A linear theory for control of non-linear stochastic systems

We address the role of noise and the issue of efficient computation in stochastic optimal control problems. We consider a class of non-linear control problems that can be formulated as a path integral and where the noise plays the role of temperature. The path integral displays symmetry breaking and there exist a critical noise value that separates regimes where optimal control yields qualitatively different solutions. The path integral can be computed efficiently by Monte Carlo integration or by Laplace approximation, and can therefore be used to solve high dimensional stochastic control problems.Comment: 5 pages, 3 figures. Accepted to PR

Persistence of a pinch in a pipe

The response of low-dimensional solid objects combines geometry and physics in unusual ways, exemplified in structures of great utility such as a thin-walled tube that is ubiquitous in nature and technology. Here we provide a particularly surprising consequence of this confluence of geometry and physics in tubular structures: the anomalously large persistence of a localized pinch in an elastic pipe whose effect decays very slowly as an oscillatory exponential with a persistence length that diverges as the thickness of the tube vanishes, which we confirm experimentally. The result is more a consequence of geometry than material properties, and is thus equally applicable to carbon nanotubes as it is to oil pipelines.Comment: 6 pages, 3 figure

Noether symmetries, energy-momentum tensors and conformal invariance in classical field theory

In the framework of classical field theory, we first review the Noether theory of symmetries, with simple rederivations of its essential results, with special emphasis given to the Noether identities for gauge theories. Will this baggage on board, we next discuss in detail, for Poincar\'e invariant theories in flat spacetime, the differences between the Belinfante energy-momentum tensor and a family of Hilbert energy-momentum tensors. All these tensors coincide on shell but they split their duties in the following sense: Belinfante's tensor is the one to use in order to obtain the generators of Poincar\'e symmetries and it is a basic ingredient of the generators of other eventual spacetime symmetries which may happen to exist. Instead, Hilbert tensors are the means to test whether a theory contains other spacetime symmetries beyond Poincar\'e. We discuss at length the case of scale and conformal symmetry, of which we give some examples. We show, for Poincar\'e invariant Lagrangians, that the realization of scale invariance selects a unique Hilbert tensor which allows for an easy test as to whether conformal invariance is also realized. Finally we make some basic remarks on metric generally covariant theories and classical field theory in a fixed curved bakground.Comment: 31 pa

Quantum Kaleidoscopes and Bell's theorem

A quantum kaleidoscope is defined as a set of observables, or states, consisting of many different subsets that provide closely related proofs of the Bell-Kochen-Specker (BKS) and Bell nonlocality theorems. The kaleidoscopes prove the BKS theorem through a simple parity argument, which also doubles as a proof of Bell's nonlocality theorem if use is made of the right sort of entanglement. Three closely related kaleidoscopes are introduced and discussed in this paper: a 15-observable kaleidoscope, a 24-state kaleidoscope and a 60-state kaleidoscope. The close relationship of these kaleidoscopes to a configuration of 12 points and 16 lines known as Reye's configuration is pointed out. The "rotations" needed to make each kaleidoscope yield all its apparitions are laid out. The 60-state kaleidoscope, whose underlying geometrical structure is that of ten interlinked Reye's configurations (together with their duals), possesses a total of 1120 apparitions that provide proofs of the two Bell theorems. Some applications of these kaleidoscopes to problems in quantum tomography and quantum state estimation are discussed.Comment: Two new references (No. 21 and 22) to related work have been adde

Medication adherence in patients with myotonic dystrophy and facioscapulohumeral muscular dystrophy

Myotonic dystrophy (DM) and facioscapulohumeral muscular dystrophy (FSHD) are the two most common adult muscular dystrophies and have progressive and often disabling manifestations. Higher levels of medication adherence lead to better health outcomes, especially important to patients with DM and FSHD because of their multisystem manifestations and complexity of care. However, medication adherence has not previously been studied in a large cohort of DM type 1 (DM1), DM type 2 (DM2), and FSHD patients. The purpose of our study was to survey medication adherence and disease manifestations in patients enrolled in the NIH-supported National DM and FSHD Registry. The study was completed by 110 DM1, 49 DM2, and 193 FSHD patients. Notable comorbidities were hypertension in FSHD (44 %) and DM2 (37 %), gastroesophageal reflux disease in DM1 (24 %) and DM2 (31 %) and arrhythmias (29 %) and thyroid disease (20 %) in DM1. Each group reported high levels of adherence based on regimen complexity, medication costs, health literacy, side effect profile, and their beliefs about treatment. Only dysphagia in DM1 was reported to significantly impact medication adherence. Approximately 35 % of study patients reported polypharmacy (taking 6 or more medications). Of the patients with polypharmacy, the DM1 cohort was significantly younger (mean 55.0 years) compared to DM2 (59.0 years) and FSHD (63.2 years), and had shorter disease duration (mean 26 years) compared to FSHD (26.8 years) and DM2 (34.8 years). Future research is needed to assess techniques to ease pill swallowing in DM1 and to monitor polypharmacy and potential drug interactions in DM and FSHD

Tools in the orbit space approach to the study of invariant functions: rational parametrization of strata

Functions which are equivariant or invariant under the transformations of a compact linear group $G$ acting in an euclidean space $\real^n$, can profitably be studied as functions defined in the orbit space of the group. The orbit space is the union of a finite set of strata, which are semialgebraic manifolds formed by the $G$-orbits with the same orbit-type. In this paper we provide a simple recipe to obtain rational parametrizations of the strata. Our results can be easily exploited, in many physical contexts where the study of equivariant or invariant functions is important, for instance in the determination of patterns of spontaneous symmetry breaking, in the analysis of phase spaces and structural phase transitions (Landau theory), in equivariant bifurcation theory, in crystal field theory and in most areas where use is made of symmetry adapted functions. A physically significant example of utilization of the recipe is given, related to spontaneous polarization in chiral biaxial liquid crystals, where the advantages with respect to previous heuristic approaches are shown.Comment: Figures generated through texdraw package; revised version appearing in J. Phys. A: Math. Ge

Some remarks on the hyperelliptic moduli of genus 3

In 1967, Shioda \cite{Shi1} determined the ring of invariants of binary octavics and their syzygies using the symbolic method. We discover that the syzygies determined in \cite{Shi1} are incorrect. In this paper, we compute the correct equations among the invariants of the binary octavics and give necessary and sufficient conditions for two genus 3 hyperelliptic curves to be isomorphic over an algebraically closed field $k$, $\ch k \neq 2, 3, 5, 7$. For the first time, an explicit equation of the hyperelliptic moduli for genus 3 is computed in terms of absolute invariants.Comment: arXiv admin note: text overlap with arXiv:1209.044

Helium Recovery in the LHC Cryogenic System following Magnet Resistive Transitions

A resistive transition (quench) of the Large Hadron Collider magnets provokes the expulsion of helium from the magnet cryostats to the helium recovery system. A high-volume, vacuum-insulated recovery line connected to several uninsulated medium-pressure gas storage tanks, forms the main constituents of the system. Besides a dedicated hardware configuration, helium recovery also implies specific procedures that should follow a quench, in order to conserve the discharged helium and possibly make use of its refrigeration capability. The amount of energy transferred after a quench from the magnets to the helium leaving the cold mass has been estimated on the basis of experimental data. Based on these data, the helium thermodynamic state in the recovery system is calculated using a lumped parameter approach. The LHC magnet quenches are classified ina parametric way from their cryogenic consequences and procedures that should follow the quench are proposed

Revisiting Weyl's calculation of the gravitational pull in Bach's two-body solution

When the mass of one of the two bodies tends to zero, Weyl's definition of the gravitational force in an axially symmetric, static two-body solution can be given an invariant formulation in terms of a force four-vector. The norm of this force is calculated for Bach's two-body solution, that is known to be in one-to-one correspondence with Schwarzschild's original solution when one of the two masses l, l' is made to vanish. In the limit when, say, l' goes to zero, the norm of the force divided by l' and calculated at the position of the vanishing mass is found to coincide with the norm of the acceleration of a test body kept at rest in Schwarzschild's field. Both norms happen thus to grow without limit when the test body (respectively the vanishing mass l') is kept at rest in a position closer and closer to Schwarzschild's two-surface.Comment: 11 pages, 2 figures. Text to appear in Classical and Quantum Gravit

Cosmology and astrophysics from relaxed galaxy clusters - IV: Robustly calibrating hydrostatic masses with weak lensing

This is the fourth in a series of papers studying the astrophysics and cosmology of massive, dynamically relaxed galaxy clusters. Here, we use measurements of weak gravitational lensing from the Weighing the Giants project to calibrate Chandra X-ray measurements of total mass that rely on the assumption of hydrostatic equilibrium. This comparison of X-ray and lensing masses provides a measurement of the combined bias of X-ray hydrostatic masses due to both astrophysical and instrumental sources. Assuming a fixed cosmology, and within a characteristic radius (r_2500) determined from the X-ray data, we measure a lensing to X-ray mass ratio of 0.96 +/- 9% (stat) +/- 9% (sys). We find no significant trends of this ratio with mass, redshift or the morphological indicators used to select the sample. In accordance with predictions from hydro simulations for the most massive, relaxed clusters, our results disfavor strong, tens-of-percent departures from hydrostatic equilibrium at these radii. In addition, we find a mean concentration of the sample measured from lensing data of c_200 = $3.0_{-1.8}^{+4.4}$. Anticipated short-term improvements in lensing systematics, and a modest expansion of the relaxed lensing sample, can easily increase the measurement precision by 30--50%, leading to similar improvements in cosmological constraints that employ X-ray hydrostatic mass estimates, such as on Omega_m from the cluster gas mass fraction.Comment: 13 pages. Submitted to MNRAS. Comments welcom