Fine-Grained Complexity of k-OPT in Bounded-Degree Graphs for Solving TSP

The Traveling Salesman Problem asks to find a minimum-weight Hamiltonian cycle in an edge-weighted complete graph. Local search is a widely-employed strategy for finding good solutions to TSP. A popular neighborhood operator for local search is k-opt, which turns a Hamiltonian cycle C into a new Hamiltonian cycle C\u27 by replacing k edges. We analyze the problem of determining whether the weight of a given cycle can be decreased by a k-opt move. Earlier work has shown that (i) assuming the Exponential Time Hypothesis, there is no algorithm that can detect whether or not a given Hamiltonian cycle C in an n-vertex input can be improved by a k-opt move in time f(k) n^o(k / log k) for any function f, while (ii) it is possible to improve on the brute-force running time of O(n^k) and save linear factors in the exponent. Modern TSP heuristics are very successful at identifying the most promising edges to be used in k-opt moves, and experiments show that very good global solutions can already be reached using only the top-O(1) most promising edges incident to each vertex. This leads to the following question: can improving k-opt moves be found efficiently in graphs of bounded degree? We answer this question in various regimes, presenting new algorithms and conditional lower bounds. We show that the aforementioned ETH lower bound also holds for graphs of maximum degree three, but that in bounded-degree graphs the best improving k-move can be found in time O(n^((23/135+epsilon_k)k)), where lim_{k -> infty} epsilon_k = 0. This improves upon the best-known bounds for general graphs. Due to its practical importance, we devote special attention to the range of k in which improving k-moves in bounded-degree graphs can be found in quasi-linear time. For k <= 7, we give quasi-linear time algorithms for general weights. For k=8 we obtain a quasi-linear time algorithm when the weights are bounded by O(polylog n). On the other hand, based on established fine-grained complexity hypotheses about the impossibility of detecting a triangle in edge-linear time, we prove that the k = 9 case does not admit quasi-linear time algorithms. Hence we fully characterize the values of k for which quasi-linear time algorithms exist for polylogarithmic weights on bounded-degree graphs

Single spin optical read-out in CdTe/ZnTe quantum dot studied by photon correlation spectroscopy

Spin dynamics of a single electron and an exciton confined in CdTe/ZnTe quantum dot is investigated by polarization-resolved correlation spectroscopy. Spin memory effects extending over at least a few tens of nanoseconds have been directly observed in magnetic field and described quantitatively in terms of a simple rate equation model. We demonstrate an effective (68%) all-optical read-out of the single carrier spin state through probing the degree of circular polarization of exciton emission after capture of an oppositely charged carrier. The perturbation introduced by the pulsed optical excitation serving to study the spin dynamics has been found to be the main source of the polarization loss in the read-out process. In the limit of low laser power the read-out efficiency extrapolates to a value close to 100%. The measurements allowed us as well to determine neutral exciton spin relaxation time ranging from 3.4 +/- 0.1 ns at B = 0 T to 16 +/- 3 ns at B = 5 T.Comment: to appear in Phys. Rev.

Optical alignment and polarization conversion of neutral exciton spin in individual InAs/GaAs quantum dots

We investigate exciton spin memory in individual InAs/GaAs self-assembled quantum dots via optical alignment and conversion of exciton polarization in a magnetic field. Quasiresonant phonon-assisted excitation is successfully employed to define the initial spin polarization of neutral excitons. The conservation of the linear polarization generated along the bright exciton eigenaxes of up to 90% and the conversion from circular- to linear polarization of up to 47% both demonstrate a very long spin relaxation time with respect to the radiative lifetime. Results are quantitatively compared with a model of pseudo-spin 1/2 including heavy-to-light hole mixing.Comment: 5 pages, 3 figure

Lineaments and Mineral Occurrences in Pennsylvania

The author has identified the following significant results. A conservative lineament map of Pennsylvania interpreted from ERTS-1 channel 7 (infrared) imagery and Skylab photography was compared with the distribution of known metallic mines and mineral occurrences. Of 383 known mineral occurrences, 116 show a geographical association to 1 km wide lineaments, another 24 lie at the intersection of two lineaments, and one lies at the intersection of three lineaments. The Perkiomen Creek lineament in the Triassic Basin is associated with 9 Cu-Fe occurrences. Six Pb-Zn occurrences are associated with the Tyrone-Mount Union lineament. Thirteen other lineaments are associated with 3, 4, or 5 mineral occurrences each

Feasibility study of an Integrated Program for Aerospace vehicle Design (IPAD). Volume 2: The design process

The extent to which IPAD is to support the design process is identified. Case studies of representative aerospace products were developed as models to characterize the design process and to provide design requirements for the IPAD computing system

Forming and confining of dipolar excitons by quantizing magnetic fields

We show that a magnetic field perpendicular to an AlGaAs/GaAs coupled quantum well efficiently traps dipolar excitons and leads to the stabilization of the excitonic formation and confinement in the illumination area. Hereby, the density of dipolar excitons is remarkably enhanced up to $\sim 10^{11} cm^{-2}$. By means of Landau level spectroscopy we study the density of excess holes in the illuminated region. Depending on the excitation power and the applied electric field, the hole density can be tuned over one order of magnitude up to $\sim 2.5$ $10^{11} cm^{-2}$ - a value comparable with typical carrier densities in modulation-doped structures.Comment: 4.3 Pages, 4 Figure

Long exciton spin memory in coupled quantum wells

Spatially indirect excitons in a coupled quantum well structure were studied by means of polarization and time resolved photoluminescence. A strong degree of circular polarization (> 50%) in emission was achieved when the excitation energy was tuned into resonance with the direct exciton state. The indirect transition remained polarized several tens of nanoseconds after the pumping laser pulse, demonstrating directly a very long relaxation time of exciton spin. The observed spin memory effect exceeds the radiative lifetime of the indirect excitons.Comment: 4 pages, 2 figure

Cytokeratin-19 positivity is acquired along cancer progression and does not predict cell origin in rat hepatocarcinogenesis

Although the expression of the stem/progenitor cell marker cytokeratin-19 (CK-19) has been associated with the worst clinical prognosis among all HCC subclasses, it is yet unknown whether its presence in HCC is the result of clonal expansion of hepatic progenitor cells (HPCs) or of de-differentiation of mature hepatocytes towards a progenitor-like cell phenotype. We addressed this question by using two rat models of hepatocarcinogenesis: the Resistant-Hepatocyte (R-H) and the Choline-methionine deficient (CMD) models. Our data indicate that the expression of CK-19 is not the result of a clonal expansion of HPCs (oval cells in rodents), but rather of a further step of preneoplastic hepatocytes towards a less differentiated phenotype and a more aggressive behavior. Indeed, although HCCs were positive for CK-19, very early preneoplastic foci (EPFs) were completely negative for this marker. While a few weeks later the vast majority of preneoplastic nodules remained CK-19 negative, a minority became positive, suggesting that CK-19 expression is the result of de-differentiation of a subset of EPFs, rather than a marker of stem/progenitor cells. Moreover, the gene expression profile of CK-19-negative EPFs clustered together with CK-19-positive nodules, but was clearly distinct from CK-19 negative nodules and oval cells. Conclusion: i) CK-19-positive cells are not involved in the early clonal expansion observed in rat hepatocarcinogenesis; ii) CK-19 expression arises in preneoplastic hepatocyte lesions undergoing malignant transformation; iii) CK-19 positivity in HCCs does not necessarily reflect the cell of origin of the tumor, but rather the plasticity of preneoplastic cells during the tumorigenic proces