Given an undirected graph G=(V,E), vertices s,t∈V, and integer k, Tracking Shortest Paths requires deciding whether there exists a set of k T⊆V such that for any two distinct shortest paths between s t, say P1 P2, we have T∩V(P1)≠T∩V(P2). In this paper, give the first polynomial size kernel problem. Specifically show existence with O(k2) edges in general graphs O(k) planar DAG This problem admi...

As in cross sectional studies, longitudinal studies involve non-Gaussian data such as binomial, Poisson, gamma, and inverse-Gaussian distributions, and multivariate exponential families. A number of statistical tools have thus been developed to deal with non-Gaussian longitudinal data, including analytic techniques to estimate parameters in both fixed and random effects models. However, as yet ...

Abstract: The paper is concerned with the existence and global exponential stability of periodic solutions for inertial Cohen-Grossberg-type BAM neural networks with time delays. With variable transformation the system is transformed to first order differential equations. Some new sufficient conditions ensuring the existence and global exponential stability of periodic solutions for the system ...

Let R be an o-minimal expansion of the field of real numbers that defines nontrivial arcs of both the sine and exponential functions. Let G be a collection of images of solutions on intervals to differential equations y′ = F (y), where F ranges over all R-linear transformations R → R. Then either the expansion of R by the elements of G is as well behaved relative to R as one could reasonably ho...

We generalize the Toda lattice (or Toda chain) equation to the square lattice, i.e., we construct an integrable nonlinear equation for a scalar field taking values on the square lattice and depending on a continuous (time) variable, characterized by an exponential law of interaction in both discrete directions of the square lattice. We construct the Darboux-Bäcklund transformations for such lat...

We develop a new setting for the exponential principle in the context of multisort species, where indecomposable objects are generated intrinsically instead of being given in advance. Our approach uses the language of functors and natural transformations (composition operators), and we show that, somewhat surprisingly, a single axiom for the composition already suffices to guarantee validity of...

A modification of the variational configuration interaction functional in the first-order interacting space for molecular electronic structure is presented. The modified functional is a fully linked expression that by construction is extensive and invariant to transformations of the underlying orbital basis and is exact for an ensemble of separated two-electron subsystems. In addition, an appro...

Pure spinor formalism and non-integrable exponential factors are used for constructing the conformal-invariant wave equation and Lagrangian density for massive fermion. It is proved that canonical Dirac Lagrangian for massive fermion is invariant under induced projective conformal transformations.