A Geometric Understanding of Deep Learning

This work introduces an optimal transportation(OT)view of generative adversarial networks(GANs).Natural datasets have intrinsic patterns,which can be summarized as the manifold distribution principle:the distribution of a class of data is close to a low-dimensional manifold.GANs mainly accomplish two tasks:manifold learning and probability distribution transformation.The latter can be carried out using the classical OT method.From the OT perspective,the generator computes the OT map,while the discriminator computes the Wasserstein distance between the generated data distribution and the real data distribution;both can be reduced to a convex geometric optimization process.Furthermore,OT theory discovers the intrinsic collaborative-instead of competitive-relation between the generator and the discriminator,and the fundamental reason for mode collapse.We also propose a novel generative model,which uses an autoencoder(AE)for manifold learning and OT map for probability distribution transformation.This AE–OT model improves the theoretical rigor and transparency,as well as the computational stability and efficiency;in particular,it eliminates the mode collapse.The experimental results validate our hypothesis,and demonstrate the advantages of our proposed model.

Hydrogen Sulfide-Specific and NIR-Light-Controllable Synergistic Activation of Fluorescent Theranostic Prodrugs for Imaging-Guided Chemo- Photothermal Cancer Therapy

Theranostic prodrugs are promising for cancer medicine;however,the inability to activate these systems exclusively at the desired tumor location compromises the specificity and efficacy of cancer treatment.Here,we developed a fluorescent theranostic nanoprodrug with synergistic hydrogen-sulfidespecific and near-infrared(NIR)-light-controllable activation for imaging-guided chemo-photothermal cancer therapy.This nanoprodrug system was fabricated by the inclusion of hydrogen sulfide(H2S)-activatable small molecule to the theranostic prodrug and a photothermal transducer in the interior of a NIR-light-responsive container.

A dual-modality hydrogen sulfide-specific probe integrating chemiluminescence with NIR fluorescence for targeted cancer imaging

Taking apart in numerous physiological and pathological activities,hydrogen sulfide(H_(2)S)has been selected as an excellent target spot for the early diagnosis of cancer.So far,there are many mature probes that apply single optical imaging to monitor endogenous H_(2)S.Nevertheless,a single modality is not an ideal method to afford accurate diagnostic information in comprehensive biological organisms.Herein,we developed a dual-modal imaging probe BWS.This designed probe showed a specific response to H_(2)S with both chemiluminescence and NIR fluorescence light-up.The concurrence of fluorescence and chemiluminescence signal provided“double insurances”for highly accurate monitoring of H_(2)S.Satisfactorily,this dual-modal imaging probe performed precise visualization of endogenous H_(2)S in living cells and in vivo.We envisaged that this chemiluminescence/fluorescence real-time dual-modality strategy for H_(2)S detection will expand and optimize the multimodal imaging methods for efficient diagnosis and treatment of cancer.

Robust edge-preserving surface mesh polycube deformation

Polycube construction and deformation are essential problems in computer graphics. In this paper, we present a robust, simple, efficient,and automatic algorithm to deform the meshes of arbitrary shapes into polycube form. We derive a clear relationship between a mesh and its corresponding polycube shape. Our algorithm is edge-preserving, and works on surface meshes with or without boundaries.Our algorithm outperforms previous ones with respect to speed, robustness, and efficiency. Our method is simple to implement. To demonstrate the robustness and effectivity of our method, we have applied it to hundreds of models of varying complexity and topology. We demonstrate that our method compares favorably to other state-of-the-art polycube deformation methods.

Robust and accurate optimal transportation map by self-adaptive

Optimal transportation plays a fundamental role in many fi elds in engineering and medicine,including surface parameterization in graphics,registration in computer vision,and generative models in deep learning.For quadratic distance cost,optimal transportation map is the gradient of the Brenier potential,which can be obtained by solving the Monge-Ampère equation.Furthermore,it is induced to a geometric convex optimization problem.The Monge-Ampère equation is highly non-linear,and during the solving process,the intermediate solutions have to be strictly convex.Specifi cally,the accuracy of the discrete solution heavily depends on the sampling pattern of the target measure.In this work,we propose a self-adaptive sampling algorithm which greatly reduces the sampling bias and improves the accuracy and robustness of the discrete solutions.Experimental results demonstrate the efficiency and efficacy of our method.

Stable Geodesic Surface Signatures

Shape analysis plays a fundamental role in computer graphics. We present a novel global and intrinsic shape representation for shape analysis, called stable geodesic signature. It is based on the theory of stable closed geodesics and surface Ricci flow. We examine the surface by dynamically deforming it by metric design through Ricci flow, then we observe the behavior of the stable closed geodesics under the evolving Riemannian metrics. When a metric is deforming some stable geodesic loops will become unstable and shrink to points, or some geodesic loops may merge. The number of stable geodesics forms the signature, which is general for arbitrary surfaces. Experiments on a large amount of surfaces demonstrate the efficiency and efficacy of the stable geodesic signature for shape analysis

Alkaline Phosphatase-Initiated Sensitive Responsiveness of Activatable Probes to Hydrogen Sulfide for Accurate Cancer Imaging and Differentiation

Optical imaging with molecular probes is becoming an essential tool for advancing biological research and clinical applications.However,most currently available molecular probes show limited sensitivity,specificity,and accuracy due to their typical responsiveness to a single stimulation for biomarker-based imaging.In this study,we develop a novel molecular probe that shows alkaline phosphatase(ALP)-instructed sensitive responsiveness to hydrogen sulfide for accurate cancer imaging and differentiation.This designed probe in an aggregated state under physiological conditions bears negatively charged surfaces,giving poor optical response to H_(2)S.The ALP-mediated dephosphorylation reaction yields an assembled product with a positively charged surface,affording significantly aggregation-enhanced responsiveness to H_(2)S with light-up NIR fluorescence at 755 nm.Such charge reversal of assembled probe from negative to positive plays a vital role in allowing precise visualization and differentiation of cancers based on differences in ALP upregulation and H_(2)S content.We envisage that our charge-reversal strategy for multiple-parameter-activated molecule probes will facilitate boosting the specificity and precision of cancer imaging.