Computing coset leaders and leader codewords of binary codes

In this paper we use the Gr\"obner representation of a binary linear code $\mathcal C$ to give efficient algorithms for computing the whole set of coset leaders, denoted by $\mathrm{CL}(\mathcal C)$ and the set of leader codewords, denoted by $\mathrm L(\mathcal C)$. The first algorithm could be adapted to provide not only the Newton and the covering radius of $\mathcal C$ but also to determine the coset leader weight distribution. Moreover, providing the set of leader codewords we have a test-set for decoding by a gradient-like decoding algorithm. Another contribution of this article is the relation stablished between zero neighbours and leader codewords

A fine grained heuristic to capture web navigation patterns

In previous work we have proposed a statistical model to capture the user behaviour when browsing the web. The user navigation information obtained from web logs is modelled as a hypertext probabilistic grammar (HPG) which is within the class of regular probabilistic grammars. The set of highest probability strings generated by the grammar corresponds to the user preferred navigation trails. We have previously conducted experiments with a Breadth-First Search algorithm (BFS) to perform the exhaustive computation of all the strings with probability above a specified cut-point, which we call the rules. Although the algorithm’s running time varies linearly with the number of grammar states, it has the drawbacks of returning a large number of rules when the cut-point is small and a small set of very short rules when the cut-point is high. In this work, we present a new heuristic that implements an iterative deepening search wherein the set of rules is incrementally augmented by first exploring trails with high probability. A stopping parameter is provided which measures the distance between the current rule-set and its corresponding maximal set obtained by the BFS algorithm. When the stopping parameter takes the value zero the heuristic corresponds to the BFS algorithm and as the parameter takes values closer to one the number of rules obtained decreases accordingly. Experiments were conducted with both real and synthetic data and the results show that for a given cut-point the number of rules induced increases smoothly with the decrease of the stopping criterion. Therefore, by setting the value of the stopping criterion the analyst can determine the number and quality of rules to be induced; the quality of a rule is measured by both its length and probability

Earthquake Source and Seismic Strain Rate: Portugal in the Context of The Western Part of the Eurasia - Africa Plate Boundary

Fault plane solutions, stress-pattern and deformation rate along the Western part of the Eurasia-Africa Plate Boundary, particu- larly between Azores triple junction and Gibraltar are analyzed. A selection of shallow depth seismic events (1.9 = M = 8.0) occurred in the period 1900-2003 have been carefully checked and analysed. The distribution of the focal mechanisms have been analysed by means of different techniques, projections and graphic representations. Seismic moment tensors, moment rate, slip velocity and b values have been estimated. Based on these results, we propose the following: 1) Between the Azores triple junction and Terceira island predominates strike- slip motion with nodal planes trending NNW-SSE and ENW-SSE; between the Terceira island and the beginning of the of Gloria fault the normal mechanisms predominate with nodal plans in the direction of islands. Deformation rate in both regions is 7.4 and 2.4 cm/year respectively. 2) In the continuation of the plate boundary, along the Gloria Fault until the Iberian continental margin we clearly have right-lateral motion in the E-W direction with a deformation rate of 1.8 cm/year. 3) The Eastern part of the Plate boundary, in Portugal continental, is very complex, however we identify some important patterns in the following regions: western Iberian margin (strike-slip), Lisboa and Vale do Tejo (dip-slip), ...vora and vicinity (strike-slip), region of Algarve (strike-slip) and inter-plates boundary zone (inverse). These regions are affected by compression oriented and a deformation rate of 0,55 cm/year

The 2007 Azores earthquakes: A case of triggering?

On 5 April (Mw=6.3) and 7 April 2007 (Mw=6.1 ) two earthquakes occur at the Formigas Islets (Azores Islands), both with same epicenter and felt (I=V/VI MSK) in S. Miguel Island. The rupture process of these earthquakes has been studied from body wave inversion of broad band data at telesesimic distances. Results obtained shown normal faulting for both shocks, with planes oriented in NW–SE direction, with focus at shallow depth (10 km and 6 km respectively). The slip distribution over the fault plane (152/44/-88) shows for the 05-04-07 event, the rupture propagating downward and a duration of 12s for the source time function. For the 07-04-07 event, the slip distribution over the fault plane (125/52/-81) shows de rupture propagating downward and duration of 10s for the STF. From these results we have estimated the static Coulomb stress change. We find that the static stress change caused by the 5 April event is higher, about 2 bar at epicenter the location of the second event (April 7), triggering the second rupture. Locations of aftershocks do not agree well with areas of increased Coulomb failure stress, which can be explained by the complexities of the rupture process oy by uncertainties at the hypocerter locatio

Recent Seismic Activity in the Azores Region

This seismic activity in the Azores Region is characterized by sequences of low-magnitude events, usually with epicenter off-shore. These seismic sequences are sometimes triggered by larger events, felt by the population, that could produce significant material and human losses. This characteristic is confirmed by the historical and instrumental seismicity, in particular by the recent earthquakes occurred on 1980 (Mw=6.8), 1997 (Mw=6.2), 1998 (Mw=6.2) and 2007 (Mw=6.3, Mw=6.1). The mechanism responsible for this spatial and temporal seismic pattern still yet not very well known. In this work we discuss the recent (2007) seismic activity of the Azores region by analyzing the spatial and temporal distribution of seismic events associated with two sequences with different characteristics. The fisrt one is a seismic swarm started on April 21st 2007, centered at about 40 kilometers west of the Faial Island (maximum magnitude mb=4.0). The second one corresponds to an aftershock sequence associated to the events of 2007/04/05 (Mw=6.3) and 2007/04/07 (Mw=6.1), both with epicenter in the Formigas Islets and felt (I=V/VI in Mercali scale) in S. Miguel. We calculate the static Coulomb stress change for both events using focal mechanisms derived from the inversion of body waves. We find that the static stress change caused by the April 5 event is higher, about 2 bar at the location of the second event (April 7), triggering the second rupture. Locations of aftershocks do not agree well with areas of increased Coulomb failure stress