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500 efferent bers, which arise from the superior olivary nuclei (80 percent from the contralateral nucleus and 20 percent from the ipsilateral one) and synapse with the afferent neurons from the hair cells (Rasmussen) The function of this efferent pathway is not clear It is thought to play some part in the auditory processing generated in the ear itself, possibly to enhance the sharpness of sound perception by some feedback mechanism (Kemp) The eighth nerve also contains adrenergic postganglionic bers that are derived from the cervical autonomic chain and innervate the cochlea and labyrinth The vestibular division of the eighth nerve arises from cells in the vestibular, or Scarpa s, ganglion, which is situated in the internal auditory meatus This ganglion is also composed of bipolar cells, the peripheral processes of which terminate in hair cells of the specialized sensory epithelium of the labyrinth (semicircular canals, saccule, and utricle) The sensory epithelium is located on hillocks (cristae) in the dilated openings or ampullae of the semicircular canals, where they are called the cristae ampullaris, and in the utricle and saccule, where they are called maculae acusticae The hair cells of the maculae are covered by the otolithic membrane, or otolith, which is composed of calcium carbonate crystals embedded in a gelatinous matrix The sensory cells of the cristae are covered by a sail-shaped gelatinous mass called a cupula (Fig 15-1) The labyrinthine semicircular canals transduce angular movements of the head, and the otoliths transduce linear movement The central bers from the cells of the spiral and vestibular ganglia are united in a common trunk, which enters the cranial cavity through the internal auditory meatus (accompanied by the facial and intermediate nerves) They traverse the cerebellopontine angle and enter the brainstem at the junction of the pons and medulla Here the cochlear and vestibular bers become separated The cochlear bers bifurcate and terminate almost at once in the dorsal and ventral cochlear nuclei The bers from each cochlear nucleus pursue separate crossing and ascending pathways; they pass to both inferior colliculi (mainly to the opposite side) via the lateral lemnisci Secondary acoustic bers project via the trapezoid body and lateral lemniscus to the medial geniculate bodies, a special component of the thalamic sensory system (Fig 15-2) Some bers terminate in the trapezoid body and superior olivary complex and subserve such re ex functions as auditory attention, sound localization, auditory startle, and oculopostural orientation to sound Both excitatory and inhibitory neurons are located at every level of these pathways At all levels there are strong commissural connections through which auditory signals come to be represented bilaterally in the cerebrum From the medial geniculate bodies, bers project to the cortex via the auditory radiations relatively compact bundles that course ventrolaterally through the posterior parts of the putamens before dispersing and ending in the transverse gyri of Heschl and other auditory cortical areas (Tanaka et al) The auditory cortical eld comprises the superior temporal gyrus and the upper bank of the sylvian ssure (Brodmann area 41; see page 387), or primary auditory cortex, and the surrounding secondary and tertiary cortices in the adjacent temporal lobe The.

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(a) Run Prim s algorithm; whenever there is a choice of nodes, always use alphabetic ordering (eg, start from node A) Draw a table showing the intermediate values of the cost array (b) Run Kruskal s algorithm on the same graph Show how the disjoint-sets data structure looks at every intermediate stage (including the structure of the directed trees), assuming path compression is used 53 Design a linear-time algorithm for the following task Input: A connected, undirected graph G Question: Is there an edge you can remove from G while still leaving G connected 54 Show that if an undirected graph with n vertices has k connected components, then it has at least n k edges Can you reduce the running time of your algorithm to O(|V |)

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Cochlear nerve Lateral Cochlea semicircular canal Round window Tympanic Posterior membrane Eustachean tube Vestibule semicircular External auditory canal canal Posterior ampulla A B Direction of head motion Endolymphatic space Otoliths Hair cell Supporting cell

MACULA Cochlear nerve Basilar membrane Semicircular canal CRISTA AMPULLA C D Figure 15-1 The auditory and vestibular systems A The right ear, viewed from the front, showing the external ear and auditory canal, the middle ear and its ossicles, and the inner ear B The main parts of the right inner ear, viewed from the front The perilymph is located between the wall of the bony labyrinth and the membranous labyrinth In the cochlea, the perilymphatic space takes the form of two coiled tubes the scala vestibuli and scala tympani The endolymph is located within the membranous labyrinth, which includes the three semicircular canals, utricle, and saccule C The organ of Corti This is the end organ of hearing; it consists of a single row of inner hair cells and three rows of outer hair cells The stereocilia of the hair cells are embedded in the tectorial membrane D Diagram of a crista ampulla, the specialized sensory epithelium of a semicircular canal The crista senses the displacement of endolymph during head rotation The direction of head rotation is indicated by the large arrow, and endolymph ow by the small arrow The macula is the locus of the sensory epithelium in the utricle and saccule Note that the tips of the hair cells are in contact with the otoliths (calcareous material), which are embedded in a gelatinous mass called the cupula

Side Effects of Chemical Peels Management Often resolves spontaneously in several months Topical hydroquinone bleaching creams Mid-level chemical peel if persistent Often permanent Extraction via 19-gauge needle and comedone extractor Topical retinoids following re-epithelialization Usually resolves spontaneously in 1 2 wks May use oral antibiotics, but topical acne therapy should be deferred until re-epithelialization is complete Rule out infection and contact dermatitis Erythema and induration may indicate impending scarring and should be treated as below Topical, intralesional, or oral corticosteroids; pulsed dye laser; intralesional 5- uorouracil, occlusive dressings, massage Obtain cultures and start empiric antibiotics Comment More common after super cial peels in darker phototypes (Fitzpatrick III VI) More common after deep peels Related to occlusive ointments Avoid aggressive extraction to prevent scarring Related to occlusive ointments

latter are of particular importance in the interpretation of sound (Celesia) Bilateral temporal lobe lesions involving the geniculocortical fasciculi result in cortical deafness, although such lesions are rare; unilateral cortical lesions do not affect hearing, but defects in function such dichotic listening can be detected by specialized tests At several levels of these ascending ber systems, there is feedback to lower structures The vestibular bers of the eighth nerve terminate in the four vestibular nuclei: superior (Bechterew), lateral (Deiters), medial (triangular, or Schwalbe), and inferior (spinal, or descending) In addition, some of the bers from the semicircular canals project directly to the cerebellum via the juxtarestiform body and terminate in the occulonodular lobe and adjacent vermian cortex (these structures are therefore called the vestibulocerebellum, as noted in Chap 5, on the cerebellum) Efferent bers from this portion of the cerebellar cortex, in turn, project ipsilaterally to the vestibular nuclei and to the fastigial nucleus; bers from the fastigial nucleus project back to the

55 Consider an undirected graph G = (V, E) with nonnegative edge weights we 0 Suppose that you have computed a minimum spanning tree of G, and that you have also computed shortest paths to all nodes from a particular node s V Now suppose each edge weight is increased by 1: the new weights are we = we + 1 (a) Does the minimum spanning tree change Give an example where it changes or prove it cannot change (b) Do the shortest paths change Give an example where they change or prove they cannot change 56 Let G = (V, E) be an undirected graph Prove that if all its edge weights are distinct, then it has a unique minimum spanning tree

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