Journal articles on the topic 'Noncanonical hypercomplex number system'
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Pulver, Sandra. "Quaternions: The hypercomplex number system." Mathematical Gazette 92, no. 525 (November 2008): 431–36. http://dx.doi.org/10.1017/s0025557200183639.
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Are there solutions of the equation x2 + 1 = 0 ? Carl Fredrich Gauss (1777–1855) conjectured that there was a solution and that it was the square root of - 1 . But since the squares of all real numbers, positive or negative, are positive, Gauss introduced a fanciful idea. His solution to this equation was , which he named i. He integrated i with the real numbers to form a set known as , the complex numbers, where each element in that set was of the form a + bi, where a, . Gauss illustrated this on a graph, the horizontal axis became the real axis and represented the real coefficient, while the vertical axis became the imaginary axis and represented the imaginary coefficient.
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KIM, JI EUN, and KWANG HO SHON. "COSET OF A HYPERCOMPLEX NUMBER SYSTEM IN CLIFFORD ANALYSIS." Bulletin of the Korean Mathematical Society 52, no. 5 (September 30, 2015): 1721–28. http://dx.doi.org/10.4134/bkms.2015.52.5.1721.
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SHU, JIAN-JUN, and YAJING LI. "HYPERCOMPLEX CROSS-CORRELATION OF DNA SEQUENCES." Journal of Biological Systems 18, no. 04 (December 2010): 711–25. http://dx.doi.org/10.1142/s0218339010003470.
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A hypercomplex representation of DNA is proposed to facilitate comparing DNA sequences with fuzzy composition. With the hypercomplex number representation, the conventional sequence analysis method, such as, dot matrix analysis, dynamic programming, and cross-correlation method have been extended and improved to align DNA sequences with fuzzy composition. The hypercomplex dot matrix analysis can provide more control over the degree of alignment desired. A new scoring system has been proposed to accommodate the hypercomplex number representation of DNA and integrated with dynamic programming alignment method. By using hypercomplex cross-correlation, the match and mismatch alignment information between two aligned DNA sequences are separately stored in the resultant real part and imaginary parts respectively. The mismatch alignment information is very useful to refine consensus sequence based motif scanning.
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SUNDHEIM, PAUL. "A MULTIPLICATIVE DETERMINANT FOR 2m-DIMENSIONAL MATRICES." Journal of Algebra and Its Applications 13, no. 01 (August 20, 2013): 1350067. http://dx.doi.org/10.1142/s0219498813500679.
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A multiplication for a specific nested collection of multidimensional matrices is defined by association with a system of n = 2m-dimensional hypercomplex numbers. A totally symmetric and multiplicative determinant is then derived from the system which extends the Cayley hyperdeterminant to these higher dimensions. The determinant is related to the zero divisors of the system of hypercomplex numbers. Properties of the determinant are then discussed.
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Кalinovskiy, Ya А., and Yu E. Boiarinova. "Method for Representing an Exponent in a Fifth-dimensional Hypercomplex Number Systems Using a Hypercomplex Computing Software." Èlektronnoe modelirovanie 43, no. 6 (December 6, 2021): 3–18. http://dx.doi.org/10.15407/emodel.43.06.003.
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The structure of method for constructing a representation of an exponential function in hypercomplex number systems (HNS) by the method of solving an associated system of linear differential equations is considered. Brief information about the hypercomplex computing software (HCS) is given. With the use of HCS, the necessary cumbersome operations on symbolic expressions were performed when constructing the representation of the exponent in the fifthdimensional HNS. Fragments of programs in the environment of HCS and results of symbolic calculations are resulted.
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BERKOVICH, Y., and A. SHENKMAN. "HYPERNION NUMBERS AND THEIR USE IN THE ANALYSIS OF NETWORKS DRIVEN BY NONSINUSOIDAL SOURCES." Journal of Circuits, Systems and Computers 13, no. 01 (February 2004): 65–76. http://dx.doi.org/10.1142/s0218126604001192.
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A method of using hypercomplex numbers for the analysis of linear electric circuits with nonsinusoidal voltages and currents has been proposed. Similar to the complex number method for circuits with sinusoidal voltages and currents, the proposed method reduces the analysis of nonsinusoidal circuits to the analysis of direct-current circuits. A special system of hypercomplex numbers, called hypernions, has been created in order to obtain a new efficient method for analyzing nonsinusoidal networks. This system is interesting in that it expands the concept of numbers and attaches meaning to equations and transformations involving discontinuous functions and makes it possible to describe various non-Euclidean spaces. It is shown that the proposed method of analysis of linear nonsinusoidal electric networks makes it possible to carry out numerical calculations for complex circuits by using standard software.
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Hauser, Jochem, and Walter Dröscher. "Gravity beyond Einstein? Part III: numbers and coupling constants, contradictory experiments, hypercomplex gravity like-fields, propellantless space propulsion." Zeitschrift für Naturforschung A 77, no. 1 (November 4, 2021): 13–86. http://dx.doi.org/10.1515/zna-2021-0147.
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Abstract This article, the last in a series of three articles, attempts to unravel the underlying physics of recent experiments regarding the contradictory properties of the neutron lifetime that has been a complete riddle for quite some time. So far, none of the advanced theories beyond the Standard Models (SMs) of particle physics and cosmology have shown sufficient potential to resolve this mystery. We also try to explain the blatant contradiction between the predictions of particle physics and experiments concerning the nature and properties of the (so far undetected) dark matter and dark energy particles. To this end the novel concepts of both negative and hypercomplex matter (giving rise to the concept of matter flavor) are introduced, replacing the field of real numbers by hypercomplex numbers. This extension of the number system in physics leads to both novel internal symmetries requiring new elementary particles – as outlined in Part I and II, and to novel types of matter. Hypercomplex numbers are employed in place of the widely accepted (but never observed) concept of extra space dimensions – and, hence, also to question the corresponding concept of supersymmetry. To corroborate this claim, we report on the latest experimental searches for novel and supersymmetric elementary particles by direct searches at the Large Hadron Collider (LHC) and other colliders as well as numerous other dedicated experiments that all have come up empty handed. The same holds true for the dark matter search at European Council for Nuclear Research (CERN) [CERN Courier Team, “Funky physics at KIT,” in CERN Courier, 2020, p. 11]. In addition, new experiments looking for dark or hidden photons (e.g., FUNK at Karlsruhe Institute of Technology, CAST at CERN, and ALPS at Desy, Hamburg) are discussed that all produced negative results for the existence of the hitherto unseen but nevertheless gravitationally noticeably dark matter. In view of this contradicting outcome, we suggest a four-dimensional Minkowski spacetime, assumed to be a quasi de Sitter space, dS 1,3, complemented by a dual spacetime, denoted by DdS 1,3, in which the dark matter particles that are supposed to be of negative mass reside. This space is endowed with an imaginary time coordinate, −it and an imaginary speed of light, ic. This means that time is considered a complex quantity, but energy m(ic)2 > 0. With this construction visible and dark matter both represent positive energies, and hence gravitation makes no distinction between these two types of matter. As dark matter is supposed to reside in dual space DdS 1,3, it is principally undetectable in our spacetime. That this is evident has been confirmed by numerous astrophysical observations. As the concept of matter flavor may possibly resolve the contradictory experimental results concerning the lifetime of the neutron [J. T. Wilson, “Space based measurement of the neutron lifetime using data from the neutron spectrometer on NASA’s messenger mission,” Phys. Rev. Res., vol. 2, p. 023216, 2020] this fact could be considered as a first experimental hint for the actual existence of hypercomplex matter. In canonical gravity the conversion of electromagnetic into gravity-like fields (as surmised by Faraday and Einstein) should be possible, but not in cosmological gravity (hence these attempts did not succeed), and thus these conversion fields are outside general relativity. In addition, the concept of hypercomplex mass in conjunction with magnetic monopoles emerging from spin ice materials is discussed that may provide the enabling technology for long sought propellantless space propulsion.
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Et. al., Dr Indrajit Patra ,. "Shifts in the Foundation: The Continual Modification and Generalization of Axioms and the Search for the Mathematical Principles that Underlie our Reality." Turkish Journal of Computer and Mathematics Education (TURCOMAT) 12, no. 2 (April 11, 2021): 1095–106. http://dx.doi.org/10.17762/turcomat.v12i2.1126.
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The study shall seek to explore the deep, underlying correspondence between the mathematical world of pure numbers and our physical reality. The study begins by pointing out that while the familiar, one-dimensional real numbers quantify many aspects of our day-to-day reality, complex numbers provide the mathematical foundations of quantum mechanics and also describe the behavior of more complicated quantum networks and multi-party correlations, and quaternions underlie Einsteinian special theory of relativity, and then poses the question whether the octonions could play a similar role in constructing a grander theory of our universe. The study then points out that by increasing the level of abstraction and generalization of axiomatic assumptions, we could construct a more powerful number system based on octonions, the seditions, or even other hypercomplex numbers so that we may more accurately describe the universe in its totality.
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Cerpa, Waldo, Elena Latorre-Esteves, and Andres Barria. "RoR2 functions as a noncanonical Wnt receptor that regulates NMDAR-mediated synaptic transmission." Proceedings of the National Academy of Sciences 112, no. 15 (March 30, 2015): 4797–802. http://dx.doi.org/10.1073/pnas.1417053112.
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Wnt signaling has a well-established role as a regulator of nervous system development, but its role in the maintenance and regulation of established synapses in the mature brain remains poorly understood. At excitatory glutamatergic synapses, NMDA receptors (NMDARs) have a fundamental role in synaptogenesis, synaptic plasticity, and learning and memory; however, it is not known what controls their number and subunit composition. Here we show that the receptor tyrosine kinase-like orphan receptor 2 (RoR2) functions as a Wnt receptor required to maintain basal NMDAR-mediated synaptic transmission. In addition, RoR2 activation by a noncanonical Wnt ligand activates PKC and JNK and acutely enhances NMDAR synaptic responses. Regulation of a key component of glutamatergic synapses through RoR2 provides a mechanism for Wnt signaling to modulate synaptic transmission, synaptic plasticity, and brain function acutely beyond embryonic development.
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Ibrayev, А. Т. "METHOD FOR CONSTRUCTING THE COMMUTATIVE ALGEBRA OF QUATERNION AND OCTONION." PHYSICO-MATHEMATICAL SERIES 6, no. 334 (December 15, 2020): 5–12. http://dx.doi.org/10.32014/2020.2518-1726.91.
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In this paper, we solve the problem of constructing a commutative algebra of quaternions and octonions. A proof of the theorem is given that the commutativity of quaternions can be ensured by specifying a set of sign coefficients of the directions of reference of the angles between the radius vectors in the coordinate planes of the vector part of the coordinate system of the quaternion space. The method proposed in the development of quaternions possessing the commutative properties of multiplication is used further to construct a commutative octonion algebra. The results obtained on improving the algebra of quaternions and octonions can be used in the development of new hypercomplex numbers with division over the field of real numbers, and can also find application for solving a number of scientific and technical problems in the areas of field theory, physical electronics, robotics, and digital processing of multidimensional signals.
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Gu, Ying-Qiu. "A Note on the Representation of Clifford Algebras." Journal of Geometry and Symmetry in Physics 62 (2021): 29–52. http://dx.doi.org/10.7546/jgsp-62-2021-29-52.
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In this note we construct explicit complex and real faithful matrix representations of the Clifford algebras $\Cl_{p,q}$. The representation is based on Pauli matrices and has an elegant structure similar to the fractal geometry. In the cases $p+q=4m$, the representation is unique in equivalent sense, and the $1+3$ dimensional space-time corresponds to the simplest and best case. Besides, the relation between the curvilinear coordinate frame and the local orthonormal basis in the curved space-time is discussed in detail, the covariant derivatives of the spinor and tensors are derived, and the connection of the orthogonal basis in tangent space is calculated. These results are helpful for both theoretical analysis and practical calculation. The basis matrices are the faithful representation of Clifford algebras in any $p+q$ dimensional Minkowski space-time or Riemann space, and the Clifford calculus converts the complicated relations in geometry and physics into simple and concise algebraic operations. Clifford numbers over any number field $\mathbb{F}$ expressed by this matrix basis form a well-defined $2^n$ dimensional hypercomplex number system. Therefore, we can expect that Clifford algebras will complete a large synthesis in science.
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Duplij, Steven. "Formulation of singular theories in a partial Hamiltonian formalism using a new bracket and multi-time dynamics." International Journal of Geometric Methods in Modern Physics 12, no. 01 (December 28, 2014): 1550001. http://dx.doi.org/10.1142/s0219887815500012.
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A formulation of singular classical theories (determined by degenerate Lagrangians) without constraints is presented. A partial Hamiltonian formalism in the phase space having an initially arbitrary number of momenta (which can be smaller than the number of velocities) is proposed. The equations of motion become first-order differential equations, and they coincide with those of multi-time dynamics, if a certain condition is imposed. In a singular theory, this condition is fulfilled in the case of the coincidence of the number of generalized momenta with the rank of the Hessian matrix. The noncanonical generalized velocities satisfy a system of linear algebraic equations, which allows an appropriate classification of singular theories (gauge and nongauge). A new antisymmetric bracket (similar to the Poisson bracket) is introduced, which describes the time evolution of physical quantities in a singular theory. The origin of constraints is shown to be a consequence of the (unneeded in our formulation) extension of the phase space, when the new bracket transforms into the Dirac bracket. Quantization is briefly discussed.
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Ivanova, Daniela, Katharine L. Dobson, Akshada Gajbhiye, Elizabeth C. Davenport, Daniela Hacker, Sila K. Ultanir, Matthias Trost, and Michael A. Cousin. "Control of synaptic vesicle release probability via VAMP4 targeting to endolysosomes." Science Advances 7, no. 18 (April 2021): eabf3873. http://dx.doi.org/10.1126/sciadv.abf3873.
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Synaptic vesicle (SV) release probability (Pr), determines the steady state and plastic control of neurotransmitter release. However, how diversity in SV composition arises and regulates the Pr of individual SVs is not understood. We found that modulation of the copy number of the noncanonical vesicular SNARE (soluble N-ethylmaleimide–sensitive factor attachment protein receptor), vesicle-associated membrane protein 4 (VAMP4), on SVs is key for regulating Pr. Mechanistically, this is underpinned by its reduced ability to form an efficient SNARE complex with canonical plasma membrane SNAREs. VAMP4 has unusually high synaptic turnover and is selectively sorted to endolysosomes during activity-dependent bulk endocytosis. Disruption of endolysosomal trafficking and function markedly increased the abundance of VAMP4 in the SV pool and inhibited SV fusion. Together, our results unravel a new mechanism for generating SV heterogeneity and control of Pr through coupling of SV recycling to a major clearing system that regulates protein homeostasis.
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Deng, Di, Xiaoqing Qian, Binjun Chen, Xiaoyu Yang, Yanmei Wang, Fanglu Chi, Yibo Huang, Yu Zhao, and Dongdong Ren. "Canonical Wnt Signaling Pathway on Polarity Formation of Utricle Hair Cells." Neural Plasticity 2021 (May 22, 2021): 1–11. http://dx.doi.org/10.1155/2021/9950533.
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As part of the inner ear, the vestibular system is responsible for sense of balance, which consists of three semicircular canals, the utricle, and the saccule. Increasing evidence has indicated that the noncanonical Wnt/PCP signaling pathway plays a significant role in the development of the polarity of the inner ear. However, the role of canonical Wnt signaling in the polarity of the vestibule is still not completely clear. In this study, we found that canonical Wnt pathway-related genes are expressed in the early stage of development of the utricle and change dynamically. We conditionally knocked out β-catenin, a canonical Wnt signaling core protein, and found that the cilia orientation of hair cells was disordered with reduced number of hair cells in the utricle. Moreover, regulating the canonical Wnt pathway (Licl and IWP2) in vitro also affected hair cell polarity and indicated that Axin2 may be important in this process. In conclusion, our results not only confirm that the regulation of canonical Wnt signaling affects the number of hair cells in the utricle but also provide evidence for its role in polarity development.
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Sullivan, Chelsea S., Jami L. Scheib, Zhong Ma, Rajan P. Dang, Johanna M. Schafer, Francis E. Hickman, Frances M. Brodsky, Kodi S. Ravichandran, and Bruce D. Carter. "The adaptor protein GULP promotes Jedi-1–mediated phagocytosis through a clathrin-dependent mechanism." Molecular Biology of the Cell 25, no. 12 (June 15, 2014): 1925–36. http://dx.doi.org/10.1091/mbc.e13-11-0658.
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During the development of the peripheral nervous system, the large number of apoptotic neurons generated are phagocytosed by glial precursor cells. This clearance is mediated, in part, through the mammalian engulfment receptor Jedi-1. However, the mechanisms by which Jedi-1 mediates phagocytosis are poorly understood. Here we demonstrate that Jedi-1 associates with GULP, the mammalian homologue of CED-6, an adaptor protein required for phagocytosis mediated by the nematode engulfment receptor CED-1. Silencing GULP or mutating the NPXY motif in Jedi-1, which is required for GULP binding, prevents Jedi-1–mediated phagocytosis. How GULP promotes engulfment is not known. Of interest, we find that Jedi-1–induced phagocytosis requires GULP binding to clathrin heavy chain (CHC). During engulfment, CHC is tyrosine phosphorylated, which is required for Jedi-mediated engulfment. Both phosphoclathrin and actin accumulate around engulfed microspheres. Furthermore, knockdown of CHC in HeLa cells prevents Jedi-1–mediated engulfment of microspheres, and knockdown in glial precursors prevents the engulfment of apoptotic neurons. Taken together, these results reveal that Jedi-1 signals through recruitment of GULP, which promotes phagocytosis through a noncanonical phosphoclathrin-dependent mechanism.
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Hirota, Simon A., Aito Ueno, Sarah E. Tulk, Helen M. Becker, L. Patrick Schenck, Mireille S. Potentier, Yan Li, et al. "Exaggerated IL-15 and Altered Expression of foxp3+ Cell-Derived Cytokines Contribute to Enhanced Colitis in Nlrp3−/− Mice." Mediators of Inflammation 2016 (2016): 1–12. http://dx.doi.org/10.1155/2016/5637685.
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The pathogenesis of Crohn’s disease (CD) involves defects in the innate immune system, impairing responses to microbes. Studies have revealed that mutations NLRP3 are associated with CD. We reported previously that Nlrp3−/− mice were more susceptible to colitis and exhibited reduced colonic IL-10 expression. In the current study, we sought to determine how the loss of NLRP3 might be altering the function of regulatory T cells, a major source of IL-10. Colitis was induced in wild-type (WT) and Nlrp3−/− mice by treatment with dextran sulphate sodium (DSS). Lamina propria (LP) cells were assessed by flow cytometry and cytokine expression was assessed. DSS-treated Nlrp3−/− mice exhibited increased numbers of colonic foxp3+ T cells that expressed significantly lower levels of IL-10 but increased IL-17. This was associated with increased expression of colonic IL-15 and increased surface expression of IL-15 on LP dendritic cells. Neutralizing IL-15 in Nlrp3−/− mice attenuated the severity of colitis, decreased the number of colonic foxp3+ cells, and reduced the colonic expression of IL-12p40 and IL-17. These data suggest that the NLRP3 inflammasome can regulate intestinal inflammation through noncanonical mechanisms, providing additional insight as to how NLRP3 variants may contribute to the pathogenesis of CD.
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Cheng, Jing, Peter C. Lucas, and Linda M. McAllister-Lucas. "Canonical and Non-Canonical Roles of GRK2 in Lymphocytes." Cells 10, no. 2 (February 3, 2021): 307. http://dx.doi.org/10.3390/cells10020307.
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G protein-coupled receptor kinase 2 (GRK2) is emerging as a key integrative signaling node in a variety of biological processes ranging from cell growth and proliferation to migration and chemotaxis. As such, GRK2 is now implicated as playing a role in the molecular pathogenesis of a broad group of diseases including heart failure, cancer, depression, neurodegenerative disease, and others. In addition to its long-known canonical role in the phosphorylation and desensitization of G protein-coupled receptors (GPCRs), recent studies have shown that GRK2 also modulates a diverse array of other molecular processes via newly identified GRK2 kinase substrates and via a growing number of protein-protein interaction binding partners. GRK2 belongs to the 7-member GRK family. It is a multidomain protein containing a specific N-terminal region (referred to as αN), followed by a regulator of G protein signaling homology (RH) domain, an AGC (Protein kinase A, G, C serine/threonine kinase family) kinase domain, and a C-terminal pleckstrin homology (PH) domain. GPCRs mediate the activity of many regulators of the immune system such as chemokines and leukotrienes, and thus GRK proteins may play key roles in modulating the lymphocyte response to these factors. As one of the predominant GRK family members expressed in immune cells, GRK2′s canonical and noncanonical actions play an especially significant role in normal immune cell function as well as in the development and progression of disorders of the immune system. This review summarizes our current state of knowledge of the roles of GRK2 in lymphocytes. We highlight the diverse functions of GRK2 and discuss how ongoing investigation of GRK2 in lymphocytes may inform the development of new therapies for diseases associated with lymphocyte dysregulation.
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Perruccio, Katia, Loredana Ruggeri, Silvia Moretti, Fabiana Topini, Antonella Tosti, Alessandra Carotti, Franco Aversa, et al. "Thymosin Alfa 1 Administration Improves Immune Reconstitution and Decreases Infection-Related Mortality After HLA-Matched Sibling T Cell-Depleted Stem Cell Transplantation." Blood 118, no. 21 (November 18, 2011): 1013. http://dx.doi.org/10.1182/blood.v118.21.1013.1013.
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Abstract Abstract 1013 Dendritic cells (DCs) play a pivotal role in initiating and modulating immune responses to pathogens. Data from experimental allogeneic bone marrow transplantation showed impaired DC function post-transplant as DCs produced mostly TNF-alfa with low amounts of IL-10, IL-12 and IFN-alpha, did not express co-stimulatory molecules upon activation with fungal antigens and were unable to phagocytose fungi. In vitro and in vivo data demonstrated Thymosin alpha 1 (T alpha 1), a naturally occurring peptide, induced DC activation, maturation and differentiation. T alpha 1 stimulated phagocytosis and functional maturation of murine pulmonary DCs upon exposure to Aspergillus conidia, accelerated lymphoid cell recovery and activated protective Th1-dependent resistance to infection. In a murine model of allogeneic bone marrow transplantation with lethal pneumonia caused by an A. fumigatus challenge, T alpha 1 promoted balanced Th1/Treg immunity and protected mice from invasive aspergillosis [1, 2]. The activation of innate immune system by T alpha 1 was mediated by distinct Toll-Like Receptor (TLR) signalling culminating in the activation of the p38 MAPK/NF-kB pathway. More recently, transcription profile of DCs exposed to T alpha 1 revealed a number of genes modulated by T alpha 1, including those involved in the regulation of the canonical/noncanonical NF-kB pathway in response to cellular stress and homeostasis. Accordingly, we designed a phase I/II clinical trial to determine the safety and efficacy of T alpha 1 administration in 30 recipients (12/30 with active disease at transplant) of HLA-matched sibling T cell-depleted stem cell transplants. Patients aged 20–69 years (median 46) with AML/MDS (12), ALL (6), lymphoma (7), MM (4), CLL (1) were conditioned with TBI or Melphalan, Thiothepa, and Fludarabine and given T alpha 1 (1.6 mg/day subcutaneously) from the day of transplant onwards for 16 weeks. Forty-five patients (25/45 with active disease at transplant), who were transplanted under the same protocol, served as controls. They were aged 20–67 years (median 53) with AML/MDS (20), ALL (4), lymphoma (11), MM (6), CLL (3), myelofibrosis (1). During and after T alfa 1 administration no adverse effects whatsoever were observed. Immune reconstitution was assessed by limiting dilution analyses of frequencies of CD4+ T cells that were specific for Aspergillus, Candida, CMV, Adenovirus, Herpes Simplex Virus, Varicella- Zoster Virus, Toxoplasma antigens. Normal donor values ranged from 600 to 1200/10e6 plated cells. Control transplant recipients acquired such pathogen-specific T cell responses from month 3 onwards in frequencies that ranged from 50 to 250/10e6 plated cells. In patients who received T alfa 1, pathogen-specific T cells appeared as early as 1 month after transplant in significantly higher frequencies which soon ranged from 250 to 500/10e6 plated cells. The cumulative incidence of non-relapse mortality (NRM) (mainly infection-related) was 33% in controls vs 7% in Thymosin-treated patients (p = 0.02). Thymosin administration did not impact upon the relapse rate (which was around 50% in both series). As a consequence of the improved TRM, Event-Free Survival was better in Thymosin treated patients (42% vs 20% in controls; p = 0.02). Multivariate analyses including diagnoses, disease status at transplant, conditioning regimen and donor lymphocyte infusions (during and after Thymosin administration) showed Thymosin treatment was a significant independent factor predicting a lower incidence of NRM (p=0.04) which tended to provide better survival (p = 0.09). In conclusion, this study shows that T alfa 1, a naturally occurring peptide of thymic origin which optimizes antigen presentation and T cell responses, could safely be administered after matched sibling T cell depleted hematopoietic transplants. T alfa 1appeared to protect from largely infectious NRM and to improve the survival of transplant recipients. It is worth noting that T cell depletion of the graft and the consequent lack of post-transplant pharmacological immune suppression may have facilitated the peptide's immune regulatory action. Disclosures: Off Label Use: Thymosin alfa 1 is a naturally occurring peptide of thymic origin that is reported to optimize antigen presentation and T cell responses.
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Szynal-Liana, Anetta, and Iwona Włoch. "Generalized commutative quaternions of the Fibonacci type." Boletín de la Sociedad Matemática Mexicana 28, no. 1 (November 17, 2021). http://dx.doi.org/10.1007/s40590-021-00386-4.
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AbstractQuaternions are a four-dimensional hypercomplex number system discovered by Hamilton in 1843 and next intensively applied in mathematics, modern physics, computer graphics and other fields. After the discovery of quaternions, modified quaternions were also defined in such a way that commutative property in multiplication is possible. That number system called as commutative quaternions is intensively studied and used for example in signal processing. In this paper we define generalized commutative quaternions and next based on them we define and explore Fibonacci type generalized commutative quaternions.
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Kobayashi, Masaki. "Stability Conditions of Bicomplex-Valued Hopfield Neural Networks." Neural Computation, January 5, 2021, 1–11. http://dx.doi.org/10.1162/neco_a_01350.
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Hopfield neural networks have been extended using hypercomplex numbers. The algebra of bicomplex numbers, also referred to as commutative quaternions, is a number system of dimension 4. Since the multiplication is commutative, many notions and theories of linear algebra, such as determinant, are available, unlike quaternions. A bicomplex-valued Hopfield neural network (BHNN) has been proposed as a multistate neural associative memory. However, the stability conditions have been insufficient for the projection rule. In this work, the stability conditions are extended and applied to improvement of the projection rule. The computer simulations suggest improved noise tolerance.
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López, Juan. "Lagrangian relative equilibria for a gyrostat in the three-body problem." Open Physics 7, no. 4 (January 1, 2009). http://dx.doi.org/10.2478/s11534-009-0040-x.
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AbstractIn this paper we consider the noncanonical Hamiltonian dynamics of a gyrostat in the three-body problem. By means of geometric mechanics methods, we study the approximate Poisson dynamics that arise when we develop the potential of the system in Legendre series and truncate this to an arbitrary order k. After reduction of the dynamics by means of the two symmetries of the system, we consider the existence and number of equilibria which we denominate of Lagrangian type, in analogy with classic results on the topic. Necessary and sufficient conditions are established for their existence in an approximate dynamics of order k, and explicit expressions for these equilibria are given, this being useful for the subsequent study of their stability. The number of Lagrangian equilibria is thoroughly studied in approximate dynamics of orders zero and one. The main result of this work indicates that the number of Lagrangian equilibria in an approximate dynamics of order k for k ≥1 is independent of the order of truncation of the potential, if the gyrostat S 0 is almost spherical. In relation to the stability of these equilibria, necessary and sufficient conditions are given for linear stability of Lagrangian equilibria when the gyrostat is almost spherical. In this way, we generalize the classical results on equilibria of the three-body problem and many results provided by other authors using more classical techniques for the case of rigid bodies.
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Kitazawa, Yugo, Nozomu Iwabuchi, Kensaku Maejima, Momoka Sasano, Oki Matsumoto, Hiroaki Koinuma, Ryosuke Tokuda, et al. "A phytoplasma effector acts as a ubiquitin-like mediator between floral MADS-box proteins and proteasome shuttle proteins." Plant Cell, March 2, 2022. http://dx.doi.org/10.1093/plcell/koac062.
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Abstract Plant pathogenic bacteria have developed effectors to manipulate host cell functions to facilitate infection. A certain number of effectors use the conserved ubiquitin–proteasome system in eukaryotic to proteolyze targets. The proteasome utilization mechanism is mainly mediated by ubiquitin interaction with target proteins destined for degradation. Phyllogens are a family of protein effectors produced by pathogenic phytoplasmas that transform flowers into leaves in diverse plants. Here, we present a noncanonical mechanism for phyllogen action that involves the proteasome and is ubiquitin-independent. Phyllogens induce proteasomal degradation of floral MADS-box transcription factors (MTFs) in the presence of RADIATION-SENSITIVE23 (RAD23) shuttle proteins, which recruit ubiquitinated proteins to the proteasome. Intracellular localization analysis revealed that phyllogen induced colocalization of MTF with RAD23. The MTF/phyllogen/RAD23 ternary protein complex was detected not only in planta but also in vitro in the absence of ubiquitin, showing that phyllogen directly mediates interaction between MTF and RAD23. A Lys-less nonubiquitinated phyllogen mutant induced degradation of MTF or a Lys-less mutant of MTF. Furthermore, the method of sequential formation of the MTF/phyllogen/RAD23 protein complex was elucidated, first by MTF/phyllogen interaction and then RAD23 recruitment. Phyllogen recognized both the evolutionarily conserved tetramerization region of MTF and the ubiquitin-associated domain of RAD23. Our findings indicate that phyllogen functionally mimics ubiquitin as a mediator between MTF and RAD23.
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Song, Ren, Orkide O. Koyuncu, Todd M. Greco, Benjamin A. Diner, Ileana M. Cristea, and Lynn W. Enquist. "Two Modes of the Axonal Interferon Response Limit Alphaherpesvirus Neuroinvasion." mBio 7, no. 1 (February 2, 2016). http://dx.doi.org/10.1128/mbio.02145-15.
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ABSTRACT Infection by alphaherpesviruses, including herpes simplex virus (HSV) and pseudorabies virus (PRV), typically begins at epithelial surfaces and continues into the peripheral nervous system (PNS). Inflammatory responses are induced at the infected peripheral site prior to invasion of the PNS. When the peripheral tissue is first infected, only the innervating axons are exposed to this inflammatory milieu, which includes the interferons (IFNs). The fundamental question is how do PNS cell bodies respond to these distant, potentially damaging events experienced by axons. Using compartmented cultures that physically separate neuron axons from cell bodies, we found that pretreating isolated axons with beta interferon (IFN-β) or gamma interferon (IFN-γ) significantly diminished the number of herpes simplex virus 1 (HSV-1) and PRV particles moving in axons toward the cell bodies in a receptor-dependent manner. Exposing axons to IFN-β induced STAT1 phosphorylation (p-STAT1) only in axons, while exposure of axons to IFN-γ induced p-STAT1 accumulation in distant cell body nuclei. Blocking transcription in cell bodies eliminated antiviral effects induced by IFN-γ, but not those induced by IFN-β. Proteomic analysis of IFN-β- or IFN-γ-treated axons identified several differentially regulated proteins. Therefore, unlike treatment with IFN-γ, IFN-β induces a noncanonical, local antiviral response in axons. The activation of a local IFN response in axons represents a new paradigm for cytokine control of neuroinvasion. IMPORTANCE Neurons are highly polarized cells with long axonal processes that connect to distant targets. PNS axons that innervate peripheral tissues are exposed to various situations that follow infection, inflammation, and damage of the tissue. After viral infection in the periphery, axons represent potential front-line barriers to PNS infection and damage. Indeed, most viral infections do not spread to the PNS, yet the mechanisms responsible are not well studied. We devised an experimental system to study how axons respond to inflammatory cytokines that would be produced by infected tissues. We found that axons respond differentially to type I and type II interferons. The response to type I interferon (IFN-β) is a rapid axon-only response. The response to type II interferon (IFN-γ) involves long-distance signaling to the PNS cell body. These responses to two interferons erect an efficient and rapid barrier to PNS infection.