What is the correct cost functional for variational data assimilation?

Variational approaches to data assimilation, and weakly constrained four dimensional variation (WC-4DVar) in particular, are important in the geosciences but also in other communities (often under different names). The cost functions and the resulting optimal trajectories may have a probabilistic interpretation, for instance by linking data assimilation with maximum aposteriori (MAP) estimation. This is possible in particular if the unknown trajectory is modelled as the solution of a stochastic differential equation (SDE), as is increasingly the case in weather forecasting and climate modelling. In this situation, the MAP estimator (or “most probable path” of the SDE) is obtained by minimising the Onsager–Machlup functional. Although this fact is well known, there seems to be some confusion in the literature, with the energy (or “least squares”) functional sometimes been claimed to yield the most probable path. The first aim of this paper is to address this confusion and show that the energy functional does not, in general, provide the most probable path. The second aim is to discuss the implications in practice. Although the mentioned results pertain to stochastic models in continuous time, they do have consequences in practice where SDE’s are approximated by discrete time schemes. It turns out that using an approximation to the SDE and calculating its most probable path does not necessarily yield a good approximation to the most probable path of the SDE proper. This suggest that even in discrete time, a version of the Onsager–Machlup functional should be used, rather than the energy functional, at least if the solution is to be interpreted as a MAP estimator

Decomposable representations and Lagrangian submanifolds of moduli spaces associated to surface groups

In this paper, we construct a Lagrangian submanifold of the moduli space associated to the fundamental group of a punctured Riemann surface (the space of representations of this fundamental group into a compact connected Lie group). This Lagrangian submanifold is obtained as the fixed-point set of an anti-symplectic involution defined on the moduli space. The notion of decomposable representation provides a geometric interpretation of this Lagrangian submanifold

Modelling production-consumption flows of goods in Europe: the trade model within Transtools3

The paper presents a new model for trade flows in Europe that is integrated with a logistics model for transport chain choice through Logsum variables. Logsums measures accessibility across an entire multi-modal logistical chain, and are calculated from a logistics model that has been estimated on disaggregated micro data and then used as an input variable in the trade model. Using Logsums in a trade model is new in applied large-scale freight models, where previous models have simply relied on the distance (e.g. crow-fly) between zones. This linkage of accessibility to the trade model makes it possible to evaluate how changes in policies on transport costs and changes in multi-modal networks will influence trade patterns. As an example the paper presents outcomes for a European-wide truck tolling scenario, which showcases to which extent trade is influenced by such a policy. The paper discusses how such a complex model can be estimated and considers the choice of mathematical formulation and the link between the trade model and logistics model. In the outcomes for the tolling scenario we decompose the total effects into effects from the trade model and effects from the logistics model

From ductile to brittle: evolution and localization of deformation below a crustal detachment (Tinos, Cyclades, Greece)

International audienceThe Cycladic Oligo-Miocene detachment of Tinos island is an example of a flat-lying extensional shear zone evolving into a low-angle brittle detachment. A clear continuum of extensional strain from ductile to brittle regime is observed in the footwall. The main brittle structures marking extension are shallow- and steeply dipping normal faults associated with subvertical extensional joints and veins. The earliest brittle structures are lowangle normal faults which commonly superimpose on, and reactivate, earlier (precursory) ductile shear bands, but newly formed low-angle normal faults could also be observed. Low-angle normal faults are cut by late steeply dipping normal faults. The inversion of fault slip data collected within, and away from, the main detachment zone shows that the direction of the minimum stress axis is strictly parallel to the NE-SW stretching lineation and that the maximum principal stress axis remained subvertical during the whole brittle evolution, in agreement with the subvertical attitude of veins throughout the island. The high angle of s1 to the main detachment suggests that the detachment was weak. This observation, together with the presence of a thick layer of cataclasites below the main detachment and the kinematic continuum from ductile to brittle, leads us to propose a kinematic model for the formation of the detachment. Boudinage at the crustal scale induces formation, near the brittle-ductile transition, of ductile shear zones near the edges of boudins. Shear zones are progressively exhumed and replaced by shallowdipping cataclastic shear zones when they reached the brittle field. Most of the displacement is achieved through cataclastic flow in the upper crust and only the last increment of strain gives rise to the formation of brittle faults. The formation of the low-angle brittle detachment is thus ''prepared'' by the ductile shear zone and the cataclasites and favored by the circulation of surface-derived fluids in the shear zone

Geometric K-Homology of Flat D-Branes

We use the Baum-Douglas construction of K-homology to explicitly describe various aspects of D-branes in Type II superstring theory in the absence of background supergravity form fields. We rigorously derive various stability criteria for states of D-branes and show how standard bound state constructions are naturally realized directly in terms of topological K-cycles. We formulate the mechanism of flux stabilization in terms of the K-homology of non-trivial fibre bundles. Along the way we derive a number of new mathematical results in topological K-homology of independent interest.Comment: 45 pages; v2: References added; v3: Some substantial revision and corrections, main results unchanged but presentation improved, references added; to be published in Communications in Mathematical Physic

Bcl-2 expression in rituximab refractory cutaneous B-cell lymphoma

Rituximab has been established as an effective and safe therapy for cutaneous B-cell lymphoma (CBCL). Different survival pathways, that is the Raf/MEK/Erk- or the p38MAPK cascade, have been suggested as downstream mediators of rituximab and may be involved in treatment failure. Biopsies from four patients, suffering from different subtypes of CBCL, which were obtained at various time points of relapse during or after therapy with 375 mg rituximab per m2 of body surface area, were analysed for the expression of CD20, CD3, Ki-67, Raf-kinase inhibitory protein (RKIP) and bcl-2 by immunohistochemistry. No CD20-loss variants, that is the suggested main tumour escape mechanism to rituximab therapy, were observed in any specimen of relapsing CBCL. Notably, the expression of proapoptotic RKIP remained increased in these tumour samples. This was concomitated by a constant to slightly reduced proliferation status as demonstrated by Ki-67 staining. However, relapsing CBCL exhibited a strong upregulation of the antiapoptotic molecule bcl-2 in comparison to pretherapeutic levels. The immunohistochemical analyses of this case series of rituximab refractory CBCL suggest that upregulation of bcl-2 may play a major role in therapy resistance

Dacarbazine (DTIC) versus vaccination with autologous peptide-pulsed dendritic cells (DC) in first-line treatment of patients with metastatic melanoma: a randomized phase III trial of the DC study group of the DeCOG

Background: This randomized phase III trial was designed to demonstrate the superiority of autologous peptide-loaded dendritic cell (DC) vaccination over standard dacarbazine (DTIC) chemotherapy in stage IV melanoma patients. Patients and methods: DTIC 850 mg/m2 intravenously was applied in 4-week intervals. DC vaccines loaded with MHC class I and II-restricted peptides were applied subcutaneously at 2-week intervals for the first five vaccinations and every 4 weeks thereafter. The primary study end point was objective response (OR); secondary end points were toxicity, overall (OS) and progression-free survival (PFS). Results: At the time of the first interim analysis 55 patients had been enrolled into the DTIC and 53 into the DC-arm (ITT). OR was low (DTIC: 5.5%, DC: 3.8%), but not significantly different in the two arms. The Data Safety & Monitoring Board recommended closure of the study. Unscheduled subset analyses revealed that patients with normal serum LDH and/or stage M1a/b survived longer in both arms than those with elevated serum LDH and/or stage M1c. Only in the DC-arm did those patients with (i) an initial unimpaired general health status (Karnofsky = 100) or (ii) an HLA-A2+/HLA-B44− haplotype survive significantly longer than patients with a Karnofsky index <100 (P = 0.007 versus P = 0.057 in the DTIC-arm) or other HLA haplotypes (P = 0.04 versus P = 0.57 in DTIC-treated patients). Conclusions: DC vaccination could not be demonstrated to be more effective than DTIC chemotherapy in stage IV melanoma patients. The observed association of overall performance status and HLA haplotype with overall survival for patients treated by DC vaccination should be tested in future trials employing DC vaccine

Gauge Field Theory Coherent States (GCS) : II. Peakedness Properties

In this article we apply the methods outlined in the previous paper of this series to the particular set of states obtained by choosing the complexifier to be a Laplace operator for each edge of a graph. The corresponding coherent state transform was introduced by Hall for one edge and generalized by Ashtekar, Lewandowski, Marolf, Mour\~ao and Thiemann to arbitrary, finite, piecewise analytic graphs. However, both of these works were incomplete with respect to the following two issues : (a) The focus was on the unitarity of the transform and left the properties of the corresponding coherent states themselves untouched. (b) While these states depend in some sense on complexified connections, it remained unclear what the complexification was in terms of the coordinates of the underlying real phase space. In this paper we resolve these issues, in particular, we prove that this family of states satisfies all the usual properties : i) Peakedness in the configuration, momentum and phase space (or Bargmann-Segal) representation, ii) Saturation of the unquenched Heisenberg uncertainty bound. iii) (Over)completeness. These states therefore comprise a candidate family for the semi-classical analysis of canonical quantum gravity and quantum gauge theory coupled to quantum gravity, enable error-controlled approximations and set a new starting point for {\it numerical canonical quantum general relativity and gauge theory}. The text is supplemented by an appendix which contains extensive graphics in order to give a feeling for the so far unknown peakedness properties of the states constructed.Comment: 70 pages, LATEX, 29 figure

Time separation as a hidden variable to the Copenhagen school of quantum mechanics

The Bohr radius is a space-like separation between the proton and electron in the hydrogen atom. According to the Copenhagen school of quantum mechanics, the proton is sitting in the absolute Lorentz frame. If this hydrogen atom is observed from a different Lorentz frame, there is a time-like separation linearly mixed with the Bohr radius. Indeed, the time-separation is one of the essential variables in high-energy hadronic physics where the hadron is a bound state of the quarks, while thoroughly hidden in the present form of quantum mechanics. It will be concluded that this variable is hidden in Feynman's rest of the universe. It is noted first that Feynman's Lorentz-invariant differential equation for the bound-state quarks has a set of solutions which describe all essential features of hadronic physics. These solutions explicitly depend on the time separation between the quarks. This set also forms the mathematical basis for two-mode squeezed states in quantum optics, where both photons are observable, but one of them can be treated a variable hidden in the rest of the universe. The physics of this two-mode state can then be translated into the time-separation variable in the quark model. As in the case of the un-observed photon, the hidden time-separation variable manifests itself as an increase in entropy and uncertainty.Comment: LaTex 10 pages with 5 figure. Invited paper presented at the Conference on Advances in Quantum Theory (Vaxjo, Sweden, June 2010), to be published in one of the AIP Conference Proceedings serie