Factors of binomial sums from the Catalan triangle

By using the Newton interpolation formula, we generalize the recent identities on the Catalan triangle obtained by Miana and Romero as well as those of Chen and Chu. We further study divisibility properties of sums of products of binomial coefficients and an odd power of a natural number. For example, we prove that for all positive integers $n_1, ..., n_m$, $n_{m+1}=n_1$, and any nonnegative integer $r$, the expression $$n_1^{-1}{n_1+n_{m}\choose n_1}^{-1} \sum_{k=1}^{n_1}k^{2r+1}\prod_{i=1}^{m} {n_i+n_{i+1}\choose n_i+k}$$ is either an integer or a half-integer. Moreover, several related conjectures are proposed.Comment: 15 pages, final versio

Identification of subgroups of early breast cancer patients at high risk of nonadherence to adjuvant hormone therapy: results of an italian survey.

The aim of this study was the identification of subgroups of patients at higher risk of nonadherence to adjuvant hormone therapy for breast cancer. Using recursive partitioning and amalgamation (RECPAM) analysis, the highest risk was observed in the group of unmarried, employed women, or housewives. This result might be functional in designing tailored intervention studies aimed at improvement of adherence. Background: Adherence to adjuvant endocrine therapy (HT) is suboptimal among breast cancer patients. A high rate of nonadherence might explain differences in survival between clinical trial and clinical practice. Tailored interventions aimed at improving adherence can only be implemented if subgroups of patients at higher risk of poor adherence are identified. Because no data are available for Italy, we undertook a large survey on adherence among women taking adjuvant HT for breast cancer. Patients and Methods: Patients were recruited from 10 cancer clinics in central Italy. All patients taking HT for at least 1 year were invited, during one of their follow-up visit, to fill a confidential questionnaire. The association of sociodemographic and clinical characteristics of participants with adherence was assessed using logistic regression. The RECPAM method was used to evaluate interactions among variables and to identify subgroups of patients at different risk of nonadherence. Results: A total of 939 patients joined the study and 18.6% of them were classified as nonadherers. Among possible predictors, only age, working status, and switching from tamoxifen to an aromatase inhibitor were predictive of nonadherence in multivariate analysis. RECPAM analysis led to the identification of 4 classes of patients with a different likelihood of nonadherence to therapy, the lowest being observed in retired women with a low level of education, the highest in the group of unmarried, employed women, or housewives. Conclusion: The identification of these subgroups of “real life” patients with a high prevalence of nonadherers might be functional in designing intervention studies aimed at improving adherenc

A probabilistic analysis of a Beverton-Holt type discrete model: Theoretical and computing analysis

"This is the peer reviewed version of the following article: Cortés, J-C, Navarro-Quiles, A, Romero, J-V, Roselló, M-D. A probabilistic analysis of a Beverton-Holt type discrete model: Theoretical and computing analysis. Comp and Math Methods. 2019; 1:e1013, which has been published in final form at https://doi.org/10.1002/cmm4.1013. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Self-Archiving."[EN] In this paper a randomized version of the Beverton-Holt type discrete model is proposed. Its solution stochastic process and the random steady state are determined. Its first probability density function and second probability density function are obtained by means of the random variable transformation method, providing a full probabilistic description of the solution. Finally, several numerical examples are shown.This work has been partially supported by the Ministerio de Economía, Industria y Competitividad under grant MTM2017-89664-P. The authors express their deepest thanks and respect to the editors and reviewers for their valuable comments.Cortés, J.; Navarro-Quiles, A.; Romero, J.; Roselló, M. (2019). A probabilistic analysis of a Beverton-Holt type discrete model: Theoretical and computing analysis. Computational and Mathematical Methods. 1(1):1-12. https://doi.org/10.1002/cmm4.1013S11211Kwasnicki, W. (2013). Logistic growth of the global economy and competitiveness of nations. Technological Forecasting and Social Change, 80(1), 50-76. doi:10.1016/j.techfore.2012.07.007De la Sen, M. (2008). The generalized Beverton–Holt equation and the control of populations. Applied Mathematical Modelling, 32(11), 2312-2328. doi:10.1016/j.apm.2007.09.007Cortés, J.-C., Navarro-Quiles, A., Romero, J.-V., & Roselló, M.-D. (2018). Computing the probability density function of non-autonomous first-order linear homogeneous differential equations with uncertainty. Journal of Computational and Applied Mathematics, 337, 190-208. doi:10.1016/j.cam.2018.01.015Casabán, M.-C., Cortés, J.-C., Navarro-Quiles, A., Romero, J.-V., Roselló, M.-D., & Villanueva, R.-J. (2017). Computing probabilistic solutions of the Bernoulli random differential equation. Journal of Computational and Applied Mathematics, 309, 396-407. doi:10.1016/j.cam.2016.02.034Cortés, J.-C., Navarro-Quiles, A., Romero, J.-V., & Roselló, M.-D. (2017). Randomizing the parameters of a Markov chain to model the stroke disease: A technical generalization of established computational methodologies towards improving real applications. Journal of Computational and Applied Mathematics, 324, 225-240. doi:10.1016/j.cam.2017.04.040Cortés, J.-C., Navarro-Quiles, A., Romero, J.-V., & Roselló, M.-D. (2017). Full solution of random autonomous first-order linear systems of difference equations. Application to construct random phase portrait for planar systems. Applied Mathematics Letters, 68, 150-156. doi:10.1016/j.aml.2016.12.01

Victorianomania: Reimagining, Refashioning, and Rewriting Victorian Literature and Culture

Ressenya del llibre: Victorianomania: Reimagining, Refashioning, and Rewriting Victorian Literature and Culture / a cura di S. Falchi, G. Perletti, M. I. Romero Ruiz. Franco Angeli, 201

Macroscopic detection of the strong stochasticity threshold in Fermi-Pasta-Ulam chains of oscillators

The largest Lyapunov exponent of a system composed by a heavy impurity embedded in a chain of anharmonic nearest-neighbor Fermi-Pasta-Ulam oscillators is numerically computed for various values of the impurity mass $M$. A crossover between weak and strong chaos is obtained at the same value $\epsilon_{_T}$ of the energy density $\epsilon$ (energy per degree of freedom) for all the considered values of the impurity mass $M$. The threshold \epsi lon_{_T} coincides with the value of the energy density $\epsilon$ at which a change of scaling of the relaxation time of the momentum autocorrelation function of the impurity ocurrs and that was obtained in a previous work ~[M. Romero-Bastida and E. Braun, Phys. Rev. E {\bf65}, 036228 (2002)]. The complete Lyapunov spectrum does not depend significantly on the impurity mass $M$. These results suggest that the impurity does not contribute significantly to the dynamical instability (chaos) of the chain and can be considered as a probe for the dynamics of the system to which the impurity is coupled. Finally, it is shown that the Kolmogorov-Sinai entropy of the chain has a crossover from weak to strong chaos at the same value of the energy density that the crossover value $\epsilon_{_T}$ of largest Lyapunov exponent. Implications of this result are discussed.Comment: 6 pages, 5 figures, revtex4 styl

PulmonDB: a curated lung disease gene expression database

14openInternationalInternational coauthor/editorChronic Obstructive Pulmonary Disease (COPD) and Idiopathic Pulmonary Fibrosis (IPF) have contrasting clinical and pathological characteristics and interesting whole-genome transcriptomic profiles. However, data from public repositories are difficult to reprocess and reanalyze. Here, we present PulmonDB, a web-based database (http://pulmondb.liigh.unam.mx/) and R library that facilitates exploration of gene expression profiles for these diseases by integrating transcriptomic data and curated annotation from different sources. We demonstrated the value of this resource by presenting the expression of already well-known genes of COPD and IPF across multiple experiments and the results of two differential expression analyses in which we successfully identified differences and similarities. With this first version of PulmonDB, we create a new hypothesis and compare the two diseases from a transcriptomics perspective.openVillaseñor-Altamirano, A.B.; Moretto, M.; Maldonado, M.; Zayas-Del Moral, A.; Munguía-Reyes, A.; Romero, Y.; García-Sotelo, J.S.; Aguilar, L.A.; Aldana-Assad, O.; Engelen, K.; Selman, M.; Collado-Vides, J.; Balderas-Martínez, Y.I.; Medina-Rivera, A.Villaseñor-Altamirano, A.B.; Moretto, M.; Maldonado, M.; Zayas-Del Moral, A.; Munguía-Reyes, A.; Romero, Y.; García-Sotelo, J.S.; Aguilar, L.A.; Aldana-Assad, O.; Engelen, K.; Selman, M.; Collado-Vides, J.; Balderas-Martínez, Y.I.; Medina-Rivera, A

Stereoselective construction of the tetracyclic scalarane skeleton from carvone

The tetracyclic scalarane skeleton 22 has been constructed from (S)-(+)-carvone using two intramolecular Diels–Alder reactions as key synthetic steps.Abad Somovilla, Antonio, [email protected] ; Agullo Blanes, M Consuelo, [email protected] ; Cuñat Romero, Ana Carmen, [email protected] ; Llosa Blasco, Maria Carmen, [email protected]

Sound absorption and diffusion by 2D arrays of Helmholtz resonators

[EN] We report a theoretical and experimental study of an array of Helmholtz resonators optimized to achieve both efficient sound absorption and diffusion. The analysis starts with a simplified 1D model where the plane wave approximation is used to design an array of resonators showing perfect absorption for a targeted range of frequencies. The absorption is optimized by tuning the geometry of the resonators, i.e., by tuning the viscothermal losses of each element. Experiments with the 1D array were performed in an impedance tube. The designed system is extended to 2D by periodically replicating the 1D array. The 2D system has been numerically modeled and experimentally tested in an anechoic chamber. It preserves the absorption properties of the 1D system and introduces efficient diffusion at higher frequencies due to the joint effect of resonances and multiple scattering inside the discrete 2D structure. The combined effect of sound absorption at low frequencies and sound diffusion at higher frequencies, may play a relevant role in the design of noise reduction systems for different applications.This research was funded by the European Space Agency under the Networking/Partnering Initiative (NPI) contract number 441-2015. In memoriam to Julián Santiago-Prowald, Senior Advisor for the Structures, Mechanisms and Materials Division of ESA, a great man that always gave us his tireless support. AC acknowledges financial support from Generalitat Valenciana through the grant APOSTD/2018/229. VRG acknowledges the financial support from RFI Le Mans Acoustique (Région Pays de la Loire) in the framework of the project HYPERMETA funded under the program Étoiles Montantes of the Région Pays de la Loire. Authors acknowledge the support of the European Space Agency under contract 441-2015 Co- Sponsored PhD ¿Acoustic Reduction Methods for the Launch Pad¿ and project TRP ESA AO/1-9479/18/NL/LvH ¿Launch Sound Level Reduction¿. This article is based upon work from COST Action DENORMS CA15125, supported by COST (European Cooperation in Science and Technology).Herrero-Durá, I.; Cebrecos, A.; Picó Vila, R.; Romero-García, V.; García-Raffi, LM.; Sánchez Morcillo, VJ. (2020). Sound absorption and diffusion by 2D arrays of Helmholtz resonators. Applied Sciences. 10(5):1-15. https://doi.org/10.3390/app10051690S115105Sigalas, M. M., & Economou, E. N. (1992). Elastic and acoustic wave band structure. Journal of Sound and Vibration, 158(2), 377-382. doi:10.1016/0022-460x(92)90059-7Matlack, K. H., Bauhofer, A., Krödel, S., Palermo, A., & Daraio, C. (2016). Composite 3D-printed metastructures for low-frequency and broadband vibration absorption. Proceedings of the National Academy of Sciences, 113(30), 8386-8390. doi:10.1073/pnas.1600171113Wormser, M., Wein, F., Stingl, M., & Körner, C. (2017). Design and Additive Manufacturing of 3D Phononic Band Gap Structures Based on Gradient Based Optimization. Materials, 10(10), 1125. doi:10.3390/ma10101125Lucklum, F., & Vellekoop, M. J. (2018). Bandgap engineering of three-dimensional phononic crystals in a simple cubic lattice. Applied Physics Letters, 113(20), 201902. doi:10.1063/1.5049663D’Alessandro, L., Ardito, R., Braghin, F., & Corigliano, A. (2019). Low frequency 3D ultra-wide vibration attenuation via elastic metamaterial. Scientific Reports, 9(1). doi:10.1038/s41598-019-44507-6Martínez-Sala, R., Sancho, J., Sánchez, J. V., Gómez, V., Llinares, J., & Meseguer, F. (1995). Sound attenuation by sculpture. Nature, 378(6554), 241-241. doi:10.1038/378241a0Cebrecos, A., Krattiger, D., Sánchez-Morcillo, V. J., Romero-García, V., & Hussein, M. I. (2019). The finite-element time-domain method for elastic band-structure calculations. Computer Physics Communications, 238, 77-87. doi:10.1016/j.cpc.2018.12.016Cebrecos, A., Romero-García, V., & Groby, J. (2019). Complex Dispersion Relation Recovery from 2D Periodic Resonant Systems of Finite Size. Applied Sciences, 9(3), 478. doi:10.3390/app9030478Hussein, M. I., Leamy, M. J., & Ruzzene, M. (2014). Dynamics of Phononic Materials and Structures: Historical Origins, Recent Progress, and Future Outlook. Applied Mechanics Reviews, 66(4). doi:10.1115/1.4026911Sanchez-Perez, J. V., Rubio, C., Martinez-Sala, R., Sanchez-Grandia, R., & Gomez, V. (2002). Acoustic barriers based on periodic arrays of scatterers. Applied Physics Letters, 81(27), 5240-5242. doi:10.1063/1.1533112Martínez-Sala, R., Rubio, C., García-Raffi, L. M., Sánchez-Pérez, J. V., Sánchez-Pérez, E. A., & Llinares, J. (2006). Control of noise by trees arranged like sonic crystals. Journal of Sound and Vibration, 291(1-2), 100-106. doi:10.1016/j.jsv.2005.05.030Garcia-Raffi, L. M., Salmerón-Contreras, L. J., Herrero-Durá, I., Picó, R., Redondo, J., Sánchez-Morcillo, V. J., … Romero-García, V. (2018). Broadband reduction of the specular reflections by using sonic crystals: A proof of concept for noise mitigation in aerospace applications. Aerospace Science and Technology, 73, 300-308. doi:10.1016/j.ast.2017.11.048Sanchez-Perez, J. V., Castineira-Ibanez, S., Romero-Garcia, V., & Garcia-Raffi, L. M. (2015). PERIODIC SYSTEMS AS ROAD TRAFFIC NOISE REDUCING DEVICES: PROTOTYPE AND STANDARDIZATION. Environmental Engineering and Management Journal, 14(12), 2759-2769. doi:10.30638/eemj.2015.293Kandula, M. (2009). Broadband shock noise reduction in turbulent jets by water injection. Applied Acoustics, 70(7), 1009-1014. doi:10.1016/j.apacoust.2008.12.001Liu, Z., Zhang, X., Mao, Y., Zhu, Y. Y., Yang, Z., Chan, C. T., & Sheng, P. (2000). Locally Resonant Sonic Materials. Science, 289(5485), 1734-1736. doi:10.1126/science.289.5485.1734Fang, N., Xi, D., Xu, J., Ambati, M., Srituravanich, W., Sun, C., & Zhang, X. (2006). Ultrasonic metamaterials with negative modulus. Nature Materials, 5(6), 452-456. doi:10.1038/nmat1644Sugimoto, N., & Horioka, T. (1995). Dispersion characteristics of sound waves in a tunnel with an array of Helmholtz resonators. The Journal of the Acoustical Society of America, 97(3), 1446-1459. doi:10.1121/1.412085Theocharis, G., Richoux, O., García, V. R., Merkel, A., & Tournat, V. (2014). Limits of slow sound propagation and transparency in lossy, locally resonant periodic structures. New Journal of Physics, 16(9), 093017. doi:10.1088/1367-2630/16/9/093017Jiménez, N., Cox, T. J., Romero-García, V., & Groby, J.-P. (2017). Metadiffusers: Deep-subwavelength sound diffusers. Scientific Reports, 7(1). doi:10.1038/s41598-017-05710-5Ballestero, E., Jiménez, N., Groby, J.-P., Dance, S., Aygun, H., & Romero-García, V. (2019). Experimental validation of deep-subwavelength diffusion by acoustic metadiffusers. Applied Physics Letters, 115(8), 081901. doi:10.1063/1.5114877Romero-García, V., Sánchez-Pérez, J. V., & Garcia-Raffi, L. M. (2011). Tunable wideband bandstop acoustic filter based on two-dimensional multiphysical phenomena periodic systems. Journal of Applied Physics, 110(1), 014904. doi:10.1063/1.3599886Lagarrigue, C., Groby, J. P., & Tournat, V. (2013). Sustainable sonic crystal made of resonating bamboo rods. The Journal of the Acoustical Society of America, 133(1), 247-254. doi:10.1121/1.4769783Krynkin, A., Umnova, O., Yung Boon Chong, A., Taherzadeh, S., & Attenborough, K. (2010). Predictions and measurements of sound transmission through a periodic array of elastic shells in air. The Journal of the Acoustical Society of America, 128(6), 3496-3506. doi:10.1121/1.3506342Koussa, F., Defrance, J., Jean, P., & Blanc-Benon, P. (2013). Acoustical Efficiency of a Sonic Crystal Assisted Noise Barrier. Acta Acustica united with Acustica, 99(3), 399-409. doi:10.3813/aaa.918621Castiñeira-Ibáñez, S., Romero-García, V., Sánchez-Pérez, J. V., & Garcia-Raffi, L. M. (2010). Overlapping of acoustic bandgaps using fractal geometries. EPL (Europhysics Letters), 92(2), 24007. doi:10.1209/0295-5075/92/24007García-Chocano, V. M., Cabrera, S., & Sánchez-Dehesa, J. (2012). Broadband sound absorption by lattices of microperforated cylindrical shells. Applied Physics Letters, 101(18), 184101. doi:10.1063/1.4764560Lardeau, A., Groby, J.-P., & Romero-García, V. (2016). Broadband Transmission Loss Using the Overlap of Resonances in 3D Sonic Crystals. Crystals, 6(5), 51. doi:10.3390/cryst6050051Cavalieri, T., Cebrecos, A., Groby, J.-P., Chaufour, C., & Romero-García, V. (2019). Three-dimensional multiresonant lossy sonic crystal for broadband acoustic attenuation: Application to train noise reduction. Applied Acoustics, 146, 1-8. doi:10.1016/j.apacoust.2018.10.020Dimitrijević, S. M., García-Chocano, V. M., Cervera, F., Roth, E., & Sánchez-Dehesa, J. (2019). Sound Insulation and Reflection Properties of Sonic Crystal Barrier Based on Micro-Perforated Cylinders. Materials, 12(17), 2806. doi:10.3390/ma12172806Stinson, M. R. (1991). The propagation of plane sound waves in narrow and wide circular tubes, and generalization to uniform tubes of arbitrary cross‐sectional shape. The Journal of the Acoustical Society of America, 89(2), 550-558. doi:10.1121/1.400379Duclos, A., Lafarge, D., & Pagneux, V. (2009). Transmission of acoustic waves through 2D phononic crystal: visco-thermal and multiple scattering effects. The European Physical Journal Applied Physics, 45(1), 11302. doi:10.1051/epjap:2008203Romero-García, V., Theocharis, G., Richoux, O., & Pagneux, V. (2016). Use of complex frequency plane to design broadband and sub-wavelength absorbers. The Journal of the Acoustical Society of America, 139(6), 3395-3403. doi:10.1121/1.4950708Romero-García, V., Theocharis, G., Richoux, O., Merkel, A., Tournat, V., & Pagneux, V. (2016). Perfect and broadband acoustic absorption by critically coupled sub-wavelength resonators. Scientific Reports, 6(1). doi:10.1038/srep19519Jiménez, N., Huang, W., Romero-García, V., Pagneux, V., & Groby, J.-P. (2016). Ultra-thin metamaterial for perfect and quasi-omnidirectional sound absorption. Applied Physics Letters, 109(12), 121902. doi:10.1063/1.4962328Jiménez, N., Romero-García, V., Pagneux, V., & Groby, J.-P. (2017). Quasiperfect absorption by subwavelength acoustic panels in transmission using accumulation of resonances due to slow sound. Physical Review B, 95(1). doi:10.1103/physrevb.95.014205Jiménez, N., Romero-García, V., Pagneux, V., & Groby, J.-P. (2017). Rainbow-trapping absorbers: Broadband, perfect and asymmetric sound absorption by subwavelength panels for transmission problems. Scientific Reports, 7(1). doi:10.1038/s41598-017-13706-4Merkel, A., Theocharis, G., Richoux, O., Romero-García, V., & Pagneux, V. (2015). Control of acoustic absorption in one-dimensional scattering by resonant scatterers. Applied Physics Letters, 107(24), 244102. doi:10.1063/1.4938121Kergomard, J., & Garcia, A. (1987). Simple discontinuities in acoustic waveguides at low frequencies: Critical analysis and formulae. Journal of Sound and Vibration, 114(3), 465-479. doi:10.1016/s0022-460x(87)80017-2Sánchez-Dehesa, J., Garcia-Chocano, V. M., Torrent, D., Cervera, F., Cabrera, S., & Simon, F. (2011). Noise control by sonic crystal barriers made of recycled materials. The Journal of the Acoustical Society of America, 129(3), 1173-1183. doi:10.1121/1.3531815Christensen, J., Romero-García, V., Picó, R., Cebrecos, A., de Abajo, F. J. G., Mortensen, N. A., … Sánchez-Morcillo, V. J. (2014). Extraordinary absorption of sound in porous lamella-crystals. Scientific Reports, 4(1). doi:10.1038/srep0467

Macroscopic evidence of microscopic dynamics in the Fermi-Pasta-Ulam oscillator chain from nonlinear time series analysis

The problem of detecting specific features of microscopic dynamics in the macroscopic behavior of a many-degrees-of-freedom system is investigated by analyzing the position and momentum time series of a heavy impurity embedded in a chain of nearest-neighbor anharmonic Fermi-Pasta-Ulam oscillators. Results obtained in a previous work [M. Romero-Bastida, Phys. Rev. E {\bf69}, 056204 (2004)] suggest that the impurity does not contribute significantly to the dynamics of the chain and can be considered as a probe for the dynamics of the system to which the impurity is coupled. The ($r,\tau$) entropy, which measures the amount of information generated by unit time at different scales $\tau$ of time and $r$ of the observable, is numerically computed by methods of nonlinear time-series analysis using the position and momentum signals of the heavy impurity for various values of the energy density $\epsilon$ (energy per degree of freedom) of the system and some values of the impurity mass $M$. Results obtained from these two time series are compared and discussed.Comment: 7 pages, 5 figures, RevTeX4 PRE format; to be published in Phys. Rev.