Universal model for soft tissue mechanics under shock waves.
problem Modeling shock wave mechanics in soft biological tissues.
method Continuum mixture theory with phase-field mechanics.
result Universal thermodynamically consistent formulation for soft porous tissues.
Continuum mechanics theory describes skin's complex anisotropic behavior.
problem Modeling the anisotropic tearing of skin.
method Finsler geometry fiber bundle approach, variational method, phase-field mechanics.
result Analytical solutions capture experimental data on skin tearing.
Data-driven approach learns effective equations for phase field interfaces.
problem Learning accurate equations for phase field interface dynamics.
method Data-driven identification of partial differential equations from phase field data.
result Data-driven equations outperform analytical approximations in certain regimes.
We explore a computational model of an incompressible fluid with a multi-phase field in three-dimensional Euclidean space. By investigating an incompressible fluid with a two-phase field geometrically, we reformulate the expression of the surface tension for the two-phase field found by Lafaurie, Nardone, Scardovelli, …
We study the phase field method for the volume preserving mean curvature flow. Given an initial C1 hypersurface we proved the existence of the weak solution for the volume preserving mean curvature flow via the reaction diffusion equation with a nonlocal term. We also show the monotonicity formula and the density up…
Machine learning predicts failure in brittle materials with high accuracy.
problem Predicting failure in brittle materials under repetitive loads.
method Phase-field model combined with supervised machine learning.
result Framework predicts failure with acceptable accuracy even in noisy data.
New proof confirms De Giorgi's conjecture about phase-field approximation of Willmore functional.
problem Proving a conjecture about the phase-field approximation of the Willmore functional.
method Using Γ-convergence and properties of the Allen-Cahn energy and its variations.
result The original De Giorgi conjecture holds with k=0.
Optimizes structure topology for ductile and brittle fracture resistance.
problem Minimizing mass while ensuring structural damage and fracture resistance.
method Phase-field approach for modeling fracture, level-set topology optimization.
result Enhanced fracture resistance through two formulations.
The homotopy theory of topological defects in ordered media fails to completely characterize systems with broken translational symmetry. We argue that the problem can be understood in terms of the lack of rotational Goldstone modes in such systems and provide an alternate approach that correctly accounts for the intera…
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 prove nonexistence of nonconstant local minimizers for a class of functionals, which typically appears in the scalar two-phase field model, over a smooth N-dimensional Riemannian manifold without boundary with non-negative Ricci curvature. Conversely for a class of surfaces possessing a simple closed geodesic along …
We consider the sharp interface limit of the Allen-Cahn equation with Dirichlet or dynamic boundary conditions and give a varifold characterization of its limit which is formally a mean curvature flow with Dirichlet or dynamic boundary conditions. In order to show the existence of the limit, we apply the phase field me…
In order to study a one-dimensional analogue of the spontaneous curvature model for two-component lipid bilayer membranes we consider planar curves that are made of a material with two phases. Each phase induces a preferred curvature to the curve, and these curvatures as well as phase boundaries may lead to the develop…
We present a new physics informed neural network (PINN) algorithm for solving brittle fracture problems. While most of the PINN algorithms available in the literature minimize the residual of the governing partial differential equation, the proposed approach takes a different path by minimizing the variational energy o…
Common models for two-phase lipid bilayer membranes are based on an energy that consists of an elastic term for each lipid phase and a line energy at interfaces. Although such an energy controls only the length of interfaces, the membrane surface is usually assumed to be at least C1 across phase boundaries. We consi…
Study proposes a nonlocal approximation of the Willmore functional using fractional Allen-Cahn energies.
problem Approximating the Willmore functional using nonlocal methods.
method Gamma-convergence and fractional Laplacian analysis in Fermi coordinates.
result Proves Γ-limsup estimate for the proposed nonlocal approximation. Study quantizes energy distribution in inhomogeneous phase transitions.
problem Quantifying energy distribution in inhomogeneous Allen-Cahn phase transitions.
method Analysis of varifolds and convergence of integer rectifiable varifolds.
result Equidistribution of energy between Dirichlet and Potential energy in phase field limit.
Variational approximations for curve flows on Riemannian manifolds.
problem Approximating solutions to curvature and elastic flow problems on Riemannian manifolds.
method Variational formulations, finite element approximations, piecewise linear elements, stability analysis.
result Derived schemes can compute rotationally symmetric self-shrinkers and geodesics.
The paper studies momentum-based minimization for Ginzburg-Landau on Euclidean spaces and graphs.
problem Minimizing the Ginzburg-Landau functional on Euclidean spaces and graphs.
method Momentum-based minimization using a convex-concave splitting-based FISTA-type time discretization.
result Momentum can lead to faster convergence if the time step size is large but not too large.
In this paper we study dynamic pricing mechanisms of financial derivatives. A typical model of such pricing mechanism is the so-called g--expectation defined by solutions of a backward stochastic differential equation with g as its generating function. Black-Scholes pricing model is a special linear case of this pricin…
A solution for the Weinstein's Problem in the general framework of generalized Lie algebroids is the target of this paper. We present the mechanical systems called by use, mechanical (?; ?)-systems, Lagrange mechanical (?; ?)-systems or Finsler mechanical (?; ?)-systems and we develop their geometries. We obtain the ca…
New mechanics on non-associative octonions discovered.
problem Discrete mechanics on non-associative groups.
method Generalized Lagrangian and Hamiltonian mechanics to non-associative objects.
result Discrete mechanics on unitary octonions achieved.
A new description, different by the classical theory of Hamiltonian Mechanics, in the general framework of generalized Lie algebroids is presented. In the particular case of Lie algebroids, new and important results are obtained. We present the \emph{dual mechanical systems} called by use, \emph{dual mechanical}$(ρ,η) …
This paper assesses Gaussian and Exponential mechanisms for certifying adversarial robustness.
problem Certifying adversarial robustness using randomized smoothing mechanisms.
method Proposes a generic framework to assess the appropriateness of randomized smoothing mechanisms.
result Gaussian mechanism is an appropriate option for certifying both ℓ2-norm and ℓ∞-norm robustness. We propose a new input perturbation mechanism for publishing a covariance matrix to achieve (ε,0)-differential privacy. Our mechanism uses a Wishart distribution to generate matrix noise. In particular, We apply this mechanism to principal component analysis. Our mechanism is able to keep the positive semi-definitene…
New mechanisms improve differential privacy for scalar queries.
problem Improving differential privacy for scalar, real-valued query functions.
method Mixing multiple Gaussian distributions to satisfy differential privacy.
result Mechanisms yield lower noise amplitudes and variances compared to the analytic Gaussian mechanism.
We design two mechanisms for the recommender system to collect user ratings. One is modified Laplace mechanism, and the other is randomized response mechanism. We prove that they are both differentially private and preserve the data utility.
Quantum mechanics models for financial Black-Scholes model.
problem Modeling financial derivatives using quantum mechanics.
method Noncommutative quantum mechanics applied to specific mechanical systems.
result Generalized noncommutative quantum mechanics of financial models.
Expands differential privacy mechanisms to include the Generalized Gaussian mechanism for improved private machine learning.
problem Improving privacy in machine learning algorithms while maintaining utility.
method Introduces and analyzes the Generalized Gaussian (GG) mechanism for differential privacy.
result The GG mechanism provides better performance than the Laplace and Gaussian mechanisms across various values of β.
Differential privacy mechanism design has traditionally been tailored for a scalar-valued query function. Although many mechanisms such as the Laplace and Gaussian mechanisms can be extended to a matrix-valued query function by adding i.i.d. noise to each element of the matrix, this method is often suboptimal as it for…
Optimal DP mechanisms for vector queries are found to be staircase distributions.
problem Designing optimal additive mechanisms for vector-valued queries under differential privacy.
method Reduction to radially symmetric distributions and convex rearrangement theory.
result Staircase mechanisms are optimal for any norm and cost function.
New approach identifies latent properties from mechanisms, not just data.
problem Identifying latent properties from data generating processes.
method Equivariance perspective on identifiable representation learning.
result Identification of latent properties is possible up to shared equivariances in known mechanisms.
New RL approach learns dynamic VCG mechanisms in unknown MDP environments.
problem Learning dynamic VCG mechanisms in unknown MDP environments.
method Reward-free online RL for exploration, combined with function approximation.
result Regret bound of O~(T2/3) for dynamic VCG mechanism learning. Paper connects dynamics of mechanical systems to Reeb dynamics.
problem Understanding dynamics in mechanical systems with Poisson structures.
method Using Jacobi bundle metrics and linear Poisson structures.
result Extends classical results on Reeb dynamics to mechanical systems.
Exact discrete mechanics for nonholonomic systems defined.
problem Discrete mechanics for nonholonomic systems.
method Constructing an exponential map and deriving exact discrete nonholonomic integrators.
result Reproduces continuous nonholonomic flow as discrete flow on constraint submanifold.
We prove optimal mechanisms for general contract spaces.
problem Optimal mechanism design under adverse selection and ambiguity.
method Existence proof for optimal mechanisms in general contract spaces.
result Centralized contracting is equivalent to delegated contracting.
A new Gaussian mechanism for differential privacy in the shuffle model is introduced.
problem Improving differential privacy in distributed learning environments.
method Characterization and upper-bounding of Rényi differential privacy (RDP) for the shuffle Gaussian mechanism.
result The shuffle Gaussian mechanism provides improved privacy guarantees compared to existing methods.
Active-memory mechanisms can replace self-attention in Transformers, but optimal results often require both.
problem Replacing self-attention with active-memory mechanisms in Transformers.
method Evaluation of various active-memory mechanisms in a Transformer model.
result Active-memory mechanisms can achieve comparable results to self-attention for language modeling, but optimal results are often achieved by combining both mechanisms.
We study the problem of what causes prices to change. We define the mechanical impact of a trading order as the change in future prices in the absence of any future changes in decision making, and its it informational impact as the remainder of the total impact once mechanical impact is removed. We introduce a method o…
New mechanism for pure differential privacy on functional summaries using Laplace-like process.
problem Challenges in achieving differential privacy for complex, structured functional summaries.
method Independent Component Laplace Process (ICLP) mechanism for infinite-dimensional Hilbert space.
result Effective enhancement of utility of private summaries through oversmoothing.
Unified framework for subsampling mechanisms with tighter privacy guarantees.
problem Improving privacy in machine learning models through subsampling.
method Conditional optimal transport for deriving mechanism-specific subsampling guarantees.
result Tighter privacy bounds for subsampled mechanisms compared to traditional methods.
New geometric mechanism solves four envelope problems.
problem Four basic problems on envelopes created by hyperplane families.
method Simple geometric mechanism of intersections of perpendicular bisectors and normal lines.
result Solves all four basic problems on envelopes at once.
This text explains how fiber bundle structure is fundamental for classical physics.
problem None explicitly stated, but implied as understanding fiber bundles is crucial for physics.
method Explains the fiber bundle structure and its universality for physics laws.
result Fiber bundle structure is fundamental for classical physics laws.
The paper improves privacy accounting for discrete-valued mechanisms and the subsampled Gaussian mechanism.
problem Improving the accuracy and efficiency of differential privacy accounting for discrete outputs.
method Uses fast Fourier transform (FFT) for rigorous error analysis and accounting of privacy loss.
result Provides strict lower and upper bounds for (ε,δ)-values, demonstrating up to 75% reduction in noise variance. This paper examines allocation mechanisms in markets with transfer costs, showing how these costs affect economic efficiency.
problem Transfer costs in decentralized exchange markets reduce economic efficiency.
method An axiomatic study of allocation mechanisms in the presence of transfer costs, providing robust and conditional mean allocation mechanisms.
result Robust and conditional mean allocation mechanisms are identified, relating to risk sharing in agent pools.
The Gaussian mechanism is an essential building block used in multitude of differentially private data analysis algorithms. In this paper we revisit the Gaussian mechanism and show that the original analysis has several important limitations. Our analysis reveals that the variance formula for the original mechanism is …
Paper introduces a new deep-learning method for quantum mechanics.
problem Simulating time-evolving Schrödinger equations efficiently.
method Generative diffusion models and stochastic mechanics.
result Significantly lower computational complexity compared to existing methods.
CICME estimates common and domain-specific causal mechanisms from multi-sensor data.
problem Inferring causal mechanisms from heterogeneous multi-sensor data across multiple domains.
method Three-step approach using Causal Transfer Learning (CTL).
result CICME reliably detects domain-invariant causal mechanisms and guides individual domain causal mechanism estimation.