The level set method for the two-sided eigenproblem

We consider the max-plus analogue of the eigenproblem for matrix pencils Ax=lambda Bx. We show that the spectrum of (A,B) (i.e., the set of possible values of lambda), which is a finite union of intervals, can be computed in pseudo-polynomial number of operations, by a (pseudo-polynomial) number of calls to an oracle that computes the value of a mean payoff game. The proof relies on the introduction of a spectral function, which we interpret in terms of the least Chebyshev distance between Ax and lambda Bx. The spectrum is obtained as the zero level set of this function.Comment: 34 pages, 4 figures. Changes with respect to the previous version: we explain relation to mean-payoff games and discrete event systems, and show that the reconstruction of spectrum is pseudopolynomia

Computing the vertices of tropical polyhedra using directed hypergraphs

We establish a characterization of the vertices of a tropical polyhedron defined as the intersection of finitely many half-spaces. We show that a point is a vertex if, and only if, a directed hypergraph, constructed from the subdifferentials of the active constraints at this point, admits a unique strongly connected component that is maximal with respect to the reachability relation (all the other strongly connected components have access to it). This property can be checked in almost linear-time. This allows us to develop a tropical analogue of the classical double description method, which computes a minimal internal representation (in terms of vertices) of a polyhedron defined externally (by half-spaces or hyperplanes). We provide theoretical worst case complexity bounds and report extensive experimental tests performed using the library TPLib, showing that this method outperforms the other existing approaches.Comment: 29 pages (A4), 10 figures, 1 table; v2: Improved algorithm in section 5 (using directed hypergraphs), detailed appendix; v3: major revision of the article (adding tropical hyperplanes, alternative method by arrangements, etc); v4: minor revisio

WNT signaling regulates self-renewal and differentiation of prostate cancer cells with stem cell characteristics

Prostate cancer cells with stem cell characteristics were identified in human prostate cancer cell lines by their ability to form from single cells self-renewing prostaspheres in non-adherent cultures. Prostaspheres exhibited heterogeneous expression of proliferation, differentiation and stem cell-associated makers CD44, ABCG2 and CD133. Treatment with WNT inhibitors reduced both prostasphere size and self-renewal. In contrast, addition of Wnt3a caused increased prostasphere size and self-renewal, which was associated with a significant increase in nuclear Β-catenin, keratin 18, CD133 and CD44 expression. As a high proportion of LNCaP and C4-2B cancer cells express androgen receptor we determined the effect of the androgen receptor antagonist bicalutamide. Androgen receptor inhibition reduced prostasphere size and expression of PSA, but did not inhibit prostasphere formation. These effects are consistent with the androgen-independent self-renewal of cells with stem cell characteristics and the androgen-dependent proliferation of transit amplifying cells. As the canonical WNT signaling effector Β-catenin can also associate with the androgen receptor, we propose a model for tumour propagation involving a balance between WNT and androgen receptor activity. That would affect the self-renewal of a cancer cell with stem cell characteristics and drive transit amplifying cell proliferation and differentiation. In conclusion, we provide evidence that WNT activity regulates the self-renewal of prostate cancer cells with stem cell characteristics independently of androgen receptor activity. Inhibition of WNT signaling therefore has the potential to reduce the self-renewal of prostate cancer cells with stem cell characteristics and improve the therapeutic outcome.Peer reviewe

Abnormal Placental Development and Early Embryonic Lethality in EpCAM-Null Mice

BACKGROUND: EpCAM (CD326) is encoded by the tacstd1 gene and expressed by a variety of normal and malignant epithelial cells and some leukocytes. Results of previous in vitro experiments suggested that EpCAM is an intercellular adhesion molecule. EpCAM has been extensively studied as a potential tumor marker and immunotherapy target, and more recent studies suggest that EpCAM expression may be characteristic of cancer stem cells. METHODOLOGY/PRINCIPAL FINDINGS: To gain insights into EpCAM function in vivo, we generated EpCAM -/- mice utilizing an embryonic stem cell line with a tacstd1 allele that had been disrupted. Gene trapping resulted in a protein comprised of the N-terminus of EpCAM encoded by 2 exons of the tacstd1 gene fused in frame to betageo. EpCAM +/- mice were viable and fertile and exhibited no obvious abnormalities. Examination of EpCAM +/- embryos revealed that betageo was expressed in several epithelial structures including developing ears (otocysts), eyes, branchial arches, gut, apical ectodermal ridges, lungs, pancreas, hair follicles and others. All EpCAM -/- mice died in utero by E12.5, and were small, developmentally delayed, and displayed prominent placental abnormalities. In developing placentas, EpCAM was expressed throughout the labyrinthine layer and by spongiotrophoblasts as well. Placentas of EpCAM -/- embryos were compact, with thin labyrinthine layers lacking prominent vascularity. Parietal trophoblast giant cells were also dramatically reduced in EpCAM -/- placentas. CONCLUSION: EpCAM was required for differentiation or survival of parietal trophoblast giant cells, normal development of the placental labyrinth and establishment of a competent maternal-fetal circulation. The findings in EpCAM-reporter mice suggest involvement of this molecule in development of vital organs including the gut, kidneys, pancreas, lungs, eyes, and limbs

A comprehensive overview of radioguided surgery using gamma detection probe technology

The concept of radioguided surgery, which was first developed some 60 years ago, involves the use of a radiation detection probe system for the intraoperative detection of radionuclides. The use of gamma detection probe technology in radioguided surgery has tremendously expanded and has evolved into what is now considered an established discipline within the practice of surgery, revolutionizing the surgical management of many malignancies, including breast cancer, melanoma, and colorectal cancer, as well as the surgical management of parathyroid disease. The impact of radioguided surgery on the surgical management of cancer patients includes providing vital and real-time information to the surgeon regarding the location and extent of disease, as well as regarding the assessment of surgical resection margins. Additionally, it has allowed the surgeon to minimize the surgical invasiveness of many diagnostic and therapeutic procedures, while still maintaining maximum benefit to the cancer patient. In the current review, we have attempted to comprehensively evaluate the history, technical aspects, and clinical applications of radioguided surgery using gamma detection probe technology

Idempotent (asymptotic) mathematics and the representation theory

operations by a new set of basic operations (e.g., such as maximum or minimum), that is on replacing numerical fields by idempotent semirings and semifields. Typical (and the most common) examples are given by the so-called (max, +) algebra Rmax and (min, +) algebra Rmin. Let R be the field of real numbers. The