Using problem-based learning in a chemistry practical class for pharmacy students and engaging them with feedback

Objective: To introduce a new approach to problem based learning (PBL) used in the context of medicinal chemistry practical class teaching pharmacy students. Design: The described chemistry practical is based on independent studies by small groups of undergraduate students (4-5), who design their own practical work taking relevant professional standards into account. Students are carefully guided by feedback and acquire a set of skills important to their future profession as healthcare professionals. This model has been tailored to the application of PBL in a chemistry practical class setting for a large student cohort (150 students). Assessment: The achievement of learning outcomes is based on the submission of relevant documentation including a certificate of analysis, in addition to peer assessment. Some of the learning outcomes are also assessed in the final written examination at the end of the academic year. Conclusion: The described design of a novel PBL chemistry laboratory course for pharmacy students has been found to be successful. Self-reflective learning and engagement with feedback were encouraged, and students enjoyed the challenging learning experience. Skills that are highly essential for the students’ future careers as healthcare professionals are promoted.

A hybrid approach to learn with imbalanced classes using evolutionary algorithms

There is an increasing interest in the application of Evolutionary Algorithms (EAs) to induce classification rules. This hybrid approach can benefit areas where classical methods for rule induction have not been very successful. One example is the induction of classification rules in imbalanced domains. Imbalanced data occur when one or more classes heavily outnumber other classes. Frequently, classical machine learning (ML) classifiers are not able to learn in the presence of imbalanced data sets, inducing classification models that always predict the most numerous classes. In this work, we propose a novel hybrid approach to deal with this problem. We create several balanced data sets with all minority class cases and a random sample of majority class cases. These balanced data sets are fed to classical ML systems that produce rule sets. The rule sets are combined creating a pool of rules and an EA is used to build a classifier from this pool of rules. This hybrid approach has some advantages over undersampling, since it reduces the amount of discarded information, and some advantages over oversampling, since it avoids overfitting. The proposed approach was experimentally analysed and the experimental results show an improvement in the classification performance measured as the area under the receiver operating characteristics (ROC) curve.

The Darboux Problem for a Class of 3-D Weakly Hyperbolic Equations

Недю Попиванов, Цветан Христов - Изследвани са някои тримерни аналози на задачата на Дарбу в равнината. През 1952 М. Протер формулира нови тримерни гранични задачи както за клас слабо хиперболични уравнения, така и за някои хиперболично-елиптични уравнения. За разлика от коректността на двумерната задача на Дарбу, новите задачи са некоректни. За слабо хиперболични уравнения, съдържащи младши членове, ние намираме достатъчни условия както за съществуване и единственост на обобщени решения с изолирана степенна особеност, така и за единственост на квази-регулярни решения на задачата на Протер.

Singular Solutions of Protter’s Problem for a Class of 3-D Hyperbolic Equations

Недю Иванов Попиванов, Алексей Йорданов Николов - През 1952 г. М. Протър формулира нови гранични задачи за вълновото уравнение, които са тримерни аналози на задачите на Дарбу в равнината. Задачите са разгледани в тримерна област, ограничена от две характеристични конуса и равнина. Сега, след като са минали повече от 50 години, е добре известно, че за безброй гладки функции в дясната страна на уравнението тези задачи нямат класически решения, а обобщеното решение има силна степенна особеност във върха на характеристичния конус, която е изолирана и не се разпространява по конуса. Тук ние разглеждаме трета гранична задача за вълновото уравнение с младши членове и дясна страна във формата на тригонометричен полином. Дадена е по-нова от досега известната априорна оценка за максимално възможната особеност на решенията на тази задача. Оказва се, че при по-общото уравнение с младши членове възможната сингулярност е от същия ред като при чисто вълновото уравнение.

Optimization Problem in a Class of Linear System. Application to Multiple Drug Administration

2000 Mathematics Subject Classification: 62H15, 62P10.

Weighted S-Asymptotically omega-Periodic Solutions of a Class of Fractional Differential Equations

We study the existence of weighted S-asymptotically omega-periodic mild solutions for a class of abstract fractional differential equations of the form u' = partial derivative (alpha vertical bar 1)Au + f(t, u), 1 < alpha < 2, where A is a linear sectorial operator of negative type.

PARTIAL STABILITY FOR A CLASS OF NONLINEAR SYSTEMS

This paper studies a nonlinear, discrete-time matrix system arising in the stability analysis of Kalman filters. These systems present an internal coupling between the state components that gives rise to complex dynamic behavior. The problem of partial stability, which requires that a specific component of the state of the system converge exponentially, is studied and solved. The convergent state component is strongly linked with the behavior of Kalman filters, since it can be used to provide bounds for the error covariance matrix under uncertainties in the noise measurements. We exploit the special features of the system-mainly the connections with linear systems-to obtain an algebraic test for partial stability. Finally, motivated by applications in which polynomial divergence of the estimates is acceptable, we study and solve a partial semistability problem.

ON THE THREE-DIMENSIONAL BLASCHKE-LEBESGUE PROBLEM

The width of a closed convex subset of n-dimensional Euclidean space is the distance between two parallel supporting hyperplanes. The Blaschke-Lebesgue problem consists of minimizing the volume in the class of convex sets of fixed constant width and is still open in dimension n >= 3. In this paper we describe a necessary condition that the minimizer of the Blaschke-Lebesgue must satisfy in dimension n = 3: we prove that the smooth components of the boundary of the minimizer have their smaller principal curvature constant and therefore are either spherical caps or pieces of tubes (canal surfaces).

A STUDY OF PENALTY FORMULATIONS USED IN THE NUMERICAL APPROXIMATION OF A RADIALLY SYMMETRIC ELASTICITY PROBLEM

We consider a class of two-dimensional problems in classical linear elasticity for which material overlapping occurs in the absence of singularities. Of course, material overlapping is not physically realistic, and one possible way to prevent it uses a constrained minimization theory. In this theory, a minimization problem consists of minimizing the total potential energy of a linear elastic body subject to the constraint that the deformation field must be locally invertible. Here, we use an interior and an exterior penalty formulation of the minimization problem together with both a standard finite element method and classical nonlinear programming techniques to compute the minimizers. We compare both formulations by solving a plane problem numerically in the context of the constrained minimization theory. The problem has a closed-form solution, which is used to validate the numerical results. This solution is regular everywhere, including the boundary. In particular, we show numerical results which indicate that, for a fixed finite element mesh, the sequences of numerical solutions obtained with both the interior and the exterior penalty formulations converge to the same limit function as the penalization is enforced. This limit function yields an approximate deformation field to the plane problem that is locally invertible at all points in the domain. As the mesh is refined, this field converges to the exact solution of the plane problem.

On the loss of regularity for a class of weakly hyperbolic operators

In this paper we determine bounds for the optimal loss of regularity in the Sobolev scale for a class of weakly hyperbolic operators. (C) 2009 Elsevier Inc. All rights reserved.

The influence of oscillations on global existence for a class of semi-linear wave equations

The goal of this paper is to study the global existence of small data solutions to the Cauchy problem for the nonlinear wave equation u(tt) - a(t)(2) Delta u = u(t)(2) - a(t)(2)vertical bar del u vertical bar(2). In particular we are interested in statements for the 1D case. We will explain how the interplay between the increasing and oscillating behavior of the coefficient will influence global existence of small data solutions. Copyright c 2011 John Wiley & Sons, Ltd.

Existence of solutions for a class of abstract differential equations with nonlocal conditions

We discuss the existence of mild, classical and strict solutions for a class of abstract differential equations with nonlocal conditions. Our technical approach allows the study of partial differential equations with nonlocal conditions involving partial derivatives or nonlinear expressions of the solution. Some concrete applications to partial differential equations are considered. (C) 2010 Elsevier Ltd. All rights reserved.

Anti-Group A Streptococcal Vaccine Epitope STRUCTURE, STABILITY, AND ITS ABILITY TO INTERACT WITH HLA CLASS II MOLECULES

Streptococcus pyogenes infections remain a health problem in several countries due to poststreptococcal sequelae. We developed a vaccine epitope (StreptInCor) composed of 55 amino acids residues of the C-terminal portion of the M protein that encompasses both T and B cell protective epitopes. The nuclear magnetic resonance (NMR) structure of the StreptInCor peptide showed that the structure was composed of two microdomains linked by an 18-residue alpha-helix. A chemical stability study of the StreptInCor folding/unfolding process using far-UV circular dichroism showed that the structure was chemically stable with respect to pH and the concentration of urea. The T cell epitope is located in the first microdomain and encompasses 11 out of the 18 alpha-helix residues, whereas the B cell epitope is in the second microdomain and showed no alpha-helical structure. The prediction of StreptInCor epitope binding to different HLA class II molecules was evaluated based on an analysis of the 55 residues and the theoretical possibilities for the processed peptides to fit into the P1, P4, P6, and P9 pockets in the groove of several HLA class II molecules. We observed 7 potential sites along the amino acid sequence of StreptInCor that were capable of recognizing HLA class II molecules (DRB1*, DRB3*, DRB4*, and DRB5*). StreptInCoroverlapping peptides induced cellular and humoral immune responses of individuals bearing different HLA class II molecules and could be considered as a universal vaccine epitope.

A class of singular first order differential equations with applications in reaction-diffusion

Agências Financiadoras: FCT e MIUR

Cutting path as a rural postman problem

The Rural Postman Problem (RPP) is a particular Arc Routing Problem (ARP) which consists of determining a minimum cost circuit on a graph so that a given subset of required edges is traversed. The RPP is an NP-hard problem with significant real-life applications. This paper introduces an original approach based on Memetic Algorithms - the MARP algorithm - to solve the RPP and, also deals with an interesting Industrial Application, which focuses on the path optimization for component cutting operations. Memetic Algorithms are a class of Metaheuristics which may be seen as a population strategy that involves cooperation and competition processes between population elements and integrates “social knowledge”, using a local search procedure. The MARP algorithm is tested with different groups of instances and the results are compared with those gathered from other publications. MARP is also used in the context of various real-life applications.