ECoG gamma activity during a language task-differentiating expressive and receptive speech areas
ECoG gamma activity during a language task: differentiating expressive and receptive speech areas
V ernon L.T owle,1,2,3,4Hyun-AhY oon,1Michael Castelle,1J.Christopher Edgar,5,6Nadia M.Biassou,7 David M.Frim,2Jean-Paul Spire1,2and Michael H.Kohrman3
1Department of Neurology,2Department of Surgery,3Department of Pediatrics,4Department of Psychiatry,The University of Chicago,Chicago,IL60637,5Department of Radiology,The Children’s Hospital of Philadelphia,Philadelphia,PA,6Center for Functional Brain Imaging,New Mexico V A Healthcare System,Albuquerque,NM and7Division of Neuroradiology, Department of Imaging Sciences,National Institutes of Health,Bethesda,MD20892,USA
Correspondence to:V ernon L.T owle,PhD,Professor of Neurology,Surgery,Pediatrics and Psychiatry,
Department of Neurology,MC-2030,The University of Chicago,5841S.Maryland Avenue,Chicago,IL60637,USA
E-mail:towle@https://www.wendangku.net/doc/b216034429.html,
Electrocorticographic(ECoG)spectral patterns obtained during language tasks from12epilepsy patients(age: 12^44years)were analysed in order to identify and characterize cortical language areas.ECoG from63subdural electrodes(500Hz/channel)chronically implanted over frontal,parietal and temporal lobes were examined. T wo language tasks were performed.During the first language task,patients listened to a series of50words preceded by warning tones,and were asked to repeat each word.During a second memory task,subjects heard the50words from the first task randomly mixed with50new words and were asked to repeat the word only if it was a new word.Increases in ECoG gamma power(70^100Hz)were observed in response to hearing tones(primary auditory cortex),hearing words(posterior temporal and parietal cortex)and repeating words (lateral frontal and anterior parietal cortex).These findings were compared to direct electrical stimulation and separate analysis of ECoG gamma changes during spontaneous inter-personal conversations.The results indi-cate that high-frequency ECoG reliably differentiates cortical areas associated with receptive and expressive speech processes for individual https://www.wendangku.net/doc/b216034429.html,pared to listening to words,greater frontal lobe and decreased temporal lobe gamma activity was observed while speaking.The data support the concept of distributed func-tionally specific language modules interacting to serve receptive and expressive speech,with frontal lobe‘cor-ollary discharges’suppressing low-level receptive cortical language areas in the temporal lobe during speaking. Keywords:language mapping;cortical mapping;direct cortical stimulation;functional mapping;epilepsy surgery;electro-corticography;ECoG power
Received March27,2008.Revised May14,2008.Accepted June13,2008.Advance Access publication July11,2008
Introduction
Changes in the spectral composition of the electroencepha-logram(EEG)as a function of cognition were noted in the initial description of EEG(Berger,1929),with its potential for use for functional mapping of cortex suggested a short time later(Kornmu¨ller,1932).Studies during the interim years examined EEG correlates of cognition and laid the groundwork for utilizing spectral measures during language tasks to map cortical areas associated with speech and other cognitive functions in clinical settings(Chatrian et al.,1959; Ojemann et al.,1989a).Interest in higher frequency oscil-latory activity originated with Freeman’s observation that olfactory events were associated with localized gamma activity ($40Hz)in the rabbit olfactory bulb(Freeman,1975).Task-related gamma band dynamics have been studied at the level of single-unit activity(Gray and McCormick,1996), the ECoG(Murthy and Fetz,1992;Edwards et al.,2005; Miller et al.,2007)and scalp recordings(Pfurtscheller and Aranibar,1977).The degree to which high-frequency activity is associated with language processes has been increasingly studied(Crone et al.,1998;Aoki et al.,1999; Crone et al.,2001a,b;Xiang et al.,2001;Trautner et al., 2006;Crone et al.,2006).
Although non-invasive functional imaging has seen dramatic advances,direct electrical stimulation of cortex during language tasks remains the‘gold standard’for determining the location of eloquent cortex in surgical settings(Penfield and Boldrey,1937;Penfield and Roberts, 1959;Ojemann et al.,1989b;Lesser et al.,1994).Although haemodynamic techniques have been used to locate
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cortical and subcortical language areas (Peterson et al .,1988;Mummery et al .,1999;Belin et al .,2000;Binder et al .,2000),several problems have precluded its utilization in the surgical suite:the lack of clear indexes of reliability and validity,difficulty testing children,discordance with other neurophysiological findings,and issues regarding accurate registration of the functional findings to the operative setting (Bookheimer et al .,1997;Sinai et al .,2005;Powell and Duncan,2006).However,direct electrical stimulation of cortex has limitations as well:proper application is time-consuming,it is difficult to perform on children,direct stimulation may cause seizures and mapping areas related to higher cognitive function,such as receptive speech and the various forms of memory,is difficult (Boatman et al .,1995).We report here the analysis of spectral changes in electrocorticographic (ECoG)patterns from adult and paediatric epileptic patients performing a simple language task.ECoG findings reveal that perisylvian frontal,parietal and temporal cortical areas differentially and dynamic-ally express localized high-frequency gamma activity (70–100Hz)while hearing,recognizing and speaking words.The present findings suggest that ECoG gamma measures may be helpful in identifying eloquent language areas.
Methods
Subjects
Twelve epilepsy patients were studied during invasive work-up for medically intractable seizures.Patient demographics,diagnoses,grid placement and outcome are listed in Table 1.One 10-year-old child was excluded because she could not perform the task.Patients were tested during stable interictal periods,after seizures had been recorded and characterized using ECoG video monitor-ing from 52to 157subdural electrodes chronically implanted over frontal,parietal and temporal lobes (10or 7.5mm spacing).Electrode arrays were placed according to the clinical needs of the patient.A gap between the frontal and parietal arrays occasionally precluded coverage of the motor-mouth region.Two patients received bilateral implants.The location of the arrays relative to
cortical gyral anatomy was photographed both at implant and explant.None of the patients experienced a post-operative language deficit.Written consent was obtained from each patient or their parent,according to the direction of the institutional review board at the University of Chicago.
Direct cortical stimulation
Eloquent cortex was identified using direct electrical stimulation at the bedside after an adequate number of seizures had been recorded.Trains of pulses lasting 2–10s (biphasic pulses,0.3ms duration,50Hz,2–10mA)were systematically applied to pairs of electrodes in an attempt to elicit positive or negative functional signs or symptoms,without afterdischarges.Depending on the cortical location,behavioural or language tasks were employed to
identify motor,sensory or language-related cortical areas (Lu
¨ders et al .,1988;Ojemann et al .,1989b ).
Evoked potentials
Somatosensory evoked potentials (N/P20)were recorded from 64channels (1Hz–1kHz bandpass)in response to contralateral median nerve stimulation (0.2ms duration pulses at motor threshold, 5.7Hz)to confirm the location of the primary somatosensory hand area within the central sulcus (Wood et al .,1988).Similarly,auditory evoked potentials (N/P100)(1–100Hz bandpass)elicited by 800Hz tones (250ms duration)were used to locate primary auditory cortex within the Sylvian fissure (Celesia,1976;Lee et al .,1984).
Language tasks
Two language tasks were performed during a 30min recording session.For the first language task,patients listened to a series of 50words preceded by warning tones,and were simply asked to repeat each word aloud.During the second language task,subjects heard the 50words from the first task randomly mixed with 50new words.They were asked to repeat only the new words.The warning tones (800Hz)were followed 2s later by presentation of one-or two-syllable common words that would be familiar to children (e.g.‘rain’,‘sweater’,‘tighten’)spoken by a male voice presented through open-field speakers adjusted to a comfortable hearing level.They were common nouns,verbs or adjectives that
T able 1Patient demographics,diagnoses,electrode locations and surgical outcomes
Patient Age Gender Onset Freq Grids Seizures Dx Path Rx
Outcome 112F Infancy 3/day Lf,Lt,Lp t-C w/G TS Dysplasia L f,L p,topect,VNS Class III 213F 2month 4/day Rf,Rt,Rp CP
Stroke Necrosis R TLE,R Occ topect Class I 314F 20month 3/month Lf,Lp,Lt CP w/G L TLE NF 1
L SAH Class I 414F 6years 3/week Lf,Lp,Lt CP w/G L TLE Hip scleros L TL
Class I 515M 10years 3/week Lf,Lp,Lt CP
L FTLE Infarct L f topect Class IV 616M 6years 1/week Bf,Lt,Bt CP w/G L TLE Dysplasia None Class IV 718M 14years 2/year Lf,Lp,Lt CP w/G L TLE Gliosis L t topect
Class I 820F 11years 2/day Lf,Lp,Lt CP w/G L FLE Heterotop L f,L p topect,VNS Class III 921M 1years 10/month Lf,Lp,Lt CP w/G L FLE None
VNS Class III 1022F 8years 2/month Bf,Rp,Bt CP
R TLE Hip Scleros R SAH Class I 1130F 9years 4/year Lf,Lt t-C w/G L TLE Atrophy L SAH Class I 12
43
F
8years
4/day
Lf,Lp,Lt
CP
L FTLE
None
L SAH
Class II
L =left;R =right;B =bilateral;f =frontal;p =parietal;t =temporal;CP =complex partial seizures;G =generalization;TLE =temporal lobe epilepsy;NF =neurofibromatosis;TS =tuberous sclerosis;SAH =selective amigdalohippocampectomy;topect =topectomy;TL =temporal lobectomy;VNS =vagal nerve stimulator .
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were easy to pronounce.The Kucera–Francis word frequency count per 100000words for the word lists was 72(145SD)and the number of phonemes per word was 3.7(0.9SD).A practice trial of different words was rehearsed to familiarize the patient with the task.Each trial lasted 7s,including 5s to repeat the word.The trials were presented in the same voice and timing in both tasks.The computer stimuli and patient’s voice were recorded with a microphone and processed along with the ECoG recordings.Stimuli were presented using the GENTASK function of the Compumedics STIM 2system (Compumedics,Inc.,El Paso,TX).
ECoG recordings
ECoG was recorded from 52to 63subdural electrodes (500Hz/channel,1–100Hz bandpass,12dB/octave roll-off)located over the traditional expressive and receptive peri-Sylvian language areas of the lateral convexity of the frontal and parietal lobes,and temporal lobe language areas.A 64th channel recorded the acoustic impression of the tone and word stimuli and the patient’s voice.This channel usually prevented recording the ECoG from the proximal end of one of the 1?8strips.All ECoG channels were recorded referenced to P z (F pz ground),and then digitally converted to a grand mean reference.TTL triggers marked tone onset (t),word onset (w)and voice-onset time (vot),the last of which was placed manually by visual review of the microphone channel using the EDIT function of SYNAMPS (Compumedics,Inc.,El Paso,TX).
Calculations of power
ECoG recordings were analysed by computing averaged power spectra for each of the 63channels,after parsing the files into 512-point non-overlapping epochs.The frequency specificity of the event-related changes in ECoG power was assessed by subtracting the power during the 1s epoch immediately preceding the trigger from the epoch immediately after the trigger.Visual inspection of these normally distributed samples revealed no effect at lower frequency bands.Power spectra were obtained at the midpoint of conventional EEG frequency bands [1.95(delta),5.86(theta),9.77(alpha),20.51(beta),40.04(low gamma)and 84.96Hz (high gamma)].Changes in high gamma band power were computed for all 63channels using averaged event-related band-pass filtering (85Hz centre frequency,15Hz roll-off,100-point smoothing,non-phase locked),computed across an 8s interval (Thatcher et al .,1994;Andrew and Pfurtscheller,1996).
Gamma activation during normal conversations
Over 100h of video recordings of five patients were examined to identify times patients were conversing with family or staff.ECoG power spectra were calculated (0–200Hz)while patients were engaged in conversation.Gamma power during non-talking periods was subtracted from talking periods to isolate the effect of conversing.These epochs were 1–2min in duration.No reference was made to whether the patient was speaking or listening during the conversation.
Image visualization and co-registration
Radiological findings for the 12patients are summarized in Table 2.Precise location of the implanted electrodes was determined from post-operative CT scans using pbrain,an open source application developed in our laboratory (http://neuroima https://www.wendangku.net/doc/b216034429.html,/)(Hunter et al .,2005).Cortex segmentation was
achieved with the open-source ITK-SNAP segmenting software (https://www.wendangku.net/doc/b216034429.html,/)(Yushkevich et al .,2006).Co-registra-tion of MRI and CT coordinate data were performed by selecting between 5and 12fiducial points common to the respective scans and solving for a transformation matrix using a local software implementation of the generalized solution to the least-squares ‘Procrustes’problem (Schonemann and Carroll,1970).Fiducial points included the tip of the nose,nasion,the centre of the globes,the pre-auricular fossae,the tympanic membranes,the centre of the foramen magnum,the optic chiasm,the cella and the inion.Co-registration allowed simultaneous visualization of the cortex,subdural electrodes and neurophysiologic recordings (Fig.1).The final location of the ECoG electrodes on the cortex was verified by comparing their location with photographs taken during surgery.To visualize the spatial distribution of each patient’s electrodes with respect to a single cortex,each subject’s data were co-registered to a single subject’s CT scan.
Statistical analyses
Mean power in each band was determined to be greater than zero using single-sample t -tests (all P 50.05)(SPSS V.14.0,SPSS,Chicago,IL).Comparison of talking and non-talking event-related gamma power was evaluated using conventional two-sample t -tests.The accuracy of the patient’s verbal response during the memory task was assessed using ROC curves and signal detection analyses (Swets,1979).
Results
V oice-onset-time
The latency of the patient’s verbal response (voice-onset time)was determined by visual inspection of the micro-phone channel and calculated relative to the onset of the word stimuli.Typical reaction-time distributions were
T able 2Radiological findings for the 12patients
Patient Hand MRI
Wada PET
1R T uberous scler .No No
2R R POT cyst No Reduced R PTO
3R MTS (L 4R)B language (L 4R)Reduced B T (L 4R)
4R Normal No Reduced B T (L 4R),LP 5
R L T incr .signal L language,L memory Reduced L T 6R Normal L language,R memory Reduced L T 7L L F cyst R language,B memory Reduced L FTP 8R L F schizenceph.No Normal
9R Normal
No
Reduced B T 10R R T incr .signal L language,B memory Normal 11R Normal L language,B memory No 12
R
Normal
No
No
L =left;R =right;B =bilateral;F =frontal;O =occipital;P =parietal;T =temporal;MTS =mesial temporal sclerosis.ECoG gamma activity during a language task
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obtained (Fig.2).The mean delay increased by 0.44s for the memory task compared to the repetition task (1.29?0.35s versus 1.74?0.60s).During the repetition task,patients repeated almost all words correctly.For the memory task,in addition to having a delayed response,subject’s mean correct response rate decreased from 99%for the simple repetition task,to 69%(57–88%).
Subjects were able to correctly discriminate new words from old words with an average sensitivity of 0.78and specificity of 0.56,with the accuracy of responses ranging from d 0=1.5to d 0=0.26.Response bias for the memory task ranged widely from b =0.01to b =5.9.Variations in the patient’s performance were not related to the patient’s age or clinical assessment of their memory abilities.
Sensory evoked potentials
The first step in obtaining functional maps of the patient’s cortex was to establish the location of primary sensory and motor areas.The primary sensory hand area was identified by recording the average evoked response to contralateral median nerve stimulation.In all subjects,a high-amplitude N/P20component was observed over the lateral convexity of the central region.The inversion identified the
Rolandic
Fig.1The identification and registration of electrodes and fiducial points on CT and MRI scans.(A )Electrodes as identified in CT image of head.Up to 12fiducial points were identified and marked with a cursor:tip of nose (No),nasion (Nz),optic chiasm (OC),cella (Ce),pre-auricular fossae (P AF),centre of foramen magnum (FM),inion (In).(B )The same locations displayed in a 3D rendered image of the skull as imaged by CT .(C )The electrodes and fiducial points brought into registration with the 3D rendered brain from MRI using a Procrustes
algorithm.
Fig.2The distribution of voice-onset-time latency (vot)for all 12patients for the simple repetition task (top)and the recognition memory task (bottom).V oice-onset-time was delayed and skewed to the right for the memory task.Time is calculated from the onset of the computer-presented word.
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Fissure.Localization of primary somatosensory cortex was confirmed via direct electrical stimulation to elicit paraes-thesias or involuntary movements of the hand and face.Similarly,auditory cortex was located by analysis of the distribution of the early cortical auditory evoked potentials elicited by tones.For all patients with electrodes over the parietal–temporal junction,the inversion of polarity of the primary cortical response (N/P100)was located in the region of the posterior Sylvian fissure,consistent with the putative location of primary auditory cortex.The auditory 100ms component peaked at a mean of 90(?16)ms,with latencies not significantly different for tones or words.Location of the electrodes with the earliest auditory evoked response is shown in Fig.3.Early auditory evoked potentials with separate cortical distributions were also recorded over frontal (8/10patients)and parietal cortex (6/12patients).
ECoG power
Compared to baseline,power spectra from electrodes placed near the primary auditory cortex,computed 1s after the triggers,were significantly enhanced in the high gamma band (70–100Hz)for all 12patients.Increases in ECoG gamma (power ratios greater than 1)were observed in response to hearing tones (primary auditory cortex)(t =2.7,df =11,P 50.05),hearing words (usually posterior temporal cortex)(t =1.2,df =11,P 50.001)and repeating words (usually lateral frontal cortex)(t =1.2,df =11,P 50.001).Similar pre-to post-stimulus changes were not reliably observed in the lower frequency bands (Fig.4).
Gamma activity
As only gamma band changes were reliably observed,subsequent analyses were restricted to high gamma activity (70–100Hz).Gamma activity was examined using the average event-related band power function of the Neuroscan EDIT module.Non-phase-locked gamma activ-ity emitted during the event was calculated.The few channels that contained inter-ictal spiking,which contrib-uted unpredictable artefacts into high-frequency bands,were removed.Event-related activation was clearly observed in approximately one-fifth of the electrodes (145/721).A comparison of the first 25trials to the second 25trials showed the distribution of gamma activity to be highly reliable (Fig.5).For 8/12patients with electrodes placed over the Sylvian fissure,21/721electrodes (3%)revealed activation to all three event types (Fig.6,top functions).The majority of the 145responding electrodes,however,showed selective activation.No electrodes sites
were
Fig.4Ratios (post-stim/pre-stim)indicating changes in ECoG power in all six frequency bands caused by (A )hearing tones,(B )hearing words and (C )repeating words.The greatest enhancement was observed at 85Hz for hearing and repeating
words.
Fig.3The location of the inversion of the initial component of the left hemisphere auditory evoked potential to tone stimulation for eight patients determined the location of primary auditory cortex (small black dots),compared to the location of tone-induced gamma activity (large white spheres).Pipes link data from individual patients.Small white dots indicate the location of each subject ’s fiducial points after registration with the fiducial points within the MRI from Patient 5.
ECoG gamma activity during a language task Brain (2008),131,2013^20272017
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observed that responded only to tones.Increased gamma activity was observed over the posterior superior temporal gyrus for all 12patients.Gamma responses to the tones were located immediately posterior to the early auditory evoked potential for 8/12patients.Gamma responses were also activated by hearing words.Interestingly,39/721(5%)of electrodes with a widespread temporal lobe distribution exhibited gamma activation while hearing and speaking the words.These superior temporal gyrus areas were the same areas in which the early tone auditory evoked potentials were recorded for 8/12patients.For two patients,hearing words caused increased gamma activity in the premotor hand area.Forty-three of the 721electrodes (6%)were activated only when the patients (11/12)repeated words (Fig.6,bottom functions).These changes were located over frontal or parietal cortex,as well as the temporal lobe.In contrast,42of the electrodes located over the temporal lobe showed no activity while words were spoken by the patient,even though these sites showed increased activity after computer presentation of the words,apparently being suppressed during speaking (Fig.6,middle functions).Seven patients showed a brief reduction in gamma activity over the most anterior dorsal lateral frontal cortex immediately before the word was presented,which was usually associated with an increase in power in the lower frequency bands,suggestive of transient ECoG slowing.Examples of the anterior shift in
the distribution of gamma activity when the patients heard the word compared to when they spoke the word for three patients is shown in https://www.wendangku.net/doc/b216034429.html,rmal analyses regarding whether differences in gamma activation were related to the patient’s age,or memory performance,or whether a specific word was remembered correctly in Task 2or 1(Dm )were inconclusive.
Grouped data
Electrodes exhibiting task-specific gamma activations for all 12subjects were registered and superimposed onto Patient 5’s brain (Fig.8).The accuracy with which the location
of
Fig.6Changes in ECoG power in the high gamma band (70^100Hz)for each event.Within each box,each tracing represents a different subject.(A )ECoG channels close to the primary auditory cortex showed increased gamma activity for all events.(B )ECoG channels located over primary auditory areas of the temporal lobe responded to all external events except the subject ’s own voice.(C )Frontal/parietal ECoG channels showed increased gamma activity only when the subjects said the
words.
Fig.5Gamma activations for eight selected channels for Patients 6and 9showing differential activation to hearing the tone,hearing the word and speaking the word.T wo replications of 25averaged trials are superimposed and normalized to reveal the reliability of the activations duringT ask 1.The location of the functions is
indicated by a^h below .Similar reproducibility was observed for T ask 2.
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the electrodes identified in CT scans could be registered with the subject’s MRI scans depends on the consistency with which the same fiducial points could be identified in the MRI and CT images.The discrepancy between the two scans is detailed in Table 3,including within-subject and between-subject registration accuracy.Because some fiducial points were difficult to identify in both scans,the two most discrepant fiducial points were omitted.Fiducial points behind the optic chiasm were always included to ensure that the points were widely spread throughout the field-of-view.This process yielded a registration accuracy of about 3mm.Within-patient registration was further improved by comparing registered electrodes with photo-graphs taken during surgery.
Electrodes that exhibited gamma activation in response to tones were located over the superior temporal cortex,immediately below or posterior to the motor strip,and over posterior regions of the temporal lobe (the more posterior tone-related activations were also distributed more infer-iorly).A greater number of electrodes exhibited gamma activation in response to words.These electrodes had a distribution similar to those responding to tones,but gamma activity was additionally observed over primary motor hand and face areas.Gamma activation while
speaking the word was observed over sensory and motor face areas,as well as anteriorally over Broca’s area.Recordings of 92electrodes located over the right hemi-sphere of two subjects revealed similar findings.
Gamma suppression
A quantification of the above categorizations for separating the activation functions into three categories is illustrated in Fig.9.High gamma band power was measured while subjects listened to the word and while repeating the word.A comparison of the ratios of these measurements (power while repeating the word/power while hearing the word)is shown for each of the categorizations (a square-root transformation was utilized to create homogeneity of variance).A one-way analysis of variance with post hoc comparisons revealed that all three categorizations were significantly different from each other (F =166,df =2,128,P 50.001).The finding that the power ratio of the ‘hearing only-others’category was significantly lower than the ‘hearing everything’category supports the idea that the processing of one’s own voice is suppressed.
A comparison of peak gamma power emitted while hearing each voice for the 87recordings
containing
Fig.7Distribution of gamma activity for Patients 3,5and 8during the presentation of the words (left)and while the patient repeated the word (right).Greatest activation to hearing the words was over the posterior superior temporal gyrus.Activation over the frontal lobe was observed when the patient repeated the words.White dots =fiducial points.
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Fig.8Findings from all patients are superimposed on the brain from Patient 5.(A )The locations of all of the electrodes visible over the left hemisphere (black dots)after registering them based on their fiducial points (white circles).(B )Widespread gamma activity was observed during the presentation of words (green).(C )When the patients repeated the words,activation was primarily observed over frontal and parietal cortex (red).(D )Electrodes that responded to hearing the words when presented by the computer ,but not when the patient repeated the word (yellow).
T able 3Breakdown of the CT /MRI fiducial point registration discrepancy (mm)
Within-subject Between-subjects mean
(max)mean (max)All possible fiducial points
4.2
(7.5)
5.9
(10.7)
Individual fiducial points Nose tip 2.8
(2.8) 3.3
(3.9)Nasion 3.7(7.6) 4.7(7.0)Globes
3.0(5.9)7.0(12.2)
Optic chiasm 2.5(4.4) 3.4(4.4)
Cella 3.8(6.1) 4.8(9.2)T ympanic
membranes Pre-auricular fossae 4.3(6.0)7.0(11.2)Foramen magnum 6.4(8.3)8.1(12.1)Inion
5.4(9.3)8.2(10.8)Subset of best fiducial points
3.1
(5.0)
3.2
(4.8)
Fig.9Three primary patterns of activation were observed:Increasedgamma activityonly when thepatientheard theword presentedby the computer (superior temporal cortex),increased gamma activity to both the heard and spoken word (posterior
temporal/parietal cortex),andincreasedgamma activityonly during speaking theword (frontal/parietal cortex).These categories were confirmedby calculating a ratio of maximum power during speaking/power during hearing the wordpresentedby the computer .
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responses to these events revealed that the mean amplitude ratio of the activation to one’s own voice compared to that of others was 0.63,indicating a 37%attenuation of high gamma activity when hearing one’s own voice (t =9.2,df =86,P 50.001).The suppressed receptive areas were distributed more anterior than unsuppressed temporal lobe language areas (Fig.8).
Gamma onset/offset
Although gamma activation was observed within a few milliseconds of the onset of the tone and word,on average,gamma activity lasted 211ms longer than the tone stimulus,and 394ms longer than words.Over the temporal lobe,gamma activity associated with speaking the word was similar,beginning near voice-onset-time and ending 537ms after the word.However,over the frontal lobe,a different pattern was observed.Frontal gamma activity started 805ms before voice-onset time,but like the tone,only extended 203ms beyond the end of the spoken word (Fig.10).If our own voice was unusually loud,one would expect that the temporal lobe gamma activity associated with hearing one’s own voice to last longer than the acoustic event itself (Table 4).This was not the case.This suggests that gamma activity in response to one’s voice is attenuated to be perceptually comparable to external auditory events.Frontal gamma activity not only preceded the spoken word,it covaried with it in a linear fashion.The temporal relationship between voice-onset time (VOT)and gamma activity associated with speech production is illustrated in Fig.11.Trials were divided into quartiles and averaged in order to make the measurements.The peak of the gamma activity covaried with VOT for each subject (r 2=0.56).
Clinical confirmation
Independent confirmation of these electrophysiologic find-ings was obtained.First,the gamma activations were compared to the results of direct electrical stimulation of cortex and the evoked potential maps.Of the sixty-four positive and negative signs and symptoms elicited by direct electrical stimulation and routing mapping studies,forty-four of them were associated with increased gamma activity,yielding a sensitivity of 63%.Specificity was 57%.A common type of confirmation was that an increase in gamma power during speaking the word was observed for electrodes in which electrical stimulation caused a disrup-tion of speech (5/12patients),often accompanied by motor signs or paraesthesias in the mouth.However,unambig-uous increases in gamma activity were observed from
145Fig.11Scatterplot of the temporal relationship between gamma activity and voice-onset time over the frontal lobe during the memory task for each patient.On trials with delayed voice-onset times the onset of the gamma activity was also delayed,relative to those trials with early voice-onset times.Activity was grouped into VOT quartiles (N =25)in order to reliably measure the gamma
parameters.
Fig.10A schematic diagram of the mean onset and offset times of gamma activity relative to the task events.During the presenta-tion of the tones and words,the onset of gamma activation was close to the onset of the stimulus,but lasted longer than the auditory event.When the patient repeated the word,the onset of gamma activation from electrodes over the temporal lob was similar to hearing the tone and word.Over the frontal lobe the onset of gamma activation associated with repeating the words started before voice-onset time,suggesting preparation to speak.
T able 4The duration of high-frequency ECoG activation relative to the acoustical event (ms)
Acoustic event Gamma activity T otal
gamma
duration
Onset Offset Onset Offset External tone 025*********External word 0450********Spoken word (T emporal lobe)0450à1389361074Spoken word (Frontal lobe)
0450
à805
653
1451
ECoG gamma activity during a language task
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electrodes,many of which did not respond to electrical stimulation.The most frequent confirmation was that the early averaged auditory evoked potential was recorded from electrodes that exhibited increased gamma in response to hearing the tone (10/12patients).For one patient,a left anterior temporal area was resected under 1/11electrodes that exhibited a small increase in gamma activity in response to hearing the word.None of our patients had any documented post-operative language deficits.Overall,the discriminability of the gamma activations in terms of predicting the clinical maps was modest (d 0=0.63),with a bias toward false alarms (C =–0.15).Our impression is that these numbers are deflated because of the limitations of our direct electrical stimulation protocol,in which bipolar stimulation is administered through adjacent pairs of electrodes,sometimes leaving uncertainty about which electrode was causing the symptoms.Also,the clinical language mapping tasks were not identical to the experi-mental task.
Gamma power during conversations
Similar language-related gamma changes in ECoG power spectra were observed when patients engaged in sponta-neous conversation.Increased power in the high gamma band was maximal over the perisylvian frontal lobe and the posterior superior temporal gyrus,reminiscent of activation observed during the formal language tasks (depicted for Patient 5in Fig.12,and compare with Patient 5,Fig.7).This was true for two of the five patients studied.
Discussion
Mapping ECoG activation in the high gamma band between 70and 100Hz reliably identified cortical areas associated with receptive and expressive speech processes in individual patients.Activation associated with hearing tones was primarily restricted to the posterior superior temporal gyrus,indicating activation of the primary auditory cortex as well as more posterior auditory areas.Activation associated with hearing words was more widespread,and included posterior superior temporal gyrus and lateral parietal regions,suggestive of activation in Wernicke’s and surrounding areas (Wernicke,1874).This activation included and extended beyond areas showing the primary auditory evoked response,and these areas and direct electrical stimulation of these areas usually produced no positive or negative language signs (Hashimoto et al .,2000).Whereas hearing words did not activate Broca’s area,activation associated with repeating words was located in the perisylvian frontal and parietal cortex,consistent with activation of the sensory/motor mouth area and Broca’s language area (Broca,1865).Analysis of recordings obtained during spontaneous interpersonal conversations confirmed many of these findings,and revealed additional widespread areas of activation over motor cortex and over the anterior frontal lobe.The widespread activation likely reflects the fact that self-directed conversations involve more executive processes than the simple language tasks employed in the word-repetition task.
Present results confirm findings reported by Crone et al .(2001a ,b )and others reporting increases in gamma band activity during language tasks.The gamma increases are broad-band,with activity observed between 40Hz and our highest recorded frequency (100Hz).Others,digitizing at rates higher than us,have reported activation reaching above 200Hz (Hart et al .,1998).As increased gamma
band
Fig.12The distribution of increased high gamma activity during inter-personal conversations.Increased gamma activity was
observed over the perisylvian frontal lobe and posterior superior temporal gyrus during periods when Patient 5was involved in interpersonal
conversations.
Fig.13The proportion of electrodes that exhibited each of the seven possible different patterns of activation (S =speaking,
H =hearing,T =tone).Gamma activity was suppressed for 10%of the electrodes during speaking.
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power was reliably observed for all 12patients,this technique may have value in assessing and planning resections for individual patients.These increases in power at high frequencies were also associated with reductions in power in lower frequency bands (Towle et al .,1995;Miller et al .,2007).The overall pattern of activation is consistent with the concept that language functions are mediated by a distributed network of modules that contribute to different aspects of expressive and receptive speech,located in the perisylvian frontal,parietal and temporal lobes (Goldman-Rakic,1988;Mesulam,1990;Bressler,1995).When viewed over time in individual patients,the pattern of activity was often spatially non-contiguous,reminiscent of the mosaic pattern described by Ojemann et al .(1989b ).Areas of activation much larger than a square centimeter were also observed.Consistent with Berger’s original observations,Miller et al .(2007)report that increases in gamma activity are associated with reductions in power at lower frequencies.We have previously reported a suppression of frontal lobe alpha activity related to performing difficult language tasks (Towle et al .,1995),but did not analyse a possible increase in high-frequency activity in that study.In the present study we observed reductions in gamma power preceding voice-onset time,which in this word repetition task may reflect a brief relaxation of receptive speech-related processes and an initiation of expressive processes.Observed in the most anterior frontal electrodes,this reduction was associated with an increase in delta and theta power.Jokisch and Jensen (2007)interpreted similar task-related increases of alpha activity during a visual memory task as indicating inhibition of information processing.Freeman-like cortical gamma activity has been elicited in response to stimulation of the posterior intralaminar region of the ventral acoustic thalamus in the rat (Brett and Barth,1997).Event-related gamma activity has also been reported in other cortical regions,such as in rat and monkey motor and somatosensory area (Murthy and Fetz,1992;Jones and Barth,1995;MacDonald and Barth,1995),suggesting it is a general correlate of cortical information processing.
Investigations of the primate auditory system reveal multiple parallel pathways (Rauschecker,1998a ),each with different functional specialization.For example,primate vocalizations activate A1superior temporal gyrus,whereas less complex sounds activate the caudomedial area (Rauschecker,1998b ).Similar functional specificity has been described in humans (Jasper and Penfield,1949;Wise et al .,2001).It is clear from human PET and functional MRI studies that widely distributed cortical areas are involved while listening to words (Peterson et al .,1988;Bookheimer et al .,1997).Six distinct mirror-image tonotopically organized regions have been identified in human auditory cortex using functional MRI (Talavage et al .,2004).Casual observation might give the impres-sion that superior temporal gyrus activation was posterior to primary auditory cortex.Cytoarchitectonic and
morphometric investigations,however,reveal that the auditory cortex includes,in addition to Heschl’s Gyrus and planum temporale (Brodmann,1909),area A1centred about 4cm from the anterior tip of the temporal lobe,and STA extending almost 6cm from the temporal pole (Rivier and Clarke,1997).Auditory areas extend to the most posterior extent of the Sylvian Fissure (Zetzsche et al .,2001),to include the ascending posterior planum (Merlo et al .,1998)and even rostral into the parietal lobe (Galaburda and Sanides,1980).Recent multimodal archi-tectonic mapping reveals that auditory cortex (Te3)includes the lateral portion of the posterior temporal gyrus,and extends rostrally and caudally (Morosan et al .,2005).The auditory areas for which one’s own voice was suppressed were at or immediately posterior to the early tone evoked potential,and anterior through most of the receptive speech processing areas.The suppression of one’s own voice is likely due to frontal areas suppressing activity in cortical auditory areas such as area Te3.
The previous findings indicate that the human language system involves widespread areas of the cortex,and includes language modules that serve a variety of linguistic needs.In the clinical setting it is important to discriminate between areas essential and less essential for language.In the present study,a one-to-one association between areas showing increased gamma activity and language areas identified via cortical stimulation was not observed.These findings suggest that many of the areas where activity was observed are likely ‘boutique’language processing centres,adding to the richness of the language experience,but in some circumstances,potentially resectable.Such areas have also been identified in functional MRI and PET studies of language.Disrupting these areas with electrical stimulation or even resecting these areas might not cause a deficit evident on casual clinical observation (although likely demonstrable with more detailed testing).It therefore seems reasonable to consider the location of these areas when planning how much of the anterior temporal lobe or peri-Sylvian areas to resect.Unfortunately,given that it was not possible to deviate from our standard clinical evalua-tion,the research language task and cortical stimulation findings could not be directly compared.Future studies using a common task are needed to better assess associations between gamma activity and essential and non-essential language areas.
An interesting problem of speech perception is the question of how one’s own voice is processed.Do we perceive our own speech in the same way we monitor the speech of others?Why does not our own voice,generated so close to our ears,resonate louder than other voices and cause auditory desensitization?One mechanism to accom-plish perceptual normalization is peripheral sensory gating.In humans,the stapedius reflex mechanically reduces sound transmission through the middle ear by 20–25dB,and is activated just before one speaks.Similar reflexes exist in many sound-generating animals,including non-human
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primates (Mu
¨ller-Preuss and Ploog,1981;Eliades and Wang,2003),birds (Coleman et al .,2007),bats (Suga and Schlegel,1972),electric fish (Bell,2001)and crickets (Poulet and Hedwig,2003).Distal sensory gating tends to attenuate all auditory input.In addition to the previous mechanism,a second mechanism of ‘corollary discharge’has been proposed,in which frontal areas regulate activity in superior temporal gyrus auditory regions (Creutzfeldt et al .,1989b ;Houde et al.,2002;Heinks-Maldonado et al .,2005).For example,it has been hypothesized that a lack of frontal modulation of superior temporal gyrus activity underlies the failure in individuals with schizophrenia to recognize inner speech as self-generated,and may partially account for auditory hallucinations (Ford et al .,2002).Similar frontal lobe modulation of primary/secondary sensory areas is thought to account for the visual phenomenon of saccadic suppression (Ross et al .,2001)and gaze stabilization during movement (Cullen and Roy,2004),to explain why one cannot tickle oneself (Blakemore et al .,2000),and to explain why ‘biting the bullet’suppresses pain (Le Pera et al .,2007).Our findings support a similar mechanism during speaking.
Although perception of our own voice is seemingly desirable,allowing us to monitor and modulate its intensity and prosody,portions of the receptive language system in the superior temporal lobe are deactivated when we speak,a process that may help us to differentiate our voice from others,as well as to speak and listen at the same time.Suppression during speaking was observed for 10%of the implanted electrodes (Fig.13).Creutzfeldt et al .(1989b )reported activation and suppression of single-unit spiking in response to hearing one’s own voice.Their recordings from the superior temporal gyrus mainly revealed activation of spiking activity.However,in the middle temporal gyrus they encountered roughly equal amounts of activation and suppression of single unit spiking during speaking,imply-ing the activation of selective gating or inhibitory processes (Trautner et al .,2006).The finding that processing of one’s own voice tended to be suppressed in more anterior voice processing regions near primary auditory cortex suggests that the suppression,likely coming from frontal cortex,acts on relatively low level cortical auditory areas.Similarly,input from other sensory modalities is thought to be integrated with visual processing at low cortical levels (Schroeder and Foxe,2005).
We were unable to reliably demonstrate increased lateral coherence or phase synchrony between activated areas in the gamma band (Gray et al .,1989;Shen et al .,1999;Weiss and Mueller,2003).We also did not see a tendency for greater gamma activity related to words that contained coarse fricative phonemes (Creutzfeldt et al .,1989a ).We did not observe reliable activation of Broca’s area while hearing words (Xiang et al .,2001;Matsumoto et al .,2004).We were unable to support the role of the medial temporal lobe in distinguishing new versus old words (Daselaar et al .,2006),perhaps to limited electrode coverage in that region.
A major limitation of this study is the constraint on the number of electrodes from which we could record.Recordings were only obtained from about half of the implanted electrodes.This somewhat sparse spatial sam-pling of the cortex probably explains why not all phe-nomena were observed for all patients.Cortical areas specifically related to recognition memory during the second task were not evident in these recordings,perhaps due to the sparse coverage of medial temporal regions.However,a similar failure to observe changes in high gamma activity in the basal temporal region during an auditory new word/old word discrimination task was reported by Tanji et al .(2005),even though they found clear gamma activations in this region for visual character reading tasks.Our similar findings reinforce the concept that the superior temporal gyrus is devoted to auditory processing,but more inferior regions are dedicated to visual processing.Although we only had a limited number of electrodes placed over the right hemisphere,we did not detect any hemispheric difference.Similarly,we did not observe any systematic differences related to gender or patient age.
The functional analyses described in this study do not require that the patient undergo an MRI or CT scan.This is an advantage for younger patients,who may not be able to tolerate awake scanning,and reduces the complexity and cost of this type of work-up.Although many of the electrophysiological phenomena were observed to arise under a few adjacent electrodes,some patterns followed the course of a gyrus or were unique to a single electrode,suggesting that volume conduction was not a major issue.Because the width of cortical gyri is about 1cm,a more desirable inter-electrode spacing would be on the order of 5mm.Although closer spacing of electrodes is possible,the need for greater spatial resolution must be balanced with practical constraints of chronic wires safely exiting the scalp.Because our findings indicate that expressive and receptive speech areas may be identified from the analysis of passive ECoG recordings,direct electrical stimulation of cortex may potentially be relegated to a more abbreviated confirmatory role in functional mapping.The finding that similar patterns of activation were observed during language tasks and during spontaneous conversation increases our confidence in the external validity of these findings.More extensive analysis of spontaneous conversa-tions might ultimately eliminate the need of formal language tasks.Such innovations,if validated,could shorten and reduce the risk,discomfort and staffing necessary to manage the invasive epilepsy work-up.
Our capacity to simultaneously record from only about half (721/1486)of the total number of implanted electrodes suggests that our findings may underestimate the total area of superficial cortex activated by speech.We preferentially chose to record from electrodes near traditional speech areas and also excluded 24electrodes with frequent inter-ictal spiking,which tended to contaminate the gamma band.
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In spite of these limitations,the data support the concept of widely distributed and functionally specific language modules dynamically interacting to serve receptive and expressive speech.The findings also indicate that wide-spread areas of the temporal lobe are suppressed when a person speaks.As increased gamma band power was reliably observed for all 12subjects,this technique may have clinical value in assessing and planning surgical resections for individual patients.Recent advances in our understanding of the anatomical basis of speech challenge the classical description of language processes,in which Broca’s Area in the left frontal lobe exclusively serves expressive speech (Broca,1865),and Wernicke’s Area in the left posterior temporal lobe mediates receptive speech (Wernicke,1874;Wise et al .,2001).Using non-invasive haemodynamic functional imaging techniques,activity in additional brain regions is observed when performing various speech processes (Peterson et al .,1988;Price et al .,1996;Bookheimer et al.,1997;Belin et al .,2000).These brain regions extend beyond those identified via the classical technique of applying direct electrical stimulation to the cortex to disrupt normal language function (Penfield and Roberts,1959;Ojemann et al .,1989a ;Lesser et al .,1994;Boatman et al .,1995).Although multiple language areas have been identified using haemodynamic imaging techniques,the slow time course of the haemodynamic response makes it difficult to determine how brain regions differently respond to constantly changing linguistic demands.Neural activity within cortical regions occurs on a millisecond time scale,making some brain processes associated with cognition better explored by examining the electrophysiological signals associated with neural activity.The origin of the alleged corollary discharges escapes the present analysis,but may become evident from analysis of cross-correlations,coherence or phase synchrony relation-ships between recorded channels.
Acknowledgements
This study was supported in part by NIH 5R01NS40514,The Brain Research Foundation and the Susman and Asher Foundation.We are also grateful to Daniel Choi,Simone Davion,Diana Hanan,Gioconda Mojica,Jeff Wang,Brent Parris and Anna Poon,who worked on various aspects of this study.
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(完整版)经济增加值eva计算方法
EVA计算方法 说明: 经济增加值(EVA)＝税后净营业利润（NOPAT）－资本成本（cost of capital） 资本成本＝资本×资本成本率 由上知，计算EVA可以分做四个大步骤：（1）税后净营业利润（NOPAT）的计算; (2)资本的计算；(3)资本成本率的计算；（4）EVA的计算。下面列出EVA的计算步骤，并以深万科（0002）为例说明EVA（2000年）的计算。 深万科（0002）简介： 公司名称：万科企业股份有限公司公司简称：深万科Ａ上市日期：1991-01-29 上市地点：上海证券交易所行业：房地产业股本结构：A 股398711877股，B股121755136 股，国有股、境内法人股共110504928股，股权合计数：630971941股。 一、税后净营业利润（NOPAT）的计算 1．以表格列出的计算步骤 下表中，最左边一列（以IS开头）代表损益表中的利润计算步骤，最右边一列（以NOPAT开头）代表计算EVA所用的税后净营业利润（NOPAT）的计算步骤。空格代表在计算相应指标（如NOPAT）的步骤中不包含该行所对应的项。
损益表中的利润计算步骤 税后净营业 利润 （NOPAT） 的计算步骤主营业务收入 - 销售折扣和折让- - 主营业务税金及附加- - 主营业务成本- 主营业务利润 + 其它业务利润+ 当年计提或冲销的坏帐准备+ - 当年计提的存货跌价准备 - 管理费用- - 销售费用- = 营业利润/调整后的营业利润 + 投资收益+
= 总利润/税前营业利润 - EVA税收调整* - = 净利润/税后净营业利润 2. 计算公式：(蓝色斜体代表有原始数据，紫色下划线代表此数据需由原始数据推算出) （1）税后净营业利润=主营业务利润＋其他业务利润＋当年计提或冲销的坏帐准备—管理费用—销售费用＋长期应付款，其他长期负债和住房公积金所隐含的利息＋投资收益—EVA税收调整 注：之所以要加上长期应付款，其他长期负债和住房公积金所隐含的利息是因为sternstewart公司在计算长期负债的利息支出时，所用的长期负债中包含了其实不用付利息的长期应付款，其他长期负债和住房公积金。即，高估了长期负债的利息支出，所以需加回。 （2）主营业务利润＝主营业务收入—销售折扣和折让—营业税金及附加—主营业务成本 注: 主营业务利润已在sternstewart公司所提供的原始财务数据中直接给出 (3)EVA税收调整=利润表上的所得税＋税率×（财务费用＋长期应
标准正态分布的密度函数样本
幻灯片1 正态分布 第二章 第七节 一、标准正态分布的密度函数 二、标准正态分布的概率计算 三、一般正态分布的密度函数 四、正态分布的概率计算幻灯片2 正态分布的重要性正态分布是概率论中最重要的分布, 这能够由 以下情形加以说明: ⑴ 正态分布是自然界及工程技术中最常见的分布之一, 大量的随机现象都是服从或近似服从正态分布的．能够证明, 如果一个随机指标受到诸多因素的影响, 但其中任何一个因素都不起决定性作用, 则该随机指标一定服从或近似服从正态分布． 这些性质是其它 ⑵ 正态分布有许多良好的性质, 许多分布所不具备的． ⑶ 正态分布能够作为许多分布的近似分布．幻灯片3 －标准正态分布下面我们介绍一种最重要的正态分布 一、标准正态分布的密度函数若连续型随机变量X 的密度函数为定义 则称X 服从标准正态分布,
记为标准正态分布是一种特别重要的它的密度函数经常被使用, 分布。 幻灯片4 密度函数的验证 则有 ( 2) 根据反常积分的运算有能够推出 幻灯片5 标准正态分布的密度函数的性质若随机变量 , X 的密度函数为 则密度函数的性质为: 的图像称为标准正态( 高斯) 曲线幻灯片6 随机变量 由于 由图像可知, 阴影面积为概率值。对同一长度的区间 , 若这区间越靠近 其对应的曲边梯形面积越大。标准正态分布的分布规律时”中间多, 两头少” . 幻灯片7 二、标准正态分布的概率计算 1、分布函数分布函数为幻灯片8 2、标准正态分布表书末附有标准正态分布函数数值表, 有了它, 能够解决标准正态分布的概率计算.表中给的是x > 0时，①(x)的值. 幻灯片9 如果由公式得令则幻灯片10
怎样理解分布函数
怎样理解分布函数 概率论中一个非常重要的函数就是分布函数,知道了随机变量的 分布函数,就知道了它的概率分布,也就可以计算概率了。 一、理解好分布函数的定义: F(x)=P(X≤x), 所以分布函数在任意一点x的值,表示随机变量落在x点左边(X≤x)的概率。它的定义域是(-∞,+∞),值域是[0,1]. 二、掌握好分布函数的性质: (1)0≤F(x)≤1; (2)F(+∞)=1,F(-∞)=0; 可以利用这条性质确定分布函数中的参数,例如: 设随机变量X的分布函数为:F(x)=A+Barctanx,求常数A与B. 就应利用本性质计算出A=1/2,B=1/π. (3)单调不减; (4)右连续性。 三、会利用分布函数求概率 在利用分布函数求概率时,以下公式经常利用。
(1)P(a PSCAD 使用说明 1.PSCAD安装 PSCAD / EMTDC常见4.0.2 ctacked版本或版本，这个版本PSCAD被封装成一个ISO文档，如图1-1，可用虚拟光驱或winrar打开。下面使用winrar将其解包。 图1-1PSCAD封包形式 在系统安装了以上版本后，可以直接双击这个iso文档，然后点击“解压到”图标，如图1-2，就可以对其进行解包。 如图1-2 使用winrar解PSCAD的封包 解压后可以得到三个文件夹，如下图1-3所示： 图1-3 PSCAD须按以下步骤安装，否则，装好后可能不运行。另外，操作系统最好 使用WinXP专业版，曾在WinXP Home版本上出现过不明原因的PSCAD不能运行情况。 安装步骤： （1）首先，运行PSCAD 目录下的，一路按OK或者NEXT在选择安装列表时选中“PSCAD(all Editions)”，如图1-4，不要选择License Manager和Real Time Playback (它需要硬件采集设备支持，否则只是评估版)这两项。使用附带的EGCS/GNU Fortran77编译器就选中“GNU Fortran Compiler”，如果要使用之前自行安装的Fortran90编译器就不要选这一项。 图1-4 2、当License Manger选择对话框出现时，如图1-5，选择“I will only be using Single-user/single-machine licenses.”或“professal”这一项，随后一路OK即可。 注意：选the Student Edition 版本，模型只允许15个结点。 经济增加值(eva)计算方式 (四)（Economic value added (EVA) calculation (four)） Next, the calculation method of economic value added is introduced The calculation model of EVA is given below. Computational model of 1 and EVA Economic value added = net operating profit after tax - cost of capital = net operating profit after tax - total capital * weighted average cost of capital Among them: Net operating profit after tax net profit after tax interest expense + = + + minority income this year amortization of goodwill + deferred tax credit balances increase reserve balances increased + + other capitalized research and development costs, capitalized research and development costs in the years of amortization Total capital = common equity + minority interests + deferred tax credit (debit balance is negative) + + (cumulative amortization of goodwill reserve inventory impairment provision for bad debts, etc.) + + + capitalization amount of short-term loans for research and development costs of long term loan + short-term long-term loans due in part EVA 计算方法 说明: 经济增加值(EV A)＝税后净营业利润（NOPA T ）－资本成本（cost of capital ） 资本成本＝资本×资本成本率 由上知，计算EV A 可以分做四个大步骤： （1）税后净营业利润（NOPA T ）的计算; (2)资本的 计算； (3)资本成本率的计算； （4）EV A 的计算。下面列出EV A 的计算步骤，并以深万科（0002）为例说明EV A （2000年）的计算。 深万科（0002）简介： 公司名称：万科企业股份有限公司 公司简称：深万科Ａ 上市日期：1991-01-29 上市地点：上海证券交易所 行业：房地产业 股本结构：A 股398711877股，B 股121755136 股，国有股、境内法人股共110504928股，股权合计数：630971941股。 一、税后净营业利润（NOPA T ）的计算 1． 以表格列出的计算步骤 下表中，最左边一列（以IS 开头）代表损益表中的利润计算步骤，最右边一列（以NOPA T 开头）代表计算EV A 所用的税后净营业利润（NOPA T ）的计算步骤。空格代表在计算相应指标（如NOPA T ）的步骤中不包含该行所对应的项。 损益表中的利润计算步骤 税后净营业 利润 （NOPA T ）的计算步骤 主营业务收入 - 销售折扣和折让 - - 主营业务税金及附加 - - 主营业务成本 - 主营业务利润 - 管理费用 - - 销售费用 - = 营业利润/调整后的营业利润 + 投资收益 + = 总利润/税前营业利润 - EVA 税收调整* - = 净利润/税后净营业利润 2.计算公式：(蓝色斜体代表有原始数据，紫色下划线代表此数据需由原始数据推算出) （1）税后净营业利润=主营业务利润＋其他业务利润＋当年计提或冲销的坏帐准备—管理费用—销售费用＋长期应付款，其他长期负债和住房公积金所隐含的利息＋投资收益—EV A 税收调整 注：之所以要加上长期应付款，其他长期负债和住房公积金所隐含的利息是因为sternstewart公司在计算长期负债的利息支出时，所用的长期负债中包含了其实不用付利息的长期应付款，其他长期负债和住房公积金。即，高估了长期负债的利息支出，所以需加回。 （2）主营业务利润＝主营业务收入—销售折扣和折让—营业税金及附加—主营业务成本注: 主营业务利润已在sternstewart公司所提供的原始财务数据中直接给出 (3)EV A税收调整=利润表上的所得税＋税率×（财务费用＋长期应付款，其他长期负债 和住房公积金所隐含的利息＋营业外支出－营业外收入－补贴收入） (4)长期应付款，其他长期负债和住房公积金所隐含的利息＝长期应付款，其他长期负债 和住房公积金×3～5 年中长期银行贷款基准利率 长期应付款，其他长期负债和住房公积金=长期负债合计—长期借款—长期债券 税率=0.33（从1998年，1999年和2000年） 说明：上面计算公式所用数据大多直接可以在sternstewart公司所提供的原始财务数据中找到（主营业务利润已直接给出）。而长期应付款，其他长期负债和住房公积金所隐含的利息需由原始财务数据推算得出。 3. 计算深万科的税后净营业利润（NOPAT 2000年） 首先计算出需由其他原始财务数据推算的间接数据项－长期应付款，其他长期负债和住房公积金所隐含的利息和EV A税收调整，然后利用计算结果及其他数据计算出NOPA T. （1）长期应付款，其他长期负债和住房公积金所隐含的利息的计算； 单位：元 长期负债合计123895991.54 减：长期借款80000000.00 减：长期债券 ――――――――――――――――――――――――――――― 长期应付款，其他长期负债和住房公积金43895991.54 乘：3～5 年中长期银行贷款基准利率 6.03％ 长期应付款，其他长期负债2646928.29 和住房公积金所隐含的利息 （2）EV A税收调整的计算； 财务费用1403648.37 加：长期应付款，其他长期负债2646928.29 和住房公积金所隐含的利息 加：营业外支出6595016.31 减：营业外收入23850214.53 各位，pscad有三种版本，student，educational，以及professional。student只支持15个节点，可以免费使用，但是其余两种都是收费的。现在很多的crack程序crack成所谓的professional版本，其实都只是educational的，最多支持200个节点，我到现在也没有解决这个问题，很是郁闷。但是200个节点的版本对初学者来说很多时候已经够用了，现在上传一个，希望对初学pscad的同学有帮助，另外有哪位同学能真正crack成为无节点限制的professional版本，也请多多指教！ 浏览了很多发crack程序的同学，大都把安装文件也发了上来，很多想下载的同学都因为没有流量而郁闷不已，下面这个方法可以帮助大家，附件里只是crack文件，很小 1.先从官网上下载4. 2.1，Free Evaluation Download of PSCAD? PSCAD? V4.2.1 Program download (46.3MB)，网址如下： https://https://www.wendangku.net/doc/b216034429.html,/products/pscad/free_downloads/ 2.解压，应该是一个名为PSCAD421_2007_Eval 的文件夹，注意里面有一个egcs的文件夹，之后需要替换 3.再从官网上下载GCS/GNU F77 Fortran download (11.4MB)（相同的网址，如上），解压后是一个egcs的文件夹，将这个文件夹代替PSCAD421_2007_Eval中的egcs文件夹，注意文件夹名别搞错了 4.运行PSCAD421_2007_Eval文件夹中的setup.exe，安装过程中注意勾选GUN fortune complier 5.下载附件中的crack程序，直接运行，crack会提示你找到安装好pscad的位置，如果安装在C盘，应该在这个路径下：C:\Program Files\PSCAD421Eval\bin\win。crack里面的pscad.exe 即可。 这样就可以得到professional版本了（其实是200个节点educational版本） 以上内容纯手打，我感觉已经说得很清楚了，相信对大家有用！ 原文标题：pscad4.2.1crack方法及详细流程，一定能用（内容纯手打）- PSCAD资料共享- PSCAD - 中国电力研学论坛专注电力技术应用，关注电力科技前沿，打造专业电力社区！- Powered by Discuz! 原文链接：https://www.wendangku.net/doc/b216034429.html,/viewthread.php?tid=71992&highlight=pscad4.2.1 EV A计算方法 说明: 经济增加值(EV A)＝税后净营业利润（NOPAT）－资本成本（cost of capital） 资本成本＝资本×资本成本率 由上知，计算EV A可以分做四个大步骤： （1）税后净营业利润（NOPAT）的计算; （2）资本的计算； （3）资本成本率的计算； （4）EV A的计算。 下面列出EV A的计算步骤，并以深万科（0002）为例说明EV A（2000年）的计算。 深万科（0002）简介： 公司名称：万科企业股份有限公司公司简称：深万科Ａ上市日期：1991-01-29 上市地点：上海证券交易所行业：房地产业股本结构：A股398711877 股，B股121755136 股，国有股、境内法人股共110504928股，股权合计数：630971941股。一、税后净营业利润（NOPAT）的计算 1．以表格列出的计算步骤 下表中，最左边一列（以IS开头）代表损益表中的利润计算步骤，最右边一列（以NOPA T 开头）代表计算EV A所用的税后净营业利润（NOPA T）的计算步骤。空格代表在计算相 应指标（如NOPA T）的步骤中不包含该行所对应的项。 损益表中的利润计算步骤 税后净营业 利润 （NOPAT） 的计算步骤主营业务收入 - 销售折扣和折让- - 主营业务税金及附加- - 主营业务成本- 主营业务利润 - 管理费用- = 营业利润/调整后的营业利润 + 投资收益+ = 总利润/税前营业利润 = 净利润/税后净营业利润 2.计算公式：(蓝色斜体代表有原始数据，紫色下划线代表此数据需由原始数据推算出) （1）税后净营业利润=主营业务利润＋其他业务利润＋当年计提或冲销的坏帐准备—管理费用—销售费用＋长期应付款，其他长期负债和住房公积金所隐含的利息＋投资收益—EV A 税收调整 注：之所以要加上长期应付款，其他长期负债和住房公积金所隐含的利息是因为sternstewart公司在计算长期负债的利息支出时，所用的长期负债中包含了其实不用付利息的长期应付款，其他长期负债和住房公积金。即，高估了长期负债的利息支出，所以需加回。 （2）主营业务利润＝主营业务收入—销售折扣和折让—营业税金及附加—主营业务成本注: 主营业务利润已在sternstewart公司所提供的原始财务数据中直接给出 (3)EVA税收调整=利润表上的所得税＋税率×（财务费用＋长期应付款，其他长期负债 和住房公积金所隐含的利息＋营业外支出－营业外收入－补贴收入） (4)长期应付款，其他长期负债和住房公积金所隐含的利息＝长期应付款，其他长期负债 和住房公积金×3～5 年中长期银行贷款基准利率 长期应付款，其他长期负债和住房公积金=长期负债合计—长期借款—长期债券 税率=0.33（从1998年，1999年和2000年） 说明：上面计算公式所用数据大多直接可以在sternstewart公司所提供的原始财务数据中找到（主营业务利润已直接给出）。而长期应付款，其他长期负债和住房公积金所隐含的利息需由原始财务数据推算得出。 3. 计算深万科的税后净营业利润（NOPAT 2000年） 首先计算出需由其他原始财务数据推算的间接数据项－长期应付款，其他长期负债和住房公积金所隐含的利息和EV A税收调整，然后利用计算结果及其他数据计算出NOPA T. （1）长期应付款，其他长期负债和住房公积金所隐含的利息的计算； 单位：元 长期负债合计123895991.54 减：长期借款80000000.00 减：长期债券 ――――――――――――――――――――――――――――― 长期应付款，其他长期负债和住房公积金43895991.54 乘：3～5 年中长期银行贷款基准利率 6.03％ 长期应付款，其他长期负债2646928.29 和住房公积金所隐含的利息 （2）EV A税收调整的计算； 财务费用1403648.37 PSCAD4使用入门指南 何海昉 本指南仅供入门级PSCAD学习者参考，通过简单实例从元件输入到参数设置到最后仿真一个完 整的过程来介绍PSCAD4的基本工作方式。 界面介绍 通过一个简单实例来介绍PSCAD 的使用 1. 新建一个工程项目 将得到一个名为noname 的工程项目，右击该项目将其另存为 example 2.为新项目添加电源元件，双击系统主库master[Master Library] 的子项[Main] Main Page，元件库 图标在编辑区域出现。 双击上图的Sources图标，进入到电源元件库中 移动水平和垂直滚动条，选择单相RRL型交流电源，并将其复制（Ctrl＋V），切换到example 项目Main的编辑区域，单击右键粘贴（Ctrl＋V）,此电源就被加载到了用户定义的工程项目中 3. 设定电源参数 双击编辑区域中的交流电源元件，进入电源属性设定对话框，这里电源 的configuration属性页采用默认的值，即采用内部输入式交流RRL型，该电源一端接地， 通常有些元件的参数比较多，可能需要点击下拉列表框来获 得另外的属性页。其它元件的 参数设定也是一样通过双击进入属性编辑对话框来设置 选择下拉列表中的Signal Parameters子项 设定电压值、频率、初相等参数值，如果不明白参数所表示的实际意义，单击Help按钮进入 帮助界面，帮助系统会给出要求用户填写的所有参数所代表 的涵义 4.绘制理想导线 单击右边元件工具栏中的导线，移动到编辑区域中，再单击鼠标。导线随即定位。再次单击导 线时，则选取了该导线，这时导线两端将出现绿色的小方形，点击并拖动小方形，可以调整导 线在该方向上的长度。如果选取了导线后，按键盘上的R键，则导线会顺时针方向旋转90O， 当两条导线（或者是元件的管脚）的有一端相连时，会自动形成电气连接特性; 但如果两条导线 （或者是元件的管脚）相交，但导线的所有末端都不相连， 则两条导线是相互绝缘的， 即实际 上电气上是不相通的， 如果要使两导线交点成为电气节点， 正态分布 第二章 第七节 一、标准正态分布的密度函数 二、标准正态分布的概率计算 三、一般正态分布的密度函数 四、正态分布的概率计算 幻灯片2 正态分布的重要性正态分布是概率论中最重要的分布， 这可以由 以下情形加以说明： ⑴正态分布是自然界及工程技术中最常见的分布 之一， 大量的随机现象都是服从或近似服从正态分布的． 可以证明， 如果一个随机指标受到诸多因素的影响, 但其中任何一个因素都不起决定性作用， 则该随机指标 一定服从或近似服从正态分布． 这些性质是其它 ⑵正态分布有许多良好的性质， 许多分布所不具备的． ⑶正态分布可以作为许多分布的近似分布． 幻灯片3 －标准正态分布 下面我们介绍一种最重要的正态分布 一、标准正态分布的密度函数 若连续型随机变量X的密度函数为 定义 则称X服从标准正态分布， 记为 标准正态分布是一种特别重要的 它的密度函数经常被使用， 分布。 幻灯片4 密度函数的验证 则有 （2）根据反常积分的运算有 可以推出 幻灯片5 标准正态分布的密度函数的性质 ，X的密度函数为 则密度函数的性质为： 的图像称为标准正态（高斯）曲线。 幻灯片6 随机变量 由于 由图像可知，阴影面积为概率值。 对同一长度的区间 ，若这区间越靠近 其对应的曲边梯形面积越大。 标准正态分布的分布规律时“中间多，两头少”. 幻灯片7 二、标准正态分布的概率计算 1、分布函数 分布函数为 幻灯片8 2、标准正态分布表 书末附有标准正态分布函数数值表，有了它，可以解决标准正态分布的概率计算. 表中给的是x > 0时, Φ(x)的值. 幻灯片9 如果 由公式得 令 则 幻灯片10 例1 解 幻灯片11 由标准正态分布的查表计算可以求得， 当X～N(0,1)时， 这说明，X 的取值几乎全部集中在[-3,3]区间内，超出这个范围的可能性仅占不到0.3%. 幻灯片12 三、一般正态分布的密度函数 如果连续型随机变量X的密度函数为 （其中 为参数） 的正态分布，记为 则随机变量X服从参数为 所确定的曲线叫 作正态(高斯）曲线. 幻灯片13 PSCAD简明使用手册 Chapter 1: EMTDC/PSCAD简介 (1 1.1 功能 (1 1.2 技术背景 (1 1.3 主要的研究范围 (1 1.4 目前应用情况 (2 1.5 各版本限制 (3 1.6 目前最新版本:PSCAD 第四版 (3 Chapter 2: 安装及License设置 (4 2.1 安装 (4 2.2 License设置 (6 Chapter 3: PSCAD工作环境 (9 3.1 术语和定义 (9 3.1.1 元件 (9 3.1.2 模块 (10 3.1.3 工程 (10 3.2 各工作区介绍 (10 3.2.1 工作空间窗口 (10 3.2.2 输出窗口 (14 3.2.3 设计编辑器 (16 3.3 工作区设置 (16 3.4 在线帮助系统 (18 Chapter 4: 基本操作 (19 4.1 工程 (19 4.2 元件和模块 (22 4.2.1 元件 (22 4.2.2 模块 (25 4.3 常用工具栏及快捷键 (25 4.3.1常用工具栏 (25 4.3.2快捷键 (27 Chapter 5: 在线绘图和控制 (29 5.1 控制或显示数据的获取 (29 5.2 图形框 (30 5.3 图、曲线及轨迹 (31 5.4 在线控制器及仪表 (34 5.5 几种特殊表计 (36 5.5.1 XY绘图 (36 5.5.2多测计 (38 5.5.3相量计 (39 参考文献 (41 Chapter 1: EMTDC/PSCAD简介 Dennis Woodford博士于1976年在加拿大曼尼托巴水电局开发完成了EMTDC 的初版,是一种世界各国广泛使用的电力系统仿真软件,PSCAD是其用户界 面,PSCAD的开发成功,使得用户能更方便地使用EMTDC进行电力系统分析,使电力系统复杂部分可视化成为可能,而且软件可以作为实时数字仿真器的前置端。可模拟任意大小的交直流系统。操作环境为:UNIX OS, Windows95, 98,NT等;Fortran 编辑器;浏览器和TCP/IP协议。 1.1 功能 ?可以发现系统中断路器操作、故障及雷击时出现的过电压 ?可对包含复杂非线性元件(如直流输电设备的大型电力系统进行全三相的精确模拟,其输入、输出界面非常直观、方便 ?进行电力系统时域或频域计算仿真 ?电力系统谐波分析及电力电子领域的仿真计算 ?实现高压直流输电、FACTS控制器的设计 1.2 技术背景 程序EMTDC(Electro Magnetic Transient in DC System是目前世界上被广泛使用的一种电力系统仿真分析软件,它即可以研究交直流电力系统问题,又能完成电力电子仿真及其非线性控制的多功能(V ersatile Tool工具。PSCAD(Power System Computer Aided Design是EMTDC的前处理程序,用户在面板上可以构造电气连接图,输入各元件的参数值,运行时则通过FORTRAN编译器进行编译、连接,运行的结 目录 1. 均匀分布 (1) 2. 正态分布（高斯分布） (2) 3. 指数分布 (2) 4. Beta分布（：分布） (2) 5. Gamm 分布 (3) 6. 倒Gamm分布 (4) 7. 威布尔分布（Weibull分布、韦伯分布、韦布尔分布） (5) 8. Pareto 分布 (6) 9. Cauchy分布（柯西分布、柯西-洛伦兹分布） (7) 2 10. 分布（卡方分布） (7) 8 11. t分布................................................ 9 12. F分布 ............................................... 10 13. 二项分布............................................ 10 14. 泊松分布（Poisson 分布）............................. 11 15. 对数正态分布........................................ 1. 均匀分布 均匀分布X ~U（a,b）是无信息的，可作为无信息变量的先验分布。 2. 正态分布（高斯分布） 当影响一个变量的因素众多，且影响微弱、都不占据主导地位时，这个变量 很可能服从正态分布，记作 X~N （」f 2）。正态分布为方差已知的正态分布 N （*2）的参数」的共轭先验分布。 1 空 f （x ）： —— e 2- J2 兀 o' E(X)， Var(X) _ c 2 3. 指数分布 指数分布X ~Exp （ ）是指要等到一个随机事件发生，需要经历多久时间。其 中，.0为尺度参数。指数分布的无记忆性： Plx s t|X = P{X t}。 f （X ）二 y o i E(X) 一 4. Beta 分布（一：分布） f （X ）二 E(X) Var(X)= (b-a)2 12 Var(X)二 1 ~2 EVA 计算方法 说明: 经济增加值（EVA ）=税后净营业利润（NOPAT ）—资本成 本（cost of capital ） 资本成本=资本x 资本成本率 由上知，计算EVA 可以分做四个大步骤： （1 ）税后净 营 业利润（NOPAT ）的计算;（2）资本的计算；（3）资本成本率的计算； （4） EVA 的计算。下面列出EVA 的计算步骤，并以深万科（0002 ） 为例说明EVA （2000年）的计算。 深万科（0002 ）简介： 公司名称：万科企业股份有限公司 A 上市日期：1991-01-29 股 398711877 股，B 股 121755136 股共110504928 股，股权合计数：630971941 股 一、税后净营业利润（NOPAT ）的计算 1 .以表格列出的计算步骤 下表中，最左边一列（以IS 开头）代表损益表中的利润计算步骤， 最右边一列（以NOPAT 开头）代表计算EVA 所用的税后净营业利 润（NOPAT ）的计算步骤。空格代表在计算相应指标（如NOPAT ） 的步骤中不包含该行所对应的 公司简称：深万科 上市地点：上海证券交 易所 行业：房地产业 股本结构：A 股，国有股、境内法人 项。 = 总利润/税前营业利润 -EVA税收调整* - 少数股东权益 = 净利润/税后净营业利润 2.计算公式：（蓝色斜体代表有原始数据，紫色下划线代表此数据需 由原始数据推算出） （1）税后净营业利润二主营业务利润+其他业务利润+当年计提或冲销的坏帐准备一管理费用一销售费用+长期应付款，其他长期负债和住房公积金所隐含的利息 +投资收益一EVA税收调整 注：之所以要加上长期应付款，其他长期负债和住房公积金所隐含的利息是因为sternstewart公司在计算长期负债的利息支出时，所用的长期负债中包含了其实不用付利息的长期应付款，其他长期负债和住房公积金。即，高估了长期负债的利息支出，所以需加回。 （2）主营业务利润=主营业务收入一销售折扣和折让一营业税金及附加一主营业务成本 注：主营业务利润已在sternstewart公司所提供的原始财务数据中直接给出 ⑶EVA税收调整二利润表上的所得税+税率x（财务费用+长期应 付款，其他长期负债和住房公积金所隐含的利息 +营业外支出- 营业外收 目录 1. 均匀分布 ...................................................................................................... 1 2. 正态分布（高斯分布） ........................................................................... 2 3. 指数分布 ...................................................................................................... 2 4. Beta 分布（β分布） .............................................................................. 2 5. Gamma 分布 .............................................................................................. 3 6. 倒Gamma 分布 ......................................................................................... 4 7. 威布尔分布(Weibull 分布、韦伯分布、韦布尔分布) ..................... 5 8. Pareto 分布 ................................................................................................. 6 9. Cauchy 分布（柯西分布、柯西-洛伦兹分布） (7) 10. 2χ分布（卡方分布） (7) 11. t 分布 ......................................................................................................... 8 12. F 分布 ........................................................................................................ 9 13. 二项分布 ................................................................................................ 10 14. 泊松分布（Poisson 分布） .............................................................. 10 15. 对数正态分布 ....................................................................................... 11 1. 均匀分布 均匀分布~(,)X U a b 是无信息的，可作为无信息变量的先验分布。 1 ()f x b a =- Generated by Foxit PDF Creator ? Foxit Software https://www.wendangku.net/doc/b216034429.html, For evaluation only. 经济增加值(EVA)计算方式(四) 八 下介绍经济增加值的计算方式 下面给出EVA的计算模式。 1、EVA的计算模型 经济附加值= 税后净营业利润—资本成本 = 税后净营业利润—资本总额* 加权平均资本成本 其中： 税后净营业利润= 税后净利润+ 利息费用+ 少数股东损益+ 本年商誉摊销+ 递延税项贷方余额的增加+ 其他准备金余额的增加+ 资本化研究发展费用—资本化研究发展费用在本年的摊销 资本总额= 普通股权益+ 少数股东权益+ 递延税项贷方余额（借方余额则为负值）+ 累计商誉摊销+ 各种准备金（坏帐准备、存货跌价准备等）+ 研究发展费用的资本化金额+ 短期借款+ 长期借款+ 长期借款中短期内到期的部分 加权平均资本成本= 单位股本资本成本+ 单位债务资本成本。 2、报表和账目的调整。 由于根据会计准则编制的财务报表对公司绩效的反映存在部分失真，在计算经济附加值时需要对一些会计报表科目的处理方法进行调整。 Stern Stewart财务顾问公司列出了160多项可能需要调整的会计项目，包括存货成本、重组费用、税收、营销费用、无形资产、货币贬值、坏帐准备金、重组费用以及商誉摊销等。但在考察具体企业时，一般一个企业同时涉及的调整科目不超过15项。但由于EVA是Stern Stewart财务顾问公司注册的商标，其具体的账目调整和运算目前尚没有对外公开。 （1）、单位债务资本成本 单位债务资本成本指的是税后成本，计算公式如下： 税后单位债务资本成本=税前单位债务资本成本*（企业所得税税率） 我国上市公司的负债主要是银行贷款，这与国外上市公司大量发行短期票据和长期债券的做法不同，因此可以以银行贷款利率作为单位债务资本成本。 根据有关研究，我国上市公司的短期债务占总债务的90%以上，由于我国的银行贷款利率尚未放开，不同公司贷款利率基本相同。因此，可用中国人民银行公布的一年期流动资金贷款利率作为税前单位债务资本成本，并根据央行每年调息情况加权平均。不同公司的贷款利率实际上存在一定差别，可根据自身情况进行调整。 （2）、单位股本资本成本 单位股本资本成本是普通股和少教股东权益的机会成本。通常根据资本资产价模型确定，计算公式如下： 普通股单位资本成本=无风险收益+β*市场组合的风险溢价 其中无风险利率可采用5年期银行存款的内部收益率。 国外一般以国债收益作为无风险收益表，我国的流通国债市场规模较小，居民的无风险投资以银行存款为主，因此以5年期银行存款的内部收益率代替。随着国债市场发展，将来也可以国债收益率为基准。 β 系数反映该公司股票相对于整个市场（一般用股票市场指数来代替）的系统风险，β系数越大，说明该公司股票相对于整个市而言风险越高，波动越大。 β值可通过公司股票收益率对同期股票市场指数（上证综指）的收益率回归计算得来。 市场组合的风险溢价反映整个证券市场相对于无风险收益率的溢价，目前有一些学者将我国的市场风险溢价定为4%。 （3）、研究发展费用和市场开拓费用 现行会计制度规定，公司必须在研究发展费用和市场开拓费用发生的当年将期间费用一次性予以核销。这种处理方法实际上否认了两种费用对企业未来成长所起的关键作用，而把它与一般的期间费用等同起来。 这种处理方法的一个重要缺点就是可能会诱使经营者减少对这两项费用的投入，这在效益不好的年份和管理人员即将退休的前几年尤为明显。美国的有关研究表明，当管理人员临近退休之际，研究发展费用的增长幅度确实有所降低。 图 6-2 正态分布概率密度函数的曲线 正态曲线可用方程式表示。当n→∞时，可由二项分布概率函数方程推导出正态分布曲线的方程： f(x)= （6.16 ） 式中： x —所研究的变数； f(x) —某一定值 x 出现的函数值，一般称为概率密度函数（由于间断性分布已转变成连续性分布，因而我们只能计算变量落在某一区间的概率，不能计算变量取某一值，即某一点时的概率，所以用“概率密度”一词以与概率相区分），相当于曲线 x 值的纵轴高度； p —常数，等于 3.14 159 ……； e —常数，等于 2.71828 ……；μ为总体参数，是所研究总体的平均数，不同的正态总体具有不同的μ，但对某一定总体的μ是一个常数；δ也为总体参数，表示所研究总体的标准差，不同的正态总体具有不同的δ，但对某一定总体的δ是一个常数。 上述公式表示随机变数 x 的分布叫作正态分布，记作 N( μ , δ2 ) ，读作“具平均数为μ，方差为δ 2 的正态分布”。正态分布概率密度函数的曲线叫正态曲线，形状见图 6-2 。 （二）正态分布的特性 1 、正态分布曲线是以 x= μ为对称轴，向左右两侧作对称分布。因的数值无论正负，只要其绝对值相等，代入公式（ 6.16 ）所得的 f(x) 是相等的，即在平均数μ的左方或右方，只要距离相等，其 f(x) 就相等，因此其分布是对称的。在正态分布下，算术平均数、中位数、众数三者合一位于μ点上。 2 、正态分布曲线有一个高峰。随机变数 x 的取值范围为（ - ∞，+ ∞ ），在（ - ∞ ，μ）正态曲线随 x 的增大而上升，；当 x= μ时， f(x) 最大；在（μ，+ ∞ ）曲线随 x 的增大而下降。 3 、正态曲线在︱x-μ︱=1 δ处有拐点。曲线向左右两侧伸展，当x →± ∞ 时，f(x) →0 ，但 f(x) 值恒不等于零，曲线是以 x 轴为渐进线，所以曲线全距从 -∞到+ ∞。 4 、正态曲线是由μ和δ两个参数来确定的，其中μ确定曲线在 x 轴上的位置 [ 图 6-3] ，δ确定它的变异程度 [ 图 6-4] 。μ和δ不同时，就会有不同的曲线位置和变异程度。所以，正态分布曲线不只是一条曲线，而是一系列曲线。任何一条特定的正态曲线只有在其μ和δ确定以后才能确定。 5 、正态分布曲线是二项分布的极限曲线，二项分布的总概率等于 1 ，正态分布与 x 轴之间的总概率（所研究总体的全部变量出现的概率总和）或总面积也应该是等于 1 。而变量 x 出现在任两个定值 x1到x2(x1≠x2)之间的概率，等于这两个定值之间的面积占总面积的成数或百分比。正态曲线的任何两个定值间的概率或面积，完全由曲线的μ和δ确定。常用的理论面积或概率如下： 区间μ ± 1 δ面积或概率 =0.6826 μ ± 2 δ =0.9545 μ ± 3 δ=0.9973 μ± 1.960δ=0.9500 μ ±2.576 δ =0.9900PSCAD简单入门教程
经济增加值(eva)计算方式 (四)(Economic value added (EVA) calculation (four))
经济增加值EVA计算方法
pscad安装指导
经济增加值EVA的计算方法
PSCAD入门样例(强力推荐!!)
标准正态分布的密度函数
PSCAD使用手册(中文版)
16种常见概率分布概率密度函数、意义及其应用
经济增加值eva计算方法
16种常见概率分布概率密度函数、意义及其应用
正态分布概率公式(部分)
图 62正态分布概率密度函数的曲线 正态曲线可用方程式表示。 n 当 →∞时，可由二项分布概率函数方程推导出正态 分布曲线的方程：
fx= （61 ） () .6
式中： x—所研究的变数； fx —某一定值 x出现的函数值，一般称为概率 () 密度函数 （由于间断性分布已转变成连续性分布，因而我们只能计算变量落在某 一区间的概率， 不能计算变量取某一值， 即某一点时的概率， 所以用 “概率密度” 一词以与概率相区分），相当于曲线 x值的纵轴高度； p—常数，等于 31 .4 19……； e— 常数，等于 2788……； μ 为总体参数，是所研究总体 5 .12 的平均数， 不同的正态总体具有不同的 μ ， 但对某一定总体的 μ 是一个常数； δ 也为总体参数， 表示所研究总体的标准差， 不同的正态总体具有不同的 δ ， 但对某一定总体的 δ 是一个常数。 上述公式表示随机变数 x的分布叫作正态分布， 记作 N μ ,δ2 )， “具 ( 读作 2 平均数为 μ，方差为 δ 的正态分布”。正态分布概率密度函数的曲线叫正态 曲线，形状见图 62。 （二）正态分布的特性
1、正态分布曲线是以 x μ 为对称轴，向左右两侧作对称分布。因 =
的
数值无论正负， 只要其绝对值相等， 代入公式 61 ） （ .6 所得的 fx 是相等的， () 即在平均数 μ 的左方或右方，只要距离相等，其 fx 就相等，因此其分布是 () 对称的。在正态分布下，算术平均数、中位数、众数三者合一位于 μ 点上。经济增加值(EVA)计算方式 (四) 八
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