Infinite dimensional integrals beyond Monte Carlo methods: yet another approach to normalized infinite dimensional integrals

An approach to (normalized) infinite dimensional integrals, including normalized oscillatory integrals, through a sequence of evaluations in the spirit of the Monte Carlo method for probability measures is proposed. in this approach the normalization through the partition function is included in the definition. For suitable sequences of evaluations, the ("classical") expectation values of cylinder functions are recoveredComment: Submitted as a communication in the ICMSQUARE conference, september 201

Modulation Equations: Stochastic Bifurcation in Large Domains

We consider the stochastic Swift-Hohenberg equation on a large domain near its change of stability. We show that, under the appropriate scaling, its solutions can be approximated by a periodic wave, which is modulated by the solutions to a stochastic Ginzburg-Landau equation. We then proceed to show that this approximation also extends to the invariant measures of these equations

DOP69 Tofacitinib in ulcerative colitis: Early ‘real-world’ experience from four UK tertiary centres

Background Tofacitinib is a partially selective Janus kinase inhibitor that was approved for the treatment of refractory moderate to severe ulcerative colitis (UC) in 2018. We report the real-world clinical effectiveness and adverse effects of tofacitinib in UC. Methods We conducted a retrospective observational cohort study of tofacitinib-treated patients with UC between October 2018 to October 2019 from 4 UK centres. Disease activity was assessed using the Simple Clinical Colitis Activity Index (SCCAI) or Partial Mayo Score (PMS) depending on the study site. Response and remission were defined at week 8 and 26 as a reduction in SCCAI or PMS of ≥3, and SCCAI <3 or PMS <2, respectively. Corticosteroid-free remission was defined as remission with no corticosteroid use at the time of assessment irrespective of baseline corticosteroid status. Results We included 140 patients (65% M; median age 37y [range 16–81]) with a median disease duration of 5.5y (IQR 2.2–11.8). Forty-six per cent (65/140) were receiving corticosteroids at baseline and 83% (116/140) had previously received at least one biologic (62 anti-TNF, 4 vedolizumab, 50 both). Median (IQR) serum CRP and faecal calprotectin levels at baseline were 4 mg/l (1.6–15) and 540 µg/g (316–1175). Response and remission rates were 73% (81/111) and 56% (62/111) respectively at week 8 (median ΔSCCAI of −3 [IQR -6 to -1], median ΔPMS −4 [−6 to −1]) and 48% (39/82) and 39% (32/82) respectively at week 26 (median ΔSCCAI −3 [IQR −7 to –1], median ΔPMS −4 [−6 to –1]). Steroid-free remission was seen in 47% (52/111) and 37% (30/82) patients at week 8 and 26. Patients with response or remission had a significantly lower CRP (p = 0.02) but not calprotectin (p = 0.38) levels at baseline. Response and remission rates were no different stratified by prior biologic use (p = 0.56). Treatment was discontinued after a median of 3 months (IQR 2–4) in 43 patients: 32 with primary non-response, 9 loss of response and in 1 each because of an adverse drug reaction (headache) and patient choice. 7/17 patients had a clinical response to dose re-escalation following a loss of response on dose reduction. The median time to dose de-escalation was 67 (IQR 25–240) days. Seven patients were hospitalised and 5 underwent colectomy. Six serious infections were noted including 2 herpes zoster infections but there were no venous thromboembolic events. Median total cholesterol, low-density lipoprotein and high-density lipoprotein increased from 4.4 mmol/l (IQR 3.7–5.2), 2.47 (1.9–2.9) and 1.5 (1.1–1.9) to 4.8 mmol/l (4.1–6.0), 2.8 (2.13.5) and 1.7 (1.4–1.9) respectively after 8 weeks of tofacitinib. graphic Conclusion Clinical effectiveness and side-effect profile of tofacitinib in UC in this multi-centre real-world cohort were similar to that reported in the pivotal OCTAVE clinical trials.This article is freely available via Open Access. Click on the Publisher URL to access it via the publisher's site.published version, accepted version (12 month embargo), submitted versio

ANVIL: a system for the retrieval of captioned images using NLP techniques

ANVIL is a system designed for the retrieval of images annotated with short captions. It uses NLP techniques to extract dependency structures from captions and queries, and then applies a robust matching algorithm to recursively explore and compare them. There are currently two main interfaces to ANVIL: a list-based display and a 2D spatial layout that allows users to interact with and navigate between similar images. ANVIL was designed to operate as part of a publicly accessible, WWW-based image retrieval server. Consequently, product-level engineering standards were required. This paper examines both the research aspects of the system and also looks at some of the design and evaluation issues.

Decomposing generalized measurements into continuous stochastic processes

One of the broadest concepts of measurement in quantum theory is the generalized measurement. Another paradigm of measurement--arising naturally in quantum optics, among other fields--is that of continuous-time measurements, which can be seen as the limit of a consecutive sequence of weak measurements. They are naturally described in terms of stochastic processes, or time-dependent random variables. We show that any generalized measurement can be decomposed as a sequence of weak measurements with a mathematical limit as a continuous stochastic process. We give an explicit construction for any generalized measurement, and prove that the resulting continuous evolution, in the long-time limit, collapses the state of the quantum system to one of the final states generated by the generalized measurement, being decomposed, with the correct probabilities. A prominent feature of the construction is the presence of a feedback mechanism--the instantaneous choice weak measurement at a given time depends on the outcomes of earlier measurements. For a generalized measurement with $n$ outcomes, this information is captured by a real $n$-vector on an $n$-simplex, which obeys a simple classical stochastic evolution.Comment: 9 pages, LaTeX, name changed, typos correcte

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

Brownian bridges to submanifolds

We introduce and study Brownian bridges to submanifolds. Our method involves proving a general formula for the integral over a submanifold of the minimal heat kernel on a complete Riemannian manifold. We use the formula to derive lower bounds, an asymptotic relation and derivative estimates. We also see a connection to hypersurface local time. This work is motivated by the desire to extend the analysis of path and loop spaces to measures on paths which terminate on a submanifold

On arbitrages arising from honest times

In the context of a general continuous financial market model, we study whether the additional information associated with an honest time gives rise to arbitrage profits. By relying on the theory of progressive enlargement of filtrations, we explicitly show that no kind of arbitrage profit can ever be realised strictly before an honest time, while classical arbitrage opportunities can be realised exactly at an honest time as well as after an honest time. Moreover, stronger arbitrages of the first kind can only be obtained by trading as soon as an honest time occurs. We carefully study the behavior of local martingale deflators and consider no-arbitrage-type conditions weaker than NFLVR.Comment: 25 pages, revised versio

Dominant Topologies in Euclidean Quantum Gravity

The dominant topologies in the Euclidean path integral for quantum gravity differ sharply according on the sign of the cosmological constant. For $\Lambda>0$, saddle points can occur only for topologies with vanishing first Betti number and finite fundamental group. For $\Lambda<0$, on the other hand, the path integral is dominated by topologies with extremely complicated fundamental groups; while the contribution of each individual manifold is strongly suppressed, the ``density of topologies'' grows fast enough to overwhelm this suppression. The value $\Lambda=0$ is thus a sort of boundary between phases in the sum over topologies. I discuss some implications for the cosmological constant problem and the Hartle-Hawking wave function.Comment: 14 pages, LaTeX. Minor additions (computability, relation to ``minimal volume'' in topology); error in eqn (3.5) corrected; references added. To appear in Class. Quant. Gra