We study the following communication variant of local search. There is some fixed, commonly known graph G. Alice holds fA and Bob holds fB, both are functions that specify a value for each vertex. The goal is to find a local maximum of fA + fB with respect to G, i.e., a vertex v for which (fA + fB)(v) ≥ (fA + fB)(u) for every neighbor u of v. Our main result is that finding a local maximum requ...

A bstract We investigate the exact WKB method for quantum Seiberg-Witten curve of 4d N = 2 pure SU(3) Yang-Mills in language abelianization. The relevant differential equation is a third-order on ℂℙ 1 with two irregular singularities. employ to study solutions such and associated Stokes phenomena. also quantization condition certain spectral problem. Moreover, analysis leads us consider new Dar...

Power grid vulnerability is a major concern of our society, and its protection problem is often formulated as a tri-level defender-attacker-defender model. However, this tri-level problem is computationally challenging. In this paper, we design and implement a Column-and-Constraint Generation algorithm to derive its optimal solutions. Numerical results on an IEEE system show that: (i) the devel...

Shape memory alloy (SMA) structures are usually analyzed numerically; there are very few closed-form solutions in the literature. In this paper, we study the pure torsion of SMA bars with circular cross sections. First, a three-dimensional phenomenological macroscopic constitutive model for polycrystalline SMAs is reduced to the one-dimensional pure shear case and then a closed-form solution fo...

If R̂ is the pure-injective hull of a valuation ring R, it is proved that R̂ ⊗R M is the pure-injective hull of M , for every finitely generated Rmodule M . Moreover R̂ ⊗R M ∼= ⊕1≤k≤nR̂/AkR̂, where (Ak)1≤k≤n is the annihilator sequence of M . The pure-injective hulls of uniserial or polyserial modules are also investigated. Any two pure-composition series of a countably generated polyserial module a...

Current DNA sequencing technologies do not read an entire chromosome from end to end but instead produce sets of short reads, i.e. fragments of the genome. Haplotype assembly is the problem of assigning each read to the correct chromosome in the set of chromosomes in a homologous group, with the aid of the reference sequence. In this paper, we extend an existing exact algorithm for haplotype as...

For triples of probability measures, pure quantum states and mixed quantum states we obtain the exact constraints on the fidelities of pairs in the sequence. We show that it is impossible to decide between a quantum model, either pure or mixed, and a classical model on the basis of the fidelities alone. Next, we introduce a quantum three state invariant called phase and show that any sequence o...

In this work we show that the most general class of anti-unitary operators are nonphysical in nature through the existence of incomparable pure bipartite entangled states. It is also shown that a large class of inner-product-preserving operations defined only on the three qubits having spin-directions along x, y and z are impossible. If we perform such an operation locally on a particular pure ...

Nonhomogeneous systems governed by second-order linear differential equations with pure delay are considered. As an application, the exact solutions of these and their delayed matrix functions used to obtain finite-time stability results. Our results extend improve some previous removing restrictive conditions. Finally, example is provided illustrate our theoretical