Artificial Symmetries for Calculating Vibrational Energies of Linear Molecules

Linear molecules usually represent a special case in rotational-vibrational calculations due to a singularity of the kinetic energy operator that arises from the rotation about the a (the principal axis of least moment of inertia, becoming the molecular axis at the linear equilibrium geometry) being undefined. Assuming the standard ro-vibrational basis functions, in the 3N−6 approach, of the form ∣∣ν1,ν2,νℓ33;J,k,m⟩ , tackling the unique difficulties of linear molecules involves constraining the vibrational and rotational functions with k=ℓ3 , which are the projections, in units of ℏ, of the corresponding angular momenta onto the molecular axis. These basis functions are assigned to irreducible representations (irreps) of the C2v (M) molecular symmetry group. This, in turn, necessitates purpose-built codes that specifically deal with linear molecules. In the present work, we describe an alternative scheme and introduce an (artificial) group that ensures that the condition ℓ3=k is automatically applied solely through symmetry group algebra. The advantage of such an approach is that the application of symmetry group algebra in ro-vibrational calculations is ubiquitous, and so this method can be used to enable ro-vibrational calculations of linear molecules in polyatomic codes with fairly minimal modifications. To this end, we construct a—formally infinite—artificial molecular symmetry group D∞h (AEM), which consists of one-dimensional (non-degenerate) irreducible representations and use it to classify vibrational and rotational basis functions according to ℓ and k. This extension to non-rigorous, artificial symmetry groups is based on cyclic groups of prime-order. Opposite to the usual scenario, where the form of symmetry adapted basis sets is dictated by the symmetry group the molecule belongs to, here the symmetry group D∞h (AEM) is built to satisfy properties for the convenience of the basis set construction and matrix elements calculations. We believe that the idea of purpose-built artificial symmetry groups can be useful in other applications

Self-similar length-displacement scaling achieved by scale-dependent growth processes: Evidence from the Atacama Fault System

The complex process of tip-propagation and growth of natural faults remains poorly understood. We analyse field structural data of strike-slip faults from the Atacama Fault System using fracture mechanics theory to depict the mechanical controls of fault growth in crystalline rocks. We calculate the displacement-length relationship of faults developed in the same rock type and tectonic regime, covering a range of five orders of magnitude, showing a linear scaling defined by dmax = 0.0337L^1.02. A multiple linear regression approach based on the cohesive end zone (CEZ) crack model was formulated to estimate the range of possible effective elastic moduli, cohesive endzone lengths, stress drops, and fracture energies from displacement distributions mapped on natural faults. Our results challenge the existent paradigm wherein the self-similarity of fault growth is only achieved under the condition of invariable stresses and elastic properties. We propose a model of self-similar fault growth with scale-dependent evolution of shear modulus, cohesive end zone length and stress drop. These results also have implications for determination of stress drop for small earthquakes that are consistent with recent advances in observational seismology

Transformation Properties under the Operations of the Molecular Symmetry Groups G36 and G36(EM) of Ethane H3CCH3

In the present work, we report a detailed description of the symmetry properties of the eight-atomic molecule ethane, with the aim of facilitating the variational calculations of rotation-vibration spectra of ethane and related molecules. Ethane consists of two methyl groups CH3 where the internal rotation (torsion) of one CH3 group relative to the other is of large amplitude and involves tunnelling between multiple minima of the potential energy function. The molecular symmetry group of ethane is the 36-element group G36, but the construction of symmetrised basis functions is most conveniently done in terms of the 72-element extended molecular symmetry group G36(EM). This group can subsequently be used in the construction of block-diagonal matrix representations of the ro-vibrational Hamiltonian for ethane. The derived transformation matrices associated with G36(EM) have been implemented in the variational nuclear motion program TROVE (Theoretical ROVibrational Energies). TROVE variational calculations are used as a practical example of a G36(EM) symmetry adaptation for large systems with a non-rigid, torsional degree of freedom. We present the derivation of irreducible transformation matrices for all 36 (72) operations of G36(M) (G36(EM)) and also describe algorithms for a numerical construction of these matrices based on a set of four (five) generators. The methodology presented is illustrated on the construction of the symmetry-adapted representations both of the potential energy function of ethane and of the rotation, torsion and vibration basis set functions

The Bregman chord divergence

Distances are fundamental primitives whose choice significantly impacts the performances of algorithms in machine learning and signal processing. However selecting the most appropriate distance for a given task is an endeavor. Instead of testing one by one the entries of an ever-expanding dictionary of {\em ad hoc} distances, one rather prefers to consider parametric classes of distances that are exhaustively characterized by axioms derived from first principles. Bregman divergences are such a class. However fine-tuning a Bregman divergence is delicate since it requires to smoothly adjust a functional generator. In this work, we propose an extension of Bregman divergences called the Bregman chord divergences. This new class of distances does not require gradient calculations, uses two scalar parameters that can be easily tailored in applications, and generalizes asymptotically Bregman divergences.Comment: 10 page

CDK-dependent nuclear localization of B-Cyclin Clb1 promotes FEAR activation during meiosis I in budding yeast

Cyclin-dependent kinases (CDK) are master regulators of the cell cycle in eukaryotes. CDK activity is regulated by the presence, post-translational modification and spatial localization of its regulatory subunit cyclin. In budding yeast, the B-cyclin Clb1 is phosphorylated and localizes to the nucleus during meiosis I. However the functional significance of Clb1's phosphorylation and nuclear localization and their mutual dependency is unknown. In this paper, we demonstrate that meiosis-specific phosphorylation of Clb1 requires its import to the nucleus but not vice versa. While Clb1 phosphorylation is dependent on activity of both CDK and polo-like kinase Cdc5, its nuclear localization requires CDK but not Cdc5 activity. Furthermore we show that increased nuclear localization of Clb1 during meiosis enhances activation of FEAR (Cdc Fourteen Early Anaphase Release) pathway. We discuss the significance of our results in relation to regulation of exit from meiosis I

Concurrent Validity of the Child Behavior Checklist DSM-Oriented Scales: Correspondence with DSM Diagnoses and Comparison to Syndrome Scales

This study used receiver operating characteristic (ROC) methodology and discriminative analyses to examine the correspondence of the Child Behavior Checklist (CBCL) rationally-derived DSM-oriented scales and empirically-derived syndrome scales with clinical diagnoses in a clinic-referred sample of children and adolescents (N = 476). Although results demonstrated that the CBCL Anxiety, Affective, Attention Deficit/Hyperactivity, Oppositional and Conduct Problems DSM-oriented scales corresponded significantly with related clinical diagnoses derived from parent-based structured interviews, these DSM-oriented scales did not evidence significantly greater correspondence with clinical diagnoses than the syndrome scales in all cases but one. The DSM-oriented Anxiety Problems scale was the only scale that evidenced significantly greater correspondence with diagnoses above its syndrome scale counterpart —the Anxious/Depressed scale. The recently developed and rationally-derived DSM-oriented scales thus generally do not add incremental clinical utility above that already afforded by the syndrome scales with respect to corresponding with diagnoses. Implications of these findings are discussed

The effect of downsizing on innovation outputs: The role of resource slack and constraints

Although the practice of downsizing is prevalent, its effects on organisational outcomes remain poorly understood. This article examines how and when downsizing affects organisational innovation. Using a unique data set of UK firms over a period of 22 years, we test the effect of downsizing on innovation outputs by considering the moderating role of resource slack and constraints. We argue and empirically demonstrate that downsizing has a dual effect on innovation, contingent on the firm’s level of resources. Our results reveal that downsizing affects innovation outputs positively in firms experiencing resource slack and negatively in firms experiencing resource constraints. We also show that the effect is more immediate in resource-constrained firms. Theoretical and managerial implications of these results are discussed

The renin‐angiotensin‐aldosterone system and its suppression

Peer Reviewedhttps://deepblue.lib.umich.edu/bitstream/2027.42/148403/1/jvim15454-sup-0001-supinfo.pdfhttps://deepblue.lib.umich.edu/bitstream/2027.42/148403/2/jvim15454-sup-0002-figures.pdfhttps://deepblue.lib.umich.edu/bitstream/2027.42/148403/3/jvim15454-sup-0005-TableS3.pdfhttps://deepblue.lib.umich.edu/bitstream/2027.42/148403/4/jvim15454-sup-0004-TableS2.pdfhttps://deepblue.lib.umich.edu/bitstream/2027.42/148403/5/jvim15454-sup-0007-TableS5.pdfhttps://deepblue.lib.umich.edu/bitstream/2027.42/148403/6/jvim15454_am.pdfhttps://deepblue.lib.umich.edu/bitstream/2027.42/148403/7/jvim15454.pdfhttps://deepblue.lib.umich.edu/bitstream/2027.42/148403/8/jvim15454-sup-0006-TableS4.pdfhttps://deepblue.lib.umich.edu/bitstream/2027.42/148403/9/jvim15454-sup-0003-TableS1.pd