Kleshchev's decomposition numbers and branching coefficients in the Fock space

10.1090/S0002-9947-07-04202-XTransactions of the American Mathematical Society36031179-119

Regulatory T cells in melanoma revisited by a computational clustering of FOXP3+ T cell subpopulations

CD4+ T cells that express the transcription factor FOXP3 (FOXP3+ T cells) are commonly regarded as immunosuppressive regulatory T cells (Treg). FOXP3+ T cells are reported to be increased in tumour-bearing patients or animals, and considered to suppress anti-tumour immunity, but the evidence is often contradictory. In addition, accumulating evidence indicates that FOXP3 is induced by antigenic stimulation, and that some non-Treg FOXP3+ T cells, especially memory-phenotype FOXP3low cells, produce proinflammatory cytokines. Accordingly, the subclassification of FOXP3+ T cells is fundamental for revealing the significance of FOXP3+ T cells in tumour immunity, but the arbitrariness and complexity of manual gating have complicated the issue. Here we report a computational method to automatically identify and classify FOXP3+ T cells into subsets using clustering algorithms. By analysing flow cytometric data of melanoma patients, the proposed method showed that the FOXP3+ subpopulation that had relatively high FOXP3, CD45RO, and CD25 expressions was increased in melanoma patients, whereas manual gating did not produce significant results on the FOXP3+ subpopulations. Interestingly, the computationally-identified FOXP3+ subpopulation included not only classical FOXP3high Treg but also memory-phenotype FOXP3low cells by manual gating. Furthermore, the proposed method successfully analysed an independent dataset, showing that the same FOXP3+ subpopulation was increased in melanoma patients, validating the method. Collectively, the proposed method successfully captured an important feature of melanoma without relying on the existing criteria of FOXP3+ T cells, revealing a hidden association between the T cell profile and melanoma, and providing new insights into FOXP3+ T cells and Treg

Parallelotope tilings and q-decomposition numbers

We provide closed formulas for a large subset of the canonical basis vectors of the Fock space representation of Uq(slₑ). These formulas arise from parallelotopes which assemble to form polytopal complexes. The subgraphs of the Ext¹ -quivers of v-Schur algebras at complex e-th roots of unity generated by simple modules corresponding to these canonical basis vectors are given by the 1-skeletons of the polytopal complexes

A v-analogue of Peel's theorem

We compute the v-decomposition numbers dλμ(v) for λ being a hook partition, and μ e-regular

Orlov's Equivalence and Maximal Cohen-Macaulay Modules over the Cone of an Elliptic Curve

We describe a method for doing computations with Orlov's equivalence between the bounded derived category of certain hypersurfaces and the stable category of graded matrix factorisations of the polynomials describing these hypersurfaces. In the case of a smooth elliptic curve over an algebraically closed field we describe the indecomposable graded matrix factorisations of rank one. Since every indecomposable Maximal Cohen-Macaulay module over the completion of a smooth cubic curve is gradable, we obtain explicit descriptions of all indecomposable rank one matrix factorisations of such potentials. Finally, we explain how to compute all indecomposable matrix factorisations of higher rank with the help of a computer algebra system.Comment: 26 page

Persistent Homology Over Directed Acyclic Graphs

We define persistent homology groups over any set of spaces which have inclusions defined so that the corresponding directed graph between the spaces is acyclic, as well as along any subgraph of this directed graph. This method simultaneously generalizes standard persistent homology, zigzag persistence and multidimensional persistence to arbitrary directed acyclic graphs, and it also allows the study of more general families of topological spaces or point-cloud data. We give an algorithm to compute the persistent homology groups simultaneously for all subgraphs which contain a single source and a single sink in $O(n^4)$ arithmetic operations, where $n$ is the number of vertices in the graph. We then demonstrate as an application of these tools a method to overlay two distinct filtrations of the same underlying space, which allows us to detect the most significant barcodes using considerably fewer points than standard persistence.Comment: Revised versio

Polarised target for Drell-Yan experiment in COMPASS at CERN, part I

In the polarised Drell-Yan experiment at the COMPASS facility in CERN pion beam with momentum of 190 GeV/c and intensity about $10^8$ pions/s interacted with transversely polarised NH$_3$ target. Muon pairs produced in Drel-Yan process were detected. The measurement was done in 2015 as the 1st ever polarised Drell-Yan fixed target experiment. The hydrogen nuclei in the solid-state NH$_3$ were polarised by dynamic nuclear polarisation in 2.5 T field of large-acceptance superconducting magnet. Large helium dilution cryostat was used to cool the target down below 100 mK. Polarisation of hydrogen nuclei reached during the data taking was about 80 %. Two oppositely polarised target cells, each 55 cm long and 4 cm in diameter were used. Overview of COMPASS facility and the polarised target with emphasis on the dilution cryostat and magnet is given. Results of the polarisation measurement in the Drell-Yan run and overviews of the target material, cell and dynamic nuclear polarisation system are given in the part II.Comment: 4 pages, 2 figures, Proceedings of the 22nd International Spin Symposium, Urbana-Champaign, Illinois, USA, 25-30 September 201

Boundedness of Pseudodifferential Operators on Banach Function Spaces

We show that if the Hardy-Littlewood maximal operator is bounded on a separable Banach function space $X(\mathbb{R}^n)$ and on its associate space $X'(\mathbb{R}^n)$, then a pseudodifferential operator $\operatorname{Op}(a)$ is bounded on $X(\mathbb{R}^n)$ whenever the symbol $a$ belongs to the H\"ormander class $S_{\rho,\delta}^{n(\rho-1)}$ with $0<\rho\le 1$, $0\le\delta<1$ or to the the Miyachi class $S_{\rho,\delta}^{n(\rho-1)}(\varkappa,n)$ with $0\le\delta\le\rho\le 1$, $0\le\delta0$. This result is applied to the case of variable Lebesgue spaces $L^{p(\cdot)}(\mathbb{R}^n)$.Comment: To appear in a special volume of Operator Theory: Advances and Applications dedicated to Ant\'onio Ferreira dos Santo