The Three-Dimensional Interpretation of a Class of Simple Line-Drawings

We provide a theory of the three-dimensional interpretation of a class of line-drawings called p-images, which are interpreted by the human vision system as parallelepipeds ("boxes"). Despite their simplicity, p-images raise a number of interesting vision questions: *Why are p-images seen as three-dimensional objects? Why not just as flatimages? *What are the dimensions and pose of the perceived objects? *Why are some p-images interpreted as rectangular boxes, while others are seen as skewed, even though there is no obvious distinction between the images? *When p-images are rotated in three dimensions, why are the image-sequences perceived as distorting objects---even though structure-from-motion would predict that rigid objects would be seen? *Why are some three-dimensional parallelepipeds seen as radically different when viewed from different viewpoints? We show that these and related questions can be answered with the help of a single mathematical result and an associated perceptual principle. An interesting special case arises when there are right angles in the p-image. This case represents a singularity in the equations and is mystifying from the vision point of view. It would seem that (at least in this case) the vision system does not follow the ordinary rules of geometry but operates in accordance with other (and as yet unknown) principles.

Low Molecular Weight Opioid Peptide Esters Could be Developed as a New Class of Analgesics.

Low molecular weight opioid peptide esters (OPE) could become a class of analgesics with different side effect profiles than current opiates. OPE may have sufficient plasma stability to cross the blood brain barrier (BBB), undergo ester hydrolysis and produce analgesia. OPE of dipeptides, tyr-pro and tyr-gly conjugated to ethanol have a structure similar to the anesthestic agent, etomidate. Based upon the analgesic activity of dipeptide opioids, Lipinski's criteria, and permeability of select GABA esters to cross the BBB, opioid peptides (OP) conjugated to ethanol, cholesterol or 3-glucose are lead recommendations. Preliminary animal data suggests that tyr-pro-ethyl ester crosses the BBB and unexpectedly produces hyperalgesia. Currently, there are no approved OP analgesics available for clinical use. Clinical trials of good manufacturing practice OP administered to patients suffering from chronic pain with indwelling intrathecal pumps could resolve the issue that OP may be superior to opiates and may redirect research.

Ethnomathematical research and drama in education techniques: developing a dialogue in a geometry class of 10th grade students

Ethnomathematical research, together with digital technologies (WebQuest) and Drama-in- Education (DiE) techniques, can create a fruitful learning environment in a mathematics classroom—a hybrid/third space—enabling increased student participation and higher levels of cognitive engagement. This article examines how ethnomathematical ideas processed within the experiential environment established by the Drama-in-Education techniques challenged students‘ conceptions of the nature of mathematics, the ways in which students engaged with mathematics learning using mind and body, and the ̳dialogue‘ that was developed between the Discourse situated in a particular practice and the classroom Discourse of mathematics teaching. The analysis focuses on an interdisciplinary project based on an ethnomathematical study of a designing tradition carried out by the researchers themselves, involving a search for informal mathematics and the connections with context and culture; 10th grade students in a public school in Athens were introduced to the mathematics content via an original WebQuest based on this previous ethnomathematical study; Geometry content was further introduced and mediated using the Drama-in-Education (DiE) techniques. Students contributed in an unfolding dialogue between formal and informal knowledge, renegotiating both mathematical concepts and their perception of mathematics as a discipline.

A class of generalized Lévy Laplacians in infinite dimensional calculus

A class of generalized Lévy Laplacians which contain as a special case the ordinary Lévy Laplacian are considered. Topics such as limit average of the second order functional derivative with respect to a certain equally dense (uniformly bounded) orthonormal base, the relations with Kuo’s Fourier transform and other infinite dimensional Laplacians are studied.

A novel structural class of photoswitchable oligonucleotide

Directed Michaelis–Arbuzov reactions of support-bound internucleotide O-benzyl- or O-methyl-phosphite triesters with meta-phenylazobenzylamine or alkane-/glycol-linked a,x-diamines were effected in the presence of iodine. The corresponding tritylated phosphoramidate-linked 11-mers were fully deprotected and released from the support under standard conditions and the fast- and slow-diastereoisomers of both the E- and the Z-meta-phenylazobenzyl-appended oligomers were readily resolved by RP-HPLC. The primary amine-functionalised oligonucleotides were either purified, detritylated and then finally treated with Nhydroxysuccinimidyl carboxylic acid ester derivatives of photoswitchable moieties (Route A) or first derivatised and then subsequently purified and detritylated (Route B). This latter route enabled resolution of fast- and slow-isomers of the trityl-on oligomers bearing novel photoswitchable azopyridine or 9-alkoxyanthracene moieties using RP-HPLC, following which the pure diastereoisomers were detritylated and characterised by MALDI-MS.

Peptide DV-28 amide: Prototype of a novel class of bradykinin receptor antagonist isolated from the defensive skin secretion of bombinid toads

Kinestatin, isolated from the skin of the Chinese toad, Bombina maxima, was the first bradykinin B2 receptor antagonist identified in amphibians. Molecular cloning established that it is co-encoded with the bradykinin-related peptide, maximakinin, within one of several skin kininogens. To examine other species within the genus Bombina for the presence of structural homologues of kinestatin, we subjected skin secretion of the toad, Bombina orientalis, to HPLC fractionation with subsequent bioassay of fractions for antagonism of bradykinin activity using an isolated rat tail artery smooth muscle preparation. A single fraction was located that inhibited bradykinin-induced relaxation of rat arterial smooth muscle and MALDI-TOF analysis of this fraction revealed that it contained a single peptide of molecular mass 3198.5 Da. Further primary structural analysis of this peptide showed that it was a 28-mer with an N-terminal Asp (D) residue and a C-terminal Val (V) residue that was amidated. The peptide was named DV-28 amide in accordance with these primary structural attributes. Synthetic DV-28 amide replicated the observed bradykinin antagonistic effect within the smooth muscle bioassay in a dose-dependent manner. In addition, it was observed to inhibit the proliferation of human microvessel endothelial cells (HMECs) as assessed by MTT assay. Bioinformatic analysis revealed that DV-28 amide was, like kinestatin, co-encoded with a bradykinin receptor agonist on one of two skin kininogens identified in B. orientalis. DV-28 amide thus represents a novel class of bradykinin antagonist from skin secretions of bombinid toads that appear to be a rich source of such novel peptides.

Hybridization of a class of "second order" models of traffic flow

Despite the simultaneous progress of traffic modelling both on the macroscopic and microscopic front, recent works [E. Bourrel, J.B. Lessort, Mixing micro and macro representation of traffic flow: a hybrid model based on the LWR theory, Transport. Res. Rec. 1852 (2003) 193–200; D. Helbing, M. Treiber, Critical discussion of “synchronized flow”, Coop. Transport. Dyn. 1 (2002) 2.1–2.24; A. Hennecke, M. Treiber, D. Helbing, Macroscopic simulations of open systems and micro–macro link, in: D. Helbing, H.J. Herrmann, M. Schreckenberg, D.E. Wolf (Eds.), Traffic and Granular Flow ’99, Springer, Berlin, 2000, pp. 383–388] highlighted that one of the most promising way to simulate efficiently traffic flow on large road networks is a clever combination of both traffic representations: the hybrid modelling. Our focus in this paper is to propose two hybrid models for which the macroscopic (resp. mesoscopic) part is based on a class of second order model [A. Aw, M. Rascle, Resurection of second order models of traffic flow?, SIAM J. Appl. Math. 60 (2000) 916–938] whereas the microscopic part is a Follow-the Leader type model [D.C. Gazis, R. Herman, R.W. Rothery, Nonlinear follow-the-leader models of traffic flow, Oper. Res. 9 (1961) 545–567; R. Herman, I. Prigogine, Kinetic Theory of Vehicular Traffic, American Elsevier, New York, 1971]. For the first hybrid model, we define precisely the translation of boundary conditions at interfaces and for the second one we explain the synchronization processes. Furthermore, through some numerical simulations we show that the waves propagation is not disturbed and the mass is accurately conserved when passing from one traffic representation to another.