Computations on Sofic S-gap Shifts

Let $S=\{s_{n}\}$ be an increasing finite or infinite subset of $\mathbb N \bigcup \{0\}$ and $X(S)$ the $S$-gap shift associated to $S$. Let $f_{S}(x)=1-\sum\frac{1}{x^{s_{n}+1}}$ be the entropy function which will be vanished at $2^{h(X(S))}$ where $h(X(S))$ is the entropy of the system. Suppose $X(S)$ is sofic with adjacency matrix $A$ and the characteristic polynomial $\chi_{A}$. Then for some rational function $Q_{S}$, $\chi_{A}(x)=Q_{S}(x)f_{S}(x)$. This $Q_{S}$ will be explicitly determined. We will show that $\zeta(t)=\frac{1}{f_{S}(t^{-1})}$ or $\zeta(t)=\frac{1}{(1-t)f_{S}(t^{-1})}$ when $|S|<\infty$ or $|S|=\infty$ respectively. Here $\zeta$ is the zeta function of $X(S)$. We will also compute the Bowen-Franks groups of a sofic $S$-gap shift.Comment: This paper has been withdrawn due to extending results about SFT shifts to sofic shifts (Theorem 2.3). This forces to apply some minor changes in the organization of the paper. This paper has been withdrawn due to a flaw in the description of the adjacency matrix (2.3

Functional polyoxometalates from solvothermal reactions of VOSO4 with tripodal alkoxides – a study on the reactivity of different “tris” derivatives

We report a study on the structure directing effects of functional groups and counterions. The aim was to find a facile and high yielding synthetic procedure to obtain polyoxometalate (POM) building blocks for post- functionalisation. Therefore, solvothermal reactions of VOSO4 with various tris(hydroxymethyl)methane derivatives in alkaline methanolic solutions were investigated. In doing so, new POM fragments were isolated and characterised. The binding modes of the functionalised tripodal alkoxides turned out to be surprisingly different

Computational Complexity of Iterated Maps on the Interval (Extended Abstract)

The exact computation of orbits of discrete dynamical systems on the interval is considered. Therefore, a multiple-precision floating point approach based on error analysis is chosen and a general algorithm is presented. The correctness of the algorithm is shown and the computational complexity is analyzed. As a main result, the computational complexity measure considered here is related to the Ljapunow exponent of the dynamical system under consideration

Imprecision and DNA break repair biased towards incompatible end joining in leukemia

Cancer is a genetic disease caused by mutations and chromosomal abnormalities that contribute to uncontrolled cell growth. In addition, cancer cells can rapidly respond to conventional and targeted therapies by accumulating novel and often specific genetic lesions leading to acquired drug resistance and relapsing disease. In chronic lymphocytic leukemia (CLL), however, diverse chromosomal aberrations often occur. In many cases, improper repair of DNA double-strand breaks (DSB) is a major source for genomic abnormalities. Therefore, this study examined the repair of DNA DSBs by nonhomologous end joining (NHEJ) in CLL by performing plasmid-based repair assays in primary CLL cells and normal B cells, isolated from patients, as well as TALEN/Cas9–induced chromosomal deletions in the CLL cell line Mec1. It is demonstrated that DNA repair is aberrant in CLL cells, featuring perturbed DNA break structure preference with efficient joining of noncohesive ends and more deletions at repair junctions. In addition, increased microhomology-mediated end joining (MMEJ) of DNA substrates was observed in CLL together with increased expression of MMEJ-specific repair factors. In summary, these data identify major differences in DNA repair efficiency between CLL cells and normal B cells isolated from patients

Dynamical properties of S-gap shifts and other shift spaces

We study the dynamical properties of certain shift spaces. To help study these properties we introduce two new classes of shifts, namely boundedly supermultiplicative (BSM) shifts and balanced shifts. It turns out that any almost specified shift is both BSM and balanced, and any balanced shift is BSM. However, as we will demonstrate, there are examples of shifts which are BSM but not balanced. We also study the measure theoretic properties of balanced shifts. We show that a shift space admits a Gibbs state if and only if it is balanced. Restricting ourselves to S-gap shifts, we relate certain dynamical properties of an S-gap shift to combinatorial properties from expansions in non-integer bases. This identification allows us to use the machinery from expansions in non-integer bases to give straightforward constructions of S -gap shifts with certain desirable properties. We show that for any q∈(0,1) there is an S-gap shift which has the specification property and entropy q . We also use this identification to address the question, for a given q∈(0,1), how many S-gap shifts exist with entropy q? For certain exceptional values of q there is a unique S-gap shift with this entropy

Cycloaddition Strategies for the Synthesis of Diverse Heterocyclic Spirocycles for Fragment-Based Drug Discovery.

In recent years the pharmaceutical industry has benefited from the advances made in fragment-based drug discovery (FBDD) with more than 30 fragment-derived drugs currently marketed or progressing through clinical trials. The success of fragment-based drug discovery is entirely dependent upon the composition of the fragment screening libraries used. Heterocycles are prevalent within marketed drugs due to the role they play in providing binding interactions; consequently, heterocyclic fragments are important components of FBDD libraries. Current screening libraries are dominated by flat, sp2-rich compounds, primarily owing to their synthetic tractability, despite the superior physicochemical properties displayed by more three-dimensional scaffolds. Herein, we report step-efficient routes to a number of biologically relevant, fragment-like heterocyclic spirocycles. The use of both electron-deficient and electron-rich 2-atom donors was explored in complexity-generating [3+2]-cycloadditions to furnish products in 3 steps from commercially available starting materials. The resulting compounds were primed for further fragment elaboration through the inclusion of synthetic handles from the outset of the syntheses

Time-dependent changes in mortality and transformation risk in MDS

In myelodysplastic syndromes (MDSs), the evolution of risk for disease progression or death has not been systematically investigated despite being crucial for correct interpretation of prognostic risk scores. In a multicenter retrospective study, we described changes in risk over time, the consequences for basal prognostic scores, and their potential clinical implications. Major MDS prognostic risk scoring systems and their constituent individual predictors were analyzed in 7212 primary untreated MDS patients from the International Working Group for Prognosis in MDS database. Changes in risk of mortality and of leukemic transformation over time from diagnosis were described. Hazards regarding mortality and acute myeloid leukemia transformation diminished over time from diagnosis in higher-risk MDS patients, whereas they remained stable in lower-risk patients. After approximately 3.5 years, hazards in the separate risk groups became similar and were essentially equivalent after 5 years. This fact led to loss of prognostic power of different scoring systems considered, which was more pronounced for survival. Inclusion of age resulted in increased initial prognostic power for survival and less attenuation in hazards. If needed for practicability in clinical management, the differing development of risks suggested a reasonable division into lower- and higher-risk MDS based on the IPSS-R at a cutoff of 3.5 points. Our data regarding time-dependent performance of prognostic scores reflect the disparate change of risks in MDS subpopulations. Lower-risk patients at diagnosis remain lower risk whereas initially high-risk patients demonstrate decreasing risk over time. This change of risk should be considered in clinical decision making