A Feynman-Kac Formula for Anticommuting Brownian Motion

Motivated by application to quantum physics, anticommuting analogues of Wiener measure and Brownian motion are constructed. The corresponding Ito integrals are defined and the existence and uniqueness of solutions to a class of stochastic differential equations is established. This machinery is used to provide a Feynman-Kac formula for a class of Hamiltonians. Several specific examples are considered.Comment: 21 page

Cretaceous provenance change in the Hegang Basin and its connection with the Songliao Basin, NE China: Evidence for lithospheric extension driven by palaeo-Pacific roll-back

The Cretaceous Hegang Basin is located on the Jiamusi Block, NE China, and separated from the Songliao Basin by the Lesser Xing'an Range (LXR). Seismic interpretation shows that the Chengzihe, Muling and Dongshan formations of the Hegang Basin thicken eastwards with westwards onlap, indicating that the LXR existed as a palaeo-uplift during that period, whereas the Houshigou Formation shows no thickness change, indicating that the LXR was possibly under water at this time. This is supported by results of detrital zircon analysis from the Hegang Basin in which the Chengzihe Formation is dominated by approximately 180 Ma zircons, which can only be provided by the LXR, whereas the Houshigou Formation records no Early Jurassic ages. This view is consistent with previous studies of the Songliao Basin for a provenance change between the Denglouku and Quantou formations. We conclude that the LXR was a highland during deposition of the Chengzihe, Muling and Dongshan formations but that it was under water when the Houshigou Formation was deposited. There was thus a connection between the Hegang and Songliao basins, which marks an eastwards migration of the depositional and extensional centre of the Songliao-Hegang basin system. This eastwards migration implies lithospheric extension driven by palaeo-Pacific roll-back

Two Neoarchean tectonothermal events on the western edge of the North Atlantic Craton, as revealed by SIMS dating of the Saglek Block, Nain Province, Labrador

The Saglek Block forms the northern part of the Nain Province and underwent widespread metamorphism at c. 2.7 Ga, producing the dominant gneissosity and intercalation of supracrustal sequences. Zircon dating of gneiss samples collected along 80 km of the Labrador coast from Ramah Bay in the north to Hebron Fjord in the south confirms the widespread extent of high-grade metamorphism between 2750 and 2700 Ma. In addition, a distinct event between 2550 and 2510 Ma produced felsic melt with peritectic garnet in metavolcanic gneiss and granoblastic recrystallization in mafic granulite. Ductile deformation of granite emplaced at c. 2550 Ma indicates that this later event involved a degree of tectonism during high-T metamorphism. Such tectonism may be related to a hypothesized post-2.7 Ga juxtaposition of the predominantly Eoarchean Saglek Block against the Mesoarchean Hopedale Block, along a north–south boundary that extends from the coast near Nain to offshore of Saglek Bay. Evidence of reworking of c. 2.7 Ga gneisses by c. 2.5 Ga tectonothermal activity has been found elsewhere on the margins of the North Atlantic Craton, of which the Nain Province represents thewestern margin. In particular, a recent suggestion that c. 2.5 Ga metamorphic ages along the northern margin of the North Atlantic Craton inSWGreenland may record the final assembly of the craton could also apply to the western margin as represented by the rocks of the Nain Province

Integral equation methods for acoustic scattering by fractals

We study sound-soft time-harmonic acoustic scattering by general scatterers, including fractal scatterers, in 2D and 3D space. For an arbitrary compact scatterer $\Gamma$ we reformulate the Dirichlet boundary value problem for the Helmholtz equation as a first kind integral equation (IE) on $\Gamma$ involving the Newton potential. The IE is well-posed, except possibly at a countable set of frequencies, and reduces to existing single-layer boundary IEs when $\Gamma$ is the boundary of a bounded Lipschitz open set, a screen, or a multi-screen. When $\Gamma$ is uniformly of $d$-dimensional Hausdorff dimension in a sense we make precise (a $d$-set), the operator in our equation is an integral operator on $\Gamma$ with respect to $d$-dimensional Hausdorff measure, with kernel the Helmholtz fundamental solution, and we propose a piecewise-constant Galerkin discretization of the IE, which converges in the limit of vanishing mesh width. When $\Gamma$ is the fractal attractor of an iterated function system of contracting similarities we prove convergence rates under assumptions on $\Gamma$ and the IE solution, and describe a fully discrete implementation using recently proposed quadrature rules for singular integrals on fractals. We present numerical results for a range of examples and make our software available as a Julia code

Quantum delocalization in photon-pair generation

The generation of correlated photon pairs is a key to the production of entangled quantum states, which have a variety of applications within the area of quantum information. In spontaneous parametric down-conversion—the primary method of generating correlated photon pairs—the associated photon annihilation and creation events are generally thought of as being colocated: The correlated pair of photons is localized with regards to the pump photon and its positional origin. A detailed quantum electrodynamical analysis highlights a mechanism exhibiting the possibility of a delocalized origin for paired output photons: The spatial extent of the region from which the pair is generated can be much larger than previously thought. The theory of both localized and nonlocalized degenerate down-conversion is presented, followed by a quantitative analysis using discrete-volume computational methods. The results may have significant implications for quantum information and imaging applications, and the design of nonlinear optical metamaterials

New insight into tuning magnetic phases of RMn6Sn6 kagome metals

Kagome metals with magnetic order offer the possibility of tuning topological electronic states via external control parameters such as temperature or magnetic field. ErMn$_6$Sn$_6$ (Er$166$) is a member of a group of $R166$, $R=$~rare earth, compounds hosting ferromagnetic Mn kagome nets whose magnetic moment direction and layer-to-layer magnetic correlations are strongly influenced by coupling to $R$ magnetic moments in neighboring triangular layers. Here, we use neutron diffraction and magnetization data to examine the temperature-driven transition in Er$166$ from a planar-ferrimagnetic to distorted-triple-spiral magnetic order. These data inform mean-field calculations which highlight the fragile, tunable nature of the magnetism caused by competing Mn-Mn and Mn-Er interlayer magnetic exchange couplings and Mn and Er magnetic anisotropies. This competition results in the near degeneracy of a variety of collinear, non-collinear, and non-coplanar magnetic phases which we show are readily selected and adjusted via changing temperature or magnetic field. Thermal fluctuations of the Er moment direction provide the key to this tunability.Comment: 10 pages, 7 figures, Supplementary Informatio

The First Provenance Challenge

The first Provenance Challenge was set up in order to provide a forum for the community to help understand the capabilities of different provenance systems and the expressiveness of their provenance representations. To this end, a Functional Magnetic Resonance Imaging workflow was defined, which participants had to either simulate or run in order to produce some provenance representation, from which a set of identified queries had to be implemented and executed. Sixteen teams responded to the challenge, and submitted their inputs. In this paper, we present the challenge workflow and queries, and summarise the participants contributions

The Precambrian Khondalite Belt in the Daqingshan area, North China Craton: evidence for multiple metamorphic events in the Palaeoproterozoic era

High-grade pelitic metasedimentary rocks (khondalites) are widely distributed in the northwestern part of the North China Craton and were named the ‘Khondalite Belt’. Prior to the application of zircon geochronology, a stratigraphic division of the supracrustal rocks into several groups was established using interpretative field geology. We report here SHRIMP U–Pb zircon ages and Hf-isotope data on metamorphosed sedimentary and magmatic rocks at Daqingshan, a typical area of the Khondalite Belt. The main conclusions are as follows: (1) The early Precambrian supracrustal rocks belong to three sequences: a 2.56–2.51 Ga supracrustal unit (the previous Sanggan ‘group’), a 2.51–2.45 Ga supracrustal unit (a portion of the previous upper Wulashan ‘group’) and a 2.0–1.95 Ga supracrustal unit (including the previous lower Wulashan ‘group’, a portion of original upper Wulashan ‘group’ and the original Meidaizhao ‘group’) the units thus do not represent a true stratigraphy; (2) Strong tectono-thermal events occurred during the late Neoarchaean to late Palaeoproterozoic, with four episodes recognized: 2.6–2.5, 2.45–2.37, 2.3–2.0 and 1.95–1.85 Ga, with the latest event being consistent with the assembly of the Palaeoproterozoic supercontinent Columbia; (3) During the late Neoarchaean to late Palaeoproterozoic (2.55–2.5, 2.37 and 2.06 Ga) juvenile, mantle-derived material was added to the crust

Critical research gaps and recommendations to inform research prioritisation for more effective prevention and improved outcomes in colorectal cancer

OBJECTIVE: Colorectal cancer (CRC) leads to significant morbidity/mortality worldwide. Defining critical research gaps (RG), their prioritisation and resolution, could improve patient outcomes.DESIGN: RG analysis was conducted by a multidisciplinary panel of patients, clinicians and researchers (n=71). Eight working groups (WG) were constituted: discovery science; risk; prevention; early diagnosis and screening; pathology; curative treatment; stage IV disease; and living with and beyond CRC. A series of discussions led to development of draft papers by each WG, which were evaluated by a 20-strong patient panel. A final list of RGs and research recommendations (RR) was endorsed by all participants.RESULTS: Fifteen critical RGs are summarised below: RG1: Lack of realistic models that recapitulate tumour/tumour micro/macroenvironment; RG2: Insufficient evidence on precise contributions of genetic/environmental/lifestyle factors to CRC risk; RG3: Pressing need for prevention trials; RG4: Lack of integration of different prevention approaches; RG5: Lack of optimal strategies for CRC screening; RG6: Lack of effective triage systems for invasive investigations; RG7: Imprecise pathological assessment of CRC; RG8: Lack of qualified personnel in genomics, data sciences and digital pathology; RG9: Inadequate assessment/communication of risk, benefit and uncertainty of treatment choices; RG10: Need for novel technologies/interventions to improve curative outcomes; RG11: Lack of approaches that recognise molecular interplay between metastasising tumours and their microenvironment; RG12: Lack of reliable biomarkers to guide stage IV treatment; RG13: Need to increase understanding of health related quality of life (HRQOL) and promote residual symptom resolution; RG14: Lack of coordination of CRC research/funding; RG15: Lack of effective communication between relevant stakeholders.CONCLUSION: Prioritising research activity and funding could have a significant impact on reducing CRC disease burden over the next 5 years.</p