Application of the Branch and Cut Method to the Vehicle Routing Problem

The successful application of Branch and Cut methods to the TSP has drawn attention also to the polyhedral properties of the symmetric capacitated vehicle routing problem, which is the capacitated counterpart of the TSP. We investigate three classes of valid inequalities for the CVRP, multistars, pathbin inequalities and hypotours and give computational results we obtained with a Branch and Cut implementation

New evidence for super-roughening in crystalline surfaces with disordered substrate

We study the behavior of the Binder cumulant related to long distance correlation functions of the discrete Gaussian model of disordered substrate crystalline surfaces. We exhibit numerical evidence that the non-Gaussian behavior in the low-$T$ region persists on large length scales, in agreement with the broken phase being super-rough.Comment: 10 pages and 4 figures, available at http://chimera.roma1.infn.it/index_papers_complex.html . We have extended the RG discussion and minor changes in the tex

The Genetics of Basal Cell Carcinoma of the Skin

BCC is the commonest cancer in European-derived populations and Australia has the highest recorded incidence in the world, creating enormous individual and societal cost in management of this disease. The incidence of this cancer has been increasing internationally, with evidence of a 1 to 2% rise in incidence in Australia per year over the last two decades. The main four epidemiological risk factors for the development of BCC are ultraviolet radiation (UVR) exposure, increasing age, male sex, and inability to tan. The pattern and timing of UVR exposure is important to BCC risk, with childhood and intermittent UVR exposure both associated with an increased risk. The complex of inherited characteristics making up an individual’s ‘sun sensitivity’ is also important in determining BCC risk. Very little is known about population genetic susceptibility to BCC outside of the rare genodermatosis Gorlin syndrome. Mutations in the tumour suppressor gene patched (PTCH) are responsible for this BCC predisposition syndrome and the molecular pathway and target genes of this highly conserved pathway are well described. Derangments in this pathway occur in sporadic BCC development, and the PTCH gene is an obvious candidate to contribute to non-syndromic susceptibility to BCC. The melanocortin 1 receptor (MC1R) locus is known to be involved in pigmentary traits and the cutaneous response to UVR, and variants have been associated with skin cancer risk. Many other genes have been considered with respect to population BCC risk and include p53, HPV, GSTs, and HLAs. There is preliminary evidence for specific familial aggregation of BCC, but very little known about the causes. 56 individuals who developed BCC under the age of 40 in the year 2000 were recruited from the Skin and Cancer Foundation of Australia’s database. This represents the youngest 7 – 8% of Australians with BCC from a database that captures approximately 10% of Sydney’s BCCs. 212 of their first degree relatives were also recruited, including 89 parents and 123 siblings of these 56 probands. All subjects were interviewed with respect to their cancer history and all reports of cancer verified with histopathological reports where possible. The oldest unaffected sibling for each proband (where available) was designated as an intra-family control. All cases and control siblings filled out a questionnaire regarding their pigmentary and sun sensitivity factors and underwent a skin examination by a trained examiner. Peripheral blood was collected from these cases and controls for genotyping of PTCH. All the exons of PTCH for which mutations have been documented in Gorlin patients were amplified using PCR. PCR products were screened for mutations using dHPLC, and all detectable variants sequenced. Prevalence of BCC and SCC for the Australian population was estimated from incidence data using a novel statistical approach. Familial aggregation of BCC, SCC and MM occurred within the 56 families studied here. The majority of families with aggregation of skin cancer had a combination of SCC and BCC, however nearly one fifth of families in this study had aggregation of BCC to the exclusion of SCC or MM, suggesting that BCCspecific risk factors are also likely to be at work. Skin cancer risks for first-degree relatives of people with early onset BCC were calculated: sisters and mothers of people with early-onset BCC had a 2-fold increased risk of BCC; brothers had a 5-fold increased risk of BCC; and sisters and fathers of people with early-onset BCC had over four times the prevalence of SCC than that expected. For melanoma, the increased risk was significant for male relatives only, with a 10-fold increased risk for brothers of people with early-onset BCC and 3-fold for fathers. On skin examination of cases and controls, several phenotypic factors were significantly associated with BCC risk. These included increasing risk of BCC with having fair, easyburning skin (ie decreasing skin phototype), and with having signs of cumulative sun damage to the skin in the form of actinic keratoses. Signs reflecting the combination of pigmentary characteristics and sun exposure - in the form of arm freckling and solar lentigines - also gave subjects a significantly increased risk BCC. Constitutive red-green reflectance of the skin was associated with decreased risk of BCC, as measured by spectrophotometery. Other non-significant trends were seen that may become significant in larger studies including associations of BCC with propensity to burn, moderate tanning ability and an inability to tan. No convincing trend for risk of BCC was seen with the pigmentary variables of hair or eye colour, and a non-significant reduced risk of BCC was associated with increasing numbers of seborrhoeic keratoses. Twenty PTCH exons (exons 2, 3, 5 to 18, and 20 to 23) were screened, accounting for 97% of the coding regions with published mutations in PTCH. Nine of these 20 exons were found to harbour single nucleotide polymorphisms (SNPs), seen on dHPLC as variant melting curves and confirmed on direct sequencing. SNPs frequencies were not significantly different to published population frequencies, or to Australian general population frequencies where SNP database population data was unavailable. Assuming a Poisson distribution, and having observed no mutations in a sample of 56, we can be 97.5% confident that if there are any PTCH mutations contributing to early-onset BCC in the Australian population, then their prevalence is less than 5.1%. Overall, this study provides evidence that familial aggregation of BCC is occurring, that first-degree relatives are at increased risk of all three types of skin cancer, and that a combination of environmental and genetic risk factors are likely to be responsible. The PTCH gene is excluded as a major cause of this increased susceptibility to BCC in particular and skin cancer in general. The weaknesses of the study design are explored, the possible clinical relevance of the data is examined, and future directions for research into the genetics of basal cell carcinoma are discussed

The critical exponents of the two-dimensional Ising spin glass revisited: Exact Ground State Calculations and Monte Carlo Simulations

The critical exponents for T -> 0 of the two-dimensional Ising spin glass model with Gaussian couplings are determined with the help of exact ground states for system sizes up to L=50 and by a Monte Carlo study of a pseudo-ferromagnetic order parameter. We obtain: for the stiffness exponent y(= heta)=-0.281 ±0.002 , for the magnetic exponent delta=1.48 ±0.01 and for the chaos exponent zeta=1.05 ±0.05 . From Monte Carlo simulations we get the thermal exponent u=3.6 ±0.2 . The scaling prediction y=-1/u is fulfilled within the error bars, whereas there is a disagreement with the relation y=1-delta

Ground state properties of solid-on-solid models with disordered substrates

We study the glassy super-rough phase of a class of solid-on-solid models with a disordered substrate in the limit of vanishing temperature by means of exact ground states, which we determine with a newly developed minimum cost flow algorithm. Results for the height-height correlation function are compared with analytical and numerical predictions. The domain wall energy of a boundary induced step grows logarithmically with system size, indicating the marginal stability of the ground state, and the fractal dimension of the step is estimated. The sensibility of the ground state with respect to infinitesimal variations of the quenched disorder is analyzed.Comment: 4 pages RevTeX, 3 eps-figures include

Using network-flow techniques to solve an optimization problem from surface-physics

The solid-on-solid model provides a commonly used framework for the description of surfaces. In the last years it has been extended in order to investigate the effect of defects in the bulk on the roughness of the surface. The determination of the ground state of this model leads to a combinatorial problem, which is reduced to an uncapacitated, convex minimum-circulation problem. We will show that the successive shortest path algorithm solves the problem in polynomial time.Comment: 8 Pages LaTeX, using Elsevier preprint style (macros included

A Graph Theoretical Approach To The Shunting Problem

n/

Dislocations in the ground state of the solid-on-solid model on a disordered substrate

We investigate the effects of topological defects (dislocations) to the ground state of the solid-on-solid (SOS) model on a simple cubic disordered substrate utilizing the min-cost-flow algorithm from combinatorial optimization. The dislocations are found to destabilize and destroy the elastic phase, particularly when the defects are placed only in partially optimized positions. For multi defect pairs their density decreases exponentially with the vortex core energy. Their mean distance has a maximum depending on the vortex core energy and system size, which gives a fractal dimension of $1.27 \pm 0.02$. The maximal mean distances correspond to special vortex core energies for which the scaling behavior of the density of dislocations change from a pure exponential decay to a stretched one. Furthermore, an extra introduced vortex pair is screened due to the disorder-induced defects and its energy is linear in the vortex core energy.Comment: 6 pages RevTeX, eps figures include

Super-roughening as a disorder-dominated flat phase

We study the phenomenon of super-roughening found on surfaces growing on disordered substrates. We consider a one-dimensional version of the problem for which the pure, ordered model exhibits a roughening phase transition. Extensive numerical simulations combined with analytical approximations indicate that super-roughening is a regime of asymptotically flat surfaces with non-trivial, rough short-scale features arising from the competition between surface tension and disorder. Based on this evidence and on previous simulations of the two-dimensional Random sine-Gordon model [Sanchez et al., Phys. Rev. E 62, 3219 (2000)], we argue that this scenario is general and explains equally well the hitherto poorly understood two-dimensional case.Comment: 7 pages, 4 figures. Accepted for publication in Europhysics Letter

Numerical study of the strongly screened vortex glass model in an external field

The vortex glass model for a disordered high-T_c superconductor in an external magnetic field is studied in the strong screening limit. With exact ground state (i.e. T=0) calculations we show that 1) the ground state of the vortex configuration varies drastically with infinitesimal variations of the strength of the external field, 2) the minimum energy of global excitation loops of length scale L do not depend on the strength of the external field, however 3) the excitation loops themself depend sensibly on the field. From 2) we infer the absence of a true superconducting state at any finite temperature independent of the external field.Comment: 6 pages RevTeX, 5 eps-figures include