Causal Geometry

Information geometry has offered a way to formally study the efficacy of scientific models by quantifying the impact of model parameters on the predicted effects. However, there has been little formal investigation of causation in this framework, despite causal models being a fundamental part of science and explanation. Here, we introduce causal geometry, which formalizes not only how outcomes are impacted by parameters, but also how the parameters of a model can be intervened upon. Therefore, we introduce a geometric version of “effective information”—a known measure of the informativeness of a causal relationship. We show that it is given by the matching between the space of effects and the space of interventions, in the form of their geometric congruence. Therefore, given a fixed intervention capability, an effective causal model is one that is well matched to those interventions. This is a consequence of “causal emergence,” wherein macroscopic causal relationships may carry more information than “fundamental” microscopic ones. We thus argue that a coarse-grained model may, paradoxically, be more informative than the microscopic one, especially when it better matches the scale of accessible interventions—as we illustrate on toy examples.     

Robust optimization in spline regression models for multi-model regulatory networks under polyhedral uncertainty

In our study, we integrate the data uncertainty of real-world models into our regulatory systems and robustify them. We newly introduce and analyse robust time-discrete target–environment regulatory systems under polyhedral uncertainty through robust optimization. Robust optimization has reached a great importance as a modelling framework for immunizing against parametric uncertainties and the integration of uncertain data is of considerable importance for the model’s reliability of a highly interconnected system. Then, we present a numerical example to demonstrate the efficiency of our new robust regression method for regulatory networks. The results indicate that our approach can successfully approximate the target–environment interaction, based on the expression values of all targets and environmental factors.     

Constructions of categories of setoids from proof-irrelevant families

When formalizing mathematics in constructive type theories, or more practically in proof assistants such as Coq or Agda, one is often using setoids (types with explicit equivalence relations). In this note we consider two categories of setoids with equality on objects and show, within intensional Martin-Löf type theory, that they are isomorphic. Both categories are constructed from a fixed proof-irrelevant family F of setoids. The objects of the categories form the index setoid I of the family, whereas the definition of arrows differs. The first category has for arrows triples \((a,b,f:F(a)\,\rightarrow \,F(b))\) where f is an extensional function. Two such arrows are identified if appropriate composition with transportation maps (given by F) makes them equal. In the second category the arrows are triples \((a,b,R \hookrightarrow \Sigma (I,F)^2)\) where R is a total functional relation between the subobjects \(F(a), F(b) \hookrightarrow \Sigma (I,F)\) of the setoid sum of the family. This category is simpler to use as the transportation maps disappear. Moreover we also show that the full image of a category along an E-functor into an E-category is a category.     

Where Does the Electron Go? Stable and Metastable Peptide Cation Radicals Formed by Electron Transfer

Electron transfer to doubly and triply charged heptapeptide ions containing polar residues Arg, Lys, and Asp in combination with nonpolar Gly, Ala, and Pro or Leu generates stable and metastable charge-reduced ions, (M + 2H)^+●, in addition to standard electron-transfer dissociation (ETD) fragment ions. The metastable (M + 2H)^+● ions spontaneously dissociate upon resonant ejection from the linear ion trap, giving irregularly shaped peaks with offset m/z values. The fractions of stable and metastable (M + 2H)^+● ions and their mass shifts depend on the presence of Pro-4 and Leu-4 residues in the peptides, with the Pro-4 sequences giving larger fractions of the stable ions while showing smaller mass shifts for the metastables. Conversion of the Asp and C-terminal carboxyl groups to methyl esters further lowers the charge-reduced ion stability. Collisional activation and photodissociation at 355 nm of mass-selected (M + 2H)^+● results in different dissociations that give sequence specific MS³ spectra. With a single exception of charge-reduced (LKGLADR + 2H)^+●, the MS³ spectra do not produce ETD sequence fragments of the c and z type. Hence, these (M + 2H)^+● ions are covalent radicals, not ion–molecule complexes, undergoing dramatically different dissociations in the ground and excited electronic states. The increased stability of the Pro-4 containing (M + 2H)^+● ions is attributed to radicals formed by opening of the Pro ring and undergoing further stabilization by hydrogen atom migrations. UV–VIS photodissociation action spectroscopy and time-dependent density functional theory calculations are used in a case in point study of the stable (LKGPADR + 2H)^+● ion produced by ETD. In contrast to singly-reduced peptide ions, doubly reduced (M + 3H)⁺ ions are stable only when formed from the Pro-4 precursors and show all characteristics of even electron ions regarding no photon absorption at 355 nm or ion-molecule reactions, and exhibiting proton driven collision induced dissociations.

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Determination of exciton-phonon coupling elements in single-walled carbon nanotubes by Raman overtone analysis

Raman excitation profiles are obtained and compared for carbon nanotube radial breathing mode (RBM) fundamental and overtone vibrations for 5 specific chiralities. Fitting of the Raman excitation data is performed using Raman transform theory. The Huang-Rhys factors obtained from the modeling are directly related to the magnitude of the RBM exciton-phonon coupling element, which is shown to be in a weak coupling limit. The values of exciton-phonon coupling strengths and the possible role of revealed non-Condon effects are in agreement with quantum-chemical modeling.     

Third and fourth optical transitions in semiconducting carbon nanotubes

We have studied the optical transition energies of single-wall carbon nanotubes over broad diameter (0.7-2.3 nm) and energy (1.26-2.71 eV) ranges, using their radial breathing mode Raman spectra. We establish the diameter and chiral angle dependence of the poorly studied third and fourth optical transitions in semiconducting tubes. Comparative analysis between the higher lying transitions and the first and second transitions show two different diameter scalings. Quantum mechanical calculations explain the result showing strongly bound excitons in the first and second transitions and a delocalized electron wave function in the third transition.     

A novel improved method for analysis of 2D diffusion-relaxation data--2D PARAFAC-Laplace decomposition

This paper demonstrates how the multi-linear PARAFAC model can with advantage be used to decompose 2D diffusion-relaxation correlation NMR spectra prior to 2D-Laplace inversion to the T(2)-D domain. The decomposition is advantageous for better interpretation of the complex correlation maps as well as for the quantification of extracted T(2)-D components. To demonstrate the new method seventeen mixtures of wheat flour, starch, gluten, oil and water were prepared and measured with a 300 MHz nuclear magnetic resonance (NMR) spectrometer using a pulsed gradient stimulated echo (PGSTE) pulse sequence followed by a Carr-Purcell-Meiboom-Gill (CPMG) pulse echo train. By varying the gradient strength, 2D diffusion-relaxation data were recorded for each sample. From these double exponentially decaying relaxation data the PARAFAC algorithm extracted two unique diffusion-relaxation components, explaining 99.8% of the variation in the data set. These two components were subsequently transformed to the T(2)-D domain using 2D-inverse Laplace transformation and quantitatively assigned to the oil and water components of the samples. The oil component was one distinct distribution with peak intensity at D=3 x 10(-12) m(2) s(-1) and T(2)=180 ms. The water component consisted of two broad populations of water molecules with diffusion coefficients and relaxation times centered around correlation pairs: D=10(-9) m(2) s(-1), T(2)=10 ms and D=3 x 10(-13) m(2) s(-1), T(2)=13 ms. Small spurious peaks observed in the inverse Laplace transformation of original complex data were effectively filtered by the PARAFAC decomposition and thus considered artefacts from the complex Laplace transformation. The oil-to-water ratio determined by PARAFAC followed by 2D-Laplace inversion was perfectly correlated with known oil-to-water ratio of the samples. The new method of using PARAFAC prior to the 2D-Laplace inversion proved to have superior potential in analysis of diffusion-relaxation spectra, as it improves not only the interpretation, but also the quantification.     

Influence of molecular geometry on the adsorption orientation for oligophenylene-ethynylenes on Au(111)

The adsorption structures formed from a class of oligophenylene-ethynylenes on Au(111) under ultrahigh vacuum conditions is compared based on high-resolution scanning tunneling microscopy (STM) measurements. The molecules consist of three or four benzene rings connected by ethynylene spokes and are all functionalized identically with an aldehyde, a hydroxyl, and a bulky tert-butyl group. Compounds with the conjugated spokes placed in the para, meta, and threefold configurations were previously found to exclusively form molecular layers with flat-lying adsorption geometries. In contrast, the associated compound with spokes in the ortho configuration surprisingly differs in its adsorption by forming only structures with an upright adsorption orientation. The packing density for the structures formed by the compound with the ortho configuration is less dense than that in conventional self-assembled monolayers while still keeping the conducting backbone in an upright orientation. These structures are thus interesting from the perspective of performing single-molecule conduction measurements on the oligophenylene-ethynylene backbones.     

Evaporation of femtoliter sessile droplets monitored with nanomechanical mass sensors

We present a time-resolved study of the evaporation in air of minuscule sessile droplets deposited by nanodispensing techniques. Highly sensitive nanomechanical resonators are designed to monitor in time the mass variation of evaporating liquid droplets. The precision of the measurement setup enables the study of droplets with diameters in the 1 mum range, which correspond to volumes of femtoliters and smaller, 9 orders of magnitude smaller than most of presently published data. Experimental data are compared with macroscopic models.     

Coarse-grained molecular dynamics modeling of strongly associating fluids: thermodynamics, liquid structure, and dynamics of symmetric binary mixture fluids

Symmetric binary mixtures capable of strong association via a highly directional and saturable specific interaction between unlike molecules are investigated by canonical molecular dynamics simulations. The specific interaction of the molecules is defined in a new coarse-grained pair potential that can be applied in continuous molecular dynamics as well as in Monte Carlo simulations. The thermodynamic, structural, and dynamic properties of the associating mixture fluids are investigated as a function of density, temperature, and association strength of the specific interaction. Detailed analysis of the simulation data confirms a two-stage mechanism in the formation of specific bonds with increasing interaction strength, including a fast dimerization process and a subsequent stage of perfecting the bonds. A large heat capacity peak is found during the formation or breaking of the bonds, reflecting the large energy fluctuation introduced by the strong association. The fractions of nonbonded molecules obtained from the simulations as a function of density, temperature, and interaction strength are in excellent agreement with the predictions of Wertheim's thermodynamic perturbation theory. The translational and rotational dynamics of the Tmer mixture are effectively retarded with increasing association strength and are analyzed in terms of autocorrelation functions and a non-Gaussian parameter for the translational dynamics. The lifetimes of molecules in bonded and nonbonded states provide detailed information about the transformation of molecules between the bonded state and the nonbonded state. Finally, simulation sampling problems inherent to strongly interacting systems are easily overcome using the parallel tempering simulation technique. This latter result confirms that with the new continuous coarse-grained simulation potential we have a versatile and flexible interaction potential that can be used with many available molecular dynamics and Monte Carlo algorithms under various ensembles.