Novel Lower Bounds on the Entropy Rate of Binary Hidden Markov Processes

Recently, Samorodnitsky proved a strengthened version of Mrs. Gerber's Lemma, where the output entropy of a binary symmetric channel is bounded in terms of the average entropy of the input projected on a random subset of coordinates. Here, this result is applied for deriving novel lower bounds on the entropy rate of binary hidden Markov processes. For symmetric underlying Markov processes, our bound improves upon the best known bound in the very noisy regime. The nonsymmetric case is also considered, and explicit bounds are derived for Markov processes that satisfy the $(1,\infty)$-RLL constraint

Isoperimetric properties of the mean curvature flow

In this paper we discuss a simple relation, which was previously missed, between the high co-dimensional isoperimetric problem of finding a filling with small volume to a given cycle, and extinction estimates for singular, high co-dimensional, mean curvature flow. The utility of this viewpoint is first exemplified by two results which, once casted in the light of this relation, are almost self evident. The first is a genuine, 5-lines proof, for the isoperimetric inequality for $k$-cycles in $\mathbb{R}^n$, with a constant differing from the optimal constant by a factor of only $\sqrt{k}$, as opposed to a factor of $k^k$ produced by all of the other soft methods (like Michael-Simon's or Gromov's). The second is a 3-lines proof of a lower bound for extinction for arbitrary co-dimensional, singular, mean curvature flows starting from cycles, generalizing the main result of a paper of Giga and Yama-uchi. We then turn to use the above mentioned relation to prove a bound on the parabolic Hausdorff measure of the space time track of high co-dimensional, singular, mean curvature flow starting from a cycle, in terms of the mass of that cycle. This bound is also reminiscent of a Michael-Simon Isoperimetric inequality. To prove it, we are lead to study the geometric measure theory of Euclidean rectifiable sets in parabolic space, and prove a co-area formula in that setting. This formula, the proof of which occupies most this paper, may be of independent interes

The role of recombinant epidermal growth factor and serotonin in the stimulation of tumor growth in a SCCHN xenograft model

One challenge of squamous cell carcinoma of the head and neck (SCCHN) chemotherapy is a small percentage of tumor cells that arrest in the G0 phase of the cell cycle and are thus not affected by chemotherapy. This could be one reason for tumor recurrence at a later date. The recruitment of these G0-arresting cells into the active cell cycle and thus, proliferation, may increase the efficacy of chemotherapeutic agents. The aim of this study was to investigate whether stimulation with recombinant epidermal growth factor (EGF) or serotonin leads to an increased tumor cell proliferation in xenografts. Detroit 562 cells were injected into NMRI-Foxn1nu mice. Treatment was performed with 15 µg murine or human EGF, or 200 µg serotonin. The control mice were treated with Lactated Ringer's solution (5 mice/group). Tumor size was measured on days 4, 8 and 12 after tumor cell injection. The EGF stimulated mice showed a significantly higher tumor growth compared to the serotonin-stimulated mice and the untreated controls. In the present study, we show that it is possible to stimulate tumor cells in xenografts by EGF and thus, enhance cell proliferation, resulting in a higher tumor growth compared to the untreated control group. In our future investigations, we plan to include a higher number of mice, an adjustment of the EGF dosage and cell subanalysis, considering the heterogeneity of SCCHN tumors