Finding topological subgraphs is fixed-parameter tractable

We show that for every fixed undirected graph $H$, there is a $O(|V(G)|^3)$ time algorithm that tests, given a graph $G$, if $G$ contains $H$ as a topological subgraph (that is, a subdivision of $H$ is subgraph of $G$). This shows that topological subgraph testing is fixed-parameter tractable, resolving a longstanding open question of Downey and Fellows from 1992. As a corollary, for every $H$ we obtain an $O(|V(G)|^3)$ time algorithm that tests if there is an immersion of $H$ into a given graph $G$. This answers another open question raised by Downey and Fellows in 1992

From ab initio quantum chemistry to molecular dynamics: The delicate case of hydrogen bonding in ammonia

The ammonia dimer (NH3)2 has been investigated using high--level ab initio quantum chemistry methods and density functional theory (DFT). The structure and energetics of important isomers is obtained to unprecedented accuracy without resorting to experiment. The global minimum of eclipsed C_s symmetry is characterized by a significantly bent hydrogen bond which deviates from linearity by about 20 degrees. In addition, the so-called cyclic C_{2h} structure is extremely close in energy on an overall flat potential energy surface. It is demonstrated that none of the currently available (GGA, meta--GGA, and hybrid) density functionals satisfactorily describe the structure and relative energies of this nonlinear hydrogen bond. We present a novel density functional, HCTH/407+, designed to describe this sort of hydrogen bond quantitatively on the level of the dimer, contrary to e.g. the widely used BLYP functional. This improved functional is employed in Car-Parrinello ab initio molecular dynamics simulations of liquid ammonia to judge its performance in describing the associated liquid. Both the HCTH/407+ and BLYP functionals describe the properties of the liquid well as judged by analysis of radial distribution functions, hydrogen bonding structure and dynamics, translational diffusion, and orientational relaxation processes. It is demonstrated that the solvation shell of the ammonia molecule in the liquid phase is dominated by steric packing effects and not so much by directional hydrogen bonding interactions. In addition, the propensity of ammonia molecules to form bifurcated and multifurcated hydrogen bonds in the liquid phase is found to be negligibly small.Comment: Journal of Chemical Physics, in press (305335JCP

Quasi-chemical study of Be2+^{2+}(aq) speciation

Be$^{2+}$(aq) hydrolysis can to lead to the formation of multi-beryllium clusters, but the thermodynamics of this process has not been resolved theoretically. We study the hydration state of an isolated Be$^{2+}$ ion using both the quasi-chemical theory of solutions and ab initio molecular dynamics. These studies confirm that Be$^{2+}$(aq) is tetra-hydrated. The quasi-chemical approach is then applied to then the deprotonation of Be(H_2O)_4^{2+}} to give BeOH(H_2O)_3{}^{+}}. The calculated pK$_a$ of 3.8 is in good agreement with the experimentally suggested value around 3.5. The calculated energetics for the formation of BeOHBe$^{3+}$ are then obtained in fair agreement with experiments.Comment: 11 pages, 3 figure

Calibrating for Class Weights by Modeling Machine Learning

A much studied issue is the extent to which the confidence scores provided by machine learning algorithms are calibrated to ground truth probabilities. Our starting point is that calibration is seemingly incompatible with class weighting, a technique often employed when one class is less common (class imbalance) or with the hope of achieving some external objective (cost-sensitive learning). We provide a model-based explanation for this incompatibility and use our anthropomorphic model to generate a simple method of recovering likelihoods from an algorithm that is miscalibrated due to class weighting. We validate this approach in the binary pneumonia detection task of Rajpurkar, Irvin, Zhu, et al. (2017).Comment: 14 pages, 4 figure

Exponential Time Complexity of the Permanent and the Tutte Polynomial

We show conditional lower bounds for well-studied #P-hard problems: (a) The number of satisfying assignments of a 2-CNF formula with n variables cannot be counted in time exp(o(n)), and the same is true for computing the number of all independent sets in an n-vertex graph. (b) The permanent of an n x n matrix with entries 0 and 1 cannot be computed in time exp(o(n)). (c) The Tutte polynomial of an n-vertex multigraph cannot be computed in time exp(o(n)) at most evaluation points (x,y) in the case of multigraphs, and it cannot be computed in time exp(o(n/polylog n)) in the case of simple graphs. Our lower bounds are relative to (variants of) the Exponential Time Hypothesis (ETH), which says that the satisfiability of n-variable 3-CNF formulas cannot be decided in time exp(o(n)). We relax this hypothesis by introducing its counting version #ETH, namely that the satisfying assignments cannot be counted in time exp(o(n)). In order to use #ETH for our lower bounds, we transfer the sparsification lemma for d-CNF formulas to the counting setting

Process Mining for Advanced Service Analytics – From Process Efficiency to Customer Encounter and Experience

With the ongoing trend of servitization nurtured through digital technologies, the analysis of services as a starting point for improvement is gaining more and more importance. Service analytics has been defined as a concept to analyze the data generated during service execution to create value for providers and customers. To create more useful insights from the data, there is a continuous need for more advanced solutions for service analytics. One promising technology is process mining which has its origins in business process management. Our work provides insights into how process mining is currently used to analyze service processes and how it could be used along the service process. We find that process mining is increasingly applied for the analysis of the providers' internal operations, but more emphasis should be put on analyzing the customer interaction and experience

Ab initio molecular dynamics simulations of Aluminum solvation

The solvation of Al and its hydrolyzed species in water clusters has been studied by means of ab initio molecular dynamics simulations. The hexa-hydrate aluminum ion formed a stable complex in the finite temperature cluster simulation of one aluminum ion and 16 waters. The average dipole moment of strongly polarized hydrated water molecules in the first solvation shell of the hexa-hydrate aluminum ion was found to be 5.02 Debye. The deprotonated hexa-hydrate complex evolves into a tetra-coordinated aluminate ion with two water molecules in the second solvation shell forming hydrogen bonds to the hydroxyl groups in agreement with the observed coordination.Comment: 12 pages in Elsevier LaTeX, 5 figures in Postscript, 2 last figures are in color, submitted to Chemical Physics Letter

Enumerating Homomorphisms

The homomorphism problem for relational structures is an abstract way of formulating constraint satisfaction problems (CSP) and various problems in database theory. The decision version of the homomorphism problem received a lot of attention in literature; in particular, the way the graph-theoretical structure of the variables and constraints influences the complexity of the problem is intensively studied. Here we study the problem of enumerating all the solutions with polynomial delay from a similar point of view. It turns out that the enumeration problem behaves very differently from the decision version. We give evidence that it is unlikely that a characterization result similar to the decision version can be obtained. Nevertheless, we show nontrivial cases where enumeration can be done with polynomial delay

Selective nanomechanics of aromatic versus aliphatic thiolates on gold surfaces

Thiolated gold nanointerfaces play a key role in numerous fields of science, technology, as well as modern medicine to coat, functionalize, and protect. Our computational study reveals that the mechanical vs thermal stabilities of aliphatic thiolates on gold surfaces are strikingly different from those of aromatic thiolates. The aliphatic thiolates feature, at the same time, a higher thermal desorption energy but a lower mechanical rupture force than thiophenolates. Our analysis discloses that this most counterintuitive property is due to different mechanochemical detachment mechanisms. Electronic structure analyses along the detachment pathways trace this back to the distinct electronic properties of the S─Au bond in stretched nanojunctions. The discoveries that it is a higher thermal stability that entails a lower mechanical stability and that mechanical loads generate different local nanostructures depending on the nature of the thiolate are highly relevant for the rational design of improved thiol-gold nanocontacts