Word Length Perturbations in Certain Symmetric Presentations of Dihedral Groups

Given a finite group with a generating subset there is a well-established notion of length for a group element given in terms of its minimal length expression as a product of elements from the generating set. Recently, certain quantities called $\lambda_{1}$ and $\lambda_{2}$ have been defined that allow for a precise measure of how stable a group is under certain types of small perturbations in the generating expressions for the elements of the group. These quantities provide a means to measure differences among all possible paths in a Cayley graph for a group, establish a group theoretic analog for the notion of stability in nonlinear dynamical systems, and play an important role in the application of groups to computational genomics. In this paper, we further expose the fundamental properties of $\lambda_{1}$ and $\lambda_{2}$ by establishing their bounds when the underlying group is a dihedral group. An essential step in our approach is to completely characterize so-called symmetric presentations of the dihedral groups, providing insight into the manner in which $\lambda_{1}$ and $\lambda_{2}$ interact with finite group presentations. This is of interest independent of the study of the quantities $\lambda_{1},\; \lambda_{2}$. Finally, we discuss several conjectures and open questions for future consideration

Oral malodor in Special Care Patients: current knowledge

Epidemiological studies report that about 50% of the population may have oral malodor with a strong social and psychological impact in their daily life. When intra-oral causes are excluded, referral to an appropriate medical specialist is paramount for management and treatment of extra-oral causes. The intra-oral causes of halitosis are highly common, and the dentist is the central clinician to diagnose and treat them. Pseudohalitosis or halitophobia may occur and an early identification of these conditions by the dentist is important in order to avoid unnecessary dental treatments for patients who need psychological or psychiatric therapy. The organoleptic technique is still considered the most reliable examination method to diagnose genuine halitosis. Special needs patients are more prone than others to have oral malodor because of concurrent systemic or metabolic diseases, and medications. The present report reviews halitosis, its implications, and the management in special care dentistry

Bioinformatics tools for marine biotechnology: A practical tutorial with a metagenomic approach

Background: Bioinformatics has pervaded all fields of biology and has become an indispensable tool for almost all research projects. Although teaching bioinformatics has been incorporated in all traditional life science curricula, practical hands-on experiences in tight combination with wet-lab experiments are needed to motivate students. Results: We present a tutorial that starts from a practical problem: finding novel enzymes from marine environments. First, we introduce the idea of metagenomics, a recent approach that extends biotechnology to non-culturable microbes. We presuppose that a probe for the screening of metagenomic cosmid library is needed. The students start from the chemical structure of the substrate that should be acted on by the novel enzyme and end with the sequence of the probe. To attain their goal, they discover databases such as BRENDA and programs such as BLAST and Clustal Omega. Students' answers to a satisfaction questionnaire show that a multistep tutorial integrated into a research wet-lab project is preferable to conventional lectures illustrating bioinformatics tools. Conclusion: Experimental biologists can better operate basic bioinformatics if a problem-solving approach is chosen

Hydraulic properties of ignimbrites: matrix and fracture permeabilities in two pyroclastic flow deposits from Cimino‑Vico volcanoes (Italy)

Hydrological properties of ignimbrites are known in detail only for some areas, although these rocks cover large areas with considerable thicknesses in many volcanic regions of the world. This study investigates hydrological properties of two ignimbrites of Latium (Central Italy), different in age, composition, and origin. The dual porosity of the ignimbrites was examined through laboratory tests, pumping tests, and outcrop surveys. The degree of welding, composition, and stratigraphy of the two ignimbrites are the main factors determining their hydrological properties. The two ignimbrites share a low matrix permeability, showing a different fracturing degree. The more welded ignimbrite is characterized by lower porosity of the matrix and higher fracturing degree, while the less welded ignimbrite is characterized by higher porosity of the matrix and lower fracturing degree. Hydraulic conductivity and storage capacity of the highly welded ignimbrite mainly depend on the denser network of discontinuities. The hydraulic conductivity of the younger ignimbrite, less welded, mainly depend on the sparser network of discontinuities and on the layer of unconsolidated coarse pyroclastic deposits at its base, while the storage capacity depends on the more porous matrix. Should the pyroclastic rocks be used as aquifer for water supplies, or, in other cases, as substratum of waste disposal sites, the dual porosity of the ignimbrites must necessarily include different scales of analysis in order to evaluate the role of matrix and fractures on the permeability of rock mass. In any case, the results of laboratory and on-site tests are to be interpreted taking into account the stratigraphy of the ignimbrite