Global existence and stability for the modified Mullins–Sekerka and surface diffusion flow

<abstract><p>In this survey we present the state of the art about the asymptotic behavior and stability of the <italic>modified Mullins</italic>–<italic>Sekerka flow</italic> and the <italic>surface diffusion flow</italic> of smooth sets, mainly due to E. Acerbi, N. Fusco, V. Julin and M. Morini. First we discuss in detail the properties of the nonlocal Area functional under a volume constraint, of which the two flows are the gradient flow with respect to suitable norms, in particular, we define the <italic>strict stability</italic> property for a critical set of such functional and we show that it is a necessary and sufficient condition for minimality under $ W^{2, p} $–perturbations, holding in any dimension. Then, we show that, in dimensions two and three, for initial sets sufficiently "close" to a smooth <italic>strictly stable critical</italic> set $ E $, both flows exist for all positive times and asymptotically "converge" to a translate of $ E $.</p></abstract>

Distributed Stochastic Optimization with Large Delays

The recent surge of breakthroughs in machine learning and artificial intelligence has sparked renewed interest in large-scale stochastic optimization problems that are universally considered hard. One of the most widely used methods for solving such problems is distributed asynchronous stochastic gradient descent (DASGD), a family of algorithms that result from parallelizing stochastic gradient descent on distributed computing architectures (possibly) asychronously. However, a key obstacle in the efficient implementation of DASGD is the issue of delays: when a computing node contributes a gradient update, the global model parameter may have already been updated by other nodes several times over, thereby rendering this gradient information stale. These delays can quickly add up if the computational throughput of a node is saturated, so the convergence of DASGD may be compromised in the presence of large delays. Our first contribution is that, by carefully tuning the algorithm’s step size, convergence to the critical set is still achieved in mean square, even if the delays grow unbounded at a polynomial rate. We also establish finer results in a broad class of structured optimization problems (called variationally coherent), where we show that DASGD converges to a global optimum with a probability of one under the same delay assumptions. Together, these results contribute to the broad landscape of large-scale nonconvex stochastic optimization by offering state-of-the-art theoretical guarantees and providing insights for algorithm design.

The Menin-MLL1 interaction is a molecular dependency in NUP98-rearranged AML

Translocations involving the NUP98 gene produce NUP98-fusion proteins and are associated with a poor prognosis in acute myeloid leukemia (AML). MLL1 is a molecular dependency in NUP98-fusion leukemia, and therefore we investigated the efficacy of therapeutic blockade of the Menin-MLL1 interaction in NUP98-fusion leukemia models. Using mouse leukemia cell lines driven by NUP98-HOXA9 and NUP98-JARID1A fusion oncoproteins, we demonstrate that NUP98-fusion driven leukemia is sensitive to the Menin-MLL1 inhibitor VTP50469, with an IC50 similar to what we have previously reported for MLL-rearranged and NPM1c leukemia cells. Menin-MLL1 inhibition upregulates markers of differentiation such as CD11b and downregulates expression of pro-leukemogenic transcription factors such as Meis1 in NUP98-fusion transformed leukemia cells. We demonstrate that MLL1 and the NUP98 fusion protein itself are evicted from chromatin at a critical set of genes that are essential for maintenance of the malignant phenotype. In addition to these in vitro studies, we established patient-derived xenograft (PDX) models of NUP98-fusion driven AML to test the in vivo efficacy of Menin-MLL1 inhibition. Treatment with VTP50469 significantly prolongs survival of mice engrafted with NUP98-NSD1 and NUP98-JARID1A leukemias. Gene expression analysis revealed that Menin-MLL1 inhibition simultaneously suppresses a pro-leukemogenic gene expression program, including downregulation of the HOXA cluster, and upregulates tissue-specific markers of differentiation. These preclinical results suggest that Menin-MLL1 inhibition may represent a rational, targeted therapy for patients with NUP98-rearranged leukemias.

Integrable Systems on Singular Symplectic Manifolds: From Local to Global

In this article, we consider integrable systems on manifolds endowed with symplectic structures with singularities of order one. These structures are symplectic away from a hypersurface where the symplectic volume goes either to infinity or to zero transversally, yielding either a $b$-symplectic form or a folded symplectic form. The hypersurface where the form degenerates is called critical set. We give a new impulse to the investigation of the existence of action-angle coordinates for these structures initiated in [34] and [35] by proving an action-angle theorem for folded symplectic integrable systems. Contrary to expectations, the action-angle coordinate theorem for folded symplectic manifolds cannot be presented as a cotangent lift as done for symplectic and $b$-symplectic forms in [34]. Global constructions of integrable systems are provided and obstructions for the global existence of action-angle coordinates are investigated in both scenarios. The new topological obstructions found emanate from the topology of the critical set $Z$ of the singular symplectic manifold. The existence of these obstructions in turn implies the existence of singularities for the integrable system on $Z$.

A Block-Based Arduino Programming Platform for Developing Computational Thinking Skills for K-12 Students

As a critical set of skills in the 21st century, computational thinking has attracted increasing attention in K-12 education. Microcontrollers, combined with LEDs, actuators, and a variety of sensors, provide students countless real-world projects, such as autonomous vehicles, smart homes, and robotics. By solving those projects through programming, students will not only learn computational skills but also benefit from the hands-on activities to get some experience on solving real-world problems. It makes microcontroller projects a perfect tool to develop the computational thinking skills of K-12 students. Our previous work has proposed a solution for higher graders to program Arduino through Ch, a C/C++ interpreter. It is necessary, however, to develop a platform for lower graders (K-6) since most of them do not have the ability to type through the keyboard. This paper extends our previous work such that students can program Arduino on RoboBlockly, a block-based programming platform. In the paper, we will present two case studies to demonstrate how to build blocks to control the Arduino board and what concepts students will learn from those projects. In addition, the proposed platform also provides an interactive way of transitioning students from the block-based program to a text-based program in Ch.

A population of descending neurons that regulate the flight motor of Drosophila

Like many insect species, Drosophila melanogaster are capable of maintaining a stable flight trajectory for periods lasting up to several hours(1, 2). Because aerodynamic torque is roughly proportional to the fifth power of wing length(3), even small asymmetries in wing size require the maintenance of subtle bilateral differences in flapping motion to maintain a stable path. Flies can even fly straight after losing half of a wing, a feat they accomplish via very large, sustained kinematic changes to the both damaged and intact wings(4). Thus, the neural network responsible for stable flight must be capable of sustaining fine-scaled control over wing motion across a large dynamic range. In this paper, we describe an unusual type of descending neurons (DNg02) that project directly from visual output regions of the brain to the dorsal flight neuropil of the ventral nerve cord. Unlike most descending neurons, which exist as single bilateral pairs with unique morphology, there is a population of at least 15 DNg02 cell pairs with nearly identical shape. By optogenetically activating different numbers of DNg02 cells, we demonstrate that these neurons regulate wingbeat amplitude over a wide dynamic range via a population code. Using 2-photon functional imaging, we show that DNg02 cells are responsive to visual motion during flight in a manner that would make them well suited to continuously regulate bilateral changes in wing kinematics. Collectively, we have identified a critical set of DNs that provide the sensitivity and dynamic range required for flight control.

CLIGEN parameter regionalization for mainland China

The stochastic weather generator CLIGEN can simulate long-term weather sequences as input to WEPP for erosion predictions. Its use, however, has been somewhat restricted by limited observations at high spatial–temporal resolutions. Long-term daily temperature, daily, and hourly precipitation data from 2405 stations and daily solar radiation from 130 stations distributed across mainland China were collected to develop the most critical set of site-specific parameter values for CLIGEN. Ordinary kriging (OK) and universal kriging (UK) with auxiliary covariables, i.e., longitude, latitude, elevation, and the mean annual rainfall, were used to interpolate parameter values into a 10 km×10 km grid, and the interpolation accuracy was evaluated based on the leave-one-out cross-validation. Results showed that UK generally outperformed OK. The root mean square error between UK-interpolated and observed temperature-related parameters was ≤0.88 ∘C (1.58 ∘F). The Nash–Sutcliffe efficiency coefficient for precipitation- and solar-radiation-related parameters was ≥0.87, except for the skewness coefficient of daily precipitation, which was 0.78. In addition, CLIGEN-simulated daily weather sequences using UK-interpolated and observed parameters showed consistent statistics and frequency distributions. The mean absolute discrepancy between the two sequences for temperature was <0.51 ∘C, and the mean absolute relative discrepancy for solar radiation, precipitation amount, duration, and maximum 30 min intensity was <5 % in terms of the mean and standard deviation. These CLIGEN parameter values at 10 km resolution would meet the minimum data requirements for WEPP application throughout mainland China. The dataset is available at http://clicia.bnu.edu.cn/data/cligen.html (last access: 20 May 2021) and https://doi.org/10.12275/bnu.clicia.CLIGEN.CN.gridinput.001 (Wang et al., 2020).

Structural basis for late maturation steps of the human mitoribosomal large subunit

Mitochondrial ribosomes (mitoribosomes) synthesize a critical set of proteins essential for oxidative phosphorylation. Therefore, mitoribosomal function is vital to the cellular energy supply. Mitoribosome biogenesis follows distinct molecular pathways that remain poorly understood. Here, we determine the cryo-EM structures of mitoribosomes isolated from human cell lines with either depleted or overexpressed mitoribosome assembly factor GTPBP5, allowing us to capture consecutive steps during mitoribosomal large subunit (mt-LSU) biogenesis. Our structures provide essential insights into the last steps of 16S rRNA folding, methylation and peptidyl transferase centre (PTC) completion, which require the coordinated action of nine assembly factors. We show that mammalian-specific MTERF4 contributes to the folding of 16S rRNA, allowing 16 S rRNA methylation by MRM2, while GTPBP5 and NSUN4 promote fine-tuning rRNA rearrangements leading to PTC formation. Moreover, our data reveal an unexpected involvement of the elongation factor mtEF-Tu in mt-LSU assembly, where mtEF-Tu interacts with GTPBP5, similar to its interaction with tRNA during translational elongation.

Periodic points of post-critically algebraic holomorphic endomorphisms

A holomorphic endomorphism of ${{\mathbb {CP}}}^n$ is post-critically algebraic if its critical hypersurfaces are periodic or preperiodic. This notion generalizes the notion of post-critically finite rational maps in dimension one. We will study the eigenvalues of the differential of such a map along a periodic cycle. When $n=1$ , a well-known fact is that the eigenvalue along a periodic cycle of a post-critically finite rational map is either superattracting or repelling. We prove that, when $n=2$ , the eigenvalues are still either superattracting or repelling. This is an improvement of a result by Mattias Jonsson [Some properties of 2-critically finite holomorphic maps of P2. Ergod. Th. & Dynam. Sys.18(1) (1998), 171–187]. When $n\geq 2$ and the cycle is outside the post-critical set, we prove that the eigenvalues are repelling. This result improves one obtained by Fornæss and Sibony [Complex dynamics in higher dimension. II. Modern Methods in Complex Analysis (Princeton, NJ, 1992) (Annals of Mathematics Studies, 137). Ed. T. Bloom, D. W. Catlin, J. P. D’Angelo and Y.-T. Siu, Princeton University Press, 1995, pp. 135–182] under a hyperbolicity assumption on the complement of the post-critical set.