Some results and problems for anisotropic random walks on the plane

This is an expository paper on the asymptotic results concerning path behaviour of the anisotropic random walk on the two-dimensional square lattice Z^2. In recent years Mikl\'os and the authors of the present paper investigated the properties of this random walk concerning strong approximations, local times and range. We give a survey of these results together with some further problems.Comment: 20 page

Trapping in complex networks

We investigate the trapping problem in Erdos-Renyi (ER) and Scale-Free (SF) networks. We calculate the evolution of the particle density $\rho(t)$ of random walkers in the presence of one or multiple traps with concentration $c$. We show using theory and simulations that in ER networks, while for short times $\rho(t) \propto \exp(-Act)$, for longer times $\rho(t)$ exhibits a more complex behavior, with explicit dependence on both the number of traps and the size of the network. In SF networks we reveal the significant impact of the trap's location: $\rho(t)$ is drastically different when a trap is placed on a random node compared to the case of the trap being on the node with the maximum connectivity. For the latter case we find \rho(t)\propto\exp\left[-At/N^\frac{\gamma-2}{\gamma-1}\av{k}\right] for all $\gamma>2$, where $\gamma$ is the exponent of the degree distribution $P(k)\propto k^{-\gamma}$.Comment: Appendix adde

Measuring degree-degree association in networks

The Pearson correlation coefficient is commonly used for quantifying the global level of degree-degree association in complex networks. Here, we use a probabilistic representation of the underlying network structure for assessing the applicability of different association measures to heavy-tailed degree distributions. Theoretical arguments together with our numerical study indicate that Pearson's coefficient often depends on the size of networks with equal association structure, impeding a systematic comparison of real-world networks. In contrast, Kendall-Gibbons' $\tau_{b}$ is a considerably more robust measure of the degree-degree association

Tunneling and Metastability of continuous time Markov chains

We propose a new definition of metastability of Markov processes on countable state spaces. We obtain sufficient conditions for a sequence of processes to be metastable. In the reversible case these conditions are expressed in terms of the capacity and of the stationary measure of the metastable states

Limiting Behaviour of the Mean Residual Life

In survival or reliability studies, the mean residual life or life expectancy is an important characteristic of the model. Here, we study the limiting behaviour of the mean residual life, and derive an asymptotic expansion which can be used to obtain a good approximation for large values of the time variable. The asymptotic expansion is valid for a quite general class of failure rate distributions--perhaps the largest class that can be expected given that the terms depend only on the failure rate and its derivatives.Comment: 19 page

The role of the emergency department in the management of acute heart failure: an international perspective on education and research

Emergency departments are a major entry point for the initial management of acute heart failure (AHF) patients throughout the world. The initial diagnosis, management and disposition - the decision to admit or discharge - of AHF patients in the emergency department has significant downstream implications. Misdiagnosis, under or overtreatment, or inappropriate admission may place patients at increased risk for adverse events, and add costs to the healthcare system. Despite the critical importance of initial management, data are sparse regarding the impact of early AHF treatment delivered in the emergency department compared to inpatient or chronic heart failure management. Unfortunately, outcomes remain poor, with nearly a third of patients dying or re-hospitalised within 3 months post-discharge. In the absence of robust research evidence, consensus is an important source of guidance for AHF care. Thus, we convened an international group of practising emergency physicians, cardiologists and advanced practice nurses with the following goals to improve outcomes for AHF patients who present to the emergency department or other acute care setting through: (a) a better understanding of the pathophysiology, presentation and management of the initial phase of AHF care; (b) improving initial management by addressing knowledge gaps between best practices and current practice through education and research; and (c) to establish a framework for future emergency department-based international education and research

Shared decision making in patients with low risk chest pain: prospective randomized pragmatic trial.

OBJECTIVE: To compare the effectiveness of shared decision making with usual care in choice of admission for observation and further cardiac testing or for referral for outpatient evaluation in patients with possible acute coronary syndrome. DESIGN: Multicenter pragmatic parallel randomized controlled trial. SETTING: Six emergency departments in the United States. PARTICIPANTS: 898 adults (aged \u3e17 years) with a primary complaint of chest pain who were being considered for admission to an observation unit for cardiac testing (451 were allocated to the decision aid and 447 to usual care), and 361 emergency clinicians (emergency physicians, nurse practitioners, and physician assistants) caring for patients with chest pain. INTERVENTIONS: Patients were randomly assigned (1:1) by an electronic, web based system to shared decision making facilitated by a decision aid or to usual care. The primary outcome, selected by patient and caregiver advisers, was patient knowledge of their risk for acute coronary syndrome and options for care; secondary outcomes were involvement in the decision to be admitted, proportion of patients admitted for cardiac testing, and the 30 day rate of major adverse cardiac events. RESULTS: Compared with the usual care arm, patients in the decision aid arm had greater knowledge of their risk for acute coronary syndrome and options for care (questions correct: decision aid, 4.2 v usual care, 3.6; mean difference 0.66, 95% confidence interval 0.46 to 0.86), were more involved in the decision (observing patient involvement scores: decision aid, 18.3 v usual care, 7.9; 10.3, 9.1 to 11.5), and less frequently decided with their clinician to be admitted for cardiac testing (decision aid, 37% v usual care, 52%; absolute difference 15%; P CONCLUSIONS: Use of a decision aid in patients at low risk for acute coronary syndrome increased patient knowledge about their risk, increased engagement, and safely decreased the rate of admission to an observation unit for cardiac testing.Trial registration ClinicalTrials.gov NCT01969240

Using deep learning for ordinal classification of mobile marketing user conversion

In this paper, we explore Deep Multilayer Perceptrons (MLP) to perform an ordinal classification of mobile marketing conversion rate (CVR), allowing to measure the value of product sales when an user clicks an ad. As a case study, we consider big data provided by a global mobile marketing company. Several experiments were held, considering a rolling window validation, different datasets, learning methods and performance measures. Overall, competitive results were achieved by an online deep learning model, which is capable of producing real-time predictions.This article is a result of the project NORTE-01-0247-FEDER-017497, supported by Norte Portugal Regional Operational Programme (NORTE 2020), under the PORTUGAL 2020 Partnership Agreement, through the European Regional Development Fund (ERDF). This work was also supported by Funda¸c˜ao para a Ciˆencia e Tecnologia (FCT) within the Project Scope: UID/CEC/00319/201

Mutation, selection, and ancestry in branching models: a variational approach

We consider the evolution of populations under the joint action of mutation and differential reproduction, or selection. The population is modelled as a finite-type Markov branching process in continuous time, and the associated genealogical tree is viewed both in the forward and the backward direction of time. The stationary type distribution of the reversed process, the so-called ancestral distribution, turns out as a key for the study of mutation-selection balance. This balance can be expressed in the form of a variational principle that quantifies the respective roles of reproduction and mutation for any possible type distribution. It shows that the mean growth rate of the population results from a competition for a maximal long-term growth rate, as given by the difference between the current mean reproduction rate, and an asymptotic decay rate related to the mutation process; this tradeoff is won by the ancestral distribution. Our main application is the quasispecies model of sequence evolution with mutation coupled to reproduction but independent across sites, and a fitness function that is invariant under permutation of sites. Here, the variational principle is worked out in detail and yields a simple, explicit result.Comment: 45 pages,8 figure