A mathematical view of biological complexity

This essay is a trial on giving some mathematical ideas about the concept of biological complexity, trying to explore four different attributes considered to be essential to characterize a complex system in a biological context: decomposition, heterogeneous assembly, self-organization, and adequacy. It is a theoretical and speculative approach, opening some possibilities to further numerical and experimental work, illustrated by references to several researches that applied the concepts presented here. (C) 2008 Elsevier B.V. All rights reserved.

A Equação-Mestra: atingindo o equilíbrio

In the last years, a great interest in nonequilibrium systems has been witnessed. Although the Master Equations are one of the most common methods used to describe these systems, the literature about these equations is not straightforward due to the mathematical framework used in their derivations. The goals of this work are to present the physical concepts behind the Master Equations development and to discuss their basic proprieties via a matrix approach. It is also shown how the Master Equations can be used to model typical nonequilibrium processes like multi-wells chemical reactions and radiation absorption processes.

Rumor Propagation Model: An Equilibrium Study

Compartmental epidemiological models have been developed since the 1920s and successfully applied to study the propagation of infectious diseases. Besides, due to their structure, in the 1960s an interesting version of these models was developed to clarify some aspects of rumor propagation, considering that spreading an infectious disease or disseminating information is analogous phenomena. Here, in an analogy with the SIR (Susceptible-Infected-Removed) epidemiological model, the ISS (Ignorant-Spreader-Stifler) rumor spreading model is studied. By using concepts from the Dynamical Systems Theory, stability of equilibrium points is established, according to propagation parameters and initial conditions. Some numerical experiments are conducted in order to validate the model.

Simplified Mathematical Model for an Anaerobic Sequencing Batch Biofilm Reactor Treating Lipid-Rich Wastewater Subject to Rising Organic Loading Rates

This study proposes a simplified mathematical model to describe the processes occurring in an anaerobic sequencing batch biofilm reactor (ASBBR) treating lipid-rich wastewater. The reactor, subjected to rising organic loading rates, contained biomass immobilized cubic polyurethane foam matrices, and was operated at 32 degrees C +/- 2 degrees C, using 24-h batch cycles. In the adaptation period, the reactor was fed with synthetic substrate for 46 days and was operated without agitation. Whereas agitation was raised to 500 rpm, the organic loading rate (OLR) rose from 0.3 g chemical oxygen demand (COD) . L(-1) . day(-1) to 1.2 g COD . L(-1) . day(-1). The ASBBR was fed fat-rich wastewater (dairy wastewater), in an operation period lasting for 116 days, during which four operational conditions (OCs) were tested: 1.1 +/- 0.2 g COD . L(-1) . day(-1) (OC1), 4.5 +/- 0.4 g COD . L(-1) . day(-1) (OC2), 8.0 +/- 0.8 g COD . L(-1) . day(-1) (OC3), and 12.1 +/- 2.4 g COD . L(-1) . day(-1) (OC4). The bicarbonate alkalinity (BA)/COD supplementation ratio was 1:1 at OC1, 1:2 at OC2, and 1:3 at OC3 and OC4. Total COD removal efficiencies were higher than 90%, with a constant production of bicarbonate alkalinity, in all OCs tested. After the process reached stability, temporal profiles of substrate consumption were obtained. Based on these experimental data a simplified first-order model was fit, making possible the inference of kinetic parameters. A simplified mathematical model correlating soluble COD with volatile fatty acids (VFA) was also proposed, and through it the consumption rates of intermediate products as propionic and acetic acid were inferred. Results showed that the microbial consortium worked properly and high efficiencies were obtained, even with high initial substrate concentrations, which led to the accumulation of intermediate metabolites and caused low specific consumption rates.

Deformed Gaussian-orthogonal-ensemble description of small-world networks

The study of spectral behavior of networks has gained enthusiasm over the last few years. In particular, random matrix theory (RMT) concepts have proven to be useful. In discussing transition from regular behavior to fully chaotic behavior it has been found that an extrapolation formula of the Brody type can be used. In the present paper we analyze the regular to chaotic behavior of small world (SW) networks using an extension of the Gaussian orthogonal ensemble. This RMT ensemble, coined the deformed Gaussian orthogonal ensemble (DGOE), supplies a natural foundation of the Brody formula. SW networks follow GOE statistics until a certain range of eigenvalue correlations depending upon the strength of random connections. We show that for these regimes of SW networks where spectral correlations do not follow GOE beyond a certain range, DGOE statistics models the correlations very well. The analysis performed in this paper proves the utility of the DGOE in network physics, as much as it has been useful in other physical systems.

A contribution for thermoeconomic modelling: A methodology proposal

This work presents a thermoeconomic optimization methodology for the analysis and design of energy systems. This methodology involves economic aspects related to the exergy conception, in order to develop a tool to assist the equipment selection, operation mode choice as well as to optimize the thermal plants design. It also presents the concepts related to exergy in a general scope and in thermoeconomics which combines the thermal sciences principles (thermodynamics, heat transfer, and fluid mechanics) and the economic engineering in order to rationalize energy systems investment decisions, development and operation. Even in this paper, it develops a thermoeconomic methodology through the use of a simple mathematical model, involving thermodynamics parameters and costs evaluation, also defining the objective function as the exergetic production cost. The optimization problem evaluation is developed for two energy systems. First is applied to a steam compression refrigeration system and then to a cogeneration system using backpressure steam turbine. (C) 2010 Elsevier Ltd. All rights reserved.

Reliability concepts applied to cutting tool change time

This paper presents a reliability-based analysis for calculating critical tool life in machining processes. It is possible to determine the running time for each tool involved in the process by obtaining the operations sequence for the machining procedure. Usually, the reliability of an operation depends on three independent factors: operator, machine-tool and cutting tool. The reliability of a part manufacturing process is mainly determined by the cutting time for each job and by the sequence of operations, defined by the series configuration. An algorithm is presented to define when the cutting tool must be changed. The proposed algorithm is used to evaluate the reliability of a manufacturing process composed of turning and drilling operations. The reliability of the turning operation is modeled based on data presented in the literature, and from experimental results, a statistical distribution of drilling tool wear was defined, and the reliability of the drilling process was modeled. (C) 2010 Elsevier Ltd. All rights reserved.

Tailoring vibration mode shapes using topology optimization and functionally graded material concepts

Tailoring specified vibration modes is a requirement for designing piezoelectric devices aimed at dynamic-type applications. A technique for designing the shape of specified vibration modes is the topology optimization method (TOM) which finds an optimum material distribution inside a design domain to obtain a structure that vibrates according to specified eigenfrequencies and eigenmodes. Nevertheless, when the TOM is applied to dynamic problems, the well-known grayscale or intermediate material problem arises which can invalidate the post-processing of the optimal result. Thus, a more natural way for solving dynamic problems using TOM is to allow intermediate material values. This idea leads to the functionally graded material (FGM) concept. In fact, FGMs are materials whose properties and microstructure continuously change along a specific direction. Therefore, in this paper, an approach is presented for tailoring user-defined vibration modes, by applying the TOM and FGM concepts to design functionally graded piezoelectric transducers (FGPT) and non-piezoelectric structures (functionally graded structures-FGS) in order to achieve maximum and/or minimum vibration amplitudes at certain points of the structure, by simultaneously finding the topology and material gradation function. The optimization problem is solved by using sequential linear programming. Two-dimensional results are presented to illustrate the method.

Deterministic mathematical model for the prediction of the as-cast macrostructure

A multiphase deterministic mathematical model was implemented to predict the formation of the grain macrostructure during unidirectional solidification. The model consists of macroscopic equations of energy, mass, and species conservation coupled with dendritic growth models. A grain nucleation model based on a Gaussian distribution of nucleation undercoolings was also adopted. At some solidification conditions, the cooling curves calculated with the model showed oscillations (""wiggles""), which prevented the correct prediction of the average grain size along the structure. Numerous simulations were carried out at nucleation conditions where the oscillations are absent, enabling an assessment of the effect of the heat transfer coefficient on the average grain size and columnar-to-equiaxed transition.

On the solubility of proteins as a function of pH: Mathematical development and application

Thermodynamic relations between the solubility of a protein and the solution pH are presented in this work. The hypotheses behind the development are that the protein chemical potential in liquid phase can be described by Henry`s law and that the solid-liquid equilibrium is established only between neutral molecules. The mathematical development results in an analytical expression of the solubility curve, as a function of the ionization equilibrium constants, the pH and the solubility at the isoelectric point. It is shown that the same equation can be obtained either by directly calculating the fraction of neutral protein molecules or by integrating the curve of the protein average charge. The methodology was successfully applied to the description of the solubility of porcine insulin as a function of pH at three different temperatures and of bovine beta-lactoglobulin at four different ionic strengths. (C) 2011 Elsevier B.V. All rights reserved.

Is your vision consistent? A method for checking, based on scenario concepts

Common sense tells us that the future is an essential element in any strategy. In addition, there is a good deal of literature on scenario planning, which is an important tool in considering the future in terms of strategy. However, in many organizations there is serious resistance to the development of scenarios, and they are not broadly implemented by companies. But even organizations that do not rely heavily on the development of scenarios do, in fact, construct visions to guide their strategies. But it might be asked, what happens when this vision is not consistent with the future? To address this problem, the present article proposes a method for checking the content and consistency of an organization`s vision of the future, no matter how it was conceived. The proposed method is grounded on theoretical concepts from the field of future studies, which are described in this article. This study was motivated by the search for developing new ways of improving and using scenario techniques as a method for making strategic decisions. The method was then tested on a company in the field of information technology in order to check its operational feasibility. The test showed that the proposed method is, in fact, operationally feasible and was capable of analyzing the vision of the company being studied, indicating both its shortcomings and points of inconsistency. (C) 2007 Elsevier Ltd. All rights reserved.

EEG-based Brain-Computer Interfaces: An Overview of Basic Concepts and Clinical Applications in Neurorehabilitation

Some patients are no longer able to communicate effectively or even interact with the outside world in ways that most of us take for granted. In the most severe cases, tetraplegic or post-stroke patients are literally `locked in` their bodies, unable to exert any motor control after, for example, a spinal cord injury or a brainstem stroke, requiring alternative methods of communication and control. But we suggest that, in the near future, their brains may offer them a way out. Non-invasive electroencephalogram (EEG)-based brain-computer interfaces (BCD can be characterized by the technique used to measure brain activity and by the way that different brain signals are translated into commands that control an effector (e.g., controlling a computer cursor for word processing and accessing the internet). This review focuses on the basic concepts of EEG-based BC!, the main advances in communication, motor control restoration and the down-regulation of cortical activity, and the mirror neuron system (MNS) in the context of BCI. The latter appears to be relevant for clinical applications in the coming years, particularly for severely limited patients. Hypothetically, MNS could provide a robust way to map neural activity to behavior, representing the high-level information about goals and intentions of these patients. Non-invasive EEG-based BCIs allow brain-derived communication in patients with amyotrophic lateral sclerosis and motor control restoration in patients after spinal cord injury and stroke. Epilepsy and attention deficit and hyperactive disorder patients were able to down-regulate their cortical activity. Given the rapid progression of EEG-based BCI research over the last few years and the swift ascent of computer processing speeds and signal analysis techniques, we suggest that emerging ideas (e.g., MNS in the context of BC!) related to clinical neuro-rehabilitation of severely limited patients will generate viable clinical applications in the near future.

Risk Estimates of Dengue in Travelers to Dengue Endemic Areas Using Mathematical Models

Dengue has emerged as a frequent problem in international travelers. The risk depends on destination, duration, and season of travel. However, data to quantify the true risk for travelers to acquire dengue are lacking. We used mathematical models to estimate the risk of nonimmune persons to acquire dengue when traveling to Singapore. From the force of infection, we calculated the risk of dengue dependent on duration of stay and season of arrival. Our data highlight that the risk for nonimmune travelers to acquire dengue in Singapore is substantial but varies greatly with seasons and epidemic cycles. For instance, for a traveler who stays in Singapore for 1 week during the high dengue season in 2005, the risk of acquiring dengue was 0.17%, but it was only 0.00423% during the low season in a nonepidemic year such as 2002. Risk estimates based on mathematical modeling will help the travel medicine provider give better evidence-based advice for travelers to dengue endemic countries.

Concepts and determination of reference values for human biomonitoring of environmental contaminants

Human biomonitoring (HBM) of environmental contaminants plays an important role in estimating exposure and evaluating risk, and thus it has been increasingly applied in the environmental field. The results of HBM must be compared with reference values ( RV). The term ""reference values"" has always been related to the interpretation of clinical laboratory tests. For physicians, RV indicate ""normal values"" or ""limits of normal""; in turn, toxicologists prefer the terms ""background values"" or ""baseline values"" to refer to the presence of contaminants in biological fluids. This discrepancy leads to the discussion concerning which should be the population selected to determine RV. Whereas clinical chemistry employs an altered health state as the main exclusion criterion to select a reference population ( that is, a ""healthy"" population would be selected), in environmental toxicology the exclusion criterion is the abnormal exposure to xenobiotics. Therefore, the choice of population to determine RV is based on the very purpose of the RV to be determined. The present paper discusses the concepts and methodology used to determine RV for biomarkers of chemical environmental contaminants.