Fluorescence tomographic imaging in turbid media using early-arriving photons and Laplace transforms

We present a multichannel tomographic technique to detect fluorescent objects embedded in thick (6.4 cm) tissue-like turbid media using early-arriving photons. The experiments use picosecond laser pulses and a streak camera with single photon counting capability to provide short time resolution and high signal-to-noise ratio. The tomographic algorithm is based on the Laplace transform of an analytical diffusion approximation of the photon migration process and provides excellent agreement between the actual positions of the fluorescent objects and the experimental estimates. Submillimeter localization accuracy and 4- to 5-mm resolution are demonstrated. Moreover, objects can be accurately localized when fluorescence background is present. The results show the feasibility of using early-arriving photons to image fluorescent objects embedded in a turbid medium and its potential in clinical applications such as breast tumor detection.

Genetic transformation of HeLa cells by Agrobacterium

Agrobacterium tumefaciens is a soil phytopathogen that elicits neoplastic growths on the host plant species. In nature, however, Agrobacterium also may encounter organisms belonging to other kingdoms such as insects and animals that feed on the infected plants. Can Agrobacterium, then, also infect animal cells? Here, we report that Agrobacterium attaches to and genetically transforms several types of human cells. In stably transformed HeLa cells, the integration event occurred at the right border of the tumor-inducing plasmid's transferred-DNA (T-DNA), suggesting bona fide T-DNA transfer and lending support to the notion that Agrobacterium transforms human cells by a mechanism similar to that which it uses for transformation of plants cells. Collectively, our results suggest that Agrobacterium can transport its T-DNA to human cells and integrate it into their genome.

Invariance of brain-wave representations of simple visual images and their names

In two experiments, electric brain waves of 14 subjects were recorded under several different conditions to study the invariance of brain-wave representations of simple patches of colors and simple visual shapes and their names, the words blue, circle, etc. As in our earlier work, the analysis consisted of averaging over trials to create prototypes and test samples, to both of which Fourier transforms were applied, followed by filtering and an inverse transformation to the time domain. A least-squares criterion of fit between prototypes and test samples was used for classification. The most significant results were these. By averaging over different subjects, as well as trials, we created prototypes from brain waves evoked by simple visual images and test samples from brain waves evoked by auditory or visual words naming the visual images. We correctly recognized from 60% to 75% of the test-sample brain waves. The general conclusion is that simple shapes such as circles and single-color displays generate brain waves surprisingly similar to those generated by their verbal names. These results, taken together with extensive psychological studies of auditory and visual memory, strongly support the solution proposed for visual shapes, by Bishop Berkeley and David Hume in the 18th century, to the long-standing problem of how the mind represents simple abstract ideas.

New infinite families of exact sums of squares formulas, Jacobi elliptic functions, and Ramanujan’s tau function

In this paper, we give two infinite families of explicit exact formulas that generalize Jacobi’s (1829) 4 and 8 squares identities to 4n2 or 4n(n + 1) squares, respectively, without using cusp forms. Our 24 squares identity leads to a different formula for Ramanujan’s tau function τ(n), when n is odd. These results arise in the setting of Jacobi elliptic functions, Jacobi continued fractions, Hankel or Turánian determinants, Fourier series, Lambert series, inclusion/exclusion, Laplace expansion formula for determinants, and Schur functions. We have also obtained many additional infinite families of identities in this same setting that are analogous to the η-function identities in appendix I of Macdonald’s work [Macdonald, I. G. (1972) Invent. Math. 15, 91–143]. A special case of our methods yields a proof of the two conjectured [Kac, V. G. and Wakimoto, M. (1994) in Progress in Mathematics, eds. Brylinski, J.-L., Brylinski, R., Guillemin, V. & Kac, V. (Birkhäuser Boston, Boston, MA), Vol. 123, pp. 415–456] identities involving representing a positive integer by sums of 4n2 or 4n(n + 1) triangular numbers, respectively. Our 16 and 24 squares identities were originally obtained via multiple basic hypergeometric series, Gustafson’s Cℓ nonterminating 6φ5 summation theorem, and Andrews’ basic hypergeometric series proof of Jacobi’s 4 and 8 squares identities. We have (elsewhere) applied symmetry and Schur function techniques to this original approach to prove the existence of similar infinite families of sums of squares identities for n2 or n(n + 1) squares, respectively. Our sums of more than 8 squares identities are not the same as the formulas of Mathews (1895), Glaisher (1907), Ramanujan (1916), Mordell (1917, 1919), Hardy (1918, 1920), Kac and Wakimoto, and many others.

Retrovirus-mediated gene transfer of MLL-ELL transforms primary myeloid progenitors and causes acute myeloid leukemias in mice

The MLL-ELL fusion gene results from the translocation t(11;19)(q23;p13.1) that is associated with de novo and therapy-related acute myeloid leukemia. To study its transforming properties, we retrovirally transduced primary murine hematopoietic progenitors and assessed their growth properties both in vitro and in vivo. MLL-ELL increased the proliferation of myeloid colony-forming cells in methylcellulose cultures upon serial replating, whereas overexpression of ELL alone had no effect. We reconstituted lethally irradiated congenic mice with bone marrow progenitors transduced with MLL-ELL or the control MIE vector encoding the enhanced green fluorescent protein. When the peripheral blood of the mice was analyzed 11–13 weeks postreconstitution, we found that the engraftment of the MLL-ELL-transduced cells was superior to that of the MIE controls. At this time point, the contribution of the donor cells was normally distributed among the myeloid and nonmyeloid compartments. Although all of the MIE animals (n = 10) remained healthy for more than a year, all of the MLL-ELL mice (n = 20) succumbed to monoclonal or pauciclonal acute myeloid leukemias within 100–200 days. The leukemic cells were readily transplantable to secondary recipients and could be established as immortalized cell lines in liquid cultures. These studies demonstrate the enhancing effect of MLL-ELL on the proliferative potential of myeloid progenitors as well as its causal role in the genesis of acute myeloid leukemias.