The human ability of keeping balance during various locomotion tasks is attributed to our capability of withstanding complex interactions with the environment and coordinating whole-body movements. Despite this, several stability analysis methods are limited by the use of overly simplified biped and foot structures and corresponding contact models. As a result, existing stability criteria tend to be overly restrictive and do not represent the full balance capabilities of complex biped systems. The proposed methodology allows for the characterization of the balance capabilities of general biped models (ranging from reduced-order to whole-body) with segmented feet. Limits of dynamic balance are evaluated by the Boundary of Balance (BoB) and the associated novel balance indicators, both formulated in the Center of Mass (COM) state space. Intermittent heel, flat, and toe contacts are enabled by a contact model that maps discrete contact modes into corresponding center of pressure constraints. For demonstration purposes, the BoB and balance indicators are evaluated for a whole-body biped model with segmented feet representative of the human-like standing posture in the sagittal plane. The BoB is numerically constructed as the set of maximum allowable COM perturbations that the biped can sustain along a prescribed direction. For each point of the BoB, a constrained trajectory optimization algorithm generates the biped’s whole-body trajectory as it recovers from extreme COM velocity perturbations in the anterior–posterior direction. Balance capabilities for the cases of flat and segmented feet are compared, demonstrating the functional role the foot model plays in the limits of postural balance. The state-space evaluation of the BoB and balance indicators allows for a direct comparison between the proposed balance benchmark and existing stability criteria based on reduced-order models [e.g., Linear Inverted Pendulum (LIP)] and their associated stability metrics [e.g., Margin of Stability (MOS)]. The proposed characterization of balance capabilities provides an important benchmarking framework for the stability of general biped/foot systems.

A journey to 'tame a small metazoan organism', ‡ seen through the artistic eyes of C. elegans researchers

Abstract. In this study, we introduce and examine the concepts of asymptotically lacunary statistical equivalent of order α in probability and strong asymptotically lacunary equivalent of order α in probability. We give some relations connected to these concepts.

Purpose: By investigating the MACC1 gene (metastasis-associated in colon cancer 1) in cancer stem cells (CSC) resistant to chemotherapy and in cancer stem cells (CSC) resistant to chemotherapy and in cancer cells (CS) sensitive to chemotherapy we determineda steady expression in both types of cells in head and neck cancer. In conformity with the result we examined if this gene could be a competitor gene for chemotherapy. According to literature, the MACC1 gene shows a clear expression in head and neck cancer cells [1]. Here we examined MACC1 expression in CSC and investigated it as a possible biomarker.Methods: Our experiments were performed in the UT -SCC -74 in primary head and neck cancer cell line. We examined the MACC -1 gene expression by Real Time PCR from both isolated CSC and CS.Results: Expression of MACC -1 gene of cancer stem cells showed an two-fold increase compared with cancer cells. Based on the positive expression of MACC1 in both CS and CSC, this gene may serve as a potential biomarker in head and neck cancer. By comparing the results of this study with the novel features of MACC1, two important hypotheses could be examined. The first hypothesis is that MACC1 is a possible transcripton factor in colon cancer, which influences a high expression of CSC in head and neck and affects the expression of three biomarkers of the CSC control group biomarkers. The second hypothesisis is that the positive expression of MACC1 in patients with a malignant prognosis of tongue cancer, which belongs to head and neck cancer types, operates a faster development of CSC to cancer cells.SUPPLEMENT