Criticality in Translation-Invariant Parafermion Chains

In this work we numerically study critical phases in translation-invariant $\mathbb{Z}_N$ parafermion chains with both nearest- and next-nearest-neighbor hopping terms. The model can be mapped to a $\mathbb{Z}_N$ spin model with nearest-neighbor couplings via a generalized Jordan-Wigner transformation and translation invariance ensures that the spin model is always self-dual. We first study the low-energy spectrum of chains with only nearest-neighbor coupling, which are mapped onto standard self-dual $\mathbb{Z}_N$ clock models. For $3\leq N\leq 6$ we match the numerical results to the known conformal field theory(CFT) identification. We then analyze in detail the phase diagram of a $N=3$ chain with both nearest and next-nearest neighbor hopping and six critical phases with central charges being $4/5$, 1 or 2 are found. We find continuous phase transitions between $c=1$ and $c=2$ phases, while the phase transition between $c=4/5$ and $c=1$ is conjectured to be of Kosterlitz-Thouless type.Comment: published versio

Topology and Criticality in Resonating Affleck-Kennedy-Lieb-Tasaki loop Spin Liquid States

We exploit a natural Projected Entangled-Pair State (PEPS) representation for the resonating Affleck-Kennedy-Lieb-Tasaki loop (RAL) state. By taking advantage of PEPS-based analytical and numerical methods, we characterize the RAL states on various two-dimensional lattices. On square and honeycomb lattices, these states are critical since the dimer-dimer correlations decay as a power law. On kagome lattice, the RAL state has exponentially decaying correlation functions, supporting the scenario of a gapped spin liquid. We provide further evidence that the RAL state on the kagome lattice is a $\mathbb{Z}_2$ spin liquid, by identifying the four topological sectors and computing the topological entropy. Furthermore, we construct a one-parameter family of PEPS states interpolating between the RAL state and a short-range Resonating Valence Bond state and find a critical point, consistent with the fact that the two states belong to two different phases. We also perform a variational study of the spin-1 kagome Heisenberg model using this one-parameter PEPS.Comment: 10 pages, 14 figures, published versio

Chiral projected entangled-pair state with topological order

We show that projected entangled-pair states (PEPS) can describe chiral topologically ordered phases. For that, we construct a simple PEPS for spin-1/2 particles in a two-dimensional lattice. We reveal a symmetry in the local projector of the PEPS that gives rise to the global topological character. We also extract characteristic quantities of the edge conformal field theory using the bulk-boundary correspondence.Comment: 11 pages, 7 figure

Generating Synergistic Formulaic Alpha Collections via Reinforcement Learning

In the field of quantitative trading, it is common practice to transform raw historical stock data into indicative signals for the market trend. Such signals are called alpha factors. Alphas in formula forms are more interpretable and thus favored by practitioners concerned with risk. In practice, a set of formulaic alphas is often used together for better modeling precision, so we need to find synergistic formulaic alpha sets that work well together. However, most traditional alpha generators mine alphas one by one separately, overlooking the fact that the alphas would be combined later. In this paper, we propose a new alpha-mining framework that prioritizes mining a synergistic set of alphas, i.e., it directly uses the performance of the downstream combination model to optimize the alpha generator. Our framework also leverages the strong exploratory capabilities of reinforcement learning~(RL) to better explore the vast search space of formulaic alphas. The contribution to the combination models' performance is assigned to be the return used in the RL process, driving the alpha generator to find better alphas that improve upon the current set. Experimental evaluations on real-world stock market data demonstrate both the effectiveness and the efficiency of our framework for stock trend forecasting. The investment simulation results show that our framework is able to achieve higher returns compared to previous approaches.Comment: Accepted by KDD '23, ADS trac

Optimisation- based time slot assignment and synchronisation for TDMA MAC in industrial wireless sensor network

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/166209/1/cmu2bf02232.pd

ELODI: Ensemble Logit Difference Inhibition for Positive-Congruent Training

Negative flips are errors introduced in a classification system when a legacy model is replaced with a new one. Existing methods to reduce the negative flip rate (NFR) either do so at the expense of overall accuracy using model distillation, or use ensembles, which multiply inference cost prohibitively. We present a method to train a classification system that achieves paragon performance in both error rate and NFR, at the inference cost of a single model. Our method introduces a generalized distillation objective, Logit Difference Inhibition (LDI), that penalizes changes in the logits between the new and old model, without forcing them to coincide as in ordinary distillation. LDI affords the model flexibility to reduce error rate along with NFR. The method uses a homogeneous ensemble as the reference model for LDI, hence the name Ensemble LDI, or ELODI. The reference model can then be substituted with a single model at inference time. The method leverages the observation that negative flips are typically not close to the decision boundary, but often exhibit large deviations in the distance among their logits, which are reduced by ELODI.Comment: Tech repor

CharacterChat: Learning towards Conversational AI with Personalized Social Support

In our modern, fast-paced, and interconnected world, the importance of mental well-being has grown into a matter of great urgency. However, traditional methods such as Emotional Support Conversations (ESC) face challenges in effectively addressing a diverse range of individual personalities. In response, we introduce the Social Support Conversation (S2Conv) framework. It comprises a series of support agents and the interpersonal matching mechanism, linking individuals with persona-compatible virtual supporters. Utilizing persona decomposition based on the MBTI (Myers-Briggs Type Indicator), we have created the MBTI-1024 Bank, a group that of virtual characters with distinct profiles. Through improved role-playing prompts with behavior preset and dynamic memory, we facilitate the development of the MBTI-S2Conv dataset, which contains conversations between the characters in the MBTI-1024 Bank. Building upon these foundations, we present CharacterChat, a comprehensive S2Conv system, which includes a conversational model driven by personas and memories, along with an interpersonal matching plugin model that dispatches the optimal supporters from the MBTI-1024 Bank for individuals with specific personas. Empirical results indicate the remarkable efficacy of CharacterChat in providing personalized social support and highlight the substantial advantages derived from interpersonal matching. The source code is available in \url{https://github.com/morecry/CharacterChat}.Comment: 10 pages, 6 figures, 5 table