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Use the construction in the proof of Theorem 1.45 to give

Introduction to the Theory of Computation | 3rd Edition | ISBN: 9781133187790 | Authors: Michael Sipser ISBN: 9781133187790 221

Solution for problem 1.8 Chapter 1

Introduction to the Theory of Computation | 3rd Edition

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Introduction to the Theory of Computation | 3rd Edition | ISBN: 9781133187790 | Authors: Michael Sipser

Introduction to the Theory of Computation | 3rd Edition

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Problem 1.8

Use the construction in the proof of Theorem 1.45 to give the state diagrams of NFAs recognizing the union of the languages described ina. Exercises 1.6a and 1.6b. b. Exercises 1.6c and 1.6f.

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Behavioral Neuroscience - Week 11 EXAMPLE QUESTION: Damage to the left lateral geniculate nucleus would lead to: A. Complete blindness B. Blindness in the right visual field C. Blindness in the Left Visual Field Answer: Blindness in the right visual field EXAMPLE QUESTION: Bilateral damage to the primary visual cortex would lead to D. Complete blindness E. Blindness in the right visual field F. Blindness in the Left Visual Field Answer: Complete blindness Cortical Representations - Area V1 - Ventral Stream - Dorsal stream Area V1 V1 organization = Retinotropic organization  Posterior part of V1 represents: central parts of visual field (most central = fovea)  More Anterior part of V1 represents: Peripheral parts of visual field o spatial representation is mapped onto V1 in an orderly fashion -V1 = Cortical magnification  A larger portion of cortex devoted to the fovea and macula DAMAGE  Damage to the most posterior part of the V1 means that you would lose vision only in the center of space  Damage in a peripheral area creates a notch of blindness on the right and left side of space Black dot = blind spot As you move along the blue arrow you are moving across different cortical columns so you are going through different types of cortical responses (3 types of receptive fields explained below) Layers: - The striate cortex consists of six principal layers arranged in bands parallel to the surface (I, II, III IV, etc…) V1 Receptve Fields **Neurons in the visual cortex do not simply respond to spots of light; they selectively respond to specific features of the visual world. To understand the visual world the visual cortex must combine information from several sources. 1. Binocularity: Refers to a neuron having a receptive field in each eye **EVERYTHING IS MONOCULAR in the visual process until you reach the Primary visual cortex (v1) a. Monocularity a cell in the right eye is NOT responsive to a stimulus in the left eye 2. Orientation selectivity : Responds preferentially to edges with a particular orientation  The cell has a region of space that it is receptive too where it can receive visual stimulus. But the cell discharges the most when the visual stimulus aligns at its preferred orientation in the receptive field 3. Direction selectivity: receptive fields respond preferentially to a stimulus with a particular orientation moving in a particular direction a. The visual stimulus has to move across the receptive field in a particular direction (ie. left to right = stimulated cell response, right to left = inhibited cell response) 4. Color selectivity: receptive fields respond preferentially to particular color. V1 color selective cells exhibit response properties much more complex than those in the retina or LGN Organization of Receptive fields = Columnar organization V1 Module (= A patch of cortex that is devoted to processing the features within a small region of the visual field (Image on the right) - Orientation Columns = Sections of V1 that contain neurons exhibiting similar orientation selectivity (i.e. Section I has cells with similar orientation selectivity which is different than those in section II) - Ocular dominance columns: portions of V1 that respond preferentially to input from one eye - Cytochrome oxidase blobs: portions of V1 that contain neurons with color selectivity Blindsight - Vision without awareness - Patients rendered cortically blind (V1 damage) may still be able to perform simple visual tasks even though they lack conscious vision - Damaged retinogeniculostriate pathway but intact retinocollicular pathway Dorsal V. Ventral Stream Ventral Stream Ventral Stream = “What” Pathway - The ventral stream involves the ventral flow of visual information from V1 to inferotemporal cortex - The ventral stream is involved in the identification of visual objects (“what” an object is) o This stream is how you elaborate simple features and combine them along the ventral stream to have a complex informational result Ventral Stream DAMAGE - Visual Agnosia: the inability to identify familiar objects visually o Object recognition is impaired with agnosia but dorsal stream functions remain intact. o Though unable to identify objects visually, patients may be able to recognize an object through other sensory modalities (e.g., touch) Important Areas - Lateral occipital Cortex(LOC): Object sensitive visual area that responds to a wide range of objects, figures, and shapes - Fusiform Face Area (FFA): Responds selectively to faces  damage can lead to prosopagnosia-an inability to identify faces - Parahippocampal Place Area (PPA): Responds selectively to visual scenes and backgrounds (beaches, forests, cities) Dorsal Stream Dorsal Stream = “Where” Pathway - Involved in the processing of spatial information (“where” objects are) - The dorsal stream involves the dorsal flow of visual information from V1 to posterior parietal cortex Damage - Akinetopsia: an inability to perceive motion - Optic Ataxia: –failure to generate visually guided movements o Example: A person would be unable to stick their hand through a hoop (they could tell you the orientation of that hoop but be unable to guide their hand through it) - Neglect Syndrome: Neurological disorder that occurs after damage to the posterior parietal labe o Typically the right posterior parietal is damaged  they would neglect the left side of space  Example: If they were to draw a clock they would probably draw only the right side of the clock (12->6)  Ignore the left side of space on a large and small/detailed scale (ex: in the clock example above maybe they would only draw the right portion of the 6) Important areas - Middle Temporal Area: Involved in the processing of motion o Damage can lead to Akinetopsia - Posterior Parietal Cortex (PPC): Consists of several subareas that represent space as it pertains to the orienting of attention, planning and compensation of eye movements, and visual control of limbs o All about representing space in some way and how you interact with that space o Damage can lead to optic ataxia or neglect syndrome Lesion Studies in monkeys: - Monkeys without the inferotemporal cortex cannot perform object identification tasks o Object identification task= be able to differentiate between different objects o = ventral stream is affected - Monkeys without the posterior parietal areas cannot perform a landmark task o Landmark task= Be able to space things at the appropriate distance from each other o = dorsal stream is affected The dorsal and ventral pathways contain a number of functionally distinct visual areas

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Chapter 1, Problem 1.8 is Solved
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Textbook: Introduction to the Theory of Computation
Edition: 3
Author: Michael Sipser
ISBN: 9781133187790

Introduction to the Theory of Computation was written by and is associated to the ISBN: 9781133187790. This textbook survival guide was created for the textbook: Introduction to the Theory of Computation, edition: 3. The answer to “Use the construction in the proof of Theorem 1.45 to give the state diagrams of NFAs recognizing the union of the languages described ina. Exercises 1.6a and 1.6b. b. Exercises 1.6c and 1.6f.” is broken down into a number of easy to follow steps, and 33 words. The full step-by-step solution to problem: 1.8 from chapter: 1 was answered by , our top Science solution expert on 01/05/18, 06:19PM. Since the solution to 1.8 from 1 chapter was answered, more than 1139 students have viewed the full step-by-step answer. This full solution covers the following key subjects: . This expansive textbook survival guide covers 11 chapters, and 401 solutions.

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Use the construction in the proof of Theorem 1.45 to give