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1. An arrayed optofluidic system for three-dimensional (3D) focal control via electrowetting

   https://doi.org/10.1364/OE.489508  

   Lee, Yeonwoo; Lee, Cheng-Hsun; Park, Sung-Yong (January 2023, Optics Express)

   A new lens capability for three-dimensional (3D) focal control is presented using an optofluidic system consisting ofn × narrayed liquid prisms. Each prism module contains two immiscible liquids in a rectangular cuvette. Using the electrowetting effect, the shape of the fluidic interface can be rapidly adjusted to create its straight profile with the prism’s apex angle. Consequently, an incoming ray is steered at the tilted interface due to the refractive index difference between two liquids. To achieve 3D focal control, individual prisms in the arrayed system are simultaneously modulated, allowing incoming light rays to be spatially manipulated and converged on a focal point located atP_focal(f_x,f_y,f_z) in 3D space. Analytical studies were conducted to precisely predict the prism operation required for 3D focal control. Using three liquid prisms positioned on thex-,y-, and 45°-diagonal axes, we experimentally demonstrated 3D focal tunability of the arrayed optofluidic system, achieving focal tuning along lateral, longitudinal, and axial directions as wide as 0 ≤ f_x ≤ 30 mm, 0 ≤ f_y ≤ 30 mm, and 500 mm ≤ f_z ≤ ∞. This focal tunability of the arrayed system allows for 3D control of the lens’s focusing power, which could not be attained by solid-type optics without the use of bulky and complex mechanical moving components. This innovative lens capability for 3D focal control has potential applications in eye-movement tracking for smart displays, autofocusing of smartphone cameras, or solar tracking for smart photovoltaic systems. 

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2. Tailoring Ion Transport in Li _3‐3y Ho _1+y Cl _6‐x Br _x via Transition‐Metal Free Structural Planes and Charge Carrier Distribution

   https://doi.org/10.1002/advs.202409668  

   Ogbolu, Bright O; Poudel, Tej P; Dikella, Thilina_N_D D; Truong, Erica; Chen, Yudan; Hou, Dewen; Li, Tianyi; Liu, Yuzi; Gabriel, Eric; Xiong, Hui; et al (February 2025, Advanced Science)

   Abstract Localized atomistic disorder in halide‐based solid electrolytes (SEs) can be leveraged to boost Li⁺mobility. In this study, Li⁺transport in structurally modified Li₃HoCl₆, via Br⁻introduction and Li⁺deficiency, is explored. The optimized Li_3‐3yHo_1+yCl_6‐xBr_xachieves an ionic conductivity of 3.8 mS cm⁻¹at 25 °C, the highest reported for holmium halide materials.^6,7Li nuclear magnetic resonance and relaxometry investigations unveil enhanced ion dynamics with bromination, attaining a Li⁺motional rate neighboring 116 MHz. X‐ray diffraction analyses reveal mixed‐anion‐induced phase transitions with disproportionate octahedral expansions and distortions, creating Ho‐free planes with favorable energetics for Li⁺migration. Bond valence site energy analysis highlights preferred Li⁺transport pathways, particularly in structural planes devoid of Ho³⁺blocking effects. Molecular dynamics simulations corroborate enhanced Li⁺diffusion with Br⁻introduction into Li₃HoCl₆. Li‐Ho electrostatic repulsions in the (001) plane presumably drive Li⁺diffusion into the Ho‐free (002) layer, enabling rapid intraplanar Li⁺motion and exchange between the 2d and 4h sites. Li_3‐3yHo_1+yCl_6‐xBr_xalso demonstrates good battery cycling stability. These findings offer valuable insights into the intricate correlations between structure and ion transport and will help guide the design of high‐performance fast ion conductors for all‐solid‐state batteries. 

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3. Query-Efficient Algorithm to Find all Nash Equilibria in a Two-Player Zero-Sum Matrix Game

   https://doi.org/10.1145/3732787  

   Maiti, Arnab; Boczar, Ross; Jamieson, Kevin; Ratliff, Lillian (April 2025, ACM Transactions on Economics and Computation)

   We study the query complexity of finding the set of all Nash equilibria\(\mathcal {X}_\ast \times \mathcal {Y}_\ast \)in two-player zero-sum matrix games. Fearnley and Savani [18] showed that for any randomized algorithm, there exists ann×ninput matrix where it needs to queryΩ(n²) entries in expectation to compute asingleNash equilibrium. On the other hand, Bienstock et al. [5] showed that there is a special class of matrices for which one can queryO(n) entries and compute its set of all Nash equilibria. However, these results do not fully characterize the query complexity of finding the set of all Nash equilibria in two-player zero-sum matrix games. In this work, we characterize the query complexity of finding the set of all Nash equilibria\(\mathcal {X}_\ast \times \mathcal {Y}_\ast \)in terms of the number of rowsnof the input matrix\(A \in \mathbb {R}^{n \times n} \), row support size\(k_1 := |\bigcup \limits _{x \in \mathcal {X}_\ast } \text{supp}(x)| \), and column support size\(k_2 := |\bigcup \limits _{y \in \mathcal {Y}_\ast } \text{supp}(y)| \). We design a simple yet non-trivial randomized algorithm that returns the set of all Nash equilibria\(\mathcal {X}_\ast \times \mathcal {Y}_\ast \)by querying at mostO(nk⁵· polylog(n)) entries of the input matrix\(A \in \mathbb {R}^{n \times n} \)in expectation, wherek≔ max{k₁,k₂}. This upper bound is tight up to a factor of poly(k), as we show that for any randomized algorithm, there exists ann×ninput matrix with min {k₁,k₂} = 1, for which it needs to queryΩ(nk) entries in expectation in order to find the set of all Nash equilibria\(\mathcal {X}_\ast \times \mathcal {Y}_\ast \). 

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4. Reenacting a mouse genetic evolutionary arms race in yeast reveals that SLXL1/SLX compete with SLY1/2 for binding to Spindlins

   https://doi.org/10.1073/pnas.2421446122  

   Arlt, Martin F; Kruger, Alyssa N; Swanepoel, Callie M; Mueller, Jacob L (February 2025, Proceedings of the National Academy of Sciences)

   The house mouse X and Y chromosomes have recently acquired multicopy, rapidly evolving gene families representing an evolutionary arms race. This arms race between proteins encoded by X-linkedSlxl1/Slxand Y-linkedSlygene families can distort offspring sex ratio, but how these proteins compete remains unknown. Here, we report howSlxl1/SlxandSlyencoded proteins compete in a protein family–specific and dose-dependent manner using yeast. Specifically, SLXL1 competes with SLY1 and SLY2 for binding to the Spindlin SPIN1. Similarly, SLX competes with SLY2 for binding the Spindlin SSTY2. These competitions are driven by the N termini of SLXL1, SLX, SLY1, and SLY2 binding to the third Tudor domains of SPIN1 and SSTY2. SLY1 and SLY2 form homo- and heterodimers, suggesting that the competition is between complex multimers. Residues under positive selection mapping to the interaction domains and rapid exon gain/loss are consistent with competition between the X- and Y-linked gene families. Our findings support a model in which dose-dependent competition of these X- and Y-linked encoded proteins to bind Spindlins occurs in haploid X- and Y-spermatids to influence X- versus Y-sperm fitness and thus sex ratio. 

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5. Nonlinear Information Bottleneck

   https://doi.org/10.3390/e21121181  

   Kolchinsky, Artemy; Tracey, Brendan D.; Wolpert, David H. (December 2019, Entropy)

   Information bottleneck (IB) is a technique for extracting information in one random variable X that is relevant for predicting another random variable Y. IB works by encoding X in a compressed “bottleneck” random variable M from which Y can be accurately decoded. However, finding the optimal bottleneck variable involves a difficult optimization problem, which until recently has been considered for only two limited cases: discrete X and Y with small state spaces, and continuous X and Y with a Gaussian joint distribution (in which case optimal encoding and decoding maps are linear). We propose a method for performing IB on arbitrarily-distributed discrete and/or continuous X and Y, while allowing for nonlinear encoding and decoding maps. Our approach relies on a novel non-parametric upper bound for mutual information. We describe how to implement our method using neural networks. We then show that it achieves better performance than the recently-proposed “variational IB” method on several real-world datasets. 

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