Partition Functions in Statistical Mechanics, Symmetric Functions, and Group Representations

Partition functions for non-interacting particles are known to be symmetric functions. It is shown that powerful group-theoretical techniques can be used not only to derive these relationships, but also to significantly simplify calculation of the partition functions for particles that carry internal quantum numbers. The partition function is shown to be a sum of one or more group characters. The utility of character expansions in calculating the partition functions is explored. Several examples are given to illustrate these techniques.Comment: 16 pages of RevTe

The self and others in the experience of pride

Pride is seen as both a self-conscious emotion as well as a social emotion. These categories are not mutually exclusive, but have brought forth different ideas about pride as either revolving around the self or as revolving around one’s relationship with others. Current measures of pride do not include intrapersonal elements of pride experiences. Social comparisons, which often cause experiences of pride, contain three elements: the self, the relationship between the self and another person, and the other person. From the literature on pride, we distilled three related elements; perceptions and feelings of self-inflation, other-distancing, and other-devaluation. In four studies, we explored whether these elements were present in pride experiences. We did so at an implicit (Experiment 1; N = 218) and explicit level (Experiment 2; N = 125), in an academic setting with in vivo (Experiment 3; N = 203) and imagined pride experiences (Experiment 4; N = 126). The data consistently revealed that the experience of pride is characterised by self-inflation, not by other-distancing nor other-devaluation

The Physics of Ultraperipheral Collisions at the LHC

We discuss the physics of large impact parameter interactions at the LHC: ultraperipheral collisions (UPCs). The dominant processes in UPCs are photon-nucleon (nucleus) interactions. The current LHC detector configurations can explore small $x$ hard phenomena with nuclei and nucleons at photon-nucleon center-of-mass energies above 1 TeV, extending the $x$ range of HERA by a factor of ten. In particular, it will be possible to probe diffractive and inclusive parton densities in nuclei using several processes. The interaction of small dipoles with protons and nuclei can be investigated in elastic and quasi-elastic $J/\psi$ and $\Upsilon$ production as well as in high $t$ $\rho^0$ production accompanied by a rapidity gap. Several of these phenomena provide clean signatures of the onset of the new high gluon density QCD regime. The LHC is in the kinematic range where nonlinear effects are several times larger than at HERA. Two-photon processes in UPCs are also studied. In addition, while UPCs play a role in limiting the maximum beam luminosity, they can also be used a luminosity monitor by measuring mutual electromagnetic dissociation of the beam nuclei. We also review similar studies at HERA and RHIC as well as describe the potential use of the LHC detectors for UPC measurements.Comment: 229 Pages, 121 figure

Cellular and ultrastructural characterization of the grey-morph phenotype in southern right whales (Eubalaena australis)

Southern right whales (SRWs, Eubalena australis) are polymorphic for an X-linked pigmentation pattern known as grey morphism. Most SRWs have completely black skin with white patches on their bellies and occasionally on their backs; these patches remain white as the whale ages. Grey morphs (previously referred to as partial albinos) appear mostly white at birth, with a splattering of rounded black marks; but as the whales age, the white skin gradually changes to a brownish grey color. The cellular and developmental bases of grey morphism are not understood. Here we describe cellular and ultrastructural features of grey-morph skin in relation to that of normal, wild-type skin. Melanocytes were identified histologically and counted, and melanosomes were measured using transmission electron microscopy. Grey-morph skin had fewer melanocytes when compared to wild-type skin, suggesting reduced melanocyte survival, migration, or proliferation in these whales. Grey-morph melanocytes had smaller melanosomes relative to wild-type skin, normal transport of melanosomes to surrounding keratinocytes, and normal localization of melanin granules above the keratinocyte nuclei. These findings indicate that SRW grey-morph pigmentation patterns are caused by reduced numbers of melanocytes in the skin, as well as by reduced amounts of melanin production and/or reduced sizes of mature melanosomes. Grey morphism is distinct from piebaldism and albinism found in other species, which are genetic pigmentation conditions resulting from the local absence of melanocytes, or the inability to synthesize melanin, respectively

Regulatory control and the costs and benefits of biochemical noise

Experiments in recent years have vividly demonstrated that gene expression can be highly stochastic. How protein concentration fluctuations affect the growth rate of a population of cells, is, however, a wide open question. We present a mathematical model that makes it possible to quantify the effect of protein concentration fluctuations on the growth rate of a population of genetically identical cells. The model predicts that the population's growth rate depends on how the growth rate of a single cell varies with protein concentration, the variance of the protein concentration fluctuations, and the correlation time of these fluctuations. The model also predicts that when the average concentration of a protein is close to the value that maximizes the growth rate, fluctuations in its concentration always reduce the growth rate. However, when the average protein concentration deviates sufficiently from the optimal level, fluctuations can enhance the growth rate of the population, even when the growth rate of a cell depends linearly on the protein concentration. The model also shows that the ensemble or population average of a quantity, such as the average protein expression level or its variance, is in general not equal to its time average as obtained from tracing a single cell and its descendants. We apply our model to perform a cost-benefit analysis of gene regulatory control. Our analysis predicts that the optimal expression level of a gene regulatory protein is determined by the trade-off between the cost of synthesizing the regulatory protein and the benefit of minimizing the fluctuations in the expression of its target gene. We discuss possible experiments that could test our predictions.Comment: Revised manuscript;35 pages, 4 figures, REVTeX4; to appear in PLoS Computational Biolog

The authorial delusion: counting lady Macbeth’s children

In 1933, literary critic L. C. Knights published a caustic essay against the notion cultivated by certain of his colleagues, predominantly A. C. Bradley, that Shakespeare is a ‘great creator of characters’. Knights (1973) regarded the examination of isolated particles such as ‘character’ as disorientating, alleging that an analysis of this sort obscures the greater merit of language. Knight’s polemic essentially stands in the threshold of the dissention between formalists and realists: the former consider the examination of the fictional narrative as anything but a textual construct a scholarly faux pas; the latter regard the referential relationship between text and the world as a foundation for the creation of fiction. This is a pseudo-dilemma. The notion that literature is denuded of its artistic merit once it is defined by its constituent artefacts is disorienting, for it completely bypasses the dynamics of its creation. Put differently, a post-event analysis can exist as a standalone act, albeit it cannot challenge or dismiss the foundational principles of the event’s creation process

Red Queen Coevolution on Fitness Landscapes

Species do not merely evolve, they also coevolve with other organisms. Coevolution is a major force driving interacting species to continuously evolve ex- ploring their fitness landscapes. Coevolution involves the coupling of species fit- ness landscapes, linking species genetic changes with their inter-specific ecological interactions. Here we first introduce the Red Queen hypothesis of evolution com- menting on some theoretical aspects and empirical evidences. As an introduction to the fitness landscape concept, we review key issues on evolution on simple and rugged fitness landscapes. Then we present key modeling examples of coevolution on different fitness landscapes at different scales, from RNA viruses to complex ecosystems and macroevolution.Comment: 40 pages, 12 figures. To appear in "Recent Advances in the Theory and Application of Fitness Landscapes" (H. Richter and A. Engelbrecht, eds.). Springer Series in Emergence, Complexity, and Computation, 201

Isolation of Flow and Nonflow Correlations by Two- and Four-Particle Cumulant Measurements of Azimuthal Harmonics in sNN=\sqrt{s_{_{\rm NN}}} = 200 GeV Au+Au Collisions

A data-driven method was applied to measurements of Au+Au collisions at $\sqrt{s_{_{\rm NN}}} =$ 200 GeV made with the STAR detector at RHIC to isolate pseudorapidity distance $\Delta\eta$-dependent and $\Delta\eta$-independent correlations by using two- and four-particle azimuthal cumulant measurements. We identified a component of the correlation that is $\Delta\eta$-independent, which is likely dominated by anisotropic flow and flow fluctuations. It was also found to be independent of $\eta$ within the measured range of pseudorapidity $|\eta|<1$. The relative flow fluctuation was found to be $34\% \pm 2\% (stat.) \pm 3\% (sys.)$ for particles of transverse momentum $p_{T}$ less than $2$ GeV/$c$. The $\Delta\eta$-dependent part may be attributed to nonflow correlations, and is found to be $5\% \pm 2\% (sys.)$ relative to the flow of the measured second harmonic cumulant at $|\Delta\eta| > 0.7$

Measurements of D0D^{0} and D∗D^{*} Production in pp + pp Collisions at s\sqrt{s} = 200 GeV

We report measurements of charmed-hadron ($D^{0}$, $D^{*}$) production cross sections at mid-rapidity in $p$ + $p$ collisions at a center-of-mass energy of 200 GeV by the STAR experiment. Charmed hadrons were reconstructed via the hadronic decays $D^{0}\rightarrow K^{-}\pi^{+}$, $D^{*+}\rightarrow D^{0}\pi^{+}\rightarrow K^{-}\pi^{+}\pi^{+}$ and their charge conjugates, covering the $p_T$ range of 0.6$-$2.0 GeV/$c$ and 2.0$-$6.0 GeV/$c$ for $D^{0}$ and $D^{*+}$, respectively. From this analysis, the charm-pair production cross section at mid-rapidity is $d\sigma/dy|_{y=0}^{c\bar{c}}$ = 170 $\pm$ 45 (stat.) $^{+38}_{-59}$ (sys.) $\mu$b. The extracted charm-pair cross section is compared to perturbative QCD calculations. The transverse momentum differential cross section is found to be consistent with the upper bound of a Fixed-Order Next-to-Leading Logarithm calculation.Comment: 15 pages, 16 figures. Revised version submitted to Phys. Rev.