By O. Tangach. Wabash College.
In contrast generic elimite 30 gm mastercard, in transmission tomography buy 30gm elimite amex, a radi- ation source (x-rays or a radioactive source) projects an intense beam of radiation photons through the patient’s body elimite 30 gm with mastercard, and the transmitted beam is detected by the detector and further processed for image formation cheap elimite 30 gm with mastercard. Single Photon Emission Computed Tomography 155 The detector head rotates around the long axis of the patient at small angle increments (3° to 10°) for collection of data over 180° or 360° purchase elimite 30gm on line. The data are collected in the form of pulses at each angular position and normally stored in a 64 × 64 or 128 × 128 matrix in the computer for later reconstruction of the images of the planes of interest. Transverse (short axis), sagittal (vertical long axis), and coronal (horizontal long axis) images can be gen- erated from the collected data. Multihead gamma cameras collect data in several projections simultaneously and thus reduce the time of imaging. For example, a three-head camera collects a set of data in about one third of the time required by a single-head camera for 360° data acquisition. Data Acquisition The details of data collection and storage such as digitization of pulses, use of frame mode or list mode, choice of matrix size, etc. Data are acquired by rotating the detector head around the long axis of the patient over 180° or 360°. Although 180° data collection is commonly used (particularly in cardiac studies), 360° data acquisition is preferred by some investigators, because it minimizes the effects of attenuation and vari- ation of resolution with depth. In some situations, the arithmetic mean (A1 + A2)/2 or the geometric mean (A × A )1/2 of the counts,A and A , of the two heads 1 2 1 2 are calculated to correct for attenuation of photons in tissue. However, in 180° collection, a dual-head camera with heads mounted at 90° angles to each other has the advantage of shortening the imaging time required to sample 180° by half (Table 12. Dual-head cameras with heads mounted at 90° or 180° angles to each other and triple-head cameras with heads ori- ented at 120° to each other are commonly used for 360° data acquisition and offer shorter imaging time than a one-head camera for this type of angular sampling. The sensitivity of a multihead system increases with the number of heads depending on the orientation of the heads and whether 180° or 360° acquisition is made. Older cameras were initially designed to rotate in circular orbits around the body. Relationship of sensitivity and time of imaging for 180° and 360° acqui- sitions for different camera head conﬁgurations. This causes loss of data and hence loss of spatial resolution in these projections. Data collection can be made in either continuous motion or “step-and- shoot” mode. In continuous acquisition, the detector rotates continuously at a constant speed around the patient, and the acquired data are later binned into the number of segments equal to the number of projections desired. In the step-and-shoot mode, the detector moves around the patient at selected incremental angles (e. Image Reconstruction Data collected in two-dimensional projections give planar images of the object at each projection angle. To obtain information along the depth of the object, tomographic images are reconstructed using these projections. Two common methods of image reconstruction using the acquired data are the backprojection method and the iterative method, of which the former is the more popular, although lately the latter is gaining more attention. Simple Backprojection The principle of simple backprojection in image reconstruction is illustrated in Figure 12. In the two-dimensional data acquisi- tion, each pixel count in a projection represents the sum of all counts along the straight-line path through the depth of the object (Fig. Recon- struction is performed by assigning each pixel count of a given projection in the acquisition matrix to all pixels along the line of collection (perpen- dicular to the detector face) in the reconstruction matrix (Fig. This Single Photon Emission Computed Tomography 157 is called simple backprojection. When many projections are backprojected, a ﬁnal image is produced as shown in Figure 12. Backprojection can be better explained in terms of data acquisition in the computer matrix. Suppose the data are collected in a 4 × 4 acquisition matrix, as shown in Figure 12. In this matrix, each row represents a slice, projection, or proﬁle of a certain thickness and is backprojected individu- ally. Counts in each pixel are considered to be the sum of all counts along the depth of the view.
If the Unmoved Mover is referred to discount elimite 30gm visa, then the wording ‘principle of movement’ (rc t¦v kinsewv) cheap 30gm elimite mastercard, which is usually set aside for efﬁcient causality purchase elimite 30gm with amex, is awkward cheap 30gm elimite otc, since the Unmoved Mover moves as a ﬁnal cause (but see Potscher (¨ 1970) 57) buy elimite 30gm overnight delivery. But it is questionable whether the theology of Metaphysics should serve as a guiding principle here: passages such as Pol. The same applies to 1248 a 38: ‘he sees well both the future and the present’ (toÓto kaª eÔ ¾r kaª t¼ mllon kaª t¼ Àn), which seems inconsistent with God’s activity of ‘thinking of thinking’ (nosewv n»hsiv)inMetaph. This contrast supports the view that Aristotle here does not, as Effe (1970) argues (cf. The presence of the word nqousiasm»v (‘divine inspiration’) here in Aristotle’s text does not alter this view, for this is used by Aristotle elsewhere to denote an affection (a pqov) of the human soul (cf. The conclusion that eutuchia is found among simple-minded people is therefore not incompatible with the statement that eutuchia is ‘divine’ (qe©a): the psycho-physiological process that Aristotle here has in mind does not presuppose an active and purposive divine choice (pimleia or fil©a) – whereas the theory rejected in 1247 a 28–9 does presuppose such a choice, as the verb ‘love’ (filw) shows – but is based on a general physi- cal divine movement which works more strongly with those people whose reasoning faculty is disengaged. The process seems similar to the workings of the ‘superhuman nature’ (daimon©a fÅsiv), to which Aristotle ascribes the phenomenon of prophetic dreams in On Divination in Sleep (463 b 14); there the susceptibility of simple-minded people to foresight and clear dream images, as well as the absence of this susceptibility in intelligent people, is accounted for by the absence (or, in the case of the intelligent people, the presence) of rational activity: ‘for the mind of such [i. By contrast, in intelligent people the presence of ‘their own proper movements’ (o«ke±ai kinseiv) prevents this susceptibility. Il faut plutot rapprocher ce passage des dialogues de Platon´ ˆ ˆ ou l’on voit cites les memes phenomenes psychiques et notamment de Menon. Gigon (` ´ ˆ ´ ` ´ 1969) 211: ‘Man wird allerdings auch zugestehen mussen, daß der Einschub uber den Enthusiasmus verwirrend¨ ¨ wirkt: denn in ihm liegt eine gottliche Einwirkung vor, die ihrer besonderen Art nach kaum¨ sunecv genannt werden kann. Thisiscalled Aristotle on divine movement and human nature 247 form of ‘divine concern’ (qe©a pimleia), but the theory of others that a god ‘sends’ (pmpei) dreams to people does suppose divination in sleep to be such, for ‘sending’ presupposes an active and purposive divine choice, whereas such a choice is for Aristotle, as we have seen, incompatible with the fact that prophetic dreams are found among simple people and not among the best and wisest. For this reason he uses three times the same distribution argument as that in Eth. The second part of the solution is in that the movement of God is, in principle, not limited to the class of the ‘irrational’ (logoi) people, but extends to the ‘wise and intelligent’ (sofoª kaª fr»nimoi) as well. To demonstrate this I shall ﬁrst summarise my interpretation of the passage 1248 a 15ff. Having established that eutuchia proceeds from natural desire (¾rma© and piqum©ai), Aristotle asks in turn for the starting-point of this desire, probably because it is not yet clear why this natural desire should be aimed in the right direction. He considers that this starting-point will also be the origin of rational activity (noÓv and boÅleusiv), and having disposed of ‘chance’ (tÅch) as an evidently unsatisfactory candidate for this function he argues that the starting-point wanted is in fact the starting-point of movement in the soul; then it is clear that this starting-point is God. Thus God is the starting-point of all psychic activity, both of reasoning (no¦sai) and of the irrational impulses (¾rma©) on which eutuchia is based. God is even more powerful than the divine principle in man, the intellect (noÓv), and it is for this reason that people who are devoid of rational activity, too, can make the right choice: they succeed without reasoning because they still have God, although the wise people also have God and use his movement in their calculation of the future, either by experience or by habit: thus there is a more rational form of divination as well. Both irrational and rational divination, then, ‘use’ God (who sees the future as well as the present), but God moves more strongly in those people whose reasoning faculty is disengaged. Thus God’s movement is present both in the irrational people daimonia because it is beyond human control, as is indicated by the use of the word daim»niov in Somn. The individual human nature is further called daimonia because it works more strongly when reason is inactive, and because it plays the part of intermediary between God and man, which Greek tradition assigned to demons. This is an obvious reference to the distribution argument in 1247 a 28–9, where it was stated that it is ‘paradoxical’ that a god or demon should love simple people, not the best and wisest (m t¼n bltiston kaª fronimÛtaton); evidently Aristotle remains aware of the distribution argument and anticipates it by means of a careful presentation of his own explanation. For the purpose of clarity I will print ﬁrst a text and a translation of each section and then add comments on the section in question. The text of the manuscript tradition will be followed as closely as possible; any deviations from it will be accounted for from line to line. It seems to me that the numerousproblemsofinterpretationinthischapteraredueatleastasmuchtoAristotle’sconciseand often frankly clumsy way of writing as to possible corruptions in the text. Therefore the interpreter should maintain a fundamental distinction between hypotheses concerning the original text which Aristotle wrote down, and hypotheses concerning what he intended to say. This distinction seems to have often been ignored, and apparently interpreters have, with an appeal to the abysmal state of the text, proposed many conjectures with a view to making the text comply with interpretations mainly prompted by theological assertions in other Aristotelian writings. The unfortunate consequence of this process is that there is no generally accepted text on which to base a debate concerning the tenability of a particular interpretation: in order to scrutinise it, one has to be willing to accept, for the sake of argument, the readings proposed by the interpreter, while these readings were actually chosen to support the interpretation. This account should be based principally on the immediate context and only secondarily on statements on the subject in other Aristotelian writings. Aristotle on divine movement and human nature 249 23 panta staiá £35 sti tiv rc ¨v oÉk stin llh xw, aÌth 24 d di t¼ toiaÅth e²nai toioÓto dÅnatai poie±n;36 t¼ d 25 zhtoÅmenon toÓtì sti, t©v ¡ t¦v kinsewv rc n t¦ yuc¦; d¦lon 26 d ãsper n tä Âlw qe¼v kn ke©nw.
Compute z : σ 5 σ > 1N 5 15> 125 5 3; obt X X ■ When predicting that X will be higher than buy elimite 30 gm low price, the z 5 1X 2 2>σ 5 1108 elimite 30 gm line. Those not learning statistics have 5 100 Say that a different mean produced zobt 511 purchase 30 gm elimite otc. Because a successful diet lowers weight scores You test the effectiveness of a new weight-loss diet order 30 gm elimite amex. Or a report might say that we obtained a “significant z”: The zobt is beyond the zcrit cheap elimite 30gm otc. Notice that instead of using we use p (for probability), and with significant results, we say that p is less than. Type I Errors: Rejecting H0 When H0 Is True Sometimes, the variables we investigate are not related in nature, so H0 is really true. When in this situation, if we obtain data that cause us to reject H0, then we make an error. In other words, we conclude that the independent variable works when it really doesn’t. Thus, when we rejected H0 and claimed that the pill worked, it’s possible that it did not work and we made a Type I error. Because our sample was exactly what the sampling distribution indicated it was: a very unlikely and unrepre- sentative sample from the population having a of 100. In fact, the sample so poorly represented the situation where the pill did not work, we mistakenly thought that the pill did work. In a Type I error, there is so much sampling error that we—and our Errors in Statistical Decision Making 225 statistical procedures—are fooled into concluding that the predicted relationship exists when it really does not. Think of it as being in the “Type I situation” whenever you discuss the situation in which the pre- dicted relationship does not exist. If you retain H0 in this situation, then you’ve avoided a Type I error: By not concluding that the pill works, you’ve made the correct decision because, in reality, the pill doesn’t work. We never know if we’re making a Type I error because only nature knows if the variables are related. However, we do know that the theoretical probability of a Type I error equals our. If we repeated this experiment many times, then the sampling distribution in Figure 10. Rejecting H0 when it is true is a Type I error, so over the long run, the relative frequency of Type I errors would be. Therefore, anytime we reject H0, the theoretical probability that we’ve just made a Type I error is. This is because, if 5% of the time samples are in the region of rejection when H0 is true, then 95% of the time they are not in the region of rejection when H0 is true. Therefore, 95% of the time we will not obtain sam- ple means that cause us to erroneously reject H0: Anytime you retain H0, the theoreti- cal probability is. Although the theoretical probability of a Type I error equals , the actual probabil- ity is slightly less than. We cannot determine the pre- cise area under the curve at zcrit, so we can’t remove it from our 5%. We can only say that the region of rejection is slightly less than 5% of the curve. Thus, in our examples when we rejected H0, the probability that we made a Type I error was slightly less than. This commu- nicates that we did not call this result significant because to do so would require a region greater than 5% of the curve. This may not sound like a big deal, but the next time you fly in an airplane, consider that the designer’s belief that the wings will stay on may actually be a Type I error: He’s been misled by sampling error into erroneously think- ing the wings will stay on. A 5% chance of this is scary enough—we certainly don’t want more than a 5% chance that the wings will fall off. In science, we are skeptical and careful, so we want to be convinced that sampling error did not produce our results. Type I errors are the reason a study must meet the assumptions of a statistical proce- dure. If we violate the assumptions, then the true probability of a Type I error will be larger than our (so it’s larger than we think it is). This is allowed because the probability of a Type I error will still be close to (it will be only, say,. Sometimes making a Type I error is so dangerous that we want to reduce its proba- bility even further.