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Deformation of Rigid Conjugate Self-dual Galois Representations

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Acta Mathematica Sinica,English Series 2024年第7期40卷 1599-1644页

作者： Yi Feng LIU Yi Chao TIAN Liang XIAO Wei ZHANG Xin Wen ZHU Institute for Advanced Study in Mathematics Zhejiang UniversityHangzhou 310058P.R.China Morningside Center of Mathematics AMSSChinese Academy of SciencesBeijing 100190P.R.China New Cornerstone Lab Beijing International Center for Mathematical ResearchPeking Ui Beijing 100871P.R.China Department of Mathematics Massachusetts Institute of TechnologyCambridge MA 02139United States Department of Mathematics Stanford UniversityStanfordCA 94305United States

In this article,we study deformations of conjugate self-dual Galois *** study is ***,we prove an R=T type theorem for a conjugate self-dual Galois representation with coefficients in a finite field,satisfying a certain property called ***,we study the rigidity property for the family of residue Galois representations attached to a symmetric power of an elliptic curve,as well as to a regular algebraic conjugate self-dual cuspidal representation.

关键词： Galois deformation rigid conjugate self-dual Galois representations

Exploring tree diversity and stand structure of savanna woodlands in southeastern Sudan

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Journal of Arid Land 2020年第4期12卷 609-617页

作者： Ahmed M M HASOBA Ahmed A H SIDDIG Yousif E YAGOUB Faculty of Forest Sciences and Technology University of GeziraMadani 22212Sudan Faculty of Forestry University of KhartoumKhartoum North 13314Sudan Department of Environmental Conservation University of Massachusetts AmherstAmherst 01003USA

Savanna woodlands in Sudan host great biodiversity, provide a plethora of ecosystem goods and services to local communities, and sustain numerous ecological functions. Although the importance of the Acacia trees in these areas is well known, up-to-date information about these woodlands' diversity is limited and changes in their woody vegetation composition, density, diversity and relative frequency are not monitored over time. This study explored tree diversity and stand stage structure in Nuara Reserved Forest, a typical savanna woodland ecosystem in southeastern Sudan. A total of 638 circular sample plots(1000 m^2 for each) were established using a systematic sampling grid method. The distance between plots was 200 m. In each plot, all living trees with diameter at breast height(DBH) ≥5.00 cm were identified and counted, and their DBH values were recorded. From these data, tree composition, diversity, density and stage structure were assessed. There were 12,259 individual trees representing four species(Acacia seyal, Balanites aegyptiaca, Acacia Senegal and Acacia mellifera) that belong to two families. The dominant species was Acacia seyal. Average tree density was 191 trees/hm^2 and the Shannon-Weiner index for trees diversity was 0.204. Overall, young trees comprised 86.30% of the forest. The state of tree richness and density in the study area was low compared to other similar environments in the region and around the world. We recommended adoption of a proper management system that includes monitoring of woody vegetation diversity in this forest, and management actions to enhance tree diversity and sustain ecosystem services to local communities. In addition to care for the dominant Acacia seyal stands, more attention and conservation should be devoted to reestablishing Acacia senegal and Acacia mellifera trees because of their high ecological and economic values for local communities.

关键词： species diversity stand structure savanna woodland ecosystem forest monitoring forest management ecosystem services Nuara Reserved Forest

Longitudinal bending stiffness does not affect running economy in Nike Vaporfly Shoes

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Journal of Sport and Health Science 2022年第3期11卷 285-292页

作者： Laura A.Healey Wouter Hoogkamer Integrative Locomotion Laboratory Department of KinesiologyUniversity of MassachusettsAmherstMA 01003-9258USA

Purpose This study aimed to determine the independent effect of the curved carbon-fiber plate in the Nike Vaporfly 4%shoe on running economy and running *** Fifteen healthy male runners completed a metabolic protocol and a biomechanics *** both protocols participants wore 2 different shoes,an intact Nike Vaporfly 4%(VF_(intact))and a cut Nike Vaporfly 4%(VF_(cut)).The VF_(cut) had 6 medio-lateral cuts through the carbon-fiber plate in the forefoot to reduce the effectiveness of the *** the metabolic protocol,participants ran at 14 km/h for 5 min,twice with each shoe,on a force-measuring treadmill while we measured metabolic *** the biomechanics protocol,participants ran across a runway with embedded force plates at 14 km/*** calculated running economy,kinetics,and lower limb joint *** Running economy did not significantly differ between shoe conditions(on average,0.55%±1.77%(mean±SD))worse in the VF_(cut) compared to the VF_(intact);95%confidence interval(-1.44%to 0.40%).Biomechanical differences were only found in the metatarsophalangeal(MTP)joint with increased MTP dorsiflexion angle,angular velocity,and negative power in the VF_(cut).Contact time was 1%longer in the VF_(intact).Conclusion Cutting the carbon-fiber plate and reducing the longitudinal bending stiffness did not have a significant effect on the energy savings in the Nike Vaporfly 4%.This suggests that the plate's stiffening effect on the MTP joint plays a limited role in the reported energy savings,and instead savings are likely from a combination and interaction of the foam,geometry,and plate.

关键词： Biomechanics Footwear Mechanical doping Metabolic rate Performance

Modelling the unexpected dynamics of COVID-19 in Manaus,Brazil

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Infectious Disease Modelling 2024年第2期9卷 557-568页

作者： Daihai He Yael Artzy-Randrup Salihu S.Musa Tiago Gräf Felipe Naveca Lewi Stone Department of Applied Mathematics Hong Kong Polytechnic UniversityHong Kong SARChina Department of Theoretical and Computational Ecology IBEDUniversity of AmsterdamAmsterdamNetherlands Department of Genomics and Computational Biology University of Massachusetts Chan Medical SchoolWorcesterMA01605USA Department of Mathematics Aliko Dangote University of Science and TechnologyKanoNigeria Instituto Gonçalo Moniz FiocruzSalvadorBahiaBrazil Instituto Leônidas e Maria Deane FiocruzManausBrazil Mathematical Sciences School of ScienceRMIT UniversityMelbourneAustralia Biomathematics Unit School of ZoologyFaculty of Life SciencesTel Aviv UniversityTel AvivIsrael

In late March 2020,SARS-CoV-2 arrived in Manaus,Brazil,and rapidly developed into a large-scale epidemic that collapsed the local health system and resulted in extreme death *** key studies reported that∼76%of residents of Manaus were infected(attack rate AR≃76%)by October 2020,suggesting protective herd immunity had been *** this,an unexpected second wave of COVID-19 struck again in November and proved to be larger than the first,creating a catastrophe for the unprepared *** has been suggested that this could be possible if the second wave was driven by ***,it is widely reported that reinfections were at a low rate(before the emergence of Omicron),and reinfections tend to be ***,we use novel methods to model the epidemic from mortality data without considering reinfection-caused deaths and evaluate the impact of interventions to explain why the second wave *** method fits a“flexible”reproductive numberR_(0)(t)that changes over the epidemic,and it is demonstrated that the method can successfully reconstruct R_(0)(t)from simulated *** Manaus,the method finds AR≃34%by October 2020 for the first wave,which is far less than required for herd immunity yet in-line with seroprevalence *** work is complemented by a two-strain *** genomic data,the model estimates transmissibility of the new P.1 virus lineage as 1.9 times higher than that of the ***,an age class model variant that considers the high mortality rates of older adults show very similar *** models thus provide a reasonable explanation for the two-wave dynamics in Manaus without the need to rely on large reinfection rates,which until now have only been found in negligible to moderate numbers in recent surveillance efforts.

关键词： Modelling COVID-19 Reproduction number Herd immunity Reinfection

THE VACUUM IN NONISENTROPIC GAS DYNAMICS

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Acta Mathematica Scientia 2012年第1期32卷 339-351页

作者： Geng Chen Robin Young Department of Mathematics Pennsylvania State University University Park PA 16802 USA Department of Mathematics University of Massachusetts Amherst MA 01003 USA

We investigate the vacuum in nonisentropic gas dynamics in one space vari- able, with the most general equation of states allowed by thermodynamics. We recall physical constraints on the equations of state and give explicit and easily checkable conditions under which vacuums occur in the solution of the Riemann problem. We then present a class of models for which the Riemann problem admits unique global solutions without vacuums.

关键词： nonisentropic gas dynamics conservation laws vacuum large data Riemann problem

iSeeBetter: Spatio-temporal video super-resolution using recurrent generative back-projection networks

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Computational Visual Media 2020年第3期6卷 307-317页

作者： Aman Chadha John Britto M.Mani Roja Department of Computer Science Stanford University450 Serra MallStanfordCA 94305USA Department of Computer Science University of Massachusetts AmherstAmherstMA 01003USA Department of Electronics and Telecommunication Engineering University of MumbaiMumbaiMaharashtra 400032India

Recently,learning-based models have enhanced the performance of single-image superresolution(SISR).However,applying SISR successively to each video frame leads to a lack of temporal *** neural networks(CNNs)outperform traditional approaches in terms of image quality metrics such as peak signal to noise ratio(PSNR)and structural similarity(SSIM).On the other hand,generative adversarial networks(GANs)offer a competitive advantage by being able to mitigate the issue of a lack of finer texture details,usually seen with CNNs when super-resolving at large upscaling *** present i See Better,a novel GAN-based spatio-temporal approach to video super-resolution(VSR)that renders temporally consistent super-resolution videos.i See Better extracts spatial and temporal information from the current and neighboring frames using the concept of recurrent back-projection networks as its ***,to improve the"naturality"of the superresolved output while eliminating artifacts seen with traditional algorithms,we utilize the discriminator from super-resolution generative adversarial *** mean squared error(MSE)as a primary loss-minimization objective improves PSNR/SSIM,these metrics may not capture fine details in the image resulting in misrepresentation of perceptual *** address this,we use a four-fold(MSE),perceptual,adversarial,and total-variation loss *** results demonstrate that i See Better offers superior VSR fidelity and surpasses state-of-the-art performance.

关键词： networks resolution projection

LINEAR WAVES THAT EXPRESS THE SIMPLEST POSSIBLE PERIODIC STRUCTURE OF THE COMPRESSIBLE EULER EQUATIONS

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Acta Mathematica Scientia 2009年第6期29卷 1749-1766页

作者： Blake Temple Robin Young Department of Mathematics University of California Davis CA 95616 USA Department of Mathematics and Statistics University of Massachusetts Amherst MA 01003 USA

In this paper we show how the simplest wave structure that balances compression and rarefaction in the nonlinear compressible Euler equations can be represented in a solution of the linearized compressible Euler equations. Such waves are exact solutions of the equations obtained by linearizing the compressible Euler equations about the periodic extension of two constant states separated by entropy jumps. Conditions on the states and the periods are derived which allow for the existence of solutions in the Fourier 1-mode. In [3, 4, 5] it is shown that these are the simplest linearized waves such that, for almost every period, they are isolated in the kernel of the linearized operator that imposes periodicity, and such that they perturb to nearby nonlinear solutions of the compressible Euler equations that balance compression and rarefaction along characteristics in the formal sense described in [3]. Their fundamental nature thus makes them of interest in their own right.

关键词： compressible Euler periodic solutions conservation laws

Predictors of the placebo response in a nutraceutical randomized controlled trial for depression

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Journal of Integrative Medicine 2024年第1期22卷 46-53页

作者： Rosemary Arnold Jenifer Murphy-Smith Chee H.Ng David Mischoulon Gerard J.Byrne Chad A.Bousman Con Stough Michael Berk Jerome Sarris Professorial Unit the Melbourne ClinicDepartment of PsychiatryUniversity of MelbourneRichmond 3121Australia Depression Clinical and Research Program Department of PsychiatryMassachusetts General HospitalHarvard Medical SchoolBostonMA 02115USA Faculty of Medicine Discipline of PsychiatryCentre for Clinical ResearchRoyal Brisbane&Women’s HospitalHerstonthe University of QueenslandBrisbane 4006Australia Departments of Medical Genetics PsychiatryPhysiology&Pharmacology and Community Health SciencesUniversity of CalgaryCalgaryAB T2N 1N4Canada Department of Psychiatry the University of MelbourneMelbourne 3052Australia Centre for Human Psychopharmacology Swinburne UniversityMelbourne 3122Australia The Institute for Mental and Physical Health and Clinical Translation School of MedicineBarwon HealthDeakin UniversityGeelong 3220Australia The Centre of Excellence in Youth Mental Health the University of MelbourneParkville 3052Australia Florey Institute of Neuroscience and Mental Health the University of MelbourneParkville 3052Australia NICM Health Research Institute Western Sydney UniversityWestmeadNSW 2145Australia

Objective The placebo response in depression studies is the change in symptoms amongst those who receive an inactive *** well-designed randomized controlled trials(RCTs)of depression have a high proportion of placebo responders,with little understanding as to *** present study assesses characteristics associated with the placebo response in a nutraceutical trial with a large proportion of placebo *** This is a secondary analysis of a nutraceutical depression RCT which identified no overall treatment benefit relative to placebo(n=69 in placebo group).We investigated participant characteristics such as socio-demographics,clinical features,and recruitment methods,and their association with the placebo *** genetic polymorphisms were also *** response was measured based on change in Montgomery-Asberg Depression Rating Scale *** association of these hypothesis-driven variables of interest and the placebo response was examined using linear mixed effects *** Greater levels of education,particularly pursuing post-high school education,better self-reported general health,marriage/de facto,greater improvement in the first trial week,and more failed antidepressant therapies in the current depressive episode were associated with greater placebo *** increased placebo response was not found in those recruited via social media nor in those with concomitant antidepressant *** nucleotide polymorphisms from the tryptophan hydroxylase 1(TPH1)gene(A779C and A218C)were weakly associated with greater placebo response,although the evidence was attenuated after accounting for multiple *** This is,to our knowledge,the first study within nutraceutical research for depression to assess the association between participant characteristics and variation in the placebo *** variables appeared to predict the placebo *** findings may encourage future trial design

关键词： Randomized controlled trial Placebo Depression Nutraceutical Psychiatry

POLY (β-HYDROXYALKANOATES): NATURAL BIOCOMPATIBLE AND BIODEGRADABLE POLYESTERS PRODUCED BY BACTERIA

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Chinese Journal of Polymer Science 1989年第4期7卷 289-298页

作者： ROBERT W. LENZ RICHARD A. GROSS HELMUT BRANDL R. CLINTON FULLER Department of Polymer Science and Engineering University of MassachusettsAmherstMA 01003USADepartment of ChemistryUniversity of Lowell1 University Ave.LowellMA 01854USAInstitute for Plant BiologyZollikerstrasse 1078008 ZurichSwitzerlandDepartment of BiochemistryUniversity of MassachusettsAmherstMA 01003USA

A wide variety of different types of microorganisms are known to produce intracellular energy and carbon storage products, which have been generally described as being poly (β-hydroxybutyrate), PHB, but which are, more often than not, copolymers containing different alkyl groups at the β-position. Hence, PHB belongs to the family ofpoly (β-hydroxyalkanoastes), PHA, all of which are usually formed as intracellular inclusions in bacteria under unbalanced growth conditions. Recently, it became of industrial interest to evaluate these PHA polyesters as natural biodegradable and biocompatible plastics for a wide range of possible applications, such as surgical sutures or packaging containers. For industrial applications, the controlled incorporation of repeating units with different chain lengths into a series of copolymers is desirable in order to produce polyesters with a range of material properties because physical and chemical characteristics depend strongly on the polymer composition. Such 'tailor-made' copolymers can be produced under controlled growth conditions in that, if a defined mixture of substrates for a certain type of microorganisms is supplied, a well defined and reproducible copolymer is formed.

关键词： PHB POLY HYDROXYALKANOATES NATURAL BIOCOMPATIBLE AND BIODEGRADABLE POLYESTERS PRODUCED BY BACTERIA