Multiple solitary-waves due to second harmonic generation in quadratic media

A detailed mathematical analysis is undertaken of solitary wave solutions of a system of coupled NLS equations describing second harmonic generation in optical materials with (2) nonlinearity. The so called bright-bright case is studied exclusively. The system depends on a single dimensionless parameter ff which includes both wave and material properties. Using variational methods, the first rigorous mathematical proof is given that at least one solitary wave exists for all positive ff. Recently bound states (multi-pulsed solitary waves) have been found numerically. Using numerical continuation, the region of existence of these solutions is revealed to be ff 2 (0; 1) and the bifurcations occuring at the two extremes of this interval are uncovered

Completability and optimal factorization norms in tensor products of Banach function spaces

[EN] Given s-finite measure spaces ( 1, 1, mu 1) and ( 2, 2, mu 2), we consider Banach spaces X1(mu 1) and X2(mu 2), consisting of L0(mu 1) and L0(mu 2) measurable functions respectively, and study when the completion of the simple tensors in the projective tensor product X1(mu 1). p X2(mu 2) is continuously included in the metric space of measurable functions L0(mu 1. mu 2). In particular, we prove that the elements of the completion of the projective tensor product of L p-spaces are measurable functions with respect to the product measure. Assuming certain conditions, we finally showthat given a bounded linear operator T : X1(mu 1). p X2(mu 2). E (where E is a Banach space), a norm can be found for T to be bounded, which is ` minimal' with respect to a given property (2-rectangularity). The same technique may work for the case of n-spaces.J. M. Calabuig and M. Fernandez-Unzueta were supported by Ministerio de Economia, Industria y Competitividad (Spain) under project MTM2014-53009-P. M. Fernandez-Unzueta was also suported by CONACyT 284110. F. Galaz-Fontes was supported by Ministerio de Ciencia e Innovacion (Spain) and FEDER under project MTM2009-14483-C02-01. E. A. Sanchez Perez was supported by Ministerio de Economia, Industria y Competitividad (Spain) and FEDER under project MTM2016-77054-C2-1-P.Calabuig, JM.; Fernández-Unzueta, M.; Galaz-Fontes, F.; Sánchez Pérez, EA. (2019). Completability and optimal factorization norms in tensor products of Banach function spaces. Revista de la Real Academia de Ciencias Exactas Físicas y Naturales Serie A Matemáticas. 113(4):3513-3530. https://doi.org/10.1007/s13398-019-00711-7S351335301134Abramovich, Y.A., Aliprantis, C.D.: An invitation to operator theory. Graduate Studies in Mathematics, Vol 50, AMS (2002)Bennett, C., Sharpley, R.: Interpolation of Operators. Academic Press, Boston (1988)Bu, Q., Buskes, G., Kusraev, A.G.: Bilinear maps on products of vector lattices: a survey. In: Boulabiar, K., Buskes, G., Triki, A. (eds.) Positivity-Trends in Mathematics. Birkhäser Verlag AG, Basel, pp. 97–26 (2007)Buskes, G., Van Rooij, A.: Bounded variation and tensor products of Banach lattices. Positivity 7, 47–59 (2003)Calabuig, J.M., Fernández-Unzueta, M., Galaz-Fontes, F., Sánchez-Pérez, E.A.: Extending and factorizing bounded bilinear maps defined on order continuous Banach function spaces. RACSAM 108(2), 353–367 (2014)Calabuig, J.M., Fernández-Unzueta, M., Galaz-Fontes, F., Sánchez-Pérez, E.A.: Equivalent norms in a Banach function space and the subsequence property. J. Korean Math. Soc. https://doi.org/10.4134/JKMS.j180682Curbera, G.P., Ricker, W.J.: Optimal domains for kernel operators via interpolation. Math. Nachr. 244, 47–63 (2002)Curbera, G.P., Ricker, W.J.: Vector measures, integration and applications. In: Positivity. Birkhäuser Basel, pp. 127–160 (2007)Gil de Lamadrid, J.: Uniform cross norms and tensor products. J. Duke Math. 32, 797–803 (1965)Dunford, N., Schwartz, J.: Linear Operators, Part I: General Theory. Interscience Publishers Inc., New York (1958)Fremlin, D.H.: Tensor products of Archimedean vector lattices. Am. J. Math. 94(3), 777–798 (1972)Fremlin, D.H.: Tensor products of Banach lattices. Math. Ann. 211(2), 87–106 (1974)Yew, K.L.: Completely $$p$$-summing maps on the operator Hilbert space OH. J. Funct. Anal. 255, 1362–1402 (2008)Kwapien, S., Pelczynski, A.: The main triangle projection in matrix spaces and its applications. Stud. Math. 34(1), 43–68 (1970)Lindenstrauss, J., Tzafriri, L.: Classical Banach spaces II. Springer, Berlin (1979)Luxemburg, W.A.J., Zaanen, A.C.: Riesz Spaces I. North-Holland Publishing Company, Amsterdam (1971)Milman, M.: Some new function spaces and their tensor products. Depto. de Matemática, Facultad de Ciencias, U. de los Andes, Mérida, Venezuela (1978)Okada, S., Ricker, W.J., Sánchez Pérez, E.A.: Optimal domain and integral extension of operators acting in function spaces. Oper. Theory Adv. Appl., vol. 180. Birkhäuser, Basel (2008)Schep, A.R.: Factorization of positive multilinear maps. Illinois J. Math. 579–591 (1984)Zaanen, A.C.: Integration. North-Holland Publishing Company, Amsterdam-New York (1967)Zaanen, A.C.: Riesz Spaces II. North-Holland Publishing Company, Amsterdam (1983

Epidemiological risk factors for adult dengue in Singapore: an 8-year nested test negative case control study

10.1186/s12879-016-1662-4BMC Infectious Diseases16132

Micro-CT imaging reveals<i> Mekk3 </i>heterozygosity prevents cerebral cavernous malformations in <i>Ccm2</i>-deficient mice

Mutations in CCM1 (aka KRIT1), CCM2, or CCM3 (aka PDCD10) gene cause cerebral cavernous malformation in humans. Mouse models of CCM disease have been established by deleting Ccm genes in postnatal animals. These mouse models provide invaluable tools to investigate molecular mechanism and therapeutic approaches for CCM disease. However, the full value of these animal models is limited by the lack of an accurate and quantitative method to assess lesion burden and progression. In the present study we have established a refined and detailed contrast enhanced X-ray micro-CT method to measure CCM lesion burden in mouse brains. As this study utilized a voxel dimension of 9.5μm (leading to a minimum feature size of approximately 25μm), it is therefore sufficient to measure CCM lesion volume and number globally and accurately, and provide high-resolution 3-D mapping of CCM lesions in mouse brains. Using this method, we found loss of Ccm1 or Ccm2 in neonatal endothelium confers CCM lesions in the mouse hindbrain with similar total volume and number. This quantitative approach also demonstrated a rescue of CCM lesions with simultaneous deletion of one allele of Mekk3. This method would enhance the value of the established mouse models to study the molecular basis and potential therapies for CCM and other cerebrovascular diseases

Inhibition of Hypoxia-Inducible Factor-1α (HIF-1α) Protein Synthesis by DNA damage inducing agents

10.1371/journal.pone.0010522PLoS ONE55

Estimating Dengue Transmission Intensity from Sero-Prevalence Surveys in Multiple Countries

BACKGROUND:Estimates of dengue transmission intensity remain ambiguous. Since the majority of infections are asymptomatic, surveillance systems substantially underestimate true rates of infection. With advances in the development of novel control measures, obtaining robust estimates of average dengue transmission intensity is key for assessing both the burden of disease from dengue and the likely impact of interventions. METHODOLOGY/PRINCIPAL FINDINGS:The force of infection (λ) and corresponding basic reproduction numbers (R0) for dengue were estimated from non-serotype (IgG) and serotype-specific (PRNT) age-stratified seroprevalence surveys identified from the literature. The majority of R0 estimates ranged from 1-4. Assuming that two heterologous infections result in complete immunity produced up to two-fold higher estimates of R0 than when tertiary and quaternary infections were included. λ estimated from IgG data were comparable to the sum of serotype-specific forces of infection derived from PRNT data, particularly when inter-serotype interactions were allowed for. CONCLUSIONS/SIGNIFICANCE:Our analysis highlights the highly heterogeneous nature of dengue transmission. How underlying assumptions about serotype interactions and immunity affect the relationship between the force of infection and R0 will have implications for control planning. While PRNT data provides the maximum information, our study shows that even the much cheaper ELISA-based assays would provide comparable baseline estimates of overall transmission intensity which will be an important consideration in resource-constrained settings

Synergistic Apoptosis Induction in Leukemic Cells by the Phosphatase Inhibitor Salubrinal and Proteasome Inhibitors

Cells adapt to endoplasmic reticulum (ER)-stress by arresting global protein synthesis while simultaneously activating specific transcription factors and their downstream targets. These processes are mediated in part by the phosphorylation-dependent inactivation of the translation initiation factor eIF2alpha. Following restoration of homeostasis protein synthesis is resumed when the serine/threonine-protein phosphatase PP1 dephosphorylates and reactivates eIF2alpha. Proteasome inhibitors, used to treat multiple myeloma patients evoke ER-stress and apoptosis by blocking the ER-associated degradation of misfolded proteins (ERAD), however, the role of eIF2alpha phosphorylation in leukemic cells under conditions of proteasome inhibitor-mediated ER stress is currently unclear.Bcr-Abl-positive and negative leukemic cell lines were used to investigate the functional implications of PP1-related phosphatase activities on eIF2alpha phosphorylation in proteasome inhibitor-mediated ER stress and apoptosis. Rather unexpectedly, salubrinal, a recently identified PP1 inhibitor capable to protect against ER stress in various model systems, strongly synergized with proteasome inhibitors to augment apoptotic death of different leukemic cell lines. Salubrinal treatment did not affect the phosphorlyation status of eIF2alpha. Furthermore, the proapoptotic effect of salubrinal occurred independently from the chemical nature of the proteasome inhibitor, was recapitulated by a second unrelated phosphatase inhibitor and was unaffected by overexpression of a dominant negative eIF2alpha S51A variant that can not be phosphorylated. Salubrinal further aggravated ER-stress and proteotoxicity inflicted by the proteasome inhibitors on the leukemic cells since characteristic ER stress responses, such as ATF4 and CHOP synthesis, XBP1 splicing, activation of MAP kinases and eventually apoptosis were efficiently abrogated by the translational inhibitor cycloheximide.Although PP1 activity does not play a major role in regulating the ER stress response in leukemic cells, phosphatase signaling nevertheless significantly limits proteasome inhibitor-mediated ER-stress and apoptosis. Inclusion of specific phosphatase inhibitors might therefore represent an option to improve current proteasome inhibitor-based treatment modalities for hematological cancers

Comprehensive annotation of the Parastagonospora nodorum reference genome using next-generation genomics, transcriptomics and proteogenomics

Parastagonospora nodorum, the causal agent of Septoria nodorum blotch (SNB), is an economically important pathogen of wheat (Triticum spp.), and a model for the study of necrotrophic pathology and genome evolution. The reference P. nodorum strain SN15 was the first Dothideomycete with a published genome sequence, and has been used as the basis for comparison within and between species. Here we present an updated reference genome assembly with corrections of SNP and indel errors in the underlying genome assembly from deep resequencing data as well as extensive manual annotation of gene models using transcriptomic and proteomic sources of evidence (https://github.com/robsyme/Parastagonospora_nodorum_SN15). The updated assembly and annotation includes 8,366 genes with modified protein sequence and 866 new genes. This study shows the benefits of using a wide variety of experimental methods allied to expert curation to generate a reliable set of gene models