Fractal dimension of transport coefficients in a deterministic dynamical system

In many low-dimensional dynamical systems transport coefficients are very irregular, perhaps even fractal functions of control parameters. To analyse this phenomenon we study a dynamical system defined by a piece-wise linear map and investigate the dependence of transport coefficients on the slope of the map. We present analytical arguments, supported by numerical calculations, showing that both the Minkowski-Bouligand and Hausdorff fractal dimension of the graphs of these functions is 1 with a logarithmic correction, and find that the exponent $\gamma$ controlling this correction is bounded from above by 1 or 2, depending on some detailed properties of the system. Using numerical techniques we show local self-similarity of the graphs. The local self-similarity scaling transformations turn out to depend (irregularly) on the values of the system control parameters.Comment: 17 pages, 6 figures; ver.2: 18 pages, 7 figures (added section 5.2, corrected typos, etc.

Sixty Years of Fractal Projections

Sixty years ago, John Marstrand published a paper which, among other things, relates the Hausdorff dimension of a plane set to the dimensions of its orthogonal projections onto lines. For many years, the paper attracted very little attention. However, over the past 30 years, Marstrand's projection theorems have become the prototype for many results in fractal geometry with numerous variants and applications and they continue to motivate leading research.Comment: Submitted to proceedings of Fractals and Stochastics

Wavelets techniques for pointwise anti-Holderian irregularity

In this paper, we introduce a notion of weak pointwise Holder regularity, starting from the de nition of the pointwise anti-Holder irregularity. Using this concept, a weak spectrum of singularities can be de ned as for the usual pointwise Holder regularity. We build a class of wavelet series satisfying the multifractal formalism and thus show the optimality of the upper bound. We also show that the weak spectrum of singularities is disconnected from the casual one (denoted here strong spectrum of singularities) by exhibiting a multifractal function made of Davenport series whose weak spectrum di ers from the strong one

The Persistence Length of a Strongly Charged, Rod-like, Polyelectrolyte in the Presence of Salt

The persistence length of a single, intrinsically rigid polyelectrolyte chain, above the Manning condensation threshold is investigated theoretically in presence of added salt. Using a loop expansion method, the partition function is consistently calculated, taking into account corrections to mean-field theory. Within a mean-field approximation, the well-known results of Odijk, Skolnick and Fixman are reproduced. Beyond mean-field, it is found that density correlations between counterions and thermal fluctuations reduce the stiffness of the chain, indicating an effective attraction between monomers for highly charged chains and multivalent counterions. This attraction results in a possible mechanical instability (collapse), alluding to the phenomenon of DNA condensation. In addition, we find that more counterions condense on slightly bent conformations of the chain than predicted by the Manning model for the case of an infinite cylinder. Finally, our results are compared with previous models and experiments.Comment: 13 pages, 2 ps figure

Piecewise Linear Models for the Quasiperiodic Transition to Chaos

We formulate and study analytically and computationally two families of piecewise linear degree one circle maps. These families offer the rare advantage of being non-trivial but essentially solvable models for the phenomenon of mode-locking and the quasi-periodic transition to chaos. For instance, for these families, we obtain complete solutions to several questions still largely unanswered for families of smooth circle maps. Our main results describe (1) the sets of maps in these families having some prescribed rotation interval; (2) the boundaries between zero and positive topological entropy and between zero length and non-zero length rotation interval; and (3) the structure and bifurcations of the attractors in one of these families. We discuss the interpretation of these maps as low-order spline approximations to the classic ``sine-circle'' map and examine more generally the implications of our results for the case of smooth circle maps. We also mention a possible connection to recent experiments on models of a driven Josephson junction.Comment: 75 pages, plain TeX, 47 figures (available on request

Retrieving sequences of enzymes experimentally characterized but erroneously annotated : the case of the putrescine carbamoyltransferase

BACKGROUND: Annotating genomes remains an hazardous task. Mistakes or gaps in such a complex process may occur when relevant knowledge is ignored, whether lost, forgotten or overlooked. This paper exemplifies an approach which could help to ressucitate such meaningful data. RESULTS: We show that a set of closely related sequences which have been annotated as ornithine carbamoyltransferases are actually putrescine carbamoyltransferases. This demonstration is based on the following points : (i) use of enzymatic data which had been overlooked, (ii) rediscovery of a short NH(2)-terminal sequence allowing to reannotate a wrongly annotated ornithine carbamoyltransferase as a putrescine carbamoyltransferase, (iii) identification of conserved motifs allowing to distinguish unambiguously between the two kinds of carbamoyltransferases, and (iv) comparative study of the gene context of these different sequences. CONCLUSIONS: We explain why this specific case of misannotation had not yet been described and draw attention to the fact that analogous instances must be rather frequent. We urge to be especially cautious when high sequence similarity is coupled with an apparent lack of biochemical information. Moreover, from the point of view of genome annotation, proteins which have been studied experimentally but are not correlated with sequence data in current databases qualify as "orphans", just as unassigned genomic open reading frames do. The strategy we used in this paper to bridge such gaps in knowledge could work whenever it is possible to collect a body of facts about experimental data, homology, unnoticed sequence data, and accurate informations about gene context

Preoperative elevation of serum C – reactive protein is predictive for prognosis in myeloma bone disease after surgery

We investigated whether preoperative levels of serum C-reactive protein (CRP) and its correlation with tumour clinicopathological findings adds prognostic information beyond the time of diagnosis in patients with myeloma bone disease (MM) to facilitate the surgical decision-making process. Six hundred and fifty-eight myeloma patients were evaluated retrospectively for surgery. Clinicopathological variables of patients who underwent surgery (n=71) were compared between patients with preoperative CRP ⩾6 mg l−1 and those with CRP <6 mg l−1. Univariate and multivariate analyses were performed to identify prognostic factors after surgery. Patients with an increase of CRP prior to surgery showed inferior survival compared to patients with normal levels. Patients with normal CRP levels at diagnosis but elevations prior to surgery do seem to have a similar unfavourable overall survival (OS) than patients with an increase both, at diagnosis and at surgery. Conversely, patients with normal CRP levels prior to surgery still have the best OS, irrespective of their basic values. Multivariate analysis revealed preoperative CRP levels above 6 mg l−1 Lactate dehydrogenase (LDH) above normal, and osteolyses in long weight bearing bones as independent predictors of survival. These findings suggest that in patients with MM serum levels of CRP increase during disease activity and might be significantly correlated with specific disease characteristics including adverse prognostic features such as osteolyses in long weight bearing bones. Thus, preoperative elevated CRP serum levels might be considered as independent predictor of prognosis and could provide additional prognostic information for the risk stratification before surgical treatment in patients with myeloma bone disease

Molecular purging of multiple myeloma cells by ex-vivo culture and retroviral transduction of mobilized-blood CD34+ cells

<p>Abstract</p> <p>Background</p> <p>Tumor cell contamination of the apheresis in multiple myeloma is likely to affect disease-free and overall survival after autografting.</p> <p>Objective</p> <p>To purge myeloma aphereses from tumor contaminants with a novel culture-based purging method.</p> <p>Methods</p> <p>We cultured myeloma-positive CD34⁺PB samples in conditions that retained multipotency of hematopoietic stem cells, but were unfavourable to survival of plasma cells. Moreover, we exploited the resistance of myeloma plasma cells to retroviral transduction by targeting the hematopoietic CD34⁺cell population with a retroviral vector carrying a selectable marker (the truncated form of the human receptor for nerve growth factor, ΔNGFR). We performed therefore a further myeloma purging step by selecting the transduced cells at the end of the culture.</p> <p>Results</p> <p>Overall recovery of CD34⁺cells after culture was 128.5%; ΔNGFR transduction rate was 28.8% for CD34⁺cells and 0% for CD138-selected primary myeloma cells, respectively. Recovery of CD34⁺cells after ΔNGFR selection was 22.3%. By patient-specific Ig-gene rearrangements, we assessed a decrease of 0.7–1.4 logs in tumor load after the CD34⁺cell selection, and up to 2.3 logs after culture and ΔNGFR selection.</p> <p>Conclusion</p> <p>We conclude that <it>ex-vivo </it>culture and retroviral-mediated transduction of myeloma leukaphereses provide an efficient tumor cell purging.</p