When the velocity field of the subsurface contains strong lateral variations, traveltimes of reflection and/or transmission data can become multi-valued. Migrating these data with operators that contain first arrivals only causes migration artefacts, because energy contained in later arrivals is not accounted for (Geoltrain and Brac, 1993). The most simple solution to this problem is to account...

Random sequences attain the highest entropy rate. The estimation of entropy rate for an ergodic source can be done using the Lempel Ziv complexity measure yet, the exact entropy rate value is only reached in the infinite limit. We prove that typical random sequences of finite length fall short of the maximum Lempel-Ziv complexity, contrary to common belief. We discuss that, for a finite length,...

A compression algorithm takes a finite structure of a class K as input and produces a finite structure of a different class K’ as output. Given a property P on the class K defined in a logicL, we study the definability of property P on the class K’. We consider two compression schemas on unary ordered structures (words), compression by runlength encoding and the classical Lempel-Ziv. First-orde...

In the implementation of lossless compression, the traditional Lempel-Ziv dictionary algorithm produces good compression performance, but at a relatively slow processing speed for use in real-time applications. This paper highlights a technique to speed up the overall compression process through introduction of a prediction pre-processor stage. A variety of predictors are applied to two variati...

In this paper, a natural extension of the Lempel-Ziv complexity for several finitetime sequences, defined on finite size alphabets is proposed. Some results on the defined joint Lempel-Ziv complexity are given, as well as properties in connection with the Lempel-Ziv complexity of the individual sequences. Also, some links with Shannon entropies are exhibited and, by analogy, some derived quanti...

The weakly coupled WKB system captures high frequency wave dynamics in many applications. For such a system a level set method framework has been recently developed to compute multi-valued solutions to the Hamilton-Jacobi equation and evaluate position density accordingly. In this paper we propose two approaches for computing multi-valued quantities related to density, momentum as well as energ...

The Linearization of Nonlinear feedback shift registers (NFSRs) is to find their state transition matrices. In this paper, we investigate the linearization multi-valued NFSRs by considering it as a logical network via a semi-tensor product approach. A new state transition matrix is found for an multi-valued NFSR, which can be simply computed from the truth table of its feedback function, and th...

This paper studies abstraction and refinement techniques in the setting of multi-valued model checking for the μ-calculus. Two dimensions of abstractions are identified and studied: Abstraction by joining states of the underlying multi-valued Kripke structure as well as abstraction of truth values, for each following both an optimistic and pessimistic account. It is shown that our notion of abs...

In supervised machine-learning applications to natural language processing, tasks are typically formulated as classiication tasks mapping multi-valued features to multi-valued classes. Memory-based or instance-based learning algorithms are suited for such representations , but they are not restricted to them; both features and classes may be unpacked in binary values. We demonstrate in a matrix...

We present a new complete multi-valued SAT solver, based on current state-of-the-art SAT technology. It features watched literal propagation and conflict driven clause learning. We combine this technology with state-of-the-art CP methods for branching and introduce quantitative supports which augment the watched literal scheme with a watched domain size scheme. Most importantly, we adapt SAT no...