Dependence of ground state energy of classical n-vector spins on n

We study the ground state energy E_G(n) of N classical n-vector spins with the hamiltonian H = - \sum_{i>j} J_ij S_i.S_j where S_i and S_j are n-vectors and the coupling constants J_ij are arbitrary. We prove that E_G(n) is independent of n for all n > n_{max}(N) = floor((sqrt(8N+1)-1) / 2) . We show that this bound is the best possible. We also derive an upper bound for E_G(m) in terms of E_G(n), for m<n. We obtain an upper bound on the frustration in the system, as measured by F(n), which is defined to be (\sum_{i>j} |J_ij| + E_G(n)) / (\sum_{i>j} |J_ij|). We describe a procedure for constructing a set of J_ij's such that an arbitrary given state, {S_i}, is the ground state.Comment: 6 pages, 2 figures, submitted to Physical Review

Improved Approximation for Tree Augmentation: Saving by Rewiring

The Tree Augmentation Problem (TAP) is a fundamental network design problem in which we are given a tree and a set of additional edges, also called \emph{links}. The task is to find a set of links, of minimum size, whose addition to the tree leads to a $2$-edge-connected graph. A long line of results on TAP culminated in the previously best known approximation guarantee of $1.5$ achieved by a combinatorial approach due to Kortsarz and Nutov [ACM Transactions on Algorithms 2016], and also by an SDP-based approach by Cheriyan and Gao [Algorithmica 2017]. Moreover, an elegant LP-based $(1.5+\epsilon)$-approximation has also been found very recently by Fiorini, Gro\ss, K\"onemann, and Sanit\'a [SODA 2018]. In this paper, we show that an approximation factor below $1.5$ can be achieved, by presenting a $1.458$-approximation that is based on several new techniques

Physical accessible transformations on a finite number of quantum states

We consider to treat the usual probabilistic cloning, state separation, unambiguous state discrimination, \emph{etc} in a uniform framework. All these transformations can be regarded as special examples of generalized completely positive trace non-increasing maps on a finite number of input states. From the system-ancilla model we construct the corresponding unitary implementation of pure $\to$ pure, pure $\to$ mixed, mixed $\to$ pure, and mixed $\to$ mixed states transformations in the whole system and obtain the necessary and sufficient conditions on the existence of the desired maps. We expect our work will be helpful to explore what we can do on a finite set of input states.Comment: 7 page

ON THE CONNECTIONS BETWEEN SEMIDEFINITE OPTIMIZATION AND VECTOR OPTIMIZATION

This paper works out connections between semidefinite optimization and vector optimization. It is shown that well-known semidefinite optimization problems are scalarized versions of a general vector optimization problem. This scalarization leads to the minimization of the trace or the maximal eigenvalue

Finite quantum tomography via semidefinite programming

Using the the convex semidefinite programming method and superoperator formalism we obtain the finite quantum tomography of some mixed quantum states such as: qudit tomography, N-qubit tomography, phase tomography and coherent spin state tomography, where that obtained results are in agreement with those of References \cite{schack,Pegg,Barnett,Buzek,Weigert}.Comment: 25 page

A Randomized Placebo-Controlled Phase 3 Trial of an Antisense Oligonucleotide, Drisapersen, in Duchenne Muscular Dystrophy

This 48-week, randomized, placebo-controlled phase 3 study (DMD114044; NCT01254019) evaluated efficacy and safety of subcutaneous drisapersen 6 mg/kg/week in 186 ambulant boys aged ≥5 years, with Duchenne muscular dystrophy (DMD) resulting from an exon 51 skipping amenable mutation. Drisapersen was generally well tolerated, with injection-site reactions and renal events as most commonly reported adverse events. A nonsignificant treatment difference (P = 0.415) in the change from baseline in six-minute walk distance (6MWD; primary efficacy endpoint) of 10.3 meters in favor of drisapersen was observed at week 48. Key secondary efficacy endpoints (North Star Ambulatory Assessment, 4-stair climb ascent velocity, and 10-meter walk/run velocity) gave consistent findings. Lack of statistical significance was thought to be largely due to greater data variability and subgroup heterogeneity. The increased standard deviation alone, due to less stringent inclusion/exclusion criteria, reduced the statistical power from pre-specified 90% to actual 53%. Therefore, a post-hoc analysis was performed in 80 subjects with a baseline 6MWD 300-400 meters and ability to rise from floor. A statistically significant improvement in 6MWD of 35.4 meters (P = 0.039) in favor of drisapersen was observed in this subpopulation. Results suggest that drisapersen could have benefit in a less impaired population of DMD subjects

Research trends in combinatorial optimization

Acknowledgments This work has been partially funded by the Spanish Ministry of Science, Innovation, and Universities through the project COGDRIVE (DPI2017-86915-C3-3-R). In this context, we would also like to thank the Karlsruhe Institute of Technology. Open access funding enabled and organized by Projekt DEAL.Peer reviewedPublisher PD