Quantum Dynamics of Mesoscopic Driven Duffing Oscillators

We investigate the nonlinear dynamics of a mesoscopic driven Duffing oscillator in a quantum regime. In terms of Wigner function, we identify the nature of state near the bifurcation point, and analyze the transient process which reveals two distinct stages of quenching and escape. The rate process in the escape stage allows us to extract the transition rate, which displays perfect scaling behavior with the driving distance to the bifurcation point. We numerically determine the scaling exponent, compare it with existing result, and propose open questions to be resolved.Comment: 4 pages, 4 figures; revised version accepted for publication in EP

Complex phase diagram and supercritical matter

Supercritical region is often described as uniform with no definite transitions. The distinct behaviors of the matter therein, e.g., as liquid-like and gas-like, however, indicate their should-be different belongings. Here, we provide a mathematical description of these phenomena by revisiting the Lee-Yang (LY) theory and using a complex phase diagram, e.g. a 4-D one with complex $T$ and $p$. Beyond the critical point, the 2-D phase diagram with real $T$ and $p$, i.e. the physical plane, is free of LY zeros and hence no criticality emerges. But off-plane zeros in this 4-D scenario still come into play by inducing critical anomalies for different physical properties. This is evidenced by the correlation between the Widom lines and LY edges in van der Waals model and water. The present distinct criteria to distinguish the supercritical matter manifest the high-dimensional feature of the phase diagram: e.g. when the LY zeros of complex $T$ or $p$ are projected onto the physical plane, a boundary defined by isobaric heat capacity $C_p$ or adiabatic compression coefficient $K_T$ emanates. These results demonstrate the incipient phase transition nature of the supercritical matter

The Value of Backers’ Word-of-Mouth in Screening Crowdfunding Projects: An Empirical Investigation

Reward-based crowdfunding is an emerging financing channel for entrepreneurs to raise money for their innovative projects. How to screen the crowdfunding projects is critical for crowdfunding platform, project founder, and potential backers. This study aims to investigate whether backers’ word-of-mouth (WOM) is a valuable input to generate collective intelligence for project screening. Specially, we answer three questions. First, is backers’ WOM an effective signal for implementation performance of crowdfunding projects? Second, how do the WOM help screen projects during the fund-raising process? Third, which kind of comments (positive or negative) is more effective in screening crowdfunding projects? Research hypotheses were developed based on theories of collective intelligence and WOM communication. Using a cross section dataset and a panel dataset, we get the following findings. First, backers’ negative WOM can effectively predict project implementation performance, however positive WOM does not have that prediction power. The prediction power of positive and negative WOM differs significantly. One possible reason is that negative WOM does contain more information of project quality. Second, project with more accumulative negative WOM tend to attract fewer subsequent backers. However, accumulative positive WOM is not helpful for attracting more potential backers. We conclude that negative WOM is useful for project screening project, because it is a signal of project quality, and meanwhile it could prevent backers make subsequent investments

Self-Supervised Visual Representation Learning with Semantic Grouping

In this paper, we tackle the problem of learning visual representations from unlabeled scene-centric data. Existing works have demonstrated the potential of utilizing the underlying complex structure within scene-centric data; still, they commonly rely on hand-crafted objectness priors or specialized pretext tasks to build a learning framework, which may harm generalizability. Instead, we propose contrastive learning from data-driven semantic slots, namely SlotCon, for joint semantic grouping and representation learning. The semantic grouping is performed by assigning pixels to a set of learnable prototypes, which can adapt to each sample by attentive pooling over the feature and form new slots. Based on the learned data-dependent slots, a contrastive objective is employed for representation learning, which enhances the discriminability of features, and conversely facilitates grouping semantically coherent pixels together. Compared with previous efforts, by simultaneously optimizing the two coupled objectives of semantic grouping and contrastive learning, our approach bypasses the disadvantages of hand-crafted priors and is able to learn object/group-level representations from scene-centric images. Experiments show our approach effectively decomposes complex scenes into semantic groups for feature learning and significantly benefits downstream tasks, including object detection, instance segmentation, and semantic segmentation. Code is available at: https://github.com/CVMI-Lab/SlotCon.Comment: Accepted at NeurIPS 202

On Crystal-Structure Matches in Solid-Solid Phase Transitions

The exploration of solid-solid phase transition (SSPT) suffers from the uncertainty of how two crystal structures match. We devised a theoretical framework to describe and classify crystal-structure matches (CSM). Such description fully exploits the translational and rotational symmetries and is independent of the choice of supercells. This is enabled by the use of the Hermite normal form, an analog of reduced echelon form for integer matrices. With its help, exhausting all CSMs is made possible, which goes beyond the conventional optimization schemes. As a demonstration, our enumeration algorithm unveils the long-sought concerted mechanisms in the martensitic transformation of steel accounting for the most commonly observed Kurdjumov-Sachs (KS) orientation relationship (OR) and the Nishiyama-Wassermann OR. Especially, the predominance of KS OR is explained. Given the unprecedented comprehensiveness and efficiency, our enumeration scheme provide a promising strategy for SSPT mechanism research.Comment: main text: 6 pages, 4 figures; supplemental materials: 14 pages, 6 figure