Visual sense of number vs. sense of magnitude in humans and machines

Numerosity perception is thought to be foundational to mathematical learning, but its computational bases are strongly debated. Some investigators argue that humans are endowed with a specialized system supporting numerical representations; others argue that visual numerosity is estimated using continuous magnitudes, such as density or area, which usually co-vary with number. Here we reconcile these contrasting perspectives by testing deep neural networks on the same numerosity comparison task that was administered to human participants, using a stimulus space that allows the precise measurement of the contribution of non-numerical features. Our model accurately simulates the psychophysics of numerosity perception and the associated developmental changes: discrimination is driven by numerosity, but non-numerical features also have a significant impact, especially early during development. Representational similarity analysis further highlights that both numerosity and continuous magnitudes are spontaneously encoded in deep networks even when no task has to be carried out, suggesting that numerosity is a major, salient property of our visual environment

Chiral spin liquid and emergent anyons in a Kagome lattice Mott insulator

Topological phases in frustrated quantum spin systems have fascinated researchers for decades. One of the earliest proposals for such a phase was the chiral spin liquid put forward by Kalmeyer and Laughlin in 1987 as the bosonic analogue of the fractional quantum Hall effect. Elusive for many years, recent times have finally seen a number of models that realize this phase. However, these models are somewhat artificial and unlikely to be found in realistic materials. Here, we take an important step towards the goal of finding a chiral spin liquid in nature by examining a physically motivated model for a Mott insulator on the Kagome lattice with broken time-reversal symmetry. We first provide a theoretical justification for the emergent chiral spin liquid phase in terms of a network model perspective. We then present an unambiguous numerical identification and characterization of the universal topological properties of the phase, including ground state degeneracy, edge physics, and anyonic bulk excitations, by using a variety of powerful numerical probes, including the entanglement spectrum and modular transformations.Comment: 9 pages, 9 figures; partially supersedes arXiv:1303.696

INVOLVEMENT OF BASIC FIBROBLAST GROWTH-FACTOR IN SURAMIN-INDUCED INHIBITION OF V79/AP4 FIBROBLAST CELL-PROLIFERATION

The V79/AP4 Chinese hamster fibroblasts were densely stained with the anti-basic fibroblast growth factor (bFGF) antibody demonstrating an endogenous production of the peptide. The in vitro proliferation of these cells was stimulated by exogenous bFGF and the maximum growth (259% increase in H-3-thymidine incorporation into DNA) was reached with bFGF 10 ng ml-1. Inhibition of bFGF-mediated mitogenic pathway was obtained with a 15-mer antisense oligodeoxynucleotide targeted against bFGF mRNA and with suramin, a drug which blocks the biological activity of heparin-binding growth factors. bFGF antisense oligomer reduced the synthesis of DNA by 79.5 and 89.5% at 20 and 60 muM, respectively; this effect was reversed by the addition of exogenous bFGF to the culture medium. A short-term exposure to suramin 300 mug ml-1 produced a modest reduction in H-3-thymidine incorporation but suppressed the mitogenic effect of bFGF on V79/AP4 cells. In cells treated with suramin 300 mug ml-1 the drug concentration increased linearly over 3 days, reaching 13.15 mug mg-1 of protein; cell proliferation was inhibited in a dose-related manner as evaluated by the colony formation assay (IC50: 344.22 mug ml-1) and by the number of mitoses observed in culture. Furthermore, the drug induced ultrastructural alterations, consisting of perinuclear cisternae swelling, chromatin condensation, nucleolar segregation and cytoplasmic vacuolations. These findings demonstrated that the endogenous production of bFGF plays an important role in V79/AP4 fibroblasts proliferation, and the inhibition of bFGF-mediated mitogenic signalling with bFGF antisense oligomer or suramin is an effective mean of reducing cell growth

Involvement of basic fibroblast growth factor in suramin-induced inhibition of V79/AP4 fibroblast cell proliferation.

The V79/AP4 Chinese hamster fibroblasts were densely stained with the anti-basic fibroblast growth factor (bFGF) antibody demonstrating an endogenous production of the peptide. The in vitro proliferation of these cells was stimulated by exogenous bFGF and the maximum growth (259% increase in 3H-thymidine incorporation into DNA) was reached with bFGF 10 ng ml-1. Inhibition of bFGF-mediated mitogenic pathway was obtained with a 15-mer antisense oligodeoxynucleotide targeted against bFGF mRNA and with suramin, a drug which blocks the biological activity of heparin-binding growth factors. bFGF antisense oligomer reduced the synthesis of DNA by 79.5 and 89.5% at 20 and 60 microM, respectively; this effect was reversed by the addition of exogenous bFGF to the culture medium. A short-term exposure to suramin 300 micrograms ml-1 produced a modest reduction in 3H-thymidine incorporation but suppressed the mitogenic effect of bFGF on V79/AP4 cells. In cells treated with suramin 300 micrograms ml-1 the drug concentration increased linearly over 3 days, reaching 13.15 micrograms mg-1 of protein; cell proliferation was inhibited in a dose-related manner as evaluated by the colony formation assay (IC50: 344.22 micrograms ml-1) and by the number of mitoses observed in culture. Furthermore, the drug induced ultrastructural alterations, consisting of perinuclear cisternae swelling, chromatin condensation, nucleolar segregation and cytoplasmic vacuolations. These findings demonstrated that the endogenous production of bFGF plays an important role in V79/AP4 fibroblasts proliferation, and the inhibition of bFGF-mediated mitogenic signalling with bFGF antisense oligomer or suramin is an effective mean of reducing cell growth

C55-groups

We classify the C55-groups, i.e., finite groups in which the centralizer of every 5-element is a 5-group