Numerical Ranges of KMS Matrices

A KMS matrix is one of the form J_n(a)=[{array}{ccccc} 0 & a & a^2 &... & a^{n-1} & 0 & a & \ddots & \vdots & & \ddots & \ddots & a^2 & & & \ddots & a 0 & & & & 0{array}] for $n\ge 1$ and $a$ in $\mathbb{C}$. Among other things, we prove the following properties of its numerical range: (1) $W(J_n(a))$ is a circular disc if and only if $n=2$ and $a\neq 0$, (2) its boundary $\partial W(J_n(a))$ contains a line segment if and only if $n\ge 3$ and $|a|=1$, and (3) the intersection of the boundaries $\partial W(J_n(a))$ and $\partial W(J_n(a)[j])$ is either the singleton \{\min\sigma(\re J_n(a))\} if $n$ is odd, $j=(n+1)/2$ and $|a|>1$, or the empty set $\emptyset$ if otherwise, where, for any $n$-by-$n$ matrix $A$, $A[j]$ denotes its $j$th principal submatrix obtained by deleting its $j$th row and $j$th column ($1\le j\le n$), \re A its real part $(A+A^*)/2$, and $\sigma(A)$ its spectrum.Comment: 35 page

Ready, Set, Network! Research Speed Networking for Clinicians, Scientists and Engineers

Objectives: A 2013 Institute of Medicine report urged researchers to “engage in additional substantive and productive collaborations” to address important clinical/translational science questions. To encourage team science among our researchers, Tompkins-McCaw Library for the Health Sciences and Center for Clinical and Translational Research hosted a speed networking event, specifically targeting engineers, clinicians, and basic scientists; an analysis of the event is below. Methods: Invitations were distributed to clinicians, engineers, and basic scientists. To maximize interactions without increasing time spent at the event, researchers were divided into three groups. The event was planned such that each group would meet everyone from the other two groups; researchers were placed into appropriate groups according to their interests. Seated at tables of three, attendees introduced themselves and discussed their research interests for three minutes; then they rotated according to their group’s instructions. Lunch was provided afterwards to give attendees an opportunity to follow up with potential collaborators. Results: Twenty-one faculty researchers attended the speed networking event, which took about 30 minutes, excluding lunch. Using a 5-point Likert scale, all participants selected “strongly agree” or “agree” to respond to questions about whether the event was a valuable use of their time. Also, 53% of attendees “strongly” agreed with the statement “I met a potential collaborator” at the event. Discussion: Subjective evaluations show that researchers see speed networking as an effective way to meet potential collaborators. Objective data including sustained research partnerships and collaborative grant and publication submissions will be tracked

Weighted Shift Matrices: Unitary Equivalence, Reducibility and Numerical Ranges

An $n$-by-$n$ ($n\ge 3$) weighted shift matrix $A$ is one of the form [{array}{cccc}0 & a_1 & & & 0 & \ddots & & & \ddots & a_{n-1} a_n & & & 0{array}], where the $a_j$'s, called the weights of $A$, are complex numbers. Assume that all $a_j$'s are nonzero and $B$ is an $n$-by-$n$ weighted shift matrix with weights $b_1,..., b_n$. We show that $B$ is unitarily equivalent to $A$ if and only if $b_1... b_n=a_1...a_n$ and, for some fixed $k$, $1\le k \le n$, $|b_j| = |a_{k+j}|$ ($a_{n+j}\equiv a_j$) for all $j$. Next, we show that $A$ is reducible if and only if $A$ has periodic weights, that is, for some fixed $k$, $1\le k \le \lfloor n/2\rfloor$, $n$ is divisible by $k$, and $|a_j|=|a_{k+j}|$ for all $1\le j\le n-k$. Finally, we prove that $A$ and $B$ have the same numerical range if and only if $a_1...a_n=b_1...b_n$ and $S_r(|a_1|^2,..., |a_n|^2)=S_r(|b_1|^2,..., |b_n|^2)$ for all $1\le r\le \lfloor n/2\rfloor$, where $S_r$'s are the circularly symmetric functions.Comment: 27 page

Power Partial Isometry Index and Ascent of a Finite Matrix

We give a complete characterization of nonnegative integers $j$ and $k$ and a positive integer $n$ for which there is an $n$-by-$n$ matrix with its power partial isometry index equal to $j$ and its ascent equal to $k$. Recall that the power partial isometry index $p(A)$ of a matrix $A$ is the supremum, possibly infinity, of nonnegative integers $j$ such that $I, A, A^2, \ldots, A^j$ are all partial isometries while the ascent $a(A)$ of $A$ is the smallest integer $k\ge 0$ for which $\ker A^k$ equals $\ker A^{k+1}$. It was known before that, for any matrix $A$, either $p(A)\le\min\{a(A), n-1\}$ or $p(A)=\infty$. In this paper, we prove more precisely that there is an $n$-by-$n$ matrix $A$ such that $p(A)=j$ and $a(A)=k$ if and only if one of the following conditions holds: (a) $j=k\le n-1$, (b) $j\le k-1$ and $j+k\le n-1$, and (c) $j\le k-2$ and $j+k=n$. This answers a question we asked in a previous paper.Comment: 11 page

Higher rank numerical ranges of normal matrices

The higher rank numerical range is closely connected to the construction of quantum error correction code for a noisy quantum channel. It is known that if a normal matrix $A \in M_n$ has eigenvalues $a_1, \..., a_n$, then its higher rank numerical range $\Lambda_k(A)$ is the intersection of convex polygons with vertices $a_{j_1}, \..., a_{j_{n-k+1}}$, where $1 \le j_1 < \... < j_{n-k+1} \le n$. In this paper, it is shown that the higher rank numerical range of a normal matrix with $m$ distinct eigenvalues can be written as the intersection of no more than $\max\{m,4\}$ closed half planes. In addition, given a convex polygon ${\mathcal P}$ a construction is given for a normal matrix $A \in M_n$ with minimum $n$ such that $\Lambda_k(A) = {\mathcal P}$. In particular, if ${\mathcal P}$ has $p$ vertices, with $p \ge 3$, there is a normal matrix $A \in M_n$ with $n \le \max\left\{p+k-1, 2k+2 \right\}$ such that $\Lambda_k(A) = {\mathcal P}$.Comment: 12 pages, 9 figures, to appear in SIAM Journal on Matrix Analysis and Application

Biological control of apple scab and fire blight by the application of the non-pathogenic bacterium Pseudomonas fluorescens Bk3 to the leaf surface

The biological control of plant diseases by application of antagonistic microorganisms to the plant phyllosphere is an alternative strategy to prevent the frequent treatment of plants by pesticides. Microbiological antagonists can firstly interact directly against the pathogen by releasing antimicrobial compounds and/or secondly induce the plant resistance of the host plant by expression of pathogenesis-related proteins (PR proteins). The focus of our study is on the interaction of the non-pathogenic bacterium Pseudomonas fluorescens Bk3 to the plant phyllosphere of Malus domestica cv. Holsteiner Cox. After application of P. fluorescens Bk3 to the phyllosphere of M. domestica cv. Holsteiner Cox we observed dramatic changes in the protein composition of the apoplast of the host plant. Sequencing of the induced proteins by ESI-Q-ToF mass spectrometry and homology search identified these additional proteins as pathogenesis related proteins (PR) like ß-1,3- glucanase, thaumatin-like protein, chitinase and hevein-like protein. To confirm these findings, a suppressive subtractive hybridization with total RNA from leaves before and after inoculation of P. fluorescens Bk3 to the leaves of the host plant was performed. It revealed an increased expression level of many PR and stress related genes. The induction of PR proteins and plant defence genes in host plants after application of non-pathogenic bacterial antagonists to the plant phylloshere can presumably prevent or reduce successful infections by plant pathogens

Phänotypische Merkmale für die Selektion heimischer Leguminosen auf Methioninreichtum in der Pflanzenzüchtung

Ein Problem der Fütterung von Schweinen und Geflügel mit 100 % Futtermitteln aus Ökologischen Landbau sind die unzureichenden Methionin-(Met)-Gehalte im Protein europäischer Körnerleguminosen. Ziel der hier präsentierten Arbeiten ist es, neue Leguminosen Kultivare mit hohem Met-Gehalt im Samenprotein zu identifizieren. Neben der direkten Analyse der Aminosäuregehalte eines Zuchtsortiments der Pflanzenarten wird dazu die Übertragbarkeit der Methoden eines bei Soja (Glycine max) erfolgreich angewandten Verfahrens zur phänotypischen Selektion Met-reicher Pflanzen nach Imsande (2001) an Erbsen (Pisum sativum (L.)), Ackerbohnen (Vicia faba (L.)) and Lupinen (Lupinus angustifolius (L.)) erprobt. Als Indikatoren für Pflanzen mit hohem Metgehalt dienten der Chlorophyllgehalt der Blätter und das Wurzelwachstum von Keimlingen in einer Ethionin Lösung (0,75 mM). Erste Ergebnisse im Labormaßstab an unter Met-Zugabe aufgezogenen Pflanzen zeigten bei L. angustifolius and V. faba eine positive Korrelation zwischen der Met-Versorgung und den Chlorophyllgehalten. Met-reiche Pflanzen zeigten im Vergleich zu den unbehandelten Pflanzen um bis zu 59 % (L. angustifolius) bzw. bis zu 34 % (V. faba) erhöhte Chlorophyllgehalte in den Blättern. In einem zweiten Ansatz wurde der phytotoxische Effekt von Ethionin, einem chemischen Derivat zu Met, zum Screening auf Met-reiche Pflanzen genutzt. Der phytotoxische Effekt wird durch ansteigende Met-Konzentrationen gemindert. In einer 1 mM Met Lösung inkubierte Samen bildeten in Ethionin Lösung bis zu 33 % (P. sativum) bzw. bis zu 18 % (V. faba) längere Wurzeln aus. Die Erfolg versprechenden Ansätze zur Selektion Met-reicher Pflanzen mit direkt mit Met behandelten Pflanzen werden derzeit an Feldpopulationen erprobt