Generalization of the convex-hull-and-line traveling salesman problem

Two instances of the traveling salesman problem, on the same node set (1,2 n} but with different cost matrices C and C, are equivalent iff there exist {a, hi: -1, n} such that for any 1 _i, j _n, j, C(i, j) C(i,j) q-a -t-bj [7]. One ofthe well-solved special cases of the traveling salesman problem (TSP) is the convex-hull-and-line TSP. We extend the solution scheme for this class of TSP given in [9] to a more general class which is closed with respect to the above equivalence relation. The cost matrix in our general class is a certain composition of Kalmanson matrices. This gives a new, non-trivial solvable case of TSP

Some Necessary Conditions and a General Sufficiency Condition for the Validity of A Gilmore-Gomory Type Patching Scheme for the Traveling

One of the most celebrated polynomially solvable cases of the TSP is the Gilmore-Gomory TSP. The patching scheme for the problem developed by Gilmore and Gomory has several interesting features. Its generalization, called the GG-scheme, has been studied by several researchers and polynomially testable sufficiency conditions for its validity have been given, leading to polynomial schemes for large subclasses of the TSP. A good characterization of the subclass of the TSP for which the GG-scheme produces an optimal solution, is an outstanding open problem of both theoretical and practical significance. We give some necessary conditions and a new, polynomially testable sufficiency condition for the validity of the GG-scheme that properly includes all previously known such conditions. Key words: Traveling salesman problem, Gilmore-Gomory TSP, Patching Scheme, Polynomially solvable case

2-Commodity Integer Network Synthesis Problem

We consider the following 2-commodity, integer network synthesis problem: Given two n×n, non-negative, symmetric, integer-valued matrices R = (rij) and S = (sij) of minimum flow requirements of 2 different commodities, construct an undirected network G = [N, E, c] on node set N = {1, 2, . . . , n} with integer edge capacities {c(e) : e ∈ E}, such that: (i) for any two pairs (i, j) and (k, l), i ≠ j, k ≠ l, of nodes in N, we can simultaneously send rij units of flow of commodity 1 from i to j and skl units of flow of commodity 2 from k to l in G; and (ii) z = Σ {c(e) : e ∈ E} is minimum. We present strongly polynomial, combinatorial algorithms for certain special cases of the problem; and for the general problem, we present a strongly polynomial, combinatorial algorithm that produces a feasible solution with objective function value no more than (the optimal objective function value +3)

Proteomics: in pursuit of effective traumatic brain injury therapeutics

Effective traumatic brain injury (TBI) therapeutics remain stubbornly elusive. Efforts in the field have been challenged by the heterogeneity of clinical TBI, with greater complexity among underlying molecular phenotypes than initially conceived. Future research must confront the multitude of factors comprising this heterogeneity, representing a big data challenge befitting the coming informatics age. Proteomics is poised to serve a central role in prescriptive therapeutic development, as it offers an efficient endpoint within which to assess post-TBI biochemistry. We examine rationale for multifactor TBI proteomic studies and the particular importance of temporal profiling in defining biochemical sequences and guiding therapeutic development. Lastly, we offer perspective on repurposing biofluid proteomics to develop theragnostic assays with which to prescribe, monitor and assess pharmaceutics for improved translation and outcome for TBI patients

Combinatorial CRISPR-Cas9 screens for de novo mapping of genetic interactions.

We developed a systematic approach to map human genetic networks by combinatorial CRISPR-Cas9 perturbations coupled to robust analysis of growth kinetics. We targeted all pairs of 73 cancer genes with dual guide RNAs in three cell lines, comprising 141,912 tests of interaction. Numerous therapeutically relevant interactions were identified, and these patterns replicated with combinatorial drugs at 75% precision. From these results, we anticipate that cellular context will be critical to synthetic-lethal therapies

Effect of Aging on A1C Levels in Individuals Without Diabetes: Evidence from the Framingham Offspring Study and the National Health and Nutrition Examination Survey 2001–2004

OBJECTIVE—Although glycemic levels are known to rise with normal aging, the nondiabetic A1C range is not age specific. We examined whether A1C was associated with age in nondiabetic subjects and in subjects with normal glucose tolerance (NGT) in two population-based cohorts

Effect of strongly magnetized electrons and Ions on heat flow and symmetry of inertial fusion implosions

This Letter presents the first observation on how a strong, 500 kG, externally applied B field increases the mode-two asymmetry in shock-heated inertial fusion implosions. Using a direct-drive implosion with polar illumination and imposed field, we observed that magnetization produces a significant increase in the implosion oblateness (a 2.5 × larger P 2 amplitude in x-ray self-emission images) compared with reference experiments with identical drive but with no field applied. The implosions produce strongly magnetized electrons ( ω e τ e ≫ 1 ) and ions ( ω i τ i > 1 ) that, as shown using simulations, restrict the cross field heat flow necessary for lateral distribution of the laser and shock heating from the implosion pole to the waist, causing the enhanced mode-two shape

Lawson criterion for ignition exceeded in an inertial fusion experiment

For more than half a century, researchers around the world have been engaged in attempts to achieve fusion ignition as a proof of principle of various fusion concepts. Following the Lawson criterion, an ignited plasma is one where the fusion heating power is high enough to overcome all the physical processes that cool the fusion plasma, creating a positive thermodynamic feedback loop with rapidly increasing temperature. In inertially confined fusion, ignition is a state where the fusion plasma can begin "burn propagation" into surrounding cold fuel, enabling the possibility of high energy gain. While "scientific breakeven" (i.e., unity target gain) has not yet been achieved (here target gain is 0.72, 1.37 MJ of fusion for 1.92 MJ of laser energy), this Letter reports the first controlled fusion experiment, using laser indirect drive, on the National Ignition Facility to produce capsule gain (here 5.8) and reach ignition by nine different formulations of the Lawson criterion