Cyclicity versus center problem

We prove that there are one-parameter families of planar differential equations for which the center problem has a trivial solution and on the other hand the cyclicity of the weak focus is arbitrarily high. We illustrate this phenomenon in several examples for which this cyclicity is computed.

The transcriptional network activated by Cln3 cyclin at the G1-to-S transition of the yeast cell cycle

Background: The G1-to-S transition of the cell cycle in the yeast Saccharomyces cerevisiae involves an extensive transcriptional program driven by transcription factors SBF (Swi4-Swi6) and MBF (Mbp1-Swi6). Activation of these factors ultimately depends on the G1 cyclin Cln3. Results: To determine the transcriptional targets of Cln3 and their dependence on SBF or MBF, we first have used DNA microarrays to interrogate gene expression upon Cln3 overexpression in synchronized cultures of strains lacking components of SBF and/or MBF. Secondly, we have integrated this expression dataset together with other heterogeneous data sources into a single probabilistic model based on Bayesian statistics. Our analysis has produced more than 200 transcription factor-target assignments, validated by ChIP assays and by functional enrichment. Our predictions show higher internal coherence and predictive power than previous classifications. Our results support a model whereby SBF and MBF may be differentially activated by Cln3. Conclusions: Integration of heterogeneous genome-wide datasets is key to building accurate transcriptional networks. By such integration, we provide here a reliable transcriptional network at the G1-to-S transition in the budding yeast cell cycle. Our results suggest that to improve the reliability of predictions we need to feed our models with more informative experimental data.

Improving Information Problem Solving skills in Secondary Education through embedded instruction

This empirical study consists in an investigation of the effects, on the development of Information Problem Solving (IPS) skills, of a long-term embedded, structured and supported instruction in Secondary Education. Forty secondary students of 7th and 8th grades (13–15 years old) participated in the 2-year IPS instruction designed in this study. Twenty of them participated in the IPS instruction, and the remaining twenty were the control group. All the students were pre- and post-tested in their regular classrooms, and their IPS process and performance were logged by means of screen capture software, to warrant their ecological validity. The IPS constituent skills, the web search sub-skills and the answers given by each participant were analyzed. The main findings of our study suggested that experimental students showed a more expert pattern than the control students regarding the constituent skill ‘defining the problem’ and the following two web search sub-skills: ‘search terms’ typed in a search engine, and ‘selected results’ from a SERP. In addition, scores of task performance were statistically better in experimental students than in control group students. The paper contributes to the discussion of how well-designed and well-embedded scaffolds could be designed in instructional programs in order to guarantee the development and efficiency of the students’ IPS skills by using net information better and participating fully in the global knowledge society.

The impact of balancing on problem hardness in a highly structured domain

Random problem distributions have played a key role in the study and design of algorithms for constraint satisfaction and Boolean satisfiability, as well as in ourunderstanding of problem hardness, beyond standard worst-case complexity. We consider random problem distributions from a highly structured problem domain that generalizes the Quasigroup Completion problem (QCP) and Quasigroup with Holes (QWH), a widely used domain that captures the structure underlying a range of real-world applications. Our problem domain is also a generalization of the well-known Sudoku puz- zle: we consider Sudoku instances of arbitrary order, with the additional generalization that the block regions can have rectangular shape, in addition to the standard square shape. We evaluate the computational hardness of Generalized Sudoku instances, for different parameter settings. Our experimental hardness results show that we can generate instances that are considerably harder than QCP/QWH instances of the same size. More interestingly, we show the impact of different balancing strategies on problem hardness. We also provide insights into backbone variables in Generalized Sudoku instances and how they correlate to problem hardness.

A survey on the inverse integrating factor

The relation between limit cycles of planar differential systems and the inverse integrating factor was first shown in an article of Giacomini, Llibre and Viano appeared in 1996. From that moment on, many research articles are devoted to the study of the properties of the inverse integrating factor and its relationwith limit cycles and their bifurcations. This paper is a summary of all the results about this topic. We include a list of references together with the corresponding related results aiming at being as much exhaustive as possible. The paper is, nonetheless, self-contained in such a way that all the main results on the inverse integrating factor are stated and a complete overview of the subject is given. Each section contains a different issue to which the inverse integrating factor plays a role: the integrability problem, relation with Lie symmetries, the center problem, vanishing set of an inverse integrating factor, bifurcation of limit cycles from either a period annulus or from a monodromic ω-limit set and some generalizations.

Spontaneous Emergence of Chirality in the Limited Enantioselectivity Model: Autocatalytic Cycle Driven by an External Reagent

The emergence of chirality in enantioselective autocatalysis for compounds unable to transform according to the Frank-like reaction network is discussed with respect to the controversial limited enantioselectivity (LES) model composed of coupled enantioselective and non-enantioselective autocatalyses. The LES model cannot lead to spontaneous mirror symmetry breaking (SMSB) either in closed systems with a homogeneous temperature distribution or in closed systems with a stationary non-uniform temperature distribution. However, simulations of chemical kinetics in a two-compartment model demonstrate that SMSB may occur if both autocatalytic reactions are spatially separated at different temperatures in different compartments but coupled under the action of a continuous internal flow. In such conditions, the system can evolve, for certain reaction and system parameters, toward a chiral stationary state; that is, the system is able to reach a bifurcation point leading to SMSB. Numerical simulations in which reasonable chemical parameters have been used suggest that an adequate scenario for such a SMSB would be that of abyssal hydrothermal vents, by virtue of the typical temperature gradients found there and the role of inorganic solids mediating chemical reactions in an enzyme-like role.