Towards an effective potential for the monomer, dimer, hexamer, solid and liquid forms of hydrogen fluoride

We present an attempt to build up a new two-body effective potential for hydrogen fluoride, fitted to theoretical and experimental data relevant not only to the gas and liquid phases, but also to the crystal. The model is simple enough to be used in Molecular Dynamics and Monte Carlo simulations. The potential consists of: a) an intra-molecular contribution, allowing for variations of the molecular length, plus b) an inter-molecular part, with three charged sites on each monomer and a Buckingham "exp-6" interaction between fluorines. The model is able to reproduce a significant number of observables on the monomer, dimer, hexamer, solid and liquid forms of HF. The shortcomings of the model are pointed out and possible improvements are finally discussed.Comment: LaTeX, 24 pages, 2 figures. For related papers see also http://www.chim.unifi.it:8080/~valle

Exponential families of mixed Poisson distributions

If I=(I1,…,Id) is a random variable on [0,∞)d with distribution μ(dλ1,…,dλd), the mixed Poisson distribution MP(μ) on View the MathML source is the distribution of (N1(I1),…,Nd(Id)) where N1,…,Nd are ordinary independent Poisson processes which are also independent of I. The paper proves that if F is a natural exponential family on [0,∞)d then MP(F) is also a natural exponential family if and only if a generating probability of F is the distribution of v0+v1Y1+cdots, three dots, centered+vqYq for some qless-than-or-equals, slantd, for some vectors v0,…,vq of [0,∞)d with disjoint supports and for independent standard real gamma random variables Y1,…,Yq

Families of spectral sets for Bernoulli convolutions

In this paper, we study the harmonic analysis of Bernoulli measures. We show a variety of orthonormal Fourier bases for the L^2 Hilbert spaces corresponding to certain Bernoulli measures, making use of contractive transfer operators. For other cases, we exhibit maximal Fourier families that are not orthonormal bases.Comment: 25 pages, same result

Double Whammy - How ICT Projects are Fooled by Randomness and Screwed by Political Intent

The cost-benefit analysis formulates the holy trinity of objectives of project management - cost, schedule, and benefits. As our previous research has shown, ICT projects deviate from their initial cost estimate by more than 10% in 8 out of 10 cases. Academic research has argued that Optimism Bias and Black Swan Blindness cause forecasts to fall short of actual costs. Firstly, optimism bias has been linked to effects of deception and delusion, which is caused by taking the inside-view and ignoring distributional information when making decisions. Secondly, we argued before that Black Swan Blindness makes decision-makers ignore outlying events even if decisions and judgements are based on the outside view. Using a sample of 1,471 ICT projects with a total value of USD 241 billion - we answer the question: Can we show the different effects of Normal Performance, Delusion, and Deception? We calculated the cumulative distribution function (CDF) of (actual-forecast)/forecast. Our results show that the CDF changes at two tipping points - the first one transforms an exponential function into a Gaussian bell curve. The second tipping point transforms the bell curve into a power law distribution with the power of 2. We argue that these results show that project performance up to the first tipping point is politically motivated and project performance above the second tipping point indicates that project managers and decision-makers are fooled by random outliers, because they are blind to thick tails. We then show that Black Swan ICT projects are a significant source of uncertainty to an organisation and that management needs to be aware of

Unitary groups and spectral sets

We study spectral theory for bounded Borel subsets of \br and in particular finite unions of intervals. For Hilbert space, we take $L^2$ of the union of the intervals. This yields a boundary value problem arising from the minimal operator \Ds = \frac1{2\pi i}\frac{d}{dx} with domain consisting of $C^\infty$ functions vanishing at the endpoints. We offer a detailed interplay between geometric configurations of unions of intervals and a spectral theory for the corresponding selfadjoint extensions of \Ds and for the associated unitary groups of local translations. While motivated by scattering theory and quantum graphs, our present focus is on the Fuglede-spectral pair problem. Stated more generally, this problem asks for a determination of those bounded Borel sets $\Omega$ in \br^k such that $L^2(\Omega)$ has an orthogonal basis of Fourier frequencies (spectrum), i.e., a total set of orthogonal complex exponentials restricted to $\Omega$. In the general case, we characterize Borel sets $\Omega$ having this spectral property in terms of a unitary representation of (\br, +) acting by local translations. The case of $k = 1$ is of special interest, hence the interval-configurations. We give a characterization of those geometric interval-configurations which allow Fourier spectra directly in terms of the selfadjoint extensions of the minimal operator \Ds. This allows for a direct and explicit interplay between geometry and spectra. As an application, we offer a new look at the Universal Tiling Conjecture and show that the spectral-implies-tile part of the Fuglede conjecture is equivalent to it and can be reduced to a variant of the Fuglede conjecture for unions of integer intervals.Comment: We improved the paper and partition it into several independent part

How interface geometry dictates water's thermodynamic signature in hydrophobic association

As a common view the hydrophobic association between molecular-scale binding partners is supposed to be dominantly driven by entropy. Recent calorimetric experiments and computer simulations heavily challenge this established paradigm by reporting that water's thermodynamic signature in the binding of small hydrophobic ligands to similar-sized apolar pockets is enthalpy-driven. Here we show with purely geometric considerations that this controversy can be resolved if the antagonistic effects of concave and convex bending on water interface thermodynamics are properly taken into account. A key prediction of this continuum view is that for fully complementary binding of the convex ligand to the concave counterpart, water shows a thermodynamic signature very similar to planar (large-scale) hydrophobic association, that is, enthalpy-dominated, and hardly depends on the particular pocket/ligand geometry. A detailed comparison to recent simulation data qualitatively supports the validity of our perspective down to subnanometer scales. Our findings have important implications for the interpretation of thermodynamic signatures found in molecular recognition and association processes. Furthermore, traditional implicit solvent models may benefit from our view with respect to their ability to predict binding free energies and entropies.Comment: accepted for publication in J. Stat. Phys., special issue on water&associated liquid