Mathematical Modeling for the Assessment of Public Policies in the Cancer Health-Care System Implemented for the Colombian Case

The incidence of cancer has been constantly growing worldwide, placing pressure on health systems and increasing the costs associated with the treatment of cancer. In particular, low- and middle-income countries are expected to face serious challenges related to caring for the majority of the world's new cancer cases in the next 10 years. In this study, we propose a mathematical model that allows for the simulation of different strategies focused on public policies by combining spending and epidemiological indicators. In this way, strategies aimed at efficient spending management with better epidemiological indicators can be determined. For validation and calibration of the model, we use data from Colombia-which, according to the World Bank, is an upper-middle-income country. The results of the simulations using the proposed model, calibrated and validated for Colombia, indicate that the most effective strategy for reducing mortality and financial burden consists of a combination of early detection and greater efficiency of treatment in the early stages of cancer. This approach is found to present a 38% reduction in mortality rate and a 20% reduction in costs (% GDP) when compared to the baseline scenario. Hence, Colombia should prioritize comprehensive care models that focus on patient-centered care, prevention, and early detection.

TDS Similarity: Outlier Analysis Using a Similarity Index to Compare Time-Series Responses of Temporal Dominance of Sensations Tasks

Temporal dominance of sensations (TDS) methods are used to record temporally developing sensations while eating food samples. Results of TDS tasks are typically discussed using averages across multiple trials and panels, and few methods have been developed to analyze differences between individual trials. We defined a similarity index between two time-series responses of TDS tasks. This index adopts a dynamic level to determine the importance of the timing of attribute selection. With a small dynamic level, the index focuses on the duration for attributes to be selected rather than on the timing of the attribute selection. With a large dynamic level, the index focuses on the temporal similarity between two TDS tasks. We performed an outlier analysis based on the developed similarity index using the results of TDS tasks performed in an earlier study. Certain samples were categorized as outliers irrespective of the dynamic level, whereas the categorization of a few samples depended on the level. The similarity index developed in this study achieved individual analyses of TDS tasks, including outlier detection, and adds new analysis techniques to TDS methods.

Global Consensus of High-Order Discrete-Time Multi-Agent Systems with Communication Delay and Saturation Constraint

This article aimed to study the global consensus problem of high-order multi-agent systems with a saturation constraint and communication delay. Among them, all agents are described by discrete-time systems. Firstly, in order to compensate for the communication delay, a networked predictive control method is adopted and a predictive-based control protocol is designed. Secondly, for the neutrally stable agent model, leaderless and leader-following situations are considered and it is proven that, under a fixed communication topology, adopting the prediction-based control protocol makes the multi-agent systems with saturation constraint and communication delay achieve a global consensus. Finally, the results are illustrated via numerical simulation.

Causality in Discrete Time Physics Derived from Maupertuis Reduced Action Principle

Causality describes the process and consequences from an action: a cause has an effect. Causality is preserved in classical physics as well as in special and general theories of relativity. Surprisingly, causality as a relationship between the cause and its effect is in neither of these theories considered a law or a principle. Its existence in physics has even been challenged by prominent opponents in part due to the time symmetric nature of the physical laws. With the use of the reduced action and the least action principle of Maupertuis along with a discrete dynamical time physics yielding an arrow of time, causality is defined as the partial spatial derivative of the reduced action and as such is position- and momentum-dependent and requests the presence of space. With this definition the system evolves from one step to the next without the need of time, while (discrete) time can be reconstructed.

Discrete Survival Model Analysis of Plasmodium falciparum Response to Artemisinin-Based Combination Therapies among Children in Regions of Varying Malaria Transmission in Cameroon

The need to monitor changes in parasite clearance following treatment with artemisinin-based combination therapies (ACTs) is important in the containment of drug resistance. This study aimed to model Plasmodium falciparum response to ACTs among children in two different transmission settings (Mutengene and Garoua) in Cameroon. Using the step function, a discrete-time survival model was fitted with all the covariates included that might play a role in parasite clearance. The probability of clearing parasites within 24 h following treatment was 21.6% and 70.3% for younger children aged 6 to 59 months and 29.3% and 59.8% for older children aged 60 to 120 months in Mutengene and Garoua, respectively. After two days of treatment, the conditional probability of clearing parasites given that they were not cleared on day 1 was 76.7% and 96.6% for children aged 6–59 months and 83.1% and 93.5% for children aged 60–120 months in Mutengene and Garoua, respectively. The model demonstrated that the ecological setting, age group and pretreatment serum levels of creatinine and alanine aminotransferase were the main factors that significantly influenced parasite clearance in vivo after administration of ACTs (p < 0.05). The findings highlight the need for further investigations on host differential response to ACTs in current practice.

Probabilistic Analysis of a Buffer Overflow Duration in Data Transmission in Wireless Sensor Networks

One of the most important problems of data transmission in packet networks, in particular in wireless sensor networks, are periodic overflows of buffers accumulating packets directed to a given node. In the case of a buffer overflow, all new incoming packets are lost until the overflow condition terminates. From the point of view of network optimization, it is very important to know the probabilistic nature of this phenomenon, including the probability distribution of the duration of the buffer overflow period. In this article, a mathematical model of the node of a wireless sensor network with discrete time parameter is proposed. The model is governed by a finite-buffer discrete-time queueing system with geometrically distributed interarrival times and general distribution of processing times. A system of equations for the tail cumulative distribution function of the first buffer overflow period duration conditioned by the initial state of the accumulating buffer is derived. The solution of the corresponding system written for probability generating functions is found using the analytical approach based on the idea of embedded Markov chain and linear algebra. Corresponding result for next buffer overflow periods is obtained as well. Numerical study illustrating theoretical results is attached.

Entropy Derived from Causality

The second law of thermodynamics, with its positive change of entropy for a system not in equilibrium, defines an arrow of time. Interestingly, also, causality, which is the connection between a cause and an effect, requests a direction of time by definition. It is noted that no other standard physical theories show this property. It is the attempt of this work to connect causality with entropy, which is possible by defining time as the metric of causality. Under this consideration that time appears only through a cause–effect relationship (“measured”, typically, in an apparatus called clock), it is demonstrated that time must be discrete in nature and cannot be continuous as assumed in all standard theories of physics including general and special relativity, and classical physics. The following lines of reasoning include: (i) (mechanical) causality requests that the cause must precede its effect (i.e., antecedence) requesting a discrete time interval >0. (ii) An infinitely small time step dt>0 is thereby not sufficient to distinguish between cause and effect as a mathematical relationship between the two (i.e., Poisson bracket) will commute at a time interval dt, while not evidently within discrete time steps Δt. As a consequence of a discrete time, entropy emerges (Riek, 2014) connecting causality and entropy to each other.

Analyzing discrete competing risks data with partially overlapping or independent data sources and nonstandard sampling schemes, with application to cancer registries

This paper demonstrates the flexibility of a general approach for the analysis of discrete time competing risks data that can accommodate complex data structures, different time scales for different causes, and nonstandard sampling schemes. The data may involve a single data source where all individuals contribute to analyses of both cause-specific hazard functions, overlapping datasets where some individuals contribute to the analysis of the cause-specific hazard function of only one cause while other individuals contribute to analyses of both cause-specific hazard functions, or separate data sources where each individual contributes to the analysis of the cause-specific hazard function of only a single cause. The approach is modularized into estimation and prediction. For the estimation step, the parameters and the variance-covariance matrix can be estimated using widely available software. The prediction step utilizes a generic program with plug-in estimates from the estimation step. The approach is illustrated with three prognostic models for stage IV male oral cancer using different data structures. The first model uses only men with stage IV oral cancer from population-based registry data. The second model strategically extends the cohort to improve the efficiency of the estimates. The third model improves the accuracy for those with a lower risk of other causes of death, by bringing in an independent data source collected under a complex sampling design with additional other-cause covariates. These analyses represent novel extensions of existing methodology, broadly applicable for the development of prognostic models capturing both the cancer and noncancer aspects of a patient's health.

Path-sum solution of the Weyl quantum walk in 3 + 1 dimensions

We consider the Weyl quantum walk in 3+1 dimensions, that is a discrete-time walk describing a particle with two internal degrees of freedom moving on a Cayley graph of the group [Formula: see text], which in an appropriate regime evolves according to Weyl's equation. The Weyl quantum walk was recently derived as the unique unitary evolution on a Cayley graph of [Formula: see text] that is homogeneous and isotropic. The general solution of the quantum walk evolution is provided here in the position representation, by the analytical expression of the propagator, i.e. transition amplitude from a node of the graph to another node in a finite number of steps. The quantum nature of the walk manifests itself in the interference of the paths on the graph joining the given nodes. The solution is based on the binary encoding of the admissible paths on the graph and on the semigroup structure of the walk transition matrices.This article is part of the themed issue 'Second quantum revolution: foundational questions'.

Improving Our Ability to Evaluate Underlying Mechanisms of Behavioral Onset and Other Event Occurrence Outcomes: A Discrete-Time Survival Mediation Model

The purpose of this article is to introduce and describe a statistical model that researchers can use to evaluate underlying mechanisms of behavioral onset and other event occurrence outcomes. Specifically, the article develops a framework for estimating mediation effects with outcomes measured in discrete-time epochs by integrating the statistical mediation model with discrete-time survival analysis. The methodology has the potential to help strengthen health research by targeting prevention and intervention work more effectively as well as by improving our understanding of discretized periods of risk. The model is applied to an existing longitudinal data set to demonstrate its use, and programming code is provided to facilitate its implementation.

Equilibrium and Response Properties of the Integrate-and-Fire Neuron in Discrete Time

The integrate-and-fire neuron with exponential postsynaptic potentials is a frequently employed model to study neural networks. Simulations in discrete time still have highest performance at moderate numerical errors, which makes them first choice for long-term simulations of plastic networks. Here we extend the population density approach to investigate how the equilibrium and response properties of the leaky integrate-and-fire neuron are affected by time discretization. We present a novel analytical treatment of the boundary condition at threshold, taking both discretization of time and finite synaptic weights into account. We uncover an increased membrane potential density just below threshold as the decisive property that explains the deviations found between simulations and the classical diffusion approximation. Temporal discretization and finite synaptic weights both contribute to this effect. Our treatment improves the standard formula to calculate the neuron's equilibrium firing rate. Direct solution of the Markov process describing the evolution of the membrane potential density confirms our analysis and yields a method to calculate the firing rate exactly. Knowing the shape of the membrane potential distribution near threshold enables us to devise the transient response properties of the neuron model to synaptic input. We find a pronounced non-linear fast response component that has not been described by the prevailing continuous time theory for Gaussian white noise input.