Classification of masses in mammographic image using wavelet domain features and polynomial classifier

Breast cancer is the most common cancer among women. In CAD systems, several studies have investigated the use of wavelet transform as a multiresolution analysis tool for texture analysis and could be interpreted as inputs to a classifier. In classification, polynomial classifier has been used due to the advantages of providing only one model for optimal separation of classes and to consider this as the solution of the problem. In this paper, a system is proposed for texture analysis and classification of lesions in mammographic images. Multiresolution analysis features were extracted from the region of interest of a given image. These features were computed based on three different wavelet functions, Daubechies 8, Symlet 8 and bi-orthogonal 3.7. For classification, we used the polynomial classification algorithm to define the mammogram images as normal or abnormal. We also made a comparison with other artificial intelligence algorithms (Decision Tree, SVM, K-NN). A Receiver Operating Characteristics (ROC) curve is used to evaluate the performance of the proposed system. Our system is evaluated using 360 digitized mammograms from DDSM database and the result shows that the algorithm has an area under the ROC curve Az of 0.98 ± 0.03. The performance of the polynomial classifier has proved to be better in comparison to other classification algorithms. © 2013 Elsevier Ltd. All rights reserved.

Limit Cycles for a Class of Continuous and Discontinuous Cubic Polynomial Differential Systems

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Emerging powers, humanitarian assistance and foreign policy: the case of Brazil during the earthquake crisis in Haiti

During the management of the crisis after the earthquake occurred in Haiti in 12 January 2010, Brazil played an important role on the efforts of humanitarian assistance. Based on bibliography and documents the paper presents the role played by Brazil with the focus on the humanitarian assistance as part of country’ foreign policy as an emerging power to increase the presence into the international system. To achieve this goal the article presents some considerations about emerging powers, foreign policy and theoretical concepts about humanitarian assistance and international relations, the extension of the earthquake in Haiti and the actions performed by Brazil during the response phase of the crisis management.

Limit cycles of cubic polynomial differential systems with rational first integrals of degree 2

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

A graded subring of an inverse limit of polynomial rings

We study the power series ring R= K[[x1,x2,x3,...]]on countably infinitely many variables, over a field K, and two particular K-subalgebras of it: the ring S, which is isomorphic to an inverse limit of the polynomial rings in finitely many variables over K, and the ring R', which is the largest graded subalgebra of R. Of particular interest are the homogeneous, finitely generated ideals in R', among them the generic ideals. The definition of S as an inverse limit yields a set of truncation homomorphisms from S to K[x1,...,xn] which restrict to R'. We have that the truncation of a generic I in R' is a generic ideal in K[x1,...,xn]. It is shown in Initial ideals of Truncated Homogeneous Ideals that the initial ideal of such an ideal converge to the initial ideal of the corresponding ideal in R'. This initial ideal need no longer be finitely generated, but it is always locally finitely generated: this is proved in Gröbner Bases in R'. We show in Reverse lexicographic initial ideals of generic ideals are finitely generated that the initial ideal of a generic ideal in R' is finitely generated. This contrast to the lexicographic term order. If I in R' is a homogeneous, locally finitely generated ideal, and if we write the Hilbert series of the truncated algebras K[x1,...,xn] module the truncation of I as qn(t)/(1-t)n, then we show in Generalized Hilbert Numerators that the qn's converge to a power series in t which we call the generalized Hilbert numerator of the algebra R'/I. In Gröbner bases for non-homogeneous ideals in R' we show that the calculations of Gröbner bases and initial ideals in R' can be done also for some non-homogeneous ideals, namely those which have an associated homogeneous ideal which is locally finitely generated. The fact that S is an inverse limit of polynomial rings, which are naturally endowed with the discrete topology, provides S with a topology which makes it into a complete Hausdorff topological ring. The ring R', with the subspace topology, is dense in R, and the latter ring is the Cauchy completion of the former. In Topological properties of R' we show that with respect to this topology, locally finitely generated ideals in R'are closed.

Construction of polynomial spline spaces over quadtree and octree T-meshes

[EN]We present a new strategy for constructing tensor product spline spaces over quadtree and octree T-meshes. The proposed technique includes some simple rules for inferring local knot vectors to define spline blending functions. These rules allow to obtain for a given T-mesh a set of cubic spline functions that span a space with nice properties: it can reproduce cubic polynomials, the functions are C2-continuous, linearly independent, and spaces spanned by nested T-meshes are also nested. In order to span spaces with these properties applying the proposed rules, the T-mesh should fulfill the only requirement of being a 0-balanced quadtree or octree. ..

Construction of polynomial spline spaces over quadtree and octree T-meshes

[EN]We present a new strategy for constructing tensor product spline spaces over quadtree and octree T-meshes. The proposed technique includes some simple rules for inferring local knot vectors to define spline blending functions. These rules allow to obtain for a given T-mesh a set of cubic spline functions that span a space with nice properties: it can reproduce cubic polynomials, the functions are C2-continuous, linearly independent, and spaces spanned by nested T-meshes are also nested. In order to span spaces with these properties applying the proposed rules, the T-mesh should fulfill the only requirement of being a 0-balanced quadtree or octree. ..

The Poincaré polynomial for the Hilbert scheme of points of C^2

Questo lavoro prende in esame lo schema di Hilbert di punti di C^2, il quale viene descritto assieme ad alcune sue proprietà, ad esempio la sua struttura hyper-kahleriana. Lo scopo della tesi è lo studio del polinomio di Poincaré di tale schema di Hilbert: ciò che si ottiene è una espressione del tipo serie di potenze, la quale è un caso particolare di una formula molto più generale, nota con il nome di formula di Goettsche.

Population-based trend analysis of 2813 patients undergoing laparoscopic sigmoid resection

The use of laparoscopic sigmoid resection for diverticular disease has become increasingly popular. The objective of this trend analysis was to assess whether clinical outcomes following laparoscopic sigmoid resection for diverticular disease have improved over the past 10 years.

Efficient computation of discrete polynomial transforms

This letter presents a new recursive method for computing discrete polynomial transforms. The method is shown for forward and inverse transforms of the Hermite, binomial, and Laguerre transforms. The recursive flow diagrams require only 2 additions, 2( +1) memory units, and +1multipliers for the +1-point Hermite and binomial transforms. The recursive flow diagram for the +1-point Laguerre transform requires 2 additions, 2( +1) memory units, and 2( +1) multipliers. The transform computation time for all of these transforms is ( )

The Constitutional-Judicial Control of the Legislative and Executive Powers in Central and Eastern European Countries

This project looked at the nature, contents, methods, means and legal and political effects of the influence that constitutional courts exercise upon the legislative and executive powers in the newly established democracies of Central and Eastern Europe. The basic hypothesis was that these courts work to provide a limitation of political power within the framework of the principal constitutional values and that they force the legislature and executive to exercise their powers and duties in strict accordance with the constitution. Following a study of the documentary sources, including primarily the relevant constitutional and statutory provisions and decisions of constitutional courts, Mr. Cvetkovski prepared a questionnaire on various aspects of the topics researched and sent it to the respective constitutional courts. A series of direct interviews with court officials in six of the ten countries then served to clarify a large number of questions relating to differences in procedures etc. that arose from the questionnaires. As a final stage, the findings were compared with those described in recent publications on constitutional control in general and in Central and Eastern Europe in particular. The study began by considering the constitutional and political environment of the constitutional courts' activities in controlling legislative and executive powers, which in all countries studied are based on the principles of the rule of law and the separation of powers. All courts are separate bodies with special status in terms of constitutional law and are independent of other political and judicial institutions. The range of matters within their jurisdiction is set by the constitution of the country in question but in all cases can be exercised only with the framework of procedural rules. This gives considerable significance to the question of who sets these rules and different countries have dealt with it in different ways. In some there is a special constitutional law with the same legal force as the constitution itself (Croatia), the majority of countries allow for regulation by an ordinary law, Macedonia gives the court the autonomy to create and change its own rules of procedure, while in Hungary the parliament fixes the rules on procedure at the suggestion of the constitutional court. The question of the appointment of constitutional judges was also considered and of the mechanisms for ensuring their impartiality and immunity. In the area of the courts' scope for providing normative control, considerable differences were found between the different countries. In some cases the courts' jurisdiction is limited to the normative acts of the respective parliaments, and there is generally no provision for challenging unconstitutional omissions by legislation and the executive. There are, however, some situations in which they may indirectly evaluate the constitutionality of legislative omissions, as when the constitution contains provision for a time limit on enacting legislation, when the parliament has made an omission in drafting a law which violates the constitutional provisions, or when a law grants favours to certain groups while excluding others, thereby violating the equal protection clause of the constitution. The control of constitutionality of normative acts can be either preventive or repressive, depending on whether it is implemented before or after the promulgation of the law or other enactment being challenged. In most countries in the region the constitutional courts provide only repressive control, although in Hungary and Poland the courts are competent to perform both preventive and repressive norm control, while in Romania the court's jurisdiction is limited to preventive norm control. Most countries are wary of vesting constitutional courts with preventive norm control because of the danger of their becoming too involved in the day-to-day political debate, but Mr. Cvetkovski points out certain advantages of such control. If combined with a short time limit it can provide early clarification of a constitutional issue, secondly it avoids the problems arising if a law that has been in force for some years is declared to be unconstitutional, and thirdly it may help preserve the prestige of the legislation. Its disadvantages include the difficulty of ascertaining the actual and potential consequences of a norm without the empirical experience of the administration and enforcement of the law, the desirability of a certain distance from the day-to-day arguments surrounding the political process of legislation, the possible effects of changing social and economic conditions, and the danger of placing obstacles in the way of rapid reactions to acute situations. In the case of repressive norm control, this can be either abstract or concrete. The former is initiated by the supreme state organs in order to protect abstract constitutional order and the latter is initiated by ordinary courts, administrative authorities or by individuals. Constitutional courts cannot directly oblige the legislature and executive to pass a new law and this remains a matter of legislative and executive political responsibility. In the case of Poland, the parliament even has the power to dismiss a constitutional court decision by a special majority of votes, which means that the last word lies with the legislature. As the current constitutions of Central and Eastern European countries are newly adopted and differ significantly from the previous ones, the courts' interpretative functions should ensure a degree of unification in the application of the constitution. Some countries (Bulgaria, Hungary, Poland, Slovakia and Russia) provide for the constitutional courts' decisions to have a binding role on the constitutions. While their decisions inevitably have an influence on the actions of public bodies, they do not set criteria for political behaviour, which depends rather on the overall political culture and traditions of the society. All constitutions except that of Belarus, provide for the courts to have jurisdiction over conflicts arising from the distribution of responsibilities between different organs and levels in the country, as well for impeachment procedures against the head of state, and for determining the constitutionality of political parties (except in Belarus, Hungary, Russia and Slovakia). All the constitutions studied guarantee individual rights and freedoms and most courts have jurisdiction over complaints of violation of these rights by the constitution. All courts also have some jurisdiction over international agreements and treaties, either directly (Belarus, Bulgaria and Hungary) before the treaty is ratified, or indirectly (Croatia, Czech Republic, Macedonia, Romania, Russia and Yugoslavia). In each country the question of who may initiate proceedings of norm control is of central importance and is usually regulated by the constitution itself. There are three main possibilities: statutory organs, normal courts and private individuals and the limitations on each of these is discussed in the report. Most courts are limited in their rights to institute ex officio a full-scale review of a point of law, and such rights as they do have rarely been used. In most countries courts' decisions do not have any binding force but must be approved by parliament or impose on parliament the obligation to bring the relevant law into conformity within a certain period. As a result, the courts' position is generally weaker than in other countries in Europe, with parliament remaining the supreme body. In the case of preventive norm control a finding of unconstitutionality may act to suspend the law and or to refer it back to the legislature, where in countries such as Romania it may even be overturned by a two-thirds majority. In repressive norm control a finding of unconstitutionality generally serves to take the relevant law out of legal force from the day of publication of the decision or from another date fixed by the court. If the law is annulled retrospectively this may or may not bring decisions of criminal courts under review, depending on the provisions laid down in the relevant constitution. In cases relating to conflicts of competencies the courts' decisions tend to be declaratory and so have a binding effect inter partes. In the case of a review of an individual act, decisions generally become effective primarily inter partes but is the individual act has been based on an unconstitutional generally binding normative act of the legislature or executive, the findings has quasi-legal effect as it automatically initiates special proceedings in which the law or other regulation is to be annulled or abrogated with effect erga omnes. This wards off further application of the law and thus further violations of individual constitutional rights, but also discourages further constitutional complaints against the same law. Thus the success of one individual's complaint extends to everyone else whose rights have equally been or might have been violated by the respective law. As the body whose act is repealed is obliged to adopt another act and in doing so is bound by the legal position of the constitutional court on the violation of constitutionally guaranteed freedoms and rights of the complainant, in this situation the decision of the constitutional court has the force of a precedent.