An inductive reasoning model in linear and quadratic sequences

Presentamos algunos resultados de una investigación más amplia cuyo objetivo general es describir y caracterizar el razonamiento inductivo que utilizan estudiantes de tercero y cuarto de Secundaria al resolver tareas relacionadas con sucesiones lineales y cuadráticas (Cañadas, 2007). Identificamos diferencias en el empleo de algunos de los pasos considerados para la descripción del razonamiento inductivo en la resolución de dos de los seis problemas planteados a los estudiantes. Describimos estas diferencias y las analizamos en función de las características de los problemas.

Graphical representation and generalization in sequences problems

In this paper we present different ways used by Secondary students to generalize when they try to solve problems involving sequences. 359 Spanish students solved generalization problems in a written test. These problems were posed through particular terms expressed in different representations. We present examples that illustrate different ways of achieving various types of generalization and how students express generalization. We identify graphical representation of generalization as a useful tool of getting other ways of expressing generalization, and we analyze its connection with other ways of expressing it.

An ontological characterization of time-series and state-sequences for data mining

Time-series and sequences are important patterns in data mining. Based on an ontology of time-elements, this paper presents a formal characterization of time-series and state-sequences, where a state denotes a collection of data whose validation is dependent on time. While a time-series is formalized as a vector of time-elements temporally ordered one after another, a state-sequence is denoted as a list of states correspondingly ordered by a time-series. In general, a time-series and a state-sequence can be incomplete in various ways. This leads to the distinction between complete and incomplete time-series, and between complete and incomplete state-sequences, which allows the expression of both absolute and relative temporal knowledge in data mining.

rbcL sequences indicate a single evolutionary origin of multinucleate cells in the red algal tribe Callithamnieae.

In the Ceramiaceae, one of the largest families of the red algae, there are from 1 to 4000 nuclei in each vegetative cell, but each tribe is homogeneous with respect to the uninucleate/multinucleate character state, except for the Callithamnieae. The goals of this study were to analyze rbcL gene sequences to clarify the evolution of taxa within the tribe Callithamnieae and to evaluate the potential evolutionary significance of the development of multinucleate cells in certain taxa. The genus Aglaothamnion, segregated from Callithamnion because it is uninucleate, was paraphyletic in all analyses. Callithamnion (including Aristothamnion) was monophyletic although not robustly so, apparently due to variations between taxa in rate of sequence evolution. Morphological synapomorphies were identified at different depths in the tree, supporting the molecular phylogenetic analysis. The uninucleate character state is ancestral in this tribe. The evolution of multinucleate cells has occurred once in the Callithamnieae. Multiple nuclei in each cell may combine the benefits of small C values (rapid cell cycle) with large cells (permitting morphological elaboration) while maintaining a constant ratio of nuclear volume: cytoplasmic volume.

rbcL sequences reveal multiple cryptic introductions of the Japanese red alga Polysiphonia harveyi.

In Europe, the last 20 years have seen a spectacular increase in accidental introductions of marine species, but it has recently been suggested that both the actual number of invaders and their impacts have been seriously underestimated because of the prevalence of sibling species in marine habitats. The red alga Polysiphoniaharveyi is regarded as an alien in the British Isles and Atlantic Europe, having appeared in various locations there during the past 170 years. Similar or conspecific populations are known from Atlantic North America and Japan. To choose between three competing hypotheses concerning the origin of P. harveyi in Europe, we employed rbcL sequence analysis in conjunction with karyological and interbreeding data for samples and isolates of P. harveyi and various congeners from the Pacific and North Atlantic Oceans. All cultured isolates of P. harveyi were completely interfertile, and there was no evidence of polyploidy or aneuploidy. Thus, this biological species is both morphologically and genetically variable: intraspecific rbcL divergences of up to 2.1% are high even for red algae. Seven rbcL haplotypes were identified. The four most divergent haplotypes were observed in Japanese samples from Hokkaido and south-central Honshu, which are linked by hypothetical 'missing' haplotypes that may be located in northern Honshu. These data are consistent with Japan being the centre of diversity and origin for P. harveyi. Two non-Japanese lineages were linked to Hokkaido and Honshu, respectively. A single haplotype was found in all North Atlantic and Mediterranean accessions, except for North Carolina, where the haplotype found was the same as that invading in New Zealand and California. The introduction of P. harveyi into New Zealand has gone unnoticed because P. strictissima is a morphologically indistinguishable native sibling species. The sequence divergence between them is 4–5%, greater than between some morphologically distinct red algal species. Two different types of cryptic invasions of P. harveyi have therefore occurred. In addition to its introduction as a cryptic sibling species in New Zealand, P. harveyi has been introduced at least twice into the North Atlantic from presumed different source populations. These two introductions are genetically and probably also physiologically divergent but completely interfertile.

Methylation status of oestrogen receptor-a-gene promoter sequences in human ovarian epithelial cell lines.

We have determined the methylation status of the CpG island of the oestrogen receptor gene in seven human ovarian cell lines. Cell lines expressing oestrogen receptor showed no evidence of hypermethylation. In three of four cell lines that produced no detectable oestrogen receptor protein, hypermethylation was observed at the NotI site of the CpG island. These results indicate that aberrant hypermethylation may be responsible for a significant proportion of epithelial ovarian tumours in which oestrogen receptor expression is lost.

Measles virus minigenomes encoding two autofluorescent proteins reveal cell-to-cell variation in reporter expression dependent on viral sequences between the transcription units.

Transcription from morbillivirus genomes commences at a single promoter in the 3' non-coding terminus, with the six genes being transcribed sequentially. The 3' and 5' untranslated regions (UTRs) of the genes (mRNA sense), together with the intergenic trinucleotide spacer, comprise the non-coding sequences (NCS) of the virus and contain the conserved gene end and gene start signals, respectively. Bicistronic minigenomes containing transcription units (TUs) encoding autofluorescent reporter proteins separated by measles virus (MV) NCS were used to give a direct estimation of gene expression in single, living cells by assessing the relative amounts of each fluorescent protein in each cell. Initially, five minigenomes containing each of the MV NCS were generated. Assays were developed to determine the amount of each fluorescent protein in cells at both cell population and single-cell levels. This revealed significant variations in gene expression between cells expressing the same NCS-containing minigenome. The minigenome containing the M/F NCS produced significantly lower amounts of fluorescent protein from the second TU (TU2), compared with the other minigenomes. A minigenome with a truncated F 5' UTR had increased expression from TU2. This UTR is 524 nt longer than the other MV 5' UTRs. Insertions into the 5' UTR of the enhanced green fluorescent protein gene in the minigenome containing the N/P NCS showed that specific sequences, rather than just the additional length of F 5' UTR, govern this decreased expression from TU2.