We consider learning a sequence classifier without labeled data by using sequential output statistics. The problem is highly valuable since obtaining labels in training data is often costly, while the sequential output statistics (e.g., language models) could be obtained independently of input data and thus with low or no cost. To address the problem, we propose an unsupervised learning cost fu...

We consider the motion of a deformable interface that separates a fully-developed turbulent gas flow from a thin layer of laminar liquid. We outline a linear model to describe the interaction between the turbulent gas flow and the interfacial waves; this consists of the Orr-Sommerfeld equation with the appropriate turbulent mean flow profile, together with a turbulent stress closure scheme. Thi...

We consider learning a sequence classifier without labeled data by using sequential output statistics. The problem is highly valuable since obtaining labels in training data is often costly, while the sequential output statistics (e.g., language models) could be obtained independently of input data and thus with low or no cost. To address the problem, we propose an unsupervised learning cost fu...

Generalized thermoelastic models have been developed with the aim of eliminating the contradiction in the infinite velocity of heat propagation inherent in the classical dynamical coupled thermoelasticity theory. In these generalized models, the basic equations include thermal relaxation times and they are of hyperbolic type. Furthermore, Tzou established the dual-phase-lag heat conduction theo...

We prove the higher integrability of gradient for local minimizers thermal insulation problem: an analogue De Giorgi’s conjecture Mumford–Shah functional. deduce that singular part free boundary has Hausdorff dimension strictly less than $n - 1$.

For a large class of variational quantum circuits, we show how arbitrary-order derivatives can be analytically evaluated in terms simple parameter-shift rules, i.e., by running the same circuit with different shifts parameters. As particular cases, obtain rules for Hessian an expectation value and metric tensor state, both which efficiently used to implement second-order optimization algorithms...

The present research focuses on the use of a meshless method for solution nanoplates by considering strain gradient thin plate theory. Unlike most common finite element method, methods do not rely domain decomposition. In approach approximating functions at collocation nodes are obtained using radial basis which depend shape parameters. selection such parameters can strongly influences accuracy...