An additive subfamily of enlargements of a maximally monotone operator

We introduce a subfamily of additive enlargements of a maximally monotone operator. Our definition is inspired by the early work of Simon Fitzpatrick. These enlargements constitute a subfamily of the family of enlargements introduced by Svaiter. When the operator under consideration is the subdifferential of a convex lower semicontinuous proper function, we prove that some members of the subfamily are smaller than the classical $\epsilon$-subdifferential enlargement widely used in convex analysis. We also recover the epsilon-subdifferential within the subfamily. Since they are all additive, the enlargements in our subfamily can be seen as structurally closer to the $\epsilon$-subdifferential enlargement

Excited States of Proton-bound DNA/RNA Base Homo-dimers: Pyrimidines

We are presenting the electronic photo fragment spectra of the protonated pyrimidine DNA bases homo-dimers. Only the thymine dimer exhibits a well structured vibrational progression, while protonated monomer shows broad vibrational bands. This shows that proton bonding can block some non radiative processes present in the monomer.Comment: We acknowledge the use of the computing facility cluster GMPCS of the LUMAT federation (FR LUMAT 2764

The regeneration capacity of the flatworm Macrostomum lignano—on repeated regeneration, rejuvenation, and the minimal size needed for regeneration

The lion’s share of studies on regeneration in Plathelminthes (flatworms) has been so far carried out on a derived taxon of rhabditophorans, the freshwater planarians (Tricladida), and has shown this group’s outstanding regeneration capabilities in detail. Sharing a likely totipotent stem cell system, many other flatworm taxa are capable of regeneration as well. In this paper, we present the regeneration capacity of Macrostomum lignano, a representative of the Macrostomorpha, the basal-most taxon of rhabditophoran flatworms and one of the most basal extant bilaterian protostomes. Amputated or incised transversally, obliquely, and longitudinally at various cutting levels, M. lignano is able to regenerate the anterior-most body part (the rostrum) and any part posterior of the pharynx, but cannot regenerate a head. Repeated regeneration was observed for 29 successive amputations over a period of almost 12 months. Besides adults, also first-day hatchlings and older juveniles were shown to regenerate after transversal cutting. The minimum number of cells required for regeneration in adults (with a total of 25,000 cells) is 4,000, including 160 neoblasts. In hatchlings only 1,500 cells, including 50 neoblasts, are needed for regeneration. The life span of untreated M. lignano was determined to be about 10 months

The caudal regeneration blastema is an accumulation of rapidly proliferating stem cells in the flatworm Macrostomum lignano

Background: Macrostomum lignano is a small free-living flatworm capable of regenerating all body parts posterior of the pharynx and anterior to the brain. We quantified the cellular composition of the caudal-most body region, the tail plate, and investigated regeneration of the tail plate in vivo and in semithin sections labeled with bromodeoxyuridine, a marker for stem cells (neoblasts) in S-phase. Results: The tail plate accomodates the male genital apparatus and consists of about 3,100 cells, about half of which are epidermal cells. A distinct regeneration blastema, characterized by a local accumulation of rapidly proliferating neoblasts and consisting of about 420 cells (excluding epidermal cells), was formed 24 hours after amputation. Differentiated cells in the blastema were observed two days after amputation (with about 920 blastema cells), while the male genital apparatus required four to five days for full differentiation. At all time points, mitoses were found within the blastema. At the place of organ differentiation, neoblasts did not replicate or divide. After three days, the blastema was made of about 1420 cells and gradually transformed into organ primordia, while the proliferation rate decreased. The cell number of the tail plate, including about 960 epidermal cells, was restored to 75% at this time point. Conclusion: Regeneration after artificial amputation of the tail plate of adult specimens of Macrostomum lignano involves wound healing and the formation of a regeneration blastema. Neoblasts undergo extensive proliferation within the blastema. Proliferation patterns of S-phase neoblasts indicate that neoblasts are either determined to follow a specific cell fate not before, but after going through S-phase, or that they can be redetermined after S-phase. In pulse-chase experiments, dispersed distribution of label suggests that S-phase labeled progenitor cells of the male genital apparatus undergo further proliferation before differentiation, in contrast to progenitor cells of epidermal cells. Mitotic activity and proliferation within the blastema is a feature of M. lignano shared with many other regenerating animals

A characterization of Smyth complete quasi-metric spaces via Caristi's fixed point theorem

We obtain a quasi-metric generalization of Caristi's fixed point theorem for a kind of complete quasi-metric spaces. With the help of a suitable modification of its proof, we deduce a characterization of Smyth complete quasi-metric spaces which provides a quasi-metric generalization of the well-known characterization of metric completeness due to Kirk. Some illustrative examples are also given. As an application, we deduce a procedure which allows to easily show the existence of solution for the recurrence equation of certain algorithms.The authors are grateful to the reviewers for several suggestions which have allowed to improve the first version of the paper. This research is supported by the Ministry of Economy and Competitiveness of Spain, Grant MTM2012-37894-C02-01.Romaguera Bonilla, S.; Tirado Peláez, P. (2015). A characterization of Smyth complete quasi-metric spaces via Caristi's fixed point theorem. Fixed Point Theory and Applications. 2015:183. https://doi.org/10.1186/s13663-015-0431-1S2015:183Cobzaş, S: Functional Analysis in Asymmetric Normed Spaces. Springer, Basel (2013)Künzi, HPA: Nonsymmetric distances and their associated topologies: about the origins of basic ideas in the area of asymmetric topology. In: Aull, CE, Lowen, R (eds.) Handbook of the History of General Topology, vol. 3, pp. 853-968. Kluwer Academic, Dordrecht (2001)Reilly, IL, Subrhamanyam, PV, Vamanamurthy, MK: Cauchy sequences in quasi-pseudo-metric spaces. Monatshefte Math. 93, 127-140 (1982)Künzi, HPA, Schellekens, MP: On the Yoneda completion of a quasi-metric spaces. Theor. Comput. Sci. 278, 159-194 (2002)Romaguera, S, Valero, O: Domain theoretic characterisations of quasi-metric completeness in terms of formal balls. Math. Struct. Comput. Sci. 20, 453-472 (2010)Künzi, HPA: Nonsymmetric topology. In: Proc. Szekszárd Conf. Bolyai Society of Math. Studies, vol. 4, pp. 303-338 (1993)García-Raffi, LM, Romaguera, S, Schellekens, MP: Applications of the complexity space to the general probabilistic divide and conquer algorithms. J. Math. Anal. Appl. 348, 346-355 (2008)Stoltenberg, RA: Some properties of quasi-uniform spaces. Proc. Lond. Math. Soc. 17, 226-240 (1967)Caristi, J: Fixed point theorems for mappings satisfying inwardness conditions. Trans. Am. Math. Soc. 215, 241-251 (1976)Kirk, WA: Caristi’s fixed point theorem and metric convexity. Colloq. Math. 36, 81-86 (1976)Abdeljawad, T, Karapınar, E: Quasi-cone metric spaces and generalizations of Caristi Kirk’s theorem. Fixed Point Theory Appl. 2009, Article ID 574387 (2009)Acar, O, Altun, I: Some generalizations of Caristi type fixed point theorem on partial metric spaces. Filomat 26(4), 833-837 (2012)Acar, O, Altun, I, Romaguera, S: Caristi’s type mappings on complete partial metric spaces. Fixed Point Theory 14, 3-10 (2013)Aydi, H, Karapınar, E, Kumam, P: A note on ‘Modified proof of Caristi’s fixed point theorem on partial metric spaces, Journal of Inequalities and Applications 2013, 2013:210’. J. Inequal. Appl. 2013, 355 (2013)Cobzaş, S: Completeness in quasi-metric spaces and Ekeland variational principle. Topol. Appl. 158, 1073-1084 (2011)Hadžić, O, Pap, E: Fixed Point Theory in Probabilistic Metric Spaces. Kluwer Academic, Dordrecht (2001)Karapınar, E: Generalizations of Caristi Kirk’s theorem on partial metric spaces. Fixed Point Theory Appl. 2011, 4 (2011)Romaguera, S: A Kirk type characterization of completeness for partial metric spaces. Fixed Point Theory Appl. 2010, Article ID 493298 (2010)Park, S: On generalizations of the Ekeland-type variational principles. Nonlinear Anal. TMA 39, 881-889 (2000)Du, W-S, Karapınar, E: A note on Caristi type cyclic maps: related results and applications. Fixed Point Theory Appl. 2013, 344 (2013)Ali-Akbari, M, Honari, B, Pourmahdian, M, Rezaii, MM: The space of formal balls and models of quasi-metric spaces. Math. Struct. Comput. Sci. 19, 337-355 (2009)Romaguera, S, Schellekens, M: Quasi-metric properties of complexity spaces. Topol. Appl. 98, 311-322 (1999)Brøndsted, A: On a lemma of Bishop and Phelps. Pac. J. Math. 55, 335-341 (1974)Brøndsted, A: Fixed points and partial order. Proc. Am. Math. Soc. 60, 365-366 (1976)Smyth, MB: Quasi-uniformities: reconciling domains with metric spaces. In: Main, M, Melton, A, Mislove, M, Schmidt, D (eds.) Mathematical Foundations of Programming Language Semantics, 3rd Workshop, Tulane, 1987. Lecture Notes in Computer Science, vol. 298, pp. 236-253. Springer, Berlin (1988)Cull, P, Flahive, M, Robson, R: Difference Equations: From Rabbits to Chaos. Springer, New York (2005)Schellekens, M: The Smyth completion: a common foundation for denotational semantics and complexity analysis. Electron. Notes Theor. Comput. Sci. 1, 535-556 (1995)García-Raffi, LM, Romaguera, S, Sánchez-Pérez, EA: Sequence spaces and asymmetric norms in the theory of computational complexity. Math. Comput. Model. 49, 1852-1868 (2009)Rodríguez-López, J, Schellekens, MP, Valero, O: An extension of the dual complexity space and an application to computer science. Topol. Appl. 156, 3052-3061 (2009)Romaguera, S, Schellekens, MP, Valero, O: The complexity space of partial functions: a connection between complexity analysis and denotational semantics. Int. J. Comput. Math. 88, 1819-1829 (2011