Homogeneous structures and rigidity of isoparametric submanifolds in Hilbert space

We study isoparametric submanifolds of rank at least two in a separable Hilbert space, which are known to be homogeneous by the main result in [E. Heintze and X. Liu, Ann. of Math. (2), 149 (1999), 149-181], and with such a submanifold M and a point x in M we associate a canonical homogeneous structure I" (x) (a certain bilinear map defined on a subspace of T (x) M x T (x) M). We prove that I" (x) , together with the second fundamental form alpha (x) , encodes all the information about M, and we deduce from this the rigidity result that M is completely determined by alpha (x) and (Delta alpha) (x) , thereby making such submanifolds accessible to classification. As an essential step, we show that the one-parameter groups of isometries constructed in [E. Heintze and X. Liu, Ann. of Math. (2), 149 (1999), 149-181] to prove their homogeneity induce smooth and hence everywhere defined Killing fields, implying the continuity of I" (this result also seems to close a gap in [U. Christ, J. Differential Geom., 62 (2002), 1-15]). Here an important tool is the introduction of affine root systems of isoparametric submanifolds.

INFLUENCE OF DISCOUNT PRICE ANNOUNCEMENTS ON CONSUMER'S BEHAVIOR

The theoretical framework that underpins this research study is based on the Prospect Theory formulated by Kahneman and Tversky, and Thaler's Mental Accounting Theory. The research aims to evaluate the consumers' behavior when different patterns of discount are offered (in percentage and absolute value and for larger and smaller discounts). Two experiments were conducted to explore these patterns of behavior and the results that were obtained supported the view that the framing effect was a common occurrence. The patterns of choice of individuals in a sample were found to be different due to changes in the ways discounts were offered. This can be explained by the various ways of presenting discount rates that had an impact on the influence of purchase intentions, recommendations and quality perception.

Vascular smooth muscle cells exhibit a progressive loss of rigidity with serial culture passaging

One drawback of in vitro cell culturing is the dedifferentiation process that cells experience. Smooth muscle cells (SMC) also change molecularly and morphologically with long term culture. The main objective of this study was to evaluate if culture passages interfere in vascular SMC mechanical behavior. SMC were obtained from five different porcine arterial beds. Optical magnetic twisting cytometry (OMTC) was used to characterize mechanically vascular SMC from different cultures in distinct passages and confocal microscopy/western blotting, to evaluate cytoskeleton and extracellular matrix proteins. We found that vascular SMC rigidity or viscoelastic complex modulus (G) decreases with progression of passages. A statistically significant negative correlation between G and passage was found in four of our five cultures studied. Phalloidin-stained SMC from higher passages exhibited lower mean signal intensity per cell (confocal microscopy) and quantitative western blotting analysis showed a decrease in collagen I content throughout passages. We concluded that vascular SMC progressively lose their stiffness with serial culture passaging. Thus, limiting the number of passages is essential for any experiment measuring viscoelastic properties of SMC in culture.

Relating network rigidity, time scale hierarchies, and expression noise in gene networks

Fluctuation-dissipation theorems can be used to predict characteristics of noise from characteristics of the macroscopic response of a system. In the case of gene networks, feedback control determines the "network rigidity," defined as resistance to slow external changes. We propose an effective Fokker-Planck equation that relates gene expression noise to topology and to time scales of the gene network. We distinguish between two situations referred to as normal and inverted time hierarchies. The noise can be buffered by network feedback in the first situation, whereas it can be topology independent in the latter.

Judet quadricepsplasty in the treatment of posttraumatic knee rigidity: Long-term outcomes of 45 cases

BACKGROUND: Posttraumatic knee stiffness is a very debilitating condition. Judet's quadricepsplasty technique has been used for more than 50 years. However, few reports of quadricepsplasty results exist in the literature. METHODS: We report the results of 45 cases of posttraumatic arthrofibrosis of the knee treated with Judet's quadricepsplasty. The results of the procedure were analyzed by measuring the degrees of flexion of the operated knees at different time points (before, immediately after, and late postoperatively). RESULTS: The degree of flexion increased from 33.6 degrees (range, 5-80 degrees) preoperatively to 105 degrees (range, 45-160 degrees) immediately after surgery, followed by a slight fall in the range of motion (ROM) in the late postoperative period, which reached an average of 84.8 degrees. There was no significant correlation between knee strength and the patient's gender, but there was a slight trend of lower strength with age. Although Judet's quadricepsplasty technique dates from more than 50 years ago, it still provides good outcomes in the treatment of rigid knees of various etiologies. In general, all cases showed the same pattern of a small decrease in the ROM in the late postoperative period. CONCLUSION: Judet's quadricepsplasty can increase the ROM of rigid knees. The ROM obtained with the surgery persists long term. (J Trauma. 2012; 72: E77-E80. Copyright (C) 2012 by Lippincott Williams & Wilkins)

Influence of discount price announcements on consumer's behavior

The theoretical framework that underpins this research study is based on the Prospect Theory formulated by Kahneman and Tversky, and Thaler's Mental Accounting Theory. The research aims to evaluate the consumers' behavior when different patterns of discount are offered (in percentage and absolute value and for larger and smaller discounts). Two experiments were conducted to explore these patterns of behavior and the results that were obtained supported the view that the framing effect was a common occurrence. The patterns of choice of individuals in a sample were found to be different due to changes in the ways discounts were offered. This can be explained by the various ways of presenting discount rates that had an impact on the influence of purchase intentions, recommendations and quality perception.

Rigidity for piecewise smooth homeomorphisms on the circle

We find conditions for two piecewise 'C POT.2+V' homeomorphisms f and g of the circle to be 'C POT.1' conjugate. Besides the restrictions on the combinatorics of the maps (we assume that the maps have bounded combinatorics), and necessary conditions on the one-side derivatives of points where f and g are not differentiable, we also assume zero mean-nonlinearity for f and g.