Link invariants associated with gauge equivalent solutions of the Yang-Baxter equation: The one-parameter family of minimal typical representations of Uq[gl(2|1)]

In this paper we investigate the construction of state models for link invariants using representations of the braid group obtained from various gauge choices for a solution of the trigonometric Yang-Baxter equation. Our results show that it is possible to obtain invariants of regular isotopy (as defined by Kauffman) which may not be ambient isotopic. We illustrate our results with explicit computations using solutions of the trigonometric Yang-Baxter equation associated with the one-parameter family of minimal typical representations of the quantum superalgebra U-q,[gl(2/1)]. We have implemented MATHEMATICA code to evaluate the invariants for all prime knots up to 10 crossings.

Phylogeny of the Sporobolus indicus complex, based on internal transcribed spacer (ITS) sequences

The entire internal transcribed spacer ( ITS) region, including the 5.8S subunit of the nuclear ribosomal DNA ( rDNA), was sequenced by direct double-stranded sequencing of polymerase chain reaction (PCR) amplified fragments. The study included 40 Sporobolus ( Family Poaceae, subfamily Chloridoideae) seed collections from 14 putative species ( all 11 species from the S. indicus complex and three Australian native species). These sequences, along with those from two out-group species [ Pennisetum alopecuroides ( L.) Spreng. and Heteropogon contortus ( L.) P. Beauv. ex Roemer & Schultes, Poaceae, subfamily Panicoideae], were analysed by the parsimony method (PAUP; version 4.0b4a) to infer phylogenetic relationships among these species. The length of the ITS1, 5.8S subunit and ITS2 region were 222, 164 and 218 base pairs ( bp), respectively, in all species of the S. indicus complex, except for the ITS2 region of S. diandrus P. Beauv. individuals, which was 217 bp long. Of the 624 characters included in the analysis, 245 ( 39.3%) of the 330 variable sites contained potential phylogenetic information. Differences in sequences among the members of the S. pyramidalis P. Beauv., S. natalensis (Steud.) Dur & Schinz and S. jacquemontii Kunth. collections were 0%, while differences ranged from 0 to 2% between these and other species of the complex. Similarly, differences in sequences among collections of S. laxus B. K. Simon, S. sessilis B. K. Simon, S. elongatus R. Br. and S. creber De Nardi were 0%, compared with differences of 1-2% between these four species and the rest of the complex. When comparing S. fertilis ( Steud.) Clayton and S. africanus (Poir.) Robyns & Tourney, differences between collections ranged from 0 to 1%. Parsimony analysis grouped all 11 species of the S. indicus complex together, indicating a monophyletic origin. For the entire data set, pair-wise distances among members of the S. indicus complex varied from 0.00 to 1.58%, compared with a range of 20.08-21.44% among species in the complex and the Australian native species studied. A strict consensus phylogenetic tree separated 11 species of the S. indicus complex into five major clades. The phylogeny, based on ITS sequences, was found to be congruent with an earlier study on the taxonomic relationship of the weedy Sporobolus grasses revealed from random amplified polymorphic DNA ( RAPD). However, this cladistic analysis of the complex was not in agreement with that created on past morphological analyses and therefore gives a new insight into the phylogeny of the S. indicus complex.

Emergence of joint attention: Relationships between gaze following, social referencing, imitation, and naming in infancy

The authors investigated the extent to which the joint-attention behaviors of gaze following, social referencing, and object-directed imitation were related to each other and to infants vocabulary development in a sample of 60 infants between the ages of 8 and 14 months. Joint-attention skills and vocabulary development were assessed in a laboratory setting. Split-half reliability analyses on the joint-attention measures indicated that the tasks reliably assessed infants' capabilities. In the main analysis, no significant correlations were found among the joint-attention behaviors except for a significant relationship between gaze following and the number of names in infants' productive vocabularies. The overall pattern of results did not replicate results of previous studies (e.g., M. Carpenter, K. Nagell, & M. Tomasello, 1998) that found relationships between various emerging joint-attention behaviors.