On lattice reduction algorithms for solving weighted integer least squares problems: comparative study

Decorrelation or reduction theory deals with identifying appropriate lattice bases that aid in accelerating integer search to find the optimal integer solution of the weighted integer least squares problem. Orthogonality defect has been widely used to measure the degree of orthogonality of the reduced lattice bases for many years. This contribution presents an upper bound for the number of integer candidates in the integer search process. This upper bound is shown to be a product of three factors: (1) the orthogonality defect, (2) the absolute value of the determinant of the inverse of the generator matrix of the lattice, and (3) the radius of the search space raised to the power of the dimension of the integer ambiguity vector. Four well-known decorrelation algorithms, namely LLL, LAMBDA, MLAMBDA, and Seysen, are compared. Many simulated data with varying condition numbers and dimensions as well as real GPS data show that the Seysen reduction algorithm reduces the condition number much better than the other algorithms. Also, the number of integer candidates, before and after the reduction process, is counted for all algorithms. Comparing the number of integer candidates, condition numbers, and orthogonality defect reveals that reducing the condition number and the orthogonality defect may not necessarily result in decreasing the number of integer candidates in the search process. Therefore, contrary to the common belief, reducing the orthogonality defect and condition number do not always result in faster integer least squares estimation. The results indicate that LAMBDA and MLAMBDA perform much better in reducing the number of integer candidates than the other two algorithms, despite having a larger orthogonality defect and condition number in some cases. Therefore, these two algorithms can speed up the integer least squares estimation problem in general and the integer ambiguity resolution problem in particular.     

Petrology of ultramafic rocks and Mg-rich carbonate minerals in southeast of Dehshir,Central Iran

The study area is located southeast of Dehshir between the Urumieh-Dokhtar Magmatic Arc and Nain-Baft Ophiolite Belt comprising the Nain, Dehshir, Shahr Babak, and Baft ophiolite complexes. The Dehshir Ophiolitic Complex which obducted in the Late Cretaceous, consists mainly of ultramafic rocks. These remnants of oceanic crust are extensively faulted and fractured. The severe faulting and brecciating of the ophiolite sequence have undergone high-grade alteration and changed it to the tectonic mélange. The Dehshir colored mélange is bounded to the west by Dehshir fault which is a right-lateral offset of the Nain-Baft suture. In this research, the petrographic studies of the area showed that the ultramafic rocks consist mainly of dunite and harzburgite intruded by diabasic dikes. Syntectonic hydrothermal fluids circulated throughout these rocks. Migration of Mg-rich fluids and hydrothermal brecciating occurred within highly altered and brecciated zones. Magnesite precipitated from hydrothermal solutions and formed the massive, lenticular, and vein-type ore deposits in serpentinized-hosted rocks. Later on, magnesite turned into hydromagnesite due to hydration at the lower depths near the surface. According to the X-ray diffraction and X-ray fluorescence analysis, hydromagnesite is the most dominant and widely occurring Mg-rich carbonate mineral in this area. The main alteration is serpentinization but birbiritization also occurs as a result of interaction between fluids and ultramafic rocks.     

Sensitivity analysis of the seismic demands of RC moment resisting frames to different aspects of ground motions

A weight vector representing the relative importance of various characteristics of ground motions (GMs) and a conditioning intensity measure (IM) are required to be able to use the generalized conditional IM framework for the purpose of GM selection. An inappropriate weight vector may result in the biased distributions of some important characteristics of GMs and, consequently, the bias in the structural responses. This article aims to provide the analyst with the understanding of which properties of GMs are important in capturing the accurate structural responses, to specifically assign a suitable weight to them and to select an appropriate conditioning IM as well. To this end, 4 reinforced concrete buildings, located at the site in which the seismic hazard is dominated by shallow crustal earthquakes, are considered. The findings reveal that the appropriate weight vectors depend on the characteristics of the employed structural systems. In addition, the role played by each IM in capturing the true structural responses changes over different earthquake intensity levels implying that different weight vectors are required over different earthquake levels. Furthermore, this study shows that, even in case of shorter‐duration GMs from shallow events, GM duration should be incorporated in GM selection as it has effects on the peak‐based structural responses in the earthquake levels beyond the level of 2%‐in‐50‐years. Specifically, the findings reveal that in case of shallow events, unlike large magnitude earthquakes, the shorter the duration of GM the more rapid release of energy and, consequently, the larger the peak‐based structural responses.     

Assessment of seasonal groundwater quality and potential saltwater intrusion: a study case in Urmia coastal aquifer (NW Iran) using the groundwater quality index (GQI) and hydrochemical facies evolution diagram (HFE-D)

Coastal aquifers are at threat of salinization in most parts of the world. This work investigated the seasonal hydrochemical evolution of coastal groundwater resources in Urmia plain, NW Iran. Two recently proposed methods have been used to comparison, recognize and understand the temporal and spatial evolution of saltwater intrusion in a coastal alluvial aquifer. The study takes into account that saltwater intrusion is a dynamic process, and that seasonal variations in the balance of the aquifer cause changes in groundwater chemistry. Pattern diagrams, which constitute the outcome of several hydrochemical processes, have traditionally been used to characterize vulnerability to sea/saltwater intrusion. However, the formats of such diagrams do not facilitate the geospatial analysis of groundwater quality, thus limiting the ability of spatio-temporal mapping and monitoring. This deficiency calls for methodologies which can translate information from some diagrams such Piper diagram into a format that can be mapped spatially. Distribution of groundwater chemistry types in Urmia plain based on modified Piper diagram using GQI_Piper(mix) and GQI_Piper(dom) indices that Mixed Ca–Mg–Cl and Ca-HCO₃ are the dominant water types in the wet and dry seasons, respectively. In this study, a groundwater quality index specific to seawater intrusion (GQI_SWI) was used to check its efficiency for the groundwater samples affected by Urmia hypersaline Lake, Iran. Analysis of the main processes, by means of the Hydrochemical Facies Evolution Diagram (HFE-Diagram), provides essential knowledge about the main hydrochemical processes. Subsequently, analysis of the spatial distribution of hydrochemical facies using heatmaps helps to identify the general state of the aquifer with respect to saltwater intrusion during different sampling periods. The HFE-D results appear to be very successful for differentiating variations through time in the salinization processes caused by saltwater intrusion into the aquifer, distinguishing the phase of saltwater intrusion from the phase of recovery, and their respective evolutions. Both GQI and HFE-D methods show that hydrochemical variations can be read in terms of the pattern of saltwater intrusion and groundwater quality status. But generally, in this case (i.e. saltwater and not seawater intrusion) the HFE-D method was presented better efficiency than GQI method (including GQI_Piper and GQI_SWI).     

Neural network prediction of solar cycle 24

The ability to predict the future behavior of solar activity has become extremely import due to its effect on the environment near the Earth.Predictions of both the amplitude and timing of the next solar cycle will assist in estimating the various consequences of space weather.The level of solar activity is usually expressed by international sunspot number (Rz).Several prediction techniques have been applied and have achieved varying degrees of success in the domain of solar activity prediction.We predict a...     

Data-snooping procedure applied to errors-in-variables models

The theory of Baarda’s data snooping — normal and F tests respectively based on the known and unknown posteriori variance — is applied to detect blunders in errors-invariables (EIV) models, in which gross errors are in the vector of observations and/or in the coefficient matrix. This work is a follow-up to an earlier work in which we presented the formulation of the weighted total least squares (WTLS) based on the standard least squares theory. This method allows one to directly apply the existing body of knowledge of the least squares theory to the errors-in-variables models. Among those applications, data snooping methods in an EIV model are of particular interest, which is the subject of discussion in the present contribution. This paper generalizes the Baarda’s data snooping procedure of the standard least squares theory to an EIV model. Two empirical examples, a linear regression model and a 2-D affine transformation, using simulated and real data are presented to show the efficacy of the presented formulation. It is highlighted that the method presented is capable of detecting outlying equations (rather than outlying observations) in a straightforward manner. Further, the WTLS method can be used to handle different TLS problems. For example, the WTLS problem for the conditions and mixed models, the WTLS problem subject to constraints and variance component estimation for an EIV model can easily be established. These issues are in progress for future publications.     

Biomonitoring of Ni and V Contamination Using Oysters (Saccostrea cucullata) at Lengeh Port,Persian Gulf,Iran

Vanadium and nickel are two important indicators of oil pollution. Lengthy exposure to these elements causes serious harmful effects in human health, different harsh allergies being examples. The accumulation of two heavy metals (Ni and V) in sediment and the soft and hard tissues of Saccostrea cucullata were analyzed at three sampling sites along the coast of Lengeh Port, Persian Gulf. Results indicated at all the sampling sites; the Ni levels in soft tissues (STs) were higher than in the shells (SHs) and sediments, whereas the V levels were higher in the sediments. In addition, meaningful relationship (r = 0.65; p < 0.05) was observed across Ni levels in ST of S. cucullata and sediment, while for V concentrations a strong relationship (r = 0.83; p < 0.01) was found in SH of S. cucullata and sediment. This indicates that ST and SH of oyster can be considered as a biomonitoring agent for Ni and V levels, in coastal waters, respectively. The exposure of the consumer is compared directly to minimal risk level and provisional maximum tolerable daily intake. Result indicated that levels of Ni and V were within the safety limits for human consumption.     

The effect of road unevenness on the dynamic vehicle response and ground-borne vibrations due to road traffic

In this paper, the relation between road unevenness, the dynamic vehicle response, and ground-borne vibrations is studied. In situ measurements of road unevenness and the dynamic vehicle response for six roads with different types of pavement are supplemented by numerical predictions of ground vibrations. The predictions are performed in two stages. In the first stage, the dynamic vehicle response is computed based on the measured road unevenness. The vehicle model is validated by comparing the predicted and measured vehicle response and subsequently used to predict the dynamic vehicle loads. In the second stage, the dynamic road–soil interaction problem is considered and the transfer functions between the road and the soil are computed. The effect of the pavement type (continuous, jointed, or composed of individual pavers) on the road–soil transfer functions is investigated and the free field vibrations are calculated using the dynamic vehicle loads computed in the first stage. The predicted free field vibrations are validated by measurements at one of the measurement sites before and after rehabilitation of a deteriorated concrete pavement. Finally, the results are used to investigate the relation between indicators of road unevenness such as the ISO 8608 road class, the International Roughness Index, and the coefficient of evenness on one hand, and the dynamic vehicle response and level of ground-borne vibration on the other hand.