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Fang Li

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Published work

55 published item(s)

preprint2026arXiv

SpaAct: Spatially-Activated Transition Learning with Curriculum Adaptation for Vision-Language Navigation

Vision-and-Language Navigation (VLN) aims to enable an embodied agent to follow natural-language instructions and navigate to a target location in unseen 3D environments. We argue that adapting VLMs to VLN requires endowing them with two complementary capabilities for acquiring such awareness, namely backward action reasoning (why) and forward transition prediction~(how). Based on this insight, we propose SpaAct, a simple yet effective training framework that activates the dynamic spatial awareness in VLMs. Specifically, SpaAct introduces two spatial activation tasks: Action Retrospection, which asks the model to infer the executed action sequence from visual transitions, and Future Frame Selection, which forces the model to predict the visual transitions conditioned on history and action. These two objectives provide lightweight supervision on both backward action reasoning and forward transition prediction, encouraging the model to build dynamic spatial awareness in a VLM-friendly way. To further stabilize adaptation, we design TriPA, a Tri-factor Progressive Adaptive curriculum learning method that organizes training samples from easy to hard, allowing the model to gradually acquire navigation skills from basic locomotion to long-horizon reasoning. Experiments on standard VLN-CE benchmarks show that SpaAct consistently improves VLM-based navigation and achieves state-of-the-art performance. We will release the code and models to support future research.

preprint2022arXiv

Domain-specific Learning of Multi-scale Facial Dynamics for Apparent Personality Traits Prediction

Human personality decides various aspects of their daily life and working behaviors. Since personality traits are relatively stable over time and unique for each subject, previous approaches frequently infer personality from a single frame or short-term behaviors. Moreover, most of them failed to specifically extract person-specific and unique cues for personality recognition. In this paper, we propose a novel video-based automatic personality traits recognition approach which consists of: (1) a \textbf{domain-specific facial behavior modelling} module that extracts personality-related multi-scale short-term human facial behavior features; (2) a \textbf{long-term behavior modelling} module that summarizes all short-term features of a video as a long-term/video-level personality representation and (3) a \textbf{multi-task personality traits prediction module} that models underlying relationship among all traits and jointly predict them based on the video-level personality representation. We conducted the experiments on ChaLearn First Impression dataset, and our approach achieved comparable results to the state-of-the-art. Importantly, we show that all three proposed modules brought important benefits for personality recognition.

preprint2022arXiv

Large-Scale Simulation of Quantum Computational Chemistry on a New Sunway Supercomputer

Quantum computational chemistry (QCC) is the use of quantum computers to solve problems in computational quantum chemistry. We develop a high performance variational quantum eigensolver (VQE) simulator for simulating quantum computational chemistry problems on a new Sunway supercomputer. The major innovations include: (1) a Matrix Product State (MPS) based VQE simulator to reduce the amount of memory needed and increase the simulation efficiency; (2) a combination of the Density Matrix Embedding Theory with the MPS-based VQE simulator to further extend the simulation range; (3) A three-level parallelization scheme to scale up to 20 million cores; (4) Usage of the Julia script language as the main programming language, which both makes the programming easier and enables cutting edge performance as native C or Fortran; (5) Study of real chemistry systems based on the VQE simulator, achieving nearly linearly strong and weak scaling. Our simulation demonstrates the power of VQE for large quantum chemistry systems, thus paves the way for large-scale VQE experiments on near-term quantum computers.

preprint2022arXiv

Mixed-UNet: Refined Class Activation Mapping for Weakly-Supervised Semantic Segmentation with Multi-scale Inference

Deep learning techniques have shown great potential in medical image processing, particularly through accurate and reliable image segmentation on magnetic resonance imaging (MRI) scans or computed tomography (CT) scans, which allow the localization and diagnosis of lesions. However, training these segmentation models requires a large number of manually annotated pixel-level labels, which are time-consuming and labor-intensive, in contrast to image-level labels that are easier to obtain. It is imperative to resolve this problem through weakly-supervised semantic segmentation models using image-level labels as supervision since it can significantly reduce human annotation efforts. Most of the advanced solutions exploit class activation mapping (CAM). However, the original CAMs rarely capture the precise boundaries of lesions. In this study, we propose the strategy of multi-scale inference to refine CAMs by reducing the detail loss in single-scale reasoning. For segmentation, we develop a novel model named Mixed-UNet, which has two parallel branches in the decoding phase. The results can be obtained after fusing the extracted features from two branches. We evaluate the designed Mixed-UNet against several prevalent deep learning-based segmentation approaches on our dataset collected from the local hospital and public datasets. The validation results demonstrate that our model surpasses available methods under the same supervision level in the segmentation of various lesions from brain imaging.

preprint2022arXiv

Optimisation of total population in logistic model with nonlocal dispersals and heterogeneous environments

In this paper, we investigate the issue of maximizing the total equilibrium population with respect to resources distribution m(x) and diffusion rates d under the prescribed total amount of resources in a logistic model with nonlocal dispersals. Among other things, we show that for $d\ge1$, there exist $C_0, C_1>0$, depending on the $\|m\|_{L^1}$ only, such that $$C_0\sqrt{d}<\mbox{supremum~ of~ total~ population}<C_1\sqrt{d}.$$ However, when replaced by random diffusion, a conjecture, proposed by Ni and justified in [3], indicates that in the one-dimensional case, supremum of total population$=3\|m\|_{L^1}$. This reflects serious discrepancies between models with local and nonlocal dispersal strategies.

preprint2022arXiv

Some elementary properties of Laurent phenomenon algebras

Let $Σ$ be Laurent phenomenon (LP) seed of rank $n$, $\mathcal{A}(Σ)$, $\mathcal{U}(Σ)$ and $\mathcal{L}(Σ)$ be its corresponding Laurent phenomenon algebra, upper bound and lower bound respectively. We prove that each seed of $\mathcal{A}(Σ)$ is uniquely defined by its cluster, and any two seeds of $\mathcal{A}(Σ)$ with $n-1$ common cluster variables are connected with each other by one step of mutation. The method in this paper also works for (totally sign-skew-symmetric) cluster algebras. Moreover, we show that $\mathcal{U}(Σ)$ is invariant under seed mutations when each exchange polynomials coincides with its exchange Laurent polynomials of $Σ$. Besides, we obtain the standard monomial bases of $\mathcal{L}(Σ)$. We also prove that $\mathcal{U}(Σ)$ coincides with $\mathcal{L}(Σ)$ under certain conditions.

preprint2020arXiv

Extreme-Scale Density Functional Theory High Performance Computing of DGDFT for Tens of Thousands of Atoms using Millions of Cores on Sunway TaihuLight

High performance computing (HPC) is a powerful tool to accelerate the Kohn-Sham density functional theory (KS-DFT) calculations on modern heterogeneous supercomputers. Here, we describe a massively extreme-scale parallel and portable implementation of discontinuous Galerkin density functional theory (DGDFT) method on the Sunway TaihuLight supercomputer. The DGDFT method uses the adaptive local basis (ALB) functions generated on-the-fly during the self-consistent field (SCF) iteration to solve the KS equations with the high precision comparable to that of plane-wave basis set. In particular, the DGDFT method adopts a two-level parallelization strategy that makes use of different types of data distribution, task scheduling, and data communication schemes, and combines with the feature of master-slave multi-thread heterogeneous parallelism of SW26010 processor, resulting in extreme-scale HPC KS-DFT calculations on the Sunway TaihuLight supercomputer. We show that the DGDFT method can scale up to 8,519,680 processing cores (131,072 core groups) on the Sunway TaihuLight supercomputer for investigating the electronic structures of two-dimensional (2D) metallic graphene systems containing tens of thousands of carbon atoms.

preprint2020arXiv

On inner Poisson structures of a quantum cluster algebra without coefficients

The main aim of this article is to characterize inner Poisson structure on a quantum cluster algebra without coefficients. Mainly, we prove that inner Poisson structure on a quantum cluster algebra without coefficients is always a standard Poisson structure. In order to relate with compatible Poisson structure, we introduce the concept of so-called locally inner Poisson structure on a quantum cluster algebra and then show it is equivalent to locally standard Poisson structure in the case without coefficients. Based on the result from \cite{LP} we obtain finally the equivalence between locally inner Poisson structure and compatible Poisson structure in this case.

preprint2020arXiv

On maximal green sequences in abelian length categories

In this article, we study the relationship among maximal green sequences, complete forward hom-orthogonal sequences and stability functions in abelian length categories. Mainly, we firstly give a one-to-one correspondence between maximal green sequences and complete forward hom-orthogonal sequences via mutual constructions, and then prove that a maximal green sequence can be induced by a central charge if and only if it satisfies crossing inequalities. As applications, we show that crossing inequalities can be computed by $c$-vectors for finite dimensional algebras; finally, we give the Rotation Lemma for finite dimensional Jacobian algebras.

preprint2020arXiv

Periodicities in cluster algebras and cluster automorphism groups

In this paper, we study the relations between groups related to cluster automorphism groups which are defined by Assem, Schiffler and Shamchenko in \cite{ASS}. We establish the relationship among (strict) direct cluster automorphism groups and those groups consisting of periodicities of respectively labeled seeds and exchange matrices in the language of short exact sequences. As an application, we characterize automorphism-finite cluster algebras in the cases with bipartite seeds or finite mutation type. Finally, we study the relation between the groups $\mathrm{Aut}\mathcal{A}$ and $\mathrm{Aut}_{M_n}S$ and give the negative answer via counter-examples to King and Pressland's a problem in \cite{KP}.

preprint2020arXiv

Poisson structure and second quantization of quantum cluster algebras

Motivated by the phenomenon that compatible Poisson structures on a cluster algebra play a key role on its quantization (that is, quantum cluster algebra), we introduce the second quantization of a quantum cluster algebra, which means the correspondence between compatible Poisson structures of the quantum cluster algebra and its secondly quantized cluster algebras. Based on this observation, we find that a quantum cluster algebra possesses dual quantum cluster algebras such that their second quantization is essentially the same. As an example, we give the secondly quantized cluster algebra $A_{p,q}(SL(2))$ of $Fun_{\mathbb C}(SL_{q}(2))$ in \S5.2.1 and show that it is a non-trivial second quantization, which may be realized as a parallel supplement to two parameters quantization of the general quantum group. Furthermore, we obtain a class of quantum cluster algebras with coefficients which possess a non-trivial second quantization. Its one special kind is quantum cluster algebras with almost principal coefficients with an additional condition. Finally, we prove that the compatible Poisson structures of a quantum cluster algebra without coefficients is always a locally standard Poisson structure. Following this, it is shown that the second quantization of a quantum cluster algebra without coefficients is in fact trivial.

preprint2020arXiv

Semi-wave and spreading speed of the nonlocal Fisher-KPP equation with free boundaries

In Cao, Du, Li and Li [8], a nonlocal diffusion model with free boundaries extending the local diffusion model of Du and Lin [12] was introduced and studied. For Fisher-KPP type nonlinearities, its long-time dynamical behaviour is shown to follow a spreading-vanishing dichotomy. However, when spreading happens, the question of spreading speed was left open in [8]. In this paper we obtain a rather complete answer to this question. We find a condition on the kernel function such that spreading grows linearly in time exactly when this condition holds, which is achieved by completely solving the associated semi-wave problem that determines this linear speed; when the kernel function violates this condition, we show that accelerating spreading happens.

preprint2020arXiv

Zero-Shot Recognition through Image-Guided Semantic Classification

We present a new embedding-based framework for zero-shot learning (ZSL). Most embedding-based methods aim to learn the correspondence between an image classifier (visual representation) and its class prototype (semantic representation) for each class. Motivated by the binary relevance method for multi-label classification, we propose to inversely learn the mapping between an image and a semantic classifier. Given an input image, the proposed Image-Guided Semantic Classification (IGSC) method creates a label classifier, being applied to all label embeddings to determine whether a label belongs to the input image. Therefore, semantic classifiers are image-adaptive and are generated during inference. IGSC is conceptually simple and can be realized by a slight enhancement of an existing deep architecture for classification; yet it is effective and outperforms state-of-the-art embedding-based generalized ZSL approaches on standard benchmarks.

preprint2018arXiv

The enough $g$-pairs property and denominator vectors of cluster algebras

In this paper, we introduce the enough $g$-pairs property for a principal coefficients cluster algebra, which can be understood as a strong version of the sign-coherence of the $G$-matrices. Then we prove that any skew-symmetrizable principal coefficients cluster algebra has the enough $g$-pairs property. As an application, we prove the positivity of denominator vectors for any skew-symmetrizable cluster algebra. In fact, we give complete answers to some long standing conjectures on denominator vectors of cluster variables (see Conjecture 1.1 below), which are proposed by Fomin and Zelevinsky in [Compos. Math. 143(2007), 112-164]. In addition, we prove that the seeds whose clusters contain particular cluster variables form a connected subgraph of the exchange graph of this cluster algebra. Lastly, a criterion to distinguish whether particular cluster variables belong to one common cluster is given.

preprint2017arXiv

A conjecture on $C$-matrices of cluster algebras

For a skew-symmetrizable cluster algebra $\mathcal A_{t_0}$ with principal coefficients at $t_0$, we prove that each seed $Σ_t$ of $\mathcal A_{t_0}$ is uniquely determined by its {\bf C-matrix}, which was proposed by Fomin and Zelevinsky in \cite{FZ3} as a conjecture. Our proof is based on the fact that the positivity of cluster variables and sign-coherence of $c$-vectors hold for $\mathcal A_{t_0}$, which was actually verified in \cite{GHKK}. More discussion is given in the sign-skew-symmetric case so as to obtain a conclusion as weak version of the conjecture in this general case.

preprint2016arXiv

A Multiphase Image Segmentation Based on Fuzzy Membership Functions and L1-norm Fidelity

In this paper, we propose a variational multiphase image segmentation model based on fuzzy membership functions and L1-norm fidelity. Then we apply the alternating direction method of multipliers to solve an equivalent problem. All the subproblems can be solved efficiently. Specifically, we propose a fast method to calculate the fuzzy median. Experimental results and comparisons show that the L1-norm based method is more robust to outliers such as impulse noise and keeps better contrast than its L2-norm counterpart. Theoretically, we prove the existence of the minimizer and analyze the convergence of the algorithm.

preprint2016arXiv

Global and exponential attractors of the three dimensional viscous primitive equations of large-scale moist atmosphere

This paper is concerned with the long-time behavior of solutions for the three dimensional viscous primitive equations of large-scale moist atmosphere. We prove the existence of a global attractor for the three dimensional viscous primitive equations of large-scale moist atmosphere by asymptotic a priori estimate and construct an exponential attractor by using the smoothing property of the semigroup generated by the three dimensional viscous primitive equations of large-scale moist atmosphere. As a byproduct, we obtain the fractal dimension of the global attractor for the semigroup generated by the three dimensional viscous primitive equations of large-scale moist atmosphere is finite, which is in consistent with the results in \cite{jn2,jn1}.

preprint2016arXiv

On Structure of cluster algebras of geometric type I: In view of sub-seeds and seed homomorphisms

Our motivation is to build a systematic method in order to investigate the structure of cluster algebras of geometric type. The method is given through the notion of mixing-type sub-seeds, the theory of seed homomorphisms and the view-point of gluing of seeds. As an application, for (rooted) cluster algebras, we completely classify rooted cluster subalgebras and characterize rooted cluster quotient algebras in detail. Also, we build the relationship between the categorification of a rooted cluster algebra and that of its rooted cluster subalgebras. Note that cluster algebras of geometric type studied here are of the sign-skew-symmetric case.

preprint2016arXiv

On Structure of cluster algebras of geometric type, II: Green's equivalences and paunched surfaces

Following our previous work [18], we introduce the notions of partial seed homomorphisms and partial ideal rooted cluster morphisms. Related to the theory of Green's equivalences, the isomorphism classes of sub-rooted cluster algebras of a rooted cluster algebra are corresponded one-by-one to the regular $\mathcal D$-classes of the semigroup consisting of partial seed endomorphisms of the initial seed. Moreover, for a rooted cluster algebra from a Riemannian surface, they are also corresponded to the isomorphism classes of the so-called paunched surfaces.

preprint2016arXiv

Unfolding of acyclic sign-skew-symmetric cluster algebras and applications to positivity and $F$-polynomials

In this paper, we build the unfolding approach from acyclic sign-skew-symmetric matrices of finite rank to skew-symmetric matrices of infinite rank, which can be regard as an improvement of that in the skew-symmetrizable case. Using this approach, we give a positive answer to the problem by Berenstein, Fomin and Zelevinsky in \cite{fz3} which asks whether an acyclic sign-skew-symmetric matrix is always totally sign-skew-symmetric. As applications, the positivity for cluster algebras in acyclic sign-skew-symmetric case is given; further, the $F$-polynomials of cluster algebras are proved to have constant term 1 in acyclic sign-skew-symmetric case.

preprint2015arXiv

600-T Magnetic Fields due to Cold Electron Flow in a simple Cu-Coil irradiated by High Power Laser pulses

A new simple mechanism due to cold electron flow to produce strong magnetic field is proposed. A 600-T strong magnetic field is generated in the free space at the laser intensity of 5.7x10^15 Wcm^-2. Theoretical analysis indicates that the magnetic field strength is proportional to laser intensity. Such a strong magnetic field offers a new experimental test bed to study laser-plasma physics, in particular, fast-ignition laser fusion research and laboratory astrophysics.

preprint2015arXiv

Determining phase-space properties of the IHEP RFQ output beam using the RMS beam widths from wire-scanners

A beam line is built after the IHEP RFQ for halo study. To determine transverse emittance and ellipse parameters of the RFQ output beam, beam size data obtained from the first two of 14 wire scanners are employed. By using the transfer matrix method and the least square method, a set of linear equations were set up and solved. The solutions were then applied as initial beam parameters in multi-particle simulations to check the method of calculation. It is shown that difference between the simulated RMS beam size and the measured one at the measurement location is less than 7%, which is acceptable in our experiments.

preprint2015arXiv

Diffusive KPP Equations with Free Boundaries in Time Almost Periodic Environments: I. Spreading and Vanishing Dichotomy

In this series of papers, we investigate the spreading and vanishing dynamics of time almost periodic diffusive KPP equations with free boundaries. Such equations are used to characterize the spreading of a new species in time almost periodic environments with free boundaries representing the spreading fronts. In this first part, we show that a spreading-vanishing dichotomy occurs for such free boundary problems, that is, the species either successfully spreads to all the new environment and stabilizes at a time almost periodic positive solution, or it fails to establish and dies out eventually. The results of this part extend the existing results on spreading-vanishing dichotomy for time and space independent, or time periodic and space independent, or time independent and space periodic diffusive KPP equations with free boundaries. The extension is nontrivial and is ever done for the first time.

preprint2015arXiv

Diffusive KPP Equations with Free Boundaries in Time Almost Periodic Environments: II. Spreading Speeds and Semi-Wave

In this series of papers, we investigate the spreading and vanishing dynamics of time almost periodic diffusive KPP equations with free boundaries. Such equations are used to characterize the spreading of a new species in time almost periodic environments with free boundaries representing the spreading fronts. In the first part of the series, we showed that a spreading-vanishing dichotomy occurs for such free boundary problems (see [16]). In this second part of the series, we investigate the spreading speeds of such free boundary problems in the case that the spreading occurs. We first prove the existence of a unique time almost periodic semi-wave solution associated to such a free boundary problem. Using the semi-wave solution, we then prove that the free boundary problem has a unique spreading speed.

preprint2015arXiv

Experimental generation of 8.4 dB entangled state with an optical cavity involving a wedged type-II nonlinear crystal

Entangled state of light is one of the essential quantum resources in quantum information science and technology. Especially, when the fundamental principle experiments have been achieved in labs and the applications of continuous variable quantum information in the real world are considered, it is crucial to design and construct the generation devices of entangled states with high entanglement and compact configuration. We have designed and built an efficient and compact light source of entangled state, which is a non-degenerate optical parametric amplifier (NOPA) with the triple resonance of the pump and two subharmonic modes. A wedged type-II KTP crystal inside the NOPA is used for implementing frequency-down-conversion of the pump field to generate the optical entangled state and achieving the dispersion compensation between the pump and the subharmonic waves. The EPR entangled state of light with quantum correlations of 8.4 dB for both amplitude and phase quadratures are experimentally produced by a single NOPA under the pump power of 75 mW.

preprint2015arXiv

Global dynamics of competition models with nonlocal dispersals I: Symmetric kernels

In this paper, the global dynamics of two-species Lotka-Volterra competition models with nonlocal dispersals is studied. Under the assumption that dispersal kernels are symmetric, we prove that except for very special situations, local stability of semi-trivial steady states implies global stability, while when both semi-trivial steady states are locally unstable, the positive steady state exists and is globally stable. Moreover, our results cover the case that competition coefficients are location-dependent and dispersal strategies are mixture of local and nonlocal dispersals.

preprint2015arXiv

On Mathematical Symbols in China

When studying the history of mathematical symbols, one finds that the development of mathematical symbols in China is a significant piece of Chinese history; however, between the beginning of mathematics and modern day mathematics in China, there exists a long blank period. Let us focus on the development of Chinese mathematical symbols, and find out the significance of their origin, evolution, rise and fall within Chinese mathematics.

preprint2015arXiv

Representations of Frobenius-type triangular matrix algebras

The aim of this paper is mainly to build a new representation-theoretic realization of finite root systems through the so-called Frobenius-type triangular matrix algebras by the method of reflection functors over any field. Finally, we give an analog of APR-tilting module for this class of algebras. The major conclusions contains the known results as special cases, e.g. that for path algebras over an algebraically closed field and for path algebras with relations from symmetrizable cartan matrices. Meanwhile, it means the corresponding results for some other important classes of algebras, that is, the path algebras of quivers over Frobenius algebras and the generalized path algebras endowed by Frobenius algebras at vertices.

preprint2014arXiv

Far-field Imaging beyond the Diffraction Limit Using a Single Radar

Far-field imaging beyond the diffraction limit is a long sought-after goal in various imaging applications, which requires usually an array of antennas or mechanical scanning. Here, we present an alternative and novel concept for this challenging problem: a single radar system consisting of a spatial-temporal resonant aperture antenna (referred to as the slavery antenna) and a broadband horn antenna (termed the master antenna). We theoretically demonstrate that such resonant aperture antenna is responsible for converting parts of the evanescent waves into propagating waves, and delivering them to the far-field. We also demonstrate that there are three basic requirements on the proposed subwavelength imaging strategy: the strong spatial-temporal dispersive aperture, the near-field coupling, and the temporal (or broadband) illumination. Such imaging concept of a single radar provides unique ability to produce real-time data when an object is illuminated by broadband electromagnetic waves, which lifts up the harsh requirements such as near-field scanning, mechanical scanning or antenna arrays remarkably. We expect that this imaging methodology will make breakthroughs in super-resolution imaging in the microwave, terahertz, optical, and ultrasound regimes.

preprint2014arXiv

Far-field subwavelength imaging from a single broadband antenna in combined with strongly disordered medium

The far-field subwavlength imaging is a challenging issue. In this letter we demonstrate numerically that the far-field subwavelength imaging of weakly scattering objects can be obtained by processing the data acquired by a single antenna, which benefits from the use of the strongly disordered medium. A mathematical model has been proposed for solving such problem based on the idea of sparse reconstruction. Moreover, this study leads to an important conclusion that the strongly disordered medium can serves as an efficient apparatus for the single-antenna compressive measurement, which shifts the complexity of devising compressive sensing (CS) hardware from the design, fabrication and electronic control. The proposed method and associated results can find applications in several imaging disciplines, such as optics, THz, RF or ultrasound imaging.

preprint2014arXiv

Finite time blowup of the stochastic shadow Gierer-Meinhardt System

By choosing some special (random) initial data, we prove that with probability $1$, the stochastic shadow Gierer-Meinhardt system blows up pointwisely in finite time. We also give a (random) upper bound for the blowup time and some estimates about this bound. By increasing the amplitude of the initial data, we can get the blowup in any short time with positive probability.

preprint2014arXiv

Genuses of cluster quivers of finite mutation type

In this paper, we study the distribution of the genuses of cluster quivers of finite mutation type. First, we prove that in the $11$ exceptional cases, the distribution of genuses is $0$ or $1$. Next, we consider the relationship between the genus of an oriented surface and that of cluster quivers from this surface. It is verified that the genus of an oriented surface is an upper bound for the genuses of cluster quivers from this surface. Furthermore, for any non-negative integer $n$ and a closed oriented surface of genus $n$, we show that there always exist a set of punctures and a triangulation of this surface such that the corresponding cluster quiver from this triangulation is exactly of genus $n$.

preprint2014arXiv

Modulation and natural valued quiver of an algebra

The concept of modulation is generalized to pseudo-modulation and its subclasses including pre-modulation, generalized modulation and regular modulation. The motivation is to define the valued analogue of natural quiver, called {\em natural valued quiver}, of an artinian algebra so as to correspond to its valued Ext-quiver when this algebra is not $k$-splitting over the field $k$. Moreover, we illustrate the relation between the valued Ext-quiver and the natural valued quiver. The interesting fact we find is that the representation categories of a pseudo-modulation and of a pre-modulation are equivalent respectively to that of a tensor algebra of $\mathcal A$-path type and of a generalized path algebra. Their examples are given respectively from two kinds of artinian hereditary algebras. Furthermore, the isomorphism theorem is given for normal generalized path algebras with finite (acyclic) quivers and normal pre-modulations. Four examples of pseudo-modulations are given: (i) group species in mutation theory as a semi-normal generalized modulation; (ii) viewing a path algebra with loops as a pre-modulation with valued quiver which has not loops; (iii) differential pseudo-modulation and its relation with differential tensor algebras; (iv) a pseudo-modulation is considered as a free graded category.

preprint2014arXiv

On representation rings in the context of monoidal categories

In general, representation rings are well-known as Green rings from module categories of Hopf algebras. In this paper, we study Green rings in the context of monoidal categories such that representations of Hopf algebras can be investigated through Green rings of various levels from module categories to derived categories in the unified view-point. Firstly, as analogue of representation rings of Hopf algebras, we set up the so-called Green rings of monoidal categories, and then list some such categories including module categories, complex categories, homotopy categories, derived categories and (derived) shift categories, etc. and the relationship among their corresponding Green rings. The main part of this paper is to characterize representation rings and derived rings of a class of inite dimensional Hopf algebras constructed from the Nakayama truncated algebras $KZ_{n}/J^{d}$ with certain constraints. For the representation ring $r(KZ_{n}/J^{d})$, we completely determine its generators and the relations of generators via the method of Pascal triangle. For the derived ring $dr(KZ_{n}/J^{2})$(i.e., $d=2$), we determine its generators and give the relations of generators. In these two aspects, the polynomial characterizations of the representation ring and the derived ring are both given.

preprint2014arXiv

On the first Hochschild cohomology of admissible algebras

Our aim in this paper is to investigate the first Hochschild cohomology of {\em admissible algebras} which can be seen as a generalization of basic algebras. For this purpose, we study differential operators on an admissible algebra. Firstly, differential operators from a path algebra to its quotient algebra as an admissible algebra are discussed. Based on this discussion, the first cohomology with admissible algebras as coefficient modules is characterized, including their dimension formula. Besides, for planar quivers, the $k$-linear bases of the first cohomology of acyclic complete monomial algebras and acyclic truncated quiver algebras are constructed over the field $k$ of characteristic $0$.

preprint2014arXiv

Positive definite matrices in the view-points of planar networks and cluster subalgebras

As an improvement of the combinatorial realization of totally positive matrices via the essential positive weightings of certain planar network by S.Fomin and A.Zelevisky \cite{[4]}, in this paper, we give the test method of positive definite matrices via the planar networks and the so-called cluster subalgebra respectively, introduced here originally. This work firstly gives a combinatorial realization of all matrices through planar network, and then sets up a test method for positive definite matrices by $LDU$-decompositions and the horizontal weightings of all lines in their planar networks. On the other hand, mainly the relationship is built between positive definite matrices and cluster subalgebras.

preprint2014arXiv

Representations of skew group algebras induced from isomorphically invariant modules over path algebras

Suppose that $Q$ is a connected quiver without oriented cycles and $σ$ is an automorphism of $Q$. Let $k$ be an algebraically closed field whose characteristic does not divide the order of the cyclic group $\langleσ\rangle$. The aim of this paper is to investigate the relationship between indecomposable $kQ$-modules and indecomposable $kQ\#k\langleσ\rangle$-modules. It has been shown by Hubery that any $kQ\#k\langleσ\rangle$-module is an isomorphically invariant $kQ$-module, i.e., ii-module (in this paper, we call it $\langleσ\rangle$-equivalent $kQ$-module), and conversely any $\langleσ\rangle$-equivalent $kQ$-module induces a $kQ\#k\langleσ\rangle$-module. In this paper, the authors prove that a $kQ\#k\langleσ\rangle$-module is indecomposable if and only if it is an indecomposable $\langleσ\rangle$-equivalent $kQ$-module. Namely, a method is given in order to induce all indecomposable $kQ\#k\langleσ\rangle$-modules from all indecomposable $\langleσ\rangle$-equivalent $kQ$-modules. The number of non-isomorphic indecomposable $kQ\#k\langleσ\rangle$-modules induced from the same indecomposable $\langleσ\rangle$-equivalent $kQ$-module is given. In particular, the authors give the relationship between indecomposable $kQ\#k\langleσ\rangle$-modules and indecomposable $kQ$-modules in the cases of indecomposable simple, projective and injective modules.

preprint2014arXiv

Status of CSNS H- ion source

A new H^- ion source has been installed successfully and will be used to serve the China Spallation Neutron Source (CSNS). In this paper, we report various components of the ion source, including discharge chamber, temperature, cooling system, extraction electrodes, analyzing magnet, remote control system and so on. Compared to the previous experimental ion source, some improvements have been made to make the ion source more compact and convenient. In the present arrangement, the Penning field is generated by a pair of pole tip extensions on the analyzing magnet instead of by a separate circuit. For the remote control system, F3RP61-2L is applied to the accelerator online control system for the first time. In the running of the ion source, a stable pulse H- beam with a current of 50 mA at an energy of 50 keV is produced. The extraction frequency and pulse width is 25 Hz and 500microsecond, respectively. Furthermore, an emittance scanner has been installed and measurements are in progress.

preprint2014arXiv

Subwavelength imaging of sparse broadband sources surrounded by an open disordered medium from a single antenna

In this letter we study the subwavelength imaging of sparse broadband sources inside a disordered medium by processing the data acquired by a single antenna. A mathematical model has been developed for solving such problem based on the idea of sparse reconstruction. We show that the strongly disordered medium can serves as an efficient apparatus for compressive measurement, which shifts the complexity of devising compressive sensing (CS) hardware from the design, fabrication and electronic control. The proposed method and associated results can find applications in several imaging disciplines, such as optics, THz, RF or ultrasound imaging.

preprint2014arXiv

The natural quiver of an artinian algebra

The motivation of this paper is to study the natural quiver of an artinian algebra, a new kind of quivers, as a tool independing upon the associated basic algebra. In \cite{Li}, the notion of the natural quiver of an artinian algebra was introduced and then was used to generalize the Gabriel theorem for non-basic artinian algebras splitting over radicals and non-basic finite dimensional algebras with 2-nilpotent radicals via pseudo path algebras and generalized path algebras respectively. In this paper, firstly we consider the relationship between the natural quiver and the ordinary quiver of a finite dimensional algebra. Secondly, the generalized Gabriel theorem is obtained for radical-graded artinian algebras. Moreover, Gabriel-type algebras are introduced to outline those artinian algebras satisfying the generalized Gabriel theorem here and in \cite{Li}. For such algebras, the uniqueness of the related generalized path algebra and quiver holds up to isomorphism in the case when the ideal is admissible. For an artinian algebra, there are two basic algebras, the first is that associated to the algebra itself; the second is that associated to the correspondent generalized path algebra. In the final part, it is shown that for a Gabriel-type artinian algebra, the first basic algebra is a quotient of the second basic algebra. In the end, we give an example of a skew group algebra in which the relation between the natural quiver and the ordinary quiver is discussed.

preprint2014arXiv

Theory of the far-field imaging beyond the Rayleigh limit based on the super-resonant lens

Essentially, the idea of improving the resolution of a given imaging system is to enhance its information capacity represented usually by the temporal-bandwidth (or, spatial-spectrum) product. This letter introduces the concept of super-resonant lens, and demonstrates theoretically that the information capacity of a far-field imaging system can be efficiently driven up when three basic requirements are satisfied: the super-resonance, the near-field coupling between imaged objects and the used super-resonant lens, and the broadband illumination, which leads to the subwavelength image of imaged objects from far-field measurements. Furthermore, a single-view imaging scheme is proposed and examined for the far-field imaging beyond the diffraction limit. This new approach will be a breakthrough in nanolithography, detection, sensing or sub-wavelength imaging in the near future.

preprint2013arXiv

A Basis of the $q$-Schur Module

In this paper, we construct the $q$-Schur modules as left principle ideals of the cyclotomic $q$-Schur algebras, and prove that they are isomorphic to those cell modules defined in \cite{8} and \cite{15} at any level $r$. Then we prove that these $q$-Schur modules are free modules and construct their bases. This result gives us new versions of several results about the standard basis and the branching theorem. With the help of such realizations and the new bases, we re-prove the Branch rule of Weyl modules which was first discovered and proved by Wada in \cite{23}.

preprint2013arXiv

Approach to artinian algebras via natural quivers

Given an Artinian algebra $A$ over a field $k$, there are several combinatorial objects associated to $A$. They are the diagram $D_A$ as defined in [DK], the natural quiver $Δ_A$ defined in \cite{Li} (cf. Section 2), and a generalized version of $k$-species $(A/r, r/r^2)$ with $r$ being the Jacobson radical of $A$. When $A$ is splitting over the field $k$, the diagram $D_A$ and the well-known ext-quiver $Γ_A$ are the same. The main objective of this paper is to investigate the relations among these combinatorial objects and in turn to use these relations to give a characterization of the algebra $A$.

preprint2013arXiv

Beat the Rayleigh limit: OAM based super-resolution diffraction tomography

This letter is the first to report that a super-resolution imaging beyond the Rayleigh limit can be achieved by using classical diffraction tomography (DT) extended with orbital angular momentum (OAM), termed as OAM based diffraction tomography (OAM-DT). It is well accepted that the orbital angular momentum (OAM) provides additional electromagnetic degrees of freedom. This concept has been widely applied in science and technology. In this letter we revisit the DT problem extended with OAM, demonstrate theoretically and numerically that there is no physical limits on imaging resolution in principle by the OAM-DT. This super-resolution OAM-DT imaging paradigm, has no requirement for evanescent fields, subtle focusing lens, complicated post-processing, etc., thus provides a new approach to realize the wavefield imaging of universal objects with sub-wavelength resolution.

preprint2013arXiv

Characterization Of Left Artinian Algebras Through Pseudo Path Algebras

In this paper, using pseudo path algebras, we generalize Gabriel's Theorem on elementary algebras to left Artinian algebras over a field $k$ when it is splitting over its radical, in particular, when the dimension of the quotient algebra decided by the $n$'th Hochschild cohomology is less than 2 (for example, $k$ is finite or char$k=0$). Using generalized path algebras, the generalized Gabriel's Theorem is given for finite dimensional algebras with 2-nilpotent radicals which is splitting over its radical. As a tool, the so-called pseudo path algebras are introduced as a new generalization of path algebras, which can cover generalized path algebras (see Fact 2.5). The main result is that (i) for a left Artinian $k$-algebra $A$ and $r=r(A)$ the radical of $A$, when the quotient algebra $A/r$ can be lifted, it holds that $A\cong PSE_k(Δ,\mathcal{A},ρ)$ with $J^{s}\subset<ρ>\subset J$ for some $s$ (Theorem 3.2); (ii) for a finite dimensional $k$-algebra $A$ with $r=r(A)$ 2-nilpotent radical, when the quotient algebra $A/r$ can be lifted, it holds that $A\cong k(Δ,\mathcal{A},ρ)$ with $\widetilde J^{2}\subset<ρ>\subset\widetilde J^{2}+\widetilde J\cap$ \textrm{Ker}$\widetildeφ$ (Theorem 4.3), where $Δ$ is the quiver of $A$ and $ρ$ is a set of relations. Meantime, the uniqueness of the quivers and generalized path algebra/pseudo path algebras satisfying the isomorphism relations is obtained in the case when the ideals generated by the relations are admissible (see Theorem 3.5 and 4.4).

preprint2012arXiv

Structure of Hochschild cohomology of path algebras and differential formulation of Euler's polyhedron formula

This article studies the Lie algebra $Diff(KΓ)$ of derivations on the path algebra $KΓ$ of a quiver $Γ$ and the Lie algebra on the first Hochschild cohomology group $H^1(KΓ)$. We relate these Lie algebras to the algebraic and combinatorial properties of the path algebra. Characterizations of derivations on a path algebra are obtained, leading to a canonical basis of $Diff(KΓ)$ and its Lie algebra properties. Special derivations are associated to the vertices, arrows and faces of a quiver, and the concepts of a connected matrix and boundary matrix are introduced to study the relations among these derivations, concluding that the space of edge derivations is the direct sum of the spaces of the vertex derivations and the face derivations, while the dimensions of the latter spaces are the largest possible. By taking dimensions, this relation among spaces of derivations recovers Euler's polyhedron formula. This relation also leads a combinatorial construction of a canonical basis of the Lie algebra $H^1(KΓ)$, together with a semidirect sum decomposition of $H^1(KΓ)$.

preprint2011arXiv

An ultra-thin waveguide twist constructed using fish-scale metallic wires

This study theoretically and experimentally investigates the transmission properties of a metamaterial slab comprised of two layers of metallic fish-scale structure arrays and a sandwiched dielectric layer. Calculations show that the asymmetric transmission can be tuned by varying the slab thickness, due to evanescent interlayer coupling. The spatial evolution of the local field inside the structure indicates that the slab functions as a perfect polarization transformer at certain frequencies in the manner of a waveguide twist. Measured transmission spectra are in good agreement with calculated results when material dissipation is considered.

preprint2011arXiv

Metallic helix array as a broadband wave plate

This study proposes that a metallic helix array can operate as a highly-transparent broadband wave plate in propagation directions perpendicular to the axis of helices. The functionality arises from a special property of the helix array, namely that the eigenstates of elliptically right-handed and left-handed polarization are dominated by Bragg scattering and local resonance respectively, and can be modulated separately with nearly fixed difference between their wavevectors in a wide frequency range. The wave plate functionality is theoretically and experimentally demonstrated by the transformation of polarized states in a wide frequency range.

preprint2009arXiv

Invisibility Cloaks Modeled by Anisotropic Metamaterials Based on Inductor-capacitor Networks

Based on the transformation optics, a novel transmission-line (TL) approach to realize invisibility cloaking using planar anisotropic metamaterials (MTMs) is proposed. The two-dimensional cylindrical cloaks are modeled based on inductor-capacitor (L-C) MTMs networks. The three elements of the constitutive parameters are all allowed to be spatially inhomogeneous which lead to the full parameter realization of a cylindrical cloak. As an example, a cloak working at VHF band is modeled and its invisibility behavior is demonstrated based on the solution of the node voltage distribution. Due to the non-resonant properties of the L-C elements, the broadband characteristic of the proposed cloaks is also evident.