We introduce a symmetric operad whose algebras are the operator product expansion (OPE) Algebras of quantum fields. There is a natural classical limit for the algebras over this operad and they are ...commutative associative algebras with derivations. The latter are the algebras of classical fields. In this paper we completely develop our approach to models of quantum fields, which come from vertex algebras in higher dimensions. However, our approach to OPE algebras can be extended to general quantum fields even over curved space–time. We introduce a notion of OPE operations based on the new notion of semi-differential operators. The latter are linear operators
Γ
:
M
→
N
between two modules of a commutative associative algebra
A
, such that for every
m
∈
M
the assignment
a
↦
Γ
(
a
·
m
)
is a differential operator
A
→
N
in the usual sense. The residue of a meromorphic function at its pole is an example of a semi-differential operator.
Rankings occur when a set of items is ordered in agreement with some criteria or personal opinions and can be found in various problems ranging from voting and elections to food preferences. ...Distances on permutations are commonly used in rank data analysis and are an efficient tool for constructing probability models for rankings. In this paper, we consider the optimal property of the distance-based Mallows model in terms of the Kullback–Leibler divergence and propose a generalization based on the ϕ-divergence. In the sequel, we focus on a special parametric family of models induced by the Cressie–Read power divergence. For the suggested models, we provide parameter estimating algorithms and model fitting methods. Furthermore, we propose a simple approach for the specification of the consensus ranking, based on modal complete or partial rankings modal rankings, that could be used alternatively to complete search algorithms. As an illustration, the described procedures are applied to three examples of rank data.
The American College of Rheumatology and the US Food and Drug Administration co-sponsored a public meeting in May 2022 about challenges in the clinical development of drugs for rheumatoid arthritis ...(RA) and psoriatic arthritis (PsA), focusing on innovative clinical trial designs, outcome measures, and data collection methods. Recommendations include early dose-ranging studies and use of active comparators. Challenges and opportunities in assessing long-term safety by leveraging real-world data from electronic health records (EHRs) and claims data are discussed, along with insights from European registries and the evolving role of real-world evidence and artificial intelligence in regulatory evaluations. Endpoints for assessing disease activity and outcome measures used in RA and PsA trials are explored, emphasizing challenges in defining remission, assessing clinical response, and evaluating structural progression. The need for outcome measures that better reflect treatment targets and the potential of advanced imaging in future trials are highlighted. Challenges with placebo-controlled trials in RA are discussed and use of non-inferiority clinical trial design, in which new drugs are evaluated with active comparators, is proposed. Pragmatic trials in RA and PsA, employing decentralized approaches, are highlighted for their real-world relevance and administrative efficiencies. Strategies for identifying at-risk populations for RA and the challenges of using EHRs and insurance claims data in drug development are discussed. Registry data and digital health technologies show promise in bridging the gap between clinical trials and real-world effectiveness.
Objective
There is an unmet need for therapies that target the underlying pathophysiology of osteoarthritis (OA). However, defining appropriate measures for clinical trials of such therapies is ...challenging. Our objective was to propose concept clinical end points that directly capture clinical benefit in this setting and evaluate the feasibility of their use.
Methods
This analysis used the multicenter, longitudinal, observational Osteoarthritis Initiative (OAI) database. OAI participants primarily had knee OA, with follow‐up of up to 9 years and assessments of joints, surgical interventions, performance outcomes, and patient‐reported outcomes. We examined this data set to identify existing outcome measures of direct clinical benefit. We evaluated the feasibility of conducting trials using these candidate end points by estimating incidence rates and resulting required sample sizes and study durations in time‐to‐event analyses.
Results
We identified candidate end points based on total knee replacement (TKR) and composite end points defined by TKR and conservative thresholds of patient‐reported outcomes of pain and function. Using time to TKR as an end point, a study with an average follow‐up time of 3 years requires approximately 3,000 to 18,000 subjects, depending on effect size. Alternatively, for a composite end point, such as “time to TKR or severe pain or severely impaired functioning,” the required sample sizes ranged from approximately 2,000 to 11,000 for a 3‐year study.
Conclusion
The proposed concept end points can reliably and feasibly evaluate the effectiveness of therapies for this unmet need. In particular, the composite end point approach can substantially reduce sample sizes (up to approximately 40%) compared to the use of TKR alone.
We study the asymptotic behaviour of Betti numbers, twisted torsion and other spectral invariants of sequences of locally symmetric spaces. Our main results are uniform versions of the ...DeGeorge–Wallach Theorem, of a theorem of Delorme and various other limit multiplicity theorems. A basic idea is to adapt the notion of Benjamini–Schramm convergence (BS-convergence), originally introduced for sequences of finite graphs of bounded degree, to sequences of Riemannian manifolds, and analyze the possible limits. We show that BS-convergence of locally symmetric spaces Γ\G/K implies convergence, in an appropriate sense, of the normalized relative Plancherel measures associated to L 2 (Γ\G). This then yields convergence of normalized multiplicities of unitary representations, Betti numbers and other spectral in-variants. On the other hand, when the corresponding Lie group G is simple and of real rank at least two, we prove that there is only one possible BS-limit, i.e. when the volume tends to infinity, locally symmetric spaces always BS-converge to their universal cover G/K. This leads to various general uniform results. When restricting to arbitrary sequences of congruence covers of a fixed arithmetic manifold we prove a strong quantitative version of BS-convergence which in turn implies upper estimates on the rate of convergence of normalized Betti numbers in the spirit of Sarnak–Xue. An important role in our approach is played by the notion of Invariant Random Subgroups. For higher rank simple Lie groups G, we exploit rigidity theory, and in particular the Nevo–Stück–Zimmer theorem and Kazhdan's property (T), to obtain a complete understanding of the space of IRSs of G.
The solution of nonconvex parameter estimation problems with deterministic global optimization methods is desirable but challenging, especially if large measurement datasets are considered. We ...propose to exploit the structure of this class of optimization problems to enable their solution with the spatial branch-and-bound algorithm. In detail, we start with a reduced dataset in the root node and progressively augment it, converging to the full dataset. We show for nonlinear programs (NLPs) that our algorithm converges to the global solution of the original problem considering the full dataset. The implementation of the algorithm extends our open-source solver MAiNGO. A numerical case study with a mixed-integer nonlinear program (MINLP) from chemical engineering and a dynamic optimization problem from biochemistry both using noise-free measurement data emphasizes the potential for savings of computational effort with our proposed approach.
Display omitted
•Deterministic global optimization of large scale nonconvex problems is challenging.•Exploit structure of parameter estimation problems with large datasets.•In proposed branch-and-bound algorithm, reduced set grows gradually to full dataset.•Convergence properties of nonlinear programs retained when using growing datasets.•Real-world case study with noise-free data shows significant CPU time savings.
ABSTRACT
High-resolution Doppler-resolved spectroscopy has opened up a new window into the atmospheres of both transiting and non-transiting exoplanets. Here, we present VLT/UVES observations of a ...transit of WASP-121b, an ‘ultra-hot’ Jupiter previously found to exhibit a temperature inversion and detections of multiple species at optical wavelengths. We present initial results using the blue arm of UVES (≈3700–5000 Å), recovering a clear signal of neutral Fe in the planet’s atmosphere at >8$\, \sigma$, which could contribute to (or even fully explain) the temperature inversion in the stratosphere. However, using standard cross-correlation methods, it is difficult to extract physical parameters such as temperature and abundances. Recent pioneering efforts have sought to develop likelihood ‘mappings’ that can be used to directly fit models to high-resolution data sets. We introduce a new framework that directly computes the likelihood of the model fit to the data, and can be used to explore the posterior distribution of parametrised model atmospheres via MCMC techniques. Our method also recovers the physical extent of the atmosphere, as well as account for time- and wavelength-dependent uncertainties. We measure a temperature of $3710^{+490}_{-510}$ K, indicating a higher temperature in the upper atmosphere when compared to low-resolution observations. We also show that the Fe i signal is physically separated from the exospheric Fe ii. However, the temperature measurements are highly degenerate with aerosol properties; detection of additional species, using more sophisticated atmospheric models, or combining these methods with low-resolution spectra should help break these degeneracies.
ABSTRACT
We report transmission spectroscopy of the bloated hot Jupiter WASP-74b in the wavelength range from 4000 to 6200 Å. We observe two transit events with the Very Large Telescope (VLT) Focal ...Reducer and Spectrograph and present a new method to measure the exoplanet transit depth as a function of wavelength. The new method removes the need for a reference star in correcting the spectroscopic light curves for the impact of atmospheric extinction. It also provides improved precision, compared to other techniques, reaching an average transit depth uncertainty of 211 ppm for a solar-type star of V = 9.8 mag and over wavelength bins of 80 Å. The VLT transmission spectrum is analysed both individually and in combination with published data from Hubble Space Telescope and Spitzer. The spectrum is found to exhibit a mostly featureless slope and equilibrium chemistry retrievals with platon favour hazes in the upper atmosphere of the exoplanet. Free chemistry retrievals with aura further support the presence of hazes. While additional constraints are possible depending on the choice of atmospheric model, they are not robust and may be influenced by residual systematics in the data sets. Our results demonstrate the utility of new techniques in the analysis of optical, ground-based spectroscopic data and can be highly complementary to follow-up observations in the infrared with JWST.
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