Worst case and probabilistic analysis of the 2-Opt algorithm for the TSP

2-Opt is probably the most basic local search heuristic for the TSP. This heuristic achieves amazingly good results on “real world” Euclidean instances both with respect to running time and approximation ratio. There are numerous experimental studies on the performance of 2-Opt. However, the theoretical knowledge about this heuristic is still very limited. Not even its worst case running time on 2-dimensional Euclidean instances was known so far. We clarify this issue by presenting, for every p∈N , a family of L p instances on which 2-Opt can take an exponential number of steps. Previous probabilistic analyses were restricted to instances in which n points are placed uniformly at random in the unit square [0,1]2, where it was shown that the expected number of steps is bounded by O~(n10) for Euclidean instances. We consider a more advanced model of probabilistic instances in which the points can be placed independently according to general distributions on [0,1] d , for an arbitrary d≥2. In particular, we allow different distributions for different points. We study the expected number of local improvements in terms of the number n of points and the maximal density ϕ of the probability distributions. We show an upper bound on the expected length of any 2-Opt improvement path of O~(n4+1/3⋅ϕ8/3) . When starting with an initial tour computed by an insertion heuristic, the upper bound on the expected number of steps improves even to O~(n4+1/3−1/d⋅ϕ8/3) . If the distances are measured according to the Manhattan metric, then the expected number of steps is bounded by O~(n4−1/d⋅ϕ) . In addition, we prove an upper bound of O(ϕ√d) on the expected approximation factor with respect to all L p metrics. Let us remark that our probabilistic analysis covers as special cases the uniform input model with ϕ=1 and a smoothed analysis with Gaussian perturbations of standard deviation σ with ϕ∼1/σ d

Exotic Meson Production in the f1(1285)π−f_{1}(1285)\pi^{-} System observed in the Reaction π−p→ηπ+π−π−p\pi^{-} p \to \eta\pi^{+}\pi^{-}\pi^{-} p at 18 GeV/c

This letter reports results from the partial wave analysis of the $\pi^{-}\pi^{-}\pi^{+}\eta$ final state in $\pi^{-}p$ collisions at 18GeV/c. Strong evidence is observed for production of two mesons with exotic quantum numbers of spin, parity and charge conjugation, $J^{PC} = 1^{-+}$ in the decay channel $f_{1}(1285)\pi^{-}$. The mass $M = 1709 \pm 24 \pm 41$ MeV/c^2 and width $\Gamma = 403 \pm 80 \pm 115$ MeV/c^2 of the first state are consistent with the parameters of the previously observed $\pi_{1}(1600)$. The second resonance with mass $M = 2001 \pm 30 \pm 92$ MeV/c^2 and width $\Gamma = 333 \pm 52 \pm 49$ MeV/c^2 agrees very well with predictions from theoretical models. In addition, the presence of $\pi_{2}(1900)$ is confirmed with mass $M = 2003 \pm 88 \pm 148$ MeV/c^2 and width $\Gamma = 306 \pm 132 \pm 121$ MeV/c^2 and a new state, $a_{1}(2096)$, is observed with mass $M = 2096 \pm 17 \pm 121$ MeV/c^2 and width $\Gamma = 451 \pm 41 \pm 81$ MeV/c^2. The decay properties of these last two states are consistent with flux tube model predictions for hybrid mesons with non-exotic quantum numbers

Observation of Pseudoscalar and Axial Vector Resonances in pi- p -> K+ K- pi0 n at 18 GeV

A new measurement of the reaction pi- p -> K+ K- pi0 n has been made at a beam energy of 18 GeV. A partial wave analysis of the K+ K- pi0 system shows evidence for three pseudoscalar resonances, eta(1295), eta(1416), and eta(1485), as well as two axial vectors, f1(1285), and f1(1420). Their observed masses, widths and decay properties are reported. No signal was observed for C(1480), an IG J{PC} = 1+ 1{--} state previously reported in phi pi0 decay.Comment: 7 pages, 6 figs, to be submitted to Phys. Let

A study of the reaction pim p --> omega pim p at 18 GeV/c: The D and S decay amplitudes for b1(1235) --> omega pi

The reaction pim p --> omega pim p, omega --> pip pim pi0 has been studied at 18 GeV/c. The omega pim mass spectrum is found to be dominated by the b1(1235). Partial Wave Analysis shows that b1 production is dominated by natural parity exchange. The S-wave and D-wave amplitudes for b1(1235) --> omega pi have been determined, and it is found that the amplitude ratio, |D/S| = 0.269 +/- (0.009)stat +/- (0.01)sys and the phase difference, phi(D-S) = 10.54 deg +/- (2.4)stat +/- (3.9)sys.Comment: 7 pages, 9 figures, revtex4 format, to be published in Physics Letters

Genome-wide meta-analysis for Alzheimer's disease cerebrospinal fluid biomarkers

Altres ajuts: European Alzheimer DNA BioBank, EADB; EU Joint Programme, Neurodegenerative Disease Research (JPND); Neurodegeneration research program of Amsterdam Neuroscience; Stichting Alzheimer Nederland; Stichting VUmc fonds; Stichting Dioraphte; JPco-fuND FP-829-029 (ZonMW projectnumber 733051061); Dutch Federation of University Medical Centers; Dutch Government (from 2007-2011); JPND EADB grant (German Federal Ministry of Education and Research (BMBF) grant: 01ED1619A); German Research Foundation (DFG RA 1971/6-1, RA1971/7-1, RA 1971/8-1); Grifols SA; Fundación bancaria 'La Caixa'; Fundació ACE; CIBERNED; Fondo Europeo de Desarrollo Regional (FEDER-'Una manera de hacer Europa'); NIH (P30AG066444, P01AG003991); Alzheimer Research Foundation (SAO-FRA), The Research Foundation Flanders (FWO), and the University of Antwerp Research Fund. FK is supported by a BOF DOCPRO fellowship of the University of Antwerp Research Fund; Siemens Healthineers; Valdecilla Biobank (PT17/0015/0019); Academy of Finland (338182); German Center for Neurodegenerative Diseases (DZNE); German Federal Ministry of Education and Research (BMBF 01G10102, 01GI0420, 01GI0422, 01GI0423, 01GI0429, 01GI0431, 01GI0433, 04GI0434, 01GI0711); ZonMW (#73305095007); Health~Holland, Topsector Life Sciences & Health (PPP-allowance #LSHM20106); Hersenstichting; Edwin Bouw Fonds; Gieskes-Strijbisfonds; NWO Gravitation program BRAINSCAPES: A Roadmap from Neurogenetics to Neurobiology (NWO: 024.004.012); Swedish Alzheimer Foundation (AF-939988, AF-930582, AF-646061, AF-741361); Dementia Foundation (2020-04-13, 2021-04-17); Swedish state under the agreement between the Swedish government and the county councils, the ALF-agreement (ALF 716681); Swedish Research Council (11267, 825-2012-5041, 2013-8717, 2015-02830, 2017-00639, 2019-01096); Swedish Research Council for Health, Working Life and Welfare (2001-2646, 2001-2835, 2001-2849, 2003-0234, 2004-0150, 2005-0762, 2006-0020, 2008-1229, 2008-1210, 2012-1138, 2004-0145, 2006-0596, 2008-1111, 2010-0870, 2013-1202, 2013-2300, 2013-2496); Swedish Brain Power, Hjärnfonden, Sweden (FO2016-0214, FO2018-0214, FO2019-0163); Alzheimer's Association Zenith Award (ZEN-01-3151); Alzheimer's Association Stephanie B. Overstreet Scholars (IIRG-00-2159); Alzheimer's Association (IIRG-03-6168, IIRG-09-131338); Bank of Sweden Tercentenary Foundation; Swedish state under the agreement between the Swedish government and the county councils, the ALF-agreement (ALFGBG-81392, ALFGBG-771071); Swedish Alzheimer Foundation (AF-842471, AF-737641, AF-939825); Swedish Research Council (2019-02075); Swedish Research Council (2016-01590); BRAINSCAPES: A Roadmap from Neurogenetics to Neurobiology (024.004.012); Swedish Research Council (2018-02532); Swedish State Support for Clinical Research (ALFGBG-720931); Alzheimer Drug Discovery Foundation (ADDF), USA (201809-2016862); UK Dementia Research Institute at UCL; Swedish Research Council (#2017-00915); Alzheimer Drug Discovery Foundation (ADDF), USA (#RDAPB-201809-2016615); Swedish Alzheimer Foundation (#AF-742881); Hjärnfonden, Sweden (#FO2017-0243); Swedish state under the agreement between the Swedish government and the County Councils, the ALF-agreement (#ALFGBG-715986); National Institute of Health (NIH), USA, (#1R01AG068398-01); Alzheimer's Association 2021 Zenith Award (ZEN-21-848495); National Institutes of Health (R01AG044546, R01AG064877, RF1AG053303, R01AG058501, U01AG058922, RF1AG058501, R01AG064614); Chuck Zuckerberg Initiative (CZI).Amyloid-beta 42 (Aβ42) and phosphorylated tau (pTau) levels in cerebrospinal fluid (CSF) reflect core features of the pathogenesis of Alzheimer's disease (AD) more directly than clinical diagnosis. Initiated by the European Alzheimer & Dementia Biobank (EADB), the largest collaborative effort on genetics underlying CSF biomarkers was established, including 31 cohorts with a total of 13,116 individuals (discovery n = 8074; replication n = 5042 individuals). Besides the APOE locus, novel associations with two other well-established AD risk loci were observed; CR1 was shown a locus for Aβ42 and BIN1 for pTau. GMNC and C16orf95 were further identified as loci for pTau, of which the latter is novel. Clustering methods exploring the influence of all known AD risk loci on the CSF protein levels, revealed 4 biological categories suggesting multiple Aβ42 and pTau related biological pathways involved in the etiology of AD. In functional follow-up analyses, GMNC and C16orf95 both associated with lateral ventricular volume, implying an overlap in genetic etiology for tau levels and brain ventricular volume