A necessary condition for generic rigidity of bar-and-joint frameworks in dd-space

A graph $G=(V,E)$ is $d$-sparse if each subset $X\subseteq V$ with $|X|\geq d$ induces at most $d|X|-{{d+1}\choose{2}}$ edges in $G$. Maxwell showed in 1864 that a necessary condition for a generic bar-and-joint framework with at least $d+1$ vertices to be rigid in ${\mathbb R}^d$ is that $G$ should have a $d$-sparse subgraph with $d|X|-{{d+1}\choose{2}}$ edges. This necessary condition is also sufficient when $d=1,2$ but not when $d\geq 3$. Cheng and Sitharam strengthened Maxwell's condition by showing that every maximal $d$-sparse subgraph of $G$ should have $d|X|-{{d+1}\choose{2}}$ edges when $d=3$. We extend their result to all $d\leq 11$.Comment: There was an error in the proof of Theorem 3.3(b) in version 1 of this paper. A weaker statement was proved in version 2 and then used to derive the main result Theorem 4.1 when $d\leq 5$. The proof technique was subsequently refined in collaboration with Hakan Guler to extend this result to all $d\leq 11$ in Theorem 3.3 of version

Coincident Rigidity of 2-Dimensional Frameworks

Fekete, Jord\'an and Kaszanitzky [4] characterised the graphs which can be realised as 2-dimensional, infinitesimally rigid, bar-joint frameworks in which two given vertices are coincident. We formulate a conjecture which would extend their characterisation to an arbitrary set T of vertices and verify our conjecture when |T| = 3

Economical Analysis of Ablactation of Eastern Anatolian Red (EAR) Calves in Different Periods

In this research, economic analysis of ablactation of Eastern Anatolian Red calves in different periods was made under the conditions of Firat University Research and Implementation Farm. In the research a total of 21 pedigree Eastern Anatolian Red Calves were used in three different groups, each group included 7 calves.  The calves ablactated in the 5th month and used as control group consisted the 1st group, the calves ablactated in the 4th month consisted the 2nd group and those ablactated in the 2nd month consisted the 3rd group. In formation of each group, it was paid attention that calves with the closest birth weights and birth dates were selected. When live weights of groups in day 180 were examined in the research, it was determined that the live weight value of the 1st Group was 86,07 kg, that of the 2nd Group was 99.93 kg and that of the 3rd Group was 86.93 kg.  To make an economical conclusion, total milk and feed cost was found for 1 kg of live weight gain and this cost was determined as 632.08 TRY for the 1st group, 716.27 TRY for the 2nd group and 920.89 TRY for the 3rd group. As a result, it was determined that the ablactation time in which consumed milk and feed amount is most economic for both live weight increase and 1 kg live weight gain is 120 days. Keywords: Calf, Eastern Anatolian Red, Economic Analysis, Ablactation, Milk

Rigidity of Frameworks

PhDA d-dimensional (bar-and-joint) framework is a pair (G; p) where G = (V;E) is a graph and p : V > Rd is a function which is called the realisation of the framework (G; p). A motion of a framework (G; p) is a continuous function P : [0; 1] x V > Rd which preserves the edge lengths for all t 2 [0; 1]. A motion is rigid if it also preserves the distances between non-adjacent pairs of vertices of G. A framework is rigid if all of its motions are rigid motions. An in nitesimal motion of a d-dimensional framework (G; p) is a function q : V > Rd such that [p(u) - p(v)] ~ [q(u) - q(v)] = 0 for all uv 2 E. An in nitesimal motion of the framework (G; p) is rigid if we have [p(u) - p(v)] . [q(u) - q(v)] = 0 also for non-adjacent pairs of vertices. A framework (G; p) is in nitesimally rigid if all of its in nitesimal motions are rigid in nitesimal motions. A d-dimensional framework (G; p) is generic if the coordinates of the positions of vertices assigned by p are algebraically independent. For generic frameworks rigidity and in nitesimal rigidity are equivalent. We construct a matrix of size |E| xd|V| for a given d-dimensional framework (G; p) as follows. The rows are indexed by the edges of G and the set of d consecutive columns corresponds to a vertex of G. The entries of a row indexed by uv 2 E contain the d coordinates of p(u) - p(v) and p(v) - p(u) in the d consecutive columns corresponding to u and v, respectively, and the remaining entries are all zeros. This matrix is the rigidity matrix of the framework (G; p) and denoted by R(G; p). Translations and rotations of a given framework (G; p) give rise to a subspace of dimension d+1 2 of the null space of R(G; p) when p(v) affinely spans Rd. Therefore we have rankR(G; p) djV j�� d+1 2 if p(v) affinely spans Rd, and the framework is in infinitesimally rigid if equality holds. We construct a matroid corresponding to the framework (G; p) from the rigidity matrix R(G; p) in which F E is independent if and only if the rows of R(G; p) indexed by F are linearly independent. This matroid is called the rigidity matroid of the framework (G; p). It is clear that any two generic realisations of G give rise to the same rigidity matroid. In this thesis we will investigate rigidity properties of some families of frameworks. We rst investigate rigidity of linearly constrained frameworks i.e., 3- dimensional bar-and-joint frameworks for which each vertex has an assigned plane to move on. Next we characterise rigidity of 2-dimensional bar-and-joint frameworks (G; p) for which three distinct vertices u; v;w 2 V (G) are mapped to the same point, that is p(u) = p(v) = p(w), and this is the only algebraic dependency of p. Then we characterise rigidity of a family of non-generic body-bar frameworks in 3-dimensions. Finally, we give an upper bound on the rank function of a d-dimensional bar-and-joint framework for 1 < d < 11.Turkish Ministry of National Educatio

The design and fabrication of supramolecular semiconductor nanowires formed by benzothienobenzothiophene (BTBT)-conjugated peptides

π-Conjugated small molecules based on a [1]benzothieno[3,2-b]benzothiophene (BTBT) unit are of great research interest in the development of solution-processable semiconducting materials owing to their excellent charge-transport characteristics. However, the BTBT π-core has yet to be demonstrated in the form of electro-active one-dimensional (1D) nanowires that are self-assembled in aqueous media for potential use in bioelectronics and tissue engineering. Here we report the design, synthesis, and self-assembly of benzothienobenzothiophene (BTBT)–peptide conjugates, the BTBT–peptide (BTBT-C3–COHN-Ahx-VVAGKK-Am) and the C8-BTBT–peptide (C8-BTBT-C3–COHN-Ahx-VVAGKK-Am), as β-sheet forming amphiphilic molecules, which self-assemble into highly uniform nanofibers in water with diameters of 11–13(±1) nm and micron-size lengths. Spectroscopic characterization studies demonstrate the J-type π–π interactions among the BTBT molecules within the hydrophobic core of the self-assembled nanofibers yielding an electrical conductivity as high as 6.0 × 10−6 S cm−1. The BTBT π-core is demonstrated, for the first time, in the formation of self-assembled peptide 1D nanostructures in aqueous media for potential use in tissue engineering, bioelectronics and (opto)electronics. The conductivity achieved here is one of the highest reported to date in a non-doped state

Germline Pathogenic Variants Identified by Targeted Next-Generation Sequencing of Susceptibility Genes in Pheochromocytoma and Paraganglioma

The aim of this study was to evaluate germline variant frequencies of pheochromocytoma and paraganglioma targeted susceptibility genes with next-generation sequencing method. Germline DNA from 75 cases were evaluated with targeted next-generation sequencing on an Illumina NextSeq550 instrument. KIF1B, RET, SDHB, SDHD, TMEM127, and VHL genes were included in the study, and Sanger sequencing was used for verifying the variants. The pathogenic/likely pathogenic variants were in the VHL, RET, SDHB, and SDHD genes, and the diagnosis rate was 24% in this study. Three different novel pathogenic variants were determined in five cases. This is the first study from Turkey, evaluating germline susceptibility genes of pheochromocytoma and paraganglioma with a detection rate of 24% and three novel variants. All patients with pheochromocytoma and paraganglioma need clinical genetic testing with expanded targeted gene panels for higher diagnosis rates

Optimisation of railway track maintenance and renewal works by genetic algorithms

This paper describes a new approach to optimisation of railway track maintenance and renewal works via genetic algorithms. Decision support systems and genetic algorithms are used in this study to optimise railway track maintenance and renewal activities. The results obtained in the scope of this study show that planned maintenance and renewal management systems can be developed and successfully used instead of resorting to corrective maintenance activities

A necessary condition for global rigidity

Non UBCUnreviewedAuthor affiliation: Queen Mary, University of LondonGraduat