New ABC method for Bayesian inference of neural models.
problem Challenging to identify which mechanistic models quantitatively reproduce neural data.
method Likelihood-free inference using neural networks and Bayesian mixture-density networks.
result Efficiently estimates posterior distributions and recovers ground-truth parameters.
Paper formulates governing equations for membrane O surfaces.
problem Formulating equations for membrane O surfaces.
method Formulated governing equations for membrane O surfaces of the 1st and 2nd kind.
result Membrane O surfaces are a subclass of Demoulin's Ω surfaces.
This paper uses deep reinforcement learning to automate electric transmission voltage control.
problem Automating voltage control in electric transmission systems.
method Deep reinforcement learning (DRL) applied to voltage control, with a novel DQN modification.
result DRL can automate voltage control at scale, but more research is needed.
This paper identifies critical cases for evaluating PV investment impacts on MV networks efficiently.
problem Challenges in maintaining and controlling voltages in MV distribution networks due to increasing PV generation.
method Clustering MV nodes based on electrical adjacency and time blocks, identifying critical cases for further study.
result A scalable method to time efficiently identify critical cases for PV investment evaluation.
We use ellipsoids to solve power system voltage regulation problems.
problem Voltage regulation in power systems under uncertainty.
method Tractable ellipsoidal approximation for chance constrained optimizations.
result Efficiently trained machine learning model approximates uncertainty region.
New multi-spiral approach improves packaging of thick membranes.
problem Deploying thick membranes on curved surfaces efficiently.
method Multi-spiral folding approach with prismatic folding lines.
result Improved deployment performance of thick membranes on curved surfaces.
New theory shows how membranes can break symmetry.
problem Understanding symmetry breaking in membranes with boundaries.
method Applied bifurcation theory and reduced membrane equation.
result Existence of symmetry breaking bifurcation in membrane solutions.
This review reports some theoretical results on the Geometry of membranes. The governing equations to describe equilibrium configurations of lipid vesicles, lipid membranes with free edges, and chiral lipid membranes are derived from the variation of free energies of these structures. Some analytic solutions to these e…
Study the stability of membranes using Helfrich energy and second variation formula.
problem Stability of membranes under various conditions.
method Developed and applied a second variation formula for the Helfrich energy for a class of surfaces.
result Studied the second variation of the area functional for a specific example.
Recent theoretical advances in elasticity of membranes following Helfrich's famous spontaneous curvature model are summarized in this review. The governing equations describing equilibrium configurations of lipid vesicles, lipid membranes with free edges, and chiral lipid membranes are presented. Several analytic solut…
Proves C1,1 regularity for multiple membrane solutions.
problem Stationary C1,α solutions to the multiple membrane problem. method Uses C1,1-regularity estimate. result Proves C1,1 regularity for stationary solutions. Theory and methods for particle dynamics in curved lipid membranes.
problem Understanding particle behavior in curved lipid membranes.
method Developed theory and computational methods for hydrodynamic coupling.
result Membrane curvature and topology affect particle mobility.
The purpose of this paper is to study the shapes and stabilities of bio-membranes within the framework of exterior differential forms. After a brief review of the current status in theoretical and experimental studies on the shapes of bio-membranes, a geometric scheme is proposed to discuss the shape equation of closed…
Periodic surfaces have a limited number of bending modes, equal to their membrane modes.
problem Understanding the limitations of bending modes in periodic surfaces.
method Analyzing deformation modes of periodic, piecewise smooth, simply connected surfaces.
result Effective membrane modes and bending modes are orthogonal, limiting the total number of modes to 3.
This paper reviews low voltage load forecasting methods and applications.
problem Reliable forecasting for low voltage networks is needed for decarbonization.
method Comprehensive survey of current approaches, challenges, and trends.
result Established an open list of low voltage datasets for further research.
This review reports some key results in theoretical investigations on configurations of lipid membranes and presents several challenges in this field which involve (i) exact solutions to the shape equation of lipid vesicles; (ii) exact solutions to the governing equations of open lipid membranes; (iii) neck condition o…
The paper tackles voltage control in distribution systems with uncertainties using chance constraints.
problem Voltage control in distribution systems with high uncertainties from distributed energy resources.
method Chance constraint approach accounting for arbitrary correlations, solved via stochastic quasi gradient method.
result The method is more robust and computationally tractable compared to conventional approaches.
New model considers spontaneous curvature for lipid bilayer membranes, including discontinuities.
problem Modeling discontinuities at interfaces in lipid bilayer membranes.
method Introduced a family of energies for smooth surfaces and phase fields, derived a sharp interface limit.
result Theoretical result extends classical model by assigning bending energy to tangential discontinuities.
Investigates geometric aspects of double field theory and its membrane sigma-model formulation.
problem Capturing geometric and non-geometric flux backgrounds in DFT.
method Determines a splitting and projection of the Courant algebroid, constructs a membrane sigma-model, and analyzes gauge invariance.
result Unified description of geometric and non-geometric flux backgrounds in DFT.
The paper proposes a data-driven method for optimal power flow and voltage regulation in distribution grids.
problem Optimal power flow and voltage regulation in decentralized power grids.
method The approach uses a network model, historic data, and regression to find functions approximating optimal reactive power injections for inverters.
result The method achieves near-optimal results in voltage- and capacity-constrained loss minimization and voltage flattening.
Study connects hyperbolic geometry to membrane shapes.
problem Understanding the shapes of biological membranes.
method Relates geometry of hyperbolic space to Helfrich model.
result Establishes a connection between membrane shapes and hyperbolic geometry.
We construct membrane homology groups $\h(M)$ associated with each compact connected oriented smooth manifold, and show that $\h(M)$ is matrix graded algebra.
We define a topological quantum membrane theory on a seven dimensional manifold of G2 holonomy. We describe in detail the path integral evaluation for membrane geometries given by circle bundles over Riemann surfaces. We show that when the target space is CY3×S1 quantum amplitudes of non-local observables …
We construct a gauge fixed action for topological membranes on G2-manifold such that its bosonic part is the standard membrane theory in a particular gauge. We prove that quantum mechanically the path-integral in this gauge localizes on associative submanifolds. Moreover on M×S1 the theory naturally reduces…
Study of symplectic manifolds degenerating into singular spaces.
problem Understanding degenerations of symplectic manifolds into singular spaces.
method Topological framework focusing on Lagrangian manifolds and holomorphic membranes.
result Degenerations into singular toric varieties yield exotic Lagrangian tori.
Study derives the limit of lipid bilayer membranes, proving their smooth transition across interfaces.
problem Understanding the smooth transition of lipid bilayer membranes across interfaces.
method Rigorous derivation of the Γ-limit for rotationally symmetric two-phase bilayer membranes. result Limit membranes are C1 across interfaces and can consist of multiple topological spheres. Neural network predicts electrochemical cell faults with 53% less error.
problem Predicting faults in electrochemical cells to avoid safety hazards and reduce costs.
method Self-supervised encoder-decoder neural network that learns degradation from operating conditions.
result Predicted voltage with 53% less error than parametric models, 64% faster fault prediction.
Proves Payne conjecture for buckling and membrane eigenvalues.
problem Proving Payne conjecture for buckling and membrane eigenvalues.
method Analytical proof for buckling and membrane eigenvalues.
result Proves Payne conjecture for n-dimensional case (n≥2). Current-mode memristor crossbars enable neuromemristive systems with similar accuracy but different weight distributions.
problem Implementing weight matrices in neuromemristive systems via current-mode memristor crossbars.
method Derived theoretical results for weight range and distribution, developed a modified gradient descent rule for current-mode design, and performed behavioral simulations.
result Current-mode and voltage-mode designs achieve similar accuracy but use different feature representations.
We give a definition of higher dimensional iterated integrals based on integration over membranes. We prove basic properties of this definition and formulate a conjecture which extends Chen's de Rham Theorem for iterated integrals to the membrane case.
Optimal Volt/VAR control rules designed using deep learning.
problem Designing optimal Volt/VAR control rules for DERs to regulate voltage fluctuations.
method Formulated as a deep learning problem, where a DNN emulates Volt/VAR dynamics and optimizes rule parameters.
result DNN-based optimization outperforms MINLP in efficiency and accuracy.
For a membrane in the plane the multiplicity of the k-th eigenvalue is known to be not greater than 2k−1. Here we prove that it is actually not greater than 2k−3, for k≥3.
A surface functional theory for p-dimensional extended objects, the p-branes, was proposed in previous papers. The field equations for toroidal p-branes was exactly solved in d=p+2 dimensions, yielding equally spaced mass-squared spectrum with massless states. In this paper, we obtain the asymptotic distribution of m…
Non-linear control rules improve smart inverter performance in fluctuating grids.
problem Optimizing smart inverter control for voltage regulation and energy efficiency in fluctuating grids.
method Customized non-linear control rules designed as a kernel-based regression task, leveraging a linearized grid model and convex optimization.
result Non-linear control rules achieve near-optimal performance in real-world tests, minimizing voltage deviations and ohmic losses.
Transforming cylindrical packings into bicontinuous surfaces.
problem Understanding the early development of bicontinuous structures in plant plastids.
method Geometric modeling and computational simulations of cylinder packings.
result Specific cylinder packings with cubic symmetry transform into TPMS.
LEAP nets model power grid disruptions for rapid response.
problem Modeling and predicting power grid disruptions.
method Transfer learning neural network embedding approach.
result LEAP nets can rapidly assess human operators' actions in emergencies.
Proves existence and regularity of spherical minimizers for lipid membrane energy.
problem Existence and regularity of minimizers for the Canham-Helfrich energy.
method Establishes lower semicontinuity and proves existence through weak convergence of immersions.
result Proves existence and regularity of minimizers for the Canham-Helfrich energy on spheres.
This paper mainly aims to establish the well-posedness on time interval [0,ε−21T] of the classical initial problem for the bosonic membrane in the light cone gauge. Here ε is the small parameter measures the nonlinear effects. In geometric, the bosonic membrane are timelike submanifo…
Bayesian modeling predicts hydroxide ion conductivity in polymer membranes.
problem Quantitative relationship between hydrophilic domain size and hydroxide ion conductivity in polymer membranes is unknown.
method Bayesian sparse modeling applied to copolymer composition data.
result Composition-derived features are identified as critical for predicting hydroxide ion conductivity.
This thesis reviews Leibniz algebroids and generalized geometry for string theory.
problem Describing string and membrane backgrounds using generalized geometry.
method Review of Leibniz algebroids, generalized geometry, and Nambu-Poisson structures.
result Foundation laid for describing string and membrane backgrounds in generalized geometry.
Generates tubular and membranous shapes using curvature functionals.
problem Difficult analysis of tubular and membranous shapes.
method Modeling as curvature optimization problem, phase-field formulation, GPU algorithm.
result Wide continuum of shape textures discovered.
We present a Hamiltonian framework for higher-dimensional vortex filaments (or membranes) and vortex sheets as singular 2-forms with support of codimensions 2 and 1, respectively, i.e. singular elements of the dual to the Lie algebra of divergence-free vector fields. It turns out that the localized induction approximat…
New surfaces described that are symmetric and solve a specific equation.
problem Understanding symmetric shapes of membranes.
method Characterized and described axially symmetric Helfrich spheres using the reduced membrane equation.
result These surfaces are symmetric and belong to a specific family.
We study the dg-Lie algebra f_n generated by the coefficients of the universal translation invariant flat dg-connection on the n-dimensional affine space. We describe its "semiabelianization" (in particular, the universal quotient which is a crossed module of Lie algebras) in terms of closed differential forms of arbit…
Study finds minimizers for complex membrane models without symmetry assumptions.
problem Minimizing the Canham-Helfrich functional in multiple phases for heterogeneous biological membranes.
method Reformulated as oriented curvature varifolds, proving existence without symmetry assumptions.
result Existence of minimizers for single- and multiphase models under constraints.
The paper uses Frenet frame to unify electrical and geometric quantities.
problem Defining time derivatives of electrical quantities in various conditions.
method Utilizes Frenet frame from differential geometry to define time derivatives in both stationary and transient conditions.
result Unifies and generalizes time- and phasor-domain frameworks.
Studying the M-branes leads us naturally to new structures that we call Membrane-, Membrane^c-, String^K(Z,3)- and Fivebrane^K(Z,4)-structures, which we show can also have twisted counterparts. We study some of their basic properties, highlight analogies with structures associated with lower levels of the Whitehead tow…
Lipid necks, large curvature bridges, are shown to be metastable.
problem Understanding the energetically prohibitive yet ubiquitous lipid necks in cell membranes.
method Geometric triality approach to demonstrate metastability.
result Lipid necks can exist for finite but potentially long times without stabilizing mechanisms.