuses on transmission around the symptom onset. The model is calibrated against incubation period and pairwise transmission statistics during the initial outbreaks of the pandemic outside Wuhan with minimal non-pharmaceutical interventions. Mathematical treatment of the model yields explicit expressions for the size of latent and pre-symptomatic subpopulations during the exponential growth phase, with the local epidemic growth rate as input. We then explore reduction of the basic reproduction number R_0 through specific disease control measures such as contact tracing, testing, social distancing, wearing masks and sheltering in place. When these measures are implemented in combination, their effects on R_0 multiply. We also compare our model behaviour to the first wave of the COVID-19 spreading in various affected regions and highlight generic and less generic features of the pandemic development.

q-bio.PE↗

arXiv2020

The first cohomology, derivations and the reductivity of a (meromorphic open-string) vertex algebra

We give a criterion for the complete reducibility of modules satisfying a composability condition for a meromorphic open-string vertex algebra $V$ using the first cohomology of the algebra. For a $V$-bimodule $M$, let $\hat{H}^{1}_{\infty}(V, M)$ be the first cohomology of $V$ with the coefficients in $M$. Let $\hat{Z}^{1}_{\infty}(V, M)$ be the subspace of $\hat{H}^{1}_{\infty}(V, M)$ canonically isomorphic to the space of derivations obtained from the zero mode of the right vertex operators of weight $1$ elements such that the difference between the skew-symmetric opposite action of the left action and the right action on these elements are Laurent polynomials in the variable. If $\hat{H}^{1}_{\infty}(V, M)= \hat{Z}^{1}_{\infty}(V, M)$ for every $\Z$-graded $V$-bimodule $M$, then every left $V$-module satisfying a composability condition is completely reducible. In particular, since a lower-bounded $\Z$-graded vertex algebra $V$ is a special meromorphic open-string vertex algebra and left $V$-modules are in fact what has been called generalized $V$-modules with lower-bounded weights (or lower-bounded generalized $V$-modules), this result provides a cohomological criterion for the complete reducibility of lower-bounded generalized modules for such a vertex algebra. We conjecture that the converse of the main theorem above is also true. We also prove that when a grading-restricted vertex algebra $V$ contains a subalgebra satisfying some familiar conditions, the composability condition for grading-restricted generalized $V$-modules always holds and we need $\hat{H}^{1}_{\infty}(V, M)= \hat{Z}^{1}_{\infty}(V, M)$ only for every $\Z$-graded $V$-bimodule $M$ generated by a grading-restricted subspace in our complete reducibility theorem.

math.QA↗