Jensen's Operator Inequality

We establish what we consider to be the definitive versions of Jensen's operator inequality and Jensen's trace inequality for functions defined on an interval. This is accomplished by the introduction of genuine non-commutative convex combinations of operators, as opposed to the contractions used in earlier versions of the theory. As a consequence, we no longer need to impose conditions on the interval of definition. We show how this relates to the pinching inequality of Davis, and how Jensen's trace inequlity generalizes to C*-algebras..Comment: 12 p

Convex Multivariable Trace Functions

For any densely defined, lower semi-continuous trace \tau on a C*-algebra A with mutually commuting C*-subalgebras A_1, A_2, ... A_n, and a convex function f of n variables, we give a short proof of the fact that the function (x_1, x_2, ..., x_n) --> \tau (f(x_1, x_2, ..., x_n)) is convex on the space \bigoplus_{i=1}^n (A_i)_{self-adjoint}. If furthermore the function f is log-convex or root-convex, so is the corresponding trace function. We also introduce a generalization of log-convexity and root-convexity called \ell-convexity, show how it applies to traces, and give a few examples. In particular we show that the trace of an operator mean is always dominated by the corresponding mean of the trace values.Comment: 13 pages, AMS TeX, Some remarks and results adde

A Ginsparg-Wilson approach to lattice CP\mathcal{CP} symmetry

There is a long standing challenge in lattice QCD concerning the relationship between $\mathcal{CP}$-symmetry and lattice chiral symmetry: na\"ively the chiral symmetry transformations are not invariant under $\mathcal{CP}$. With results similar to a recent work by Igarashi and Pawlowski, I show that this is because charge conjugation symmetry has been incorrectly realised on the lattice. The naive approach, to directly use the continuum charge conjugation relations on the lattice, fails because the renormalisation group blockings required to construct a doubler free lattice theory from the continuum are not invariant under charge conjugation. Correctly taking into account the transformation of these blockings leads to a modified lattice $\mathcal{CP}$ symmetry for the fermion fields, which, for gauge field configurations with trivial topology, has a smooth limit to continuum $\mathcal{CP}$ as the lattice spacing tends to zero. After constructing $\mathcal{CP}$ transformations for one particular group of lattice chiral symmetries, I construct a lattice chiral gauge theory which is $\mathcal{CP}$ invariant and whose measure is invariant under gauge transformations and $\mathcal{CP}$.Comment: 7 pages, Lattice 2010 (Theoretical Developments

Trajectories of Big Five Personality Traits: A Coordinated Analysis of 16 Longitudinal Samples

This study assessed change in self‐reported Big Five personality traits. We conducted a coordinated integrative data analysis using data from 16 longitudinal samples, comprising a total sample of over 60 000 participants. We coordinated models across multiple datasets and fit identical multi‐level growth models to assess and compare the extent of trait change over time. Quadratic change was assessed in a subset of samples with four or more measurement occasions. Across studies, the linear trajectory models revealed declines in conscientiousness, extraversion, and openness. Non‐linear models suggested late‐life increases in neuroticism. Meta‐analytic summaries indicated that the fixed effects of personality change are somewhat heterogeneous and that the variability in trait change is partially explained by sample age, country of origin, and personality measurement method. We also found mixed evidence for predictors of change, specifically for sex and baseline age. This study demonstrates the importance of coordinated conceptual replications for accelerating the accumulation of robust and reliable findings in the lifespan developmental psychological sciences. © 2020 European Association of Personality PsychologyPeer Reviewedhttps://deepblue.lib.umich.edu/bitstream/2027.42/156004/1/per2259.pdfhttps://deepblue.lib.umich.edu/bitstream/2027.42/156004/2/per2259-sup-0001-Data_S1.pdfhttps://deepblue.lib.umich.edu/bitstream/2027.42/156004/3/per2259-sup-0002-Open_Practices_Disclosure_Form.pdfhttps://deepblue.lib.umich.edu/bitstream/2027.42/156004/4/per2259_am.pd