Recent differentiable rendering techniques have become key tools to tackle many inverse problems in graphics and vision. Existing models, however, assume steady-state light transport, i.e., infinite speed of light. While this is a safe assumption for applications, recent advances ultrafast imaging leverage the wealth information that can be extracted from exact time flight In context, physicall...

This note is a sequel to [7] where we investigated the endomorphisms of a certain class of Banach algebras of infinitely differentiable functions on the unit interval. Start with a perfect, compact plane setX. We say that a complex-valued function f defined on X is complex-differentiable at a point a ∈ X if the limit f (a) = lim z→a, z∈X f(z)− f(a) z − a exists. We call f ′(a) the complex deriv...

If the world is a differential equation, as Boltzmann thought, the problem of the origin of the "nowhere differentiable nature of reality" (cf. Mandelbrot [1]) poses itself [2]. To our knowledge, only two differentiable maps exist in the literature which produce nowhere differentiable behavior, the 3-D diffeomorphisms indicated by Grebogi et al. [3] and by Kaneko [4], The first map [3] which co...

Artificial reverberation (AR) models play a central role in various audio applications. Therefore, estimating the AR model parameters (ARPs) of reference is crucial task. Although few recent deep-learning-based approaches have shown promising performance, their non-end-to-end training scheme prevents them from fully exploiting potential deep neural networks. This motivates introduction differen...

It should be evident to you that (1.5) is equivalent to (1.3). Visually, if the graph of a function f at (a, f(a)) either has no unique tangent line or has a vertical tangent line then f is not differentiable at the point a. A function that is differentiable at every point in Dom(f) is said to be differentiable. A function that is differentiable at every point in a set S ⊂ Dom(f) is said to be ...

We consider a family of smooth maps on an infinite cylinder which have invariant curves that are nowhere smooth. Most points on such a curve are buried deep within its spiked structure, and the outermost exposed points of the curve constitute an invariant subset which we call the "facade" of the curve. We find that for surprisingly many of the maps in the family, all points in the facades of th...

A function F on the space of n × n real symmetric matrices is called spectral if it depends only on the eigenvalues of its argument. Spectral functions are just symmetric functions of the eigenvalues. We show that a spectral function is twice (continuously) differentiable at a matrix if and only if the corresponding symmetric function is twice (continuously) differentiable at the vector of eige...