Convergence Guarantees for Stochastic Subgradient Methods in Nonsmooth Nonconvex Optimization

In this paper, we investigate the convergence properties of the stochastic gradient descent (SGD) method and its variants, especially in training neural networks built from nonsmooth activation functions. We develop a novel framework that assigns different timescales to stepsizes for updating the momentum terms and variables, respectively. Under mild conditions, we prove the global convergence of our proposed framework in both single-timescale and two-timescale cases. We show that our proposed framework encompasses a wide range of well-known SGD-type methods, including heavy-ball SGD, SignSGD, Lion, normalized SGD and clipped SGD. Furthermore, when the objective function adopts a finite-sum formulation, we prove the convergence properties for these SGD-type methods based on our proposed framework. In particular, we prove that these SGD-type methods find the Clarke stationary points of the objective function with randomly chosen stepsizes and initial points under mild assumptions. Preliminary numerical experiments demonstrate the high efficiency of our analyzed SGD-type methods.Comment: 30 pages, the introduction part is modified and some typos are correcte

Method and apparatus for nanoparticle electrogenerated chemiluminescence amplification

Methods, compositions and kits for analyzing a chemical analyte using an electrochemical cell connected to a measuring apparatus are provided. The electrochemical cell contains a solution having one or more conductive or redox active NPs (nanoparticles), one or more chemical analytes, and an indicator. In addition, the electrochemical cell contains one or more electrodes in communication with the solution. One or more catalytic ECL properties are generated by the interaction of the one or more conductive or redox active NPs and the liquid sample and measured at the one or more electrodes or with an optical detection system.Board of Regents, University of Texas Syste

Method for metal nanoparticle electrocatalytic amplification

The present invention includes methods, compositions and kits for analyzing a chemical analyte having an electrochemical cell connected to a measuring apparatus. The electrochemical cell contains a solution having one or more nanoparticles, one or more chemical analytes, an indicator. In addition, the electrochemical cell contains one or more electrodes in communication with the solution. One or more electrocatalytic properties are generated by the interaction of the one or more nanoparticles and the liquid sample and measured at the one or more electrodes.Board of Regents, University of Texas Syste

CDOpt: A Python Package for a Class of Riemannian Optimization

Optimization over the embedded submanifold defined by constraints $c(x) = 0$ has attracted much interest over the past few decades due to its wide applications in various areas. Plenty of related optimization packages have been developed based on Riemannian optimization approaches, which rely on some basic geometrical materials of Riemannian manifolds, including retractions, vector transports, etc. These geometrical materials can be challenging to determine in general. Existing packages only accommodate a few well-known manifolds whose geometrical materials are easily accessible. For other manifolds which are not contained in these packages, the users have to develop the geometric materials by themselves. In addition, it is not always tractable to adopt advanced features from various state-of-the-art unconstrained optimization solvers to Riemannian optimization approaches. We introduce CDOpt (available at https://cdopt.github.io/), a user-friendly Python package for a class Riemannian optimization. Based on constraint dissolving approaches, Riemannian optimization problems are transformed into their equivalent unconstrained counterparts in CDOpt. Therefore, solving Riemannian optimization problems through CDOpt directly benefits from various existing solvers and the rich expertise gained over decades for unconstrained optimization. Moreover, all the computations in CDOpt related to any manifold in question are conducted on its constraints expression, hence users can easily define new manifolds in CDOpt without any background on differential geometry. Furthermore, CDOpt extends the neural layers from PyTorch and Flax, thus allows users to train manifold constrained neural networks directly by the solvers for unconstrained optimization. Extensive numerical experiments demonstrate that CDOpt is highly efficient and robust in solving various classes of Riemannian optimization problems.Comment: 31 page

Highly ordered tailored three-dimensional hierarchical nano/microporous gold–carbon architectures

The preparation and characterization of three-dimensional hierarchical architectures, consisting of monolithic nanoporous gold or silver films formed on highly ordered 3D microporous carbon supports, are described. The formation of these nano/microporous structures involves the electrodeposition or sputtering of metal alloys onto the lithographically patterned multi-layered microporous carbon, followed by preferential chemical dealloying of the less noble component. The resulting hierarchical structure displays a highly developed 3D interconnected network of micropores with a nanoporous metal coating. Tailoring the nanoporosity of the metal films and the diameter of the large micropores has been accomplished by systematically changing the alloy compositions via control of the deposition potential, plating solution and coarsening time. SEM imaging illustrates the formation of unique biomimetic nanocoral- or nanocauliflower-like self-supporting structures, depending on the specific preparation conditions. The new 3D hierarchical nano/microporous architectures allow for enhanced mass transport and catalytic activity compared to common nanoporous films prepared on planar substrates. The functionality of this new carbon–gold hierarchical structure is illustrated for the greatly enhanced performance of enzymatic biofuel cells where a substantially higher power output is observed compared to the bare microporous carbon substrate

Protective role of curcumin in disease progression from non-alcoholic fatty liver disease to hepatocellular carcinoma: a meta-analysis

Background: Pathological progression from non-alcoholic fatty liver disease (NAFLD) to liver fibrosis (LF) to hepatocellular carcinoma (HCC) is a common dynamic state in many patients. Curcumin, a dietary supplement derived from the turmeric family, is expected to specifically inhibit the development of this progression. However, there is a lack of convincing evidence.Methods: The studies published until June 2023 were searched in PubMed, Web of Science, Embase, and the Cochrane Library databases. The SYstematic Review Center for Laboratory animal Experimentation (SYRCLE) approach was used to evaluate the certainty of evidence. StataSE (version 15.1) and Origin 2021 software programs were used to analyze the critical indicators.Results: Fifty-two studies involving 792 animals were included, and three disease models were reported. Curcumin demonstrates a significant improvement in key indicators across the stages of NAFLD, liver fibrosis, and HCC. We conducted a detailed analysis of common inflammatory markers IL-1β, IL-6, and TNF-α, which traverse the entire disease process. The research results reveal that curcumin effectively hinders disease progression at each stage by suppressing inflammation. Curcumin exerted hepatoprotective effects in the dose range from 100 to 400 mg/kg and treatment duration from 4 to 10 weeks. The mechanistic analysis reveals that curcumin primarily exerts its hepatoprotective effects by modulating multiple signaling pathways, including TLR4/NF-κB, Keap1/Nrf2, Bax/Bcl-2/Caspase 3, and TGF-β/Smad3.Conclusion: In summary, curcumin has shown promising therapeutic effects during the overall progression of NAFLD–LF–HCC. It inhibited the pathological progression by synergistic mechanisms related to multiple pathways, including anti-inflammatory, antioxidant, and apoptosis regulation

Bio-inspired nanocomposite assemblies as smart skin components.

There is national interest in the development of sophisticated materials that can automatically detect and respond to chemical and biological threats without the need for human intervention. In living systems, cell membranes perform such functions on a routine basis, detecting threats, communicating with the cell, and triggering automatic responses such as the opening and closing of ion channels. The purpose of this project was to learn how to replicate simple threat detection and response functions within artificial membrane systems. The original goals toward developing 'smart skin' assemblies included: (1) synthesizing functionalized nanoparticles to produce electrochemically responsive systems within a lipid bilayer host matrices, (2) calculating the energetics of nanoparticle-lipid interactions and pore formation, and (3) determining the mechanism of insertion of nanoparticles in lipid bilayers via imaging and electrochemistry. There are a few reports of the use of programmable materials to open and close pores in rigid hosts such as mesoporous materials using either heat or light activation. However, none of these materials can regulate themselves in response to the detection of threats. The strategies we investigated in this project involve learning how to use programmable nanomaterials to automatically eliminate open channels within a lipid bilayer host when 'threats' are detected. We generated and characterized functionalized nanoparticles that can be used to create synthetic pores through the membrane and investigated methods of eliminating the pores either through electrochemistry, change in pH, etc. We also focused on characterizing the behavior of functionalized gold NPs in different lipid membranes and lipid vesicles and coupled these results to modeling efforts designed to gain an understanding of the interaction of nanoparticles within lipid assemblies

Hollow Microneedle-based Sensor for Multiplexed Transdermal Electrochemical Sensing

The development of a minimally invasive multiplexed monitoring system for rapid analysis of biologically-relevant molecules could offer individuals suffering from chronic medical conditions facile assessment of their immediate physiological state. Furthermore, it could serve as a research tool for analysis of complex, multifactorial medical conditions. In order for such a multianalyte sensor to be realized, it must be minimally invasive, sampling of interstitial fluid must occur without pain or harm to the user, and analysis must be rapid as well as selective

Analysis of risk factors associated with pre-myopia among primary school students in the Mianyang Science City Area

Objectives To find out the prevalence rate of pre-myopia among primary school students in the Mianyang Science City Area, analyze its related risk factors, and thus provide a reference for local authorities to formulate policies on the prevention and control of myopia for primary school students. Methods　 October 2022, Cluster sampling was adopted by our research group to obtain the vision levels of 2278 primary school students employing a diopter test in the Science City Area. In addition, questionnaires were distributed to help us find the risk factors associated with pre-myopia. Results The prevalence rate of pre-myopia among primary school students in the Science  City Area was 45.27%, of which 43.82% were boys and 46.92% were girls, with no statistically significant difference in the prevalence rate of myopia between boys and girls (c2 =2.171, P=0.141). Multiple logistic regression analysis demonstrated that the main risk factors for pre-myopia were having at least one parent with severe myopia, spending less than 2 hours a day outdoors, lack of sleep looking at electronic screens for more than 1 hours, and having an improper reading and writing posture. Outdoor activity time less than 2 hours per day, lack of sleep, looking at the electronic screen for more than 1 hour per day, and incorrect reading and writing posture were all positively associated with the pre-myopia (P values < 0.05). Conclusion The Science City Area has a high prevalence rate of pre-myopia among primary school students. It is proposed that students, schools, families, and local authorities work together to increase the time spent outdoors, get adequate sleep, reduce the time spent staring at digital screens and develop scientific use of eye habits