Z-Pencils

The matrix pencil (A,B) = {tB-A | t \in C} is considered under the assumptions that A is entrywise nonnegative and B-A is a nonsingular M-matrix. As t varies in [0,1], the Z-matrices tB-A are partitioned into the sets L_s introduced by Fiedler and Markham. As no combinatorial structure of B is assumed here, this partition generalizes some of their work where B=I. Based on the union of the directed graphs of A and B, the combinatorial structure of nonnegative eigenvectors associated with the largest eigenvalue of (A,B) in [0,1) is considered.Comment: 8 pages, LaTe

Local and global stability for Lotka-Volterra systems with distributed delays and instantaneous negative feedbacks

This paper addresses the local and global stability of n-dimensional Lotka-Volterra systems with distributed delays and instantaneous negative feedbacks. Necessary and sufficient conditions for local stability independent of the choice of the delay functions are given, by imposing a weak nondelayed diagonal dominance which cancels the delayed competition effect. The global asymptotic stability of positive equilibria is established under conditions slightly stronger than the ones required for the linear stability. For the case of monotone interactions, however, sharper conditions are presented. This paper generalizes known results for discrete delays to systems with distributed delays. Several applications illustrate the results.Fundação para a Ciência e a Tecnologia (FCT) - programa POCI, projecto PDCT/ MAT/56476/2004.Portugal-FEDE

Global Stability of Infectious Disease Models Using Lyapunov Functions

Two systematic methods are presented to guide the construction of Lyapunov functions for general infectious disease models and are thus applicable to establish their global dynamics. Specifically, a matrix-theoretic method using the Perron eigenvector is applied to prove the global stability of the disease-free equilibrium, while a graph-theoretic method based on Kirchhoff\u27s matrix tree theorem and two new combinatorial identities are used to prove the global stability of the endemic equilibrium. Several disease models in the literature and two new cholera models are used to demonstrate the applications of these methods

Global exponential stability of nonautonomous neural network models with continuous distributed delays

For a family of non-autonomous differential equations with distributed delays, we give sufficient conditions for the global exponential stability of an equilibrium point. This family includes most of the delayed models of neural networks of Hopfield type, with time-varying coefficients and distributed delays. For these models, we establish sufficient conditions for their global exponential stability. The existence and global exponential stability of a periodic solution is also addressed. A comparison of results shows that these results are general, news, and add something new to some earlier publications.Fundação para a Ciência e a Tecnologia (FCT

Automated analysis of retinal imaging using machine learning techniques for computer vision

There are almost two million people in the United Kingdom living with sight loss, including around 360,000 people who are registered as blind or partially sighted. Sight threatening diseases, such as diabetic retinopathy and age related macular degeneration have contributed to the 40% increase in outpatient attendances in the last decade but are amenable to early detection and monitoring. With early and appropriate intervention, blindness may be prevented in many cases. Ophthalmic imaging provides a way to diagnose and objectively assess the progression of a number of pathologies including neovascular (“wet”) age-related macular degeneration (wet AMD) and diabetic retinopathy. Two methods of imaging are commonly used: digital photographs of the fundus (the ‘back’ of the eye) and Optical Coherence Tomography (OCT, a modality that uses light waves in a similar way to how ultrasound uses sound waves). Changes in population demographics and expectations and the changing pattern of chronic diseases creates a rising demand for such imaging. Meanwhile, interrogation of such images is time consuming, costly, and prone to human error. The application of novel analysis methods may provide a solution to these challenges. This research will focus on applying novel machine learning algorithms to automatic analysis of both digital fundus photographs and OCT in Moorfields Eye Hospital NHS Foundation Trust patients. Through analysis of the images used in ophthalmology, along with relevant clinical and demographic information, Google DeepMind Health will investigate the feasibility of automated grading of digital fundus photographs and OCT and provide novel quantitative measures for specific disease features and for monitoring the therapeutic success

Global asymptotic stability for neural network models with distributed delays

In this paper, we obtain the global asymptotic stability of the zero solution of a general n-dimensional delayed differential system, by imposing a condition of dominance of the nondelayed terms which cancels the delayed effect. We consider several delayed differential systems in general settings, which allow us to study, as subclasses, the well known neural network models of Hopfield, Cohn-Grossberg, bidirectional associative memory, and static with S-type distributed delays. For these systems, we establish sufficient conditions for the existence of a unique equilibrium and its global asymptotic stability, without using the Lyapunov functional technique. Our results improve and generalize some existing ones.Fundação para a Ciência e a Tecnologia (FCT

From regional pulse vaccination to global disease eradication: insights from a mathematical model of Poliomyelitis

Mass-vaccination campaigns are an important strategy in the global fight against poliomyelitis and measles. The large-scale logistics required for these mass immunisation campaigns magnifies the need for research into the effectiveness and optimal deployment of pulse vaccination. In order to better understand this control strategy, we propose a mathematical model accounting for the disease dynamics in connected regions, incorporating seasonality, environmental reservoirs and independent periodic pulse vaccination schedules in each region. The effective reproduction number, $R_e$, is defined and proved to be a global threshold for persistence of the disease. Analytical and numerical calculations show the importance of synchronising the pulse vaccinations in connected regions and the timing of the pulses with respect to the pathogen circulation seasonality. Our results indicate that it may be crucial for mass-vaccination programs, such as national immunisation days, to be synchronised across different regions. In addition, simulations show that a migration imbalance can increase $R_e$ and alter how pulse vaccination should be optimally distributed among the patches, similar to results found with constant-rate vaccination. Furthermore, contrary to the case of constant-rate vaccination, the fraction of environmental transmission affects the value of $R_e$ when pulse vaccination is present.Comment: Added section 6.1, made other revisions, changed titl

Mastering the game of Go without human knowledge

A long-standing goal of artificial intelligence is an algorithm that learns, tabula rasa, superhuman proficiency in challenging domains. Recently, AlphaGo became the first program to defeat a world champion in the game of Go. The tree search in AlphaGo evaluated positions and selected moves using deep neural networks. These neural networks were trained by supervised learning from human expert moves, and by reinforcement learning from self-play. Here we introduce an algorithm based solely on reinforcement learning, without human data, guidance or domain knowledge beyond game rules. AlphaGo becomes its own teacher: a neural network is trained to predict AlphaGo’s own move selections and also the winner of AlphaGo’s games. This neural network improves the strength of the tree search, resulting in higher quality move selection and stronger self-play in the next iteration. Starting tabula rasa, our new program AlphaGo Zero achieved superhuman performance, winning 100–0 against the previously published, champion-defeating AlphaGo

Identification of a Serum-Induced Transcriptional Signature Associated With Type 1 Diabetes in the BioBreeding Rat

OBJECTIVE - Inflammatory mediators associated with type 1 diabetes are dilute and difficult to measure in the periphery, necessitating development of more sensitive and informative biomarkers for studying diabetogenic mechanisms, assessing preonset risk, and monitoring therapeutic interventions. RESEARCH DESIGN AND METHODS - We previously utilized a novel bioassay in which human type 1 diabetes sera were used to induce a disease-specific transcriptional signature in unrelated, healthy peripheral blood mononuclear cells (PBMCs). Here, we apply this strategy to investigate the inflammatory state associated with type 1 diabetes in biobreeding (BB) rats. RESULTS - Consistent with their common susceptibility, sera of both spontaneously diabetic BB DRlyp/lyp and diabetes inducible BB DR+/+ rats induced transcription of cytokines, immune receptors, and signaling molecules in PBMCs of healthy donor rats compared with control sera. Like the human type 1 diabetes signature, the DRlyp/lyp signature, which is associated with progression to diabetes, was differentiated from that of the DR+/+ by induction of many interleukin (IL)-1-regulated genes. Supplementing cultures with an IL-1 receptor antagonist (IL-1Ra) modulated the DRlyp/lyp signature (P < 10-6), while administration of IL-1Ra to DRlyp/lyp rats delayed onset (P = 0.007), and sera of treated animals did not induce the characteristic signature. Consistent with the presence of immunoregulatory cells in DR+/+ rats was induction of a signature possessing negative regulators of transcription and inflammation. CONCLUSIONS - Paralleling our human studies, serum signatures in BB rats reflect processes associated with progression to type 1 diabetes. Furthermore, these studies support the potential utility of this approach to detect changes in the inflammatory state during therapeutic intervention

Convergence of asymptotic systems of non-autonomous neural network models with infinite distributed delays

In this paper we investigate the global convergence of solutions of non-autonomous Hopfield neural network models with discrete time-varying delays, infinite distributed delays, and possible unbounded coefficient functions. Instead of using Lyapunov functionals, we explore intrinsic features between the non-autonomous systems and their asymptotic systems to ensure the boundedness and global convergence of the solutions of the studied models. Our results are new and complement known results in the literature. The theoretical analysis is illustrated with some examples and numerical simulations.The paper was supported by the Research Centre of Mathematics of the University of Minho with the Portuguese Funds from the "Fundacao para a Ciencia e a Tecnologia", through the Project PEstOE/MAT/UI0013/2014. The author thanks the referee for valuable comments.info:eu-repo/semantics/publishedVersio