Estimation Of Current Density Research Articles

Bootstrap methods for long-memory processes: a review

This manuscript summarized advances in bootstrap methods for long-range dependent time series data. The stationary linear long-memory process is briefly described, which is a target process for bootstrap methodologies on time-domain and frequency-domain in this review. We illustrate time-domain bootstrap under long-range dependence, moving or non-overlapping block bootstraps, and the autoregressive-sieve bootstrap. In particular, block bootstrap methodologies need an adjustment factor for the distribution estimation of the sample mean in contrast to applications to weak dependent time processes. However, the autoregressive-sieve bootstrap does not need any other modification for application to long-memory. The frequency domain bootstrap for Whittle estimation is provided using parametric spectral density estimates because there is no current nonparametric spectral density estimation method using a kernel function for the linear long-range dependent time process.

Estimation of the exchange current density and comparative analysis of morphology of electrochemically produced lead and zinc deposits

The processes of lead and zinc electrodeposition from the very dilute electrolytes were compared by the analysis of polarization characteristics and by the scanning electron microscopic (SEM) analysis of the morphology of the deposits obtained in the galvanostatic regime of electrolysis. The exchange current densities for lead and zinc were estimated by comparison of experimentally obtained polarization curves with the simulated ones obtained for the different the exchange current density to the limiting diffusion current density ratios. Using this way for the estimation of the exchange current density, it is shown that the exchange current density for Pb was more than 1300 times higher than the one for Zn. In this way, it is confirmed that the Pb electrodeposition processes are considerably faster than the Zn electrodeposition processes. The difference in the rate of electrochemical processes was confirmed by a comparison of morphologies of lead and zinc deposits obtained at current densities which corresponded to 0.25 and 0.50 values of the limiting diffusion current densities.

Density estimation on manifolds with boundary

Density estimation is a crucial component of many machine learning methods, and manifold learning in particular, where geometry is to be constructed from data alone. A significant practical limitation of the current density estimation literature is that methods have not been developed for manifolds with boundary, except in simple cases of linear manifolds where the location of the boundary is assumed to be known. This limitation is overcome by developing a density estimation method for manifolds with boundary that does not require any prior knowledge of the location of the boundary. To construct an appropriate estimator, statistics are introduced that provably approximate the distance and direction of the boundary, which allows us to apply a cut-and-normalize boundary correction. Then, multiple cut-and-normalize estimators are used to build a consistent kernel density estimator that has uniform bias, at interior and boundary points, on manifolds with boundary.

Current kernel density estimation based transistor open‐circuit fault diagnosis in two‐level three phase rectifier

Two-level three phase rectifiers are widely used in industrial applications due to their superior performance. Their reliability has attracted lots of attention in recent decades. Transistor is one of the most fragile component because they suffer from voltage surge and thermic cycling. A fault diagnosis method based on current kernel density estimation for transistor open-circuit faults is proposed. The proposed method needs no extra sensors and it includes three steps: current kernel density estimation, Euclidean distance, fault detection and isolation. Experimental results show the proposed diagnosis method is highly efficient in single open-circuit fault and multiple open-circuit fault on the same leg.

Interactive effect of 5-HTTLPR genotype and age on sources of cortical rhythms in healthy women

This study was aimed to localize the effects of 5-HTTLPR (serotonin-transporter-linked polymorphic region) on the age differences of spontaneous EEG activity in women using neuroimaging analysis sLORETA (Standardized Low Resolution brain Electromagnetic Tomography). DNA samples extracted from cheek swabs and resting-state EEG recorded at 60 standard leads were collected from young (YW, N=86, 18–35years) and older (OW, N=45; 55–80years) healthy women. We have shown that advanced age was associated with increased posterior EEG desynchronization in S′/S′. S′ (LG allele was grouped with S alleles owing to its functional equivalence and this group was labeled as S′) genotype carriers denoted by decrease of delta – beta1 current source density, and to a lesser extent in L/L homozygotes denoted by decrease in delta activity. In heterozygotes OW, as compared with heterozygotes YW, higher source density estimates of beta1 in frontal and temporal cortex were observed. Age differences were more pronounced in the right hemisphere in S′/S′ and L/L carriers and in the left hemisphere in heterozygotes. We also found that in OW, current source density estimates of theta, alpha1, alpha2, alpha3 and beta1 sources in the right occipital lobe were higher in S′/L than in S′/S′ carriers. These results may have implications for understanding 5-HTT-dependent variation in the effect of aging on brain activity.

(Invited) Modelling and Experimental Results for the Hydrogen Oxidation/Hydrogen Evolution Reactions: New Insights into the Performance of Polymer Electrolyte Fuel Cells and Electrolyzers

An alternative approach to the rotating disk electrode (RDE) for characterising fuel cell electrocatalysts has been recently demonstrated1. The approach combines high mass transport with a flat, uniform, and homogeneous catalyst deposition process, well suited for studying intrinsic catalyst properties at realistic operating conditions of a polymer electrolyte fuel cell (PEFC). Uniform catalyst layers were produced with loadings as low as 0.16 μgPt cm-2 and thicknesses as low as 200 nm. Such ultra thin catalyst layers are considered advantageous to minimize internal resistances and mass transport limitations leading to very high performance at low platinum loadings. Modelling of the associated diffusion field suggests that such high performance is enabled by fast lateral diffusion within the electrode. The electrodes operate over a wide potential range with insignificant mass transport losses, allowing the study of the hydrogen oxidation reaction (HOR) and hydrogen evolution reaction (HER) at high overpotentials. For the HOR, geometric current densities as high as 5.7 A cm-2 Geo were experimentally achieved at a loading of 10.15 μgPt cm-2 at room temperature (561 A mgPt -1), which is three orders of magnitude higher than current densities achievable with the RDE. For the HER specific current densities greater than 5 A cm-2 Specific have been achieved. The latter corresponds to a turnover frequency of almost 20,000 hydrogen molecules per surface platinum site per second.We have taken these results and applied a new microkinetic model for hydrogen evolution/oxidation based around the classical Heyrovsky-Tafel-Volmer mechanistic steps. This new mechanistic formalism is easy to implement and provides insights into the HOR/HER. For each of the different mechanisms, an “atlas” of Hads coverage with overpotential and corresponding current density is provided, allowing an understanding of all possible responses depending on the dimensionless parameters. Analysis of these mechanisms provides the limiting reaction orders of the exchange current density for protons and bimolecular hydrogen for each of the different mechanisms, as well as the possible Tafel slopes as a function of the molecular symmetry factor, b. Only the HV mechanism is influenced by pH whereas the TV,HT, and HTV mechanisms are not. The cases where the equations simplify to limiting forms are discussed. Analysis of the exchange current density from experimental data is discussed, and it is shown that fitting the linear region around the equilibrium potential underestimates the true exchange current density for all of the mechanisms studied. Furthermore, estimates of exchange current density via back-extrapolation from large overpotentials is also shown to be highly inaccurate. Analysis of Tafel slopes is discussed along with the mechanistic information which can and cannot be determined. Finally, some interesting effects are discussed which show that the HER can be accelerated under certain conditions.

1D Current Source Density (CSD) Estimation in Inverse Theory: A Unified Framework for Higher-Order Spectral Regularization of Quadrature and Expansion-Type CSD Methods.

Estimation of current source density (CSD) from the low-frequency part of extracellular electric potential recordings is an unstable linear inverse problem. To make the estimation possible in an experimental setting where recordings are contaminated with noise, it is necessary to stabilize the inversion. Here we present a unified framework for zero- and higher-order singular-value-decomposition (SVD)-based spectral regularization of 1D (linear) CSD estimation from local field potentials. The framework is based on two general approaches commonly employed for solving inverse problems: quadrature and basis function expansion. We first show that both inverse CSD (iCSD) and kernel CSD (kCSD) fall into the category of basis function expansion methods. We then use these general categories to introduce two new estimation methods, quadrature CSD (qCSD), based on discretizing the CSD integral equation with a chosen quadrature rule, and representer CSD (rCSD), an even-determined basis function expansion method that uses the problem's data kernels (representers) as basis functions. To determine the best candidate methods to use in the analysis of experimental data, we compared the different methods on simulations under three regularization schemes (Tikhonov, tSVD, and dSVD), three regularization parameter selection methods (NCP, L-curve, and GCV), and seven different a priori spatial smoothness constraints on the CSD distribution. This resulted in a comparison of 531 estimation schemes. We evaluated the estimation schemes according to their source reconstruction accuracy by testing them using different simulated noise levels, lateral source diameters, and CSD depth profiles. We found that ranking schemes according to the average error over all tested conditions results in a reproducible ranking, where the top schemes are found to perform well in the majority of tested conditions. However, there is no single best estimation scheme that outperforms all others under all tested conditions. The unified framework we propose expands the set of available estimation methods, provides increased flexibility for 1D CSD estimation in noisy experimental conditions, and allows for a meaningful comparison between estimation schemes.

Objective extraction of concealed information by Visual Evoked Potentials (VEPs) and Standardized Low Resolution Brain Electromagnetic Tomography (sLORETA)

Objective To study the application of VEP’s to identify cortical measures differentiating between lie and true concealed information. This was tested in memorized and retrieval paradigm. Methods VEP’s were recoded from 31 electrodes among 15 subjects in response to modified “Sternberg paradigm”, which included implemented concealed information both in the three memorized items (Memory set) and the retrieval stimulus (Probe). Subjects were instructed to lie only on specific stimulus and to correctly report to the others serving as the “true stimulus” that contained control stimulus. Latency, amplitude, and source current density estimation were compared across Lie and control stimuli. Results Amplitude of P3b was significantly augmented in the lie stimulus of the “memory set” compared to the controls. Moreover, this was associated in excitation of right prefrontal cortex as reflected by sLORETA. Probe lie stimuli were associated with prolonged P3 latency and prolonged reaction time, as well as increased brain activity in right parietal lobe. Conclusions For the first time, VEP’s could extract objectively measures to differentiate between lie and true concealed information. These findings may have important application to the brain processes associating with the memory and recall of lie information. Key message Lie detector by visual ERP’s.

Nature of the Impedance at Low States of Charge for High-Capacity, Lithium and Manganese-Rich Cathode Materials

High-capacity, lithium and manganese-rich cathodes (HCMR) have aroused great interest in their application in lithium-ion batteries (LIBs) due to their high coulombic capacites and low cost. However, its commercial application has been hindered by various fundamental and practical challenges. In this paper, one of those challenges, the source of the high impedance at low states of charge (SOC) is investigated via electrochemical impedance spectroscopic (EIS) measurements of four different HCMR materials. It is found that the property of both solid state lithium diffusion and charge transfer make significant and comparable contributions to the impedance rise between 3.3 V and 3.7 V; while below 3.3 V, the charge transfer kinetics improve and offset the continuous impedance rise attributed to solid state lithium diffusion. Estimates of the exchange current densities and diffusion coefficients at various SOCs are provided. Methods aimed both at enhancing the solid state lithium diffusion process and the exchange current density should be targeted to promote the commercialization of HCMR.

Preliminary Upper Estimate of Peak Currents in Transcranial Magnetic Stimulation at Distant Locations From a TMS Coil.

Transcranial magnetic stimulation (TMS) is increasingly used as a diagnostic and therapeutic tool for numerous neuropsychiatric disorders. The use of TMS might cause whole-body exposure to undesired induced currents in patients and TMS operators. The aim of this study is to test and justify a simple analytical model known previously, which may be helpful as an upper estimate of eddy current density at a particular distant observation point for any body composition and any coil setup. We compare the analytical solution with comprehensive adaptive mesh refinement-based FEM simulations of a detailed full-body human model, two coil types, five coil positions, about 100000 observation points, and two distinct pulse rise times; thus, providing a representative number of different datasets for comparison, while also using other numerical data. Our simulations reveal that, after a certain modification, the analytical model provides an upper estimate for the eddy current density at any location within the body. In particular, it overestimates the peak eddy currents at distant locations from a TMS coil by a factor of 10 on average. The simple analytical model tested in this study may be valuable as a rapid method to safely estimate levels of TMS currents at different locations within a human body. At present, safe limits of general exposure to TMS electric and magnetic fields are an open subject, including fetal exposure for pregnant women.

Multispacecraft current estimates at swarm

AbstractDuring the first several months of the three‐spacecraft Swarm mission all three spacecraft came repeatedly into close alignment, providing an ideal opportunity for validating the proposed dual‐spacecraft method for estimating current density from the Swarm magnetic field data. Two of the Swarm spacecraft regularly fly side‐by‐side in closely similar orbits, while the third at times approaches the other two. This provides a data set which under certain assumptions of stationarity of the magnetic field can produce 2, 3, 4, 5 (or more) point measurements, which can be cross compared. We find that at low Earth orbit the use of time‐shifted positions allow stable estimates of current density to be made and can verify temporal effects as well as validating the interpretation of the current components as arising predominantly from field‐aligned currents. In the case of four‐spacecraft configurations we can resolve the full vector current and therefore can check the perpendicular as well as parallel current density components directly, together with the quality factor for the estimates directly (for the first time in situ at low Earth orbit).

Significance of Non-phase Locked Oscillatory Brain Activity in Response to Noxious Stimuli.

Although current pain-evoked electroencephalographic (EEG) studies provide valuable information regarding human brain regions involved in pain, they have mostly considered neuronal responses which oscillate in phase following a painful event. In many instances, cortical neurons respond by generating bursts of activity that are slightly out of phase from trial-to-trial. These types of activity bursts are known as induced brain responses. The significance of induced brain responses to pain is still unknown. In this study, 23 healthy subjects were given both non-painful and painful transcutaneous electrical stimulations in separate testing blocks (stimulation strength was kept constant within blocks). Subjective intensity was rated using a numerical rating scale, while cerebral activity tied to each stimulation was measured using EEG recordings. Induced brain responses were identified using a time frequency wavelet transform applied to average-removed single trials. Results showed a pain-specific burst of induced theta activity occurring between 180 and 500 ms post-shock onset. Source current density estimations located this activity within the dorsolateral prefrontal cortex (DLPFC, bilaterally), however, only right DLPFC activity predicted a decrease in subjective pain as testing progressed. This finding suggests that non-phase locked neuronal responses in the right DLPFC contribute to the endogenous attenuation of pain through time. This article presents neuroimaging findings demonstrating that, in response to pain, non-phase locked bursts of theta activity located in the right dorsolateral prefrontal cortex are associated with a progressive decrease in subjective pain intensity, which has potentially important implications regarding how humans endogenously control their experiences of pain.

Investigation of the argon arc binding to the lanthanated tungsten cathode

Pyrometric and spectroscopic investigations of lanthanated tungsten cathode in argon arc plasma discharge at atmospheric pressure are reported. The distribution of the surface cathode temperature was measured. Calculations and estimates of the emission current density are performed. Experimental data of the total current density are compared with the obtained results of estimation. The possible reasons for the discrepancy between the experimental and theoretical values of the total current were discussed.

Spatial and temporal resolutions of EEG: Is it really black and white? A scalp current density view

Among the different brain imaging techniques, electroencephalography (EEG) is classically considered as having an excellent temporal resolution, but a poor spatial one. Here, we argue that the actual temporal resolution of conventional (scalp potentials) EEG is overestimated, and that volume conduction, the main cause of the poor spatial resolution of EEG, also distorts the recovered time course of the underlying sources at scalp level, and hence degrades the actual temporal resolution of EEG. While Current Source Density (CSD) estimates, through the Surface Laplacian (SL) computation, are well known to dramatically reduce volume conduction effects and hence improve EEG spatial resolution, its positive impact on EEG temporal resolution is much less recognized. In two simulation studies, we first show how volume conduction and reference electrodes distort the scalp potential time course, and how SL transform provides a much better spatio-temporal description. We then exemplify similar effects on two empirical datasets. We show how the time courses of the scalp potentials mis-estimate the latencies of the relevant brain events and that CSD provides a much richer, and much more accurate, view of the spatio-temporal dynamics of brain activity.

The reintroduction of a flagship ungulate Capra pyrenaica: Assessing sustainability by surveying woody vegetation

Reintroductions of flagship species, including charismatic wild ungulates, are becoming increasingly frequent to protect endangered species or stimulate conservation awareness. However, indicators that go beyond the target species are still needed to ensure the ecological sustainability of past and future reintroductions. Here, we examined woody vegetation to assess the ecological sustainability 25years after the reintroduction of a wild ungulate, the Iberian ibex or Iberian wild goat (Capra pyrenaica). We used browsing intensity, foraging preferences, regeneration probability and pellet counting to estimate sustainable population densities. Currently, almost one quarter of the woody species showed unsustainable levels of browsing. Threatened woody species were more vulnerable to ungulate damage, with 50% lacking natural regeneration. Current density estimations (47indkm−2) represent the highest densities ever recorded for this wild ungulate species and should be reduced by an effective population control. Predicted probability on tree regeneration reveals that a 50% reduction in current densities would increase the probability of successful regeneration by nearly 60%. Browsing was found to be an efficient indicator to assess the ecological sustainability and integrate management practices. Additionally, certain woody species that are both widely distributed and highly-preferred by ungulates could work as key indicators of unsustainability. We highlight that surveying browsing and successful regeneration in woody plant communities are essential monitoring tools to provide an early warning of ungulate overpopulation and to assess the suitability of a particular area to hold new ungulates. Thus, we recommend surveying woody vegetation before and after ungulate reintroductions to ensure the ecological sustainability of highly valuable woody ecosystems.

Experimental investigation of the transient phase of the Lorentz force response to the time-dependent velocity at finite magnetic Reynolds number

The working principle of Lorentz force velocimetry (LFV) is based on a linear dependence between measured force and velocity. We consider a case when a violation of that linear law takes place in order to take this effect into account for LFV. The response of the Lorentz force to a time-dependent velocity of solid conducting rods is experimentally studied. Solid conductors were chosen due to the fact that at a limited length of imposed magnetic field the end effects of secondary field generation are identical both in liquid and solid conductors. Thus one can simulate clearly a distortion of the imposed magnetic field in the case of non-stationary fluid flows. The magnetic Reynolds number based on advection time was of the order of unity. It is demonstrated that magnetic field advection effects lead to a Lorentz force difference in low- and finite- cases. The induced magnetic field measurements and experimental estimation of the eddy current density are reported.

Gender differences in association between serotonin transporter gene polymorphism and resting-state EEG activity

Human brain oscillations represent important features of information processing and are highly heritable. Gender has been observed to affect association between the 5-HTTLPR (serotonin-transporter-linked polymorphic region) polymorphism and various endophenotypes. This study aimed to investigate the effects of 5-HTTLPR on the spontaneous electroencephalography (EEG) activity in healthy male and female subjects. DNA samples extracted from buccal swabs and resting EEG recorded at 60 standard leads were collected from 210 (101 men and 109 women) volunteers. Spectral EEG power estimates and cortical sources of EEG activity were investigated. It was shown that effects of 5-HTTLPR polymorphism on electrical activity of the brain vary as a function of gender. Women with the S/L genotype had greater global EEG power compared to men with the same genotype. In men, current source density was markedly different among genotype groups in only alpha 2 and alpha 3 frequency ranges: S/S allele carriers had higher current source density estimates in the left inferior parietal lobule in comparison with the L/L group. In women, genotype difference in global power asymmetry was found in the central-temporal region. Contrasting L/L and S/L genotype carriers also yielded significant effects in the right hemisphere inferior parietal lobule and the right postcentral gyrus with L/L genotype carriers showing lower current source density estimates than S/L genotype carriers in all but gamma bands. So, in women, the effects of 5-HTTLPR polymorphism were associated with modulation of the EEG activity in a wide range of EEG frequencies. The significance of the results lies in the demonstration of gene by sex interaction with resting EEG that has implications for understanding sex-related differences in affective states, emotion and cognition.

Fabrication of High Thermal Conductivity Cu/Diamond Composites By Electrodeposition

Introduction Diamond has a very high thermal conductivity (1000-2000 W m-1 K-1). Metal/diamond composites have been extensively investigated for heat dissipation applications.1,2) Typically, metal/diamond composites are formed under high temperature and pressure conditions.3) However, composites made by sintering do not yield improved thermal conductivities because of the formation of gaps between the metal matrix and diamond particles due to low wettability. In comparison, fabrication of metal/diamond composites using an electrodeposition technique can be carried out at room temperature and atmospheric pressure, and there are no issues regarding wettability. We have already reported the fabrication of nickel/diamond composites by electrodeposition and an investigation of their thermal conductivities.4) In this study, Cu/diamond composites were fabricated by electrodeposition and their thermal conductivity was evaluated. Experimental The Cu/diamond composite plating bath was prepared using a copper sulfuric bath (0.85 M CuSO4·5H2O + 0.55 M H2SO4) as the base, to which diamond particles (mean diameters of 10, 25, 45, 195 and 230 μm) were mixed. Electrodeposition was carried out under galvanostatic conditions. Pure copper plates were used for the cathode and the anode. The electrodes were arranged horizontally with the cathode set at the bottom position. First, diamond particles were precipitated on the cathode in the plating bath; electrodeposition was then carried out to fill the gaps between the diamond particles. Surface and cross-sectional morphologies of the composites were observed by field-emission scanning electron microscopy (FE-SEM). A cross-section polisher was used to prepare cross-sectional samples. The thermal conductivity was calculated as a product of the density, specific heat capacity and thermal diffusivity. The thermal diffusivity was measured by a xenon laser flash thermal property analyzer. In order to estimate the net current density during formation of the Cu/diamond composites, the Butler-Volmer equation was used. The exchange current density and the transfer coefficient were obtained from a Tafel plot.Simulation of the thermal conductivity of the Cu/diamond composites was carried out using the Hasselman-Johnson equation, for comparison with the measured values. Results and Discussion Figures 1 and 2 show cross-sectional SEM images of the Cu/diamond composite at two magnifications. No voids or cracks were observed between the Cu matrix and diamond. The thermal conductivities of the fabricated Cu/diamond composites were almost consistent with the simulation values. The largest value was 687 W m-1 K-1, using 230 μm size diamond particles with a diamond content in the composite of 61 vol%. Estimation of the net current density during the formation of the composites will be discussed at the meeting. References 1) J. Flaquer, A. Ríos, A. Martín-Meizoso, S. Nogales, H. Böhm, Computational Materials Science, 41, 156-163 (2007). 2) M-T. Lee, M-H. Fu, J-L. Wu, C-Y. Chung, S-J. Lin, Diamond & Related Materials, 20, 130-133 (2011).3) H. Feng, J. K. Yu, W. Tan, Materials Chemistry and Physics, 124, 851-855 (2010).4) S. Arai, Y. Tashiro, V. Hoang, Y. Suzuki, of the 220th ECS Meeting, #2337 (2011).

Mismatch negativity to acoustical illusion of beat: How and where the change detection takes place?

In case of binaural presentation of two tones with slightly different frequencies the structures of brainstem can no longer follow the interaural time differences (ITD) resulting in an illusionary perception of beat corresponding to frequency difference between the two prime tones. Hence, the beat-frequency does not exist in the prime tones presented to either ear. This study used binaural beats to explore the nature of acoustic deviance detection in humans by means of magnetoencephalography (MEG). Recent research suggests that the auditory change detection is a multistage process. To test this, we employed 26Hz-binaural beats in a classical oddball paradigm. However, the prime tones (250Hz and 276Hz) were switched between the ears in the case of the deviant-beat. Consequently, when the deviant is presented, the cochleae and auditory nerves receive a “new afferent”, although the standards and the deviants are heard identical (26Hz-beats). This allowed us to explore the contribution of auditory periphery to change detection process, and furthermore, to evaluate its influence on beats-related auditory steady-state responses (ASSRs). LORETA-source current density estimates of the evoked fields in a typical mismatch negativity time-window (MMN) and the subsequent difference-ASSRs were determined and compared. The results revealed an MMN generated by a complex neural network including the right parietal lobe and the left middle frontal gyrus. Furthermore, difference-ASSR was generated in the paracentral gyrus. Additionally, psychophysical measures showed no perceptual difference between the standard- and deviant-beats when isolated by noise. These results suggest that the auditory periphery has an important contribution to novelty detection already at sub-cortical level. Overall, the present findings support the notion of hierarchically organized acoustic novelty detection system.

CHARACTERISTICS OF THE PHOTOSPHERIC MAGNETIC FIELD ASSOCIATED WITH SOLAR FLARE INITIATION

The physical environment governing the solar flare initiation is not fully understood, although there are significant efforts to address the relationship between magnetic non-potential parameters and early flare signatures. In this study, we attempt to characterize the flare initiation based on the processed Helioseismic and Magnetic Imager vector magnetograms, Atmospheric Imaging Assembly 1600 A, and RHESSI hard X-ray observations. Three flare events, the M6.6 flare on 2011 February 13, the X2.2 flare on 2011 February 15, and the X2.1 flare on 2011 September 6, in two active regions AR 11158 and AR 11283 are investigated. We analyze the source field strength in the photosphere, which is defined as the magnitude of the observed magnetic field deviation from the potential field. It is found that one of the strong source field regions above the magnetic polarity inversion line well connects the initial bright kernels of two conjugate ribbons. The results imply that the distribution of the photospheric source field strength can be used to locate the initiation site of flaring loops regardless of the configuration of pre-flare magnetic fields or the evolution of active regions. Moreover, the field configuration in the strong source field regions tends to become more inclined after flares, which is consistent with the coronal implosion scenario. We also employ a fast method to derive the total current density from the photospheric vector magnetogram in the framework of force-free field. This method can provide fast estimation of photospheric current density within a reasonable accuracy without appealing for the more accurate calculation from a model extrapolation.