No abstract

We report an in situ method of probing the structure of living epithelial cells, based on light scattering spectroscopy with polarized light. The method makes it possible to distinguish between single backscattering from uppermost epithelial cells and multiply scattered light. The spectrum of the single backscattering component can be further analyzed to provide histological information about the epithelial cells such as the size distribution of the cell nuclei and their refractive index. These are valuable quantities to detect and diagnose precancerous changes in human tissues.

Biomedical imaging with light-scattering spectroscopy (LSS) is a novel optical technology developed to probe the structure of living epithelial cells in situ without need for tissue removal. LSS makes it possible to distinguish between single backscattering from epithelial-cell nuclei and multiply scattered light. The spectrum of the single backscattering component is further analyzed to provide quantitative information about the epithelial-cell nuclei such as nuclear size, degree of pleomorphism, degree of hyperchromasia and amount of chromatin. LSS imaging allows mapping these histological properties over wide areas of epithelial lining. Because nuclear enlargement, pleomorphism and hyperchromasia are principal features of nuclear atypia associated with precancerous and cancerous changes in virtually all epithelia, LSS imaging can be used to detect precancerous lesions in optically accessible organs.

We present a novel instrument for imaging the angular distributions of light backscattered by biological cells and tissues. The intensities in different regions of the image are due to scatterers of different sizes. We exploit this to study scattering from particles smaller than the wavelength of light used, even when they are mixed with larger particles. We show that the scattering from subcellular structure in both normal and cancerous human cells is best fitted to inverse power-law distributions for the sizes of the scattering objects, and propose that the distribution of scattering objects may be different in normal versus cancerous cells.

Abstract. We give a n O(log n) -time (n is the input size) blackbox polynomial identity testing algorithm for unknown-order read-once oblivious algebraic branching programs (ROABP). The best time-complexity known for this class was n O(log 2 n) due to Forbes-Saptharishi-Shpilka (STOC 2014), and that too only for multilinear ROABP. We get rid of their exponential dependence on the individual degree. With this, we match the time-complexity for the unknown order ROABP with the known order ROABP (due to Forbes-Shpilka (FOCS 2013)) and also with the depth-3 setmultilinear circuits (due to Agrawal-Saha-Saxena (STOC 2013)). Our proof is simpler and involves a new technique called basis isolation.The depth-3 model has recently gained much importance, as it has become a stepping-stone to understanding general arithmetic circuits. Its restriction to multilinearity has known exponential lower bounds but no nontrivial blackbox identity tests. In this paper, we take a step towards designing such hitting-sets. We give the first subexponential whitebox PIT for the sum of constantly many setmultilinear depth-3 circuits. To achieve this, we define notions of distance and base sets. Distance, for a multilinear depth-3 circuit (say, in n variables and k product gates), measures how far are the partitions from a mere refinement. The 1-distance strictly subsumes the set-multilinear model, while n-distance captures general multilinear depth-3. We design a hitting-set in time (nk) O(∆ log n) for ∆-distance. Further, we give an extension of our result to models where the distance is large (close to n) but it is small when restricted to certain base sets (of variables).We also explore a new model of read-once algebraic branching programs (ROABP) where the factor-matrices are invertible (called invertible-factor ROABP). We design a hitting-set in time poly(n w 2 ) for width-w invertible-factor ROABP. Further, we could do without the invertibility restriction when w = 2. Previously, the best result for width-2 ROABP was quasi-polynomial time (Forbes-Saptharishi-Shpilka, STOC 2014).