For the Artin-Schreier curve y − y = f(x) defined over a finite field Fq of q elements, the celebrated Weil bound for the number of Fqr -rational points can be sharp, especially in supersingular cases and when r is divisible. In this paper, we show how the Weil bound can be significantly improved, using ideas from moment L-functions and Katz’s work on `-adic monodromy calculations. Roughly spea...

We use Fraunhofer diffraction theory and meterological data to determine the nature of cloud-particle distributions and the mean particle sizes required for interpreting photographs of coronas and iridescence in mountain wave clouds. Traditional descriptions of coronas and iridescence usually explain these optical phenomena as diffraction by droplets of liquid water. Our analysis shows that the...

Bitmap indexing, though e ective for low cardinality attributes, can be rather costly in storage overhead for high cardinality attributes. Range-based bitmap (RBM) indexing can be used to reduce this storage overhead. The attribute values are partitioned into ranges and a bitmap vector is used to represent a range. With RBM, however, the number of records assigned to di erent ranges can be high...

We demonstrate some simple but powerful methods that ease the problem of describing and generating circuits that exhibit a degree of regularity, but are not as beautifully regular as the text-book examples. Our motivating example is not a circuit, but a piece of C code that is widely used in graphics applications. It is a sequence of compare-andswap operations that computes the median of 25 inp...

Control of legged locomotion across uneven terrain is poorly understood from a theoretical perspective, despite strong relevance to clinical and robotic applications. Gait research has typically examined locomotion on smooth and level surfaces with uniform steps. Identifying key gait parameters that permit agile locomotion across uneven surfaces could lead to a clearer understanding of control ...

By a proof by assumption, or for short an assumption proof, I mean the following. The proof proves a conclusion of the form ‘If P then Q’. It proceeds by making a sequence of statements S1, . . . , Sn (possibly with added commentary), where P is S1, Q is Sn, and for each Si with i > 1 there are earlier Sj . . . such that the conditional ‘If Sj . . . , then Si’ is already known. The reason for c...

The Bled eConference quite often gets connected to the notion of eRegion. Therefore in this paper we will have a closer look at how the idea of an eRegion has been addressed by the conference over the past. After briefly looking at the emergence of the term eRegion, we summarize the contribution of the Bled eConference to the field of eRegion in the Research Track as well as in the Business Tra...