Constant state of change: engagement inequality in temporal dynamic networks

Tracking Dynamic Resting-State Networks with High Temporal Resolution fMRI

plot of the average signals in (a) visual (b) sensory-motor networks. Tracking Dynamic Resting-State Networks with High Temporal Resolution fMRI H-L. Lee, B. Zahneisen, T. Grotz, P. LeVan, and J. Hennig Medical Physics, University Medical Center Freiburg, Freiburg, Germany Introduction Resting-state fMRI detects spontaneous BOLD signal fluctuations when no specific cognitive task is being perfo...

Constant-space reasoning in dynamic Bayesian networks

Temporal Navigation in Dynamic Networks

We present GraphDiaries, an interface for temporal navigation in dynamic networks with changing topology. Navigation in time is necessary for the exploration of single network states at different points in time and to explore higher level changes over periods of time. GraphDiaries enhances conventional node link diagrams with staged animated transitions between any time steps and small multiple...

Improvements of Young inequality using the Kantorovich constant

‎Some improvements of Young inequality and its reverse for positive‎ ‎numbers with Kantorovich constant $K(t‎, ‎2)=frac{(1+t)^2}{4t}$‎ ‎are given‎. ‎Using these inequalities some operator inequalities and‎ ‎Hilbert-Schmidt norm versions for matrices are proved‎. ‎In‎ ‎particular‎, ‎it is shown that if $a‎, ‎b$ are positive numbers and‎ ‎$0 leqslant nu leqslant 1,$ then for all integers $ kgeqsl...

Best Constant in Sobolev Inequality

The equality sign holds in (1) i] u has the Jorm: (3) u(x) = [a + btxI,~',-'] 1-~1~ , where Ix[ = (x~ @ ...-~x~) 1⁄2 and a, b are positive constants. Sobolev inequalities, also called Sobolev imbedding theorems, are very popular among writers in part ial differential equations or in the calculus of variations, and have been investigated by a great number of authors. Nevertheless there is a ques...