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Structural organization of the spongy mesophyll
Summary Many plant leaves have two layers of photosynthetic tissue: the palisade and spongy mesophyll. Whereas palisade mesophyll consists of tightly packed columnar cells, the structure of spongy mesophyll is not well characterized and often treated as a random assemblage of irregularly shaped cells. Using micro‐computed tomography imaging, topological analysis, and a comparative physiological framework, we examined the structure of the spongy mesophyll in 40 species from 30 genera with laminar leaves and reticulate venation. A spectrum of spongy mesophyll diversity encompassed two dominant phenotypes: first, an ordered, honeycomblike tissue structure that emerged from the spatial coordination of multilobed cells, conforming to the physical principles of Euler’s law; and second, a less‐ordered, isotropic network of cells. Phenotypic variation was associated with transitions in cell size, cell packing density, mesophyll surface‐area‐to‐volume ratio, vein density, and maximum photosynthetic rate. These results show that simple principles may govern the organization and scaling of the spongy mesophyll in many plants and demonstrate the presence of structural patterns associated with leaf function. This improved understanding of mesophyll anatomy provides new opportunities for spatially explicit analyses of leaf development, physiology, and biomechanics.
High-Pressure Electrides: A Quantum Chemical Perspective
It has long been assumed that all matter will adopt simple close-packed lattices and become metallic under pressure, in accordance with the Thomas–Fermi–Dirac (TFD) model. However, this model struggles to explain pressure-driven complex structural transitions that have been observed in elements, including sodium, challenging our conventional understanding of compressed matter. Moreover, in stark contrast to the TFD model, first-principles calculations suggest that various elements and compounds become electrides under pressure. Electrides, characterized by concentrations of charge density at interstitial regions, can be thought of as ionic compounds where electrons behave as the anions. Though ambient-pressure molecular electrides have been extensively studied via experiments and computations, high-pressure electrides (HPEs) are not well-understood. The identification and characterization of HPEs have been, to date, based purely on theory, including topological analysis of the electron density and the electron localization function. Here, we review these theoretical analysis tools and suggest guidelines that can be used to classify systems as electrides. Moreover, we describe models used to rationalize the electronic structure of HPEs, drawing parallels with ambient-pressure molecular systems, and encourage the development of experimental techniques that provide evidence for the theoretically calculated charge localization.
Streaming Statistics
In the context of a larger effort for in situ data analytics, there is a need to calculate basic statistics metrics (e.g., count, mean, median) online as new data points become available. Originally, the code for such online, or in other words streaming, statistics was part of the TALASS (Topological Analysis of Large- Scale Simulations) library. We isolated the relevant code and created a standalone library from it called Streaming Statistics. We also added an ability to serialize and deserialize the statistics objects so that the library can be used in distributed, task-based processing. To use the Streaming Statistics library, the user chooses a statistic, constructs an object for it, and then "adds" values to it, which means the statistic is augmented.
Elucidating the Determinants of Alkali Ionic Conductivity in Oxide and Sulfide Frameworks
The aim of this project is to elucidate the structural and chemical factors determining alkali conductivity in oxide and sulfide frameworks using large scale first principles calculations and topological analysis. The facile conduction of alkali ions in oxide and sulfide host structures is of critical importance in energy storage. Today, the dominant form of energy storage in portable electronics is the rechargeable alkali-ion battery, a device that functions entirely on the basis of the reversible transport of alkali ions. The Li+/Na+ conductivity of a cathode has a direct influence on the rate capability of a Li/Na-ion battery, i.e., the speed at which it can be charged and discharged. Alkali conductivity is arguably of even greater importance in the solid electrolytes currently being investigated for high safety, high energy all-solid-state batteries. The research performed in this project has provided critical new insights into the diffusion mechanisms in state-of-the-art alkali superionic conductors such as Li 7 P 3 S 11 , Li 3 OCl 1-x Br x anti-perovskite, argyrodite Li 6 PS 5 Cl. Two potential novel lithium superionic conductors (Li 3 Y(PS 4 ) 2 and Li 5 PS 4 Cl 2 ) with improved electrochemical stabilities were predicted. We have also conducted in-depth studies into alkali conduction in several important classes of electrodes, including the layered P2 NaMO 2 oxides and the highly promising novel disordered rock salt Li 3+x V 2 O 5 anode for high-rate applications. This project has resulted in more than 10 peer-reviewed articles in highly regarded journals as well as a new open-source software framework (pymatgen-analysis-diffusion) that is widely used by the materials research community for the study of diffusion in materials.
Phase Boundaries, Isotope Effect and Superconductivity of Lithium Under Hydrostatic Conditions
We present theoretical and experimental studies of superconductivity and low temperature structural phase boundaries in lithium. We mapped the structural phase diagram of 6Li and 7Li under hydrostatic conditions between 5 – 55 GPa and within the temperature range of 15 – 75 K, observing the FCC → hR1 → cI16 phase transitions. 6Li and 7Li show some differences at the structural boundaries, with a potential shift of the phase boundaries of 6Li to lower pressures. Density functional theory calculations and topological analysis of the electron density elucidates the superconducting properties and interatomic interactions within these phases of lithium.
Mars: Noachian hydrology by its statistics and topology
Discrimination between fluvial features generated by surface drainage and subsurface aquifer discharges will provide clues to the understanding of early Mars' climatic history. Our approach is to define the process of formation of the oldest fluvial valleys by statistical and topological analyses. Formation of fluvial valley systems reached its highest statistical concentration during the Noachian Period. Nevertheless, they are a scarce phenomenom in Martian history, localized on the craterized upland, and subject to latitudinal distribution. They occur sparsely on Noachian geological units with a weak distribution density, and appear in reduced isolated surface (around 5 x 10(exp 3)(sq km)), filled by short streams (100-300 km length). Topological analysis of the internal organization of 71 surveyed Noachian fluvial valley networks also provides information on the mechanisms of formation.
The Anomalous Low State of LMC X-3
Archival RXTE ASM and PCA observations of the black hole binary LMC X-3 reveal a dramatic and extended low state lasting from December 8, 2003 until March 18, 2004, unprecedented both in its Low luminosity (Lx(2-10keV)=4.2x 1035 ergs s-1, approximately 4 times fainter than ever before seen from LMC X-3 in its low/hard state, and representing 0.15% of its X-ray luminosity during the high/soft state); and Long duration (approximately equal to 100 days, as compared with 5-20 days for 'normal' low/hard state excursions). During this anomalous low state no significant variability is observed on timescales of days-weeks, and the spectrum is well described by a simple power law with index 1.7 plus or minus 0.2. We examine the variability characteristics of LMC X-3 before and after this event using conventional and topological methods, and show that with the exception of the anomalous low state itself the long-term behavior of the source in topological phase space can be completely described in terms of a well-understood nonlinear dynamics system known as the Duffing oscillator, implying that the accretion disk in LMC X-3 is a driven, dissipative system with two solutions competing for control of its time evolution. This work shows that dynamical information and constraints revealed by topological analysis methods can provide a valuable addition to traditional studies of accretion disk behavior.
Sensitivity Analysis of Compensation Topologies for Dynamic WPT System
The dynamic wireless power transfer (DWPT) or in-motion charging of electric vehicles (EVs) may alleviate the challenges encountered by the plug-in charging systems and assist in the penetration of the EVs at a larger scale. Similar to its stationary charging counterpart, DPWT also makes use of compensation circuits to reduce the inductive reactance for enabling higher current on the coupler winding and improve the power transfer. However, the behavior of compensation circuits has not been comprehensively analyzed in a DWPT system. This paper analyzes in detail the performance of three compensation topologies applied to the DWPT system. A combination of finite element analysis (FEA) and circuit analysis is employed to study the compensation topologies when the receiving coil moves over the transmitting coil. Moreover, the variations in operating frequency have also been considered in the analysis. Furthermore, the theoretical calculations for the dynamic WPT system are verified using PLECS simulation model.
Truss topology optimization with simultaneous analysis and design
Strategies for topology optimization of trusses for minimum weight subject to stress and displacement constraints by Simultaneous Analysis and Design (SAND) are considered. The ground structure approach is used. A penalty function formulation of SAND is compared with an augmented Lagrangian formulation. The efficiency of SAND in handling combinations of general constraints is tested. A strategy for obtaining an optimal topology by minimizing the compliance of the truss is compared with a direct weight minimization solution to satisfy stress and displacement constraints. It is shown that for some problems, starting from the ground structure and using SAND is better than starting from a minimum compliance topology design and optimizing only the cross sections for minimum weight under stress and displacement constraints. A member elimination strategy to save CPU time is discussed.
Topological structure of complex predictions
Abstract Current complex prediction models are the result of fitting deep neural networks, graph convolutional networks or transducers to a set of training data. A key challenge with these models is that they are highly parameterized, which makes describing and interpreting the prediction strategies difficult. We use topological data analysis to transform these complex prediction models into a simplified topological view of the prediction landscape. The result is a map of the predictions that enables inspection of the model results with more specificity than dimensionality-reduction methods such as tSNE and UMAP. The methods scale up to large datasets across different domains. We present a case study of a transformer-based model previously designed to predict expression levels of a piece of DNA in thousands of genomic tracks. When the model is used to study mutations in the BRCA1 gene, our topological analysis shows that it is sensitive to the location of a mutation and the exon structure of BRCA1 in ways that cannot be found with tools based on dimensionality reduction. Moreover, the topological framework offers multiple ways to inspect results, including an error estimate that is more accurate than model uncertainty. Further studies show how these ideas produce useful results in graph-based learning and image classification.
A Laplace-Domain Circuit Model for Fault and Stability Analysis Considering Unbalanced Topology
For systems subject to unbalanced faults, analytical model building for stability assessment is a challenging task. This letter presents a straightforward modeling approach. A generalized dynamic circuit representation is achieved by use of the Laplacian transform variable s . Here, we translate the voltage and current relationship at the fault location into the relationship of three subsystems. The final circuit model is an interconnected sequence network with impedances in the Laplace domain. This circuit can be directly converted from a steady-state sequence network. This modeling procedure is illustrated by an example case of an induction motor served by a grid through a series compensated line. Electromagnetic transient simulation results demonstrate that sub-synchronous oscillations can be mitigated when a single-line to ground fault is applied at the motor terminal. Stability analysis results based on the dynamic circuit corroborate the simulation results. What's more, the derived circuit effortlessly reveals why unbalance can enhance stability.
Quantitative µ-CT Analysis of Scale Topology Formed During Oxidation of High SiMo Cast Iron
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Statistical analysis of topologically-tracked fast flows
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Topology design and performance analysis of an integrated communication network
A research study on the topology design and performance analysis for the Space Station Information System (SSIS) network is conducted. It is begun with a survey of existing research efforts in network topology design. Then a new approach for topology design is presented. It uses an efficient algorithm to generate candidate network designs (consisting of subsets of the set of all network components) in increasing order of their total costs, and checks each design to see if it forms an acceptable network. This technique gives the true cost-optimal network, and is particularly useful when the network has many constraints and not too many components. The algorithm for generating subsets is described in detail, and various aspects of the overall design procedure are discussed. Two more efficient versions of this algorithm (applicable in specific situations) are also given. Next, two important aspects of network performance analysis: network reliability and message delays are discussed. A new model is introduced to study the reliability of a network with dependent failures. For message delays, a collection of formulas from existing research results is given to compute or estimate the delays of messages in a communication network without making the independence assumption. The design algorithm coded in PASCAL is included as an appendix.
Computer evaluation of topological formulas for network analysis
Single tree-finding program for digital computer evaluation of topological formulas for network analysis
The persistence of large scale structures. Part I. Primordial non-Gaussianity
Abstract We develop an analysis pipeline for characterizing the topology of large scale structure and extracting cosmological constraints based on persistent homology . Persistent homology is a technique from topological data analysis that quantifies the multiscale topology of a data set, in our context unifying the contributions of clusters, filament loops, and cosmic voids to cosmological constraints. We describe how this method captures the imprint of primordial local non-Gaussianity on the late-time distribution of dark matter halos, using a set of N-body simulations as a proxy for real data analysis. For our best single statistic, running the pipeline on several cubic volumes of size 40 (Gpc/h) 3 , we detect f NL loc =10 at 97.5% confidence on ~ 85% of the volumes. Additionally wetest our ability to resolve degeneracies betweenthe topological signature of f NL loc and variation of σ 8 and argue that correctly identifying nonzero f NL loc in this case is possible via an optimal template method. Our method relies on information living at $\mathcal{O}$(10) Mpc/h, a complementary scale with respect to commonly used methods such as the scale-dependent bias in the halo/galaxy power spectrum. Therefore, while still requiring a large volume, our method does not require sampling long-wavelength modes to constrain primordial non-Gaussianity. Moreover, our statistics are interpretable: we are able to reproduce previous results in certain limits and we make new predictions for unexplored observables, such as filament loops formed by dark matter halos in a simulation box.
Robustness of topological persistence in knowledge distillation for wearable sensor data
Topological data analysis (TDA) has shown great success in various applications involving wearable sensor data. However, there are difficulties in leveraging topological features in machine learning and wearable sensors because of the large time consumption and computational resources required to extract the features. To address this problem, knowledge distillation (KD) is utilized to generate a small model and accommodate topological features with persistence image (PI) representations from the raw time series data. Deploying topological knowledge in KD enables the student to achieve better performance compared to the one trained solely on raw time series data. However, it is not yet known if there are coherent characteristics for topological features in PI, which can aid in improving the performance during KD. In this paper, we investigate the suitability and challenges of utilizing topological features in KD for wearable sensor data, thereby contributing to the advancement of the field. Our study explores the impact of transferred topological features by comparing the Teacher-to-Student framework with Multiple Teachers-to-Student where teachers utilize both time series data and persistence images obtained by TDA as inputs. Additionally, we conduct a rigorous examination of topological knowledge effects by testing under various corruptions, knowledge types, and learning strategies in the context of human activity recognition tasks. Our analysis of topological features in KD presents the optimal strategy for incorporating these features. This study includes datasets of varying scales, window lengths, and activity classes, providing a comprehensive evaluation. Our results demonstrate that leveraging topological features in KD to enhance performance across databases.