During initiation of limb-bud outgrowth in vertebrate embryos, the polarising region (limb-bud organizer) is established upon activation of the Sonic Hedgehog (SHH) signaling molecule at the posterior limb-bud margin. Another hallmark of establishing anteroposterior limb-bud identities is the colinear activation of HoxD genes located at the 5' end of the cluster (5'HoxD genes). The unique and s...

We consider a discrete, time invariant, nonlinear system with one input and nx states that can be represented by the following state equation: xt+1 = g(xt, ut) + et, (1) where t ∈ Z is the discrete time step, ut ∈ R is the control input, xt ∈ Rx is the vector of states and et ∈ Rx is the vector of disturbance signals that accounts for the contribution of both the measurement and process disturb...

A dominating set S of a graph G is a locating-dominating-set, LD-set for short, if every vertex v not in S is uniquely determined by the set of neighbors of v belonging to S. Locating-dominating sets of minimum cardinality are called LDcodes and the cardinality of an LD-code is the location-domination number, λ(G). An LD-set S of a graph G is global if it is an LD-set for both G and its complem...

A dominating set S of a graph G is a locating-dominating-set, LD-set for short, if every vertex v not in S is uniquely determined by the set of neighbors of v belonging to S. Locating-dominating sets of minimum cardinality are called LDcodes and the cardinality of an LD-code is the location-domination number, λ(G). An LD-set S of a graph G is global if it is an LD-set for both G and its complem...

where c > 0 and the supremum is taken over all admissible controls v satisfying vt 2 [ 0; 1] for all t up to = inf f t > 0 j Xt = 2 (`0; `1) g with 0 < 0 < 1 and `0 < 0 < `1 given and fixed. The following control v is proved to be optimal: ’Pull as hard as possible’ that is v t = 0 if Xt < g (St) , and ’push as hard as possible’ that is v t = 1 if Xt > g (St) , where s 7! g (s) is a switching c...

Given the maximum process (St) = (max 0≤r≤t Xr) associated with a diffusion ((Xt),Px), and a continuous function g satisfying g(s) < s, we show how to compute the expectation of the Azéma-Yor stopping time τg = inf{ t > 0 : Xt ≤ g(St) } as a function of x. The method of proof is based upon verifying that the expectation solves a differential equation with two boundary conditions. The third ‘mis...

We study the L2-time regularity of the Z-component of a Markovian BSDE, whose terminal condition is a function g of a forward SDE (Xt)0≤t≤T . When g is Lipschitz continuous, Zhang [1] proved that the related squared L2-time regularity is of order one with respect to the size of the time mesh. We extend this type of result to any function g, including irregular functions such as indicator functi...

Let the (log-)prices of a collection of securities be given by a d–dimensional Lévy process Xt having infinite activity and a smooth density. The value of a European contract with payoff g(x) maturing at T is determined by E[g(XT )]. Let X̄T be a finite activity approximation to XT , where diffusion is introduced to approximate jumps smaller than a given truncation level ! > 0. The main result o...