We show that for any k-connected graph having cocircumference c∗, there is a cycle which intersects every cocycle of size c∗ − k+2 or greater. We use this to show that in a 2connected graph, there is a family of at most c∗ cycles for which each edge of the graph belongs to at least two cycles in the family. This settles a question raised by Oxley. A certain result known for cycles and cocycles ...

This paper proposes templates for positive and negative control Toffoli gates for post synthesis optimization of reversible circuits. Templates 1 − 5 can be applied to two adjacent Toffoli gates T1(C1, t1) and T2(C2, t2) where Ci is the set of controls, |C1| = |C2|, and |t1| = |t2|. Templates 6−7 can be applied to two different size Toffoli gates T1(C1, t1) and T2(C2, t2) where Ci is the set of...

Spinal muscular atrophy (SMA) is caused by loss of SMN1. A nearly identical gene, SMN2, fails to compensate for the loss of SMN1 because SMN2 produces mainly an exon 7-skipped product. The +6C in SMN1 exon 7 proceeds to include exon 7 into mRNA, while the +6U in SMN2 causes skipping of exon 7. Here, approximately 45kD proteins bound to the SMN exon 7 RNA probe was found, and identified as hnRNP...

Little [12] showed that, in a certain sense, the only minimal non-Pfaffian bipartite matching covered graph is the brace K3,3. Using a stronger notion of minimality than the one used by Little, we show that every minimal nonPfaffian brick G contains two disjoint odd cycles C1 and C2 such that the subgraph G − V (C1 ∪ C2) has a perfect matching. This implies that the only minimal non-Pfaffian so...

Given the firstand kth-order rate functions, where k ≥ 2, we define gk(t1, · · · , tk;Ni) = λk(t1, · · · , tk;Ni) λ(t1;Ni) · · ·λ(tk;Ni) . Throughout this section, let c, c1 and c2 denote three positive real numbers where c1 < c2. Let β0 denote the true but unknown value of β. Let ρ (1) i (β) denote the vector of partial derivatives of ρi(β) with respect to β. Let || · || be the Euclidean norm....

We analyze the optimal dividend payment problem in the dual model under constant transaction costs. We show, for a general spectrally positive Lévy process, an optimal strategy is given by a (c1, c2)-policy that brings the surplus process down to c1 whenever it reaches or exceeds c2 for some 0 ≤ c1 < c2. The value function is succinctly expressed in terms of the scale function. A series of nume...

OBJECTIVE The purpose of this study was to compare the radiological and neurological outcomes between two atlantoaxial fusion method for atlantoaxial stabilization; C1 lateral mass-C2 pedicle screws (screw-rod constructs, SRC) versus C1-2 transarticular screws (TAS). METHODS Forty-one patients in whom atlantoaxial instability was treated with atlantoaxial fixation by SRC group (27 patients, f...

Motivated by the recent discovery of metallic kagome lattice materials, ${\mathrm{AV}}_{3}{\mathrm{Sb}}_{5}$ (A = K, Rb, Cs), we investigate ground state half-filled Hubbard model employing density-matrix renormalization group method. We identify a metal-insulator transition around $U\ensuremath{\sim}{U}_{c1}$ and four distinct phases as function $U/t$ on narrower cylinders, including phase at ...

This equation is regular and already in normal form. We obtain the eigenvalues from the characteristic equation: α + ω = 0 α = −ω α = ±iω This gives {e} as eigenfunctions. However, since the original equation has real coefficients, we would like a basis of real-valued eigenfunctions. Since Re(e) = cosωx and Im(e) = sinωx, we take {cosωx, sinωx} as a basis. Thus the eigenfunctions of (?1) are al...

STUDY DESIGN A retrospective study. PURPOSE To compare clinical and radiological outcomes between bilateral C2 pedicle screwing (C2PS) and unilateral C2PS, combined with contralateral C2 laminar screwing (LS), for posterior atlantoaxial fixation. OVERVIEW OF LITERATURE Posterior fixation with C1 lateral mass screwing (C1LMS) and C2PS (C1LMS-C2PS method) is an accepted procedure for rigid at...