New Findings in Old Geometry: Using Triangle Centers to Create Similar or Congruent Triangles

The Euler line of a triangle passes through several important points, including three specific triangle centers: the centroid, orthocenter, and circumcenter. Each of these centers is the intersection of lines related to the triangle, mainly its medians, altitudes, and perpendicular bisectors, respectively. We present three theorems which initially share a similar construction. Each involves starting with a triangle and a point. After connecting the triangle’s vertices to that point, creating additional triangles, we establish connections to either the centroids, orthocenters, or circumcenters of the new triangles

Mathematics Versus Statistics

Mathematics and statistics are both important and useful subjects, but the former has maintained prominence in the American education system. On the other hand, statistics is more prevalent in daily life and is an increasingly marketable subject to know. This article gives a personal history of one mathematician’s bumpy road to learning and teaching statistics. Additionally, arguments for how and why to include statistics in the K-12 and college curricula are provided

QUI TRANSULIT SUSTINET: He who transplanted sustains; The shift in political alliances on the national, state and local level in the year after Kelo v. New London

This paper does not have an abstract

Role of Secondary Motifs in Fast Folding Polymers: A Dynamical Variational Principle

A fascinating and open question challenging biochemistry, physics and even geometry is the presence of highly regular motifs such as alpha-helices in the folded state of biopolymers and proteins. Stimulating explanations ranging from chemical propensity to simple geometrical reasoning have been invoked to rationalize the existence of such secondary structures. We formulate a dynamical variational principle for selection in conformation space based on the requirement that the backbone of the native state of biologically viable polymers be rapidly accessible from the denatured state. The variational principle is shown to result in the emergence of helical order in compact structures.Comment: 4 pages, RevTex, 4 eps figure

Crystallographic studies on carp Fishelectin (FEL)

A few years ago we isolated and sequenced a novel glycoprotein present in the eggs of the carp (Cyprinus carpio) (1). The protein, that binds to a Sepharose 4B matrix column and can be eluted with 0.4 M N-acetyl glucosamine, behaves like a lectin of molecular mass 26686 Da. On the basis of DLS experiments the lectin is present in solution as a stable dimer. We have determined its 238 amino acid long sequence, the position of its 4 disulfide bridges and the structure of its single N-linked carbohydrate chain. The lectin shows a very low agglutinating activity for human A-type erythrocytes and interacts with both Gram positive and negative bacteria, these last interactions are inhibited by N-acetyl glucosamine. A data base search shows that its amino acid sequence is significantly similar to that of the members of an invertebrate lectin family that includes tachylectin-1, present in the amebocytes of the horseshoe crab Tachypleus tridentatus, and known to participate in the innate defense system of this species (2.3) and two other lectins, characterized in the plasmodium Physarum polycephalum, that are called Tectonins I and II and are located in the external surface of the plasma membrane (4). We have proposed the name fishelectins (by analogy with tachylectins) for this new vertebrate protein family. Homologous genes are present in other bony fish. The carp protein has 85 % identity with a gene expressed in the crucian carp (Carassius auratus gibelio) (5) and 78 % identity with a gene in the cDNA library of the zebrafish (Danio rerio). We have prepared three different crystal forms of the apo protein and two of co-crystals with N-acetyl glucosamine. The orthorhombic form of the apoprotein belongs to space group P212121 and was solved first using the MIR method. Our poster will present the data collection statistics of the best apo and holo forms of the lectin and the refinement statistics of the holo form and will discuss the structure and similarity of this newly identified family of vertebrate proteins to a well known invertebrate protein family

Crystallographic studies on carp Fishelectin (FEL)

A few years ago we isolated and sequenced a novel glycoprotein present in the eggs of the carp (Cyprinus carpio). The protein, that binds to a Sepharose 4B matrix column and can be eluted with 0.4 M N-acetyl glucosamine, behaves like a lectin of molecular mass 26686 Da. On the basis of DLS experiments the lectin is present in solution as a stable dimer. We have determined its 238 amino acid long sequence, the position of its 4 disulfide bridges and the structure of its single N-linked carbohydrate chain. The lectin shows a very low agglutinating activity for human A-type erythrocytes and interacts with both Gram positive and negative bacteria, these last interactions are inhibited by N-acetyl glucosamine. A data base search shows that its amino acid sequence is significantly similar to that of the members of an invertebrate lectin family that includes tachylectin-1, present in the amebocytes of the horseshoe crab Tachypleus tridentatus, and known to participate in the innate defense system of this species and two other lectins, characterized in the plasmodium Physarum polycephalum, that are called Tectonins I and II and are located in the external surface of the plasma membrane. We have proposed the name fishelectins (by analogy with tachylectins) for this new vertebrate protein family. Homologous genes are present in other bony fish. The carp protein has 85 % identity with a gene expressed in the crucian carp (Carassius auratus gibelio) and 78 % identity with a gene in the cDNA library of the zebrafish (Danio rerio). We have prepared three different crystal forms of the apo protein and two of co-crystals with N-acetyl glucosamine. The orthorhombic form of the apoprotein belongs to space group P212121 and was solved first using the MIR method. Our poster will present the data collection statistics of the best apo and holo forms of the lectin and the refinement statistics of the holo form and will discuss the structure and similarity of this newly identified family of vertebrate proteins to a well known invertebrate protein family

A self-organized model for cell-differentiation based on variations of molecular decay rates

Systemic properties of living cells are the result of molecular dynamics governed by so-called genetic regulatory networks (GRN). These networks capture all possible features of cells and are responsible for the immense levels of adaptation characteristic to living systems. At any point in time only small subsets of these networks are active. Any active subset of the GRN leads to the expression of particular sets of molecules (expression modes). The subsets of active networks change over time, leading to the observed complex dynamics of expression patterns. Understanding of this dynamics becomes increasingly important in systems biology and medicine. While the importance of transcription rates and catalytic interactions has been widely recognized in modeling genetic regulatory systems, the understanding of the role of degradation of biochemical agents (mRNA, protein) in regulatory dynamics remains limited. Recent experimental data suggests that there exists a functional relation between mRNA and protein decay rates and expression modes. In this paper we propose a model for the dynamics of successions of sequences of active subnetworks of the GRN. The model is able to reproduce key characteristics of molecular dynamics, including homeostasis, multi-stability, periodic dynamics, alternating activity, differentiability, and self-organized critical dynamics. Moreover the model allows to naturally understand the mechanism behind the relation between decay rates and expression modes. The model explains recent experimental observations that decay-rates (or turnovers) vary between differentiated tissue-classes at a general systemic level and highlights the role of intracellular decay rate control mechanisms in cell differentiation.Comment: 16 pages, 5 figure

30 days wild: development and evaluation of a large-scale nature engagement campaign to improve well-being

There is a need to increase people’s engagement with and connection to nature, both for human well-being and the conservation of nature itself. In order to suggest ways for people to engage with nature and create a wider social context to normalise nature engagement, The Wildlife Trusts developed a mass engagement campaign, 30 Days Wild. The campaign asked people to engage with nature every day for a month. 12,400 people signed up for 30 Days Wild via an online sign-up with an estimated 18,500 taking part overall, resulting in an estimated 300,000 engagements with nature by participants. Samples of those taking part were found to have sustained increases in happiness, health, connection to nature and pro-nature behaviours. With the improvement in health being predicted by the improvement in happiness, this relationship was mediated by the change in connection to nature

Selected reactive oxygen species and antioxidant enzymes in common bean after Pseudomonas syringae pv. phaseolicola and Botrytis cinerea infection

Phaseolus vulgaris cv. Korona plants were inoculated with the bacteria Pseudomonas syringae pv. phaseolicola (Psp), necrotrophic fungus Botrytis cinerea (Bc) or with both pathogens sequentially. The aim of the experiment was to determine how plants cope with multiple infection with pathogens having different attack strategy. Possible suppression of the non-specific infection with the necrotrophic fungus Bc by earlier Psp inoculation was examined. Concentration of reactive oxygen species (ROS), such as superoxide anion (O2 -) and H2O2 and activities of antioxidant enzymes such as superoxide dismutase (SOD), catalase (CAT) and peroxidase (POD) were determined 6, 12, 24 and 48 h after inoculation. The measurements were done for ROS cytosolic fraction and enzymatic cytosolic or apoplastic fraction. Infection with Psp caused significant increase in ROS levels since the beginning of experiment. Activity of the apoplastic enzymes also increased remarkably at the beginning of experiment in contrast to the cytosolic ones. Cytosolic SOD and guaiacol peroxidase (GPOD) activities achieved the maximum values 48 h after treatment. Additional forms of the examined enzymes after specific Psp infection were identified; however, they were not present after single Bc inoculation. Subsequent Bc infection resulted only in changes of H2O2 and SOD that occurred to be especially important during plant–pathogen interaction. Cultivar Korona of common bean is considered to be resistant to Psp and mobilises its system upon infection with these bacteria. We put forward a hypothesis that the extent of defence reaction was so great that subsequent infection did not trigger significant additional response