62 SCIENTIFIC AMERICAN NOVEMBER 2006 COPYRIGHT 2006 SCIENTIFIC AMERICAN, INC. SPECIAL SECTION: NEUROSCIENCE BROKEN A THEORY MIRRORS OF AUTISM Studies of the mirror neuron system may reveal clues to the causes of autism and help researchers develop new ways to diagnose and treat the disorder By Vilayanur S. Ramachandran and Lindsay M. Oberman

t first glance you might not no- order, which afflicts about 0.5 percent of tice anything odd on meeting a American children. Neither researcher young boy with autism. But if had any knowledge of the other’s work, you try to talk to him, it will and yet by an uncanny coincidence each ) quickly become obvious that gave the syndrome the same name: autism, Asomething is seriously wrong. He may not which derives from the Greek word autos, make eye contact with you; instead he may meaning “self.” The name is apt, because avoid your gaze and fidget, rock his body the most conspicuous feature of the disor- photoillustration to and fro, or bang his head against the der is a withdrawal from social interac- wall. More disconcerting, he may not be tion. More recently, doctors have adopted able to conduct anything remotely resem- the term “autism spectrum disorder” to bling a normal conversation. Even though make it clear that the illness has many re- he can experience emotions such as fear, lated variants that range widely in severity

); JEN CHRISTIANSEN ( rage and pleasure, he may lack genuine but share some characteristic symptoms. empathy for other people and be oblivious Ever since autism was identified, re- to subtle social cues that most children searchers have struggled to determine photograph would pick up effortlessly. what causes it. Scientists know that sus- In the 1940s two physicians—Ameri- ceptibility to autism is inherited, although CHILDREN WITH AUTISM may struggle with social interaction can psychiatrist Leo Kanner and Austrian environmental risk factors also seem to because their mirror neuron systems pediatrician Hans Asperger—indepen- play a role [see “The Early Origins of Au-

CARY WOLINSKY ( are not functioning properly. dently discovered this developmental dis- tism,” by Patricia M. Rodier; Scientific

www.sciam.com SCIENTIFIC AMERICAN 63 COPYRIGHT 2006 SCIENTIFIC AMERICAN, INC. American, February 2000]. Starting in ings. Equally puzzling is the fact that they Frith of University College London and the late 1990s, investigators in our labo- frequently show an extreme aversion to Simon Baron-Cohen of the University of ratory at the University of California, certain sounds that, for no obvious rea- Cambridge, who posit that the main ab- San Diego, set out to explore whether son, set off alarm bells in their minds. normality in autism is a deficit in the there was a connection between autism The theories that have been proposed ability to construct a “theory of other and a newly discovered class of nerve to explain autism can be divided into two minds.” Frith and Baron-Cohen argue cells in the brain called mirror neurons. groups: anatomical and psychological. that specialized neural circuitry in the Because these neurons appeared to be (Researchers have rejected a third group brain allows us to create sophisticated involved in abilities such as empathy and of theories—such as the “refrigerator hypotheses about the inner workings of the perception of another individual’s in- mother” hypothesis—that blame the dis- other people’s minds. These hypotheses, tentions, it seemed logical to hypothesize order on poor upbringing.) Eric Cour- in turn, enable us to make useful predic- that a dysfunction of the mirror neuron chesne of U.C.S.D. and other anatomists tions about others’ behavior. Frith and system could result in some of the symp- have shown elegantly that children with Baron-Cohen are obviously on the right toms of autism. Over the past decade, autism have characteristic abnormalities track, but their theory does not provide several studies have provided evidence in the cerebellum, the brain structure re- a complete explanation for the constel- for this theory. Further investigations of sponsible for coordinating complex vol- lation of seemingly unrelated symptoms of autism. Indeed, saying that people with autism cannot interact socially be- Mirror neurons appear to be cause they lack a “theory of other performing precisely the same functions minds” does not go very far beyond re- stating the symptoms. What researchers that are disrupted in autism. need to identify are the brain mecha- nisms whose known functions match those that are disrupted in autism. mirror neurons may explain how autism untary muscle movements. Although One clue comes from the work of arises, and in the process physicians may these observations must be taken into ac- Giacomo Rizzolatti and his colleagues at develop better ways to diagnose and suc- count in any final explanation of autism, the University of Parma in Italy, who in cessfully treat the disorder. it would be premature to conclude that the 1990s studied neural activity in the damage to the cerebellum is the sole brains of macaque monkeys while the Explaining the Symptoms cause of the disorder. Cerebellar damage animals were performing goal-directed although the chief diagnostic inflicted by a stroke in a child usually actions [see “Mirrors in the Mind,” by signs of autism are social isolation, lack produces tremors, swaying gait and ab- Giacomo Rizzolatti, Leonardo Fogassi of eye contact, poor language capacity normal eye movements—symptoms rare- and Vittorio Gallese, on page 54]. Re- and absence of empathy, other less well ly seen in autism. Conversely, one does searchers have known for decades that known symptoms are commonly evi- not see any of the symptoms typical of certain neurons in the premotor cortex— dent. Many people with autism have autism in patients with cerebellar dis- part of the brain’s frontal lobe—are in- problems understanding metaphors, ease. It is possible that the cerebellar volved in controlling voluntary move- sometimes interpreting them literally. changes observed in children with autism ments. For instance, one neuron will fire They also have difficulty miming other may be unrelated side effects of abnor- when the monkey reaches for a peanut, people’s actions. Often they display an mal genes whose other effects are the another will fire when the animal pulls a eccentric preoccupation with trifles yet true causes of the disorder. lever, and so on. These brain cells are ignore important aspects of their envi- Perhaps the most ingenious of the often referred to as motor command ronment, especially their social surround- psychological theories is that of Uta neurons. (Bear in mind that the neuron whose activity is recorded does not con- Overview/Mirror Neurons and Autism trol the arm by itself; it is part of a circuit that can be monitored by observing the ■ Because mirror neurons appear to be involved in social interaction, signals in the constituent neurons.) dysfunctions of this neural system could explain some of the primary What surprised Rizzolatti and his co- symptoms of autism, including isolation and absence of empathy. workers was that a subset of the motor ■ Studies of people with autism show a lack of mirror neuron activity in several command neurons also fired when the regions of the brain. Researchers speculate that treatments designed to monkey watched another monkey or a restore this activity could alleviate some of autism’s symptoms. researcher perform the same action. For ■ A complementary hypothesis, the salience landscape theory, could account example, a neuron involved in control- for secondary symptoms of autism such as hypersensitivity. ling the reach-for-the-peanut action fired when the monkey saw one of his fellows

64 SCIENTIFIC AMERICAN NOVEMBER 2006 COPYRIGHT 2006 SCIENTIFIC AMERICAN, INC. making that movement. Brain-imaging cortex of awake human subjects, investi- also requires a remapping of sorts be- techniques subsequently showed that gators found that certain neurons that tween brain areas. To imitate the moth- these so-called mirror neurons also exist typically fi re in response to pain also fi red er’s or father’s words, the child’s brain in the corresponding regions of the hu- when the person saw someone else in must transform auditory signals in the man cortex. These observations implied pain. Mirror neurons may also be in- hearing centers of the brain’s temporal that mirror neurons—or, more accurate- volved in imitation, an ability that ap- lobes into verbal output from the motor ly, the networks they are part of—not pears to exist in rudimentary form in the cortex. Whether mirror neurons are only send motor commands but also en- great apes but is most pronounced in hu- directly involved in this skill is not known, able both monkeys and humans to deter- mans. The propensity to imitate must be but clearly some analogous process must mine the intentions of other individuals at least partly innate: Andrew Meltzoff of be going on. Last, mirror neurons may by mentally simulating their actions. In the University of Washington has shown enable humans to see them selves as others monkeys, the role of the neurons may be that if you stick your tongue out at a new- see them, which may be an essential abil- limited to predicting simple goal-direct- born baby, the infant will do the same. ity for self-awareness and introspection. ed actions, but in humans the mirror Because the baby cannot see its own neuron system may have evolved the abil- tongue, it cannot use visual feedback and Suppressing Mu Waves ity to interpret more complex intentions. error correction to learn the skill. Instead what has all this to do with au- Later research showed that mirror there must be a hardwired mechanism in tism? In the late 1990s our group at neurons are located in other parts of the the child’s brain for mapping the mother’s U.C.S.D. noted that mirror neurons ap- human brain, such as the cingulate and visual appearance—whether it be a pear to be performing precisely the same insular cortices, and that they may play a tongue sticking out or a smile—onto the functions that seem to be disrupted in role in empathetic emotional responses. motor command neurons. autism. If the mirror neuron system is While studying the anterior cingulate Language development in childhood indeed involved in the interpretation of complex intentions, then a breakdown THE ANATOMY OF AUTISM of this neural circuitry could explain the most striking defi cit in people with au- People with autism show reduced mirror neuron activity in the inferior frontal tism, their lack of social skills. The other gyrus, a part of the brain’s premotor cortex, perhaps explaining their inability to cardinal signs of the disorder—absence assess the intentions of others. Dysfunctions of mirror neurons in the insula and of empathy, language defi cits, poor imi- anterior cingulate cortex may cause related symptoms, such as the absence of tation, and so on—are also the kinds of empathy, and defi cits in the angular gyrus may result in language diffi culties. things you would expect to see if mirror People with autism also have structural changes in the cerebellum and brain stem. neurons were dysfunctional. Andrew Whitten’s group at the University of St. ANTERIOR CINGULATE CORTEX Regulation of empathy and Andrews in Scotland made this proposal INFERIOR FRONTAL GYRUS other emotions Guidance of movement at about the same time we did, but the and assessment fi rst experimental evidence for the hy- of intentions ANGULAR GYRUS Comprehension of pothesis came from our lab, working in word meanings collaboration with Eric L. Altschuler and combining sensory and Jaime A. Pineda of U.C.S.D. information To demonstrate mirror neuron dys- function in children with autism, we needed to fi nd a way to monitor the ac- tivity of their nerve cells without putting electrodes in their brains (as Rizzolatti and his colleagues did with their mon- keys). We realized that we could do so using an electroencephalogram (EEG) measurement of the children’s brain INSULA Involved in pain waves. For more than half a century, sci- and disgust entists have known that an EEG compo- responses nent called the mu wave is blocked any- time a person makes a voluntary muscle Brain stem Cerebellum movement, such as opening and closing one’s hands. Interestingly, this compo- nent is also blocked when a person

LUCY READING-IKKANDA watches someone else perform the same

www.sciam.com SCIENTIFIC AMERICAN 65 COPYRIGHT 2006 SCIENTIFIC AMERICAN, INC. FOCUSING ON MU WAVES To study the mirror neuron system in people with autism, of the brain’s activity. (Mu waves range from eight to 13 hertz.) researchers relied on the observation that the fi ring of Investigators monitored the mu waves of children with autism neurons in the premotor cortex suppresses the mu wave, a and control subjects as they made voluntary muscle component of the electroencephalogram (EEG) measurement movements and then watched the same actions on video.

TAKING ACTION Motor command neurons fi re whenever a person makes a voluntary muscle movement. Researchers asked all the subjects to open and close their right hands. In the children with autism and the control subjects, this action suppressed the amplitude of their mu waves, as expected.

Before muscle movement

Opening and closing hand tude i During muscle movement pl Am ve lati Re

0 10 20 30 40 50 Frequency of Brain Waves (hertz)

SIMULATING ACTION

Children with autism

tude Video of hand i

pl Control subjects opening and closing Am ve lati Re

0 10 20 30 40 50 Frequency of Brain Waves (hertz)

Mirror neurons in the premotor cortex also fi re when a person observes someone else performing an action. The investigators took EEG measurements of brain activity while the subjects observed a video of a hand opening and closing. The mu waves of the control subjects plummeted (red), but those of the children with autism showed no suppression (blue). This fi nding suggests that the mirror neuron systems of the children with autism are defi cient. LUCY READING-IKKANDA

66 SCIENTIFIC AMERICAN NOVEMBER 2006 COPYRIGHT 2006 SCIENTIFIC AMERICAN, INC. action. One of us (Ramachandran) and prefrontal cortices of individuals with inator from superficially dissimilar enti- Altschuler suggested that mu-wave sup- autism. And Hugo Théoret of the Uni- ties. Consider the bouba/kiki effect, pression might provide a simple, nonin- versity of Montreal and his co-workers which was discovered by German-Amer- vasive probe for monitoring mirror neu- used transcranial magnetic stimulation, ican psychologist Wolfgang Köhler more ron activity. a technique that induces electric cur- than 60 years ago. In this test, a re- We decided to focus our first experi- rents in the motor cortex to generate searcher displays two crudely drawn ments on a high-functioning child with muscle movements, to study mirror neu- shapes, one jagged and one curvy, to an autism—that is, a child without severe ron activity in subjects with autism. In audience and asks, “Which of these cognitive impairments. (Very young, low- the control subjects, induced hand shapes is bouba and which is kiki?” No functioning children did not participate movements became more pronounced matter what languages the respondents in this study because we wanted to con- when the subjects watched videos of the speak, 98 percent will pick the curvy firm that any differences we found were same movements; this effect was much shape as bouba and the jagged one as not a result of problems in attention, un- weaker in the subjects with autism. kiki. This result suggests that the human derstanding instructions or the general Taken together, these findings pro- brain is somehow able to extract ab- effects of mental retardation.) The EEG showed that the child had an observable mu wave that was suppressed when he These findings provide compelling evidence made a simple, voluntary movement, just as in normal children. But when the child that people with autism have watched someone else perform the ac- dysfunctional mirror neuron systems. tion, the suppression did not occur. We concluded that the child’s motor com- mand system was intact but that his mir- vide compelling evidence that people with stract properties from the shapes and ror neuron system was deficient. This autism have dysfunctional mirror neuron sounds—for example, the property of observation, which we presented at the systems. Scientists do not yet know which jaggedness embodied in both the pointy annual meeting of the Society for Neuro- genetic and environmental risk factors drawing and the harsh sound of kiki. We science in 2000, provided a striking vin- can prevent the development of mirror conjectured that this type of cross-do- dication of our hypothesis. neurons or alter their function, but many main mapping is analogous to metaphors One has to be careful, however, of research groups are now actively pursu- and must surely involve neural circuits generalizing from a single case, so our ing the hypothesis because it predicts similar to those in the mirror neuron sys- lab group later conducted a more system- symptoms that are unique to autism. In tem. Consistent with this speculation, we atic series of experiments in 10 high- addition to explaining the primary signs discovered that children with autism per- functioning individuals with autism spec- of autism, deficiencies in the mirror neu- form poorly at the bouba/kiki test, pair- trum disorder and 10 age- and gender- ron system can also account for some of ing the shapes and sounds incorrectly. matched control subjects. We saw the the less well known symptoms. For in- But which part of the human brain is expected suppression of mu waves when stance, researchers have long known that involved in this skill? The angular gyrus, the control subjects moved their hands children with autism often have problems which sits at the crossroads of the brain’s and watched videos of a moving hand, interpreting proverbs and metaphors. vision, hearing and touch centers, but the EEGs of the subjects with autism When we told one of our subjects to “get seemed to be a likely candidate—not showed mu suppression only when they a grip on yourself,” he took the message only because of its strategic location but moved their own hands. literally and started grabbing his own because nerve cells with mirror neuron– Other researchers have confirmed body. Though seen in only a subset of like properties have been identified there. our results using different techniques children with autism, this difficulty with When we studied nonautistic subjects for monitoring neural activity. A group metaphors cries out for an explanation. with damage to this area of the brain, we led by Riitta Hari of the Helsinki Uni- Understanding metaphors requires found that many of them fail the bouba/ versity of Technology found mirror neu- the ability to extract a common denom- kiki test and have a disproportionate dif- ron deficits in children with autism by employing magnetoencephalography, VILAYANUR S. RAMACHANDRAN and LINDSAY M. OBERMAN have investigated the links which measures the magnetic fields pro- between autism and the mirror neuron system at the Center for Brain and Cognition at duced by electric currents in the brain. the University of California, San Diego. Ramachandran, director of the center, earned his More recently, Mirella Dapretto of the Ph.D. in neuroscience from the University of Cambridge. A renowned expert on brain University of California, Los Angeles, abnormalities, he has also studied the phenomena of phantom limbs and synesthesia, and her colleagues used functional mag- for which he won the 2005 Henry Dale Prize and a lifetime fellowship from the Royal In- THE AUTHORS netic resonance imaging to show a re- stitution of Great Britain. Oberman is a graduate student in Ramachandran’s laboratory duction in mirror neuron activity in the at U.C.S.D., joining the group in 2002.

www.sciam.com SCIENTIFIC AMERICAN 67 COPYRIGHT 2006 SCIENTIFIC AMERICAN, INC. fi culty understanding metaphors, just THE SALIENCE LANDSCAPE THEORY like people with autism. These results suggest that cross-domain mapping may To account for some of the secondary symptoms of autism—hypersensitivity, have originally developed to aid primates avoidance of eye contact, aversion to certain sounds, and so on—researchers in complex motor tasks such as grasping have developed the salience landscape theory. In a typical child, sensory tree branches (which requires the rapid information is relayed to the amygdala, the gateway to the emotion-regulating assimilation of visual, auditory and touch limbic system. Using input from stored knowledge, the amygdala determines how the child should respond emotionally to each stimulus, creating a salience information) but eventually evolved into landscape of the child’s environment. In children with autism, though, the an ability to create metaphors. Mirror connections between the sensory areas and the amygdala may be altered, neurons allowed humans to reach for the resulting in extreme emotional responses to trivial events and objects. stars, instead of mere peanuts. TYPICAL CHILD CHILD WITH AUTISM Can the Mirrors Be Repaired? Amygdala the discovery of mirror neuron de- fi ciencies in people with autism opens Visual 1 Altered up new approaches to diagnosing and cortex connection treating the disorder. For example, phy- 1 Sensory between visual information cortex and sicians could use the lack of mu-wave is relayed to amygdala amygdala distorts child’s suppression (or perhaps the failure to response mimic a mother sticking out her tongue) 2 Child exhibits as a diagnostic tool to identify children appropriate emotional 2 Amygdala triggers with autism in early infancy, so that the response autonomous currently available behavioral therapies nervous system, raising heart rate can be started as quickly as possible. Timely intervention is critical; the be- havioral therapies are much less effec- Heart Heart 3 Child looks tive if begun after autism’s main symp- pumping pumping away to reduce distress toms appear (typically between ages normally fast two and four). An even more intriguing possibility would be to use biofeedback to treat au- tism or at least alleviate its symptoms. Doctors could monitor the mu waves of a child with autism and display them on a screen in front of the patient. If the child’s mirror neuron functions are dor- mant rather than completely lost, it may be possible for him or her to revive this ability by learning—through trial and er- in emotional responses. According to Such treatments, however, may offer ror and visual feedback—how to suppress this hypothesis, the partial depletion of only partial relief, because other symp- the mu waves on the screen. Our col- such chemicals could explain the lack of toms of autism cannot be explained by league Pineda is pursuing this approach, emotional empathy seen in autism, and the mirror neuron hypothesis—for ex- and his preliminary results look promis- therefore researchers should look for ample, repetitive motions such as rock- ing. Such therapies, though, should sup- compounds that stimulate the release of ing to and fro, avoidance of eye contact, plement rather than replace the tradi- the neuromodulators or mimic their hypersensitivity, and aversion to certain tional behavioral-training techniques. effects on mirror neurons. One candi- sounds. In an attempt to determine how Another novel therapeutic approach date for investigation is MDMA, better these secondary symptoms might arise, might rely on correcting chemical im- known as ecstasy, which has been shown our lab group (in collaboration with balances that disable the mirror neurons to foster emotional closeness and com- William Hirstein of Elmhurst College in individuals with autism. Our group munication. It is possible that research- and Portia Iversen of Cure Autism Now, (including students Mikhi Horvath and ers may be able to modify the compound a nonprofi t foundation based in Los An- Mary Vertinsky) has suggested that spe- to develop a safe, effective treatment geles) has developed what we call the cialized neuromodulators may enhance that could alleviate at least some of au- salience landscape theory.

the activity of mirror neurons involved tism’s symptoms. When a person looks at the world, he LUCY READING-IKKANDA

68 SCIENTIFIC AMERICAN NOVEMBER 2006 COPYRIGHT 2006 SCIENTIFIC AMERICAN, INC. or she is confronted with an overwhelm- children with autism had a higher over- lated by the same neural pathways, per- ing amount of sensory information— all level of autonomic arousal. Although haps the former can mitigate the latter. sights, sounds, smells, and so on. After they became agitated when exposed to The salience landscape theory could being processed in the brain’s sensory trivial objects and events, they often ig- also provide an explanation for the re- areas, the information is relayed to the nored stimuli that triggered expected petitive motions and head banging seen amygdala, which acts as a portal to the responses in the control group. in children with autism: this behavior, emotion-regulating limbic system. Using But how could a child’s salience land- called self-stimulation, may somehow input from the individual’s stored knowl- scape become so distorted? Investigators damp the child’s autonomic storms. Our edge, the amygdala determines how the have found that nearly one third of chil- studies found that self-stimulation not person should respond emotionally—for dren with autism have had temporal lobe only had a calming effect but also led to example, with fear (at the sight of a bur- epilepsy in infancy, and the proportion a measurable reduction in skin conduc- glar), lust (on seeing a lover) or indiffer- may be much higher given that many tance. This result suggests a possible ence (when facing something trivial). Messages cascade from the amygdala to the rest of the limbic system and eventu- If the child’s mirror neuron functions ally reach the autonomic nervous sys- are dormant rather than lost, tem, which prepares the body for action. If the person is confronting a burglar, for it may be possible to revive this ability. example, his heart rate will rise and his body will sweat to dissipate the heat from muscular exertion. The autonomic epileptic seizures go undetected. Caused symptomatic therapy for autism. Hir- arousal, in turn, feeds back into the by repeated random volleys of nerve im- stein is now developing a portable device brain, amplifying the emotional re- pulses traversing the limbic system, these that could monitor an autistic child’s skin sponse. Over time, the amygdala creates seizures could eventually scramble the conductance; when the device detects a salience landscape, a map that details connections between the visual cortex autonomic arousal, it could turn on an- the emotional significance of everything and the amygdala, indiscriminately en- other device, called a squeeze vest, that in the individual’s environment. hancing some links and diminishing provides a comforting pressure by gently Our group decided to explore the others. In adults, temporal lobe epilepsy tightening around the child’s body. possibility that children with autism have results in florid emotional disturbances Our two candidate theories for ex- a distorted salience landscape, perhaps but does not radically affect cognition; plaining the symptoms of autism—mir- because of altered connections between in infants, however, the seizures may ror neuron dysfunction and distorted the cortical areas that process sensory lead to a more profound disability. And, salience landscape—are not necessarily input and the amygdala or between the like autism, the risk of temporal lobe contradictory. It is possible that the limbic structures and the frontal lobes epilepsy in infancy appears to be influ- same event that distorts a child’s sa- that regulate the resulting behavior. As enced by both genetic and environmen- lience landscape—the scrambled con- a result of these abnormal connections, tal factors. Some genes, for example, nections between the limbic system and any trivial event or object could set off an could make a child more susceptible to the rest of the brain—also damages the extreme emotional response—an auto- viral infections, which could in turn pre- mirror neurons. Alternatively, the al- nomic storm—in the child’s mind. This dispose the child to seizures. tered limbic connections could be a side hypothesis would explain why children Our findings on autonomic respons- effect of the same genes that trigger the with autism tend to avoid eye contact es may help explain the old clinical ob- dysfunctions in the mirror neuron sys- and any other novel sensation that might servation that high fever sometimes tem- tem. Further experiments are needed to trigger an upheaval. The distorted per- porarily alleviates the symptoms of au- rigorously test these conjectures. The ceptions of emotional significance might tism. The autonomic nervous system is ultimate cause of autism remains to be also explain why many children with au- involved in controlling body tempera- discovered. In the meantime, our specu- tism become intensely preoccupied with ture; because fever and the emotional lations may provide a useful framework trifles such as train schedules while ex- upheavals of autism appear to be regu- for future research. pressing no interest at all in things that most children find fascinating. MORE TO EXPLORE We found some support for our hy- Autonomic Responses of Autistic Children to People and Objects. William Hirstein, Portia pothesis when we monitored autonomic Iversen and Vilayanur S. Ramachandran in Proceedings of the Royal Society of London B, Vol. 268, pages 1883–1888; 2001. responses in a group of 37 children with EEG Evidence for Mirror Neuron Dysfunction in Autism Spectrum Disorders. Lindsay M. Oberman, autism by measuring the increase in their Edward M. Hubbard, Joseph P. McCleery, Eric L. Altschuler, Jaime A. Pineda and Vilayanur S. skin conductance caused by sweating. In Ramachandran in Cognitive Brain Research, Vol. 24, pages 190–198; 2005. contrast with the control subjects, the A Brief Tour of Human Consciousness. New edition. Vilayanur S. Ramachandran. Pi Press, 2005.

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