Recent discussion in the public sphere about algorithmic classification has involved tension between competing notions of what it means for a probabilistic classification to be fair to different groups. We formalize three fairness conditions that lie at the heart of these debates, and we prove that except in highly constrained special cases, there is no method that can satisfy these three condi...

Safety verification of hybrid systems is undecidable, except for very special cases. In this paper, we circumvent undecidability by providing a verification algorithm that provably terminates for all robust problem instances, but need not necessarily terminate for non-robust problem instances. A problem instance x is robust iff the given property holds not only for x itself, but also when x is ...

In this article, we develop the Yoccoz puzzle technique to study a family of rational maps termed McMullen maps. We show that the boundary of the immediate basin of infinity is always a Jordan curve if it is connected. This gives a positive answer to the question of Devaney. Higher regularity of this boundary is obtained in almost all cases. We show that the boundary is a quasi-circle if it con...

We use tools from the multilinear oscillatory integral program developed by Christ, Li, Thiele, and Tao to treat special cases which are not covered existing theory. Consideration of leads an extended class examples for λ-power decay holds.

The general solution is found to a bilinear reduction of the higher order nonlinear Schrödinger equation. Except for the previously known special cases having multisoliton solutions, the solution has the form of a single envelope solitary wave or wave train for all other values of the parameters. We conjecture that the generic solution is limited to such a narrow class of functions because the ...


 The Norton product is defined on each eigenspace of a distance regular graph by the orthogonal projection entry-wise product. resulting algebra, known as commutative nonassociative algebra that useful in group theory due to its interesting automorphism group. We provide formula for Hamming using linear characters. construct large subgroup automorphisms and completely describe some cases....

● More than 1 in 5 architects was self-employed—about three times the proportion for all professional and related occupations. ● Licensing requirements include a professional degree in architecture, a period of practical training, and passing all divisions of the Architect Registration Examination. ● Architecture graduates may face competition, especially for jobs in the most prestigious firms;...