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They are formidable instruments, each with a The soundboards are spruce, and Guatemalan rosewood is used for the backs, sides, necks, and headplates. Klein got the idea for the design—segmented between strings 1—3 and 4—6, and much larger on the bass side—from Michael Kasha, a biochemist and guitar enthusiast who had a unique understanding of how guitars work. The bridge is engineered to help each string best transfer energy to the soundboard, with six individual ivory saddle pieces rather than a single component, allowing for precise adjustment of string height and intonation. Home News.

Klein l model

Klein l model

Klein l model

Klein l model

Of course, Occam's razor is a guiding principle, not a metaphysical mandate. Does the framing of patient cost-sharing incentives matter? This happened as follows. The model was estimated with the limited information midel likelihood method only, but alternative ordinary least squares estimations Klein l model provided by Karl A. Home News. In other projects Wikimedia Commons. It is centered around some basic Matlab code for solving, simulating, and empirically analyzing a simple dynamic discrete choice model.

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The Klein disk K, in the picture is a gnomonic projection of the hyperboloid model Hy with as center the center of the hyperboloid O and the Pascha escorts london plane tangent to the nearest point of the hyperboloid. The Minkowski inner product is given by. Wall Street Journal. American Manufacturing. Mirrlees Herbert Scarf Amartya K. See also: Cayley—Klein metric. Leave this Klein l model blank. Linear Algebra and Geometry. Williams Harold A. Support Warranty. Tool Bags and Storage

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This article has two goals. First, I want to respond to concerns voiced by Ruby Since these concerns are not limited to Ruby, they provide an opportunity to address the issues she raises for a broad audience of neuroscientists. Second, and related to my first goal, I want to alert investigators who are familiar only with our neuropsychological investigations of self-knowledge to our earlier work on model construction.

A familiarity with this foundational research can help avert concerns and issues likely to arise if one is aware only of neuropsychological extensions of our work. In a recent article in this journal, Ruby proposed that cognitive neuroscience may provide theoretical grounding for many tenets of Psychoanalytic Theory. I have no wish to debate the merit of Ruby's thesis. Specifically, a considerable proportion of her paper laments the lack of attention she feels has been accorded to UMEEs in the investigations of trait self-knowledge.

This negative assessment apparently was motivated by her reading of Klein and Gangi , a review paper describing our attempts to extend our work on trait self-knowledge to individuals suffering clinical dysfunction e. I quote the relevant sections of her paper:. For Klein and Gangi, these cases showed that episodic and semantic memory systems were separate and independent. Yet this updating occurred without his being able to episodically recollect any information about the behavioral events on which this updating presumably was based.

I believe Professor Ruby's concerns can be addressed by reference to the body of work that served as the conceptual basis for our later neuropsychological investigations.

Our argument that episodic and semantic memory systems are functionally independent was not based on data from our case studies. Rather it was based on empirical work conducted with mentally healthy participants; only later did we apply these findings and the model they resulted in to patients suffering cognitive impairments.

The goal of our formative work was to determine whether trait-relevant behavioral exemplars play a role in trait judgments about the self. To address this question, we initiated a program of research using cognitively and neurologically healthy individuals. Our patient studies came later, after we already had formulated and tested our model of trait self-knowledge.

The investigations of individuals with well-circumscribed cognitive and neurological impairments seemed a natural way to extend our initial findings and refine our model.

Our non-clinical studies used a variety of methodologies, procedures and contextual factors e. Each model had advocates, but deciding between them had proven difficult. Our strategy was to adopt experimental methods that would enable us to pit these models against one another, thereby allowing us to assess their respective merits. However, the reader should be aware that to garner convergent support we employed a variety of methods—e.

By contrast, if trait judgments are based on semantic abstractions rather than behavioral exemplars, then the activation of exemplars will not play a part in the judgment process. Accordingly, exemplar-based priming should not be observed. To cut to the chase, in over a dozen studies we consistently found that—except in certain, theoretically predicted circumstances—priming did not occur.

We concluded that trait judgments typically are not based on either the conscious or unconscious activation of behavioral exemplars; rather—in accord with the trait abstraction model—they appear to depend on access to pre-computed trait summaries in semantic memory. As noted, priming was observed in certain situations.

With model in hand, we turned our attention to patients suffering from neuropsychological disorders to see whether our theory could account for—and perhaps provide insight into—impairments of self-knowledge exhibited by individuals suffering cognitive dysfunction e.

Since, with one exception, all of our non-clinical research on self-knowledge was published in social psychology journals, many neuroscientists may not be aware of the work that provided the empirical and theoretical foundation for the model we subsequently applied to clinical populations. Our neuropsychological investigations of self-knowledge recently have captured the interests of the neuroscience community e.

Familiarity with this formative literature may help to preempt misunderstandings and address questions likely to arise when one's acquaintance with our model of self is based primarily on what can be gleaned from its neuropsychological applications. For example, an appreciation of this research reveals that we were very concerned about the potential effects of UMEEs on trait judgments.

Accordingly, we employed a variety of tasks that had been shown not to require conscious access to the content assumed to mediate their successful performance. While the findings thus far mentioned do not directly address the possibility that UMEEs play a role in the formation of semantic summaries, data presented in a later section of this article casts some doubt on that hypothesis as well.

Our interest in the potential effects of unconscious behavioral exemplars on the trait judgment process is put in sharp relief by Klein et al. Accounting for these findings by appeal to UMEEs would seem a daunting undertaking. It would have to accommodate a complex pattern of findings, obtained with a broad range of experimental conditions including variations in method, population, context and experience.

By contrast, what appears to be an erratic collection of outcomes can readily be transformed into an orderly, predictable and programmatic set of findings by appeal to the abstraction model conjoined with just two additional, theoretically-motivated principles—i. Of course, Occam's razor is a guiding principle, not a metaphysical mandate.

But, assuming that parsimony is a desirable heuristic in theory construction, it is hard to see how a model based on UMEEs can accommodate our complete set of findings in as economical a manner as the abstraction model. In the text quoted above, Ruby raises a second concern. How, she asks, can amnesic patient K. It turns out that our early work speaks to Ruby's puzzlement. Sherman and Klein demonstrated that trait updating occurs by processes occurring at encoding—not by the activation conscious or unconscious of experiences already in memory.

Indeed, since in this and other studies, we presented the trait-relevant behavioral information on which summaries presumably were based on-line via computer, there was little opportunity to access pre-stored UMEEs in memory 1.

These findings fit nicely with Tulving's SPI model of memory, according to which, information is stored in semantic memory during initial processing—not as the result of some serial process in which content first is activated from episodic memory and then converted to semantic knowledge. Thus, empirical and theoretical answers to Ruby's query i. But one needs to know where to look.

The purpose of this paper is to provide that guidance. In addition to seriously compromised episodic memory, K. And,— as predicted by the abstraction model—absent the ability to update semantic memory, K.

This is exactly what we and others found e. By contrast, K. Accordingly, his trait updating abilities—as predicted by our model—remain largely intact despite severe episodic amnesia. Non-the-less, the empirical and theoretical considerations presented cannot conclusively rule out a role for UMMEs in the formation of the semantic trait summaries that are stored and later accessed during the trait judgment process.

The possibility that the formation of the semantic knowledge on which trait judgments subsequently are based may be due, in part, to unconscious mental activity is something which currently available methodologies cannot definitively address.

National Center for Biotechnology Information , U. Journal List Front Hum Neurosci v. Front Hum Neurosci. Published online Oct Stanley B. Author information Article notes Copyright and License information Disclaimer.

Received Sep 9; Accepted Oct 3. Keywords: self, memory, trait-knowledge, neuroscience, theory, clinical populations, model testing. The use, distribution or reproduction in other forums is permitted, provided the original author s or licensor are credited and that the original publication in this journal is cited, in accordance with accepted academic practice.

No use, distribution or reproduction is permitted which does not comply with these terms. Ruby's concerns In a recent article in this journal, Ruby proposed that cognitive neuroscience may provide theoretical grounding for many tenets of Psychoanalytic Theory.

A model of trait self-knowledge in non-clinical populations The goal of our formative work was to determine whether trait-relevant behavioral exemplars play a role in trait judgments about the self. Questions concerning our neuropsychological findings likely to arise from a lack of familiarity with the foundational research Since, with one exception, all of our non-clinical research on self-knowledge was published in social psychology journals, many neuroscientists may not be aware of the work that provided the empirical and theoretical foundation for the model we subsequently applied to clinical populations.

References Dunn J. Discovering functionally independent mental processes: the principle of reversed association. Preserved knowledge of self in a case of Alzheimer's dementia.

The multiplicity of self: neuropsychological evidence and its implications for the self as a construct in psychological research. The unanticipated resilience of trait self-knowledge in the face of neural damage. Memory 18 , — The use of exemplars and abstractions in trait judgments: a model of trait knowledge about the self and others.

The functional independence of trait self-knowledge: commentary on sakaki Memory 16 , — Neural substrates of the self-memory system: new insights from a meta-analysis. Brain Mapp. Functional independence within the self-memory system: insight from two cases of developmental amnesia. Cortex 49 , — Autobiographical memory and sense of self.

Personal semantics: at the crossroads of semantic and episodic memory. Trends Cogn. What would be the benefits of a collaboration between psychoanalysis and cognitive neuroscience? The opinion of a neuroscientist. Development and representation of personality impressions. Self-knowledge of an amnesic individual is represented abstractly , in Advances in Social Cognition , Vol.

Organization of memory: quo vadis? Long-lasting perceptual and semantic learning in amnesia: a case experiment. Temporally graded semantic memory loss in Alzheimer's disease: cross—sectional and lognitudinal studies.

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Lines in this model are represented by chords of the boundary circle also called the absolute. Wilson Elhanan Helpman Hadley Richard T. Lawrence Klein. There he built a model of the United States economy to forecast the development of business fluctuations and to study the effects of government economic-political policy.

Klein l model

Klein l model

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Great Acoustics: Twin Steve Klein Ls – Acoustic Guitar

In geometry, the Beltrami—Klein model , also called the projective model , Klein disk model , and the Cayley—Klein model , is a model of hyperbolic geometry in which points are represented by the points in the interior of the unit disk or n -dimensional unit ball and lines are represented by the chords , straight line segments with ideal endpoints on the boundary sphere.

The Beltrami—Klein model is analogous to the gnomonic projection of spherical geometry , in that geodesics great circles in spherical geometry are mapped to straight lines.

The papers of Beltrami remained little noticed until recently and the model was named after Klein "The Klein disk model". This happened as follows. In Arthur Cayley used the cross-ratio definition of angle due to Laguerre to show how Euclidean geometry could be defined using projective geometry.

In , the young twenty-year-old Felix Klein became acquainted with Cayley's work. He recalled that in he gave a talk on the work of Cayley at the seminar of Weierstrass and he wrote:.

Later, Felix Klein realized that Cayley's ideas give rise to a projective model of the non-Euclidean plane. As Klein puts it, "I allowed myself to be convinced by these objections and put aside this already mature idea. The distance function for the Beltrami—Klein model is a Cayley—Klein metric. When one of the points is the origin and Euclidean distance between the points is r then the hyperbolic distance is:.

In two dimensions the Beltrami—Klein model is called the Klein disk model. It is a disk and the inside of the disk is a model of the entire hyperbolic plane. Lines in this model are represented by chords of the boundary circle also called the absolute. The points on the boundary circle are called ideal points ; although well defined , they do not belong to the hyperbolic plane.

Neither do points outside the disk, which are sometimes called ultra ideal points. The model is not conformal , meaning that angles are distorted, and circles on the hyperbolic plane are in general not circular in the model. Only circles that have their centre at the centre of the boundary circle are not distorted. All other circles are distorted, as are horocycles and hypercycles. Chords that meet on the boundary circle are limiting parallel lines. Two chords are perpendicular if, when extended outside the disk, each goes through the pole of the other.

The pole of a chord is an ultra ideal point: the point outside the disk where the tangents to the disk at the endpoints of the chord meet. Chords that go through the centre of the disk have their pole at infinity, orthogonal to the direction of the chord this implies that right angles on diameters are not distorted.

Here is how one can use compass and straightedge constructions in the model to achieve the effect of the basic constructions in the hyperbolic plane. While lines in the hyperbolic plane are easy to draw in the Klein disk model, it is not the same with circles, hypercycles and horocycles.

Circles the set of all points in a plane that are at a given distance from a given point, its center in the model become ellipses increasingly flattened as they are nearer to the edge. Also angles in the Klein disk model are deformed. The two models are related through a projection on or from the hemisphere model. When projecting the same lines in both models on one disk both lines go through the same two ideal points. Both the hyperboloid model and the Klein disk model are models of the hyperbolic plane.

The Klein disk K, in the picture is a gnomonic projection of the hyperboloid model Hy with as center the center of the hyperboloid O and the projection plane tangent to the nearest point of the hyperboloid.

Given two distinct points U and V in the open unit ball of the model in Euclidean space , the unique straight line connecting them intersects the unit sphere at two ideal points A and B , labeled so that the points are, in order along the line, A , U , V , B.

Then the distance between U and V in the modelled hyperbolic space is expressed as. The Minkowski inner product is given by. The intrinsic distance in the embedding between points u and v is then given by. The distance function, in its homogeneous form, is unchanged. Since the intrinsic lines geodesics of the hyperboloid model are the intersection of the embedding with planes through the Minkowski origin, the intrinsic lines of the Beltrami—Klein model are the chords of the sphere.

The two models are related through a projection from the center of the disk; a ray from the center passing through a point of one model line passes through the corresponding point of the line in the other model. From Wikipedia, the free encyclopedia. See also: Cayley—Klein metric. See also: Compass-and-straightedge construction.

Giornale di Mathematiche. VI : — Annali di Matematica Pura ed Applicata. Series II. Sources of hyperbolic geometry 2. Providence: American mathematical society. Philosophical Transactions of the Royal Society. Teil 1. Mathematische Annalen. Remizov Linear Algebra and Geometry. New York: Freeman. Stack Exchange. Retrieved 1 January Cannon, W. Floyd, R. Kenyon, W. Categories : Hyperbolic geometry. Namespaces Article Talk. Views Read Edit View history. In other projects Wikimedia Commons.

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Klein l model