Semi-discrete optimal transport methods for the semi-geostrophic equations

We give a new and constructive proof of the existence of global-in-time weak solutions of the 3-dimensional incompressible semi-geostrophic equations (SG) in geostrophic coordinates, for arbitrary initial measures with compact support. This new proof, based on semi-discrete optimal transport techniques, works by characterising discrete solutions of SG in geostrophic coordinates in terms of trajectories satisfying an ordinary differential equation. It is advantageous in its simplicity and its explicit relation to Eulerian coordinates through the use of Laguerre tessellations. Using our method, we obtain improved time-regularity for a large class of discrete initial measures, and we compute explicitly two discrete solutions. The method naturally gives rise to an efficient numerical method, which we illustrate by presenting simulations of a 2-dimensional semi-geostrophic flow in geostrophic coordinates generated using a numerical solver for the semi-discrete optimal transport problem coupled with an ordinary differential equation solver.

Cavovarus With a Twist: Midfoot Coronal and Axial Plane Rotational Deformity in Charcot-Marie-Tooth Disease

Background: The cavovarus deformity of Charcot-Marie-Tooth (CMT) disease is often characterized by a paradoxical relationship of hindfoot varus and forefoot valgus. The configuration of the midfoot, which links these deformities, is poorly understood. Accurate assessment of 3-dimensional alignment under physiologic loadbearing conditions is possible using weightbearing computed tomography (WBCT). This is the first study to examine the rotational deformity in the midfoot of CMT patients and, thus, provide key insights to successful correction of CMT cavovarus foot. Methods: A total of 27 WBCT scans from 21 CMT patients were compared to control WBCTs from 20 healthy unmatched adults. CMT patients with a history of bony surgery, severe degenerative joint disease, or open physes in the foot were excluded. Scans were analyzed using 3-dimensional software. Anatomic alignment of the tarsal bones was calculated relative to the anterior-posterior axis of the tibial plafond in the axial plane, and weightbearing surface in the coronal plane. Results: Maximal rotational deformity in CMT patients occurred at the transverse tarsal joints, averaging 61 degrees of external rotation (supination), compared to 34 degrees among controls ( P < .01). The talonavicular joint was also the site of peak adduction deformity in the midfoot, with an average talonavicular coverage angle measuring 12 degrees compared with −11 degrees in controls ( P < .01). Conclusion: This 3-dimensional WBCT analysis is the first to isolate and quantify the multiplanar rotational deformity in the midfoot of CMT patients. Compared with healthy unmatched control cases, CMT patients demonstrated increased axial plane adduction and coronal plane rotation at the talonavicular (TN) joint. These findings support performing soft tissue release at the TN joint to abduct and derotate the midfoot as a first step for targeted deformity correction. Level of Evidence: Level III, retrospective case-control study.

On Degree Based Topological Indices of TiO2 Crystal via M-Polynomial

Topological indices (TI) (descriptors) of a molecular graph are very much useful to study various physiochemical properties. It is also used to develop the quantitative structure-activity relationship (QSAR), quantitative structure-property relationship (QSPR) of the corresponding chemical compound. Various techniques have been developed to calculate the TI of a graph. Recently a technique of calculating degree-based TI from M-polynomial has been introduced. We have evaluated various topological descriptors for 3-dimensional TiO2 crystals using M-polynomial. These descriptors are constructed such that it contains 3 variables (m, n and t) each corresponding to a particular direction. These 3 variables facilitate us to deeply understand the growth of TiO2 in 1 dimension (1D), 2 dimensions (2D), and 3 dimensions (3D) respectively. HIGHLIGHTS Calculated degree based Topological indices of a 3D crystal from M-polynomial A relation among various Topological indices is established geometrically Variations of Topological Indices along three dimensions (directions) are shown geometrically Harmonic index approximates the degree variation of oxygen atom

Annexin A6 and NPC1 regulate LDL-inducible cell migration and distribution of focal adhesions

Cholesterol is considered indispensable for cell motility, but how physiological cholesterol pools enable cells to move forward remains to be clarified. The majority of cells obtain cholesterol from the uptake of Low-Density lipoproteins (LDL) and here we demonstrate that LDL stimulates A431 squamous epithelial carcinoma and Chinese hamster ovary (CHO) cell migration and invasion. LDL also potentiated epidermal growth factor (EGF) -stimulated A431 cell migration as well as A431 invasion in 3-dimensional environments, using organotypic assays. Blocking cholesterol export from late endosomes (LE), using Niemann Pick Type C1 (NPC1) mutant cells, pharmacological NPC1 inhibition or overexpression of the annexin A6 (AnxA6) scaffold protein, compromised LDL-inducible migration and invasion. Nevertheless, NPC1 mutant cells established focal adhesions (FA) that contain activated focal adhesion kinase (pY397FAK, pY861FAK), vinculin and paxillin. Compared to controls, NPC1 mutants display increased FA numbers throughout the cell body, but lack LDL-inducible FA formation at cell edges. Strikingly, AnxA6 depletion in NPC1 mutant cells, which restores late endosomal cholesterol export in these cells, increases their cell motility and association of the cholesterol biosensor D4H with active FAK at cell edges, indicating that AnxA6-regulated transport routes contribute to cholesterol delivery to FA structures, thereby improving NPC1 mutant cell migratory behaviour.

Structural DNA nanotechnology: Immobile Holliday junctions to artificial robots

Abstreact: DNA nanotechnology marvels the scientific world with its capabilities to design, engineer, and demonstrate nanoscale shapes. This review is a condensed version walking the reader through the structural developments in the field over the past 40 years starting from the basic design rules of the double-stranded building block to the most recent advancements in self-assembled hierarchically achieved structures to date. It builds off from the fundamental motivation of building 3-dimensional (3D) lattice structures of tunable cavities going all the way up to artificial nanorobots fighting cancer. The review starts by covering the most important developments from the fundamental bottom-up approach of building structures, which is the ‘tile’ based approach covering 1D, 2D, and 3D building blocks, after which, the top-down approach using DNA origami and DNA bricks is also covered. Thereafter, DNA nanostructures assembled using not so commonly used (yet promising) techniques like i-motifs, quadruplexes, and kissing loops are covered. Highlights from the field of dynamic DNA nanostructures have been covered as well, walking the reader through the various approaches used within the field to achieve movement. The article finally concludes by giving the authors a view of what the future of the field might look like while suggesting in parallel new directions that fellow/future DNA nanotechnologists could think about.

Pacemaker Lead Placement via Transmural Approach in an Adult With Palliated Single Ventricle Heart Disease

Given the lack of systemic venous return to the heart, palliated single ventricle patients frequently require epicardial pacemaker implantation for management of dysrhythmias including sinus node dysfunction, atrial arrhythmias, and heart block. Repeated device hardware replacement, frequently required due to high lead thresholds or other device failure, is a challenging and significant problem for this population. 3-dimensional imaging can assist in delineating the cardiac anatomy allowing for novel approaches to intervention. We review a patient with extracardiac Fontan circulation who underwent placement of an endocardial atrial pacemaker lead via a transmural approach with a 3D-printed model used for procedural guidance.

Intranuclear Positions of HIV-1 Proviruses Are Dynamic and Do Not Correlate with Transcriptional Activity

HIV-1 integrates its genomic DNA into the chromosomes of the infected cell, but how it selects the site of integration and the impact of their location in the 3-dimensional nuclear space is not well understood. Here, we examined the nuclear locations of proviruses 1 and 5 days after infection and found that integration sites are first located near the nuclear envelope but become randomly distributed throughout the nucleus after a few cell divisions, indicating that the locations of the chromosomal sites of integration that harbor transcriptionally active proviruses are dynamic.

A Study on 3D Deep Learning-Based Automatic Diagnosis of Nasal Fractures

This paper reported a study on the 3-dimensional deep-learning-based automatic diagnosis of nasal fractures. (1) Background: The nasal bone is the most protuberant feature of the face; therefore, it is highly vulnerable to facial trauma and its fractures are known as the most common facial fractures worldwide. In addition, its adhesion causes rapid deformation, so a clear diagnosis is needed early after fracture onset. (2) Methods: The collected computed tomography images were reconstructed to isotropic voxel data including the whole region of the nasal bone, which are represented in a fixed cubic volume. The configured 3-dimensional input data were then automatically classified by the deep learning of residual neural networks (3D-ResNet34 and ResNet50) with the spatial context information using a single network, whose performance was evaluated by 5-fold cross-validation. (3) Results: The classification of nasal fractures with simple 3D-ResNet34 and ResNet50 networks achieved areas under the receiver operating characteristic curve of 94.5% and 93.4% for binary classification, respectively, both indicating unprecedented high performance in the task. (4) Conclusions: In this paper, it is presented the possibility of automatic nasal bone fracture diagnosis using a 3-dimensional Resnet-based single classification network and it will improve the diagnostic environment with future research.