Symmetry as a sufficient condition for a finite flex

We show that if the joints of a bar and joint framework $(G,p)$ are positioned as `generically' as possible subject to given symmetry constraints and $(G,p)$ possesses a `fully-symmetric' infinitesimal flex (i.e., the velocity vectors of the infinitesimal flex remain unaltered under all symmetry operations of $(G,p)$), then $(G,p)$ also possesses a finite flex which preserves the symmetry of $(G,p)$ throughout the path. This and other related results are obtained by symmetrizing techniques described by L. Asimov and B. Roth in their paper `The Rigidity Of Graphs' from 1978 and by using the fact that the rigidity matrix of a symmetric framework can be transformed into a block-diagonalized form by means of group representation theory. The finite flexes that can be detected with these symmetry-based methods can in general not be found with the analogous non-symmetric methods.Comment: 26 pages, 10 figure

Locked and Unlocked Chains of Planar Shapes

We extend linkage unfolding results from the well-studied case of polygonal linkages to the more general case of linkages of polygons. More precisely, we consider chains of nonoverlapping rigid planar shapes (Jordan regions) that are hinged together sequentially at rotatable joints. Our goal is to characterize the families of planar shapes that admit locked chains, where some configurations cannot be reached by continuous reconfiguration without self-intersection, and which families of planar shapes guarantee universal foldability, where every chain is guaranteed to have a connected configuration space. Previously, only obtuse triangles were known to admit locked shapes, and only line segments were known to guarantee universal foldability. We show that a surprisingly general family of planar shapes, called slender adornments, guarantees universal foldability: roughly, the distance from each edge along the path along the boundary of the slender adornment to each hinge should be monotone. In contrast, we show that isosceles triangles with any desired apex angle less than 90 degrees admit locked chains, which is precisely the threshold beyond which the inward-normal property no longer holds.Comment: 23 pages, 25 figures, Latex; full journal version with all proof details. (Fixed crash-induced bugs in the abstract.

The orbit rigidity matrix of a symmetric framework

A number of recent papers have studied when symmetry causes frameworks on a graph to become infinitesimally flexible, or stressed, and when it has no impact. A number of other recent papers have studied special classes of frameworks on generically rigid graphs which are finite mechanisms. Here we introduce a new tool, the orbit matrix, which connects these two areas and provides a matrix representation for fully symmetric infinitesimal flexes, and fully symmetric stresses of symmetric frameworks. The orbit matrix is a true analog of the standard rigidity matrix for general frameworks, and its analysis gives important insights into questions about the flexibility and rigidity of classes of symmetric frameworks, in all dimensions. With this narrower focus on fully symmetric infinitesimal motions, comes the power to predict symmetry-preserving finite mechanisms - giving a simplified analysis which covers a wide range of the known mechanisms, and generalizes the classes of known mechanisms. This initial exploration of the properties of the orbit matrix also opens up a number of new questions and possible extensions of the previous results, including transfer of symmetry based results from Euclidean space to spherical, hyperbolic, and some other metrics with shared symmetry groups and underlying projective geometry.Comment: 41 pages, 12 figure

Management Activities of Private Forest Landowners in New York State

CaRDI Research & Policy Brief, Issue 15. Click on the PDF for the full report. Visit the HDRU website for a complete listing of HDRU publications at: http://hdru.dnr.cornell.edu/. A complete listing of CaRDI publications can be found on its site: https://cardi.cals.cornell.edu/

Characterizing the universal rigidity of generic frameworks

A framework is a graph and a map from its vertices to E^d (for some d). A framework is universally rigid if any framework in any dimension with the same graph and edge lengths is a Euclidean image of it. We show that a generic universally rigid framework has a positive semi-definite stress matrix of maximal rank. Connelly showed that the existence of such a positive semi-definite stress matrix is sufficient for universal rigidity, so this provides a characterization of universal rigidity for generic frameworks. We also extend our argument to give a new result on the genericity of strict complementarity in semidefinite programming.Comment: 18 pages, v2: updates throughout; v3: published versio

Taxon-specific responses of Southern Ocean diatoms to Fe enrichment revealed by synchrotron radiation FTIR microspectroscopy

© 2014 Author(s). Photosynthesis by marine diatoms contributes substantially to global biogeochemical cycling and ecosystem productivity. It is widely accepted that diatoms are extremely sensitive to changes in Fe availability, with numerous in situ experiments demonstrating rapid growth and increased export of elements (e.g. C, Si and Fe) from surface waters as a result of Fe addition. Less is known about the effects of Fe enrichment on the phenotypes of diatoms, such as associated changes in nutritional value-furthermore, data on taxon-specific responses are almost non-existent. Enhanced supply of nutrient-rich waters along the coast of the subantarctic Kerguelen Island provide a valuable opportunity to examine the responses of phytoplankton to natural Fe enrichment. Here we demonstrate the use of synchrotron radiation Fourier Transform Infrared (SR-FTIR) microspectroscopy to analyse changes in the macromolecular composition of diatoms collected along the coast and plateau of Kerguelen Island, Southern Ocean. SR-FTIR microspectroscopy enabled the analysis of individual diatom cells from mixed communities of field-collected samples, thereby providing insight into in situ taxon-specific responses in relation to changes in Fe availability. Phenotypic responses were taxon-specific in terms of intraspecific variability and changes in proteins, amino acids, phosphorylated molecules, silicate/silicic acid and carbohydrates. In contrast to some previous studies, silicate/silicic acid levels increased under Fe enrichment, in conjunction with increases in carbohydrate stores. The highly abundant taxon Fragilariopsis kerguelensis displayed a higher level of phenotypic plasticity than Pseudo-nitzschia spp., while analysis of the data pooled across all measured taxa showed different patterns in macromolecular composition compared to those for individual taxon. This study demonstrates that taxon-specific responses to Fe enrichment may not always be accurately reflected by bulk community measurements, highlighting the need for further research into taxon-specific phenotypic responses of phytoplankton to environmental change

X-Ray Groups of Galaxies in the Aegis Deep and Wide Fields

We present the results of a search for extended X-ray sources and their corresponding galaxy groups from 800-ks Chandra coverage of the All-wavelength Extended Groth Strip International Survey (AEGIS). This yields one of the largest X-ray selected galaxy group catalogs from a blind survey to date. The red-sequence technique and spectroscopic redshifts allow us to identify 100$$ of reliable sources, leading to a catalog of 52 galaxy groups. The groups span the redshift range $z\sim0.066-1.544$ and virial mass range $M_{200}\sim1.34\times 10^{13}-1.33\times 10^{14}M_\odot$. For the 49 extended sources which lie within DEEP2 and DEEP3 Galaxy Redshift Survey coverage, we identify spectroscopic counterparts and determine velocity dispersions. We select member galaxies by applying different cuts along the line of sight or in projected spatial coordinates. A constant cut along the line of sight can cause a large scatter in scaling relations in low-mass or high-mass systems depending on the size of cut. A velocity dispersion based virial radius can more overestimate velocity dispersion in comparison to X-ray based virial radius for low mass systems. There is no significant difference between these two radial cuts for more massive systems. Independent of radial cut, overestimation of velocity dispersion can be created in case of existence of significant substructure and also compactness in X-ray emission which mostly occur in low mass systems. We also present a comparison between X-ray galaxy groups and optical galaxy groups detected using the Voronoi-Delaunay method (VDM) for DEEP2 data in this field.Comment: Accepted for publication in AP

Photoproduction of phi(1020) mesons on the proton at large momentum transfer

The cross section for $\phi$ meson photoproduction on the proton has been measured for the first time up to a four-momentum transfer -t = 4 GeV^2, using the CLAS detector at the Thomas Jefferson National Accelerator Facility. At low four-momentum transfer, the differential cross section is well described by Pomeron exchange. At large four-momentum transfer, above -t = 1.8 GeV^2, the data support a model where the Pomeron is resolved into its simplest component, two gluons, which may couple to any quark in the proton and in the $\phi$.Comment: 5 pages; 7 figure