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Analysis of a generalized model for influenza including differential susceptibility due to immunosuppression
(SPIE-INT SOC OPTICAL ENGINEERING, 2014-01-01) Hincapié, D.; Ospina, J.; Hincapié, D.; Ospina, J.; Universidad EAFIT. Departamento de Ciencias; Lógica y Computación
Recently, a mathematical model of pandemic influenza was proposed including typical control strategies such as antivirals, vaccination and school closure; and considering explicitly the effects of immunity acquired from the early outbreaks on the ulterior outbreaks of the disease. In such model the algebraic expression for the basic reproduction number (without control strategies) and the effective reproduction number (with control strategies) were derived and numerically estimated. A drawback of this model of pandemic influenza is that it ignores the effects of the differential susceptibility due to immunosuppression and the effects of the complexity of the actual contact networks between individuals. We have developed a generalized model which includes such effects of heterogeneity. Specifically we consider the influence of the air network connectivity in the spread of pandemic influenza and the influence of the immunosuppresion when the population is divided in two immune classes. We use an algebraic expression, namely the Tutte polynomial, to characterize the complexity of the contact network. Until now, The influence of the air network connectivity in the spread of pandemic influenza has been studied numerically, but not algebraic expressions have been used to summarize the level of network complexity. The generalized model proposed here includes the typical control strategies previously mentioned (antivirals, vaccination and school closure) combined with restrictions on travel. For the generalized model the corresponding reproduction numbers will be algebraically computed and the effect of the contact network will be established in terms of the Tutte polynomial of the network. © 2014 Copyright SPIE.
Analysis of the boundary conditions for pyramidal spine fins in extended surface heat transfer
(WITPress, 2014-01-01) Carranza, R.G.; Ospina, J.; Carranza, R.G.; Ospina, J.; Universidad EAFIT. Departamento de Ciencias; Lógica y Computación
Many studies are conducted for pyramidal spine fins relating to temperature profiles and fin efficiencies. However, it is found that a deeper look into the boundary conditions is required. The conditions at the base are simple enough, but the conditions at the tip are more complicated. Despite what condition is applied to the tip, the value at the tip actually has a specific value that is a function of the square root of the Biot number. This result is proven using basic principles from calculus, like the Limit and L’Hospital’s rule. © 2014 WIT Press.
Analytical solution for transient flow of a generalized bingham fluid with memory in a movable tube using computer algebra
(SPRINGER, 2007-01-01) Ospina, Juan; Velez, Mario; Ospina, Juan; Velez, Mario; Universidad EAFIT. Departamento de Ciencias; Lógica y Computación
A rheological linear model for a certain generalized Bingham fluid with rheological memory, which flows in a movable tube is proposed and analytically solved. The model is a system of two linear and coupled partial differential equations with integral memory. We apply the Laplace transform method making the inverse transform by means of the Bromwich integral and the theorem of residues and the analytical solution are obtained using computer algebra. We deduce the explicit forms of the velocity and stress profiles for the generalized Bingham fluid in terms of Bessel and Struve functions. Various limit cases are obtained and the standard Hagen-Poiseuille and Buckingham-Reiner equations are recovered from more general equations. This works shows the powerful of Maple to solve complex rheological problems in an analytical form as it is presented here by the first time. © Springer-Verlag Berlin Heidelberg 2007.
Basic reproductive rate of a spatial epidemic model using computer algebra software
(2005-01-01) Doracelly Hincapié, P.; Juan Ospina, G.; Doracelly Hincapié, P.; Juan Ospina, G.; Universidad EAFIT. Departamento de Ciencias; Lógica y Computación
Using computer algebra software we obtain the basic reproductive rate corresponding to the propagation of a directly transmitted disease in a circular habitat when the disease is endemic at the boundary. The method used is the Laplace Transform Technique and calculus of residues. The results that were obtained include both the explicit form of the R0 for the boundary condition that was considered, as the explicit symbolic solution of the model equation. The method that was used can be extended to other more complex problems such as indirectly transmitted diseases with one or more intermediary hosts or effects of genetic, immunological, geographical or social heterogeneity in the human population. This application indicates that the computer algebra software for symbolic computation has a very promissory future in mathematical epidemiology.
Combining interactive and automatic reasoning in first order theories of functional programs
(SPRINGER, 2012-01-01) Bove, A.; Dybjer, P.; Sicard-Ramírez, A.; Bove, A.; Dybjer, P.; Sicard-Ramírez, A.; Universidad EAFIT. Departamento de Ciencias; Lógica y Computación
We propose a new approach to the computer-assisted verification of functional programs. We work in first order theories of functional programs which are obtained by extending Aczel's first order theory of combinatory formal arithmetic with positive inductive and coinductive predicates. Rather than building a special purpose system we implement our theories in Agda, a proof assistant for dependent type theory which can be used as a generic theorem prover. Agda provides support for interactive reasoning by encoding first order theories using the formulae-as-types principle. Further support is provided by off-the-shelf automatic theorem provers for first order logic which can be called by a program which translates Agda representations of first order formulae into the TPTP language understood by the provers. We show some examples where we combine interactive and automatic reasoning, covering both proof by induction and coinduction. © 2012 Springer-Verlag Berlin Heidelberg.
Computing Tutte polynomials of contact networks in classrooms
(SPIE-INT SOC OPTICAL ENGINEERING, 2013-01-01) Hincapié, D.; Ospina, J.; Hincapié, D.; Ospina, J.; Universidad EAFIT. Departamento de Ciencias; Lógica y Computación
Objective: The topological complexity of contact networks in classrooms and the potential transmission of an infectious disease were analyzed by sex and age. Methods: The Tutte polynomials, some topological properties and the number of spanning trees were used to algebraically compute the topological complexity. Computations were made with the Maple package GraphTheory. Published data of mutually reported social contacts within a classroom taken from primary school, consisting of children in the age ranges of 4-5, 7-8 and 10-11, were used. Results: The algebraic complexity of the Tutte polynomial and the probability of disease transmission increases with age. The contact networks are not bipartite graphs, gender segregation was observed especially in younger children. Conclusion: Tutte polynomials are tools to understand the topology of the contact networks and to derive numerical indexes of such topologies. It is possible to establish relationships between the Tutte polynomial of a given contact network and the potential transmission of an infectious disease within such network. © 2013 SPIE.
The Critical Proportion of Immune Individuals needed to Control Hepatitis B
(SPIE-INT SOC OPTICAL ENGINEERING, 2016-05-13) Ospina, J.; Hincapié-Palacio, D.; Ospina, J.; Hincapié-Palacio, D.; Universidad EAFIT. Departamento de Ciencias; Lógica y Computación
We estimate the critical proportion of immunity (Pc) to control hepatitis B in Medellin - Colombia, based on a random population survey of 2077 individuals of 6-64 years of age. The force of infection (Fi) was estimated according to empirical data of susceptibility by age S(a), assuming a quadratic expression. Parameters were estimated by adjusting data to a nonlinear regression. Fi was defined by -(ds(a)/da)/s(a) and according to the form of the empirical curve S(a) we assume a quadratic expression given by S(a)= Ea2+Ba+C. Then we have the explicit expression for the accumulated Fi by age given by F(a) = -a(Ea+B)/c. The expression of average infection age A is obtained as A = L + EL3/(3C)+BL2/(2C) and the basic reproductive number R-0 is obtained as R-0 = 1 + 6C/(6C+2EL2+3BL). From the las result we obtain the Pc given by Pc=6C/(12C+2EL2+3BL). Numerical simulations were performed with the age-susceptibility proportion and initial values (a=0.02, b=20, c=100), obtaining an adjusted coefficient of multiple determination of 64.83%. According to the best estimate, the algebraic expressions for S(a) and the Fi were derived. Using the result of Fi, we obtain A = 30, L = 85; R-0 CI 95%: 1.42 - 1.64 and Pc: 0-0.29. These results indicate that at the worst case, to maintain control of the disease should be immunes at least 30% of susceptible individuals. Similar results were obtained by sex and residential area.
A debugging scheme for functional logic programs
(Elsevier BV, 2002-01-01) Alpuente, M.; Correa, F.; Falaschi, M.; Alpuente, M.; Correa, F.; Falaschi, M.; Universidad EAFIT. Departamento de Ciencias; Lógica y Computación
We present a generic scheme for the declarative debugging of functional logic programs which is valid for eager as well as lazy programs. In particular we show that the framework extends naturally some previous work and applies to the most modern lazy strategies, such as needed narrowing. First we associate to our programs a semantics based on a (continuous) immediate consequence operator, TR, which models computed answers. We show that, given the intended specification of a program R, it is possible to check the correctness of R by a single step of TR. We consider then a more effective methodology which is based on abstract interpretation: by approximating the intended specification of the success set we derive a finitely terminating diagnosis method, which can be used statically and is parametric w.r.t. to the chosen approximation. In order to correct the bugs, we sketch a preliminary deductive approach which uses example-guided unfolding. We specialize the incorrect rules w.r.t. sets of positive and negative examples which are gathered (bottom-up) during the diagnosis process, so that all refutations of negative examples and no refutation of positive examples are excluded. Our debugging framework does not require the user to either provide error symptoms in advance or answer difficult questions concerning program correctness. We extend an implementation of our system to the case of needed narrowing and illustrate it through some examples which demonstrate the practicality of our approach. © 2002 Published by Elsevier Science B.V.
Declarative debugging of functional logic programs
(Elsevier BV, 2001-01-01) Alpuente, M.; Correa, F.J.; Falaschi, M.; Alpuente, M.; Correa, F.J.; Falaschi, M.; Universidad EAFIT. Departamento de Ciencias; Lógica y Computación
We present a general framework for the declarative debugging of functional logic programs, which is valid both for eager as well as lazy programs. We associate to our programs a semantics based on a (continuous) immediate consequence operator which models computed answers. Then we show that, given the intended specification of a program P, it is possible to check the correctness of P by a single step of the immediate consequence operator. We also present a more effective methodology which is based on abstract interpretation. By approximating the intended specification of the success set we derive a finitely terminating debugging method, which can be used statically. Our framework is parametric w.r.t. to the chosen approximation of the success set. We present one specific example of approximation. We provide an implementation of our debugging system which shows experimentally on a wide set of benchmarks that we are able to find some common errors in the user programs. © 2001 Published by Elsevier Science B. V.
Dynamic analysis and performance evaluation of the BIAcore surface plasmon resonance biosensor
(SPIE-INT SOC OPTICAL ENGINEERING, 2015-01-01) Simon, Laurent; Ospina, Juan; Simon, Laurent; Ospina, Juan; Universidad EAFIT. Departamento de Ciencias; Lógica y Computación
Solution procedures were proposed to analyze nonlinear mass transport through an optical biosensor. A generalized collocation technique was applied to predict the dynamic behavior of an analyte along the flow chamber as a result of convection, diffusion and chemical reaction. The method estimated the effective time constants for reaching average steady-state concentrations of the free and bound analytes in the cell. When diffusion in the direction of flow was neglected, a closed-form solution, based on double Laplace transforms, was obtained after linearizing the original system. In both models, an increase in the sample diffusion coefficient lowered the effective time constant. This approach may help researchers evaluate the performance of biosensors and meet specific design criteria. © 2015 SPIE.
Dynamic analysis of heat transfer through a fin of constant cross-sectional area: Specified fin tip temperature
(2009-01-01) Carranza, R.G.; Ospina Giraldo, J.F.; Carranza, R.G.; Ospina Giraldo, J.F.; Universidad EAFIT. Departamento de Ciencias; Lógica y Computación
A dynamic analysis is performed for heat transfer through a fin with constant cross-sectional area and with a specified fin tip temperature. The process starts with a dynamic energy balance around the fin. Laplace transforms and the Bromwich Integral are used to solve analytically the resulting partial differential equation. The final purely analytical solution is compared to the well known steady state solution. The two match exactly as time approaches infinity. Furthermore it is shown that the steady-state and dynamic characteristics of the fin are directly tied to the Biot number. Copyright © 2009 by ASME.
Dynamics of an Electrochemical Biosensor for the Detection of Toxic Substances in Water
(SPIE-INT SOC OPTICAL ENGINEERING, 2016-01-01) Simon, L.; Ospina, J.; Simon, L.; Ospina, J.; Universidad EAFIT. Departamento de Ciencias; Lógica y Computación
A proposed analytical method focuses on electrolyte transport to the electrode of an electrochemical cell. The recombinant Escherichia coli whole-cell biosensor detects toxicity in water based on a set of biochemical reactors. Previous contributions elucidated the kinetics of product formation and validated a mathematical model for its diffusion in the chamber. This work introduces an approach to investigate the dynamics of the probe using Laplace transforms and an effective time constant. The transfer function between the electrolyte production and the total current revealed a faster response for larger electrode radii. Both the first-order and effective time constants increased with the chamber height and radius. Separation of variables yields closed-form solutions and helps estimate the kinetics of p-aminophenol generation. When the bacteria were exposed to phenol concentrations of 1.6, 8.3 and 16 ppm, the corresponding overall rate constants were 5.11x10(-7), 1.13x10(-6) and 1.99x10(-6) (product concentration unit/s(2)), respectively. In addition to parameter estimation, the method can be applied to perform sensitivity analysis and aid manufacturers in meeting design specifications of biosensors.
Embedding a logical Theory of Constructions in agda
(2009-01-01) Bove, A.; Dybjer, P.; Sicard-Ra?irez, A.; Bove, A.; Dybjer, P.; Sicard-Ra?irez, A.; Universidad EAFIT. Departamento de Ciencias; Lógica y Computación
We propose a new way to reason about general recursive functional in the dependently typed programming language Agda,is based on Martin-Löf's intuitionistic type theory. We show to embed an external programming logic, Aczel's Logical Theory Constructions (LTC) inside Agda. To this end we postulate existence of a domain of untyped functional programs and the rules for these programs. Furthermore, we represent the notions in LTC (intuitionistic predicate logic with equality,totality predicates) as inductive notions in Agda. To illustrate approach we specify an LTC-style logic for PCF, and show to prove the termination and correctness of a general recursive for computing the greatest common divisor of two numbers. © 2009.
The epidemic threshold theorem with social and contact heterogeneity
(SPIE-INT SOC OPTICAL ENGINEERING, 2008-03-17) Palacio, D.H.; Giraldo, J.O.; Arias, R.D.G.; Palacio, D.H.; Giraldo, J.O.; Arias, R.D.G.; Universidad EAFIT. Departamento de Ciencias; Lógica y Computación
The threshold theorem of an epidemic SIR model was compared when infectious and susceptible individuals have homogeneous mixing and heterogeneous social status and when individuals of random networks have contact heterogeneity. Particularly the effect of vaccination in such models is considered when: individuals or nodes are exposed to impoverished, vaccination and loss of immunity. An equilibrium analysis and local stability of small perturbations about the equilibrium values were implemented using computer algebra. Numerical simulations were executed in order to describe the dynamic of transmission of diseases and changes of the basic reproductive rate. The implications of these results are examined around the threats to the global public health security.
Epidemic thresholds in SIR and SIIR models applying an algorithmic method
(SPRINGER, 2008-01-01) Hincapié P., D.; Ospina G., J.; Afuwape, A.U.; Gómez A., R.D.; Hincapié P., D.; Ospina G., J.; Afuwape, A.U.; Gómez A., R.D.; Universidad EAFIT. Departamento de Ciencias; Lógica y Computación
Epidemic thresholds were deduced and simulated from SIR models of Susceptible - Infected - Recovered individuals, through local stability analysis of the disease free and endemic equilibrium, with an algorithmic method. One and two types of infected individuals were modeled, considering the influence of sub clinical, undiagnosed or unrecognized infected cases in disease transmission. © 2008 Springer Berlin Heidelberg.
Gravitational topological quantum computation
(SPRINGER, 2007-01-01) Velez, Mario; Ospina, Juan; Velez, Mario; Ospina, Juan; Universidad EAFIT. Departamento de Ciencias; Lógica y Computación
A new model in topological quantum computing, named Gravitational Topological Quantum Computing (GTQC), is introduced as an alternative respect to the Anyonic Topological Quantum Computing and DNA Computing. In the new model the quantum computer is the quantum space-time itself and the corresponding quantum algorithms refer to the computation of topological invariants for knots, links and tangles. Some applications of GTQC in quantum complexity theory and computability theory are discussed, particularly it is conjectured that the Khovanov polynomial for knots and links is more hard than #P-hard; and that the homeomorphism problem, which is noncomputable, maybe can be computed after all via a hyper-computer based on GTQC. © Springer-Verlag Berlin Heidelberg 2007.
Implementing an active learning platform to support student learning in a numerical analysis course
(Institute of Electrical and Electronics Engineers Inc., 2017-01-01) Zabala F.J.C.; Parker H.E.; Vieira C.; Zabala F.J.C.; Parker H.E.; Vieira C.; Universidad EAFIT. Departamento de Ciencias; Lógica y Computación
Classroom instruction in the 21st century needs to incorporate innovative, research-based pedagogies. The engineering classroom is currently experiencing a shift towards more active learning activities due to both advances in educational research, and advances in technologies that enable practices such as the flipped classroom model. Given that course transformation is a gradual process that begins at the level of the instructor, educators need access to the essential tools and training in order to introduce these changes into the curricula. This paper introduces a course re-design based on Self-Determination Theory and Constructivism; and outlines effectively implemented active learning strategies using the flipped classroom model. The data were collected from a Numerical Analysis course, which is an important course across several engineering disciplines at Universidad EAFIT. This course enables engineering students to solve complex problems using mathematical and computational methods. This paper describes the implementation of an online active learning platform called "Numérico Interactivo" for two related engineering courses: Numerical Analysis (NA) and Numerical Processes (NP). The platform was available to all students, but only NA implemented it using a flipped classroom model. NP made the platform available as an optional course tool. Informed by SDT principles, "Numérico Interactivo" includes a variety of instructional materials such as explanations, examples, frequently asked questions (FAQ), self-assessment tools, and evaluation. This study compares the two courses in terms of: (1) students' perceptions about the instructional materials of the course; (2) students' use of the platform; and (3) students' perceived usefulness of the different elements within the platform. Results suggest that students in the NA course found the classroom sessions and the homework assignments more useful as compared to the students enrolled in the NP course. In addition, in the NA course students used the platform more often for class preparation and to study before each module. The way in which the platform was implemented in NA also increased student motivation in the course. Overall, the results suggest that "Numérico Interactivo" is useful to implement course re-designs into engineering and computing education courses, but such tools need to be guided by active learning practices so that students can fully benefit from them. © 2017 IEEE.
Leptospirosis risk around a potential source of infection
(SPIE-INT SOC OPTICAL ENGINEERING, 2015-01-01) Erica, Loaiza-Echeverry; Doracelly, Hincapie-Palacio; Acosta Jesus, Ochoa; Giraldo Juan, Ospina; Erica, Loaiza-Echeverry; Doracelly, Hincapie-Palacio; Acosta Jesus, Ochoa; Giraldo Juan, Ospina; Universidad EAFIT. Departamento de Ciencias; Lógica y Computación
Leptospirosis is a bacterial zoonosis with world distribution and multiform clinical spectrum in men and animals. The etiology of this disease is the pathogenic species of Leptospira, which cause diverse manifestations of the disease, from mild to serious, such as the Weil disease and the lung hemorrhagic syndrome with lethal proportions of 10% - 50%. This is an emerging problem of urban health due to the growth of marginal neighborhoods without basic sanitary conditions and an increased number of rodents. The presence of rodents and the probability of having contact with their urine determine the likelihood for humans to get infected. In this paper, we simulate the spatial distribution of risk infection of human leptospirosis according to the proximity to rodent burrows considered as potential source of infection. The Bessel function K0 with an r distance from the potential point source, and the scale parameter a in meters was used. Simulation inputs were published data of leptospirosis incidence rate (range of 5 to 79 x 10 000), and a distance of 100 to 5000 meters from the source of infection. We obtained an adequate adjustment between the function and the simulated data. The risk of infection increases with the proximity of the potential source. This estimation can become a guide to propose effective measures of control and prevention. © 2015 SPIE.
Mackendrick: A Maple Package oriented to symbolic computational epidemiology
(SPRINGER, 2006-01-01) Ospina, Juan; Hincapie, Doracelly; Ospina, Juan; Hincapie, Doracelly; Universidad EAFIT. Departamento de Ciencias; Lógica y Computación
A Maple Package named Mackendrick is presented. Such package is oriented to symbolic computational epidemiology. © Springer-Verlag Berlin Heidelberg 2006.
Mathematical model for dengue with three states of infection
(SPIE-INT SOC OPTICAL ENGINEERING, 2012-01-01) Hincapie, D.; Ospina, J.; Hincapie, D.; Ospina, J.; Universidad EAFIT. Departamento de Ciencias; Lógica y Computación
A mathematical model for dengue with three states of infection is proposed and analyzed. The model consists in a system of differential equations. The three states of infection are respectively asymptomatic, partially asymptomatic and fully asymptomatic. The model is analyzed using computer algebra software, specifically Maple, and the corresponding basic reproductive number and the epidemic threshold are computed. The resulting basic reproductive number is an algebraic synthesis of all epidemic parameters and it makes clear the possible control measures. The microscopic structure of the epidemic parameters is established using the quantum theory of the interactions between the atoms and radiation. In such approximation, the human individual is represented by an atom and the mosquitoes are represented by radiation. The force of infection from the mosquitoes to the humans is considered as the transition probability from the fundamental state of atom to excited states. The combination of computer algebra software and quantum theory provides a very complete formula for the basic reproductive number and the possible control measures tending to stop the propagation of the disease. It is claimed that such result may be important in military medicine and the proposed method can be applied to other vector-borne diseases. © 2012 SPIE.

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