Transgenic mouse models provided a powerful tool to evaluate the physiological significance of altered quantities or characteristics of specific gene products, such as cardiac ion channels. We have developed a system to record and analyze changes in the electrocardiogram in the mouse using an implantable telemetry system. The R-R and Q-T intervals were measured on individual beats and on signal...

Suppose that K is a convex polyhedron in the n-dimensional Euclidean space R. Suppose that the extreme points of K are P1, P2, . . . , Pm ( m ≥ n + 1). If P is an arbitrary interior point of K, then there exist vertices Pi1 , Pi2 , . . . , Pin+1 of K and a point Q of R n and a positive number r > 0 for which ||Pik − Q|| = r for 1 ≤ k ≤ n + 1 , ||Pj − Q|| ≤ r for 1 ≤ j ≤ m and P is an interior p...

The purpose of this short note is to provide an alternative derivation of the optimal controller for the linear quadratic optimization problem in Section 2. Consider the linear time-varying system dynamics ˙ x(t) = A(t)x(t) + B(t)u(t), x(t 0) = x 0 , (1) where x(t) ∈ R n , u(t) ∈ R n i , ∀t ∈ [t 0 ,t 1 ]. Define the quadratic cost function J(u) = 1 2 t 1 t 0 u(t) 2 2 + C(t)x(t) 2 2 dt + x(t 1) ...

In heterotic string theory compactified on T , the T-duality orbits of dyons of charge (Q,P ) are characterized by O(6, 22; R ) invariants Q, P 2 and Q · P together with a set of invariants of the discrete T-duality group O(6, 22; ZZ). We study the action of S-duality group on the discrete T-duality invariants and study its consequence for the dyon degeneracy formula. In particular we find that...

We give a new proof of the sharp form of Young’s inequality for convolutions, first proved by Beckner [Be] and Brascamp-Lieb [BL]. The latter also proved a sharp reverse inequality in the case of exponents less than 1. Our proof is simpler and gives Young’s inequality and its converse altogether. The classical convolution inequality of Young asserts that for all functions f ∈ L(R) and g ∈ L(R) ...

There is a spectrum of methods for learning robot control. At one end there are model-free methods (eg. Q-learning, AHC, bucket brigade), and at the other there are model-based methods, (eg. dynamic programming by value or policy iteration). The advantage of one technique is the weakness of the other. Model-based methods use experience eeectively, but are computationally expensive; model-free m...

The universal enveloping algebra U (G) of a Lie algebra G acts on its representation ring R through D(R), the ring of differential operators on R. A quantised universal enveloping algebra (or quantum group) is a deformation of a universal enveloping algebra and acts not through the differential operators of its representation ring but through the quantised differential operators of its represen...

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We study global dynamics of the solution to Cauchy problem for focusing semilinear Schrödinger equation with a linear potential on real line R:(NLSV){i∂tu+∂x2u−Vu+|u|p−1u=0,(t,x)∈I×R,u(0)=u0∈H, where u=u(t,x) is complex-valued unknown function (t,x)∈I×R, I denotes maximal existence time interval u, V=V(x) non-negative and in L1(R)+L∞(R), p belongs so-called mass-supercritical case, i.e. p>5, H ...