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We provide the first example of one-step replica symmetry breaking (1RSB) for the mean field Ising spin glasses at finite temperature and verify the first part of Gardner's conjecture. Specifically, Gardner conjectured that for Ising pure $p$-spin glasses with $p\geq 3,$ there are two phase transitions: the Parisi measure is Replica Symmetric (RS) at high temperatures, then transitions to One-Step Replica Symmetry Breaking (1RSB) at a lower temperature, and finally reaches Full Replica Symmetry Breaking (FRSB) at very low temperatures. Our main results verify the first part of the Gardner transition: for any $p \geq 3,$ there exists a unique $\beta^p_1>0$ such that the Parisi measure is RS for $0 < \beta \leq \beta^p_{1}$ and then 1RSB for $\beta^p_1 < \beta \leq \beta^p_1+\epsilon_p$ with some $\epsilon_p>0.$, Comment: 17 pages, 1 figure

Deep learning (DL) has shown great potential in revolutionizing the traditional communications system. Many applications in communications have adopted DL techniques due to their powerful representation ability. However, the learning-based methods can be dependent on the training dataset and perform worse on unseen interference due to limited model generalizability and complexity. In this paper, we consider the semantic communication (SemCom) system with multiple users, where there is a limited number of training samples and unexpected interference. To improve the model generalization ability and reduce the model size, we propose a knowledge distillation (KD) based system where Transformer based encoder-decoder is implemented as the semantic encoder-decoder and fully connected neural networks are implemented as the channel encoder-decoder. Specifically, four types of knowledge transfer and model compression are analyzed. Important system and model parameters are considered, including the level of noise and interference, the number of interfering users and the size of the encoder and decoder. Numerical results demonstrate that KD significantly improves the robustness and the generalization ability when applied to unexpected interference, and it reduces the performance loss when compressing the model size., Comment: Accepted by IEEE Transactions on Wireless Communications

Inspired by the problem of biofilm growth, we numerically investigate clustering in a two-dimensional suspension of active (Janus) particles of finite size confined in a circular cavity. Their dynamics is regulated by a non-reciprocal mechanism that causes them to switch from active to passive above a certain threshold of the perceived near-neighbor density (quorum sensing).A variety of cluster phases -- glassy, solid (hexatic) and liquid -- is observed depending on the particle dynamics at the boundary, the quorum sensing range, and the level of noise

We consider the spherical mixed $p$-spin models and investigate the structure of the Parisi measure at zero temperature. We prove that for the spherical spin models with $n$ components, the Parisi measure at zero temperature is at most $n$-RSB or $n$-FRSB. We also provide a necessary and sufficient computational criterion for the spherical mixed $p$-spin model to be $k$-RSB or $k$-FRSB, $k \leq n.$, Comment: 26 pages, 5 figures

We determine the structure of the Parisi measure at zero temperature for the spherical p+s spin glass model. We show that depending on the values of p and s, four scenarios may emerge, including the existence of 1-FRSB and 2-FRSB phases as predicted by Crisanti and Leuzzi [10, 11]. We also provide consequences for the model at low temperature., Comment: 39 pages, 3 figures

This paper studies properties of the mixed spherical vector p-spin model. At zero temperature, we establish and investigate a Parisi type formula for the ground state energy. At finite temperature, we provide some properties of minimizers of the Crisanti-Sommers formula recently obtained by Justin Ko. In particular, we extend some of the one-dimensional Parisi measure results of Auffinger-Chen to the vector case., Comment: 31 pages