Spatial patterns in the fruiting bodies of the cellular slime mold Polysphondylium pallidum

During morphogenesis in the slime mold Polysphondylium pallidum cell masses are periodically pinched off from the base of the developing sorogen. These masses round up and differentiate into secondary sorogens, which become radially ordered arrays of secondary fruiting bodies called whorls. Here we describe the morphogenesis of P. pallidum and characterize the spacing of whorls along the central stalk of the fruiting body and the spacing of soro-carps within whorls. We find both are highly regular. We propose that the linear spacing of whorls can be accounted for satisfactorily by a model that views the periodic release of cell masses from the base of the developing sorogen as the consequence of an imbalance between forces that orient amoebae toward the tip of the culminating sorogen, and cohesive forces between randomly moving cells in the basal region of the sorogen, which act as a retarding force. The orderly arrangement of fruiting bodies within whorls can be explained most easily by models that employ short-range activation and lateral inhibition.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/72498/1/j.1432-0436.1988.tb00200.x.pd

Generalized Wong sequences and their applications to Edmonds' problems

We design two deterministic polynomial time algorithms for variants of a problem introduced by Edmonds in 1967: determine the rank of a matrix M whose entries are homogeneous linear polynomials over the integers. Given a linear subspace B of the nxn matrices over some field F, we consider the following problems: symbolic matrix rank (SMR) is the problem to determine the maximum rank among matrices in B, while symbolic determinant identity testing (SDIT) is the question to decide whether there exists a nonsingular matrix in B. The constructive versions of these problems are asking to find a matrix of maximum rank, respectively a nonsingular matrix, if there exists one. Our first algorithm solves the constructive SMR when B is spanned by unknown rank one matrices, answering an open question of Gurvits. Our second algorithm solves the constructive SDIT when B is spanned by triangularizable matrices, but the triangularization is not given explicitly. Both algorithms work over finite fields of size at least n+1 and over the rational numbers, and the first algorithm actually solves (the non-constructive) SMR independent of the field size. Our main tool to obtain these results is to generalize Wong sequences, a classical method to deal with pairs of matrices, to the case of pairs of matrix spaces

Staging esophageal cancer1

Accurate staging of disease is necessary in patients with newly diagnosed esophageal cancer in order to prompt appropriate curative or palliative therapy. Computed tomography (CT) may be used to evaluate for local spread into adjacent structures (T4 disease) and to diagnose distant metastases (M1). Endoscopic ultrasonography (EUS) is the modality of choice for distinguishing T1 tumors from higher stage lesions and for detecting and sampling regional lymph nodes (N1 disease). Positron emission tomography (PET) scanning is most helpful for detecting previously occult distant metastases. Optimal staging generally requires a multimodality approach