Polynomial approximations to continuous functions and stochastic compositions

This paper presents a stochastic approach to theorems concerning the behavior of iterations of the Bernstein operator $B_n$ taking a continuous function $f \in C[0,1]$ to a degree-$n$ polynomial when the number of iterations $k$ tends to infinity and $n$ is kept fixed or when $n$ tends to infinity as well. In the first instance, the underlying stochastic process is the so-called Wright-Fisher model, whereas, in the second instance, the underlying stochastic process is the Wright-Fisher diffusion. Both processes are probably the most basic ones in mathematical genetics. By using Markov chain theory and stochastic compositions, we explain probabilistically a theorem due to Kelisky and Rivlin, and by using stochastic calculus we compute a formula for the application of $B_n$ a number of times $k=k(n)$ to a polynomial $f$ when $k(n)/n$ tends to a constant.Comment: 21 pages, 5 figure

Myosin Binding Protein-C: A Regulator of Actomyosin Interaction in Striated Muscle

Myosin-Binding protein-C (MyBP-C) is a family of accessory proteins of striated muscles that contributes to the assembly and stabilization of thick filaments, and regulates the formation of actomyosin cross-bridges, via direct interactions with both thick myosin and thin actin filaments. Three distinct MyBP-C isoforms have been characterized; cardiac, slow skeletal, and fast skeletal. Numerous mutations in the gene for cardiac MyBP-C (cMyBP-C) have been associated with familial hypertrophic cardiomyopathy (FHC) and have led to increased interest in the regulation and roles of the cardiac isoform. This review will summarize our current knowledge on MyBP-C and its role in modulating contractility, focusing on its interactions with both myosin and actin filaments in cardiac and skeletal muscles

Myosin Binding Protein-C Slow: An Intricate Subfamily of Proteins

Myosin binding protein C (MyBP-C) consists of a family of thick filament associated proteins. Three isoforms of MyBP-C exist in striated muscles: cardiac, slow skeletal, and fast skeletal. To date, most studies have focused on the cardiac form, due to its direct involvement in the development of hypertrophic cardiomyopathy. Here we focus on the slow skeletal form, discuss past and current literature, and present evidence to support that: (i) MyBP-C slow comprises a subfamily of four proteins, resulting from complex alternative shuffling of the single MyBP-C slow gene, (ii) the four MyBP-C slow isoforms are expressed in variable amounts in different skeletal muscles, (iii) at least one MyBP-C slow isoform is preferentially found at the periphery of M-bands and (iv) the MyBP-C slow subfamily may play important roles in the assembly and stabilization of sarcomeric M- and A-bands and regulate the contractile properties of the actomyosin filaments

Power sharing of parallel operated DC-DC converters using current-limiting droop control

In this paper, a nonlinear current-limiting droop controller is proposed to achieve accurate power sharing among parallel operated DC-DC boost converters in a DC micro-grid application. In particular, the recently developed robust droop controller is adopted and implemented as a dynamic virtual resistance in series with the inductance of each DC-DC boost converter. Opposed to the traditional approaches that use small-signal modeling, the proposed control design takes into account the accurate nonlinear dynamic model of each converter and it is analytically proven that accurate power sharing can be accomplished with an inherent current limitation for each converter independently using input-to-state stability theory. When the load requests more power that exceeds the capacity of the converters, the current-limiting capability of the proposed control method protects the devices by limiting the inductor current of each converter below a given maximum value. Extensive simulation results of two paralleled DC-DC boost converters are presented to verify the power sharing and current-limiting properties of the proposed controller under several changes of the load

Limit theorems for the maximal path weight in a directed graph on the line with random weights of edges

We consider the infinite directed graph with vertices the set of integers ...,-2,-1,0,1,2,... . Let v be a random variable taking either finite values or value "minus infinity". Consider random weights v(j,k), indexed by pairs (j,k) of integers with j<k, and assume that they are i.i.d. copies of v. The set of edges of the graph is the set (j,k), j<k. A path in the graph from vertex j to vertex k, j<k, is a finite sequence of edges (j(0), j(1)), (j(1), j(2)), ..., (j(m-1), j(m)) with j(0)=j and j(m)=j; the weight of this path is taken to be the sum v(j(0),j(1))+v(j(1),j(2))+...+v(j(m-1),j(m)) of the weights of its edges. Let w(0,n) be the maximal weight of all paths from 0 to n. We study the asymptotic behaviour of the sequence w(0,n), n=1, 2, ..., as n tends to infinity, under the assumptions that P(v>0)>0, the conditional distribution of v, given v>0, is not degenerate, and that E exp(Cv) is finite, for some C>0. We derive local limit theorems in the normal and moderate large deviations regimes in the case where v has an arithmetic distribution. We also derive an integro-local theorem in the case where v has a non-lattice distribution.Comment: 16 pages, 1 figur

THE USE OF STATISTICAL ANALYSIS IN THE LITHOSTRATIGRAPHY OF SUBMARINE FAN DEPOSITS. AN EXAMPLE FROM SOUTHEAST GREECE (KARPATHOS ISLAND)

Τα τελευταία χρόνια γίνεται προσπάθεια από πολλούς γεωλόγους στην κατεύθυνση της ποσοτικοποίησης και στατιστικής ανάλυσης των γεωλογικών δεδομένων. Ένα από τα πεδία αυτής της έρευνας είναι οι αποθέσεις υποθαλάσσιων ριπιδίων («φλύσχης»). Η στατιστική ανάλυση σε τέτοιου είδους αποθέσεις εστιάζεται κυρίως στο πάχος των στρωμάτων και έχει σαν στόχο τον προσδιορισμό παραμέτρων όπως το περιβάλλον απόθεσης, η πηγή τροφοδοσίας ιζήματος, οι υδροδυναμικές συνθήκες απόθεσης κτλ. Κύρια εργαλεία ανάλυσης είναι οι λογαριθμικές κατανομές του πάχους των στρωμάτων. Στην παρουσίαση δίνονται παραδείγματα διαφόρων ειδών λογαριθμικών κατανομών που έχουν προταθεί τα τελευταία χρόνια, καθώς και ένα παράδειγμα εφαρμογής τους σε αποθέσεις υποθαλάσσιων ριπιδίων στη ΝΑ Ελλάδα (Κάρπαθος).Examples of various types of statistical analysis of submarine fan bed thickness distributions that have been proposed in the past are reported, as well as an example of their application in Late Eocene-Oligocene submarine fan deposits of SE Greece (Karpathos Island). Generally, the sandstone bed thickness data measured in two outcrops of Karpathos submarine fans seems to follow power law (fractal) cumulative distributions. A deviation from the power law was observed as amalgamationprocedures become more frequent. These observations gave important information about Tertiary turbidite sedimentation in the area which probably was punctuated and had a single main sediment source. Information taken from statistical analysis of submarine fans bed thickness data has immediate applicability in hydrocarbon exploration because sandstones constitute ideal reservoirs