Fractional Hamilton formalism within Caputo's derivative

In this paper we develop a fractional Hamiltonian formulation for dynamic systems defined in terms of fractional Caputo derivatives. Expressions for fractional canonical momenta and fractional canonical Hamiltonian are given, and a set of fractional Hamiltonian equations are obtained. Using an example, it is shown that the canonical fractional Hamiltonian and the fractional Euler-Lagrange formulations lead to the same set of equations.Comment: 8 page

Non-relativistic effective theory of dark matter direct detection

Dark matter direct detection searches for signals coming from dark matter scattering against nuclei at a very low recoil energy scale ~ 10 keV. In this paper, a simple non-relativistic effective theory is constructed to describe interactions between dark matter and nuclei without referring to any underlying high energy models. It contains the minimal set of operators that will be tested by direct detection. The effective theory approach highlights the set of distinguishable recoil spectra that could arise from different theoretical models. If dark matter is discovered in the near future in direct detection experiments, a measurement of the shape of the recoil spectrum will provide valuable information on the underlying dynamics. We bound the coefficients of the operators in our non-relativistic effective theory by the null results of current dark matter direct detection experiments. We also discuss the mapping between the non-relativistic effective theory and field theory models or operators, including aspects of the matching of quark and gluon operators to nuclear form factors.Comment: 35 pages, 3 figures, Appendix C.3 revised, acknowledgments and references adde

Constant Curvature Coefficients and Exact Solutions in Fractional Gravity and Geometric Mechanics

We study fractional configurations in gravity theories and Lagrange mechanics. The approach is based on Caputo fractional derivative which gives zero for actions on constants. We elaborate fractional geometric models of physical interactions and we formulate a method of nonholonomic deformations to other types of fractional derivatives. The main result of this paper consists in a proof that for corresponding classes of nonholonomic distributions a large class of physical theories are modelled as nonholonomic manifolds with constant matrix curvature. This allows us to encode the fractional dynamics of interactions and constraints into the geometry of curve flows and solitonic hierarchies.Comment: latex2e, 11pt, 27 pages, the variant accepted to CEJP; added and up-dated reference

A Model of User Preferences for Semantic Services Discovery and Ranking

Current proposals on Semantic Web Services discovery and ranking are based on user preferences descriptions that often come with insufficient expressiveness, consequently making more difficult or even preventing the description of complex user desires. There is a lack of a general and comprehensive preference model, so discovery and ranking proposals have to provide ad hoc preference descriptions whose expressiveness depends on the facilities provided by the corresponding technique, resulting in user preferences that are tightly coupled with the underlying formalism being used by each concrete solution. In order to overcome these problems, in this paper an abstract and sufficiently expressive model for defining preferences is presented, so that they may be described in an intuitively and user-friendly manner. The proposed model is based on a well-known query preference model from database systems, which provides highly expressive constructors to describe and compose user preferences semantically. Furthermore, the presented proposal is independent from the concrete discovery and ranking engines selected, and may be used to extend current Semantic Web Service frameworks, such as wsmo, sawsdl, or owl-s. In this paper, the presented model is also validated against a complex discovery and ranking scenario, and a concrete implementation of the model in wsmo is outlined.Comisión Interministerial de Ciencia y Tecnología TIN2006-00472Comisión Interministerial de Ciencia y Tecnología TIN2009-07366Junta de Andalucía TIC-253

Random Convex Hulls and Extreme Value Statistics

In this paper we study the statistical properties of convex hulls of $N$ random points in a plane chosen according to a given distribution. The points may be chosen independently or they may be correlated. After a non-exhaustive survey of the somewhat sporadic literature and diverse methods used in the random convex hull problem, we present a unifying approach, based on the notion of support function of a closed curve and the associated Cauchy's formulae, that allows us to compute exactly the mean perimeter and the mean area enclosed by the convex polygon both in case of independent as well as correlated points. Our method demonstrates a beautiful link between the random convex hull problem and the subject of extreme value statistics. As an example of correlated points, we study here in detail the case when the points represent the vertices of $n$ independent random walks. In the continuum time limit this reduces to $n$ independent planar Brownian trajectories for which we compute exactly, for all $n$, the mean perimeter and the mean area of their global convex hull. Our results have relevant applications in ecology in estimating the home range of a herd of animals. Some of these results were announced recently in a short communication [Phys. Rev. Lett. {\bf 103}, 140602 (2009)].Comment: 61 pages (pedagogical review); invited contribution to the special issue of J. Stat. Phys. celebrating the 50 years of Yeshiba/Rutgers meeting

Phosphorothioate antisense oligonucleotides induce the formation of nuclear bodies

Antisense oligonucleotides are powerful tools for the in vivo regulation of gene expression. We have characterized the intracellular distribution of fluorescently tagged phosphorothioate oligodeoxynucleotides (PS-ONs) at high resolution under conditions in which PS-ONs have the potential to display antisense activity. Under these conditions PS-ONs predominantly localized to the cell nucleus where they accumulated in 20-30 bright spherical foci designated phosphorothioate bodies (PS bodies), which were set against a diffuse nucleoplasmic population excluding nucleoli. PS bodies are nuclear structures that formed in cells after PS-ON delivery by transfection agents or microinjection but were observed irrespectively of antisense activity or sequence. Ultrastructurally, PS bodies corresponded to electron-dense structures of 150-300 nm diameter and resembled nuclear bodies that were found with lower frequency in cells lacking PS-ONs. The environment of a living cell was required for the de novo formation of PS bodies, which occurred within minutes after the introduction of PS-ONs. PS bodies were stable entities that underwent noticeable reorganization only during mitosis. Upon exit from mitosis, PS bodies were assembled de novo from diffuse PS-ON pools in the daughter nuclei. In situ fractionation demonstrated an association of PS-ONs with the nuclear matrix. Taken together, our data provide evidence for the formation of a nuclear body in cells after introduction of phosphorothioate oligodeoxynucleotides

Time evolution of in vivo articular cartilage repair induced by bone marrow stimulation and scaffold implantation in rabbits

Purpose: Tissue engineering techniques were used to study cartilage repair over a 12-month period in a rabbit model. Methods: A full-depth chondral defect along with subchondral bone injury were originated in the knee joint, where a biostable porous scaffold was implanted, synthesized of poly(ethyl acrylate-co-hydroxyethyl acrylate) copolymer. Morphological evolution of cartilage repair was studied 1 and 2 weeks, and 1, 3, and 12 months after implantation by histological techniques. The 3-month group was chosen to compare cartilage repair to an additional group where scaffolds were preseeded with allogeneic chondrocytes before implantation, and also to controls, who underwent the same surgery procedure, with no scaffold implantation. Results: Neotissue growth was first observed in the deepest scaffold pores 1 week after implantation, which spread thereafter; 3 months later scaffold pores were filled mostly with cartilaginous tissue in superficial and middle zones, and with bone tissue adjacent to subchondral bone. Simultaneously, native chondrocytes at the edges of the defect started to proliferate 1 week after implantation; within a month those edges had grown centripetally and seemed to embed the scaffold, and after 3 months, hyaline-like cartilage was observed on the condylar surface. Preseeded scaffolds slightly improved tissue growth, although the quality of repair tissue was similar to non-preseeded scaffolds. Controls showed that fibrous cartilage was mainly filling the repair area 3 months after surgery. In the 12-month group, articular cartilage resembled the untreated surface. Conclusions: Scaffolds guided cartilaginous tissue growth in vivo, suggesting their importance in stress transmission to the cells for cartilage repair.This study was supported by the Spanish Ministry of Science and Innovation through MAT2010-21611-C03-00 project (including the FEDER financial support), by Conselleria de Educacion (Generalitat Valenciana, Spain) PROMETEO/2011/084 grant, and by CIBER-BBN en Bioingenieria, Biomateriales y Nanomedicina. The work of JLGR was partially supported by funds from the Generalitat Valenciana, ACOMP/2012/075 project. CIBER-BBN is an initiative funded by the VI National R&D&i Plan 2008-2011, Iniciativa Ingenio 2010, Consolider Program, CIBER Actions and financed by the - Instituto de Salud Carlos III with assistance from the European Regional Development Fund.Sancho-Tello Valls, M.; Forriol, F.; Gastaldi, P.; Ruiz Sauri, A.; Martín De Llano, JJ.; Novella-Maestre, E.; Antolinos Turpín, CM.... (2015). Time evolution of in vivo articular cartilage repair induced by bone marrow stimulation and scaffold implantation in rabbits. International Journal of Artificial Organs. 38(4):210-223. https://doi.org/10.5301/ijao.5000404S210223384Becerra, J., Andrades, J. A., Guerado, E., Zamora-Navas, P., López-Puertas, J. M., & Reddi, A. H. (2010). Articular Cartilage: Structure and Regeneration. Tissue Engineering Part B: Reviews, 16(6), 617-627. doi:10.1089/ten.teb.2010.0191Nelson, L., Fairclough, J., & Archer, C. (2009). Use of stem cells in the biological repair of articular cartilage. Expert Opinion on Biological Therapy, 10(1), 43-55. doi:10.1517/14712590903321470MAINIL-VARLET, P., AIGNER, T., BRITTBERG, M., BULLOUGH, P., HOLLANDER, A., HUNZIKER, E., … STAUFFER, E. (2003). HISTOLOGICAL ASSESSMENT OF CARTILAGE REPAIR. The Journal of Bone and Joint Surgery-American Volume, 85, 45-57. doi:10.2106/00004623-200300002-00007Hunziker, E. B., Kapfinger, E., & Geiss, J. (2007). The structural architecture of adult mammalian articular cartilage evolves by a synchronized process of tissue resorption and neoformation during postnatal development. Osteoarthritis and Cartilage, 15(4), 403-413. doi:10.1016/j.joca.2006.09.010Onyekwelu, I., Goldring, M. B., & Hidaka, C. (2009). Chondrogenesis, joint formation, and articular cartilage regeneration. Journal of Cellular Biochemistry, 107(3), 383-392. doi:10.1002/jcb.22149Ahmed, T. A. E., & Hincke, M. T. (2010). Strategies for Articular Cartilage Lesion Repair and Functional Restoration. Tissue Engineering Part B: Reviews, 16(3), 305-329. doi:10.1089/ten.teb.2009.0590Hangody, L., Kish, G., Kárpáti, Z., Udvarhelyi, I., Szigeti, I., & Bély, M. (1998). Mosaicplasty for the Treatment of Articular Cartilage Defects: Application in Clinical Practice. Orthopedics, 21(7), 751-756. doi:10.3928/0147-7447-19980701-04Steinwachs, M. R., Guggi, T., & Kreuz, P. C. (2008). Marrow stimulation techniques. Injury, 39(1), 26-31. doi:10.1016/j.injury.2008.01.042Brittberg, M., Lindahl, A., Nilsson, A., Ohlsson, C., Isaksson, O., & Peterson, L. (1994). Treatment of Deep Cartilage Defects in the Knee with Autologous Chondrocyte Transplantation. New England Journal of Medicine, 331(14), 889-895. doi:10.1056/nejm199410063311401Richter, W. (2009). Mesenchymal stem cells and cartilagein situregeneration. Journal of Internal Medicine, 266(4), 390-405. doi:10.1111/j.1365-2796.2009.02153.xBartlett, W., Skinner, J. A., Gooding, C. R., Carrington, R. W. J., Flanagan, A. M., Briggs, T. W. R., & Bentley, G. (2005). Autologous chondrocyte implantationversusmatrix-induced autologous chondrocyte implantation for osteochondral defects of the knee. The Journal of Bone and Joint Surgery. British volume, 87-B(5), 640-645. doi:10.1302/0301-620x.87b5.15905Little, C. J., Bawolin, N. K., & Chen, X. (2011). Mechanical Properties of Natural Cartilage and Tissue-Engineered Constructs. Tissue Engineering Part B: Reviews, 17(4), 213-227. doi:10.1089/ten.teb.2010.0572Vikingsson, L., Gallego Ferrer, G., Gómez-Tejedor, J. A., & Gómez Ribelles, J. L. (2014). An «in vitro» experimental model to predict the mechanical behavior of macroporous scaffolds implanted in articular cartilage. Journal of the Mechanical Behavior of Biomedical Materials, 32, 125-131. doi:10.1016/j.jmbbm.2013.12.024Weber, J. F., & Waldman, S. D. (2014). Calcium signaling as a novel method to optimize the biosynthetic response of chondrocytes to dynamic mechanical loading. Biomechanics and Modeling in Mechanobiology, 13(6), 1387-1397. doi:10.1007/s10237-014-0580-xMauck, R. L., Soltz, M. A., Wang, C. C. B., Wong, D. D., Chao, P.-H. G., Valhmu, W. B., … Ateshian, G. A. (2000). Functional Tissue Engineering of Articular Cartilage Through Dynamic Loading of Chondrocyte-Seeded Agarose Gels. Journal of Biomechanical Engineering, 122(3), 252-260. doi:10.1115/1.429656Palmoski, M. J., & Brandt, K. D. (1984). Effects of static and cyclic compressive loading on articular cartilage plugs in vitro. Arthritis & Rheumatism, 27(6), 675-681. doi:10.1002/art.1780270611Khoshgoftar, M., Ito, K., & van Donkelaar, C. C. (2014). The Influence of Cell-Matrix Attachment and Matrix Development on the Micromechanical Environment of the Chondrocyte in Tissue-Engineered Cartilage. Tissue Engineering Part A, 20(23-24), 3112-3121. doi:10.1089/ten.tea.2013.0676Agrawal, C. M., & Ray, R. B. (2001). Biodegradable polymeric scaffolds for musculoskeletal tissue engineering. Journal of Biomedical Materials Research, 55(2), 141-150. doi:10.1002/1097-4636(200105)55:23.0.co;2-jPérez Olmedilla, M., Garcia-Giralt, N., Pradas, M. M., Ruiz, P. B., Gómez Ribelles, J. L., Palou, E. C., & García, J. C. M. (2006). Response of human chondrocytes to a non-uniform distribution of hydrophilic domains on poly (ethyl acrylate-co-hydroxyethyl methacrylate) copolymers. Biomaterials, 27(7), 1003-1012. doi:10.1016/j.biomaterials.2005.07.030Horbett, T. A., & Schway, M. B. (1988). Correlations between mouse 3T3 cell spreading and serum fibronectin adsorption on glass and hydroxyethylmethacrylate-ethylmethacrylate copolymers. Journal of Biomedical Materials Research, 22(9), 763-793. doi:10.1002/jbm.820220903Kiremitçi, M., Peşmen, A., Pulat, M., & Gürhan, I. (1993). Relationship of Surface Characteristics to Cellular Attachment in PU and PHEMA. Journal of Biomaterials Applications, 7(3), 250-264. doi:10.1177/088532829300700304Lydon, M. ., Minett, T. ., & Tighe, B. . (1985). Cellular interactions with synthetic polymer surfaces in culture. Biomaterials, 6(6), 396-402. doi:10.1016/0142-9612(85)90100-0Campillo-Fernandez, A. J., Pastor, S., Abad-Collado, M., Bataille, L., Gomez-Ribelles, J. L., Meseguer-Dueñas, J. M., … Ruiz-Moreno, J. M. (2007). Future Design of a New Keratoprosthesis. Physical and Biological Analysis of Polymeric Substrates for Epithelial Cell Growth. Biomacromolecules, 8(8), 2429-2436. doi:10.1021/bm0703012Funayama, A., Niki, Y., Matsumoto, H., Maeno, S., Yatabe, T., Morioka, H., … Toyama, Y. (2008). Repair of full-thickness articular cartilage defects using injectable type II collagen gel embedded with cultured chondrocytes in a rabbit model. Journal of Orthopaedic Science, 13(3), 225-232. doi:10.1007/s00776-008-1220-zKitahara, S., Nakagawa, K., Sah, R. L., Wada, Y., Ogawa, T., Moriya, H., & Masuda, K. (2008). In Vivo Maturation of Scaffold-free Engineered Articular Cartilage on Hydroxyapatite. Tissue Engineering Part A, 14(11), 1905-1913. doi:10.1089/ten.tea.2006.0419Martinez-Diaz, S., Garcia-Giralt, N., Lebourg, M., Gómez-Tejedor, J.-A., Vila, G., Caceres, E., … Monllau, J. C. (2010). In Vivo Evaluation of 3-Dimensional Polycaprolactone Scaffolds for Cartilage Repair in Rabbits. The American Journal of Sports Medicine, 38(3), 509-519. doi:10.1177/0363546509352448Wang, Y., Bian, Y.-Z., Wu, Q., & Chen, G.-Q. (2008). Evaluation of three-dimensional scaffolds prepared from poly(3-hydroxybutyrate-co-3-hydroxyhexanoate) for growth of allogeneic chondrocytes for cartilage repair in rabbits. Biomaterials, 29(19), 2858-2868. doi:10.1016/j.biomaterials.2008.03.021Alió del Barrio, J. L., Chiesa, M., Gallego Ferrer, G., Garagorri, N., Briz, N., Fernandez-Delgado, J., … De Miguel, M. P. (2014). Biointegration of corneal macroporous membranes based on poly(ethyl acrylate) copolymers in an experimental animal model. Journal of Biomedical Materials Research Part A, 103(3), 1106-1118. doi:10.1002/jbm.a.35249Diego, R. B., Olmedilla, M. P., Aroca, A. S., Ribelles, J. L. G., Pradas, M. M., Ferrer, G. G., & Sánchez, M. S. (2005). Acrylic scaffolds with interconnected spherical pores and controlled hydrophilicity for tissue engineering. Journal of Materials Science: Materials in Medicine, 16(8), 693-698. doi:10.1007/s10856-005-2604-7Serrano Aroca, A., Campillo Fernández, A. J., Gómez Ribelles, J. L., Monleón Pradas, M., Gallego Ferrer, G., & Pissis, P. (2004). Porous poly(2-hydroxyethyl acrylate) hydrogels prepared by radical polymerisation with methanol as diluent. Polymer, 45(26), 8949-8955. doi:10.1016/j.polymer.2004.10.033Diani, J., Fayolle, B., & Gilormini, P. (2009). A review on the Mullins effect. European Polymer Journal, 45(3), 601-612. doi:10.1016/j.eurpolymj.2008.11.017Mullins, L. (1969). Softening of Rubber by Deformation. Rubber Chemistry and Technology, 42(1), 339-362. doi:10.5254/1.3539210Jurvelin, J. S., Buschmann, M. D., & Hunziker, E. B. (2003). Mechanical anisotropy of the human knee articular cartilage in compression. Proceedings of the Institution of Mechanical Engineers, Part H: Journal of Engineering in Medicine, 217(3), 215-219. doi:10.1243/095441103765212712Shapiro, F., Koide, S., & Glimcher, M. J. (1993). Cell origin and differentiation in the repair of full-thickness defects of articular cartilage. The Journal of Bone & Joint Surgery, 75(4), 532-553. doi:10.2106/00004623-199304000-00009SELLERS, R. S., ZHANG, R., GLASSON, S. S., KIM, H. D., PELUSO, D., D’AUGUSTA, D. A., … MORRIS, E. A. (2000). Repair of Articular Cartilage Defects One Year After Treatment with Recombinant Human Bone Morphogenetic Protein-2 (rhBMP-2)*. The Journal of Bone and Joint Surgery-American Volume, 82(2), 151-160. doi:10.2106/00004623-200002000-00001Hunziker, E. B., Michel, M., & Studer, D. (1997). Ultrastructure of adult human articular cartilage matrix after cryotechnical processing. Microscopy Research and Technique, 37(4), 271-284. doi:10.1002/(sici)1097-0029(19970515)37:43.0.co;2-oAppelman, T. P., Mizrahi, J., Elisseeff, J. H., & Seliktar, D. (2009). The differential effect of scaffold composition and architecture on chondrocyte response to mechanical stimulation. Biomaterials, 30(4), 518-525. doi:10.1016/j.biomaterials.2008.09.063Chung, C., & Burdick, J. A. (2008). Engineering cartilage tissue. Advanced Drug Delivery Reviews, 60(2), 243-262. doi:10.1016/j.addr.2007.08.027HUNZIKER, E. B., & ROSENBERG, L. C. (1996). Repair of Partial-Thickness Defects in Articular Cartilage. The Journal of Bone & Joint Surgery, 78(5), 721-33. doi:10.2106/00004623-199605000-00012Schulze-Tanzil, G. (2009). Activation and dedifferentiation of chondrocytes: Implications in cartilage injury and repair. Annals of Anatomy - Anatomischer Anzeiger, 191(4), 325-338. doi:10.1016/j.aanat.2009.05.003Umlauf, D., Frank, S., Pap, T., & Bertrand, J. (2010). Cartilage biology, pathology, and repair. Cellular and Molecular Life Sciences, 67(24), 4197-4211. doi:10.1007/s00018-010-0498-0Karystinou, A., Dell’Accio, F., Kurth, T. B. A., Wackerhage, H., Khan, I. M., Archer, C. W., … De Bari, C. (2009). Distinct mesenchymal progenitor cell subsets in the adult human synovium. Rheumatology, 48(9), 1057-1064. doi:10.1093/rheumatology/kep192Sakaguchi, Y., Sekiya, I., Yagishita, K., & Muneta, T. (2005). Comparison of human stem cells derived from various mesenchymal tissues: Superiority of synovium as a cell source. Arthritis & Rheumatism, 52(8), 2521-2529. doi:10.1002/art.21212Schaefer, D., Martin, I., Jundt, G., Seidel, J., Heberer, M., Grodzinsky, A., … Freed, L. E. (2002). Tissue-engineered composites for the repair of large osteochondral defects. Arthritis & Rheumatism, 46(9), 2524-2534. doi:10.1002/art.1049

On the constraints violation in forward dynamics of multibody systems

It is known that the dynamic equations of motion for constrained mechanical multibody systems are frequently formulated using the Newton-Euler’s approach, which is augmented with the acceleration constraint equations. This formulation results in the establishment of a mixed set of partial differential and algebraic equations, which are solved in order to predict the dynamic behavior of general multibody systems. The classical resolution of the equations of motion is highly prone to constraints violation because the position and velocity constraint equations are not fulfilled. In this work, a general and comprehensive methodology to eliminate the constraints violation at the position and velocity levels is offered. The basic idea of the described approach is to add corrective terms to the position and velocity vectors with the intent to satisfy the corresponding kinematic constraint equations. These corrective terms are evaluated as function of the Moore-Penrose generalized inverse of the Jacobian matrix and of the kinematic constraint equations. The described methodology is embedded in the standard method to solve the equations of motion based on the technique of Lagrange multipliers. Finally, the effectiveness of the described methodology is demonstrated through the dynamic modeling and simulation of different planar and spatial multibody systems. The outcomes in terms of constraints violation at the position and velocity levels, conservation of the total energy and computational efficiency are analyzed and compared with those obtained with the standard Lagrange multipliers method, the Baumgarte stabilization method, the augmented Lagrangian formulation, the index-1 augmented Lagrangian and the coordinate partitioning method.The first author expresses his gratitude to the Portuguese Foundation for Science and Technology through the PhD grant (PD/BD/114154/2016). This work has been supported by the Portuguese Foundation for Science and Technology with the reference project UID/EEA/04436/2013, by FEDER funds through the COMPETE 2020 – Programa Operacional Competitividade e Internacionalização (POCI) with the reference project POCI-01-0145-FEDER-006941.info:eu-repo/semantics/publishedVersio