Some ideas about quantitative convergence of collision models to their mean field limit

We consider a stochastic $N$-particle model for the spatially homogeneous Boltzmann evolution and prove its convergence to the associated Boltzmann equation when $N\to \infty$. For any time $T>0$ we bound the distance between the empirical measure of the particle system and the measure given by the Boltzmann evolution in some homogeneous negative Sobolev space. The control we get is Gaussian, i.e. we prove that the distance is bigger than $x N^{-1/2}$ with a probability of type $O(e^{-x^2})$. The two main ingredients are first a control of fluctuations due to the discrete nature of collisions, secondly a Lipschitz continuity for the Boltzmann collision kernel. The latter condition, in our present setting, is only satisfied for Maxwellian models. Numerical computations tend to show that our results are useful in practice.Comment: 27 pages, references added and style improve

Early Atomic Models - From Mechanical to Quantum (1904-1913)

A complete history of early atomic models would fill volumes, but a reasonably coherent tale of the path from mechanical atoms to the quantum can be told by focusing on the relevant work of three great contributors to atomic physics, in the critically important years between 1904 and 1913: J. J. Thomson, Ernest Rutherford and Niels Bohr. We first examine the origins of Thomson's mechanical atomic models, from his ethereal vortex atoms in the early 1880's, to the myriad "corpuscular" atoms he proposed following the discovery of the electron in 1897. Beyond predictions for the periodicity of the elements, the application of Thomson's atoms to problems in scattering and absorption led to quantitative predictions that were confirmed by experiments with high-velocity electrons traversing thin sheets of metal. Still, the much more massive and energetic {\alpha}-particles being studied by Rutherford were better suited for exploring the interior of the atom, and careful measurements on the angular dependence of their scattering eventually allowed him to infer the existence of an atomic nucleus. Niels Bohr was particularly troubled by the radiative instability inherent to any mechanical atom, and succeeded in 1913 where others had failed in the prediction of emission spectra, by making two bold hypotheses that were in contradiction to the laws of classical physics, but necessary in order to account for experimental facts.Comment: 58 Pages + References, 8 Figures. Accepted for publication in the European Physical Journal H (Historical Perspectives on Contemporary Physics). V2 - minor typos corrected and a footnote added to p.2

A practical drug discovery project at the undergraduate level

A practical drug discovery project for third-year undergraduates is described. No previous knowledge of medicinal chemistry is assumed. Initial lecture-workshops cover the basic principles; then students are asked to improve the profile of a weakly potent, poorly soluble PI3K inhibitor (1). Compound array design, molecular modelling and screening data analysis are followed by laboratory work in which each student, as part of a team, attempts to synthesise at least two target compounds. The project benefits from significant industrial support, including lectures, student mentoring and consumables. The aim is to make the learning experience as close as possible to real-life industrial situations. Forty-eight target compounds have been prepared, the best of which (5b, 5j, 6b and 6ap) improved the potency and aqueous solubility of the lead compound (1) by 100-1000 fold and 10-fold, respectively

Refining and regaining skills in fixation/diversification stage performers: The Five-A Model

Technical change is one of many factors underpinning success in elite, fixation/diversification stage performers. Surprisingly, however, there is a dearth of research pertaining to this process or the most efficacious methods used to bring about such a change. In this paper we highlight the emergent processes, yet also the lack in mechanistic comprehension surrounding technical change, addressing issues within the motor control, sport psychology, coaching and choking literature. More importantly, we seek an understanding of how these changes can be made more secure to competitive pressure, and how this can be embedded within the process of technical change. Following this review, we propose The Five-A Model based on successful coaching techniques, psychosocial concomitants, the avoidance of choking and principles of effective behaviour change. Specific mechanisms for each stage are discussed, with a focus on the use of holistic rhythm-based cues as a possible way of internalising changes. Finally, we suggest the need for further research to examine these five stages, to aid a more comprehensive construction of the content and delivery of such a programme within the applied setting

Early carboniferous brachiopod faunas from the Baoshan block, west Yunnan, southwest China

38 brachiopod species in 27 genera and subgenera are described from the Yudong Formation in the Shidian-Baoshan area, west Yunnan, southwest China. New taxa include two new subgenera: Unispirifer (Septimispirifer) and Brachythyrina (Longathyrina), and seven new species: Eomarginifera yunnanensis, Marginatia cylindrica, Unispirifer (Unispirifer) xiangshanensis, Unispirifer (Septimispirifer) wafangjieensis, Brachythyrina (Brachythyrina) transversa, Brachythyrina (Longathyrina) baoshanensis, and Girtyella wafangjieensis. Based on the described material and constraints from associated coral and conodont faunas, the age of the brachiopod fauna from the Yudon Formation is considered late Tournaisian (Early Carboniferous), with a possibility extending into earlyViseacutean.<br /

Carboniferous and Permian Rugosochonetidae (Brachiopoda) from West Spitsbergen

The rugosochonetid brachiopod species Lissochonetes geinitzianus from the Kazimovian of the Nordenskioldbreen Formation, and Dyoros (Dyoros) mucronata sp. nov., Dyoros (Dyoros) spitzbergianus and Lissochonetes superba from the Artinskian to latest Permian Kapp Starostin Formation in West Spitsbergen are described and figured. Dyoros is generally restricted to the Boreal Realm, whereas Lissochonetes is mostly distributed in the Boreal Realm, but occasionally present in the Palaeoequatorial and Gondwanan Realms<br /

Designing a broad-spectrum integrative approach for cancer prevention and treatment

Targeted therapies and the consequent adoption of "personalized" oncology have achieved notablesuccesses in some cancers; however, significant problems remain with this approach. Many targetedtherapies are highly toxic, costs are extremely high, and most patients experience relapse after a fewdisease-free months. Relapses arise from genetic heterogeneity in tumors, which harbor therapy-resistantimmortalized cells that have adopted alternate and compensatory pathways (i.e., pathways that are notreliant upon the same mechanisms as those which have been targeted). To address these limitations, aninternational task force of 180 scientists was assembled to explore the concept of a low-toxicity "broad-spectrum" therapeutic approach that could simultaneously target many key pathways and mechanisms. Using cancer hallmark phenotypes and the tumor microenvironment to account for the various aspectsof relevant cancer biology, interdisciplinary teams reviewed each hallmark area and nominated a widerange of high-priority targets (74 in total) that could be modified to improve patient outcomes. For thesetargets, corresponding low-toxicity therapeutic approaches were then suggested, many of which werephytochemicals. Proposed actions on each target and all of the approaches were further reviewed forknown effects on other hallmark areas and the tumor microenvironment. Potential contrary or procar-cinogenic effects were found for 3.9% of the relationships between targets and hallmarks, and mixedevidence of complementary and contrary relationships was found for 7.1%. Approximately 67% of therelationships revealed potentially complementary effects, and the remainder had no known relationship. Among the approaches, 1.1% had contrary, 2.8% had mixed and 62.1% had complementary relationships. These results suggest that a broad-spectrum approach should be feasible from a safety standpoint. Thisnovel approach has potential to be relatively inexpensive, it should help us address stages and types ofcancer that lack conventional treatment, and it may reduce relapse risks. A proposed agenda for futureresearch is offered