scholarly journals Estimates for the Bennequin number of Legendrian links from state models for knot polynomials

1997 ◽  
Vol 4 (1) ◽  
pp. 143-156 ◽  
Author(s):  
Serge Tabachnikov
1991 ◽  
Vol 24 (7) ◽  
pp. 59-64 ◽  
Author(s):  
R. W. Szetela

Steady-state models are presented to describe the wastewater treatment process in two activated sludge systems. One of these makes use of a single complete-mix reactor; the other one involves two complete-mix reactors arranged in series. The in-series system is equivalent to what is known as the “two-phase” activated sludge, a concept which is now being launched throughout Poland in conjunction with the PROMLECZ technology under implementation. Analysis of the mathematical models has revealed the following: (1) treatment efficiency, excess sludge production, energy consumption, and the degree of sludge stabilization are identical in the two systems; (2) there exists a technological equivalence of “two-phase” sludge with “single-phase” sludge; (3) the “two-phase” system has no technological advantage over the “single-phase” system.


2020 ◽  
Vol 128 (18) ◽  
pp. 185902
Author(s):  
S. J. Ali ◽  
D. C. Swift ◽  
C. J. Wu ◽  
R. G. Kraus

Author(s):  
Cesar A. López ◽  
Animesh Agarwal ◽  
Que N. Van ◽  
Andrew G. Stephen ◽  
S. Gnanakaran

AbstractSmall GTPase proteins are ubiquitous and responsible for regulating several processes related to cell growth and differentiation. Mutations that stabilize their active state can lead to uncontrolled cell proliferation and cancer. Although these proteins are well characterized at the cellular scale, the molecular mechanisms governing their functions are still poorly understood. In addition, there is limited information about the regulatory function of the cell membrane which supports their activity. Thus, we have studied the dynamics and conformations of the farnesylated KRAS4b in various membrane model systems, ranging from binary fluid mixtures to heterogeneous raft mimics. Our approach combines long time-scale coarse-grained (CG) simulations and Markov state models to dissect the membrane-supported dynamics of KRAS4b. Our simulations reveal that protein dynamics is mainly modulated by the presence of anionic lipids and to some extent by the nucleotide state (activation) of the protein. In addition, our results suggest that both the farnesyl and the polybasic hypervariable region (HVR) are responsible for its preferential partitioning within the liquid-disordered (Ld) domains in membranes, potentially enhancing the formation of membrane-driven signaling platforms. Graphic Abstract


2021 ◽  
Author(s):  
Arghadwip Paul ◽  
Suman Samantray ◽  
Marco Anteghini ◽  
Mohammed Khaled ◽  
Birgit Strodel

The convergence of MD simulations is tested using varying measures for the intrinsically disordered amyloid-β peptide (Aβ). Markov state models show that 20–30 μs of MD is needed to reliably reproduce the thermodynamics and kinetics of Aβ.


Sign in / Sign up

Export Citation Format

Share Document