Let Ω be a set with n elements. A transformation monoid on Ω is a set of maps from Ω to itself which is closed under composition and contains the identity. A transformation monoid M is synchronizing if it contains a map with rank 1 (that is, whose image has only one element). The notion comes from automata theory. A (finite deterministic) automaton consists of a set Ω of states and a set S of t...

Replication is a key technique in the design of efficient and reliable distributed systems. As information grows, it becomes difficult or even impossible to store all information at every replica. A common approach to deal with this problem is to rely on partial replication, where each replica maintains only a part of the total system information. As a consequence, a remote replica might need t...

We consider the problem of NON-UNIFORM GRAPH PARTITIONING, where the input is an edge-weighted undirected graph G = (V,E) and k capacities n1, . . . , nk, and the goal is to find a partition {S1, S2, . . . , Sk} of V satisfying |Sj | ≤ nj for all 1 ≤ j ≤ k, that minimizes the total weight of edges crossing between different parts. This natural graph partitioning problem arises in practical scen...

Dynamic instruction scheduling logic is one of the most critical and cycle-limiting structures in modern superscalar processors, and it is not easily pipelined without significant losses in performance. However, these performance losses are incurred only due to a small fraction of instructions, which are intolerant to the non-atomic scheduling. We first perform an empirical analysis of the inst...

We investigate in this paper the non-uniform sampling of EEG dipolar potentials and its impact on source analysis. We suppose some a priori knowledge on the approximate location of the dipole. We show that, in a noise-free situation, the electrode spacing needs to be around 3cm in the region of the dipole only, whereas it can drop to 8cm in remote regions.

Traditional designs for non-uniform filter bank (NUFB) are usually complex; involve complicated nonlinear optimization with a large number of parameters and lack of linear phase (LP) property. In this paper, we describe a simple design method for multirate near perfect reconstruction (NPR) cosine modulated filter banks with non-uniform frequency spacing and linear phase property that involves o...

Given εi ∈ [0,1) for each 1 < i < n, a particle performs the following random walk on {1,2, . . . ,n}: If the particle is at n, it chooses a point uniformly at random (u.a.r.) from {1, . . . ,n− 1}. If the current position of the particle is m (1 < m < n), with probability εm it decides to go back, in which case it chooses a point u.a.r. from {m + 1, . . . ,n}. With probability 1− εm it decides...

For a positive integer d⩾2, family F⊆([n]k) is said to be d-wise intersecting if |F1∩F2∩…∩Fd|⩾1 for all F1,F2,…,Fd∈F. A called maximal F∪{A} not any A∈([n]k)∖F. We provide refinement of O'Neill and Verstraëte's Theorem about the structure largest second non-trivial k-uniform families. also determine third fourth families k>d+1⩾4, fifth sixth 3-wise k⩾5, in asymptotic sense. Our proofs are appli...