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The granularity here is not good enough for performing real benchmarks For that, either use the times function, discussed later, or the Benchmark module, which in fact uses the times function

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when usingcubicsplines, derivatives be discontinuous can they usuallycannot detected be visuallyand consequently ignored are Because derivationof cubic splinesis somewhat the irrvolved,we havedecided first to "quapolynomialsThese illustratethe conceptof splineinterpolationusing second-order dratic splines"havecontinuous first derivativesat the knotsAlthough quadratic splines are not of practicalinrportance, they servenicely to demonstrate generalapproach dethe for velopinghi gher-order splines The objectivein quadraticsplinesis to derivea secoud-order polynomialfor each interval betweendata pointsThe polynonial for each interval can be represented generally as s i ( r ) : a i t b t Q - x i ) * c ; 1 x- r i ) 2 (165)

When comparing two different time values, it is easier to compare epoch calculated times (that is, the time values in seconds) and then extract the information accordingly For example, to calculate the number of days, hours, minutes, and seconds between dates:

rical enlargement of the pons, have a poorer prognosis than the focal or nodular tumors, which tend to occur in the dorsal brainstem and often protrude in an exophytic manner In a few instances of diffuse brainstem glioma, surgical exploration is necessary to establish the diagnosis (inspection and possibly biopsy) However, the histologic characteristics of a minute biopsy specimen of the tumor are not particularly helpful in determining prognosis or treatment and the general practice is to avoid surgery unless the tumor exhibits unusual clinical behavior or does not conform to the typical MRI appearance of the diffuse type Treatment The treatment is radiation, and if increased intracranial pressure develops as a result of hydrocephalus, ventricular shunting of CSF becomes necessary Adjuvant chemotherapy has not been helpful (Kornblith et al) A series of 16 patients treated by Pollack and colleagues emphasizes the fact that the focal and exophytic brainstem tumors are almost all low-grade astrocytomas; these tumors, in contrast to the more diffuse type, usually respond well to partial resection and permit long-term survival because they recur only slowly and do not undergo malignant transformation Gangliocytomas or mixed astrogangliocytomas are rare imitators of nodular glioma in the brainstem The rarer cystic glioma of the brainstem (Fig 31-19), a pilocytic tumor like its counterpart in the cerebellum, is treated by resection of the mural nodule and, as mentioned earlier, has an excellent prognosis Landol et al emphasized the longer survival in adults with pontine glioma (median 54 months) as compared to children Most of the patients with pontine tumors with which we are familiar proved to have malignant gliomas Glioma of the Optic Nerves and Chiasm This tumor, like the brainstem glioma, occurs most frequently during childhood and adolescence In 85 percent of cases, it appears before the age of 15 years (average 35 years), and it is twice as frequent in girls as in boys (see Cogan) The initial symptoms are dimness of vision with constricted elds, followed by bilateral eld defects of homony-.

($secdiff,$mindiff,$hourdiff,$ydaydiff) = (gmtime($newtime-$oldtime))[02,7]

wherethe notationis as in Fig 163For n datapoints (i : 1,2, , n), therearen - 1 (the intervals and,consequently, - l) unknownconstants d's b's, andc's)to evaluate 3(n Therefore equations conditions required evaluate unknowns or are 3rr to the These canbe developed fbllows: as l The function must passthrough irll the pointsThis is called a continuityconditionIt mathematically can be expressed its fi : ai I b,(t;- xi) * c;(ri - x;)l which sinrplifies to ai : Ji (166)

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The $secdiff and other variables now contain the corresponding time-value differences between $newtime and $oldtime You should use gmtime not localtime when comparing time values This is because localtime takes into account the local time zone, and, depending on the operating system you are using, any daylight saving time (DST) too The gmtime function will always return the Greenwich Mean Time (GMT), which is not affected by time zones or DST effects