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A DISCRETE MODEL FOR COMPETING STAGE-STRUCTURED SPECIES

THEORETICAL POPULATION BIOLOGY 1992年第3期41卷 372-387页

作者： CUSHING, JM Department of Mathematics Interdisciplinary Program in Applied Mathematics Building 89 University of Arizona Tucson Arizona 85721 USA

This paper deals with the problem of relating physiological properties of individual organisms to the dynamics at the total population level. A general nonlinear matrix difference equation is described which accounts for the dynamics of stage-structured populations under the assumption that individuals in the populations can be placed into well defined descriptive stages. Density feedback is modeled through an assumption that (stage-specific) fertilities and transitions are proportional to a resource uptake functional which is dependent upon a total weighted population size. It is shown how, if stage-specific differences in mortality are insignificant compared to stage-specific differences in fertility and inter-stage transitions, a nonlinear version of the strong ergodic theorem of demography mathematically separates the population level dynamics from the dynamics of the stage distribution vector, which is shown to stabilize independently of the population level dynamics. The nonlinear dynamics at the population level are governed by a key parameter π that encapsulates the stage-specific parameters and thereby affords a means by which population level dynamics can be linked to properties of individual organisms. The method is applied to a community of stagestructured populations competing for a common limiting resource, and it is seen how the parameter π determines the competitively superior species. An example of size structured competitors illustrates how the method can relate the competitive success of a species to such size-specific properties as resource conversion efficiencies and allocation fractions for individual growth and reproduction, largest adult body size, and size at birth and maturation.

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Integrating Chain-of-Thought and Retrieval Augmented Generation Enhances Rare Disease Diagnosis from Clinical Notes

arXiv

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arXiv 2025年

作者： Wu, Da Wang, Zhanliang Nguyen, Quan Wang, Kai Raymond G. Perelman Center for Cellular and Molecular Therapeutics Children's Hospital of Philadelphia PhiladelphiaPA19104 United States Applied Mathematics and Computational Science Graduate Program University of Pennsylvania PhiladelphiaPA19104 United States Bioengineering Graduate Program University of Pennsylvania PhiladelphiaPA19104 United States Department of Pathology and Laboratory Medicine Perelman School of Medicine University of Pennsylvania PhiladelphiaPA19104 United States

Background: Several studies show that large language models (LLMs) struggle with phenotype-driven gene prioritization for rare diseases. These studies typically use Human Phenotype Ontology (HPO) terms to prompt foundation models like GPT and LLaMA to predict candidate genes. However, in real-world settings, foundation models are not optimized for domain-specific tasks like clinical diagnosis, yet inputs are unstructured clinical notes rather than standardized terms. How LLMs can be instructed to predict candidate genes or disease diagnosis from unstructured clinical notes remains a major challenge. Methods: We introduce RAG-driven CoT and CoT-driven RAG, two methods that combine Chain-of-Thought (CoT) and Retrieval Augmented Generation (RAG) to analyze clinical notes. A five-question CoT protocol mimics expert reasoning, while RAG retrieves data from sources like HPO and OMIM (Online Mendelian Inheritance in Man). We evaluated these approaches on rare disease datasets, including 5,980 Phenopacket-derived notes, 255 literature-based narratives, and 220 in-house clinical notes from Children’s Hospital of Philadelphia. Results: We found that recent foundations models, including Llama 3.3-70B-Instruct and DeepSeek-R1-Distill-Llama-70B, outperformed earlier versions such as Llama 2 and GPT-3.5. We also showed that RAG-driven CoT and CoT-driven RAG both outperform foundation models in candidate gene prioritization from clinical notes;in particular, both methods with DeepSeek backbone resulted in a top-10 gene accuracy of over 40% on Phenopacket-derived clinical notes. RAG-driven CoT works better for high-quality notes, where early retrieval can anchor the subsequent reasoning steps in domain-specific evidence, while CoT-driven RAG has advantage when processing lengthy and noisy notes. Conclusions: Integrating CoT and RAG enhances LLMs’ understanding of clinical notes in the context of rare disease diagnosis, and can facilitate various downstream medical tasks. © 2025, CC

关键词： Chains

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Neutrinos and Gamma Rays from Beta Decays in an Active Galactic Nucleus NGC 1068 Jet

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Physical Review Letters 2025年第15期134卷 151005-151005页

作者： Koichiro Yasuda Nobuyuki Sakai Yoshiyuki Inoue Alexander Kusenko Department of Physics and Astronomy University of California Los Angeles Los Angeles California 90095-1547 USA Department of Earth and Space Science Graduate School of Science Osaka University Toyonaka Osaka 560-0043 Japan Interdisciplinary Theoretical & Mathematical Science Program (iTHEMS) RIKEN 2-1 Hirosawa Saitama 351-0198 Japan Kavli Institute for the Physics and Mathematics of the Universe (WPI) UTIAS The University of Tokyo Kashiwa Chiba 277-8583 Japan

We show that TeV neutrinos and high-energy gamma rays detected from the nearby active galaxy NGC 1068 can simultaneously be explained in a model based on the beta decays of neutrons produced in the photodisintegration of He4 nuclei on ultraviolet photons in the jet. The photodisintegration of nuclei occurs at energies above several PeV, which explains the 1–100 TeV energies of the observed neutrinos. The TeV gamma-ray flux accompanying the beta decays is expected to be much lower than the neutrino flux, which agrees with the observations of NGC 1068 showing a gamma-ray deficit as compared to the expectations from proton-photon interactions. Furthermore, the synchrotron and inverse Compton gamma-ray flux associated with protons’ Bethe-Heitler pair production and the photopion processes in the jet can be consistent with the observed gamma-ray flux at GeV energies for a plausible range of magnetic fields of jets. This scenario, combining beta decay and Bethe-Heitler, can be applied to other jet Seyfert galaxies such as NGC 4151. Future measurements of the neutrino flavor ratio can help confirm the beta-decay origin of the observed neutrinos.

关键词： Active Galactic Nuclei

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THE DYNAMICS OF HIERARCHICAL AGE-STRUCTURED POPULATIONS

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JOURNAL OF MATHEMATICAL BIOLOGY 1994年第7期32卷 705-729页

作者： CUSHING, JM 1. Department of Mathematics Interdisciplinary Program on Applied Mathematics Building 89 University of Arizona 85721 Tucson AZ USA

An age-structured population is considered in which the birth and death rates of an individual of age a is a function of the density of individuals older and/or younger than a. An existence/uniqueness theorem is proved for the McKendrick equation that governs the dynamics of the age distribution function. This proof shows how a decoupled ordinary differential equation for the total population size can be derived. This result makes a study of the population's asymptotic dynamics (indeed, often its global asymptotic dynamics) mathematically tractable. Several applications to models for intra-specific competition and predation are given.

关键词： AGE-STRUCTURED POPULATION DYNAMICS MCKENDRICK EQUATIONS HIERARCHICAL MODELS EXISTENCE/UNIQUENESS ASYMPTOTIC DYNAMICS GLOBAL STABILITY INTRA-SPECIFIC COMPETITION CANNIBALISM

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On the relationship between r and R₀ and its role in the bifurcation of stable equilibria of Darwinian matrix models

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Journal of Biological Dynamics 2011年第3期5卷 277-297页

作者： Cushing, J.M. Department of Mathematics Interdisciplinary Program in Applied Mathematics University of Arizona Tucson AZ 85721 United States

If the demographic parameters in a matrix model for the dynamics of a structured population are dependent on a parameter u, then the population growth rate r = r(u) and the net reproductive number R₀ = R₀(u) are functions of u. For a general matrix model, we showthat r and R₀ share critical values and extrema at values u = u^* for which r(u^*) = R₀(u^*) = 1. This allows us to re-interpret, in terms of the more analytically tractable quantity R₀, a fundamental bifurcation theorem for non-linear Darwinian matrix models from the evolutionary game theory that concerns the destabilization of the extinction equilibrium and creation of positive equilibria. Two illustrations are given: a theoretical study of trade-offs between fertility and survivorship in the evolution of an evolutionarily stable strategies and an application to an experimental study of the evolution to a genetic polymorphism. © 2011 Taylor & Francis.

关键词： Bifurcation Darwinian matrix models Equilibria Net reproductive number The evolutionary game theory

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Motor cortex repetitive transcranial magnetic stimulation in fibromyalgia: a multicentre randomised controlled trial

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British Journal of Anaesthesia 2025年第6期134卷 1756-1764页

作者： Silva, Valquíria A. Baptista, Abrahão F. Fonseca, Alessandra S. Carneiro, Adriana M. Brunoni, André R. Carrilho, Paulo.E.M. Lins, Catarina C. Kubota, Gabriel T. Fernandes, Ana Mércia B.L. Lapa, Jorge.D.S. dos Santos, Lucas M. Sasso, Ivo Monte-Silva, Katia Poindessous-Jazat, Frédérique Mori, Nobuhiko Miki, Kenji Baltar, Adriana Tanaka, Clarice Teixeira, Manoel J. Hosomi, Koichi Bouhassira, Didier Attal, Nadine Ciampi de Andrade, Daniel LIM 62 - Pain Center Department of Neurology São Paulo Brazil Service of Interdisciplinary Neuromodulation (SIN) Department and Institute of Psychiatry São Paulo Brazil Medical-Surgical Nursing Department University of São Paulo São Paulo Brazil Center for Mathematics Computation and Cognition Federal University of ABC São Paulo Brazil Mood Disorder Program (Pro-GRUDA) Department of Psychiatry University of São Paulo São Paulo Brazil Medicine School “Professor Orival Alves” State University of Western Paraná (UNIOESTE) Paraná Brazil Neurosurgery Unit Hospital de Cirurgia Sergipe Aracaju Brazil Department of Medicine Federal University of Sergipe Sergipe São Cristóvão Brazil LIM 54 - Physiotherapy Research Laboratory University of São Paulo São Paulo Brazil Applied Neuroscience Laboratory Universidade Federal de Pernambuco Cidade Universitária Pernambuco Brazil UVSQ-Paris-Saclay University Ambroise Paré Hospital Boulogne-Billancourt U987 France Department of Neurosurgery Osaka University Graduate School of Medicine Osaka Japan Faculty of Health Science Osaka Yukioka College of Health Science Osaka Japan Center for Pain Management Hayaishi Hospital Osaka Japan Center for Neuroplasticity and Pain (CNAP) Department of Health Science and Technology University of Aalborg Gistrup Denmark

Background: Despite affecting 2–4% of the population worldwide, fibromyalgia often remains refractory to treatment. Here we report the first international randomised double-blind, sham-controlled trial developed to assess the efficacy of repetitive transcranial magnetic stimulation (rTMS) as an add-on therapy for fibromyalgia. Methods: Women aged ≥18 yr with fibromyalgia refractory to best available treatment were enrolled in Brazil, France, and Japan, and randomised to 10 Hz motor cortex (M1) rTMS, 3000 pulses day⁻¹, or sham stimulation. This included 10 induction sessions over 2 weeks, followed by weekly maintenance (6 weeks), and fortnightly extended maintenance (8 weeks). Primary outcome was ≥50% pain reduction at week 8 compared with baseline. Secondary outcomes included pain interference, mood, global impression of change, and Fibromyalgia Impact Questionnaire (FIQ) scores at weeks 8 and 16. Results: We randomised 101 women (mean age 48 [range 25-83] yr) into active (n=52) or sham (n=49) arms. Bayesian analysis revealed a 99.4% probability of ≥50% pain reduction at week 8 in the active group vs sham (odds ratio [OR] 3.04;95% credible interval [95% CrI] 1.26–8.06), with a number needed to treat of 4.54. Frequentist analysis confirmed that relative pain reduction was higher in the active than in the sham group (40.4% vs 18.4%, P=0.028). At week 16, this probability reduced to 34.2% (OR 0.815;95% CrI 0.313–2.1), but the likelihood of FIQ score reduction was 79.1%. The intervention appeared safe. Conclusions: Add-on M1-repetitive transcranial magnetic stimulation reduced pain intensity up to 8 weeks in women with fibromyalgia. Although analgesic effects waned, functional improvements remained during extended maintenance at week 16. © 2025 The Authors

关键词： chronic pain clinical trial fibromyalgia neuromodulation transcranial magnetic stimulation

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Biomedical data and AI

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Science China Life Sciences 2025年第5期68卷 1536-1540页

作者： Hao Xu Shibo Zhou Zefeng Zhu Vincenzo Vitelli Liangyi Chen Ziwei Dai Ning Yang Luhua Lai Shengyong Yang Sergey Ovchinnikov Zhuoran Qiao Sirui Liu Chen Song Jianfeng Pei Han Wen Jianfeng Feng Yaoyao Zhang Zhengwei Xie Yang-Yu Liu Zhiyuan Li Fulai Jin Hao Li Mohammad Lotfollahi Xuegong Zhang Ge Yang Shihua Zhang Ge Gao Pulin Li Qi Liu Jing-Dong Jackie Han Peking-Tsinghua Center for Life Sciences (CLS) Academy for Advanced Interdisciplinary StudiesPeking University Center for Quantitative Biology (CQB) Academy for Advanced Interdisciplinary StudiesPeking University Peking University-Tsinghua University-National Institute of Biological Sciences Joint Graduate Program Academy for Advanced Interdisciplinary StudiesPeking University Department of Physics University of Chicago School of Life Sciences Southern University of Science and Technology Peking University Chengdu Academy for Advanced Interdisciplinary Biotechnologies College of Chemistry and Molecular Engineering Peking University Department of Biotherapy Cancer Center and State Key Laboratory of BiotherapyWest China HospitalSichuan University Department of Biology Massachusetts Institute of Technology Lambic Therapeutics Inc. Changping Laboratory Al for Science Institute Key Laboratory of Computational Neuroscience and Brain-Inspired Intelligence Fudan University Department of Obstetrics and Gynecology West China Second University HospitalSichuan University Peking University International Cancer Institute and Peking University-Yunnan Baiyao International Medical Institute and State Key Laboratory of Natural and Biomimetic Drugs Department of Molecular and Cellular PharmacologySchool of Pharmaceutical SciencesPeking University Health Science CenterPeking University Channing Division of Network Medicine Department of MedicineBrigham and Women's Hospital and Harvard Medical School Center for Artificial Intelligence and Modeling the Carl R.Woese Institute for Genomic BiologyUniversity of Illinois Urbana-Champaign Department of Genetics and Genome Sciences School of Medicine and Department of Computer and Data Sciences and Department of Population and Quantitative Health SciencesCase Western Reserve University Department of Biochemistry and Biophysics University of California Sanger Institute Department of Automation Tsinghua University State Key Laboratory of Multimodal Artificial Intelligence Systems I

The development of artificial intelligence(AI) and the mining of biomedical data complement each other. From the direct use of computer vision results to analyze medical images for disease screening, to now integrating biological knowledge into models and even accelerating the development of new AI based on biological discoveries, the boundaries of both are constantly expanding, and their connections are becoming closer.

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Polaronic neutron in dilute α matter: A p-wave Bose polaron

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Physical Review C 2025年第2期111卷 025802-025802页

作者： Hiroyuki Tajima Hajime Moriya Tomoya Naito Wataru Horiuchi Eiji Nakano Kei Iida Department of Physics Graduate School of Science The University of Tokyo Tokyo 113-0033 Japan RIKEN Nishina Center Wako 351-0198 Japan Research Center for Nuclear Physics Osaka University Ibaraki 567-0047 Japan Interdisciplinary Theoretical and Mathematical Science Program (iTHEMS) RIKEN Wako 351-0198 Japan Department of Physics Osaka Metropolitan University Osaka 558-8585 Japan Nambu Yoichiro Institute of Theoretical and Experimental Physics (NITEP) Osaka Metropolitan University Osaka 558-8585 Japan Department of Physics Hokkaido University Sapporo 060-0810 Japan Department of Mathematics and Physics Kochi University Kochi 780-8520 Japan

We theoretically investigate quasiparticle properties of a neutron immersed in an alpha condensate, which is one of the possible states of dilute symmetric nuclear matter. The resonant p-wave neutron-alpha scattering, which plays a crucial role in forming halo nuclei, is considered. This system is similar to a Bose polaron near the p-wave Feshbach resonance that can be realized in cold-atomic experiments. Calculating the self-energy within the field-theoretical approach, we give an analytical formula for the effective mass of a polaronic neutron as a function of alpha condensation density. Moreover, two adjacent neutrons in a medium, each of which behaves like a stable polaron having an enhanced effective mass, can form a bound dineutron, with the help of S01 neutron-neutron attraction. This is in contrast to the case of the vacuum, where a dineutron is known to be unbound. Our result is useful for understanding many-body physics in astrophysical environments as well as the formation of multinucleon clusters in neutron-halo nuclei.

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Competitive outcomes changed by evolution

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Journal of Biological Dynamics 2011年第3期5卷 227-252页

作者： Rael, R.C. Vincent, T.L. Cushing, J.M. Interdisciplinary Program in Applied Mathematics University of Arizona Tucson AZ United States Aerospace and Mechanical Engineering University of Arizona Tucson AZ United States Department of Mathematics and Interdisciplinary Program in Applied Mathematics University of Arizona Tucson AZ United States

When evolution plays a role, population dynamic models alone are not sufficient for determining the outcome of multi-species *** an expansion of Maynard Smith's concept of an evolutionarily stable strategy, evolutionary game theory (EGT) combines population and evolutionary dynamics so that natural selection becomes a dynamic game with phenotypic traits as strategies. Using EGT,we showhowevolution can change the outcome of the interaction between two competing *** are particularly interested in situations where the interaction changes from one of competitive exclusion to one of coexistence and where the interaction changes from the exclusion of one species to the exclusion of the other. There are two crucial factors that determine whether or not such events can occur: the rate of evolution (which is proportional to the amount of variability in phenotypic traits within a species) and what we term the boxer effect, a phenomenon that concerns how the intensity of interspecies competition relates to species' trait differences. We apply the theory to data from two historical competition experiments involving species of flour beetle from the genus Tribolium. In both applications, we show how EGT can explain certain seemingly 'anomalous' experimental results. © 2011 Taylor & Francis.

关键词： Competition Competitive coexistence Competitive exclusion Evolutionarily stable strategy Evolutionary game theory

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Truncated Gaussian RBF Differences are Always Inferior to Finite Differences of the Same Stencil Width

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Communications in Computational Physics 2009年第1期5卷 42-60页

作者： John P.Boyd Lei Wang Department of Atmospheric Oceanic and Space ScienceUniversity of MichiganAnn Arbor MI 48109USA Department of Mathematics and Program in Applied and Interdisciplinary Mathematics University of MichiganAnn Arbor MI 48109USA

Radial basis functions(RBFs)can be used to approximate derivatives and solve differential equations in several ***,we compare one important scheme to ordinary finite differences by a mixture of numerical experiments and theoretical Fourier analysis,that is,by deriving and discussing analytical formulas for the error in differentiating exp(ikx)for arbitrary k.‘Truncated RBF differences”are derived from the same strategy as Fourier and Chebyshev pseudospectral methods:Differentiation of the Fourier,Chebyshev or RBF interpolant generates a differentiation matrix that maps the grid point values or samples of a function u(x)into the values of its derivative on the *** Fourier and Chebyshev interpolants,the action of the differentiation matrix can be computed indirectly but efficiently by the Fast Fourier Transform(FFT).For RBF functions,alas,the FFT is inapplicable and direct use of the dense differentiation matrix on a grid of N points is prohibitively expensive(O(N2))unless N is ***,for Gaussian RBFs,which are exponentially localized,there is another option,which is to truncate the dense matrix to a banded matrix,yielding“truncated RBF differences”.The resulting formulas are identical in form to finite differences except for the difference *** a grid of spacing h with the RBF asφ(x)=exp(−α^(2)(x/h)^(2)),d f dx(0)≈∑^(∞)_(m)=1 wm{f(mh)−f(−mh)},where without approximation wm=(−1)m+12α^(2)/sinh(mα^(2)).We derive explicit formula for the differentiation of the linear function,f(X)≡X,and the errors *** show that Gaussian radial basis functions(GARBF),when truncated to give differentiation formulas of stencil width(2M+1),are significantly less accurate than(2M)-th order finite differences of the same stencil *** error of the infinite series(M=∞)decreases exponentially asα→***,truncated GARBF series have a second error(truncation error)that grows exponentially asα→*** forα∼O(1)where the sum of these two errors is minimized,it is

关键词： Pseudospectral radial basis function high order finite difference nonstandard finite differences spectral differences

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