Momentum distribution and contacts of one-dimensional spinless Fermi gases with an attractive p-wave interaction

We present a rigorous study of momentum distribution and p-wave contacts of one dimensional (1D) spinless Fermi gases with an attractive p-wave interaction. Using the Bethe wave function, we analytically calculate the large-momentum tail of momentum distribution of the model. We show that the leading ($\sim 1/p^{2}$) and sub-leading terms ($\sim 1/p^{4}$) of the large-momentum tail are determined by two contacts $C_2$ and $C_4$, which we show, by explicit calculation, are related to the short-distance behaviour of the two-body correlation function and its derivatives. We show as one increases the 1D scattering length, the contact $C_2$ increases monotonically from zero while $C_4$ exhibits a peak for finite scattering length. In addition, we obtain analytic expressions for p-wave contacts at finite temperature from the thermodynamic Bethe ansatz equations in both weakly and strongly attractive regimes.Comment: 19 pages,2 figure

Dynamic Event-Triggered Consensus of Multi-agent Systems on Matrix-weighted Networks

This paper examines event-triggered consensus of multi-agent systems on matrix-weighted networks, where the interdependencies among higher-dimensional states of neighboring agents are characterized by matrix-weighted edges in the network. Specifically, a distributed dynamic event-triggered coordination strategy is proposed for this category of generalized networks, in which an auxiliary system is employed for each agent to dynamically adjust the trigger threshold, which plays an essential role in guaranteeing that the triggering time sequence does not exhibit Zeno behavior. Distributed event-triggered control protocols are proposed to guarantee leaderless and leader-follower consensus for multi-agent systems on matrix-weighted networks, respectively. It is shown that that the spectral properties of matrix-valued weights are crucial in event-triggered mechanism design for matrix-weighted networks. Finally, simulation examples are provided to demonstrate the theoretical results

On Stability and Consensus of Signed Networks: A Self-loop Compensation Perspective

Positive semidefinite is not an inherent property of signed Laplacians, which renders the stability and consensus of multi-agent system on undirected signed networks intricate. Inspired by the correlation between diagonal dominance and spectrum of signed Laplacians, this paper proposes a self-loop compensation mechanism in the design of interaction protocol amongst agents and examines the stability/consensus of the compensated signed networks. It turns out that self-loop compensation acts as exerting a virtual leader on these agents that are incident to negative edges, steering whom towards origin. Analytical connections between self-loop compensation and the collective behavior of the compensated signed network are established. Necessary and/or sufficient conditions for predictable cluster consensus of signed networks via self-loop compensation are provided. The optimality of self-loop compensation is discussed. Furthermore, we extend our results to directed signed networks where the symmetry of signed Laplacian is not free. Simulation examples are provided to demonstrate the theoretical results

INSURE: An Information Theory Inspired Disentanglement and Purification Model for Domain Generalization

Domain Generalization (DG) aims to learn a generalizable model on the unseen target domain by only training on the multiple observed source domains. Although a variety of DG methods have focused on extracting domain-invariant features, the domain-specific class-relevant features have attracted attention and been argued to benefit generalization to the unseen target domain. To take into account the class-relevant domain-specific information, in this paper we propose an Information theory iNspired diSentanglement and pURification modEl (INSURE) to explicitly disentangle the latent features to obtain sufficient and compact (necessary) class-relevant feature for generalization to the unseen domain. Specifically, we first propose an information theory inspired loss function to ensure the disentangled class-relevant features contain sufficient class label information and the other disentangled auxiliary feature has sufficient domain information. We further propose a paired purification loss function to let the auxiliary feature discard all the class-relevant information and thus the class-relevant feature will contain sufficient and compact (necessary) class-relevant information. Moreover, instead of using multiple encoders, we propose to use a learnable binary mask as our disentangler to make the disentanglement more efficient and make the disentangled features complementary to each other. We conduct extensive experiments on four widely used DG benchmark datasets including PACS, OfficeHome, TerraIncognita, and DomainNet. The proposed INSURE outperforms the state-of-art methods. We also empirically show that domain-specific class-relevant features are beneficial for domain generalization.Comment: 10 pages, 4 figure

Vector-valued Privacy-Preserving Average Consensus

Achieving average consensus without disclosing sensitive information can be a critical concern for multi-agent coordination. This paper examines privacy-preserving average consensus (PPAC) for vector-valued multi-agent networks. In particular, a set of agents with vector-valued states aim to collaboratively reach an exact average consensus of their initial states, while each agent's initial state cannot be disclosed to other agents. We show that the vector-valued PPAC problem can be solved via associated matrix-weighted networks with the higher-dimensional agent state. Specifically, a novel distributed vector-valued PPAC algorithm is proposed by lifting the agent-state to higher-dimensional space and designing the associated matrix-weighted network with dynamic, low-rank, positive semi-definite coupling matrices to both conceal the vector-valued agent state and guarantee that the multi-agent network asymptotically converges to the average consensus. Essentially, the convergence analysis can be transformed into the average consensus problem on switching matrix-weighted networks. We show that the exact average consensus can be guaranteed and the initial agents' states can be kept private if each agent has at least one "legitimate" neighbor. The algorithm, involving only basic matrix operations, is computationally more efficient than cryptography-based approaches and can be implemented in a fully distributed manner without relying on a third party. Numerical simulation is provided to illustrate the effectiveness of the proposed algorithm