IdopNetwork as a genomic predictor of drug response.

Despite being challenging, elucidating the systematic control mechanisms of multifactorial drug responses is crucial for pharmacogenomic research. We describe a new form of statistical mechanics to reconstruct informative, dynamic, omnidirectional, and personalized networks (idopNetworks), which cover all pharmacogenomic factors and their interconnections, interdependence, and mechanistic roles. IdopNetworks can characterize how cell-cell crosstalk is mediated by genes and proteins to shape body-drug interactions and identify key roadmaps of information flow and propagation for determining drug efficacy and toxicity.

Hypernetwork modeling and topology of high-order interactions for complex systems.

Interactions among the underlying agents of a complex system are not only limited to dyads but can also occur in larger groups. Currently, no generic model has been developed to capture high-order interactions (HOI), which, along with pairwise interactions, portray a detailed landscape of complex systems. Here, we integrate evolutionary game theory and behavioral ecology into a unified statistical mechanics framework, allowing all agents (modeled as nodes) and their bidirectional, signed, and weighted interactions at various orders (modeled as links or hyperlinks) to be coded into hypernetworks.

Single-cell analysis via manifold fitting: A framework for RNA clustering and beyond.

Single-cell RNA sequencing (scRNA-seq) data, susceptible to noise arising from biological variability and technical errors, can distort gene expression analysis and impact cell similarity assessments, particularly in heterogeneous populations. Current methods, including deep learning approaches, often struggle to accurately characterize cell relationships due to this inherent noise. To address these challenges, we introduce scAMF (Single-cell Analysis via Manifold Fitting), a framework designed to enhance clustering accuracy and data visualization in scRNA-seq studies.

Exploring geometry of genome space via Grassmann manifolds.

It is important to understand the geometry of genome space in biology. After transforming genome sequences into frequency matrices of the chaos game representation (FCGR), we regard a genome sequence as a point in a suitable Grassmann manifold by analyzing the column space of the corresponding FCGR. To assess the sequence similarity, we employ the generalized Grassmannian distance, an intrinsic geometric distance that differs from the traditional Euclidean distance used in the classical k-mer frequency-based methods.

Manifold fitting with CycleGAN.

Manifold fitting, which offers substantial potential for efficient and accurate modeling, poses a critical challenge in nonlinear data analysis. This study presents an approach that employs neural networks to fit the latent manifold. Leveraging the generative adversarial framework, this method learns smooth mappings between low-dimensional latent space and high-dimensional ambient space, echoing the Riemannian exponential and logarithmic maps.

The metabolomic physics of complex diseases.

Human diseases involve metabolic alterations. Metabolomic profiles have served as a vital biomarker for the early identification of high-risk individuals and disease prevention. However, current approaches can only characterize individual key metabolites, without taking into account the reality that complex diseases are multifactorial, dynamic, heterogeneous, and interdependent.

Path Topology in Molecular and Materials Sciences.

The structures of molecules and materials determine their functions. Understanding the structure and function relationship is the holy grail of molecular and materials sciences. However, the rational design of molecules and materials with desirable functions remains a grand challenge despite decades of efforts.

A novel 2-phase residual U-net algorithm combined with optimal mass transportation for 3D brain tumor detection and segmentation.

Utilizing the optimal mass transportation (OMT) technique to convert an irregular 3D brain image into a cube, a required input format for a U-net algorithm, is a brand new idea for medical imaging research. We develop a cubic volume-measure-preserving OMT (V-OMT) model for the implementation of this conversion. The contrast-enhanced histogram equalization grayscale of fluid-attenuated inversion recovery (FLAIR) in a brain image creates the corresponding density function.

3D brain tumor segmentation using a two-stage optimal mass transport algorithm.

Optimal mass transport (OMT) theory, the goal of which is to move any irregular 3D object (i.e., the brain) without causing significant distortion, is used to preprocess brain tumor datasets for the first time in this paper.

The dynamical model for COVID-19 with asymptotic analysis and numerical implementations.

The 2019 novel coronavirus (COVID-19) emerged at the end of 2019 has a great impact on China and all over the world. The transmission mechanism of COVID-19 is still unclear. Except for the initial status and the imported cases, the isolation measures and the medical treatments of the infected patients have essential influences on the spread of COVID-19.

Evolutionary dynamics on any population structure.

Evolution occurs in populations of reproducing individuals. The structure of a population can affect which traits evolve. Understanding evolutionary game dynamics in structured populations remains difficult.

Hyperbolic Harmonic Mapping for Surface Registration.

Automatic computation of surface correspondence via harmonic map is an active research field in computer vision, computer graphics and computational geometry. It may help document and understand physical and biological phenomena and also has broad applications in biometrics, medical imaging and motion capture industries. Although numerous studies have been devoted to harmonic map research, limited progress has been made to compute a diffeomorphic harmonic map on general topology surfaces with landmark constraints.

Shape Analysis of Planar Multiply-Connected Objects Using Conformal Welding.

Shape analysis is a central problem in the field of computer vision. In 2D shape analysis, classification and recognition of objects from their observed silhouettes are extremely crucial but difficult. It usually involves an efficient representation of 2D shape space with a metric, so that its mathematical structure can be used for further analysis.

Hyperbolic harmonic brain surface registration with curvature-based landmark matching.

Brain Cortical surface registration is required for inter-subject studies of functional and anatomical data. Harmonic mapping has been applied for brain mapping, due to its existence, uniqueness, regularity and numerical stability. In order to improve the registration accuracy, sculcal landmarks are usually used as constraints for brain registration.

Brain surface conformal parameterization with the Ricci flow.

In brain mapping research, parameterized 3-D surface models are of great interest for statistical comparisons of anatomy, surface-based registration, and signal processing. Here, we introduce the theories of continuous and discrete surface Ricci flow, which can create Riemannian metrics on surfaces with arbitrary topologies with user-defined Gaussian curvatures. The resulting conformal parameterizations have no singularities and they are intrinsic and stable.

Independent component analysis-based classification of Alzheimer's disease MRI data.

There is an unmet medical need to identify neuroimaging biomarkers that allow us to accurately diagnose and monitor Alzheimer's disease (AD) at its very early stages and to assess the response to AD-modifying therapies. To a certain extent, volumetric and functional magnetic resonance imaging (fMRI) studies can detect changes in structure, cerebral blood flow, and blood oxygenation that distinguish AD and mild cognitive impairment (MCI) subjects from healthy control (HC) subjects. However, it has been challenging to use fully automated MRI analytic methods to identify potential AD neuroimaging biomarkers.

Shape analysis of vestibular systems in adolescent idiopathic scoliosis using geodesic spectra.

Adolescent Idiopathic Scoliosis (AIS) characterized by the 3D spine deformity affects about 4% schoolchildren worldwide. One of the prominent theories of the etiopathogenesis of AIS was proposed to be the poor postural balance control due to the impaired vestibular function. Thus, the morphometry of the vestibular system (VS) is of great importance for studying AIS.

Shape-based diffeomorphic registration on hippocampal surfaces using Beltrami holomorphic flow.

We develop a new algorithm to automatically register hippocampal (HP) surfaces with complete geometric matching, avoiding the need to manually label landmark features. A good registration depends on a reasonable choice of shape energy that measures the dissimilarity between surfaces. In our work, we first propose a complete shape index using the Beltrami coefficient and curvatures, which measures subtle local differences.

Quasilocal mass in general relativity.

There have been many attempts to define the notion of quasilocal mass for a spacelike two surface in spacetime by the Hamilton-Jacobi analysis. The essential difficulty in this approach is to identify the right choice of the background configuration to be subtracted from the physical Hamiltonian. Quasilocal mass should be non-negative for surfaces in general spacetime and zero for surfaces in flat spacetime.

Teichmöller shape space theory and its application to brain morphometry.

Here we propose a novel method to compute Teichmiiller shape space based shape index to study brain morphometry. Such a shape index is intrinsic, and invariant under conformal transformations, rigid motions and scaling. We conformally map a genus-zero open boundary surface to the Poincaré disk with the Yamabe flow method.

A geometric approach to problems in birational geometry.

A classical set of birational invariants of a variety are its spaces of pluricanonical forms and some of their canonically defined subspaces. Each of these vector spaces admits a typical metric structure which is also birationally invariant. These vector spaces so metrized will be referred to as the pseudonormed spaces of the original varieties.

Conformal slit mapping and its applications to brain surface parameterization.

We propose a method that computes a conformal mapping from a multiply connected mesh to the so-called slit domain, which consists of a canonical rectangle or disk in which 3D curved landmarks on the original surfaces are mapped to concentric or parallel lines in the slit domain. In this paper, we studied its application to brain surface parameterization. After cutting along some landmark curve features on surface models of the cerebral cortex, we obtain multiple connected domains.

Absolute phase-assisted three-dimensional data registration for a dual-camera structured light system.

For a three-dimensional shape measurement system with a single projector and multiple cameras, registering patches from different cameras is crucial. Registration usually involves a complicated and time-consuming procedure. We propose a new method that can robustly match different patches via absolute phase without significantly increasing its cost.