Automorphisms of linear automata

AbstractRelationships between the group, Aut(M), of automorphisms of a linear automaton M and the structure of M are determined. Linear automata in which Aut(M) is a group of translations are characterized in terms of the structure of the state space of M. Also, conditions are determined as to when Aut(M) contains only linear transformations

The centralizer of a group automorphism

AbstractLet G be a finite group. The structure of the near-ring C(A) of identity preserving functions f: G → G, which commute with a given automorphism A of G, is investigated. The results are then applied to the case in which G is a finite vector space and A is an invertible linear transformation

Gamow-Jordan Vectors and Non-Reducible Density Operators from Higher Order S-Matrix Poles

In analogy to Gamow vectors that are obtained from first order resonance poles of the S-matrix, one can also define higher order Gamow vectors which are derived from higher order poles of the S-matrix. An S-matrix pole of r-th order at z_R=E_R-i\Gamma/2 leads to r generalized eigenvectors of order k= 0, 1, ... , r-1, which are also Jordan vectors of degree (k+1) with generalized eigenvalue (E_R-i\Gamma/2). The Gamow-Jordan vectors are elements of a generalized complex eigenvector expansion, whose form suggests the definition of a state operator (density matrix) for the microphysical decaying state of this higher order pole. This microphysical state is a mixture of non-reducible components. In spite of the fact that the k-th order Gamow-Jordan vectors has the polynomial time-dependence which one always associates with higher order poles, the microphysical state obeys a purely exponential decay law.Comment: 39 pages, 3 PostScript figures; sub2.eps may stall some printers and should then be printed out separately; ghostview is o.

Atomically smooth films of CsSb: a chemically robust visible light photocathode

Alkali antimonide semiconductor photocathodes provide a promising platform for the generation of high brightness electron beams, which are necessary for the development of cutting-edge probes including x-ray free electron lasers and ultrafast electron diffraction. However, to harness the intrinsic brightness limits in these compounds, extrinsic degrading factors, including surface roughness and contamination, must be overcome. By exploring the growth of CsxSb thin films monitored by in situ electron diffraction, the conditions to reproducibly synthesize atomically smooth films of CsSb on 3C-SiC (100) and graphene coated TiO2 (110) substrates are identified, and detailed structural, morphological, and electronic characterization is presented. These films combine high quantum efficiency in the visible (up to 1.2% at 400 nm), an easily accessible photoemission threshold of 550 nm, low surface roughness (down to 600 pm on a 1 um scale), and a robustness against oxidation up to 15 times greater then Cs3Sb. These properties suggest that CsSb has the potential to operate as an alternative to Cs$_3$Sb in electron source applications where the demands of the vacuum environment might otherwise preclude the use of traditional alkali antimonides.Comment: 11 pages, 6 figures, 1 tabl

Cyclic dermal BMP signalling regulates stem cell activation during hair regeneration

In the age of stem cell engineering it is critical to understand how stem cell activity is regulated during regeneration. Hairs are mini-organs that undergo cyclic regeneration throughout adult life1, and are an important model for organ regeneration. Hair stem cells located in the follicle bulge2 are regulated by the surrounding microenvironment, or niche3. The activation of such stem cells is cyclic, involving periodic -catenin activity4, 5, 6, 7. In the adult mouse, regeneration occurs in waves in a follicle population, implying coordination among adjacent follicles and the extrafollicular environment. Here we show that unexpected periodic expression of bone morphogenetic protein 2 (Bmp2) and Bmp4 in the dermis regulates this process. This BMP cycle is out of phase with the WNT/-catenin cycle, thus dividing the conventional telogen into new functional phases: one refractory and the other competent for hair regeneration, characterized by high and low BMP signalling, respectively. Overexpression of noggin, a BMP antagonist, in mouse skin resulted in a markedly shortened refractory phase and faster propagation of the regenerative wave. Transplantation of skin from this mutant onto a wild-type host showed that follicles in donor and host can affect their cycling behaviours mutually, with the outcome depending on the equilibrium of BMP activity in the dermis. Administration of BMP4 protein caused the competent region to become refractory. These results show that BMPs may be the long-sought 'chalone' inhibitors of hair growth postulated by classical experiments. Taken together, results presented in this study provide an example of hierarchical regulation of local organ stem cell homeostasis by the inter-organ macroenvironment. The expression of Bmp2 in subcutaneous adipocytes indicates physiological integration between these two thermo-regulatory organs. Our findings have practical importance for studies using mouse skin as a model for carcinogenesis, intra-cutaneous drug delivery and stem cell engineering studies, because they highlight the acute need to differentiate supportive versus inhibitory regions in the host skin

An Ultra-Compact X-Ray Free-Electron Laser

In the field of beam physics, two frontier topics have taken center stage due to their potential to enable new approaches to discovery in a wide swath of science. These areas are: advanced, high gradient acceleration techniques, and x-ray free electron lasers (XFELs). Further, there is intense interest in the marriage of these two fields, with the goal of producing a very compact XFEL. In this context, recent advances in high gradient radio-frequency cryogenic copper structure research have opened the door to the use of surface electric fields between 250 and 500 MV/m. Such an approach is foreseen to enable a new generation of photoinjectors with six-dimensional beam brightness beyond the current state-of-the-art by well over an order of magnitude. This advance is an essential ingredient enabling an ultra-compact XFEL (UC-XFEL). In addition, one may accelerate these bright beams to GeV scale in less than 10 meters. Such an injector, when combined with inverse free electron laser-based bunching techniques can produce multi-kA beams with unprecedented beam quality, quantified by ~50 nm-rad normalized emittances. These beams, when injected into innovative, short-period (1-10 mm) undulators uniquely enable UC-XFELs having footprints consistent with university-scale laboratories. We describe the architecture and predicted performance of this novel light source, which promises photon production per pulse of a few percent of existing XFEL sources. We review implementation issues including collective beam effects, compact x-ray optics systems, and other relevant technical challenges. To illustrate the potential of such a light source to fundamentally change the current paradigm of XFELs with their limited access, we examine possible applications in biology, chemistry, materials, atomic physics, industry, and medicine which may profit from this new model of performing XFEL science.Comment: 80 pages, 24 figure

Global Analysis of Extracytoplasmic Stress Signaling in Escherichia coli

The Bae, Cpx, Psp, Rcs, and σE pathways constitute the Escherichia coli signaling systems that detect and respond to alterations of the bacterial envelope. Contributions of these systems to stress response have previously been examined individually; however, the possible interconnections between these pathways are unknown. Here we investigate the dynamics between the five stress response pathways by determining the specificities of each system with respect to signal-inducing conditions, and monitoring global transcriptional changes in response to transient overexpression of each of the effectors. Our studies show that different extracytoplasmic stress conditions elicit a combined response of these pathways. Involvement of the five pathways in the various tested stress conditions is explained by our unexpected finding that transcriptional responses induced by the individual systems show little overlap. The extracytoplasmic stress signaling pathways in E. coli thus regulate mainly complementary functions whose discrete contributions are integrated to mount the full adaptive response

Properties of the phage-shock-protein (Psp) regulatory complex that govern signal transduction and induction of the Psp response in Escherichia coli

The phage-shock-protein (Psp) response maintains the proton-motive force (pmf) under extracytoplasmic stress conditions that impair the inner membrane (IM) in bacterial cells. In Escherichia coli transcription of the pspABCDE and pspG genes requires activation of σ54-RNA polymerase by the enhancer-binding protein PspF. A regulatory network comprising PspF–A–C–B–ArcB controls psp expression. One key regulatory point is the negative control of PspF imposed by its binding to PspA. It has been proposed that under stress conditions, the IM-bound sensors PspB and PspC receive and transduce the signal(s) to PspA via protein–protein interactions, resulting in the release of the PspA–PspF inhibitory complex and the consequent induction of psp. In this work we demonstrate that PspB self-associates and interacts with PspC via putative IM regions. We present evidence suggesting that PspC has two topologies and that conserved residue G48 and the putative leucine zipper motif are determinants required for PspA interaction and signal transduction upon stress. We also establish that PspC directly interacts with the effector PspG, and show that PspG self-associates. These results are discussed in the context of formation and function of the Psp regulatory complex