Topological conjugacy and its relations for symbolic matrices

In 1988 Boyle and Krieger defined sub-matrices for representation matrices of sofic shift. This paper presents some details of relations between integral sub-matrices and representation matrices. Besides, we express a new version of the Decomposition Theorem by sub-matrices. Generally, strong shift equivalence (conjugacy) of sub-matrices does not apply to representation matrices, but we show that this result can be achieved by the fixed diagonal integral sub-matrix.Comment: 18 pages, 4 figure

Extinction of populations and a team of Lyapunov functions

We investigate the $d$-dimensional model, x_i' = \frac{d}{dt}{x_i} = x_i(c_i +\sum_{j=1}^{d'} s_{ij}z_j),\quad \text{where } i=1,\ldots,d. where each $z_j(t)$ is a time fluctuating resource. This "nonautonomous" model is a generalization of an autonomous Lotka-Volterra $d$-dimensional model. It is nonautonomous in the sense that it is not specified how the $z_j(t)$ are determined. Write $S^T$ for the transpose of $S=(s_{ij})$. When the rank of $S^T$ is equal to $d-k$ for $k >0$, we show that at least $k$ species will die out and will do so exponentially fast. For the proof, we invent a family of Lyapunov functions, a "team" of Lyapunov functions that work together to show that $k$ species must die, where $k$ is the dimension of the kernel of $S$. Each Lyapunov function provides constraints as to which species must die out and together they provide a picture of which are likely to die out. We present a "trophic" condition for that Lotka-Volterra systems that guarantees that there is a trapping region that is globally attracting.Comment: 22 pages, 5 figures, 1 tabl

Chemotaxis of Drosophila Border Cells is Modulated by Tissue Geometry Through Dispersion of Chemoattractants

Migratory cells respond to graded concentrations of diffusible chemoattractants in vitro, but how complex tissue geometries in vivo impact chemotaxis is poorly understood. To address this, we studied the Drosophila border cells. Live-imaged border cells varied in their chemotactic migration speeds, which correlated positionally with distinct architectures. We then developed a reduced mathematical model to determine how chemoattractant distribution is affected by tissue architecture. Larger extracellular volumes locally dampened the chemoattractant gradient and, when coupled with an agent-based motion of the cluster, reduced cell speeds. This suggests that chemoattractant levels vary by tissue architectures, informing cell migration behaviors locally, which we tested in vivo. Genetically elevating chemoattractant levels slowed migration in specific architectural regions, while mutants with spacious tissue structure rescued defects from high chemoattractant levels, promoting punctual migration. Our results highlight the interplay between tissue geometry and the local distribution of signaling molecules to orchestrate cell migration.We acknowledge funding from NSF DMS #1953423 to B.E.P. and M.S.-G., NSF IOS #2303587 to M.S.-G. and MERCK SHARP and DOHM LLC funding for N.A. For providing commercial fly stocks, we thank the Bloomington Drosophila Stock Center (NIH P40OD018537) and we thank Dr. Trudi Dr. Schupbach for gifting us critical mutant fly lines. We thank FlyBase (release € FB2024_05)56 for all their resourceshttps://www.sciencedirect.com/science/article/pii/S258900422500219

Chemotaxis of Drosophila border cells is modulated by tissue geometry through dispersion of chemoattractants

Summary: Migratory cells respond to graded concentrations of diffusible chemoattractants in vitro, but how complex tissue geometries in vivo impact chemotaxis is poorly understood. To address this, we studied the Drosophila border cells. Live-imaged border cells varied in their chemotactic migration speeds, which correlated positionally with distinct architectures. We then developed a reduced mathematical model to determine how chemoattractant distribution is affected by tissue architecture. Larger extracellular volumes locally dampened the chemoattractant gradient and, when coupled with an agent-based motion of the cluster, reduced cell speeds. This suggests that chemoattractant levels vary by tissue architectures, informing cell migration behaviors locally, which we tested in vivo. Genetically elevating chemoattractant levels slowed migration in specific architectural regions, while mutants with spacious tissue structure rescued defects from high chemoattractant levels, promoting punctual migration. Our results highlight the interplay between tissue geometry and the local distribution of signaling molecules to orchestrate cell migration

Secular trends of ischaemic heart disease, stroke, and dementia in high-income countries from 1990 to 2017: the Global Burden of Disease Study 2017

Background: We assessed secular trends in the burden of ischaemic heart disease (IHD), stroke, and dementia in the Organization for Economic Co-operation and Development (OECD) countries. Methods: Using the Global Burden of Disease (GBD) Study 2017, we compared sex-specific and age-standardized rates of disability-adjusted life years (DALY); mortality, incidence, and prevalence of IHD and stroke; and dementia per 100,000 people, in the world, OECD countries, and Canada. Results: From 1990 to 2017, the crude incidence number of IHD, stroke, and dementia increased 52%, 76%, and 113%, respectively. Likewise, the prevalence of IHD (75%), stroke (95%), and dementia (119%) increased worldwide. In addition during the study period, the crude global number of deaths of IHD increased 52%, stroke by 41%, and dementia by 146% (9, 6, and 3 million deaths in 2017, respectively). Despite an increase in the crude number of these diseases, the global age-standardized incidence rate of IHD, stroke, and dementia decreased by −27%, − 11%, and − 5%, respectively. Moreover, there was a decline in their age-standardized DALY rates (− 1.17%, − 1.32%, and − 0.23% per year, respectively) and death rates (− 1.29%, − 1.46%, and − 0.17% per year, respectively), with sharper downward trends in Canada and OECD countries. Almost all trends flattened during the last decade. Conclusions: From 1990 to 2017, the age-standardized burden of IHD, stroke, and dementia decreased, more prominently in OECD countries than the world. However, their rising crude numbers mainly due to population growth and ageing require urgent identification of reversible risk and protective factors