Tosio Kato (1917–1999)

Tosio Kato was born August 25, 1917, in Kanuma City, Tochigi-ken, Japan. His early training was in physics. He obtained a B.S. in 1941 and the degree of Doctor of Science in 1951, both at the University of Tokyo. Between these events he published papers on a variety of subjects, including pair creation by gamma rays, motion of an object in a fluid, and results on spectral theory of operators arising in quantum mechanics. His dissertation was entitled “On the convergence of the perturbation method”. Kato was appointed assistant professor of physics at the University of Tokyo in 1951 and was promoted to professor of physics in 1958. During this time he visited the University of California at Berkeley in 1954–55, New York University in 1955, the National Bureau of Standards in 1955–56, and Berkeley and the California Institute of Technology in 1957–58. He was appointed professor of mathematics at Berkeley in 1962 and taught there until his retirement in 1988. He supervised twenty-one Ph.D. students at Berkeley and three at the University of Tokyo. Kato published over 160 papers and 6 monographs, including his famous book Perturbation Theory for Linear Operators [K66b]. Recognition for his important work included the Norbert Wiener Prize in Applied Mathematics, awarded in 1980 by the AMS and the Society for Industrial and Applied Mathematics. He was particularly well known for his work on Schrödinger equations of nonrelativistic quantum mechanics and his work on the Navier-Stokes and Euler equations of classical fluid mechanics. His activity in the latter area remained at a high level well past retirement and continued until his death on October 2, 1999

Eigenvalue Bounds for Perturbations of Schrodinger Operators and Jacobi Matrices With Regular Ground States

We prove general comparison theorems for eigenvalues of perturbed Schrodinger operators that allow proof of Lieb--Thirring bounds for suitable non-free Schrodinger operators and Jacobi matrices.Comment: 11 page

Modulation of FAK and Src adhesion signaling occurs independently of adhesion complex composition

Integrin adhesion complexes (IACs) form mechanochemical connections between the extracellular matrix and actin cytoskeleton and mediate phenotypic responses via posttranslational modifications. Here, we investigate the modularity and robustness of the IAC network to pharmacological perturbation of the key IAC signaling components focal adhesion kinase (FAK) and Src. FAK inhibition using AZ13256675 blocked FAK(Y397) phosphorylation but did not alter IAC composition, as reported by mass spectrometry. IAC composition was also insensitive to Src inhibition using AZD0530 alone or in combination with FAK inhibition. In contrast, kinase inhibition substantially reduced phosphorylation within IACs, cell migration and proliferation. Furthermore using fluorescence recovery after photobleaching, we found that FAK inhibition increased the exchange rate of a phosphotyrosine (pY) reporter (dSH2) at IACs. These data demonstrate that kinase-dependent signal propagation through IACs is independent of gross changes in IAC composition. Together, these findings demonstrate a general separation between the composition of IACs and their ability to relay pY-dependent signals

Deconstructing pancreatic cancer using next generation-omic technologies–from discovery to knowledge-guided platforms for better patient management

Comprehensive molecular landscaping studies reveal a potentially brighter future for pancreatic ductal adenocarcinoma (PDAC) patients. Blood-borne biomarkers obtained from minimally invasive “liquid biopsies” are now being trialled for early disease detection and to track responses to therapy. Integrated genomic and transcriptomic studies using resectable tumour material have defined intrinsic patient subtypes and actionable genomic segments that promise a shift towards genome-guided patient management. Multimodal mapping of PDAC using spatially resolved single cell transcriptomics and imaging techniques has identified new potentially therapeutically actionable cellular targets and is providing new insights into PDAC tumour heterogeneity. Despite these rapid advances, defining biomarkers for patient selection remain limited. This review examines the current PDAC cancer biomarker ecosystem (identified in tumour and blood) and explores how advances in single cell sequencing and spatially resolved imaging modalities are being used to uncover new targets for therapeutic intervention and are transforming our understanding of this difficult to treat disease

Generalized iterated wreath products of symmetric groups and generalized rooted trees correspondence

Consider the generalized iterated wreath product $S_{r_1}\wr \ldots \wr S_{r_k}$ of symmetric groups. We give a complete description of the traversal for the generalized iterated wreath product. We also prove an existence of a bijection between the equivalence classes of ordinary irreducible representations of the generalized iterated wreath product and orbits of labels on certain rooted trees. We find a recursion for the number of these labels and the degrees of irreducible representations of the generalized iterated wreath product. Finally, we give rough upper bound estimates for fast Fourier transforms.Comment: 18 pages, to appear in Advances in the Mathematical Sciences. arXiv admin note: text overlap with arXiv:1409.060

mTORC2 signaling drives the development and progression of pancreatic cancer

mTOR signaling controls several critical cellular functions and is deregulated in many cancers, including pancreatic cancer. To date, most efforts have focused on inhibiting the mTORC1 complex. However, clinical trials of mTORC1 inhibitors in pancreatic cancer have failed, raising questions about this therapeutic approach. We employed a genetic approach to delete the obligate mTORC2 subunit Rictor and identified the critical times during which tumorigenesis requires mTORC2 signaling. Rictor deletion resulted in profoundly delayed tumorigenesis. Whereas previous studies showed most pancreatic tumors were insensitive to rapamycin, treatment with a dual mTORC1/2 inhibitor strongly suppressed tumorigenesis. In late-stage tumor-bearing mice, combined mTORC1/2 and PI3K inhibition significantly increased survival. Thus, targeting mTOR may be a potential therapeutic strategy in pancreatic cancer

Charge Deficiency, Charge Transport and Comparison of Dimensions

We study the relative index of two orthogonal infinite dimensional projections which, in the finite dimensional case, is the difference in their dimensions. We relate the relative index to the Fredholm index of appropriate operators, discuss its basic properties, and obtain various formulas for it. We apply the relative index to counting the change in the number of electrons below the Fermi energy of certain quantum systems and interpret it as the charge deficiency. We study the relation of the charge deficiency with the notion of adiabatic charge transport that arises from the consideration of the adiabatic curvature. It is shown that, under a certain covariance, (homogeneity), condition the two are related. The relative index is related to Bellissard's theory of the Integer Hall effect. For Landau Hamiltonians the relative index is computed explicitly for all Landau levels.Comment: 23 pages, no figure