Using Conservation Laws to Solve Toda Field Theories

We investigate the question of how the knowledge of sufficiently many local conservation laws for a model can be utilized to solve the model. We show that for models where the conservation laws can be written in one-sided forms, like \barpartial Q_s = 0, the problem can always be reduced to solving a closed system of ordinary differential equations. We investigate the $A_1$, $A_2$, and $B_2$ Toda field theories in considerable detail from this viewpoint. One of our findings is that there is in each case a transformation group intrinsic to the model. This group is built on a specific real form of the Lie algebra used to label the Toda field theory. It is the group of field transformations which leaves the conserved densities invariant.Comment: Latex, 24 page

Conservation laws for the classical Toda field theories

We have performed some explicit calculations of the conservation laws for classical (affine) Toda field theories, and some generalizations of these models. We show that there is a huge class of generalized models which have an infinite set of conservation laws, with their integrated charges being in involution. Amongst these models we find that only the $A_m$ and $A_m^{(1)}$ ($m\ge 2$) Toda field theories admit such conservation laws for spin-3. We report on our explicit calculations of spin-4 and spin-5 conservation laws in the (affine) Toda models. Our perhaps most interesting finding is that there exist conservation laws in the $A_m$ models ($m\ge4)$ which have a different origin than the exponents of the corresponding affine theory or the energy-momentum tensor of a conformal theory.Comment: 9 pages, Late

On the form of local conservation laws for some relativistic field theories in 1+1 dimensions

We investigate the possible form of local translation invariant conservation laws associated with the relativistic field equations \partial\bar\partial\phi_i=-v_i(\bphi) for a multicomponent field \bphi. Under the assumptions that (i)~the $v_i$'s can be expressed as linear combinations of partial derivatives $\partial w_j/\partial\phi_k$ of a set of functions w_j(\bphi), (ii)~the space of functions spanned by the $w_j$'s is closed under partial derivations, and (iii)~the fields \bphi take values in a simply connected space, the local conservation laws can either be transformed to the form $\partial{\bar{\cal P}}=\bar\partial\sum_j w_j {\cal Q}_j$ (where $\bar{\cal P}$ and ${\cal Q}_j$ are homogeneous polynomials in the variables $\bar\partial\phi_i$, $\bar\partial^2\phi_i$,\ldots), or to the parity transformed version of this expression $\partial\equiv(\partial_t+\partial_x)/ \sqrt{2}\rightleftharpoons\bar\partial \equiv (\partial_t-\partial_x)/\sqrt{2}$.Comment: 12 pages, Late

An evaluation of solutions to the problem of boundary change when analyzing long-term relationships on aggregate data

In Norwegen sind die Gemeinden die kleinste regionale und Verwaltungseinheit. Sie existieren als solche schon seit mehr als 150 Jahren. Deshalb sind die Gemeinden die Hauptverwalter von Daten in den offiziellen Statistiken des Landes. Dies hat zu einer langen Tradition sorgfältig gepflegter Daten auf dieser Ebene geführt. Der norwegische sozialwissenschaftliche Datendienst hat auf Teilen dieser Information eine Datenbank aufgebaut, um die Analysen von regionalen Daten voranzutreiben. Die Daten können gefunden werden für statistische Analysen und/oder kartographische Präsentation. Der Artikel setzt sich mit den Hauptproblemen eines solchen Systems auseinander, nämlich der Veränderung der zugrundeliegenden regionalen Einheiten und den daraus resultierenden Problemen für Analysen des langfristigen Verhältnisses auf einer aggregierten Datenbasis. Wenn die regionalen Einheiten sich verändern, rechnet das Datenbanksystem die Daten für die neuen Einheiten aus. Diese Neuberechnung basiert auf Information über Bevölkerungswanderungen zwischen den betroffenen Einheiten und den betroffenen spezifischen Daten. Die verschiedenen zugrundeliegenden Randbedingungen für dieses Verfahren werden diskutiert, ebenso wie die verschiedenartigen Möglichkeiten, auf diese Weise Verzerrungen in das Datenmaterial hereinzubekommen. Das Verfahren wird einer empirischen Überprüfung unterzogen, auf dessen Grundlage Empfehlungen für den Gebrauch der Daten gegeben werden. Da Datenneuberechung sowohl vorwärts und rückwärts im Zeitablauf vorgenommen werden können, wird empfohlen, daß Datennutzer Daten neu berechnen sollten, in Folge von allgemeinen Aggregationsprozessen im System der regionalen Einheit. Verschiedene Arten von statistischen Daten können allerdings nicht einem gleichartigen Verfahren unterzogen werden. Das Verfahren ist hauptsächlich für variable Größen bestimmt, die Aussagen über die Bevölkerung ermöglichen und basieren auf der Annahme, daß diese Aussagen eine homogene Verteilung in der Bevölkerung der Regionaleinheiten ermöglichen. Das Ergebnis wird beeinträchtigt, sowohl von der gewählten Zeit der abgefragten Daten, d.h. die Anzahl und die Arten der Veränderungen und der Art der abgefragten Daten. Das Hauptergebnis ist, daß Neuberechnungen der Datenbasis, wenn sich die Regionaleinheiten ändern, um Daten vergleichbar zu machen, nicht die Schlußfolgerungen ernsthaft beeinträchtigen, die auf statistischen Analysen aller oder großer Untereinheiten der Regionaleinheiten beruhen. Es wird schwieriger, langfristige Zeitreihen für Einzelfälle zu nutzen. (KWübers.)'In Norway, communes are the smallest regional political and administrative units, and have existed as such for some 150 years. For this reason the communes have been the main datacarrying unit in the offical statistics of the country. This has resulted in a long tradition of well aggregated information at this level. The Norwegian Social Science Data services has built a database containing part of this information, to further the analysis of regional data. Data may be retrieved for statistical analysis and/or cartographic presentation. The present article discusses one of the main problems of such a system, changes in regional units over time, and the problems created for analysis of long-term relationship on aggregated data. When changes occur in the system of regional units, the databse-system recalculates the data values to the new units. These recalculations are based on information about population transfers involved, and the type of data under consideration. Various underlying assumptions for this procedure are discussed, and so are the different types of error that may introduce into the data. The procedure is tested empirically, and based on the empirical results some recommendations for use are advocated. Since it is possible to recalculate data both forwards and backwards in time, it is recommended that users as a general rule should try to recalculate data following general processes of aggregation in the system of regional units. Also various types of data do not lend themselves to the same kind of treatment by this procedure. It is mainly designed for variables that give attributes with the population, and is based on the assumption that these attributes approach a homogeneous distribution across the population of a regional unit. The outcome is effected both by the time-period of the retrieved data, i.e. number and types of changes involved, and kind of data retrieved. The main conclusion is that recalculations of data when units change, to make data comparable, do not seriously affect conclusions based on statistical analyses of all, or large subsets of the regional units. It is more difficult to use long timeseries for just a few cases.' (author's abstract

Electromagnetic Casimir energy with extra dimensions

We calculate the energy-momentum tensor due to electromagnetic vacuum fluctuations between two parallel hyperplanes in more than four dimensions, considering both metallic and MIT boundary conditions. Using the axial gauge, the problem can be mapped upon the corresponding problem with a massless, scalar field satisfying respectively Dirichlet or Neumann boundary conditions. The pressure between the plates is constant while the energy density is found to diverge at the boundaries when there are extra dimensions. This can be related to the fact that Maxwell theory is then no longer conformally invariant. A similar behavior is known for the scalar field where a constant energy density consistent with the pressure can be obtained by improving the energy-momentum tensor with the Huggins term. This is not possible for the Maxwell field. However, the change in the energy-momentum tensor with distance between boundaries is finite in all cases.Comment: 16 pages, typos corrected, published versio

Abelian symmetries in multi-Higgs-doublet models

N-Higgs doublet models (NHDM) are a popular framework to construct electroweak symmetry breaking mechanisms beyond the Standard model. Usually, one builds an NHDM scalar sector which is invariant under a certain symmetry group. Although several such groups have been used, no general analysis of symmetries possible in the NHDM scalar sector exists. Here, we make the first step towards this goal by classifying the elementary building blocks, namely the abelian symmetry groups, with a special emphasis on finite groups. We describe a strategy that identifies all abelian groups which are realizable as symmetry groups of the NHDM Higgs potential. We consider both the groups of Higgs-family transformations only and the groups which also contain generalized CP transformations. We illustrate this strategy with the examples of 3HDM and 4HDM and prove several statements for arbitrary N.Comment: 33 pages, 2 figures; v2: conjecture 3 is proved and becomes theorem 3, more explanations of the main strategy are added, matches the published versio

Radiative Corrections to the Casimir Energy

The lowest radiative correction to the Casimir energy density between two parallel plates is calculated using effective field theory. Since the correlators of the electromagnetic field diverge near the plates, the regularized energy density is also divergent. However, the regularized integral of the energy density is finite and varies with the plate separation L as 1/L^7. This apparently paradoxical situation is analyzed in an equivalent, but more transparent theory of a massless scalar field in 1+1 dimensions confined to a line element of length L and satisfying Dirichlet boundary conditions.Comment: 7 pages, Late

Field induced stationary state for an accelerated tracer in a bath

Our interest goes to the behavior of a tracer particle, accelerated by a constant and uniform external field, when the energy injected by the field is redistributed through collision to a bath of unaccelerated particles. A non equilibrium steady state is thereby reached. Solutions of a generalized Boltzmann-Lorentz equation are analyzed analytically, in a versatile framework that embeds the majority of tracer-bath interactions discussed in the literature. These results --mostly derived for a one dimensional system-- are successfully confronted to those of three independent numerical simulation methods: a direct iterative solution, Gillespie algorithm, and the Direct Simulation Monte Carlo technique. We work out the diffusion properties as well as the velocity tails: large v, and either large -v, or v in the vicinity of its lower cutoff whenever the velocity distribution is bounded from below. Particular emphasis is put on the cold bath limit, with scatterers at rest, which plays a special role in our model.Comment: 20 pages, 6 figures v3:minor corrections in sec.III and added reference

WHO collaborative study to assess the suitability of the 1st International Standard and the 1st International Reference Panel for antibodies to Ebola virus

A WHO international collaborative study was undertaken to evaluate preparations of Ebola virus disease (EVD) convalescent plasmas for their suitability to serve as the WHO 1st International Standard (IS) and the WHO 1st International Reference Panel (IRP) for Ebola virus antibodies for use in the standardization and control of assays. The study involved participants testing the convalescent plasma sample preparations and additional monoclonal antibody samples in a blinded manner alongside the WHO International Reference Reagent (NIBSC code 15/220) using anti-EBOV assays established in their laboratories. The candidate 1st IS for Ebola virus antibodies (study sample code 92, NIBSC 15/262) consists of ampoules containing the freeze-dried equivalent of 0.5 mL pooled convalescent plasma obtained from six Sierra Leone patients recovered from EVD. The candidate 1st IRP of anti-Ebola virus convalescent plasmas (NIBSC 16/344) consists of freeze-dried preparations of single donations of convalescent plasma obtained from four patients and one healthy blood donor. Each panel member is an ampoule containing the equivalent of 0.25mL plasma. All convalescent plasmas are confirmed PCR-negative for Ebola virus and underwent, along with the negative plasma, solvent detergent (SD) treatment prior to their development into candidate WHO biological reference materials. In this collaborative study, 17 laboratories from 4 countries used a range of live Ebola virus neutralization assays, pseudotyped virus neutralisation assays and enzyme immunoassays to test the collaborative study samples. Surface plasmon resonance and Western blot assessments were also undertaken. The study found that the candidate International Standard has the highest absolute titre among the convalescent plasma samples, although the geometric mean titres of all the convalescent plasmas fall within ~5-fold of each other. The potencies of three of the convalescent samples fall near the detection limit of some assays. This study also demonstrated that the agreement between laboratories for potencies relative to the candidate International Standard represents an improvement compared to the agreement in absolute titres; however, there is poor agreement between relative potencies for some assays. The results obtained from accelerated thermal degradation studies at 1year indicate that the candidate IS is stable and suitable for long-term use. The results of the collaborative study indicate the suitability of the candidates to serve as WHO reference materials and it is proposed that 15/262 is established as the WHO 1st IS for EBOV antibodies with an assigned potency of 1.5 IU/mL when reconstituted as directed in the instructions for use. It is also proposed that 16/344 is established as the WHO 1st IRP of anti-EBOV convalescent plasmas with panel member code 95 (NIBSC 15/280) assigned a unitage of 1.1 IU/mL when reconstituted as directed in the instructions for use. The other panel members have not been assigned a unitage. The implementation and use by laboratories of the proposed WHO reference materials for EBOV antibodies will facilitate the characterization of the factors that contribute to assay variability and standardization of results across assays and laboratorie

ERCC1 expression and RAD51B activity correlate with cell cycle response to platinum drug treatment not DNA repair

Background: The H69CIS200 and H69OX400 cell lines are novel models of low-level platinum-drug resistance. Resistance was not associated with increased cellular glutathione or decreased accumulation of platinum, rather the resistant cell lines have a cell cycle alteration allowing them to rapidly proliferate post drug treatment. Results: A decrease in ERCC1 protein expression and an increase in RAD51B foci activity was observed in association with the platinum induced cell cycle arrest but these changes did not correlate with resistance or altered DNA repair capacity. The H69 cells and resistant cell lines have a p53 mutation and consequently decrease expression of p21 in response to platinum drug treatment, promoting progression of the cell cycle instead of increasing p21 to maintain the arrest. Conclusion: Decreased ERCC1 protein and increased RAD51B foci may in part be mediating the maintenance of the cell cycle arrest in the sensitive cells. Resistance in the H69CIS200 and H69OX400 cells may therefore involve the regulation of ERCC1 and RAD51B independent of their roles in DNA repair. The novel mechanism of platinum resistance in the H69CIS200 and H69OX400 cells demonstrates the multifactorial nature of platinum resistance which can occur independently of alterations in DNA repair capacity and changes in ERCC1