Fixed-parameter tractability of multicut parameterized by the size of the cutset

Given an undirected graph $G$, a collection $\{(s_1,t_1),..., (s_k,t_k)\}$ of pairs of vertices, and an integer $p$, the Edge Multicut problem ask if there is a set $S$ of at most $p$ edges such that the removal of $S$ disconnects every $s_i$ from the corresponding $t_i$. Vertex Multicut is the analogous problem where $S$ is a set of at most $p$ vertices. Our main result is that both problems can be solved in time $2^{O(p^3)}... n^{O(1)}$, i.e., fixed-parameter tractable parameterized by the size $p$ of the cutset in the solution. By contrast, it is unlikely that an algorithm with running time of the form $f(p)... n^{O(1)}$ exists for the directed version of the problem, as we show it to be W[1]-hard parameterized by the size of the cutset

Time-reversible Born-Oppenheimer molecular dynamics

We present a time-reversible Born-Oppenheimer molecular dynamics scheme, based on self-consistent Hartree-Fock or density functional theory, where both the nuclear and the electronic degrees of freedom are propagated in time. We show how a time-reversible adiabatic propagation of the electronic degrees of freedom is possible despite the non-linearity and incompleteness of the self-consistent field procedure. Time-reversal symmetry excludes a systematic long-term energy drift for a microcanonical ensemble and the number of self-consistency cycles can be kept low (often only 2-4 cycles per nuclear time step) thanks to a good initial guess given by the adiabatic propagation of the electronic degrees of freedom. The time-reversible Born-Oppenheimer molecular dynamics scheme therefore combines a low computational cost with a physically correct time-reversible representation of the dynamics, which preserves a detailed balance between propagation forwards and backwards in time.Comment: 4 pages, 4 figure

Optimality program in segment and string graphs

Planar graphs are known to allow subexponential algorithms running in time $2^{O(\sqrt n)}$ or $2^{O(\sqrt n \log n)}$ for most of the paradigmatic problems, while the brute-force time $2^{\Theta(n)}$ is very likely to be asymptotically best on general graphs. Intrigued by an algorithm packing curves in $2^{O(n^{2/3}\log n)}$ by Fox and Pach [SODA'11], we investigate which problems have subexponential algorithms on the intersection graphs of curves (string graphs) or segments (segment intersection graphs) and which problems have no such algorithms under the ETH (Exponential Time Hypothesis). Among our results, we show that, quite surprisingly, 3-Coloring can also be solved in time $2^{O(n^{2/3}\log^{O(1)}n)}$ on string graphs while an algorithm running in time $2^{o(n)}$ for 4-Coloring even on axis-parallel segments (of unbounded length) would disprove the ETH. For 4-Coloring of unit segments, we show a weaker ETH lower bound of $2^{o(n^{2/3})}$ which exploits the celebrated Erd\H{o}s-Szekeres theorem. The subexponential running time also carries over to Min Feedback Vertex Set but not to Min Dominating Set and Min Independent Dominating Set.Comment: 19 pages, 15 figure

Density-functional study of Cu atoms, monolayers, and coadsorbates on polar ZnO surfaces

The structure and electronic properties of single Cu atoms, copper monolayers and thin copper films on the polar oxygen and zinc terminated surfaces of ZnO are studied using periodic density-functional calculations. We find that the binding energy of Cu atoms sensitively depends on how charge neutrality of the polar surfaces is achieved. Bonding is very strong if the surfaces are stabilized by an electronic mechanism which leads to partially filled surface bands. As soon as the surface bands are filled (either by partial Cu coverage, by coadsorbates, or by the formation of defects), the binding energy decreases significantly. In this case, values very similar to those found for nonpolar surfaces and for copper on finite ZnO clusters are obtained. Possible implications of these observations concerning the growth mode of copper on polar ZnO surfaces and their importance in catalysis are discussed.Comment: 6 pages with 2 postscript figures embedded. Uses REVTEX and epsf macro

Scotland, Catalonia and the “right” to self-determination: a comment suggested by Kathryn Crameri’s “Do Catalans Have the Right to Decide?

No abstract available

Stability domains of actin genes and genomic evolution

In eukaryotic genes the protein coding sequence is split into several fragments, the exons, separated by non-coding DNA stretches, the introns. Prokaryotes do not have introns in their genome. We report the calculations of stability domains of actin genes for various organisms in the animal, plant and fungi kingdoms. Actin genes have been chosen because they have been highly conserved during evolution. In these genes all introns were removed so as to mimic ancient genes at the time of the early eukaryotic development, i.e. before introns insertion. Common stability boundaries are found in evolutionary distant organisms, which implies that these boundaries date from the early origin of eukaryotes. In general boundaries correspond with introns positions of vertebrates and other animals actins, but not much for plants and fungi. The sharpest boundary is found in a locus where fungi, algae and animals have introns in positions separated by one nucleotide only, which identifies a hot-spot for insertion. These results suggest that some introns may have been incorporated into the genomes through a thermodynamic driven mechanism, in agreement with previous observations on human genes. They also suggest a different mechanism for introns insertion in plants and animals.Comment: 9 Pages, 7 figures. Phys. Rev. E in pres

Predicting survival from colorectal cancer histology slides using deep learning: A retrospective multicenter study

BACKGROUND: For virtually every patient with colorectal cancer (CRC), hematoxylin-eosin (HE)-stained tissue slides are available. These images contain quantitative information, which is not routinely used to objectively extract prognostic biomarkers. In the present study, we investigated whether deep convolutional neural networks (CNNs) can extract prognosticators directly from these widely available images. METHODS AND FINDINGS: We hand-delineated single-tissue regions in 86 CRC tissue slides, yielding more than 100,000 HE image patches, and used these to train a CNN by transfer learning, reaching a nine-class accuracy of >94% in an independent data set of 7,180 images from 25 CRC patients. With this tool, we performed automated tissue decomposition of representative multitissue HE images from 862 HE slides in 500 stage I-IV CRC patients in the The Cancer Genome Atlas (TCGA) cohort, a large international multicenter collection of CRC tissue. Based on the output neuron activations in the CNN, we calculated a "deep stroma score," which was an independent prognostic factor for overall survival (OS) in a multivariable Cox proportional hazard model (hazard ratio [HR] with 95% confidence interval [CI]: 1.99 [1.27-3.12], p = 0.0028), while in the same cohort, manual quantification of stromal areas and a gene expression signature of cancer-associated fibroblasts (CAFs) were only prognostic in specific tumor stages. We validated these findings in an independent cohort of 409 stage I-IV CRC patients from the "Darmkrebs: Chancen der Verhütung durch Screening" (DACHS) study who were recruited between 2003 and 2007 in multiple institutions in Germany. Again, the score was an independent prognostic factor for OS (HR 1.63 [1.14-2.33], p = 0.008), CRC-specific OS (HR 2.29 [1.5-3.48], p = 0.0004), and relapse-free survival (RFS; HR 1.92 [1.34-2.76], p = 0.0004). A prospective validation is required before this biomarker can be implemented in clinical workflows. CONCLUSIONS: In our retrospective study, we show that a CNN can assess the human tumor microenvironment and predict prognosis directly from histopathological images

Exchange Monte Carlo for Molecular Simulations with Monoelectronic Hamiltonians

We introduce a general Monte Carlo scheme for achieving atomistic simulations with monoelectronic Hamiltonians including the thermalization of both nuclear and electronic degrees of freedom. The kinetic Monte Carlo algorithm is used to obtain the exact occupation numbers of the electronic levels at canonical equilibrium, and comparison is made with Fermi-Dirac statistics in infinite and finite systems. The effects of a nonzero electronic temperature on the thermodynamic properties of liquid silver and sodium clusters are presented