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The paradox of the plankton highlights the apparent contradiction between Gause’s law of competitive exclusion and the observed diversity of phytoplankton. It is well known that phytoplankton dynamics depend heavily on light availability. Here we treat light as a continuum of resources rather than a single resource by considering the visible light spectrum. We propose a spatially explicit reaction–diffusion–advection model to explore under what circumstance coexistence is possible from mathematical and biological perspectives. Furthermore, we provide biological context as to when coexistence is expected based on the degree of niche differentiation within the light spectrum and overall turbidity of the water.

Spontaneous electric polarization of solid ferroelectrics follows aligning directions of crystallographic axes. Domains of differently oriented polarization are separated by domain walls (DWs), which are predominantly flat and run along directions dictated by the bulk translational order and the sample surfaces. Here we explore DWs in a ferroelectric nematic (N_F) liquid crystal, which is a fluid with polar long-range orientational order but no crystallographic axes nor facets. We demonstrate that DWs in the absence of bulk and surface aligning axes are shaped as conic sections. The conics bisect the angle between two neighboring polarization fields to avoid electric charges. The remarkable bisecting properties of conic sections, known for millennia, play a central role as intrinsic features of liquid ferroelectrics. The findings could be helpful in designing patterns of electric polarization and space charge.

We propose a novel intensity diffraction tomography (IDT) reconstruction algorithm based on the split-step non-paraxial (SSNP) model for recovering the 3D refractive index (RI) distribution of multiple-scattering biological samples. High-quality IDT reconstruction requires high-angle illumination to encode both low- and high- spatial frequency information of the 3D biological sample. We show that our SSNP model can more accurately compute multiple scattering from high-angle illumination compared to paraxial approximation-based multiple-scattering models. We apply this SSNP model to both sequential and multiplexed IDT techniques. We develop a unified reconstruction algorithm for both IDT modalities that is highly computationally efficient and is implemented by a modular automatic differentiation framework. We demonstrate the capability of our reconstruction algorithm on both weakly scattering buccal epithelial cells and strongly scattering liveC. elegansworms and liveC. elegansembryos.

We investigate the fairness concerns of training a machine learning model using data with missing values. Even though there are a number of fairness intervention methods in the literature, most of them require a complete training set as input. In practice, data can have missing values, and data missing patterns can depend on group attributes (e.g. gender or race). Simply applying off-the-shelf fair learning algorithms to an imputed dataset may lead to an unfair model. In this paper, we first theoretically analyze different sources of discrimination risks when training with an imputed dataset. Then, we propose an integrated approach based on decision trees that does not require a separate process of imputation and learning. Instead, we train a tree with missing incorporated as attribute (MIA), which does not require explicit imputation, and we optimize a fairness-regularized objective function. We demonstrate that our approach outperforms existing fairness intervention methods applied to an imputed dataset, through several experiments on real-world datasets.

R-tree is a foundational data structure used in spatial databases and scientific databases. With the advancement of networks and computer architectures, in-memory data processing for R-tree in distributed systems has become a common platform. We have observed new performance challenges to process R-tree as the amount of multidimensional datasets become increasingly high. Specifically, an R-tree server can be heavily overloaded while the network and client CPU are lightly loaded, and vice versa. In this article, we present the design and implementation of Catfish, an RDMA-enabled R-tree for low latency and high throughput by adaptively utilizing the available network bandwidth and computing resources to balance the workloads between clients and servers. We design and implement two basic mechanisms of using RDMA for a client-server R-tree data processing system. First, in the fast messaging design, we use RDMA writes to send R-tree requests to the server and let server threads process R-tree requests to achieve low query latency. Second, in the RDMA offloading design, we use RDMA reads to offload tree traversal from the server to the client, which rescues the server as it is overloaded. We further develop an adaptive scheme to effectively switch an R-tree search between fast messaging andmore »RDMA offloading, maximizing the overall performance. Our experiments show that the adaptive solution of Catfish on InfiniBand significantly outperforms R-tree that uses only fast messaging or only RDMA offloading in both latency and throughput. Catfish can also deliver up to one order of magnitude performance over the traditional schemes using TCP/IP on 1 and 40 Gbps Ethernet. We make a strong case to use RDMA to effectively balance workloads in distributed systems for low latency and high throughput.« less