Cohomologies of modified λ\lambda-differential Lie triple systems and applications

In this paper, we introduce the concept and representation of modified $\lambda$-differential Lie triple systems. Next, we define the cohomology of modified $\lambda$-differential Lie triple systems with coefficients in a suitable representation. As applications of the proposed cohomology theory, we study 1-parameter formal deformations and abelian extensions of modified $\lambda$-differential Lie triple systems

Transfer Learning for HVAC System Fault Detection

Faults in HVAC systems degrade thermal comfort and energy efficiency in buildings and have received significant attention from the research community, with data driven methods gaining in popularity. Yet the lack of labeled data, such as normal versus faulty operational status, has slowed the application of machine learning to HVAC systems. In addition, for any particular building, there may be an insufficient number of observed faults over a reasonable amount of time for training. To overcome these challenges, we present a transfer methodology for a novel Bayesian classifier designed to distinguish between normal operations and faulty operations. The key is to train this classifier on a building with a large amount of sensor and fault data (for example, via simulation or standard test data) then transfer the classifier to a new building using a small amount of normal operations data from the new building. We demonstrate a proof-of-concept for transferring a classifier between architecturally similar buildings in different climates and show few samples are required to maintain classification precision and recall.Comment: 7 pages, 4 figures, accepted to American Control Conference 202

Emergent phases in a compass chain with multisite interactions

We study a dimerised spin chain with biaxial magnetic interacting ions in the presence of an externally induced three-site interactions out of equilibrium. In the general case, the three-site interactions play a role in renormalizing the effective uniform magnetic field. We find that the existence of zero-energy Majorana modes is intricately related to the sign of Pfaffian of the Bogoliubov-de Gennes Hamiltonian and the relevant $Z_2$ topological invariant. In contrast, we show that an exotic spin liquid phase can emerge in the compass limit through a Berezinskii-Kosterlitz-Thouless (BKT) quantum phase transition. Such a BKT transition is characterized by a large dynamic exponent $z=4$, and the spin-liquid phase is robust under a uniform magnetic field. We find the relative entropy and the quantum discord can signal the BKT transitions. We also uncover a few differences in deriving the correlation functions for the systems with broken reflection symmetry.Comment: 12 pages, 10 figure