Quench Dynamics of Topological Maximally-Entangled States

We investigate the quench dynamics of the one-particle entanglement spectra (OPES) for systems with topologically nontrivial phases. By using dimerized chains as an example, it is demonstrated that the evolution of OPES for the quenched bi-partite systems is governed by an effective Hamiltonian which is characterized by a pseudo spin in a time-dependent pseudo magnetic field $\vec{S}(k,t)$. The existence and evolution of the topological maximally-entangled edge states are determined by the winding number of $\vec{S}(k,t)$ in the $k$-space. In particular, the maximally-entangled edge states survive only if nontrivial Berry phases are induced by the winding of $\vec{S}(k,t)$. In the infinite time limit the equilibrium OPES can be determined by an effective time-independent pseudo magnetic field \vec{S}_{\mb{eff}}(k). Furthermore, when maximally-entangled edge states are unstable, they are destroyed by quasiparticles within a characteristic timescale in proportional to the system size.Comment: 5 pages, 3 figure

Multi-Label Zero-Shot Learning with Structured Knowledge Graphs

In this paper, we propose a novel deep learning architecture for multi-label zero-shot learning (ML-ZSL), which is able to predict multiple unseen class labels for each input instance. Inspired by the way humans utilize semantic knowledge between objects of interests, we propose a framework that incorporates knowledge graphs for describing the relationships between multiple labels. Our model learns an information propagation mechanism from the semantic label space, which can be applied to model the interdependencies between seen and unseen class labels. With such investigation of structured knowledge graphs for visual reasoning, we show that our model can be applied for solving multi-label classification and ML-ZSL tasks. Compared to state-of-the-art approaches, comparable or improved performances can be achieved by our method.Comment: CVPR 201

Optimal Warranty Length and Selling Price to Maximize the Profit

This study focuses on the problem of determining the optimal coverage period and selling price of warranted products from the manufacturer’s perspective. We first consider how to maximize the profit per unit under the assumption that the product can be sold or the demand is independent of the warranty policy. Then we try to maximize the total profit for a planning period for the case where the demand for the product depends on the warranty coverage period and selling price. Since the warranty period and the selling price should be positively correlated, we first solve the profit maximization problem with the warranty depended demand under the constraint that the selling price is a linear function of the warranty coverage period (warranty based pricing). Furthermore, we investigate the case when such a constraint is removed (non-warranty-based pricing). Optimizing on two independent decision variables, the coverage period and the selling price, certainly improves the total profit. Under the two variable optimal conditions, it is observed that while the positive relationship between the optimal coverage period and the optimal price is confirmed, it is more complex than a linear one. We also find that the profit advantage for the non-warranty-based pricing over the warranty-based pricing is more significant for shorter coverage period. However, when the coverage period exceeds a threshold value, such a profit advantage becomes insignificant. The results of this study provide practitioners with useful insights in designing the profit optimal product warranty in highly competitive market

Deep Learning of Phase Transitions for Quantum Spin Chains from Correlation Aspects

Using machine learning (ML) to recognize different phases of matter and to infer the entire phase diagram has proven to be an effective tool given a large dataset. In our previous proposals, we have successfully explored phase transitions for topological phases of matter at low dimensions either in a supervised or an unsupervised learning protocol with the assistance of quantum information related quantities. In this work, we adopt our previous ML procedures to study quantum phase transitions of magnetism systems such as the XY and XXZ spin chains by using spin-spin correlation functions as the input data. We find that our proposed approach not only maps out the phase diagrams with accurate phase boundaries, but also indicates some new features that have not observed before. In particular, we define so-called relevant correlation functions to some corresponding phases that can always distinguish between those and their neighbors. Based on the unsupervised learning protocol we proposed [Phys. Rev. B 104, 165108 (2021)], the reduced latent representations of the inputs combined with the clustering algorithm show the connectedness or disconnectedness between neighboring clusters (phases), just corresponding to the continuous or disrupt quantum phase transition, respectively.Comment: 18 pages, 21 figure

Paraphyly of organelle DNAs in Cycas Sect. Asiorientales due to ancient ancestral polymorphisms

<p>Abstract</p> <p>Background</p> <p>This study addresses the apportionment of genetic diversity between <it>Cycas revoluta </it>and <it>C. taitungensis</it>, species that constitute the section <it>Asiorientales </it>and represent a unique, basal lineage of the Laurasian genus <it>Cycas</it>. Fossil evidence indicates divergence of the section from the rest of <it>Cycas </it>at least 30 million years ago. Geographically, <it>C. taitungensis </it>is limited to Taiwan whereas <it>C. revoluta </it>is found in the Ryukyu Archipelago and on mainland China.</p> <p>Results</p> <p>The phylogenies of ribosomal ITS region of mtDNA and the intergenic spacer between <it>atp</it>B and <it>rbc</it>L genes of cpDNA were reconstructed. Phylogenetic analyses revealed paraphyly of both loci in the two species and also in the section <it>Asiorientales</it>. The lack of reciprocal monophyly between these long isolated sections is likely due to persistent shared ancestral polymorphisms. Molecular dating estimated that mt- and cp DNA lineages coalesced to the most recent common ancestors (TMRCA) about 327 (mt) and 204 MYA (cp), corresponding with the divergence of cycad sections in the Mesozoic.</p> <p>Conclusion</p> <p>Fates of newly derived mutations of cycads follow Klopfstein et al.'s surfing model where the majority of new mutations do not spread geographically and remain at low frequencies or are eventually lost by genetic drift. Only successful 'surfing mutations' reach very high frequencies and occupy a large portion of a species range. These mutations exist as dominant cytotypes across populations and species. Geographical subdivision is lacking in both species, even though recurrent gene flow by both pollen and seed is severely limited. In total, the contrasting levels between historical and ongoing gene flow, large population sizes, a long lifespan, and slow mutation rates in both organelle DNAs have all likely contributed to the unusually long duration of paraphyly in cycads.</p