Complexity of Leading Digit Sequences

Let $S_{a,b}$ denote the sequence of leading digits of $a^n$ in base $b$. It is well known that if $a$ is not a rational power of $b$, then the sequence $S_{a,b}$ satisfies Benford's Law; that is, digit $d$ occurs in $S_{a,b}$ with frequency $\log_{b}(1+1/d)$, for $d=1,2,\dots,b-1$. In this paper, we investigate the \emph{complexity} of such sequences. We focus mainly on the \emph{block complexity}, $p_{a,b}(n)$, defined as the number of distinct blocks of length $n$ appearing in $S_{a,b}$. In our main result we determine $p_{a,b}(n)$ for all squarefree bases $b\ge 5$ and all rational numbers $a>0$ that are not integral powers of $b$. In particular, we show that, for all such pairs $(a,b)$, the complexity function $p_{a,b}(n)$ is \emph{affine}, i.e., satisfies $p_{a,b}(n)=c_{a,b} n + d_{a,b}$ for all $n\ge1$, with coefficients $c_{a,b}\ge1$ and $d_{a,b}\ge0$, given explicitly in terms of $a$ and $b$. We also show that the requirement that $b$ be squarefree cannot be dropped: If $b$ is not squarefree, then there exist integers $a$ with $1<a<b$ for which $p_{a,b}(n)$ is not of the above form. We use this result to obtain sharp upper and lower bounds for $p_{a,b}(n)$, and to determine the asymptotic behavior of this function as $b\to\infty$ through squarefree values. We also consider the question which linear functions $p(n)=cn+d$ arise as the complexity function $p_{a,b}(n)$ of some leading digit sequence $S_{a,b}$. We conclude with a discussion of other complexity measures for the sequences $S_{a,b}$ and some open problems

Discriminating land cover types using SPOT 4 imagery in the mixed grassland ecosystem

Non-Peer ReviewedThis study was conducted at a mixed grass prairie in southern Saskatchewan. The main objective of this study is to evaluate spectral differentiations of different land cover types and grassland communities, and thus find the way of improving the utility of the land cover data product with remote sensing techniques for the pasture insurance program. Data for this study were field measurements and two SPOT 4 images acquired in the summer of 2005. Using discriminant analysis, the study extracted and analyzed spectral signals from different land cover types. The results showed that a hierarchical classification method was necessary as different level of classification uses different spectral properties. Both June and July imagery can separate the seven major classes with high accuracy and July image is 1% more accuracy than June image. The images from different dates have different advantages for separating classes based on their discriminant functions. It is easier to differentiate land cover types, such as vegetation covered area and non-vegetation covered area, however, the accuracy will be lower when separating the classes of crop and shrub, and fallow and badland due to their similar spectral properties. Three common grassland management practices (cropland, grazed grassland, and ungrazed grassland) can be spectrally discriminated, but it is difficult to separate grasslands from different topography patterns because they have similar spectral features

The haematopoietic GTPase RhoH modulates IL3 signalling through regulation of STAT activity and IL3 receptor expression

<p>Abstract</p> <p>Background</p> <p>RhoH is a constitutively active member of the family of Rho GTPases. Its expression is restricted to the haematopoietic lineage, where it serves as a positive regulator for T cell selection and mast cell function and as a negative regulator for growth-related functions in other lineages. Here, we examined the activation of signal transducer and activator of transcription (STAT) proteins in response to stimulation with interleukin 3 (IL3).</p> <p>Results</p> <p>Using the murine IL3-dependent cell line BaF3 we investigated the influence of RhoH protein expression levels on IL3-mediated cellular responses. RhoH overexpressing cells showed lower sensitivity to IL3 and decreased STAT5 activation. SiRNA-mediated repression of <it>RhoH </it>gene expression led to an increase in proliferation and STAT5 activity which correlated with an increased number of IL3 receptor α chain molecules, also known as CD123, expressed at the cell surface. Interestingly, these findings could be reproduced using human THP-1 cells as a model system for acute myeloid leukaemia, where low RhoH levels are known to be an unfavourable prognostic marker. Overexpression of RhoH on the other hand caused an induction of STAT1 activity and western blot analysis revealed that activated STAT1 is phosphorylated on Tyr701. STAT1 is known to induce apoptosis or cell cycle arrest and we detected an upregulation of cyclin-dependent kinase inhibitors (CDKI) <it>p21^Cip1</it>and <it>p27^Kip1</it>in RhoH overexpressing BaF3 cells.</p> <p>Conclusions</p> <p>We propose that RhoH functions as a negative regulator for IL3-induced signals through modulation of the JAK-STAT pathway. High levels of RhoH allow the IL3-dependent activation of STAT1 causing decreased proliferation through upregulation of <it>p21^Cip1</it>and <it>p27^Kip1</it>. Low RhoH levels on the other hand led to an upregulation of IL3-dependent cell growth, STAT5 activity and an increase of CD123 surface expression, linking RhoH to a CD123/STAT5 phenotype that has been described in AML patients.</p

Triphenylarsonium-functionalised gold nanoparticles: potential nanocarriers for intracellular therapeutics.

This article is licensed under a Creative Commons Attribution 3.0 Unported Licence.Two new triphenylarsonium alkylthiolate precursors, a thiosulfate zwitterion and a thioacetate salt, have been structurally characterised and their cytotoxicity evaluated against PC3 cells. The arsonium compounds have been used to prepare gold nanoparticles decorated with triphenylarsonium groups.Sheffield Hallam University and Indian Institute of Science (NL)

Inelastic neutron scattering study of magnetic excitations in Sr2_2RuO4_4

Magnetic excitations in \srruo ~ have been studied by inelastic neutron scattering. The magnetic fluctuations are dominated by incommensurate peaks related to the Fermi surface nesting of the quasi-one-dimensional $d_{xz}$- and $d_{yz}$-bands. The shape of the incommensurate signal agrees well with RPA calculations. At the incommensurate {\bf Q}-positions the energy spectrum considerably softens upon cooling pointing to a close magnetic instability : \srruo ~does not exhibit quantum criticality but is very close to it. $\omega / T$-scaling may be fitted to the data for temperatures above 30 K. Below the superconducting transition, the magnetic response at the nesting signal is not found to change in the energy range down to 0.4meV.Comment: 11 pages 9 figure

Functional Diversity and Structural Disorder in the Human Ubiquitination Pathway

The ubiquitin-proteasome system plays a central role in cellular regulation and protein quality control (PQC). The system is built as a pyramid of increasing complexity, with two E1 (ubiquitin activating), few dozen E2 (ubiquitin conjugating) and several hundred E3 (ubiquitin ligase) enzymes. By collecting and analyzing E3 sequences from the KEGG BRITE database and literature, we assembled a coherent dataset of 563 human E3s and analyzed their various physical features. We found an increase in structural disorder of the system with multiple disorder predictors (IUPred - E1: 5.97%, E2: 17.74%, E3: 20.03%). E3s that can bind E2 and substrate simultaneously (single subunit E3, ssE3) have significantly higher disorder (22.98%) than E3s in which E2 binding (multi RING-finger, mRF, 0.62%), scaffolding (6.01%) and substrate binding (adaptor/substrate recognition subunits, 17.33%) functions are separated. In ssE3s, the disorder was localized in the substrate/adaptor binding domains, whereas the E2-binding RING/HECT-domains were structured. To demonstrate the involvement of disorder in E3 function, we applied normal modes and molecular dynamics analyses to show how a disordered and highly flexible linker in human CBL (an E3 that acts as a regulator of several tyrosine kinase-mediated signalling pathways) facilitates long-range conformational changes bringing substrate and E2-binding domains towards each other and thus assisting in ubiquitin transfer. E3s with multiple interaction partners (as evidenced by data in STRING) also possess elevated levels of disorder (hubs, 22.90% vs. non-hubs, 18.36%). Furthermore, a search in PDB uncovered 21 distinct human E3 interactions, in 7 of which the disordered region of E3s undergoes induced folding (or mutual induced folding) in the presence of the partner. In conclusion, our data highlights the primary role of structural disorder in the functions of E3 ligases that manifests itself in the substrate/adaptor binding functions as well as the mechanism of ubiquitin transfer by long-range conformational transitions. © 2013 Bhowmick et al

Dynamic myosin phosphorylation regulates contractile pulses and tissue integrity during epithelial morphogenesis

Apical constriction is a cell shape change that promotes epithelial bending. Activation of nonmuscle myosin II (Myo-II) by kinases such as Rho-associated kinase (Rok) is important to generate contractile force during apical constriction. Cycles of Myo-II assembly and disassembly, or pulses, are associated with apical constriction during Drosophila melanogaster gastrulation. It is not understood whether Myo-II phosphoregulation organizes contractile pulses or whether pulses are important for tissue morphogenesis. Here, we show that Myo-II pulses are associated with pulses of apical Rok. Mutants that mimic Myo-II light chain phosphorylation or depletion of myosin phosphatase inhibit Myo-II contractile pulses, disrupting both actomyosin coalescence into apical foci and cycles of Myo-II assembly/disassembly. Thus, coupling dynamic Myo-II phosphorylation to upstream signals organizes contractile Myo-II pulses in both space and time. Mutants that mimic Myo-II phosphorylation undergo continuous, rather than incremental, apical constriction. These mutants fail to maintain intercellular actomyosin network connections during tissue invagination, suggesting that Myo-II pulses are required for tissue integrity during morphogenesis.National Institute of General Medical Sciences (U.S.) (Transgenic RNAi Project at Harvard Medical School, (R01-GM084947)

Establishing What Constitutes a Healthy Human Gut Microbiome: State of the Science, Regulatory Considerations, and Future Directions.

On December 17, 2018, the North American branch of the International Life Sciences Institute (ILSI North America) convened a workshop "Can We Begin to Define a Healthy Gut Microbiome Through Quantifiable Characteristics?" with &gt;40 invited academic, government, and industry experts in Washington, DC. The workshop objectives were to 1) develop a collective expert assessment of the state of the evidence on the human gut microbiome and associated human health benefits, 2) see if there was sufficient evidence to establish measurable gut microbiome characteristics that could serve as indicators of "health," 3) identify short- and long-term research needs to fully characterize healthy gut microbiome-host relationships, and 4) publish the findings. Conclusions were as follows: 1) mechanistic links of specific changes in gut microbiome structure with function or markers of human health are not yet established; 2) it is not established if dysbiosis is a cause, consequence, or both of changes in human gut epithelial function and disease; 3) microbiome communities are highly individualized, show a high degree of interindividual variation to perturbation, and tend to be stable over years; 4) the complexity of microbiome-host interactions requires a comprehensive, multidisciplinary research agenda to elucidate relationships between gut microbiome and host health; 5) biomarkers and/or surrogate indicators of host function and pathogenic processes based on the microbiome need to be determined and validated, along with normal ranges, using approaches similar to those used to establish biomarkers and/or surrogate indicators based on host metabolic phenotypes; 6) future studies measuring responses to an exposure or intervention need to combine validated microbiome-related biomarkers and/or surrogate indicators with multiomics characterization of the microbiome; and 7) because static genetic sampling misses important short- and long-term microbiome-related dynamic changes to host health, future studies must be powered to account for inter- and intraindividual variation and should use repeated measures within individuals

An unusual case of chronic meningitis

BACKGROUND: Chronic meningitis is defined as symptoms and signs of meningeal inflammation and persisting cerebrospinal fluid abnormalities such as elevated protein level and pleocytosis for at least one month. CASE PRESENTATION: A 62-year-old woman, of unremarkable past medical history, was admitted to hospital for investigation of a four-week history of vomiting, malaise an associated hyponatraemia. She had a low-grade pyrexia with normal inflammatory markers. A CT brain was unremarkable and a contrast MRI brain revealed sub-acute infarction of the right frontal cortex but with no evidence of meningeal enhancement. Due to increasing confusion and patient clinical deterioration a lumbar puncture was performed at 17 days post admission. This revealed gram-negative coccobacilli in the CSF, which was identified as Neisseria meningitidis group B. The patient made a dramatic recovery with high-dose intravenous ceftriaxone antibiotic therapy for meningococcal meningitis. CONCLUSIONS: 1) Chronic bacterial meningitis may present highly atypically, particularly in the older adult. 2) There may be an absent or reduced febrile response, without a rise in inflammatory markers, despite a very unwell patient. 3) Early lumbar puncture is to be encouraged as it is essential to confirm the diagnosis.4) Despite a delayed diagnosis appropriate antibiotic therapy can still lead to a good outcome

A BAFF-R mutation associated with non-Hodgkin lymphoma alters TRAF recruitment and reveals new insights into BAFF-R signaling

A BAFF receptor mutation associated with non-Hodgkin lymphoma provides new insight into the proximal players of normal BAFF-R signaling