Classification of phase singularities for complex scalar waves

Motivated by the importance and universal character of phase singularities which are clarified recently, we study the local structure of equi-phase loci near the dislocation locus of complex valued planar and spatial waves, from the viewpoint of singularity theory of differentiable mappings, initiated by H. Whitney and R. Thom. The classification of phase-singularities are reduced to the classification of planar curves by radial transformations due to the theory of A. du Plessis, T. Gaffney, and L. Wilson. Then fold singularities are classified into hyperbolic and elliptic singularities. We show that the elliptic singularities are never realized by any Helmholtz waves, while the hyperbolic singularities are realized in fact. Moreover, the classification and realizability of Whitney's cusp, as well as its bifurcation problem are considered in order to explain the three points bifurcation of phase singularities. In this paper, we treat the dislocation of linear waves mainly, developing the basic and universal method, the method of jets and transversality, which is applicable also to non-linear waves.Comment: 17 pages, 5 figure

Engel structures with trivial characteristic foliations

Engel structures on M x S^1 and M x I are studied in this paper, where M is a 3-dimensional manifold. We suppose that these structures have characteristic line fields parallel to the fibres, S^1 or I. It is proved that they are characterized by contact structures on the cross section M, the twisting numbers, and Legendrian foliations on both ends M x dI in the case of M x I.Comment: Published by Algebraic and Geometric Topology at http://www.maths.warwick.ac.uk/agt/AGTVol2/agt-2-11.abs.htm

Quantifying epistatic interactions among the components constituting the protein translation system

In principle, the accumulation of knowledge regarding the molecular basis of biological systems should allow the development of large-scale kinetic models of their functions. However, the development of such models requires vast numbers of parameters, which are difficult to obtain in practice. Here, we used an in vitro translation system, consisting of 69 defined components, to quantify the epistatic interactions among changes in component concentrations through Bahadur expansion, thereby obtaining a coarse-grained model of protein synthesis activity. Analyses of the data measured using various combinations of component concentrations indicated that the contributions of larger than 2-body inter-component epistatic interactions are negligible, despite the presence of larger than 2-body physical interactions. These findings allowed the prediction of protein synthesis activity at various combinations of component concentrations from a small number of samples, the principle of which is applicable to analysis and optimization of other biological systems. Moreover, the average ratio of 2- to 1-body terms was estimated to be as small as 0.1, implying high adaptability and evolvability of the protein translation system

Abnormalities of chromosome no. 1 related to blood dyscrasias: study of 10 cases.

Partial excess of chromosome 1 (q25-q32) was noted in malignant cells from all of 10 patients who had disorders such as non-African Burkitt's lymphoma, adult T-cell leukemia, myelofibrosis, malignant lymphoma, chronic lymphocytic leukemia or chronic myelocytic leukemia in blast crisis. The break points on chromosome 1 were at centromere, q12, q21, q23, q25 and q32. Variations in the specific region of the long arm of chromosome 1, q25-q32, were thought to be important in the evolution of malignant cell proliferation.</p

Developmental genetic bases behind the independent origin of the tympanic membrane in mammals and diapsids

International audienceThe amniote middle ear is a classical example of the evolutionary novelty. Although paleontological evidence supports the view that mammals and diapsids (modern reptiles and birds) independently acquired the middle ear after divergence from their common ancestor, the developmental bases of these transformations remain unknown. Here we show that lower-to-upper jaw transformation induced by inactivation of the Endothelin1-Dlx5/6 cascade involving Goosecoid results in loss of the tympanic membrane in mouse, but causes duplication of the tympanic membrane in chicken. Detailed anatomical analysis indicates that the relative positions of the primary jaw joint and first pharyngeal pouch led to the coupling of tympanic membrane formation with the lower jaw in mammals, but with the upper jaw in diapsids. We propose that differences in connection and release by various pharyngeal skeletal elements resulted in structural diversity, leading to the acquisition of the tympanic membrane in two distinct manners during amniote evolution

Comprehensive Behavioral Analysis of Calcium/Calmodulin-Dependent Protein Kinase IV Knockout Mice

Calcium-calmodulin dependent protein kinase IV (CaMKIV) is a protein kinase that activates the transcription factor CREB, the cyclic AMP-response element binding protein. CREB is a key transcription factor in synaptic plasticity and memory consolidation. To elucidate the behavioral effects of CaMKIV deficiency, we subjected CaMKIV knockout (CaMKIV KO) mice to a battery of behavioral tests. CaMKIV KO had no significant effects on locomotor activity, motor coordination, social interaction, pain sensitivity, prepulse inhibition, attention, or depression-like behavior. Consistent with previous reports, CaMKIV KO mice exhibited impaired retention in a fear conditioning test 28 days after training. In contrast, however, CaMKIV KO mice did not show any testing performance deficits in passive avoidance, one of the most commonly used fear memory paradigms, 28 days after training, suggesting that remote fear memory is intact. CaMKIV KO mice exhibited intact spatial reference memory learning in the Barnes circular maze, and normal spatial working memory in an eight-arm radial maze. CaMKIV KO mice also showed mildly decreased anxiety-like behavior, suggesting that CaMKIV is involved in regulating emotional behavior. These findings indicate that CaMKIV might not be essential for fear memory or spatial memory, although it is possible that the activities of other neural mechanisms or signaling pathways compensate for the CaMKIV deficiency