Absolute Discrimination Research Articles

Some contributions to the theory of cyclic quartic extensions of the rationals

K is a cyclic quartic extension of Q iff K = Q((rd + p d 1 2 ) 1 2 ) , where d > 1, p and r are rational integers, d squarefree, for which p 2 + q 2 = r 2 d for some integer q. Following a paper of A. A. Albert we show that the absolute discriminant, d( K Q ) , of the general cyclic quartic extension is given by d( K Q ) = (W 2d 2) for an explicitly computable rational integer W. We next find that the relative discriminant, d( K F ) , is given by d( K F ) = (W d 1 2 ) , where F = Q (d 1 2 ) is K′s uniquely determined quadratic subfield. We use this last result in conjunction with Corollary 3, page 359, of Narkiewicz's “Elementary and Analytic Theory of Algebraic Numbers” (PWN-Polish Scientific Publishers, 1974) to establish the following Theorem 1: If the (wide) class number of F = Q(d 1 2 ) is odd then every cyclic quartic extension K of Q containing F has a relative integral basis over F. We give a second, more organic, proof of Theorem 1 which also allows us to prove the following converse result, namely Theorem 2: Suppose the quadratic field F is contained in some cyclic quartic extension of Q and suppose that F has even (wide) class number. There then is a cyclic quartic extension K of Q containing F such that K has no relative integral basis over F.

Diagnostic Value of Routine Liver Tests

In 131 patients on a medical service and 97 patients on a surgical service, in whom a diagnosis of hepatobiliary disease was verified in the hospital, the diagnostic value of routine liver tests performed soon after admission was evaluated by stepwise discriminant analysis. By measurements of alanine aminotransferase, alkaline phosphatases, gamma globulin, prothrombin time, bilirubin, and albumin, half of the medical patients were correctly classified into one of seven diagnostic categories. Aminotransferase contributed most to the classification, being twice as effective as random allocation. Decreasing the number of diagnostic categories to three (hepatitis, fatty liver, and chronic liver disease) increased the frequency of correct allocation to 80%. The allocation of all the patients to seven medical and four surgical diagnostic categories by means of four tests (aminotransferase, alkaline phosphatases, prothrombin time, and bilirubin) was significantly improved by each step with a misclassification rate of 55% when all tests were used. A reduction of the diagnostic groups to five (hepatitis, fatty liver, chronic liver disease, duct obstruction and tumor) increased the frequency of correct allocation to 63%. The analysis demonstrates the limited diagnostic effectiveness of routine liver tests when used alone. The absolute discrimination values depend on the a priori frequencies of the diagnostic groups investigated, and therefore may vary from time to time and from place to place.

Absolute frequency discrimination in the barn owl

Barn owls (Tyto alba) could discriminate sound frequency by memory. Frequency differences as small as 0.7–0.5% were easily detected. The same acuity was obtained when two frequencies had to be remembered simultaneously and distinguished from other frequencies. The response latency was proportional to the difference between the reference and test frequencies and served as a sensitive criterion for discrimination.

A generalization of Stark's theorem

Let K and K′ be distinct real quadratic fields, and let L and L′ be totally imaginary quadratic extensions of K and K′, respectively, both L and L′ having class number 1. Then there exists an effectively computable constant c = c( K, K′) such that either | L | ≤ c or | d L′ | ≤ c, where d L and d L′ denote absolute discriminants.

BIOSYSTEMATICS OF NORTH AMERICANIPS(COLEOPTERA: SCOLYTIDAE): HOPPING’S GROUP IX

AbstractControlled mating experiments demonstrating total reproductive isolation, together with consistent differences in morphological and cytological detail, confirmed the validity of the closely related group IXIps:grandicollis,cribricollis,lecontei,montanus,confusus,paraconfusus, andhoppingi. The latter two species, new to science, were formerly considered to beconfusus.Matings betweengrandicollisfrom eastern Canada and North Carolina were subnormally fertile; other intraspecific matings between individuals of the same population or distant populations produced fully fertile progeny. Interspecific pairings usually resulted in insemination and normal-appearing egg galleries, but, with one exception, none of the eggs hatched.Onemontanusand twoconfusus, each mated by males of the same species, produced all-daughter broods. This "sex-ratio" condition appeared to be the result of a matrilineally transferred cytoplasmic factor lethal to male embryos only.At first meiotic metaphase all species had the karyotypic formula 15 AA + Xyp, and onlygrandicolliswas easily differentiated by bivalent configuration or size sequence. Most other species showed diagnostic differences at meiotic prophase or second meiotic metaphase. Pairing disruptions and anaphase bridges occurred ingrandicollisinterpopulational hybrids; meiosis was normal in progeny from interpopulational pairings ofconfusus,paraconfusus, andmontanus.Ingrandicollisthe median struts of the male genitalia were 1.5 times longer than the median lobe. The struts/lobe ratios for other species approximated 1.00 but differences for most comparisons between species were statistically significant. The shape of the pars stridens on females was different for most species and mean widths of striations thereon ranged from 0.517 μ forparaconfususto 0.876 μ forlecontei. This character provided absolute discrimination of females ofconfususfrom those ofparaconfususandhoppingibut the latter two species were most easily separated by differences in the density of punctures in the elytral declivity.It is hypothesized that contiguous allopatry and differences in host and ecological specialization, evidenced in species of group IX, is maintained by their high propensity for interspecific mating which fails completely to produce progeny.

Note on Pitch Discrimination Learning

Miller (1956) has suggested that the number of stimuli which can be identified in an discrimination task is 7-1 2, about 2.8 bits of transmitted information. Considering the abiliry of the human operator to handle very large amounts of stimulus information, under optimum conditions one might intuitively expect absolute discrimination to exceed Miller's magical 7 by at least an order of magnitude. A preliminary investigation suggested that pitch discrimination improves as a result of experience without informative feedback or knowledge-of-results ( K R ) and that K R training results in additional improvement. Rather marked differences across individuals were also observed. The experimental hypotheses suggested by the preliminary investigation are: (1) pitch discrimination improves as a function of experience without K R , ( 2 ) once the improvement stated in (1) has taken place, K R training will result in further improvement, and ( 3 ) performance differs across Ss. Ss were 22 introductory psychology students. The signal and response arrays were designed in a manner such that they each contained an ordinal structure and could be encoded easily by S. The stimuli were 18 simple sine-wave tones arranged in three scales with frequencies corresponding to the musical notes A, B, C, E, P , and G. The responses were coded alpha-numerical symbols. Thus A1 indicated a tone with a frequency of 220 Hertz, A 2 indicated 880 Hertz, and A3 indicated 3520 Hertz. K R was not available during the first four sessions composed of a total of 756 test tones plus 72 warm-up tones. An a priori performance stability criterion was reached by the end of the fourth session calling for implementation of K R training for the fifth session. During the K R condition, E correctly identified each tone after S had responded to it. K R was not available for Session 6; thus performance on Sessions 4 and 6 could be compared in a pre-treaunent vs post-treatment manner to test the effects of K R training. Sessions 5 and 6 were each composed of 216 test tones plus 1 8 warm-up tones. Bits of information transmitted was used (mere ly ) as the criterion measure; and appropriate non-parametric statistical tests were conducted to test the experimental hypotheses. The results supported all of the experimental hypotheses. Improvement was from 2.17 bits in Session 1 to 2.38 bits in Session 6. The results did not indicate that K R training had been continued long enough to produce a maximum effect; thus more training might have resulted in further improvement. Further research into the effects of more extensive and intensive K R training, and possibly other training techniques, is indicated.

Effects of association area lesions on auditory frequency discrimination in cat

Two groups of cats, one normal and one with prior bilateral ablation of cortical association response areas, were trained on two different types of auditory frequency discrimination. Both groups first learned an “absolute” procedure requiring response to a 250 cps tone and no response to a 2000 cps tone. They were then trained on a “repetitive” procedure where the 250 cps tone was presented as an alternation with a continuously repeated 2000 cps tone. The normal group learned both procedures equally well. The lesion group learned the absolute discrimination but were unable to learn the repetitive discrimination. This result is completely opposite to the effects of auditory cortex lesions on frequency discrimination learning.

Absolute vs. relational discrimination on the dimension of number.

Absolute vs. relational discrimination on the dimension of number.

伝書鳩の色光刺戟の弁別学習における転移

The present study on the instrumental conditioning of color discrimination by pigeons was undertaken to determine whether the learning was based on absolute or on relative discrimination. It was assumed that if the learning was based upon relative discrimination, the luminance relation of the stimuli would be transferred regardless of their wave-length and, on the other hand, if it was based upon absolute discrimination, pigeons would respond to wave-lengths without regards to luminance relations.The entire experiment was divided into two major parts, Exp. I and II, each of which comprised two groups of experiments, A1 and B1 in the case of Exp. I and A2 and B2 in the casg of Exp. II. Each group was subdivided further into four unit-experiments, 1, 2, 3 and 4. Thus, the total number of unit-experiments was 16. The experiment was conducted with the Skinner Box and with 32 pigeons as subjects, 2 pigeons participating in one unit-experiment.Each unit-experiment contained 3 problems, 1st, 2nd and 3rd, given in this order. The purpose was to see if each succeding problem was learned more rapidly than the one preceding.Stimuli and Procedure-Four colors, red, yellow, green and blue whose dominant wave-lengths were 675.6, 574.9, 538.6 466.5mμ respectively were chosen as stimulus materials. Each of these four colors was paired with each of the other three colors. The luminance ratio of the two colors in the pair was 6 : 1, the lighter one being the positive stimulus that was reinforced. The stimuli were presented one by one in random order, each for 12 seconds through filters. The number of reinforcements per day was 32 and the criterion of learning was set at 95 percent correct response. The general plan of experiments is summarized in Table 1 and 2. The mention must be made that in Exp. I, A1 and Exp. II, A2 the color pairs used in the 3rd problem were brighter than those used in the 1st and 2nd problems and in Exp. I, B1 and Exp. II, B2 the pairs in the 2nd problem were brighter than those used in the 1st and 3rd problems. In either case, the luminance ratio of the two colors in the pair was kept 6 : 1.Results-Errors made during 32 reinforcements in the preceding problem were compared with those made in the succeeding problems and the following facts were found :Table 1Plan of Exp. I.Transfer of learning of the 1st problem to the 3rd problem was based upon the luminance relation of the stimuli in both Exp. I, A1 and B1. This clearly is a case of relative discrimination.In Exp. II, A2 the pigeons showed both relative discrimination of luminance and absolute discrimination of wave-length, however, in B2 they showed only absolute discrimination.Transfer of learning of the 2nd to the 3rd was based almost on absolute discrimi-Table 2Plan of Exp. II.nation in Exp. I and relative discrimination in Exp. II.The learning of the 3rd problems in Exp. I and II was accelerated in comparison with the original learning.