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Lipschitz Carnot-Carathéodory Structures and their Limits.
Antonelli G, Le Donne E, Nicolussi Golo S. Antonelli G, et al. J Dyn Control Syst. 2023;29(3):805-854. doi: 10.1007/s10883-022-09613-1. Epub 2022 Nov 25. J Dyn Control Syst. 2023. PMID: 37745006 Free PMC article.
In the case in which the limit distance is boundedly compact, we show that the convergence of the distances is uniform on compact sets. ...Among them, we prove a subFinsler Mitchell's Theorem with continuously varying norms, and a general convergence result for Carn …
In the case in which the limit distance is boundedly compact, we show that the convergence of the distances is uniform on compact …
Unsupervised neural learning on lie group.
Fiori S. Fiori S. Int J Neural Syst. 2002 Jun-Aug;12(3-4):219-46. doi: 10.1142/S012906570200114X. Int J Neural Syst. 2002. PMID: 12370963
The neural structures considered are single non-linear layers and the learnable parameters are organized in matrices, as usual, which gives the parameters spaces the geometrical structure of the Euclidean manifold. The constraint of orthonormality for the connection-matric …
The neural structures considered are single non-linear layers and the learnable parameters are organized in matrices, as usual, which gives …
Compact negatively curved manifolds (of dim [unk] 3,4) are topologically rigid.
Farrell FT, Jones LE. Farrell FT, et al. Proc Natl Acad Sci U S A. 1989 May;86(10):3461-3. doi: 10.1073/pnas.86.10.3461. Proc Natl Acad Sci U S A. 1989. PMID: 16594041 Free PMC article.

Let M be a complete (connected) Riemannian manifold having finite volume and whose sectional curvatures lie in the interval [c(1), c(2)] with -infinity < c(1)[unk]c(2) < 0. Then any proper homotopy equivalence h:N --> M from a topological manifold N is prop

…
Let M be a complete (connected) Riemannian manifold having finite volume and whose sectional curvatures lie in the interval [c …
Classification of the irreducible representations of semisimple Lie groups.
Vogan DA. Vogan DA. Proc Natl Acad Sci U S A. 1977 Jul;74(7):2649-50. doi: 10.1073/pnas.74.7.2649. Proc Natl Acad Sci U S A. 1977. PMID: 16592410 Free PMC article.
We obtain a classification of the irreducible (nonunitary) representations of a connected semisimple Lie group G, in terms of their restriction to a maximal compact subgroup K of G. ...Langlands [(1973), mimeographed notes, Institute for Advanced Study …
We obtain a classification of the irreducible (nonunitary) representations of a connected semisimple Lie group G, in te …
A Bruhat decomposition for the loop space of a compact group: A new approach to results of Bott.
Garland H, Raghunathan MS. Garland H, et al. Proc Natl Acad Sci U S A. 1975 Dec;72(12):4716-7. doi: 10.1073/pnas.72.12.4716. Proc Natl Acad Sci U S A. 1975. PMID: 16592292 Free PMC article.
We give a new proof of Bott's result, that the loop space of a compact, simply connected, simple Lie group has a cellular decomposition of a certain type. In particular, one obtains the Poincare polynomial for the loop space and Bott periodicity for th …
We give a new proof of Bott's result, that the loop space of a compact, simply connected, simple Lie group has a …
Anatomy of synganglia, including their neurosecretory regions, in unfed, virgin female Ixodes scapularis say (Acari: Ixodidae).
Szlendak E, Oliver JH Jr. Szlendak E, et al. J Morphol. 1992 Sep;213(3):349-64. doi: 10.1002/jmor.1052130308. J Morphol. 1992. PMID: 1404406
The central nervous system of Ixodes scapularis is fused into a single compact synganglion. The esophagus runs through the synganglion and divides it into supraesophageal and subesophageal parts. ...All of these regions appear to be connected and associated with the …
The central nervous system of Ixodes scapularis is fused into a single compact synganglion. The esophagus runs through the synganglio …
Morphological and histochemical observations on the primordial and early growing oocytes of crow (Corvus splendens) and myna (Acridotheres tristis).
Chalana RK, Guraya SS. Chalana RK, et al. Poult Sci. 1979 Jan;58(1):225-31. doi: 10.3382/ps.0580225. Poult Sci. 1979. PMID: 471889 Free article.
The primordial oocytes in the myna ovary are loosely arranged in groups or nests, whereas in crow they form compact nests surrounded by highly vascularized connective tissue bands or lie in layers beneath the surface epithelium. ...
The primordial oocytes in the myna ovary are loosely arranged in groups or nests, whereas in crow they form compact nests surr …
Minimal representations, geometric quantization, and unitarity.
Brylinski R, Kostant B. Brylinski R, et al. Proc Natl Acad Sci U S A. 1994 Jun 21;91(13):6026-9. doi: 10.1073/pnas.91.13.6026. Proc Natl Acad Sci U S A. 1994. PMID: 11607478 Free PMC article.
In the framework of geometric quantization we explicitly construct, in a uniform fashion, a unitary minimal representation pio of every simply-connected real Lie group Go such that the maximal compact subgroup of Go has finite center and Go admits some …
In the framework of geometric quantization we explicitly construct, in a uniform fashion, a unitary minimal representation pio of every simp …