A jump system is a set of integer points with an exchange property, which is a generalization of a matroid, a delta-matroid, and a base polyhedron of an integral polymatroid (or a submodular system). Recently, the concept of M-convex functions on constant-parity jump systems is introduced by Murota as a class of discrete convex functions that admit a local criterion for global minimality. M-con...

| We describe a simple integer-valued \hash" function h(x), where x is a binary word of some xed length. This hash function has the properties that 1. h(x) may be computed in O(n) steps where n is the length of x, 2. h(y) may be computed in O(d) time, if h(x) is known and y and x diier at d (known) bits. 3. h is \locally collisionless:" h(x) 6 = h(y) if x 6 = y and x and y are Hamming distance ...

I study the state complexity of binary operations on regular languages over different alphabets. It is well known that if L′ m and Ln are languages over the same alphabet with m and n quotients, respectively, the state complexity of any binary boolean operation on L′ m and Ln is mn, and that of the product (concatenation) is (m − 1)2n + 2. In contrast to this, I show that if L′ m and Ln are ove...

This paper proposes a mathematical programming framew ork for combining SVMs with possibly di erent kernels. Compared to single SVMs, the advantage of this approach is tw ofold: it creates SVMs with local domains of expertise leading to local enlargements of the margin, and it allows the use of simple linear kernels combined with a xed boolean operation that is particularly well suited for buil...

We exhaustively investigate possible combinations of a boolean operation together with a catenation. In many cases we prove and improve some conjectures by Brzozowski. For each family of operation, we endeavour to provide a common witness with a small size alphabet.

Although deep neural networks (DNNs) are being a revolutionary power to open up the AI era, the notoriously huge hardware overhead has challenged their applications. Recently, several binary and ternary networks, in which the costly multiplyaccumulate operations can be replaced by accumulations or even binary logic operations, make the on-chip training of DNNs quite promising. Therefore there i...

Simple additive weighting is a well-known method for scoring and ranking alternative options based on multiple attributes. However the pitfalls associated with this approach are not widely appreciated. For example, the apparently innocuous step of normalizing the various attribute data in order to obtain comparable figures leads to markedly different rankings depending on which normalization is...