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Two-dimensional gel electrophoresis (2DGE) images are an important support for the analysis of proteins in proteomics. The registration of 2DGE images is considered as one of key elements in protein identification while it is a difficult problem. This paper proposes a new accurate nonlinear registration approach for 2DGE images, based on the exploitation of both spot distance measure and spot intensity. The method consists of three steps: multi-resolution affine registration, spot pairing and thin-plate spline interpolation. The results on both simulated and real gel images show that the proposed method significantly improves registration accuracy in comparison with thin-plate spline registration techniques.

In Ref. 11 clustering representations of the position distribution of the ideal Bose gas were considered. In principle that gives rise to possibilities concerning simulations of the system of positions of the particles. But one has to take into account that in case of low temperature the clusters are very large and their origins are far from a fixed bounded volume. For that reason we will consider some estimations of the influence of these clusters on the behavior of the subsystem of particles located in a fixed bounded volume. All points in the fixed bounded volume come from a bigger volume which the estimation (5.2) in Theorem 5.2 gives on average. Several numerical simulations in dimension two are shown in Sec. 5.

This paper proposes a novel intensity measure (IM) based on the geometric mean of acceleration response spectral ordinates to assess the probabilistic performance of structures subjected to seismic loading. Instead of relying solely on the fundamental period, the proposed IM is evaluated across a fixed period range for all structural systems, which allows consideration of higher mode effects and period changes due to nonlinearity. The proposed seismic IM is evaluated using two established indices sufficiency and efficiency. Sufficiency quantifies the independence of an engineering demand parameter at a specific intensity level with ground motion characteristics such as seismic magnitude $(M)$ and distance from site to fault plane $(R)$. It is calculated by linear regression analysis, or using gradient-based relative sufficiency measures. On the other hand, efficiency is measured as dispersion across ground motions at a given intensity level for any physical response quantity. It helps to reduce computational demand for failure probability assessment by considering a smaller number of records compared to an inefficient IM for similar confidence levels. The effectiveness of the proposed IM along with 10 other IMs is demonstrated on single degree of freedom systems with various fundamental periods by performing nonlinear time history analysis using a far-field ground motion record set. The study is also extended to five degree of freedom lumped mass stick models, 2D models (4-, 8-, and 12-story archetype steel frames), and 3D reinforced concrete shear wall building model. The results indicate that the proposed IM limits dispersion to within 10% for long-time period structures, and demonstrates improved sufficiency across different structural systems. For example, gradient of the proposed IM with respect to magnitude $M$ and site-to-source distance $R$ for a 12-story steel frame is reduced by 42.9% and 94%, respectively, compared to spectral acceleration at fundamental time period. Potential application of this research lies in efficiently conducting seismic reliability assessment and design for structural systems.

Intensity measure (IM) which describes the strength of an earthquake record plays an important role in the seismic performance assessment of structures. An improved IM that can reduce the variability in seismic demands helps reducing the number of records necessary to predict the seismic performance with sufficient accuracy. In this study, an improved RMS-based IM is developed based on the results obtained from incremental dynamic analyses of short-to relatively long-period frames under an ensemble of near-fault pulse-like earthquake records. It is observed that the root-mean-square value of pseudo spectral accelerations, (S_a)_rms, is generally superior to that of spectral velocities, (S_v)_rms, in seismic demand prediction under near-fault records. To compute (S_a)_rms as IM, two appropriate period ranges are suggested for short- and moderated-to relatively long-period frames, respectively. Comparing the efficiency of (S_a)_rms with several advanced IMs shows that (S_a)_rms is more efficient in predicting the inelastic response and collapse capacity of short-period frames. It is also found that intensity measure (S_a)_rms is sufficient with respect to the magnitude and source-to-site distance for all frames of various heights under near-fault ground motions.

Aftershock records have a considerable effect on the results of collapse assessments conducted on buildings. Thus, they should be selected cautiously. As the number of recorded aftershocks is not sufficient, mainshock records are often utilized instead. In order to increase the correlation between the aftershock time history and the seismic response of a structure, this research intends to investigate several Intensity Measures (IMs). For this study, three RC frames were considered. Forty-four far-field records from FEMAP-695 were selected as main and aftershock. Each building analysis was conducted under 44 mainshock–aftershock chains. According to the results, use of the summation of the first mode spectral acceleration value of aftershocks as the second part of a vector IM can lead to the sufficiency of the IM.