Wei Chen, Dan Wang, Ji Liu, Yongxin Chen, Sei Zhen Khong, Tamer Başar, Karl H. Johansson, Li Qiu
Signed graphs have appeared in a broad variety of applications, ranging from social networks to biological networks, from distributed control and computation to power systems. In this paper, we investigate spectral properties of signed Laplacians for undirected signed graphs. We find conditions on the negative weights under which a signed Laplacian is positive semidefinite via the Kron reduction and multiport network theory. For signed Laplacians that are indefinite, we characterize their inertias with the same framework. Furthermore, we build connections between signed Laplacians, generalized M-matrices, and eventually exponentially positive matrices.
Dan Wang, Mengqi Ji, Yong Wang, Haoqian Wang, Lu Fang
To overcome the oscillation problem in the classical momentum-based optimizer, recent work associates it with the proportional-integral (PI) controller, and artificially adds D term producing a PID controller. It suppresses oscillation with the sacrifice of introducing extra hyper-parameter. In this paper, we start by analyzing: why momentum-based method oscillates about the optimal point? and answering that: the fluctuation problem relates to the lag effect of integral (I) term. Inspired by the conditional integration idea in classical control society, we propose SPI-Optimizer, an integral-Separated PI controller based optimizer WITHOUT introducing extra hyperparameter. It separates momentum term adaptively when the inconsistency of current and historical gradient direction occurs. Extensive experiments demonstrate that SPIOptimizer generalizes well on popular network architectures to eliminate the oscillation, and owns competitive performance with faster convergence speed (up to 40% epochs reduction ratio ) and more accurate classification result on MNIST, CIFAR10, and CIFAR100 (up to 27.5% error reduction ratio) than the state-of-the-art methods.
Wei Chen, Dan Wang, Sei Zhen Khong, Li Qiu
In this paper, we introduce a definition of phase response for a class of multi-input multi-output (MIMO) linear time-invariant (LTI) systems, the frequency responses of which are cramped at all frequencies. This phase concept generalizes the notions of positive realness and negative imaginariness. We also define the half-cramped systems and provide a time-domain interpretation. As a starting point in an endeavour to develop a comprehensive phase theory for MIMO systems, we establish a small phase theorem for feedback stability, which complements the well-known small gain theorem. In addition, we derive a sectored real lemma for phase-bounded systems as a natural counterpart of the bounded real lemma.
Wei Chen, Dan Wang, Sei Zhen Khong, Li Qiu
In this paper, we define the phase response for a class of multi-input multi-output (MIMO) linear time-invariant (LTI) systems whose frequency responses are (semi-)sectorial at all frequencies. The newly defined phase concept subsumes the well-known notions of positive real systems and negative imaginary systems. We formulate a small phase theorem for feedback stability, which complements the celebrated small gain theorem. The small phase theorem lays the foundation of a phase theory of MIMO systems. We also discuss time-domain interpretations of phase-bounded systems via both energy signal analysis and power signal analysis. In addition, a sectored real lemma is derived for the computation of MIMO phases, which serves as a natural counterpart of the bounded real lemma.
Dan Wang, Xu Chen
Stably inverting a dynamic system model is the foundation of numerous servo designs. Existing inversion techniques have provided accurate model approximations that are often highly effective in feedforward controls. However, when the inverse is implemented in a feedback system, additional considerations are needed for assuring causality, closed-loop stability, and robustness. In pursuit of bridging the gap between the best model matching and a robust feedback performance under closed-loop constraints, this paper provides a modern review of frequency-domain model inversion techniques and a new treatment of unstable zeros. We provide first a pole-zero-map-based intuitive inverse tuning for motion control systems. Then for general nonminimum-phase and unstable systems, we propose an optimal inversion algorithm that can attain model accuracy at the frequency regions of interest and meanwhile constrain noise amplification elsewhere to guarantee system robustness. The design goals are achieved by a multi-objective H infinity formulation and all-pass factorization that consider model matching, causality of transfer functions, frequency-domain gain constraints, and factorization of unstable system modes in a unified scheme. The proposed algorithm is validated on motion control systems and complex high-order systems.
Dan Wang, Licheng Jiao, Jie Chen, Shuyuan Yang, Fang Liu
Difference features obtained by comparing the images of two periods play an indispensable role in the change detection (CD) task. However, a pair of bi-temporal images can exhibit diverse changes, which may cause various difference features. Identifying changed pixels with differ difference features to be the same category is thus a challenge for CD. Most nowadays' methods acquire distinctive difference features in implicit ways like enhancing image representation or supervision information. Nevertheless, informative image features only guarantee object semantics are modeled and can not guarantee that changed pixels have similar semantics in the difference feature space and are distinct from those unchanged ones. In this work, the generalized representation of various changes is learned straightforwardly in the difference feature space, and a novel Changes-Aware Transformer (CAT) for refining difference features is proposed. This generalized representation can perceive which pixels are changed and which are unchanged and further guide the update of pixels' difference features. CAT effectively accomplishes this refinement process through the stacked cosine cross-attention layer and self-attention layer. After refinement, the changed pixels in the difference feature space are closer to each other, which facilitates change detection. In addition, CAT is compatible with various backbone networks and existing CD methods. Experiments on remote sensing CD data set and street scene CD data set show that our method achieves state-of-the-art performance and has excellent generalization.
Naichung Conan Leung, Dan Wang
A compact Kähler manifold $\left( M,ω,J\right) $ with $T$-symmetry admits a natural mixed polarization $\mathcal{P}_{\mathrm{mix}}$ whose real directions come from the $T$-action. In \cite{LW1}, we constructed a one-parameter family of Kähler structures $\left( ω,J_{t}\right) $'s with the same underlying Kä hler form $ω$ and $J_{0}=J$, such that (i) there is a $T$-equivariant biholomorphism between $\left( M,J_{0}\right) $ and $\left( M,J_{t}\right) $ and (ii) Kähler polarizations $\mathcal{P} _{t}$'s corresponding to $J_{t}$'s converge to $\mathcal{P}_{\mathrm{mix}}$ as $t$ goes to infinity. In this paper, we study the quantum analog of above results. Assume $L$ is a pre-quantum line bundle on $\left( M,ω\right) $. Let $\mathcal{H}_{t}$ and $ \mathcal{H}_{\mathrm{mix}}$ be quantum spaces defined using polarizations $\mathcal{P}_{t}$ and $\mathcal{P}_{\mathrm{mix}}$ respectively. In particular, $\mathcal{H}_{t}=H_{\bar{\partial}_{t}}^{0}\left( M,L\right) $. They are both representations of $T$. We show that (i) there is a $T$-equivariant isomorphism between $\mathcal{H}_{0}$ and $\mathcal{H}_{\mathrm{mix}}$ and (ii) for regular $T$-weight $λ$, corresponding $λ$-weight spaces $ \mathcal{H}_{t,λ}$'s converge to $\mathcal{H}_{\mathrm{mix},λ}$ as $t$ goes to infinity.
Dan Wang, Shuaicheng Li, Fei Guo, Lusheng Wang
Motivation: Genome rearrangement plays an important role in evolutionary biology and has profound impacts on phenotype in organisms ranging from microbes to humans. The mechanisms for genome rearrangement events remain unclear. Lots of comparisons have been conducted among different species. To reveal the mechanisms for rearrangement events, comparison of different individuals/strains within the same species or genus (pan-genomes) is more helpful since they are much closer to each other. Results: We study the mechanism for inversion events via core-genome scaffold comparison of different strains within the same species. We focus on two kinds of bacteria, Pseudomonas aeruginosa and Escherichia coli, and investigate the inversion events among different strains of the same specie. We find an interesting phenomenon that long (larger than 10,000 bp) inversion regions are flanked by a pair of Inverted Repeats (IRs) (with lengths ranging from 385 bp to 27476 bp) which are often Insertion Sequences (ISs).This mechanism can also explain why the breakpoint reuses for inversion events happen. We study the prevalence of the phenomenon and find that it is a major mechanism for inversions. The other observation is that for different rearrangement events such as transposition and inverted block interchange, the two ends of the swapped regions are also associated with repeats so that after the rearrangement operations the two ends of the swapped regions remain unchanged. To our knowledge, this is the first time such a phenomenon is reported for transposition event.
Siqiao Zhao, Dan Wang, Raphael Douady
Dec 15, 2024·q-fin.ST·PDF The domain of hedge fund investments is undergoing significant transformation, influenced by the rapid expansion of data availability and the advancement of analytical technologies. This study explores the enhancement of hedge fund investment performance through the integration of machine learning techniques, the application of PolyModel feature selection, and the analysis of fund size. We address three critical questions: (1) the effect of machine learning on trading performance, (2) the role of PolyModel feature selection in fund selection and performance, and (3) the comparative reliability of larger versus smaller funds. Our findings offer compelling insights. We observe that while machine learning techniques enhance cumulative returns, they also increase annual volatility, indicating variability in performance. PolyModel feature selection proves to be a robust strategy, with approaches that utilize a comprehensive set of features for fund selection outperforming more selective methodologies. Notably, Long-Term Stability (LTS) effectively manages portfolio volatility while delivering favorable returns. Contrary to popular belief, our results suggest that larger funds do not consistently yield better investment outcomes, challenging the assumption of their inherent reliability. This research highlights the transformative impact of data-driven approaches in the hedge fund investment arena and provides valuable implications for investors and asset managers. By leveraging machine learning and PolyModel feature selection, investors can enhance portfolio optimization and reassess the dependability of larger funds, leading to more informed investment strategies.
Dan Wang, Haowei Chen, Yu Pang, Xiaolong Zou, Wenhui Duan
The introduction of intrinsic magnetic order in two-dimensional (2D) semiconductors offers great opportunities for investigating correlated excitonic phenomena. Here, we employ full-spinor GW plus Bethe-Salpeter equation methodology to reveal rich exciton physics in a prototypical 2D Néel-type antiferromagnetic semiconductor MnPS$_3$, enabled by the interplay among inverted dispersion of the second valence band, spin-valley coupling and magnetic order. The negative hole mass increases the reduced mass of the lowest-energy bright exciton, leading to exchange splitting enhancement of the bright exciton relative to band-edge dark exciton. Notably, such splitting couples with spontaneous valley polarization to generate distinct excitonic fine structure between $K$ and $-K$ valleys, which dictate distinct relaxation behaviors. Crucially, magnetic order transition from Néel antiferromagnetic to ferromagnetic state induces significant quasiparticle band structure reconstruction and excitonic transitions modification, with low-energy optical excitations being exclusively contributed by majority-spin channel. These findings establish 2D antiferromagnetic semiconductors as an intriguing platform to study band-spin-valley coupled exciton physics.
Dan Wang, Wei Chen, Li Qiu
In this paper, the synchronization of heterogeneous agents interacting over a dynamical network is studied. The edge dynamics can model the inter-agent communications which are often heterogeneous by nature. They can also model the controllers of the agents which may be different for each agent or uniform for all the agents. Novel synchronization conditions are obtained for both cases from a phase perspective by exploiting a recently developed small phase theorem. The conditions scale well with the network and reveal the trade-off between the phases of node dynamics and edge dynamics. We also study the synchronizability problem which aims to characterize the allowable diversity of the agents for which controllers can be designed so as to achieve synchronization. The allowable diversity is captured in terms of phase conditions engaging the residue matrices of the agents at their persistent modes. Controller design algorithms are provided for the cases of agent-dependent and uniform controllers, respectively.
Naichung Conan Leung, Dan Wang
Let $M$ be a compact Kähler manifold equipped with a pre-quantum line bundle $L$. In [9], using $T$-symmetry, we constructed a polarization $\mathcal{P}_{\mathrm{mix}}$ on $M$, which generalizes real polarizations on toric manifolds. In this paper, we obtain the following results for the quantum space $\mathcal{H}_{\mathrm{mix}}$ associated to $\mathcal{P}_{\mathrm{mix}}$. First, $\mathcal{H}_{\mathrm{mix}}$ consists of distributional sections of $L$ with supports inside $μ^{-1}(\mathfrak{t}^{*}_{\mathbb{Z}})$. This gives $\mathcal{H}_{\mathrm{mix}}=\bigoplus_{λ\in \mathfrak{t}^{*}_{\mathbb{Z}} } \mathcal{H}_{\mathrm{mix}, λ}$. Second, the above decomposition of $\mathcal{H}_{\mathrm{mix}}$ coincides with the weight decomposition for the $T$-symmetry. Third, an isomorphism $\mathcal{H}_{\mathrm{mix}, λ} \cong H^{0}( M//_λT, L//_λT)$, for regular $λ$. Namely, geometric quantization commutes with symplectic reduction.
Dan Wang, Jibing Gong, Yaxi Song
Most of the information is stored as text, so text mining is regarded as having high commercial potential. Aiming at the semantic constraint problem of classification methods based on sparse representation, we propose a weighted recurrent neural network (W-RNN), which can fully extract text serialization semantic information. For the problem that the feature high dimensionality and unclear semantic relationship in text data representation, we first utilize the word vector to represent the vocabulary in the text and use Recurrent Neural Network (RNN) to extract features of the serialized text data. The word vector is then automatically weighted and summed using the intermediate output of the word vector to form the text representation vector. Finally, the neural network is used for classification. W-RNN is verified on the news dataset and proves that W-RNN is superior to other four baseline methods in Precision, Recall, F1 and loss values, which is suitable for text classification.
Parisa Golbayani, Dan Wang, Ionut Florescu
Recent literature implements machine learning techniques to assess corporate credit rating based on financial statement reports. In this work, we analyze the performance of four neural network architectures (MLP, CNN, CNN2D, LSTM) in predicting corporate credit rating as issued by Standard and Poor's. We analyze companies from the energy, financial and healthcare sectors in US. The goal of the analysis is to improve application of machine learning algorithms to credit assessment. To this end, we focus on three questions. First, we investigate if the algorithms perform better when using a selected subset of features, or if it is better to allow the algorithms to select features themselves. Second, is the temporal aspect inherent in financial data important for the results obtained by a machine learning algorithm? Third, is there a particular neural network architecture that consistently outperforms others with respect to input features, sectors and holdout set? We create several case studies to answer these questions and analyze the results using ANOVA and multiple comparison testing procedure.
Dan Wang, Ji Liu, Philip E. Paré, Wei Chen, Li Qiu, Carolyn L. Beck, Tamer Başar
This paper formulates and studies the problem of controlling a networked SIS model using a single input in which the network structure is described by a connected undirected graph. A necessary and sufficient condition on the values of curing and infection rates for the healthy state to be exponentially stable is obtained via the analysis of signed Laplacians when the control input is the curing budget of a single agent. In the case when the healthy state is stabilizable, an explicit expression for the minimum curing budget is provided. The utility of the algorithm is demonstrated using a simulation over a network of cities in the northeastern United States.
Dan Wang
Let $(X, ω, J)$ be a toric variety of dimension $2n$ determined by a Delzant polytope $P$. As indicated in [40], $X$ admits a natural mixed polarization $\mathcal{P}_{k}$, induced by the action of a subtorus $T^{k}$. In this paper, we first establish the quantum space $\mathcal{H}_{k}$ for $\mathcal{P}_{k}$, identifying a basis parameterized by the integer lattice points of $P$. This confirms that the dimension of $\mathcal{H}_{k}$ aligns with those derived from Kähler and real polarizations. Secondly, we examine a one-parameter family of Kähler polarizations $\mathcal{P}_{k,t}$, defined via symplectic potentials, and demonstrate their convergence to $\mathcal{P}_{k}$. Thirdly, we verify that these polarizations $\mathcal{P}_{k,t}$ coincide with those induced by imaginary-time flow. Finally, we explore the relationship between the quantum space $\mathcal{H}_{k,0}$ and $\mathcal{H}_{k}$, establishing that ``$\lim_{t \rightarrow \infty} \mathcal{H}_{k,t} = \mathcal{H}_{k}$."
Naichung Conan Leung, Dan Wang
Let $(M, ω, J)$ be a Kähler manifold, equipped with an effective Hamiltonian torus action $ρ: T \rightarrow \mathrm{Diff}(M, ω, J)$ by isometries with moment map $μ: M \rightarrow \mathfrak{t}^{*}$. We first construct a singular mixed polarization $\mathcal{P}_{\mathrm{mix}}$ on $M$. Second, we construct a one-parameter family of complex structures $J_{t}$ on $M$ which are compatible with $ω$. Furthermore, the path of corresponding Kähler metrics $g_{t}$ is a complete geodesic ray in the space of Kähler metrics of $M$, when $M$ is compact. Finally, we show that the corresponding family of Kähler polarizations $\mathcal{P}_{t}$ associated to $J_{t}$ converges to $\mathcal{P}_{\mathrm{mix}}$ as $t \rightarrow \infty$.
Dan Wang, Tianrui Wang, Ionuţ Florescu
Oct 17, 2020·q-fin.ST·PDF In 2012, SEC mandated all corporate filings for any company doing business in US be entered into the Electronic Data Gathering, Analysis, and Retrieval (EDGAR) system. In this work we are investigating ways to analyze the data available through EDGAR database. This may serve portfolio managers (pension funds, mutual funds, insurance, hedge funds) to get automated insights into companies they invest in, to better manage their portfolios. The analysis is based on Artificial Neural Networks applied to the data.} In particular, one of the most popular machine learning methods, the Convolutional Neural Network (CNN) architecture, originally developed to interpret and classify images, is now being used to interpret financial data. This work investigates the best way to input data collected from the SEC filings into a CNN architecture. We incorporate accounting principles and mathematical methods into the design of three image encoding methods. Specifically, two methods are derived from accounting principles (Sequential Arrangement, Category Chunk Arrangement) and one is using a purely mathematical technique (Hilbert Vector Arrangement). In this work we analyze fundamental financial data as well as financial ratio data and study companies from the financial, healthcare and IT sectors in the United States. We find that using imaging techniques to input data for CNN works better for financial ratio data but is not significantly better than simply using the 1D input directly for fundamental data. We do not find the Hilbert Vector Arrangement technique to be significantly better than other imaging techniques.
José M. Mourão, João P. Nunes, Augusto Pereira, Dan Wang
For a symplectic toric manifold we consider half-form quantization in mixed polarizations $\mathcal{P}_\infty$, associated to the action of a subtorus $T^p\subset T^n$. The real directions in these polarizations are generated by components of the $T^p$ moment map. Polarizations of this type can be obtained by starting at a toric Kähler polarization $\mathcal{P}_0$ and then following Mabuchi rays of toric Kähler polarizations generated by the norm square of the moment map of the torus subgroup. These geodesic rays are lifted to the quantum bundle via a generalized coherent state transform (gCST) and define equivariant isomorphisms between Hilbert spaces for the Kähler polarizations and the Hilbert space for the mixed polarization. The polarizations $\mathcal{P}_\infty$ give a new way of looking at the problem of unitarity in the quantization commutes with reduction with respect to the $T^p$-action, as follows. The prequantum operators for the components of the moment map of the $T^p$-action act diagonally with discrete spectrum corresponding to the integral points of the moment polytope. The Hilbert space for the quantization with respect to $\mathcal{P}_\infty$ then naturally decomposes as a direct sum of the Hilbert spaces for all its quantizable coisotropic reductions which, in fact, are the Kähler reductions of the initial Kähler polarization $\mathcal{P}_0$. This will be shown to imply that, for the polarization $\mathcal{P}_\infty$, quantization commutes unitarily with reduction. The problem of unitarity in quantization commutes with reduction for $\mathcal{P}_0$ is then equivalent to the question of whether quantization in the polarization $\mathcal{P}_0$ is unitarily equivalent with quantization in the polarization $\mathcal{P}_\infty$. In fact, this does not hold in general in the toric case.
Haoran Ma, Yuchen Zheng, Leining Zhang, Xiaofei Chen, Dan Wang
Strain engineering provides a powerful route for tuning the electronic properties of two-dimensional (2D) materials, but exploring the full multidimensional strain space with density functional theory (DFT) is computationally prohibitive due to the nonlinear coupling between normal and shear components. In this work, we introduce a Transformer-based, multi-target surrogate model framework that achieves DFT-level bandgap prediction accuracy, reaching a mean absolute error of 0.0103 eV while retaining full interpretability through attention-weight analysis. The learned self-attention map consistently identifies shear strain as the interaction center that influences both bandgap and phonon stability, an insight not readily captured by classical feature-importance metrics. This work establishes attention-based architectures as physically interpretable surrogate models for multi-property prediction, offering a generalizable strategy for accelerating deep elastic strain engineering in materials informatics.