By associating frequencies to larger scales, we provide a simpler way derive local uniformity of multiplicative functions on average from the results Matomäki-Radziwiłł.

Classic results show that the Hawkes self-exciting point process can be viewed as a collection of temporal clusters, in which exogenously generated initial events give rise to endogenously driven descendant events. This perspective provides distribution cluster’s size through natural connection branching processes, but this is irrespective time. Insight into chronology cluster has been much mor...

We investigate computing models that are presented as families of finite computing devices with a uniformity condition on the entire family. Examples include circuits, membrane systems, DNA computers, cellular automata, tile assembly systems, and so on. However, in this list there are actually two distinct kinds of uniformity condition. The first is the most common and well-understood, where ea...

Abstract Many analyses on configurable software systems are intractable when confronted with colossal and highly-constrained configuration spaces. These could instead use statistical inference, where a tractable sample accurately predicts results for the entire space. To do so, laws of inference requires each member population to be equally likely included in sample, i.e., sampling process need...

We argue that it is unnatural and undesirable to use the non-uniform model of complexity for practice-oriented security reductions in cryptography.

Intercircuit splits occur when two or more circuits on the U.S. Courts of Appeals issue different legal rules about the same legal question. When this happens, federal law is applied differently in different parts of the country. Intercircuit splits are an indicator of legal non-uniformity, an impediment to lawyering and judging, and have real, practical consequences for American law. They are ...