Pruettha Aruvornlop, Sekkarin Ploypetch, Walasinee Sakcamduang
et al.
Feline mammary carcinoma (FMC) is the most prevalent reproductive tumor in queens and is characterized by aggressive metastatic progression and short survival. Protein phosphorylation is a crucial process in cell regulation, with dysregulation linked to cancer progression, including human breast cancer. Although phosphoproteins have emerged as diagnostic and predictive markers in human breast cancer, knowledge remains limited on their role in FMC. In this study, the phosphoproteomic profiles of specimens for FMC grades 1 (n = 6), grade 2 (n = 11), grade 3 (n = 14), and normal controls (n = 6) were compared by phosphoprotein enrichment coupled with liquid chromatography–tandem mass spectrometry. Seventeen downregulated phosphoproteins were identified across all FMC grades, many of which have established roles in human breast cancer pathogenesis and prognosis. Serine/threonine–protein phosphatase was identified as a potential growth promoter and therapeutic target, while acid phosphatase, prostate, and ribonuclease L were identified as tumor suppressors. Furthermore, the ABC-type glutathione-S-conjugate transporter was associated with multidrug resistance. Protein kinase AMP-activated noncatalytic subunit gamma 3 was associated with increased breast cancer risk. In this study, it was also found to be associated with Ki-67 expression in FMC (p = 0.03). These phosphoproteins interacted with various proteins, immune checkpoint molecules, and chemotherapy drugs associated with mammary cancer in both human and feline species. Furthermore, proteins, such as butyrophilin subfamily 1 member A1, keratin, type I cytoskeletal 10, HECT domain E3 ubiquitin protein ligase 3, nuclear receptor binding SET domain protein 3, and stomatin-like 2, were identified and implicated in cancer progression and prognosis. This study is the first phosphoproteomic investigation of FMC, highlighting the interactions of relevant phosphoproteins with other proteins and chemotherapy drugs associated with both feline and human mammary cancers. The findings provide valuable insights for the identification of diagnostic and prognostic biomarkers and potential therapeutic targets in cats with mammary carcinoma.
A seventh order ordinary differential equation (ODE) arising by reduction of the Drinfeld-Sokolov hierarchyis shown to be identical to a similarity reduction of an equationin the hierarchy of Sawada-Kotera.We also exhibit its link with a particular F-VI,a fourth order ODE isolated by Cosgrove which is likely to define a higher order Painlev\'e function.
Rafael Hernandez Heredero, Decio Levi, Christian Scimiterna
In this article we present the results obtained applying the multiple scale expansion up to the order $\varepsilon^6$ to a dispersive multilinear class of equations on a square lattice depending on 13 parameters. We show that the integrability conditions given by the multiple scale expansion give rise to 4 nonlinear equations, 3 of which seem to be new, depending at most on 2 parameters.
Sirintra Sirivisoot, Naklop Siripara, Nlin Arya
et al.
An 8-month-old, intact male, domestic shorthair cat was referred for a mass on the proximal ventral part of the tail which had been found since the animal was born, and due to the presence of a linear fissure with rows of ectopic teeth, the veterinarian suspected that the mass had recently ruptured. Tail amputation was elected and the entire mass was successfully surgically excised. From the gross examination, this mass had an open cyst-like structure with a prominent area composed of hair, teeth, and bone. Histopathology revealed two components of germinal layers including hair follicles, adnexal tissue, neural tissue, teeth, muscle, fat, bone, and lymphatic vessels. The histopathological diagnosis was consistent to mature teratoma. Although, complete excision could not be definitively confirmed histologically, this kitten is currently well and has not developed any recurrent mass at the surgical site after 2 years of post-operation.
In this paper we study a non-linear partial differential equation (PDE), proposed by N. Kudryashov [arXiv:1611.06813v1[nlin.SI]], using continuum limit approximation of mixed Fermi-Pasta-Ulam and Frenkel-Kontorova Models. This generalized semi-discrete equation can be considered as a model for the description of non-linear dislocation waves in crystal lattice and the corresponding continuous system can be called mixed generalized potential KdV and sine-Gordon equation. We obtain the Bäcklund transformation of this equation in Riccati form in inverse method. We further study the quasi-integrable deformation of this model.
We give a construction of completely integrable ($2n$)-dimensional Hamiltonian systems with symplectic brackets of the Lie-Poisson type (linear in coordinates) and with quadratic Hamilton functions. Applying to any such system the so called Kahan-Hirota-Kimura discretization scheme, we arrive at a birational ($2n$)-dimensional map. We show that this map is symplectic with respect to a symplectic structure that is a perturbation of the original symplectic structure on $\mathbb R^{2n}$, and possesses $n$ independent integrals of motion, which are perturbations of the original Hamilton functions and are in involution with respect to the invariant symplectic structure. Thus, this map is completely integrable in the Liouville-Arnold sense. Moreover, under a suitable normalization of the original $n$-tuples of commuting vector fields, their Kahan-Hirota-Kimura discretizations also commute and share the invariant symplectic structure and the $n$ integrals of motion. This paper extends our previous ones, arXiv:1606.08238 [nlin.SI] and arXiv:1607.07085 [nlin.SI], where similar results were obtained for Hamiltonian systems with a constant (canonical) symplectic structure and cubic Hamilton functions.
H. Baran, I. S. Krasil'shchik, O. I. Morozov
et al.
In our recent paper [H. Baran, I.S. Krasil'shchik, O.I. Morozov, P. Voj{č}{á}k, Symmetry reductions and exact solutions of Lax integrable $3$-dimensional systems, Journal of Nonlinear Mathematical Physics, Vol. 21, No. 4 (December 2014), 643--671; arXiv:1407.0246 [nlin.SI], DOI: 10.1080/14029251.2014.975532}], we gave a complete description of symmetry reduction of four Lax-integrable (i.e., possessing a zero-curvature representation with a non-removable parameter) $3$-dimensional equations. Here we study the behavior of the integrability features of the initial equations under the reduction procedure. We show that the ZCRs are transformed to nonlinear differential coverings of the resulting 2D-systems similar to the one found for the Gibbons-Tsarev equation in [A.V. Odesskii, V.V. Sokolov, Non-homogeneous systems of hydrodynamic type possessing Lax representations, arXiv:1206.5230, 2006]. Using these coverings we construct infinite series of (nonlocal) conservation laws and prove their nontriviality. We also show that the recursion operators are not preserved under reductions.
We present a Lagrangian for the bilinear discrete KP (or Hirota-Miwa) equation. Furthermore, we show that this Lagrangian can be extended to a Lagrangian 3-form when embedded in a higher dimensional lattice, obeying a closure relation. Thus we establish the multiform structure as proposed in arXiv:0903.4086v1 [nlin.SI] in a higher dimensional case.
In Part I [arXiv:0902.4873 [nlin.SI]] soliton solutions to the ABS list of multi-dimensionally consistent difference equations (except Q4) were derived using connection between the Q3 equation and the NQC equations, and then by reductions. In that work central role was played by a Cauchy matrix. In this work we use a different approach, we derive the $N$-soliton solutions following Hirota's direct and constructive method. This leads to Casoratians and bilinear difference equations. We give here details for the H-series of equations and for Q1; the results for Q3 have been given earlier.
The lattice Gel'fand-Dikii hierarchy was introduced by Nijhoff, Papageorgiou, Capel and Quispel in 1992 as the family of partial difference equations generalizing to higher rank the lattice Korteweg-de Vries systems, and includes in particular the lattice Boussinesq system. We present a Lagrangian for the generic member of the lattice Gel'fand-Dikii hierarchy, and show that it can be considered as a Lagrangian 2-form when embedded in a higher dimensional lattice, obeying a closure relation. Thus the multiform structure proposed in arXiv:0903.4086v2 [nlin.SI] is extended to a multi-component system.
We develop a pseudo-differential approach to the N=2 supersymmetric unconstrained matrix (k|n,m)-Generalized Nonlinear Schroedinger hierarchies and prove consistency of the corresponding Lax-pair representation (nlin.SI/0201026). Furthermore, we establish their equivalence to the integrable hierarchies derived in the super-algebraic approach of the homogeneously-graded loop superalgebra sl(2k+n|2k+m)\otimes C[{lambda},{lambda}^{-1}] (nlin.SI/0206037). We introduce an unconventional definition of N=2 supersymmetric strictly pseudo-differential operators so as to close their algebra among themselves.
AbstractThe use of Nepomnjaščiǐ's Theorem in the proofs of independence results for bounded arithmetic theories is investigated. Using this result and similar ideas, it is shown that at least one ofS1orTLSdoes not prove the Matiyasevich-Robinson-Davis-Putnam Theorem. It is also established thatTLSdoes not prove a statement that roughly means nondeterministic linear time is equal to co-nondeterministic linear time. HereS1is a conservative extension of the well-studied theoryIΔ0andTLSis a theory for LOGSPACE reasoning.