Dr TIM: Ray-tracer TIM, with additional specialist scientific capabilities

We describe several extensions to TIM, a raytracing program for ray-optics research. These include relativistic raytracing; simulation of the external appearance of Eaton lenses, Luneburg lenses and generalized focusing gradient-index (GGRIN) lenses, which are types of perfect imaging devices; raytracing through interfaces between spaces with different optical metrics; and refraction with generalised confocal lenslet arrays, which are particularly versatile METATOYs.Comment: 12 pages, 16 figure

On the normality of Higgins commutators

In a semi-abelian context, we study the condition (NH) asking that Higgins commutators of normal subobjects are normal subobjects. We provide examples of categories that do or do not satisfy this property. We focus on the relationship with the "Smith is Huq" condition (SH) and characterise those semi-abelian categories in which both (NH) and (SH) hold in terms of reflection and preservation properties of the change of base functors of the fibration of points.Comment: 15 pages; final published versio

Transcriptomic profiling of tumor-infiltrating CD4 + TIM-3 + T Cells reveals their suppressive, exhausted, and metastatic characteristics in colorectal cancer patients

T cell immunoglobulin mucin-3 (TIM-3) is an immune checkpoint identified as one of the key players in regulating T-cell responses. Studies have shown that TIM-3 is upregulated in the tumor microenvironment (TME). However, the precise role of TIM-3 in colorectal cancer (CRC) TME is yet to be elucidated. We performed phenotypic and molecular characterization of TIM-3+ T cells in the TME and circulation of CRC patients by analyzing tumor tissues (TT, TILs), normal tissues (NT, NILs), and peripheral blood mononuclear cells (PBMC). TIM-3 was upregulated on both CD4+ and CD3+CD4− (CD8+) TILs. CD4+TIM-3+ TILs expressed higher levels of T regulatory cell (Tregs)-signature genes, including FoxP3 and Helios, compared with their TIM-3− counterparts. Transcriptomic and ingenuity pathway analyses showed that TIM-3 potentially activates inflammatory and tumor metastatic pathways. Moreover, NF-κB-mediated transcription factors were upregulated in CD4+TIM-3+ TILs, which could favor proliferation/invasion and induce inflammatory and T-cell exhaustion pathways. In addition, we found that CD4+TIM-3+ TILs potentially support tumor invasion and metastasis, compared with conventional CD4+CD25+ Tregs in the CRC TME. However, functional studies are warranted to support these findings. In conclusion, this study discloses some of the functional pathways of TIM-3+ TILs, which could improve their targeting in more specific therapeutic approaches in CRC patients

Differential expression and biochemical activity of the immune receptor Tim-3 in healthy and malignant human myeloid cells

The T cell immunoglobulin and mucin domain 3 (Tim-3) is a plasma membrane-associated receptor which is involved in a variety of biological responses in human immune cells. It is highly expressed in most acute myeloid leukaemia (AML) cells and therefore may serve as a possible target for AML therapy. However, its biochemical activities in primary human AML cells remain unclear. We therefore analysed the total expression and surface presence of the Tim-3 receptor in primary human AML blasts and healthy primary human leukocytes isolated from human blood. We found that Tim-3 expression was significantly higher in primary AML cells compared to primary healthy leukocytes. Tim-3 receptor molecules were distributed largely on the surface of primary AML cells, whereas in healthy leukocytes Tim-3 protein was mainly expressed intracellularly. In primary human AML blasts, both Tim-3 agonistic antibody and galectin-9 (a Tim-3 natural ligand) significantly upregulated mTOR pathway activity. This was in line with increased accumulation of hypoxia-inducible factor 1 alpha (HIF-1α) and secretion of VEGF and TNF-α. Similar results were obtained in primary human healthy leukocytes. Importantly, in both types of primary cells, Tim-3-mediated effects were compared with those induced by lipopolysaccharide (LPS) and stem cell factor (SCF). Tim-3 induced comparatively moderate responses in both AML cells and healthy leukocytes. However, Tim-3, like LPS, mediated the release of both TNF-α and VEGF, while SCF induced mostly VEGF secretion and did not upregulate TNF-α release

Simple Lie groups without the Approximation Property

For a locally compact group G, let A(G) denote its Fourier algebra, and let M_0A(G) denote the space of completely bounded Fourier multipliers on G. The group G is said to have the Approximation Property (AP) if the constant function 1 can be approximated by a net in A(G) in the weak-* topology on the space M_0A(G). Recently, Lafforgue and de la Salle proved that SL(3,R) does not have the AP, implying the first example of an exact discrete group without it, namely SL(3,Z). In this paper we prove that Sp(2,R) does not have the AP. It follows that all connected simple Lie groups with finite center and real rank greater than or equal to two do not have the AP. This naturally gives rise to many examples of exact discrete groups without the AP.Comment: Version 4, 29 pages. Minor correction

A decomposition formula for the weighted commutator

We decompose the weighted subobject commutator of M. Gran, G. Janelidze and A. Ursini as a join of a binary and a ternary commutator.Comment: 7 pages. Dedicated to George Janelidze on the occasion of his sixtieth birthda

Some results on homology of Leibniz and Lie n-algebras

From the viewpoint of semi-abelian homology, some recent results on homology of Leibniz n-algebras can be explained categorically. In parallel with these results, we develop an analogous theory for Lie n-algebras. We also consider the relative case: homology of Leibniz n-algebras relative to the subvariety of Lie n-algebras.Comment: 14 page

Multilevel Topological Interference Management

The robust principles of treating interference as noise (TIN) when it is sufficiently weak, and avoiding it when it is not, form the background for this work. Combining TIN with the topological interference management (TIM) framework that identifies optimal interference avoidance schemes, a baseline TIM-TIN approach is proposed which decomposes a network into TIN and TIM components, allocates the signal power levels to each user in the TIN component, allocates signal vector space dimensions to each user in the TIM component, and guarantees that the product of the two is an achievable number of signal dimensions available to each user in the original network.Comment: To be presented at 2013 IEEE Information Theory Worksho