Origin of the anomalies: the modified Heisenberg equation

The origin of the anomalies is analyzed. It is shown that they are due to the fact that the generators of the symmetry do not leave invariant the domain of definition of the Hamiltonian and then a term, normally forgotten in the Heisenberg equation, gives an extra contribution responsible for the non conservation of the charges. This explanation is equivalent to that of the Fujikawa in the path integral formalism. Finally, this approach is applied to the conformal symmetry breaking in two-dimensional quantum mechanics.Comment: 7 pages, LaTe

Phase transition in the assignment problem for random matrices

We report an analytic and numerical study of a phase transition in a P problem (the assignment problem) that separates two phases whose representatives are the simple matching problem (an easy P problem) and the traveling salesman problem (a NP-complete problem). Like other phase transitions found in combinatoric problems (K-satisfiability, number partitioning) this can help to understand the nature of the difficulties in solving NP problems an to find more accurate algorithms for them.Comment: 7 pages, 5 figures; accepted for publication in Europhys. Lett. http://www.edpsciences.org/journal/index.cfm?edpsname=ep

Application of Natural Language Processing to Determine User Satisfaction in Public Services

Research on customer satisfaction has increased substantially in recent years. However, the relative importance and relationships between different determinants of satisfaction remains uncertain. Moreover, quantitative studies to date tend to test for significance of pre-determined factors thought to have an influence with no scalable means to identify other causes of user satisfaction. The gaps in knowledge make it difficult to use available knowledge on user preference for public service improvement. Meanwhile, digital technology development has enabled new methods to collect user feedback, for example through online forums where users can comment freely on their experience. New tools are needed to analyze large volumes of such feedback. Use of topic models is proposed as a feasible solution to aggregate open-ended user opinions that can be easily deployed in the public sector. Generated insights can contribute to a more inclusive decision-making process in public service provision. This novel methodological approach is applied to a case of service reviews of publicly-funded primary care practices in England. Findings from the analysis of 145,000 reviews covering almost 7,700 primary care centers indicate that the quality of interactions with staff and bureaucratic exigencies are the key issues driving user satisfaction across England

Vacuum Nodes and Anomalies in Quantum Theories

We show that nodal points of ground states of some quantum systems with magnetic interactions can be identified in simple geometric terms. We analyse in detail two different archetypical systems: i) a planar rotor with a non-trivial magnetic flux $\Phi$, ii) Hall effect on a torus. In the case of the planar rotor we show that the level repulsion generated by any reflection invariant potential $V$ is encoded in the nodal structure of the unique vacuum for $\theta=\pi$. In the second case we prove that the nodes of the first Landau level for unit magnetic charge appear at the crossing of the two non-contractible circles $\alpha_-$, $\beta_-$ with holonomies $h_{\alpha_-}(A)= h_{\beta_-}(A)=-1$ for any reflection invariant potential $V$. This property illustrates the geometric origin of the quantum translation anomaly.Comment: 14 pages, 2 ps-figures, to appear in Commun. Math. Phy

Intraspecific variability in paradoxidid trilobites from the Purujosa trilobite assemblage (middle Cambrian, northeast Spain)

Eccaparadoxides? pradoanus and Eccaparadoxides mediterraneus are both widespread trilobite species described from the middle Cambrian of the Mediterranean region. Analysis based on a pooled sample of 500 specimens demonstrates that many of the characters that have been used to define these species show continuous variations, some of which are related to ontogeny. In addition, morphometric analyses of metric characters show that the two species cannot be distinguished on the basis of these characters either. Many of the characters studied herein are widely used in definitions and descriptions of other paradoxidid species, which suggests that the taxonomic classification of other paradoxidids may be oversplit

Comparison of musculoskeletal networks of the primate forelimb

Anatomical network analysis is a framework for quantitatively characterizing the topological organization of anatomical structures, thus providing a way to compare structural integration and modularity among species. Here we apply this approach to study the macroevolution of the forelimb in primates, a structure whose proportions and functions vary widely within this group. We analyzed musculoskeletal network models in 22 genera, including members of all major extant primate groups and three outgroup taxa, after an extensive literature survey and dissections. The modules of the proximal limb are largely similar among taxa, but those of the distal limb show substantial variation. Some network parameters are similar within phylogenetic groups (e.g., non-primates, strepsirrhines, New World monkeys, and hominoids). Reorganization of the modules in the hominoid hand compared to other primates may relate to functional changes such as coordination of individual digit movements, increased pronation/supination, and knuckle-walking. Surprisingly, humans are one of the few taxa we studied in which the thumb musculoskeletal structures do not form an independent anatomical module. This difference may be caused by the loss in humans of some intrinsic muscles associated with the digits or the acquisition of additional muscles that integrate the thumb more closely with surrounding structures

Entanglement in fermionic chains with finite range coupling and broken symmetries

We obtain a formula for the determinant of a block Toeplitz matrix associated with a quadratic fermionic chain with complex coupling. Such couplings break reflection symmetry and/or charge conjugation symmetry. We then apply this formula to compute the Renyi entropy of a partial observation to a subsystem consisting of $X$ contiguous sites in the limit of large $X$. The present work generalizes similar results due to Its, Jin, Korepin and Its, Mezzadri, Mo. A striking new feature of our formula for the entanglement entropy is the appearance of a term scaling with the logarithm of the size of $X$. This logarithmic behaviour originates from certain discontinuities in the symbol of the block Toeplitz matrix. Equipped with this formula we analyse the entanglement entropy of a Dzyaloshinski-Moriya spin chain and a Kitaev fermionic chain with long range pairing.Comment: 27 pages, 5 figure

On the M\"obius transformation in the entanglement entropy of fermionic chains

There is an intimate relation between entanglement entropy and Riemann surfaces. This fact is explicitly noticed for the case of quadratic fermionic Hamiltonians with finite range couplings. After recollecting this fact, we make a comprehensive analysis of the action of the M\"obius transformations on the Riemann surface. We are then able to uncover the origin of some symmetries and dualities of the entanglement entropy already noticed recently in the literature. These results give further support for the use of entanglement entropy to analyse phase transition.Comment: 29 pages, 5 figures. Final version published in JSTAT. Two new figures. Some comments and references added. Typos correcte