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The rst case incurs a cost of 1 for this particular column, and it remains to align x[1 i 1] with y[1 j] But this is exactly the subproblem E(i 1, j)! We seem to be getting somewhere In the second case, also with cost 1, we still need to align x[1 i] with y[1 j 1] This is again another subproblem, E(i, j 1) And in the nal case, which either costs 1 (if x[i] = y[j]) or 0 (if x[i] = y[j]), what s left is the subproblem E(i 1, j 1) In short, we have expressed E(i, j) in terms of three smaller subproblems E(i 1, j), E(i, j 1), E(i 1, j 1) We have no idea which of them is the right one, so we need to try them all and pick the best: E(i, j) = min{1 + E(i 1, j), 1 + E(i, j 1), diff(i, j) + E(i 1, j 1)} where for convenience diff(i, j) is de ned to be 0 if x[i] = y[j] and 1 otherwise For instance, in computing the edit distance between EXPONENTIAL and POLYNOMIAL, subproblem E(4, 3) corresponds to the pre xes EXPO and POL The rightmost column of their best alignment must be one of the following: O or L or O L

In most autopsied cases of primary generalized epilepsy of the grand mal and absence types, the CNS has been said to be grossly and microscopically normal However, it is unlikely that the brains in these cases were examined completely at least there is not a single case that has been subjected to whole-brain serial sectioning in a search for disorders of neural migration and old scars Not surprisingly, there are also no visible lesions in the seizure states complicating drug intoxication and withdrawal, transient hyperand hyponatremia, and hyper- and hypoglycemia, which presumably represent derangements at the cellular level In contrast, most of the so-called secondary epilepsies have de nable lesions These include zones of neuronal loss and gliosis (scars) or other signs of tissue loss such as a porencephaly, heterotopia, dysgenetic cortex, hamartoma, vascular malformation, and tumor The frequency of these lesions is not fully known Certainly the focal epilepsies are associated with the highest incidence of structural abnormalities, although in certain cases no morphologic change is visible In several series of cases of temporal lobe excisions, such as that of Falconer, a speci c pattern of neuronal loss with gliosis (sclerosis) in the hippocampal and amygdaloid region was found in the majority, and this abnormality is being increasingly recognized with MRI, as noted below Vascular malformations, hamartomas, and low-grade astrocytomas were less frequent; in a small number, no abnormalities could be found The widespread use of CT and MRI represents an important surrogate approach to the pathologic study of epilepsy More than 25 years ago, Gastaut and Gastaut reported that in primary grand mal and absence epilepsies, CT abnormalities were found in approximately 10 percent of cases, whereas in the Lennox-Gastaut syndrome, the West syndrome, and partial complex epilepsies it was found in 52, 77, and 63 percent, respectively Atrophy, calci cation, and malformations were the most frequent changes MRI and particularly the FLAIR images have proved to be a particularly sensitive means of detecting epileptogenic lesions of the medialbasal portion of the temporal lobes (mesial temporal sclerosis; Fig 16-2) Repeatedly, patients are observed in whom MRI disclosed a cortical or subcortical developmental malformation such as a cortical heterotopia or another surgically treatable lesion of the temporal lobe, even after CT scanning had failed to do so More subtle epileptogenic foci may be demonstrated by positron emission tomography (PET) or by interictal single-photon emission computed tomography (SPECT) Ictal SPECT, which shows hyperperfusion of the seizure focus, is a more demanding but also more sensitive and speci c procedure.

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Figure 45-5 The shaded area represents the zone of the action potential, which is negative to all other points on the ber surface It is shown at three points in its course (from left to right) along the ber At each point, the correspondingly lettered portion of the triphasic muscle action potential displayed on the display screen re ects the potential difference between the active (vertical arrow) and reference (Ref) electrodes Polarity in this and subsequent gures is negative upward as depicted The time calibration is on the screen

becomes relatively positive again (at C) It then returns to its resting isopotential position The net result is a triphasic action potential, as in Fig 45-5 This con guration is typical of the ring of a single ber The electrical activity of various muscles is recorded both at rest and during active contraction by the patient As indicated earlier, muscle bers do not normally discharge until activated together in motor unit activity This involves the almost simultaneous contraction of all the muscle bers innervated by a single anterior horn cell Although the typical con guration of a motor unit potential (MUP) is triphasic, up to 10 percent of normal MUPs consist

Thus, E(4, 3) = min{1 + E(3, 3), 1 + E(4, 2), 1 + E(3, 2)} The answers to all the subproblems E(i, j) form a two-dimensional table, as in Figure 64 In what order should these subproblems be solved Any order is ne, as long as E(i 1, j), E(i, j 1), and E(i 1, j 1) are handled before E(i, j) For instance, we could ll in the table one row at a time, from top row to bottom row, and moving left to right across each row Or alternatively, we could ll it in column by column Both methods would ensure that by the time we get around to computing a particular table entry, all the other entries we need are already lled in With both the subproblems and the ordering speci ed, we are almost done There just remain the base cases of the dynamic programming, the very smallest subproblems In the present situation, these are E(0, ) and E( , 0), both of which are easily solved E(0, j) is the edit distance between the 0-length pre x of x, namely the empty string, and the rst j letters of y: clearly, j And similarly, E(i, 0) = i At this point, the algorithm for edit distance basically writes itself 162

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