Mathematical Systems & Solutions (United States)

The Psyche Multispectral Imager (“the Imager”) is a payload system designed to directly achieve or to indirectly enable the key scientific goals and optical navigation requirements of NASA’s Psyche mission, which will conduct the first up-close orbital investigation of the metal-rich Main Belt asteroid (16) Psyche. The Imager consists of a pair of block redundant cameras and electronics that are mounted inside the thermally controlled spacecraft body, with a view out the spacecraft −X panel that will be nadir-pointed during nominal asteroid orbital mapping operations. The two identical Camera Heads are connected to a separate Digital Electronics Assembly (DEA) box that interfaces to the spacecraft avionics and that provides power, commanding, data processing, and onboard image storage. The Imager system shares significant heritage with imaging instruments flown on the Mars Climate Orbiter, the Mars Science Laboratory and Mars 2020 rovers, and Juno. Each camera consists of a 1600 × 1200 photosensitive pixel charge-coupled device (CCD) detector and its associated electronics, a 9-position filter wheel assembly, a compact catadioptric f/2.9 telescope with a fixed focal length of 148 mm, and a sunshade to minimize stray and scattered light. The Imager CCD, filters, and optics enable broadband polychromatic (∼540 ± 250 nm) imaging plus narrowband imaging in 7 colors centered from 439 to 1015 nm. An additional neutral density filter enables protection of the CCD from direct solar illumination. Each camera has a field of view of 4.6° × 3.4° and an instantaneous field of view of 50 μrad/pixel that enables imaging of the asteroid at scales ranging from ∼35 m/pix from 700 km altitude to ∼4 m/pix at 75 km altitude. The primary camera (“Imager A”) is pointed along the spacecraft −X axis, and the backup camera (“Imager B”) is toed-out by 3.7° to potentially enable greater surface area coverage per unit time if both Imagers are operated simultaneously during some mission phases. Stereoscopic mapping is performed by observing the same surface regions with either camera over a range of off-nadir pointing angles.

We study the best low-rank Tucker decomposition of symmetric tensors. The motivating application is decomposing higher-order multivariate moments. Moment tensors have special structure and are important to various data science problems. We advocate for projected gradient descent (PGD) method and higher-order eigenvalue decomposition (HOEVD) approximation as computation schemes. Most importantly, we develop scalable adaptations of the basic PGD and HOEVD methods to decompose sample moment tensors. With the help of implicit and streaming techniques, we evade the overhead cost of building and storing the moment tensor. Such reductions make computing the Tucker decomposition realizable for large data instances in high dimensions. Numerical experiments demonstrate the efficiency of the algorithms and the applicability of moment tensor decompositions to real-world datasets. Finally we study the convergence on the Grassmannian manifold, and prove that the update sequence derived by the PGD solver achieves first-and second-order criticality.

Abstract During development, embryonic patterning systems direct a set of initially uncommitted pluripotent cells to differentiate into a variety of cell types and tissues. A core network of transcription factors, such as Zelda/POU5F1, Odd-paired (Opa)/ZIC and Ocelliless (Oc)/OTX, are conserved across animals. While Opa is essential for a second wave of zygotic activation after Zelda, it is unclear whether Opa drives head cell specification past gastrulation onset, in theDrosophilaembryo. Our hypothesis is that Opa and Oc are interacting with distinct cis-regulatory regions for shaping cell fates in the embryonic head. Using super-resolution microscopy and epigenomic meta-analysis of single cell RNAseq datasets we find thatopa’s andoc’s overlapping expression domains are dynamic in the head region, with both factors being simultaneously transcribed at the blastula stage. However, analysis of single-embryo RNAseq data reveals a subgroup of Opa-bound genes to be Opa-independent in the cellularized embryo. Interrogation of these genes against Oc ChIPseq combined with in situ data, suggests that Opa is competing with Oc for the regulation of a subgroup of genes later in gastrulation. Specifically, we find that Oc binds to late, head-specific enhancers independently and activates them in a head-specific wave of zygotic transcription, suggesting distinct roles for Oc in the blastula and gastrula stages.

Abstract Building accurate knowledge of the identity, the geographic distribution and the evolution of species is essential for the sustainable development of humanity, as well as for biodiversity conservation. However, the difficulty of identifying plants, animals and fungi is hindering the aggregation of new data and knowledge. Identifying and naming living organisms is almost impossible for the general public and is often difficult even for professionals and naturalists. Bridging this gap is a key step towards enabling effective biodiversity monitoring systems. The LifeCLEF campaign, presented in this paper, has been promoting and evaluating advances in this domain since 2011. The 2022 edition proposes five data-oriented challenges related to the identification and prediction of biodiversity: (i) PlantCLEF: very large-scale plant identification, (ii) BirdCLEF: bird species recognition in audio soundscapes, (iii) GeoLifeCLEF: remote sensing based prediction of species, (iv) SnakeCLEF: snake species identification on a global scale, and (v) FungiCLEF: fungi recognition as an open set classification problem. This paper overviews the motivation, methodology and main outcomes of that five challenges.

Data mining is an important method for understanding various phenomena and extracting useful knowledge from data.The use of data mining has become common in companies or research institutes.Recently,huge amount of data called Big Data has been gaining much attention for generating new business opportunities.Big Data Mining,that is to say,applying data mining techniques to big data also have been popular.However,because big data mining poses many difficulties,only simple analysis like aggregation has been performed.One reason is that the amount of data is so large that traditional data mining method is inapplicable.Another reason is that there exists not only persistent data like customer information,but also dynamically generated data likesensor data or stock price data.For dynamic data,data mining need to be performed in real-time,but traditional data mining methods achieve it only partially.Recently,methods such as on-line learning and data compression using Locality Sensitive Hashing(LSH) have been proposed for dealing with big data and used in practical applications.In this paper,I first introduce data mining.Next I present the definition of Big Data and difficulties in analyzing Big Data.Then we introduce on-line learning and data compression using LSH.

System identification by Auto-regressive Model that based on time series data is widely used for the purpose of estimating a mathematical model of system in various fields. However, this approach needs to estimate according to the individualized theory. In this study, considered whether this technique could be applied in the MEMS oscillator. The AR model method is generally used to estimate the unknown parameter that constitute system. So, MEMS oscillator system parameter changes with packaging before and after, can be expected to analyze. In addition, white noise including using a variety of input frequencies can be expected to establish high-throughput extraction parameters.

We present an algorithm which, based on certain properties of analytic dependence, constructs boundary perturbation expansions of arbitrary order for eigenfunctions of elliptic PDEs. The resulting Taylor series can be evaluated far outside their radii of convergence—by means of appropriate methods of analytic continuation in the domain of complex perturbation parameters. A difficulty associated with calculation of the Taylor coefficients becomes apparent as one considers the issues raised by multiplicity: domain perturbations may remove existing multiple eigenvalues and criteria must therefore be provided to obtain Taylor series expansions for all branches stemming from a given multiple point. The derivation of our algorithm depends on certain properties of joint analyticity (with respect to spatial variables and perturbations) which had not been established before this work. While our proofs, constructions and numerical examples are given for eigenvalue problems for the Laplacian operator in the plane, other elliptic operators can be treated similarly.

This paper analyzes local convergence rates of primal-dual interior point methods for general nonlinearly constrained optimization problems. For this purpose, we first discuss modified Newton methods and modified quasi-Newton methods for solving a nonlinear system of equations, and show local and Q- quadratic/Q-superlinear convergence of these methods. These methods are characterized by a perturbation of the right-hand side of the Newton equation applied to the system, an approximation of the Jacobian matrix by some matrix, and component-wise dampings of the step. By applying these convergence results for the nonlinear system of equations to the primal-dual interior point methods for nonlinear optimization, we obtain convergence results of the primal-dual interior point Newton and quasi-Newton methods. A necessary and sufficient condition for Q-superlinear convergence of the latter methods corresponds to the Dennis-More condition. Furthermore, we present some quasi-Newton updating formulae. Finally, we give an analysis of the Q-rate in a part of variables for the primal-dual interior point quasi-Newton methods, and obtain a necessary and sufficient condition for the Q-rate. This condition is a generalization of the result given by Martinez, Parada and Tapia (1995), which was done independently.