Overdetermined boundary value problems with strongly nonlinear elliptic PDE

We consider the strongly nonlinear elliptic Dirichlet problem in a connected bounded domain, overdetermined with the constant Neumann condition F(∇u) = c on the boundary. Here F is convex and positively homogeneous of degree 1, and its polar F ∗ represents the anisotropic norm on R n. We prove that, if this overdetermined boundary value problem admits a solution in a suitable weak sense, then Ω must be of Wulff shape

On a nonlocal problem for a confined plasma in a Tokamak

summary:The paper deals with a nonlocal problem related to the equilibrium of a confined plasma in a Tokamak machine. This problem involves terms $u'_{\ast }(|u>u(x)|)$ and $|u>u(x)|$, which are neither local, nor continuous, nor monotone. By using the Galerkin approximate method and establishing some properties of the decreasing rearrangement, we prove the existence of solutions to such problem

Helical structures with switchable and hierarchical chirality

Chirality is present as a trend of research in biological and chemical communities for it has a significant effect on physiological properties and pharmacological effects. Further, manipulating specific morphological chirality recently has emerged as a promising approach to design metamaterials with tailored mechanical, optical, or electromagnetic properties. However, the realization of many properties found in nature, such as switchable and hierarchical chirality, which allows electromagnetic control of the polarization of light and enhancement of mechanical properties, in man-made structures has remained a challenge. Here, we present helical structures with switchable and hierarchical chirality inspired by origami techniques. We propose eggbox-based chiral units for constructing homogeneous and heterogeneous chiral structures and demonstrate a theoretical approach for tuning the chirality of these structures by modulating their geometrical parameters and for achieving chirality switching through mechanism bifurcation. Finally, by introducing a helical tessellation between the chiral units, we design hierarchical structures with chirality transferring from construction elements to the morphological level and discover a helix with two zero-height configurations during the unwinding process. We anticipate that our design and analysis approach could facilitate the development of man-made metamaterials with chiral features, which may serve in engineering applications, including switchable electromagnetic metamaterials, morphing structures, and bionic robots

OpenDelta: A Plug-and-play Library for Parameter-efficient Adaptation of Pre-trained Models

The scale of large pre-trained models (PTMs) poses significant challenges in adapting to downstream tasks due to the high optimization overhead and storage costs associated with full-parameter fine-tuning. To address this, many studies explore parameter-efficient tuning methods, also framed as "delta tuning", which updates only a small subset of parameters, known as "delta modules", while keeping the backbone model's parameters fixed. However, the practicality and flexibility of delta tuning have been limited due to existing implementations that directly modify the code of the backbone PTMs and hard-code specific delta tuning methods for each PTM. In this paper, we present OpenDelta, an open-source library that overcomes these limitations by providing a plug-and-play implementation of various delta tuning methods. Our novel techniques eliminate the need to modify the backbone PTMs' code, making OpenDelta compatible with different, even novel PTMs. OpenDelta is designed to be simple, modular, and extensible, providing a comprehensive platform for researchers and practitioners to adapt large PTMs efficiently.Comment: Accepted to ACL 2023 Demo trac

Age-Dependent Up-Regulation of HCN Channels in Spiral Ganglion Neurons Coincide With Hearing Loss in Mice

Age-related hearing loss (AHL) is the most common sensory disorder in the elderly population, and the etiologies are diverse. To understand the underlying mechanisms of AHL, one strategy is to identify correlates of the disease for comprehensive evaluation of treatment approaches. Dysfunction and degeneration of spiral ganglion neurons (SGNs) are major contributors to AHL. Previously, we showed that one of the changes in the aging auditory system is SGN excitability increase in mice. Since hyperpolarization-activated cyclic nucleotide-gated (HCN) channels play important roles in determining neuronal excitability, we predicted that HCN channels in SGNs are involved in AHL. To investigate the contribution of HCN channels to AHL, we examined the expression and biophysical properties of HCN channels in SGNs from adult (2–3 months) and 11–12-month-old mice. We report a dramatic increase of HCN channel current (Ih) in SGNs in old mice (11–12 months old). The results matched well with increased expression of HCN1 and HCN2 subunits, suggesting that upregulation of HCN channels in SGNs is one of the important facets of the aging SGNs. Moreover, the activity of Ih produced a major impact on the firing properties of SGNs in older mice. The upregulation of Ih may contribute to AHL by regulating SGN excitability. We assessed whether increased SGNs excitability dovetail with neurodegeneration. Apoptosis-inducing factor (AIF)-mediated apoptosis in SGNs was observed in old mice and activation of HCN channels mediates AIF activation. Thus, these findings demonstrate stark correlation between age-dependent increased expression of HCN channels and Ih, and apoptosis in SGNs, which may contribute towards the varied mechanisms of AHL

Rigid-foldable tubular arches

Several types of tubular, origami-inspired plate mechanisms have been proposed for use as meta-materials and deployable structures. However, research into mechanical properties of these mechanisms is limited to rectilinear forms. This paper investigates the structural feasibility of non-rectilinear rigid-foldable cellular materials for application as deployable arch structures. An experimental and numerical investigation is first conducted on a new type of folded tubular arch, with failure contributions identified from hinge rotation and plate buckling failure mechanisms. A common geometric description is then developed between three different types of origami-inspired tubular arches, which are numerically investigated under three-point loading. The double-kite arch developed in this paper is seen to have the highest failure load

Deployable prismatic structures with rigid origami patterns

Rigid origami inspires new design technology in deployable structures with large deployable ratio due to the property of flat foldability. In this paper, we present a general kinematic model of rigid origami pattern and obtain a family of deployable prismatic structures. Basically, a four-crease vertex rigid origami pattern can be presented as a spherical 4R linkage, and the multivertex patterns are the assemblies of spherical linkages. Thus, this prismatic origami structure is modeled as a closed loop of spherical 4R linkages, which includes all the possible prismatic deployable structures consisting of quadrilateral facets and four-crease vertices. By solving the compatibility of the kinematic model, a new group of 2n-sided deployable prismatic structures with plane symmetric intersections is derived with multilayer, straight and curvy variations. The general design method for the 2n-sided multilayer deployable prismatic structures is proposed. All the deployable structures constructed with this method have single degree-of-freedom (DOF), can be deployed and folded without stretching or twisting the facets, and have the compactly flat-folded configuration, which makes it to have great potential in engineering applications

An Efficient Reliability Analysis Method Combining Improved EIF Active Learning Mechanism and Kriging Metamodel

Complex implicit performance functions widely exist in many engineering problems. The reliability analysis of these problems has always been a challenge. Using surrogate model instead of real performance function is one of the methods to solve this kind of problem. Kriging is one of the surrogate models with precise interpolation technique. In order to make the kriging model achieve higher accuracy using a small number of samples, i.e., improve its practicability and feasibility in practical engineering problems, some active learning equations are wildly studied. Expected improvement function (EIF) is one of them. However, the EIF has a great disadvantage in selecting the added sample point. Therefore, a joint active learning mechanism, J-EIF, is proposed to obtain the ideal added point. The J-EIF active learning mechanism combines the two active learning mechanisms and makes full use of the characters of kriging model. It overcomes the shortcoming of EIF active learning mechanism in the selection of added sample points. Then, using Monte Carlo Simulation (MCS) results as a reference, the reliability of two examples is estimated. The results are discussed showing that the learning efficiency and accuracy of the improved EIF are both higher than those of the traditional EIF