Zaj́ıček has recently shown that for a lower semi-continuous real-valued function on an Asplund space, the set of points where the function is Fréchet subdifferentiable but not Fréchet differentiable is first category. We introduce another variant of Fréchet differentiability, called Fréchet directional differentiability, and show that for any realvalued function on a normed linear space, the se...

on utilizing the spectral representation of selfadjoint operators in hilbert spaces, some error bounds in approximating $n$-time differentiable functions of selfadjoint operators in hilbert spaces via a taylor's type expansion are given.

We consider a family of exchange economies where consumers have multiprior preferences representing their ambiguity aversion. Under a linear independence assumption, we prove that regular economies are generic. Regular economies exhibit enjoyable properties: odd finite number of equilibrium prices, local constancy of this number and local differentiable selections of the equilibrium prices. Thu...

Feature acquisition in predictive modeling is an important task many practical applications. For example, patient health prediction, we do not fully observe their personal features and need to dynamically select acquire. Our goal acquire a small subset of that maximize prediction performance. Recently, some works reformulated feature as Markov decision process applied reinforcement learning (RL...

Procedural modeling allows for an automatic generation of large amounts similar assets, but there is limited control over the generated output. We address this problem by introducing Automatic Differentiable Modeling (ADPM). The forward procedural model generates a final editable model. user modifies output interactively, and modifications are transferred back to as its parameters solving inver...