In [13], R.M. Kashaev defined a family of complex-valued link invariants indexed by integers N>~2 using the quantum dilogarithm. Later he calculated the asymptotic behavior of his invariant, and observed that for the three simplest hyperbolic knots it grows as exp(Vol(K)N/2rr) when N goes to infinity, where Vol(K) is the hyperbolic volume of the complement of a knot K [14]. This amazing result and his conjecture that the same also holds for any hyperbolic knot have been almost ignored by mathematicians since his definition of the invariant is too complicated (though it uses only elementary tools).The aim of this paper is to reveal his mysterious definition and to show that his invariant is nothing but a specialization of the colored Jones polynomial. The colored Jones polynomial is defined for colored links (each component is decorated with an irreducible representation of the Lie algebra sl(2, C)). The original Jones polynomial corresponds to the case that all the colors are identical to the 2-dimensional fundamental representation.We show that Kashaev's invariant with parameter N coincides with the colored Jones polynomial in a certain normalization with every color the N-dimensional representation, evaluated at the primitive Nth root of unity. (We have to normalize the colored Jones polynomial so that the value for the trivial knot is one, for otherwise it always vanishes.) On the other hand, there are other colored polynomial invariants, such as the generalized multivariable Alexander polynomial defined by Y. Akutsu, T. Deguehi and T. Ohtsuki [1]. They used the same Lie algebra sl(2, C) but a different hierarchy of representations. Their invariants are parameterized by c+l parameters: an integer N This research is supported in part by Sumitomo Foundation and Grand-in-Aid for Scientific Research, The Ministry of Education, Science, Sports and Culture. 86 H. MURAKAMI AND J. MURAKAMI and complex numbers pi (i= 1, 2, ..., c) decorating the components, where c is the number of components of the link. In the case where N=2, their invariant coincides with the multivariable Alexander polynomial, and their definition is the same as that of the second author [22]. Using the Akutsu-Deguchi-Ohtsuki invariants we have another coincidence. We will show that if all the colors are 89 then the generalized Alexander polynomial is the same as Kashaev's invariant since it coincides with the specialization of the colored Jones polynomial as stated above. Therefore the set of colored Jones polynomials and the set of generalized Alexander polynomials of Akutsu-Deguchi-Ohtsuki intersect at Kashaev's invariants. The paper is organized as follows. In the first section we recall the definition of the link invariant defined by Yang-Baxter operators. In w we show that the AkutsuDeguchi-Ohtsuki invariant coincides with the colored Jones polynomial when the colors 1 (N-1) by showing that their representation becomes the usual representation are all corresponding to the irreducible N-dimensional representation of sl(2, C). In w weshow that ...

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The pond snail Lymnaea stagnalis is an excellent model system in which to study the neuronal and molecular substrates of associative learning and its consolidation into long-term memory. Until now, the presence of cyclic AMP (cAMP)-responsive element binding protein (CREB), which is believed to be a necessary component in the process of a learned behavior that is consolidated into long-term memory, has only been assumed in Lymnaea neurons. We therefore cloned and analyzed the cDNA sequences of homologues of CREB1 and CREB2 and determined the presence of these mRNAs in identifiable neurons of the central nervous system (CNS) of L. stagnalis. The deduced amino acid sequence of Lymnaea CREB1 is homologous to transcriptional activators, mammalian CREB1 and Aplysia CREB1a, in the C-terminal DNA binding (bZIP) and phosphorylation domains, whereas the deduced amino acid sequence of Lymnaea CREB2 is homologous to transcriptional repressors, human CREB2, mouse activating transcription factor-4, and Aplysia CREB2 in the bZIP domain. In situ hybridization revealed that only a relatively few neurons showed strongly positive signals for Lymnaea CREB1 mRNA, whereas all the neurons in the CNS contained Lymnaea CREB2 mRNA. Using one of the neurons (the cerebral giant cell) containing Lymnaea CREB1 mRNA, we showed that the injection of a CRE oligonucleotide inhibited a cAMP-induced, long-lasting synaptic plasticity. We therefore conclude that CREBs are present in Lymnaea neurons and may function as necessary players in behavioral plasticity.

Hepatitis C virus (HCV) is recognized as a major causative agent of parenterally transmittable non-A, non-B hepatitis. 1 HCV infection often persists for a long time and leads to chronic liver diseases; at least half of the HCV cases develop into chronic hepatitis, and 10% to 20% of cases develop into cirrhosis. 2 The high HCV mutation rate readily generates variants that contribute to establishing the persistent infection. 3

Of 21,791 pregnant women screened in Tottori Prefecture, Japan, 127 (0.58%) were positive for anti-hepatitis C virus (HCV) antibody and 84 (0.39%) were positive for HCV RNA. Of 84 children followed up for at least 6 months, 7 (8%) were infected. All of them were born to 26 mothers with a high virus load (HVL; >/=2.5x106 RNA copies/mL [27%]), compared with 0 of 58 children born to non-HVL mothers (P<.001). Because all the infected children were vaginally delivered, the infection rate among 16 vaginally delivered children born to the HVL mothers was as high as 44%. The prevalence of anti-NS4 antibody in the mothers with an infectious HVL was significantly lower than that in the mothers with a noninfectious HVL (P=.048). Analysis of our results suggests that maternal HVL, vaginal delivery, and negative anti-NS4 antibody are significant risk factors for the mother-to-child transmission of HCV.

The sequence data (H. Okamoto et al., Hepatol. Res. 10:1–16, 1998) of a newly discovered single-stranded DNA virus, TT virus (TTV), showed that it did not have the terminal structure typical of a parvovirus. Elucidation of the complete genome structure was necessary to understand the nature of TTV. We obtained a 1.0-kb amplified product from serum samples of four TTV carriers by an inverted, nested long PCR targeted for nucleotides (nt) 3025 to 3739 and 1 to 216 of TTV. The sequence of a clone obtained from serum sample TA278 was compared with those registered in GenBank. The complete circular TTV genome contained a novel sequence of 113 nt (nt 3740 to 3852 [=0]) in between the known 3′- and 5′-end arms, forming a 117-nt GC-rich stretch (GC content, 90.6% at nt 3736 to 3852). We found a 36-nt stretch (nt 3816 to 3851) with an 80.6% similarity to chicken anemia virus (CAV) (nt 2237 to 2272 of M55918), a vertebrate circovirus. A putative SP-1 site was located at nt 3834 to 3839, followed by a TATA box at nt 85 to 90, the first initiation codon of a putative VP2 at nt 107 to 109, the termination codon of a putative VP1 at nt 2899 to 2901, and a poly(A) signal at nt 3073 to 3078. The arrangement was similar to that of CAV. Furthermore, several AP-2 and ATF/CREB binding sites and an NF-κB site were arranged around the GC-rich region in both TTV and CAV. The data suggested that TTV is circular and similar to CAV in its genomic organization, implying that TTV is the first human circovirus.