Control Analysis with Modified LQR Method of Anti-Tank Missile with Vectorization of the Rocket Engine Thrust

This article approaches the issue of the optimal control of a hypothetical anti-tank guided missile (ATGM) with an innovative rocket engine thrust vectorization system. This is a highly non-linear dynamic system; therefore, the linearization of such a mathematical model requires numerous simplifications. For this reason, the application of a classic linear-quadratic regulator (LQR) for controlling such a flying object introduces significant errors, and such a model would diverge significantly from the actual object. This research paper proposes a modified linear-quadratic regulator, which analyzes state and control matrices in flight. The state matrix is replaced by a Jacobian determinant. The ATGM autopilot, through the LQR method, determines the signals that control the control surface deflection angles and the thrust vector via calculated Jacobians. This article supplements and develops the topics addressed in the authors’ previous work. Its added value includes the introduction of control in the flight direction channel and the decimation of the integration step, aimed at speeding up the computational processes of the second control loop, which is the LQR based on a linearized model.

PLANAR IMMERSIONS WITH PRESCRIBED CURL AND JACOBIAN DETERMINANT ARE UNIQUE

We prove that immersions of planar domains are uniquely specified by their Jacobian determinant, curl function and boundary values. This settles the two-dimensional version of an outstanding conjecture related to a particular grid generation method in computer graphics.

Analysis of Singular Configuration of Robotic Manipulators

Robotic manipulators inevitably encounter singular configurations in the process of movement, which seriously affects their performance. Therefore, the identification of singular configurations is extremely important. However, serial manipulators that do not meet the Pieper criterion cannot obtain singular configurations through analytical methods. A joint angle parameterization method, used to obtain singular configurations, is here creatively proposed. First, an analytical method based on the Jacobian determinant and the proposed method were utilized to obtain their respective singular configurations of the Stanford manipulator. The singular configurations obtained through the two methods were consistent, which suggests that the proposed method can obtain singular configurations correctly. Then, the proposed method was applied to a seven-degree-of-freedom (7-DOF) serial manipulator and a planar 5R parallel manipulator. Finally, the correctness of the singular configurations of the 7-DOF serial manipulator was verified through the shape of the end-effector velocity ellipsoid, the value of the determinant, the value of the condition number, and the value of the manipulability measure. The correctness of singular configurations of the planar 5R parallel manipulator was verified through the value of the determinant, the value of the condition number, and the value of the manipulability measure.

Whole-brain morphological alterations associated with trigeminal neuralgia

Background Novel neuroimaging strategies have the potential to offer new insights into the mechanistic basis for trigeminal neuralgia (TN). The present study aims to conduct whole-brain morphometry analyses of TN patients and to assess the value of group-level neocortical and subcortical structural patterns as tools for diagnostic biomarker exploration. Methods Cortical thickness, surface area, and myelin levels in the neocortex were measured via magnetic resonance imaging (MRI). The radial distance and the Jacobian determinant of the subcortex in 43 TN patients and 43 matched controls were compared. Pattern learning algorithms were employed to establish the utility of group-level MRI findings as tools for predicting TN. An additional 40 control patients with hemifacial spasms were then evaluated to assess algorithm sensitivity and specificity. Results TN patients exhibited reductions in cortical indices in the anterior cingulate cortex (ACC), the midcingulate cortex (MCC), and the posterior cingulate cortex (PCC) relative to controls. They further presented with widespread subcortical volume reduction that was most evident in the putamen, the thalamus, the accumbens, the pallidum, and the hippocampus. Whole brain-level morphological alterations successfully enable automated TN diagnosis with high specificity (TN: 95.35 %; disease controls: 46.51 %). Conclusions TN is associated with a distinctive whole-brain structural neuroimaging pattern, underscoring the value of machine learning as an approach to differentiating between morphological phenotypes, ultimately revealing the full spectrum of this disease and highlighting relevant diagnostic biomarkers.

An adaptive moving grid finite difference method

The grid generation is very crucial for the accuracy of the numerical solution of PDEs, especially for problems with very rapid variations or sharp layers, such as shock waves, wing leading and trailing edges, regions of separation, and boundary layers. The adaptive grid generation is an iterative approach to accommodate these complex structures. In this paper, we introduce a deformation based adaptive grid generation method, in which a differentiable and invertible transformation from computational domain to physical domain is constructed such that the cell volume (Jacobian determinant) of the new grid is equal to a prescribed monitor function. A vector field is obtained by solving the div-curl system and can be used to move the grids to the desired locations. By computing the inverse of Jacobian, any deformed grids can also be transformed back to the uniform grid. Several numerical results in two dimensions are presented. Some applications in image registration are discussed.

On the Determinant Problem for the Relativistic Boltzmann Equation

This article considers a long-outstanding open question regarding the Jacobian determinant for the relativistic Boltzmann equation in the center-of-momentum coordinates. For the Newtonian Boltzmann equation, the center-of-momentum coordinates have played a large role in the study of the Newtonian non-cutoff Boltzmann equation, in particular we mention the widely used cancellation lemma [1]. In this article we calculate specifically the very complicated Jacobian determinant, in ten variables, for the relativistic collision map from the momentum p to the post collisional momentum $$p'$$ p ′ ; specifically we calculate the determinant for $$p\mapsto u = \theta p'+\left( 1-\theta \right) p$$ p ↦ u = θ p ′ + 1 - θ p for $$\theta \in [0,1]$$ θ ∈ [ 0 , 1 ] . Afterwards we give an upper-bound for this determinant that has no singularity in both p and q variables. Next we give an example where we prove that the Jacobian goes to zero in a specific pointwise limit. We further explain the results of our numerical study which shows that the Jacobian determinant has a very large number of distinct points at which it is machine zero. This generalizes the work of Glassey-Strauss (1991) [8] and Guo-Strain (2012) [12]. These conclusions make it difficult to envision a direct relativistic analog of the Newtonian cancellation lemma in the center-of-momentum coordinates.

Exploring the relationship between maternal prenatal stress and brain structure in premature neonates

Background Exposure to maternal stress in utero is associated with a range of adverse outcomes. We previously observed an association between maternal stress and white matter microstructure in a sample of infants born prematurely. In this study, we aimed to investigate the relationship between maternal trait anxiety, stressful life events and brain volumes. Methods 221 infants (114 males, 107 females) born prematurely (median gestational age = 30.43 weeks [range 23.57–32.86]) underwent magnetic resonance imaging around term-equivalent age (mean = 42.20 weeks, SD = 1.60). Brain volumes were extracted for the following regions of interest: frontal lobe, temporal lobe, amygdala, hippocampus, thalamus and normalized to total brain volume. Multiple linear regressions were conducted to investigate the relationship between maternal anxiety/stress and brain volumes, controlling for gestational age at birth, postmenstrual age at scan, socioeconomic status, sex, days on total parenteral nutrition. Additional exploratory Tensor Based Morphometry analyses were performed to obtain voxel-wise brain volume changes from Jacobian determinant maps. Results and conclusion In this large prospective study, we did not find evidence of a relationship between maternal prenatal stress or trait anxiety and brain volumes. This was the case for both the main analysis using a region-of-interest approach, and for the exploratory analysis using Jacobian determinant maps. We discuss these results in the context of conflicting evidence from previous studies and highlight the need for further research on premature infants, particularly including term-born controls.

White Matter Hyperintensities, Grey Matter Atrophy, and Cognitive Decline in Neurodegenerative Diseases

Introduction: White matter hyperintensities (WMHs) as seen on T2w and FLAIR scans represent small-vessel disease related changes in the brain. WMHs are associated with cognitive decline in the normal aging population in general and more specifically in patients with neurodegenerative diseases. In this study, we assessed the different spatial patterns and relationships between WMHs and grey matter (GM) atrophy in normal aging, individuals with mild cognitive impairment (MCI), Alzheimers dementia (AD), fronto-temporal dementia (FTD), and de novo Parkinsons disease (PD). Methods: Imaging and clinical data were obtained from 3 large multi-center databases: The Alzheimers Disease Neuroimaging Initiative (ADNI), the frontotemporal lobar degeneration neuroimaging initiative (NIFD), and the Parkinsons Progression Markers Initiative (PPMI). WMHs and GM atrophy maps were measured in normal controls (N= 571), MCI (N= 577), AD (N= 222), FTD (N= 144), and PD (N= 363). WMHs were segmented using T1w and T2w/PD or FLAIR images and mapped onto 45 white matter tracts using the Yeh WM atlas. GM volume was estimated from the Jacobian determinant of the nonlinear deformation field required to map the subject MRI to a standard template. The CerebrA atlas was used to obtain volume estimates in 84 GM regions. Mixed effects models were used to compare WMH in different WM tracts and volume of multiple GM structures between patients and controls, assess the relationship between regional WMHs and GM loss for each disease, and investigate their impact on cognition. Results: MCI, AD, and FTD patients had significantly higher WMH loads than the matched controls. There was no significant difference in WMHs between PD and controls. For each cohort, significant interactions between WMH load and GM atrophy were found for several regions and tracts, reflecting additional contribution of WMH burden to GM atrophy. While these associations were more relevant for insular and parieto-occipital regions in MCI and AD cohorts, WMH burden in FTD subjects had greater impact on frontal and basal ganglia atrophy. Finally, we found additional contribution of WMH burden to cognitive deficits in AD and FTD subjects compared with matched controls, whereas their impact on cognitive performance in MCI and PD were not significantly different from controls. Conclusions: WMHs occur more extensively in MCI, AD, and FTD patients than age-matched normal controls. WMH burden on WM tracts also correlates with regional GM atrophy in regions anatomically and functionally related to those tracts, suggesting a potential involvement of WMHs in the neurodegenerative process.

Imaging surveillance after open aortic repair: a feasibility study of three-dimensional growth mapping

OBJECTIVES Confident growth assessment during imaging follow-up is often limited by substantial variability of diameter measurements and the fact that growth does not always occur at standard measurement locations. There is a need for imaging-based techniques to more accurately assess growth. In this study, we investigated the feasibility of a three-dimensional aortic growth assessment technique to quantify aortic growth in patients following open aortic repair. METHODS Three-dimensional aortic growth was measured using vascular deformation mapping (VDM), a technique which quantifies the localized rate of volumetric growth at the aortic wall, expressed in units of Jacobian (J) per year. We included 16 patients and analysed 6 aortic segments per patient (96 total segments). Growth was assessed by 3 metrics: clinically reported diameters, Jacobian determinant and targeted diameter re-measurements. RESULTS VDM was able to clearly depict the presence or absence of localized aortic growth and allows for an assessment of the distribution of growth and its relation to anatomic landmarks (e.g. anastomoses, branch arteries). Targeted diameter change showed a stronger and significant correlation with J (r = 0.20, P = 0.047) compared to clinical diameter change (r = 0.15, P = 0.141). Among 20/96 (21%) segments with growth identified by VDM, growth was confirmed by clinical measurements in 7 and targeted re-measurements in 11. Agreement of growth assessments between VDM and diameter measurements was slightly higher for targeted re-measurements (kappa = 0.38) compared to clinical measurements (kappa = 0.25). CONCLUSIONS Aortic growth is often uncertain and underappreciated when assessed via standard diameter measurements. Three-dimensional growth assessment with VDM offers a more comprehensive assessment of growth, allows for targeted diameter measurements and could be an additional tool to determine which post-surgical patients at high and low risk for future complications.

Latent traits of lung tissue patterns in former smokers derived by dual channel deep learning in computed tomography images

Chronic obstructive pulmonary disease (COPD) is a heterogeneous disease and the traditional variables extracted from computed tomography (CT) images may not be sufficient to describe all the topological features of lung tissues in COPD patients. We employed an unsupervised three-dimensional (3D) convolutional autoencoder (CAE)-feature constructor (FC) deep learning network to learn from CT data and derive tissue pattern-clusters jointly. We then applied exploratory factor analysis (EFA) to discover the unobserved latent traits (factors) among pattern-clusters. CT images at total lung capacity (TLC) and residual volume (RV) of 541 former smokers and 59 healthy non-smokers from the cohort of the SubPopulations and Intermediate Outcome Measures in the COPD Study (SPIROMICS) were analyzed. TLC and RV images were registered to calculate the Jacobian (determinant) values for all the voxels in TLC images. 3D Regions of interest (ROIs) with two data channels of CT intensity and Jacobian value were randomly extracted from training images and were fed to the 3D CAE-FC model. 80 pattern-clusters and 7 factors were identified. Factor scores computed for individual subjects were able to predict spirometry-measured pulmonary functions. Two factors which correlated with various emphysema subtypes, parametric response mapping (PRM) metrics, airway variants, and airway tree to lung volume ratio were discriminants of patients across all severity stages. Our findings suggest the potential of developing factor-based surrogate markers for new COPD phenotypes.