On defining the Hamiltonian beyond quantum theory

Energy is a crucial concept within classical and quantum physics. An essential tool to quantify energy is the Hamiltonian. Here, we consider how to define a Hamiltonian in general probabilistic theories, a framework in which quantum theory is a special case. We list desiderata which the definition should meet. For 3-dimensional systems, we provide a fully-defined recipe which satisfies these desiderata. We discuss the higher dimensional case where some freedom of choice is left remaining. We apply the definition to example toy theories, and discuss how the quantum notion of time evolution as a phase between energy eigenstates generalises to other theories.Comment: Authors' accepted manuscript for inclusion in the Foundations of Physics topical collection on Foundational Aspects of Quantum Informatio

A generative inference framework for analysing patterns of cultural change in sparse population data with evidence for fashion trends in LBK culture

Cultural change can be quantified by temporal changes in frequency of different cultural artefacts and it is a central question to identify what underlying cultural transmission processes could have caused the observed frequency changes. Observed changes, however, often describe the dynamics in samples of the population of artefacts, whereas transmission processes act on the whole population. Here we develop a modelling framework aimed at addressing this inference problem. To do so, we firstly generate population structures from which the observed sample could have been drawn randomly and then determine theoretical samples at a later time t2 produced under the assumption that changes in frequencies are caused by a specific transmission process. Thereby we also account for the potential effect of time-averaging processes in the generation of the observed sample. Subsequent statistical comparisons (e.g. using Bayesian inference) of the theoretical and observed samples at t2 can establish which processes could have produced the observed frequency data. In this way, we infer underlying transmission processes directly from available data without any equilibrium assumption. We apply this framework to a dataset describing pottery from settlements of some of the first farmers in Europe (the LBK culture) and conclude that the observed frequency dynamic of different types of decorated pottery is consistent with age-dependent selection, a preference for 'young' pottery types which is potentially indicative of fashion trends

Bilayer manganites: polarons in the midst of a metallic breakdown

The exact nature of the low temperature electronic phase of the manganite materials family, and hence the origin of their colossal magnetoresistant (CMR) effect, is still under heavy debate. By combining new photoemission and tunneling data, we show that in La{2-2x}Sr{1+2x}Mn2O7 the polaronic degrees of freedom win out across the CMR region of the phase diagram. This means that the generic ground state is that of a system in which strong electron-lattice interactions result in vanishing coherent quasi-particle spectral weight at the Fermi level for all locations in k-space. The incoherence of the charge carriers offers a unifying explanation for the anomalous charge-carrier dynamics seen in transport, optics and electron spectroscopic data. The stacking number N is the key factor for true metallic behavior, as an intergrowth-driven breakdown of the polaronic domination to give a metal possessing a traditional Fermi surface is seen in the bilayer system.Comment: 7 pages, 2 figures, includes supplementary informatio

Formation of regulatory modules by local sequence duplication

Turnover of regulatory sequence and function is an important part of molecular evolution. But what are the modes of sequence evolution leading to rapid formation and loss of regulatory sites? Here, we show that a large fraction of neighboring transcription factor binding sites in the fly genome have formed from a common sequence origin by local duplications. This mode of evolution is found to produce regulatory information: duplications can seed new sites in the neighborhood of existing sites. Duplicate seeds evolve subsequently by point mutations, often towards binding a different factor than their ancestral neighbor sites. These results are based on a statistical analysis of 346 cis-regulatory modules in the Drosophila melanogaster genome, and a comparison set of intergenic regulatory sequence in Saccharomyces cerevisiae. In fly regulatory modules, pairs of binding sites show significantly enhanced sequence similarity up to distances of about 50 bp. We analyze these data in terms of an evolutionary model with two distinct modes of site formation: (i) evolution from independent sequence origin and (ii) divergent evolution following duplication of a common ancestor sequence. Our results suggest that pervasive formation of binding sites by local sequence duplications distinguishes the complex regulatory architecture of higher eukaryotes from the simpler architecture of unicellular organisms

DNA intercalator stimulates influenza transcription and virus replication

Influenza A virus uses its host transcription machinery to facilitate viral RNA synthesis, an event that is associated with cellular RNA polymerase II (RNAPII). In this study, various RNAPII transcription inhibitors were used to investigate the effect of RNAPII phosphorylation status on viral RNA transcription. A low concentration of DNA intercalators, such as actinomycin D (ActD), was found to stimulate viral polymerase activity and virus replication. This effect was not observed in cells treated with RNAPII kinase inhibitors. In addition, the loss of RNAPIIa in infected cells was due to the shift of nonphosphorylated RNAPII (RNAPIIa) to hyperphosphorylated RNAPII (RNAPIIo)

Monotonicity of Fitness Landscapes and Mutation Rate Control

A common view in evolutionary biology is that mutation rates are minimised. However, studies in combinatorial optimisation and search have shown a clear advantage of using variable mutation rates as a control parameter to optimise the performance of evolutionary algorithms. Much biological theory in this area is based on Ronald Fisher's work, who used Euclidean geometry to study the relation between mutation size and expected fitness of the offspring in infinite phenotypic spaces. Here we reconsider this theory based on the alternative geometry of discrete and finite spaces of DNA sequences. First, we consider the geometric case of fitness being isomorphic to distance from an optimum, and show how problems of optimal mutation rate control can be solved exactly or approximately depending on additional constraints of the problem. Then we consider the general case of fitness communicating only partial information about the distance. We define weak monotonicity of fitness landscapes and prove that this property holds in all landscapes that are continuous and open at the optimum. This theoretical result motivates our hypothesis that optimal mutation rate functions in such landscapes will increase when fitness decreases in some neighbourhood of an optimum, resembling the control functions derived in the geometric case. We test this hypothesis experimentally by analysing approximately optimal mutation rate control functions in 115 complete landscapes of binding scores between DNA sequences and transcription factors. Our findings support the hypothesis and find that the increase of mutation rate is more rapid in landscapes that are less monotonic (more rugged). We discuss the relevance of these findings to living organisms

Wide-Scale Analysis of Human Functional Transcription Factor Binding Reveals a Strong Bias towards the Transcription Start Site

We introduce a novel method to screen the promoters of a set of genes with shared biological function, against a precompiled library of motifs, and find those motifs which are statistically over-represented in the gene set. The gene sets were obtained from the functional Gene Ontology (GO) classification; for each set and motif we optimized the sequence similarity score threshold, independently for every location window (measured with respect to the TSS), taking into account the location dependent nucleotide heterogeneity along the promoters of the target genes. We performed a high throughput analysis, searching the promoters (from 200bp downstream to 1000bp upstream the TSS), of more than 8000 human and 23,000 mouse genes, for 134 functional Gene Ontology classes and for 412 known DNA motifs. When combined with binding site and location conservation between human and mouse, the method identifies with high probability functional binding sites that regulate groups of biologically related genes. We found many location-sensitive functional binding events and showed that they clustered close to the TSS. Our method and findings were put to several experimental tests. By allowing a "flexible" threshold and combining our functional class and location specific search method with conservation between human and mouse, we are able to identify reliably functional TF binding sites. This is an essential step towards constructing regulatory networks and elucidating the design principles that govern transcriptional regulation of expression. The promoter region proximal to the TSS appears to be of central importance for regulation of transcription in human and mouse, just as it is in bacteria and yeast.Comment: 31 pages, including Supplementary Information and figure

Measurement of Epstein-Barr virus DNA load using a novel quantification standard containing two EBV DNA targets and SYBR Green I dye

<p>Abstract</p> <p>Background</p> <p>Reactivation of Epstein-Barr virus (EBV) infection may cause serious, life-threatening complications in immunocompromised individuals. EBV DNA is often detected in EBV-associated disease states, with viral load believed to be a reflection of virus activity. Two separate real-time quantitative polymerase chain reaction (QPCR) assays using SYBR Green I dye and a single quantification standard containing two EBV genes, Epstein-Barr nuclear antigen-1 (EBNA-1) and BamHI fragment H rightward open reading frame-1 (BHRF-1), were developed to detect and measure absolute EBV DNA load in patients with various EBV-associated diseases. EBV DNA loads and viral capsid antigen (VCA) IgG antibody titres were also quantified on a population sample.</p> <p>Results</p> <p>EBV DNA was measurable in ethylenediaminetetraacetic acid (EDTA) whole blood, peripheral blood mononuclear cells (PBMCs), plasma and cerebrospinal fluid (CSF) samples. EBV DNA loads were detectable from 8.0 × 10²to 1.3 × 10⁸copies/ml in post-transplant lymphoproliferative disease (n = 5), 1.5 × 10³to 2.0 × 10⁵copies/ml in infectious mononucleosis (n = 7), 7.5 × 10⁴to 1.1 × 10⁵copies/ml in EBV-associated haemophagocytic syndrome (n = 1), 2.0 × 10²to 5.6 × 10³copies/ml in HIV-infected patients (n = 12), and 2.0 × 10²to 9.1 × 10⁴copies/ml in the population sample (n = 218). EBNA-1 and BHRF-1 DNA were detected in 11.0% and 21.6% of the population sample respectively. There was a modest correlation between VCA IgG antibody titre and BHRF-1 DNA load (rho = 0.13, p = 0.05) but not EBNA-1 DNA load (rho = 0.11, p = 0.11).</p> <p>Conclusion</p> <p>Two sensitive and specific real-time PCR assays using SYBR Green I dye and a single quantification standard containing two EBV DNA targets, were developed for the detection and measurement of EBV DNA load in a variety of clinical samples. These assays have application in the investigation of EBV-related illnesses in immunocompromised individuals.</p

Predictability of evolutionary trajectories in fitness landscapes

Experimental studies on enzyme evolution show that only a small fraction of all possible mutation trajectories are accessible to evolution. However, these experiments deal with individual enzymes and explore a tiny part of the fitness landscape. We report an exhaustive analysis of fitness landscapes constructed with an off-lattice model of protein folding where fitness is equated with robustness to misfolding. This model mimics the essential features of the interactions between amino acids, is consistent with the key paradigms of protein folding and reproduces the universal distribution of evolutionary rates among orthologous proteins. We introduce mean path divergence as a quantitative measure of the degree to which the starting and ending points determine the path of evolution in fitness landscapes. Global measures of landscape roughness are good predictors of path divergence in all studied landscapes: the mean path divergence is greater in smooth landscapes than in rough ones. The model-derived and experimental landscapes are significantly smoother than random landscapes and resemble additive landscapes perturbed with moderate amounts of noise; thus, these landscapes are substantially robust to mutation. The model landscapes show a deficit of suboptimal peaks even compared with noisy additive landscapes with similar overall roughness. We suggest that smoothness and the substantial deficit of peaks in the fitness landscapes of protein evolution are fundamental consequences of the physics of protein folding.Comment: 14 pages, 7 figure