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This is an expanded written version of a plenary talk delivered at ICMP 2021. We describe some rigorous results in quantum field theory that have been obtained in recent years, with particular emphasis on those results on relative entropies in the setting of conformal field theory. These results are motivated in part by recent work of physicists which, however, depends on heuristic arguments—such as introducing cutoff and using path integrals and replica trick—which are hard to justify mathematically. Our main technical tools are from the theory of operator algebras, such as modular theory and the theory of subfactors. A discussion about open problems is presented at the end the paper.

 

Learning fair representations is an essential task to reduce bias in data-oriented decision making. It protects minority subgroups by requiring the learned representations to be independent of sensitive attributes. To achieve independence, the vast majority of the existing work primarily relaxes it to the minimization of the mutual information between sensitive attributes and learned representations. However, direct computation of mutual information is computationally intractable, and various upper bounds currently used either are still intractable or contradict the utility of the learned representations. In this paper, we introduce distance covariance as a new dependence measure into fair representation learning. By observing that sensitive attributes (e.g., gender, race, and age group) are typically categorical, the distance covariance can be converted to a tractable penalty term without contradicting the utility desideratum. Based on the tractable penalty, we propose FairDisCo, a variational method to learn fair representations. Experiments demonstrate that FairDisCo outperforms existing competitors for fair representation learning. 

Co-evolving sequences are ubiquitous in a variety of applications, where different sequences are often inherently inter-connected with each other. We refer to such sequences, together with their inherent connections modeled as a structured network, as network of co-evolving sequences (NoCES). Typical NoCES applications in- clude road traffic monitoring, company revenue prediction, motion capture, etc. To date, it remains a daunting challenge to accurately model NoCES due to the coupling between network structure and sequences. In this paper, we propose to modeling NoCES with the aim of simultaneously capturing both the dynamics and the inter- play between network structure and sequences. Specifically, we propose a joint learning framework to alternatively update the network representations and sequence representations as the se- quences evolve over time. A unique feature of our framework lies in that it can deal with the case when there are co-evolving sequences on both network nodes and edges. Experimental evaluations on four real datasets demonstrate that the proposed approach (1) out- performs the existing competitors in terms of prediction accuracy, and (2) scales linearly w.r.t. the sequence length and the network size. 

Raindrop size distributions (DSD) and rain rate have been estimated from polarimetric radar data using different approaches with the accuracy depending on the errors both in the radar measurements and the estimation methods. Herein, a deep neural network (DNN) technique was utilized to improve the estimation of the DSD and rain rate by mitigating these errors. The performance of this approach was evaluated using measurements from a two-dimensional video disdrometer (2DVD) at the Kessler Atmospheric and Ecological Field Station in Oklahoma as ground truth with the results compared against conventional estimation methods for the period 2006–17. Physical parameters (mass-/volume-weighted diameter and liquid water content), rain rate, and polarimetric radar variables (including radar reflectivity and differential reflectivity) were obtained from the DSD data. Three methods—physics-based inversion, empirical formula, and DNN—were applied to two different temporal domains (instantaneous and rain-event average) with three diverse error assumptions (fitting, measurement, and model errors). The DSD retrievals and rain estimates from 18 cases were evaluated by calculating the bias and root-mean-squared error (RMSE). DNN produced the best performance for most cases, with up to a 5% reduction in RMSE when model errors existed. DSD and rain estimated from a nearby polarimetric radar using the empirical and DNN methods were well correlated with the disdrometer observations; the rain-rate estimate bias of the DNN was significantly reduced (3.3% in DNN vs 50.1% in empirical). These results suggest that DNN has advantages over the physics-based and empirical methods in retrieving rain microphysics from radar observations.

 

Abstract One of the most poorly understood aspects of low-mass star formation is how multiple-star systems are formed. Here we present the results of Atacama Large Millimeter/submillimeter Array (ALMA) Band 6 observations toward a forming quadruple protostellar system, G206.93-16.61E2, in the Orion B molecular cloud. ALMA 1.3 mm continuum emission reveals four compact objects, of which two are Class I young stellar objects and the other two are likely in prestellar phase. The 1.3 mm continuum emission also shows three asymmetric ribbon-like structures that are connected to the four objects, with lengths ranging from ∼500 to ∼2200 au. By comparing our data with magnetohydrodynamic simulations, we suggest that these ribbons trace accretion flows and also function as gas bridges connecting the member protostars. Additionally, ALMA CO J = 2−1 line emission reveals a complicated molecular outflow associated with G206.93-16.61E2, with arc-like structures suggestive of an outflow cavity viewed pole-on. 

Hybrid microfluidic systems that are composed of multiple different types of substrates have been recognized as a versatile and superior platform, which can draw benefits from different substrates while avoiding their limitations. This review article introduces the recent innovations of different types of low-cost hybrid microfluidic devices, particularly focusing on cost-effective polymer- and paper-based hybrid microfluidic devices. In this article, the fabrication of these hybrid microfluidic devices is briefly described and summarized. We then highlight various hybrid microfluidic systems, including polydimethylsiloxane (PDMS)-based, thermoplastic-based, paper/polymer hybrid systems, as well as other emerging hybrid systems (such as thread-based). The special benefits of using these hybrid systems have been summarized accordingly. A broad range of biological and biomedical applications using these hybrid microfluidic devices are discussed in detail, including nucleic acid analysis, protein analysis, cellular analysis, 3D cell culture, organ-on-a-chip, and tissue engineering. The perspective trends of hybrid microfluidic systems involving the improvement of fabrication techniques and broader applications are also discussed at the end of the review. 

Knowledge of the sound velocity of core materials is essential to explain the observed anomalously low shear wave velocity (V_S) and high Poisson’s ratio (σ) in the solid inner core. To date, neitherV_Snorσof Fe and Fe-Si alloy have been measured under core conditions. Here, we presentV_Sandσderived from direct measurements of the compressional wave velocity, bulk sound velocity, and density of Fe and Fe-8.6 wt%Si up to ~230 GPa and ~5400 K. The new data show that neither the effect of temperature nor incorporation of Si would be sufficient to explain the observed lowV_Sand highσof the inner core. A possible solution would add carbon (C) into the solid inner core that could further decreaseV_Sand increaseσ. However, the physical property-based Fe-Si-C core models seemingly conflict with the partitioning behavior of Si and C between liquid and solid Fe.

 

Attributed network embedding aims to learn low dimensional node representations by combining both the network's topological structure and node attributes. Most of the existing methods either propagate the attributes over the network structure or learn the node representations by an encoder-decoder framework. However, propagation based methods tend to prefer network structure to node attributes, whereas encoder-decoder methods tend to ignore the longer connections beyond the immediate neighbors. In order to address these limitations while enjoying the best of the two worlds, we design cross fusion layers for unsupervised attributed network embedding. Specifically, we first construct two separate views to handle network structure and node attributes, and then design cross fusion layers to allow flexible information exchange and integration between the two views. The key design goals of the cross fusion layers are three-fold: 1) allowing critical information to be propagated along the network structure, 2) encoding the heterogeneity in the local neighborhood of each node during propagation, and 3) incorporating an additional node attribute channel so that the attribute information will not be overshadowed by the structure view. Extensive experiments on three datasets and three downstream tasks demonstrate the effectiveness of the proposed method.