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Heat transfer in nanocomposite materials has attracted great interest for various applications. Multilayer structures provide an important platform to study interfacial thermal transport and to engineer materials with ultralow thermal conductivity. Here we report on the fabrication and thermal characterization of [h-BN/$L1_0$-FePt]xN multilayers, where hexagonal boron nitride (h-BN) nanosheets (2.5 nm thick) and $L1_0$-FePt layers (6.5 nm thick) alternate periodically. Differential three-omega($3\omega$) measurements reveal an ultralow effective thermal conductivity of $ 0.60 \pm 0.05 W \cdot m^{-1}K^{-1}$ across the multilayer films, and a low thermal boundary conductance (TBC) of $ 67.9 \pm 6.6 MW \cdot m^{-2}K^{-1}$ for the [FePt/h-BN(2.5nm)/FePt] interface at room temperature. We attribute the ultralow thermal conductivity to the weak van der Waals bonding at h-BN/FePt interfaces, which dominates the thermal resistance of the multilayer structure. These findings provide insights into the thermal transport in 2D-material/metal multilayer nanostructures and suggest the [h-BN/FePt] superlattice as a promising material for nanoscale thermal barrier coating. Furthermore, the obtained TBC lays the foundation for analyzing heat transfer in FePt-(h-BN) nanogranular films, a promising magnetic recording media which can potentially provide high thermal gradient for heat-assisted magnetic recording (HAMR). This work advances the understanding of thermal transport in 2D-material/metal nanocomposites and demonstrates interface engineering as an effective approach to achieve materials with ultralow thermal conductivity., Comment: 22 page, 5 figures

Pretrained language models (PLMs) have made significant strides in various natural language processing tasks. However, the lack of interpretability due to their ``black-box'' nature poses challenges for responsible implementation. Although previous studies have attempted to improve interpretability by using, e.g., attention weights in self-attention layers, these weights often lack clarity, readability, and intuitiveness. In this research, we propose a novel approach to interpreting PLMs by employing high-level, meaningful concepts that are easily understandable for humans. For example, we learn the concept of ``Food'' and investigate how it influences the prediction of a model's sentiment towards a restaurant review. We introduce C$^3$M, which combines human-annotated and machine-generated concepts to extract hidden neurons designed to encapsulate semantically meaningful and task-specific concepts. Through empirical evaluations on real-world datasets, we manifest that our approach offers valuable insights to interpret PLM behavior, helps diagnose model failures, and enhances model robustness amidst noisy concept labels.

Baroreflex is critical to maintain the blood pressure homeostasis, and the quantification of the baroreflex regulation function (BRF) can provide guidance for disease diagnosis, treatment and healthcare. Current quantification of the BRF such as baroreflex sensitivity cannot represent the BRF systematically. From the perspective of complex systems, we regard that the BRF is the emergence result of the diverse states and interactions in the physiological mechanisms. Therefore, the three-layer emergence is constructed in this work, which is from the physiological mechanisms to the physiological indexes and then to the BRF. On this basis, since the entropy in statistical physics macroscopically measures the diversity of the system's states, a new index called the PhysioEnt is proposed to represent the BRF and quantify the physical relationships between the BRF and four physiological indexes, baroreflex sensitivity, heart rate, heart rate variability, and systolic blood pressure. Based on the proposed method, some new findings with medical significance are obtained, including the mechanisms that aging and obesity affect the resting-condition BRF are different, and the resting-condition BRFs of men and older people depend more on the physiological processes among organs/tissues. Based on the measurable indexes, the proposed method would support the individualized medicine prospectively., Comment: 25 pages, 7 figures

Electronic liquid-crystal phases are observed in numerous strongly-correlated systems including high-temperature superconductors. However, identifying these exotic phases and understanding their interplay with superconductivity in topological materials remain challenging. Here we employ a cryogenic scanning tunneling microscopy to discover a smectic (stripe) charge order (CO) and a primary pair-density-wave (PDW) in topological monolayer 1T$^\prime$-MoTe$_2$. The two orders are spatially modulated unidirectionally at the same wavevector, but have a marked spatial phase difference of about 2$\pi$/5. Importantly, the primary PDW state features a two-gap superconductivity below the transition temperature of 6.0 K and induces another unique particle-hole-symmetric CO at twice the PDW wavevector. Combining these results and our density functional calculations, we reveal that the two smectic orders are primarily driven by nesting behaviors between electron and hole pockets. Our findings establish monolayer 1T$^\prime$-MoTe$_2$ as a topological paradigm for exploring electronic smecticity, which intertwines with multiple preexisting symmetry-breaking states., Comment: 16 pages, 4 figures, Supplementary materials

Photoassociation of ultracold atoms is a resonant light-assisted collision process, in which two colliding atoms absorb a photon and form an excited molecule. Since the first observation about three decades ago, the photoassociation of ultracold atoms has made a significant impact on the study of ultracold atoms and molecules. Extending the photoassociation of atoms to the photoassociation of atom-molecule pairs or molecule-molecule pairs will offer many new opportunities in the study of precision polyatomic molecular spectroscopy, formation of ultracold polyatomic molecules, and quantum control of molecular collisions and reactions. However, the high density of states and the photoexcitation of the collision complex by the trapping laser make photoassociation into well-defined quantum states of polyatomic molecules extremely difficult. Here we report on the observation of photoassociation resonances in ultracold collisions between $^{23}$Na$^{40}$K molecules and $^{40}$K atoms. We perform photoassociation in a long-wavelength optical dipole trap to form deeply bound triatomic molecules in the electronically excited states. The atom-molecule Feshbach resonance is used to enhance the free-bound Franck-Condon overlap. The photoassociation into well-defined quantum states of excited triatomic molecules is identified by observing resonantly enhanced loss features. These loss features depend on the polarization of the photoassociation lasers, allowing us to assign the rotational quantum numbers. The observation of ultracold atom-molecule photoassociation resonances paves the way toward preparing ground-state triatomic molecules, provides a new high-resolution spectroscopy technique for polyatomic molecules, and is also important to atom-molecule Feshbach resonances., Comment: 8 pages, 4 figures

We investigate the production of hot electrons from the interaction of relativistically intense ($I> 10^{18} W/cm^{2}$) ultra-short (25 fs) laser pulses with sub-wavelength grating target. We measure the hot electron angular distribution and energy spectra for grating target and compare them with those from a planar mirror target. We observe that hot electrons are emitted in a collimated beam along the specular direction of the grating target. From the measured electron energy spectra we see electron temperature for grating is higher than the mirror, suggesting a higher electron yield and hence a stronger coupling with the laser. We performed numerical simulations which are in good agreement with experimental results, offer insights into the acceleration mechanism by resulting electric and magnetic fields. Such collimated fast electron beams have a wide range of applications in applied and fundamental science., Comment: 6 figures

How to identify and segment camouflaged objects from the background is challenging. Inspired by the multi-head self-attention in Transformers, we present a simple masked separable attention (MSA) for camouflaged object detection. We first separate the multi-head self-attention into three parts, which are responsible for distinguishing the camouflaged objects from the background using different mask strategies. Furthermore, we propose to capture high-resolution semantic representations progressively based on a simple top-down decoder with the proposed MSA to attain precise segmentation results. These structures plus a backbone encoder form a new model, dubbed CamoFormer. Extensive experiments show that CamoFormer surpasses all existing state-of-the-art methods on three widely-used camouflaged object detection benchmarks. There are on average around 5% relative improvements over previous methods in terms of S-measure and weighted F-measure.

Equation of state (EOS) for bcc tungsten at 300 K (or 3000 K) up to 1000 GPa (or 300 GPa) was predicted for the first time by solving the partition function via a direct integral approach (DIA) with ab initio calculations of the atoms' interactions. Compared with available experiments under static compressions up to 150 GPa (or 35 GPa) for room temperature (or 1673 K), all the calculated results are within the experimental uncertainty achieved very recently. Furthermore, the same procedure was performed to investigate the shock wave experiments on the EOS up to 400 GPa and 10000 K, and the calculated average pressure deviates the experimental measurements by only 2.0%. These facts suggest that the other calculated results of DIA for the EOS are reliable, and DIA as a universal method without any artificial parameters could be widely applied to predict EOS of various materials under various conditions., Comment: 5 figures, 14 figures

The structural phase behaviors of pure zirconium metal under compressions up to $160$ GPa at room temperature are investigated from the perspective of ensemble theory where the partition function is solved by our recently proposed method with \emph{ab initio} precision. The derived Gibbs free energy is employed as the very criterion to determine phase transitions and the calculated transition pressures of the $\alpha\rightarrow\omega\rightarrow\beta$ are $6.93$ and $24.83$ GPa respectively, the former one of which is so far the only theoretical result agreeing with multiple experimental measurements to our best knowledge. The differences between the obtained parameter-free equation of state and those from latest experiments are less than $1.5\%$ in the whole studied pressure range, and particularly, within $0.7\%$ when the applied pressure exceeds over $40$ GPa, the coincidence of which makes us support the argument that the previously observed anharmonicity-driven isostructural phase transition does not exist in the $\beta$-phase even though the thermal effects at room temperature are confirmed to be nontrivial to the phase stability by our quantitative comparisons with the results at $0$K., Comment: 9 pages, 6 figures

It is a long-time pursuit of computations with \emph{ab initio} precision of thermal contributions to phase behaviors of condensed matters under extreme conditions. In this work, the pressure induced structural phase transitions of crystalline aluminum up to $600$ GPa at room temperature are investigated based on the criterion of Gibbs free energy derived directly from the partition function that formulated in the ensemble theory with the interatomic interactions characterized by density functional theory computations. The transition pressures of the FCC$\rightarrow$HCP$\rightarrow$BCC phase transitions are determined at $194$ and $361$ GPa, the axial ratio of the stable HCP structure is found to be equal to $1.62$ and the discontinuities in the equations of states are confirmed to be associated with $-0.67\%$ and $-0.90\%$ volume changes, which are all in an excellent agreement with the measurements by one of the recent experiments but differ from other experimental observations. Compared with the results obtained by the criterion of enthalpy at $0$K, this work further shows the nontrivial thermal impacts on the structural stability of aluminum under ultrahigh-pressure circumstances even at room temperature., Comment: 11 pages, 5 figures

For realistic crystals, the free energy strictly formulated in ensemble theory can hardly be obtained because of the difficulty in solving the high-dimension integral of the partition function, the dilemma of which makes it even a doubt if the rigorous ensemble theory is applicable to phase transitions of condensed matters. In the present work, the partition function of crystal vanadium under compression up to $320$ GPa at room temperature is solved by an approach developed very recently, and the derived equation of state is in a good agreement with all the experimental measurements, especially the latest one covering the widest pressure range up to $300$ GPa. Furthermore, the derived Gibbs free energy proves the very argument to understand most of the experiments reported in the past decade on the pressure-induced phase transition, and, especially, a novel phase transition sequence concerning three different phases observed very recently and the measured angles of two phases agree with our theoretical results excellently., Comment: 5pages, 5figures

Ideally, accelerator development should be as easy as software development. Several recent design languages/tools are working toward this goal, but actually testing early designs on real applications end-to-end remains prohibitively difficult due to the costs of building specialized compiler and simulator support. We propose a new first-in-class, mostly automated methodology termed "3LA" to enable end-to-end testing of prototype accelerator designs on unmodified source applications. A key contribution of 3LA is the use of a formal software/hardware interface that specifies an accelerator's operations and their semantics. Specifically, we leverage the Instruction-Level Abstraction (ILA) formal specification for accelerators that has been successfully used thus far for accelerator implementation verification. We show how the ILA for accelerators serves as a software/hardware interface, similar to the Instruction Set Architecture (ISA) for processors, that can be used for automated development of compilers and instruction-level simulators. Another key contribution of this work is to show how ILA-based accelerator semantics enables extending recent work on equality saturation to auto-generate basic compiler support for prototype accelerators in a technique we term "flexible matching." By combining flexible matching with simulators auto-generated from ILA specifications, our approach enables end-to-end evaluation with modest engineering effort. We detail several case studies of 3LA, which uncovered an unknown flaw in a recently published accelerator and facilitated its fix.

Causal discovery between collections of time-series data can help diagnose causes of symptoms and hopefully prevent faults before they occur. However, reliable causal discovery can be very challenging, especially when the data acquisition rate varies (i.e., non-uniform data sampling), or in the presence of missing data points (e.g., sparse data sampling). To address these issues, we proposed a new system comprised of two parts, the first part fills missing data with a Gaussian Process Regression, and the second part leverages an Echo State Network, which is a type of reservoir computer (i.e., used for chaotic system modelling) for Causal discovery. We evaluate the performance of our proposed system against three other off-the-shelf causal discovery algorithms, namely, structural expectation-maximization, sub-sampled linear auto-regression absolute coefficients, and multivariate Granger Causality with vector auto-regressive using the Tennessee Eastman chemical dataset; we report on their corresponding Matthews Correlation Coefficient(MCC) and Receiver Operating Characteristic curves (ROC) and show that the proposed system outperforms existing algorithms, demonstrating the viability of our approach to discover causal relationships in a complex system with missing entries.

Iterative Green's function, based on cyclic reduction of block tridiagonal matrices, has been the ideal algorithm, through tight-binding models, to compute the surface density-of-states of semi-infinite topological electronic materials. In this paper, we apply this method to photonic and acoustic crystals, using finite-element discretizations and a generalized eigenvalue formulation, to calculate the local density-of-states on a single surface of semi-infinite lattices. The three-dimensional (3D) examples of gapless helicoidal surface states in Weyl and Dirac crystals are shown and the computational cost, convergence and accuracy are analyzed., Comment: 7 pages, 4 figures

Spin Hall effect plays an essential role in generating spin current from the injected charge current, following the Dyakonov-Perel rule that the directions of charge flow, spin flow and spin polarization are mutually perpendicular to each other. Recently, its generalization from an antiferromagnet, so-called magnetic spin Hall effect, has been studied and verified by measuring anomalous spin accumulations. Here, we investigate the magnetic spin Hall effect in bilayer materials made of a heavy metal and an antiferromagnet. The spin current generated by the magnetic spin Hall effect accomplishes spin-orbit-torque switching for ferromagnetic magnetization and exchange bias concurrently without any external magnetic field. The switching mechanism crucially relies on the non-collinear spin texture in the antiferromagnet, capable of generating symmetry-breaking components in the spin-current tensor so that the external magnetic field is no longer necessary. The zero-field concurrent switching of magnetization and exchange bias is a significant technological breakthrough. Furthermore, our findings pave the way to explore the magnetic spin Hall effects in various spin textures through spin-orbit-torque switching.

Graphene based sensor to gas molecules should be ultrasensitive and ultrafast because of the single-atomic thickness of graphene, while the response is not fast. Usually, the measured response time for many molecules, such as CO, NH3, SO2, CO2 and NO2 and so on, is on the scale of minutes or longer. In the present work, we found via \emph{ab initio} calculations there exists a potential barrier larger than 0.7 eV that hinders the gas molecule to land directly at the defective sites of graphene and retards the response. An efficient approach to the problem is suggested as modifying the graphene sheet with other molecules to reduce the potential barrier and was demonstrated by a graphene sheet modified by Fe2O3 molecules that shows fast response to H2S molecule, and the calculated response time is close to the measured one, 500 $\mu$s., Comment: 23 pages, 9 figures

In the long-time pursuit of the solution to calculate the partition function (or free energy) of condensed matter, Monte-Carlo-based nested sampling should be the state-of-the-art method, and very recently, we established a direct integral approach that works at least four orders faster. In present work, the above two methods were applied to solid argon at temperatures up to $300$K, and the derived internal energy and pressure were compared with the molecular dynamics simulation as well as experimental measurements, showing that the calculation precision of our approach is about 10 times higher than that of the nested sampling method., Comment: 6 pages, 4 figures

Very recently we developed an efficient method to calculate the free energy of 2D materials on substrates and achieved high calculation precision for graphene or $\gamma$-graphyne on copper substrates. In the present work, the method was further confirmed to be accurate by molecular dynamic simulations of silicene on Ag substrate using empirical potential and was applied to predict the optimum conditions based on \emph{ab initio} calculations for silicene growth on Ag (110) and Ag (111) surface, which are in good agreement with previous experimental observations., Comment: 11 pages, 4 figures

A method was developed to calculate the free energy of 2D materials on substrates and was demonstrated by the system of graphene and {\gamma}-graphyne on copper substrate. The method works at least 3 orders faster than state-of-the-art algorithms, and the accuracy was tested by molecular dynamics simulations, showing that the precision for calculations of the internal energy achieves up to 0.03% in a temperature range from 100 to 1300K. As expected, the calculated the free energy of a graphene sheet on Cu (111) or Ni (111) surface in a temperature range up to 3000K is always smaller than the one of a {\gamma}-graphyne sheet with the same number of C atoms, which is consistent with the fact that growth of graphene on the substrates is much easier than {\gamma}-graphyne., Comment: 16 pages, 4 figures

The key problem of statistical physics standing over one hundred years is how to exactly calculate the partition function (or free energy) of many-body interaction systems, which severely hinders application of the theory for realistic systems. Here we present a novel approach that works at least four orders faster than state-of-the-art algorithms to the problem and can be applied to predict thermal properties of large molecules or macroscopic condensed matters via \emph{ab initio} calculations.The method was demonstrated by C$_{60}$ molecules, solid and liquid copper (up to $\sim 600$GPa), solid argon, graphene and silicene on substrate, and the derived internal energy or pressure is in a good agreement with the results of vast molecular dynamics simulations in a temperature range up to $2500$K, achieving a precision at least one order higher than previous methods. And, for the first time, the realistic isochoric equation of state for solid argon was reproduced directly from the partition function., Comment: Request of supplementary information should be addressed to BYN and XJN

Modern Systems-on-Chip (SoC) designs are increasingly heterogeneous and contain specialized semi-programmable accelerators in addition to programmable processors. In contrast to the pre-accelerator era, when the ISA played an important role in verification by enabling a clean separation of concerns between software and hardware, verification of these "accelerator-rich" SoCs presents new challenges. From the perspective of hardware designers, there is a lack of a common framework for the formal functional specification of accelerator behavior. From the perspective of software developers, there exists no unified framework for reasoning about software/hardware interactions of programs that interact with accelerators. This paper addresses these challenges by providing a formal specification and high-level abstraction for accelerator functional behavior. It formalizes the concept of an Instruction Level Abstraction (ILA), developed informally in our previous work, and shows its application in modeling and verification of accelerators. This formal ILA extends the familiar notion of instructions to accelerators and provides a uniform, modular, and hierarchical abstraction for modeling software-visible behavior of both accelerators and programmable processors. We demonstrate the applicability of the ILA through several case studies of accelerators (for image processing, machine learning, and cryptography), and a general-purpose processor (RISC-V). We show how the ILA model facilitates equivalence checking between two ILAs, and between an ILA and its hardware finite-state machine (FSM) implementation. Further, this equivalence checking supports accelerator upgrades using the notion of ILA compatibility, similar to processor upgrades using ISA compatibility., Comment: 24 pages, 3 figures, 3 tables

Due to its rapid development in the past decade, air transportation system has attracted considerable research attention from diverse communities. While most of the previous studies focused on airline networks, here we systematically explore the robustness of the Chinese air route network, and identify the vital edges which form the backbone of Chinese air transportation system. Specifically, we employ a memetic algorithm to minimize the network robustness after removing certain edges hence the solution of this model is the set of vital edges. Counterintuitively, our results show that the most vital edges are not necessarily the edges of highest topological importance, for which we provide an extensive explanation from the microscope of view. Our findings also offer new insights to understanding and optimizing other real-world network systems.

It remains a challenge to independently manipulate the magnetic dipolar and the spin-exchange interactions, which are entangled in many spin systems, particularly in spin-1 Bose-Einstein condensates. For this purpose, we put forward a sequence of rf pulses and the periodic dynamical decoupling sequence of optical Feshbach resonance pulses to control the dipolar and the spin-exchange interactions, respectively. Our analytic results and the numerical simulations demonstrate that either of the two interactions can be suppressed to make the other dominate the spin dynamics; furthermore, both of the interactions can be simultaneously suppressed to realize spinor-condensate-based magnetometers with a higher sensitivity. This manipulation method may find its wide applications in magnetic resonance and spintronics., Comment: To be published in PRA (5pages, 5 figures,)

In describing the motion of atoms and clusters, we face with choosing quantum mechanics or classical mechanics under different conditions. In principle, there exist two criteria for this choice, but they do contradict in some cases though they are in agreement for other cases. Actually, this problem is closely related with the effective centre-of-mass method, the underlying application of quantum mechanics. It is shown that quantum mechanics must be selected for particle's motion when the de Broglie wave length of the mass centre is larger than the particle size, and in such case the effective centre-of-mass can be used in Quantum Mechanics. In order to test this conclusion, an easy-manufactured experiment is suggested., Comment: 9 pages, 3 figures

We present a theoretical investigation on the enhancement of the spin coherence with periodic, concatenated, or Uhrig dynamical decoupling $N$-pulse sequences in a $^{87}$Rb spin-1 Bose condensate, where the intrinsic dynamical instability in such a ferromagnetically interacting condensate causes spin decoherence and eventually leads to a multiple spatial-domain structure or a spin texture. Our results show that all the three sequences successfully enhance the spin coherence by pushing the wave vector of the most unstable mode in the condensate to a larger value. Among the three sequences with the same number of pulses, the concatenated one shows the best performance in preserving the spin coherence. Interestingly, we find that all the three sequences exactly follow the same enhancement law, $k_- T^{1/2} = c$, with $k_-$ the wave vector of the most unstable mode, $T$ the sequence period, and $c$ a sequence-dependent constant. Such a law between $k_-$ and $T$ is also derived analytically for an attractive scalar Bose condensate subjecting to a periodic dynamical decoupling sequence., Comment: 7 pages, 5 figures

We are exploring the enhancement of models of agent behaviour with more "human-like" decision making strategies than are presently available. Our motivation is to developed with a view to as the decision analysis and support for electric taxi company under the mission of energy saving and reduction of CO2, in particular car-pool and car-sharing management policies. In order to achieve the object of decision analysis for user, we provide a human-agents interactive spatial behaviour to support user making decision real time. We adopt passenger average waiting time and electric taxi average idle time as the performance measures and decision support fro electric taxi company. Finally, according to the analysis result, we demonstrate that our multi-agent simulation and GUI can help users or companies quickly make a quality and accurate decision to reduce the decision-making cost and time.

The design of multi-agent based simulations (MABS) is up to now mainly done in laboratories and based on designers' understanding of the activities to be simulated. Domain experts have little chance to directly validate agent behaviors. To fill this gap, we are investigating participatory methods of design, which allow users to participate in the design the pickup and delivery problem (PDP) in the taxi planning problem. In this paper, we present a participatory process for designing new socio-technical architectures to afford the taxi dispatch for this transportation system. The proposed dispatch architecture attempts to increase passenger satisfaction more globally, by concurrently dispatching multiple taxis to the same number of passengers in the same geographical region, and vis-avis human driver and dispatcher satisfaction., Comment: "International Journal of Computer Science Issues, IJCSI, Volume 4, Issue 1, pp10-15, September 2009"

A Higgs-Yang Mills monopole scattering spherical symmetrically along light cones is given. The left incoming anti-self-dual \alpha plane fields are holomorphic, but the right outgoing SD \beta plane fields are antiholomorphic, meanwhile the diffeomorphism symmetry is preserved with mutual inverse affine rapidity parameters \mu and \mu^{-1}. The Dirac wave function scattering in this background also factorized respectively into the (anti)holomorphic amplitudes. The holomorphic anomaly is realized by the center term of a quasi Hopf algebra corresponding to an integrable conform affine massive field. We find explicit Nahm transformation matrix(Fourier-Mukai transformation) between the Higgs YM BPS (flat) bundles (D modules) and the affinized blow up ADHMN twistors (perverse sheafs). Thus establish the algebra for the Hecke-'t Hooft operators in the Hecke correspondence of the geometric Langlands Program., Comment: Identical to the version 2 and only the acknowledgement is replaced

By extending the dressing symmetric action of IIB string in $AdS_5\times S^5$ to the $D_3$ brane, we find a gauged WZW action of Higgs Yang-Mills field including the 2-cocycle of axially anomaly. The left and right twistor structure of left and right $\alpha $-planes glue into an ambitwistor. The symmetry group of Nahm equations is central extended to an affine group, thus we explain why the spectral curve is given by affine Toda., Comment: v2: strongly revised version (especially in important section 5), notation unified, typos corrected, referrences added

In this paper we interpret the hidden symmetry of the moduli space of IIB superstring on $AdS_{5}\times S^{5}$ in terms of the chiral embedding in $AdS_{5}$, which turns to be the $\mathbb{CP}^{3}$ conformal affine Toda model. We review how the position $\mu $ of poles in the Riemann-Hilbert formulation of dressing transformation and how the value of loop parameters $\mu $ in the vertex operator of affine algebra determines the moduli space of the soliton solutions, which describes the moduli space of the Green-Schwarz superstring. We show also how this affine SU(4) symmetry affinize the conformal symmetry in the twistor space, and how a soliton string corresponds to a Robinson congruence with twist and dilation spin coefficients $\mu $ of twistor., Comment: Final version, Misprints corrected, Note added

We develop the description of non-commutative geometry of the 4-dimensional quantum Hall fluid's theory proposed recently by Zhang and Hu. The non-commutative structure of fuzzy $S^{4}$ appears naturally in this theory. The fuzzy monopole harmonics, which are the essential elements in this non-commutative geometry, are explicitly constructed and their obeying the matrix algebra is obtained. This matrix algebra is associative. We also propose a fusion scheme of the fuzzy monopole harmonics of the coupling system from those of the subsystems, and determine the fusion rule in such fusion scheme. By products, we provide some essential ingredients of the theory of SO(5) angular momentum. In particular, the explicit expression of the coupling coefficients, in the theory of SO(5) angular momentum, are given. It is discussed that some possible applications of our results to the 4-dimensional quantum Hall system and the matrix brane construction in M-theory., Comment: latex 22 pages, no figures. some references added. some results are clarified

In this paper, we set up the bi-module of the algebra ${\cal A}$ on fuzzy sphere. Based on the differential operators in moving frame, we generalize the ABS construction into fuzzy sphere case. The applications of ABS construction are investigated in various physical systems., Comment: Latex file without figure, 13 pages

The modified Seiberg-Witten monopole equations are presented in this letter. These equations have analytic solutions in the whole 1+3 Minkowski space with finite energy. The physical meaning of the equations and solutions are discussed here., Comment: RevTex, 6 page, no figure

In this paper, we introduce an $N\times N$ matrix $\epsilon^{a\bar{b}}$ in the quantum groups $SU_{q}(N)$ to transform the conjugate representation into the standard form so that we are able to compute the explicit forms of the important quantities in the bicovariant differential calculus on $SU_{q}(N)$, such as the $q$-deformed structure constant ${\bf C}_{IJ}^{~K}$ and the $q$-deformed transposition operator $\Lambda$. From the $q$-gauge covariant condition we define the generalized $q$-deformed Killing form and the $m$-th $q$-deformed Chern class $P_{m}$ for the quantum groups $SU_{q}(N)$. Some useful relations of the generalized $q$-deformed Killing form are presented. In terms of the $q$-deformed homotopy operator we are able to compute the $q$-deformed Chern-Simons $Q_{2m-1}$ by the condition $dQ_{2m-1}=P_{m}$, Furthermore, the $q$-deformed cocycle hierarchy, the $q$-deformed gauge covariant Lagrangian, and the $q$-deformed Yang-Mills equation are derived.

In this paper, from the $q$-gauge covariant condition we define the $q$-deformed Killing form and the second $q$-deformed Chern class for the quantum group $SU_{q}(2)$. Developing Zumino's method we introduce a $q$-deformed homotopy operator to compute the $q$-deformed Chern-Simons and the $q$-deformed cocycle hierarchy. Some recursive relations related to the generalized $q$-deformed Killing forms are derived to prove the cocycle hierarchy formulas directly. At last, we construct the $q$-gauge covariant Lagrangian and derive the $q$-deformed Yang-Mills equation. We find that the components of the singlet and the adjoint representation are separated in the $q$-deformed Chern class, $q$-deformed cocycle hierarchy and the $q$-deformed Lagrangian, although they are mixed in the commutative relations of BRST algebra.