Construction Of A Rich Word Containing Given Two Factors

A finite word $w$ with $\vert w\vert=n$ contains at most $n+1$ distinct palindromic factors. If the bound $n+1$ is attained, the word $w$ is called \emph{rich}. Let \Factor(w) be the set of factors of the word $w$. It is known that there are pairs of rich words that cannot be factors of a common rich word. However it is an open question how to decide for a given pair of rich words $u,v$ if there is a rich word $w$ such that \{u,v\}\subseteq \Factor(w). We present a response to this open question:\\ If $w_1, w_2,w$ are rich words, $m=\max{\{\vert w_1\vert,\vert w_2\vert\}}$, and \{w_1,w_2\}\subseteq \Factor(w) then there exists also a rich word $\bar w$ such that \{w_1,w_2\}\subseteq \Factor(\bar w) and $\vert \bar w\vert\leq m2^{k(m)+2}$, where $k(m)=(q+1)m^2(4q^{10}m)^{\log_2{m}}$ and $q$ is the size of the alphabet. Hence it is enough to check all rich words of length equal or lower to $m2^{k(m)+2}$ in order to decide if there is a rich word containing factors $w_1,w_2$

A study of environmental characterization of conventional and advanced aluminum alloys for selection and design. Phase 2: The breaking load test method

A technique is demonstrated for accelerated stress corrosion testing of high strength aluminum alloys. The method offers better precision and shorter exposure times than traditional pass fail procedures. The approach uses data from tension tests performed on replicate groups of smooth specimens after various lengths of exposure to static stress. The breaking strength measures degradation in the test specimen load carrying ability due to the environmental attack. Analysis of breaking load data by extreme value statistics enables the calculation of survival probabilities and a statistically defined threshold stress applicable to the specific test conditions. A fracture mechanics model is given which quantifies depth of attack in the stress corroded specimen by an effective flaw size calculated from the breaking stress and the material strength and fracture toughness properties. Comparisons are made with experimental results from three tempers of 7075 alloy plate tested by the breaking load method and by traditional tests of statistically loaded smooth tension bars and conventional precracked specimens

On Words with the Zero Palindromic Defect

We study the set of finite words with zero palindromic defect, i.e., words rich in palindromes. This set is factorial, but not recurrent. We focus on description of pairs of rich words which cannot occur simultaneously as factors of a longer rich word

A Novel Gaussian Extrapolation Approach for 2D Gel Electrophoresis Saturated Protein Spots

Analysis of images obtained from two-dimensional gel electrophoresis (2D-GE) is a topic of utmost importance in bioinformatics research, since commercial and academic software available currently has proven to be neither completely effective nor fully automatic, often requiring manual revision and refinement of computer generated matches. In this work, we present an effective technique for the detection and the reconstruction of over-saturated protein spots. Firstly, the algorithm reveals overexposed areas, where spots may be truncated, and plateau regions caused by smeared and overlapping spots. Next, it reconstructs the correct distribution of pixel values in these overexposed areas and plateau regions, using a two-dimensional least-squares fitting based on a generalized Gaussian distribution. Pixel correction in saturated and smeared spots allows more accurate quantification, providing more reliable image analysis results. The method is validated for processing highly exposed 2D-GE images, comparing reconstructed spots with the corresponding non-saturated image, demonstrating that the algorithm enables correct spot quantification

A novel Gaussian fitting approach for 2D gel electrophoresis saturated protein spots

Analysis of 2D-GE images is a hot topic in bioinformatics research, since currently available commercial and academic software has proven to be not really effective and not completely automatic, often requiring manual revision of spots detection and refinement of computer generated matches. In this work, we present an effective technique for the detection and the reconstruction of over-saturated protein spots. Firstly, it reveals overexposed areas where spots may be truncated, and plateau regions caused by smeared and overlapped spots. As next, the correct distribution of pixel values in the overexposed areas and plateau regions is recovered by a two-dimensional fitting based on a generalized Gaussian distribution approximating the spots volume. Pixel correction according to the generalized Gaussian curve in saturated and smeared spots allows more accurate quantifications, providing more reliable image analysis results. As validation, we process highly exposed 2D-GE image, containing saturate spots, with respect to the corresponding non-saturated image, confirming that the method can effectively fix the saturated spots and enable correct spots quantification

EFFECTS OF RESVERATROL ON VITRIFIED PORCINE OOCYTES

Vitrified MII porcine oocytes are characterized by reduced developmental competence, associated with the activation of the apoptotic pathway. Resveratrol (R), a polyphenolic compound present in several vegetal sources, has been reported to exert, among all its other biological effects, an antiapoptotic one. The aim of this study was to determine the effects of R (2\u2009\ub5M) on the apoptotic status of porcine oocytes vitrified by Cryotop method, evaluating phosphatidylserine (PS) exteriorization and caspases activation. R was added during IVM (A); 2\u2009h postwarming incubation (B); vitrification/warming and 2\u2009h postwarming incubation (C); all previous phases (D). Data on PS exteriorization showed, in each treated group, a significantly higher (P<0.05) percentage of live nonapoptotic oocytes as compared with CTR; moreover, the percentage of live apoptotic oocytes was significantly (P<0.05) lower in all R-treated groups relative to CTR. The results on caspase activation showed a tendency to an increase of viable oocytes with inactive caspases in B, C, and D, while a significant (P<0.05) increase in A compared to CTR was recorded. These data demonstrate that R supplementation in various phases of IVM and vitrification/warming procedure can modulate the apoptotic process, improving the resistance of porcine oocytes to cryopreservation-induced damage

Boltzmann Suppression of Interacting Heavy Particles

Matsumoto and Yoshimura have recently argued that the number density of heavy particles in a thermal bath is not necessarily Boltzmann-suppressed for T << M, as power law corrections may emerge at higher orders in perturbation theory. This fact might have important implications on the determination of WIMP relic densities. On the other hand, the definition of number densities in a interacting theory is not a straightforward procedure. It usually requires renormalization of composite operators and operator mixing, which obscure the physical interpretation of the computed thermal average. We propose a new definition for the thermal average of a composite operator, which does not require any new renormalization counterterm and is thus free from such ambiguities. Applying this definition to the model of Matsumoto and Yoshimura we find that it gives number densities which are Boltzmann-suppressed at any order in perturbation theory. We discuss also heavy particles which are unstable already at T=0, showing that power law corrections do in general emerge in this case.Comment: 7 pages, 5 figures. New section added, with the discussion of the case of an unstable heavy particle. Version to appear on Phys. Rev.