A constrained minimum spanning tree problem

In the classical general framework of the minimum spanning tree problem for a weighted graph we consider the case in which a predetermined vertex has a certain fixed degree. In other words, given a weighted graph G, one of its vertices v0 and a positive integer k, we consider the problem of finding the minimum spanning tree of G in which the vertex v0 has degree k, that is the number of edges coming out of v0. We recall that among the various methods for the solution of the unconstrained problem an efficient way to find the minimum spanning tree is based on the simple procedure of choosing one after the other an edge of minimum weight that has not be chosen yet and does not create cycles if added to the previously chosen edges. This technique is known as the \u201cgreedy algorithm\u201d. There are problems for which the greedy algorithm works and problems for which it does not. We prove that for the solution of the one degree constrained minimum spanning tree problem the classical greedy algorithm finds a right solution

The algebraic approach to some ranking problems

The problem of ranking a set of elements, namely giving a \u201crank\u201d to the elements of the set, may arise in very different contexts and may be handled in some possible different ways, depending on the ways these elements are set in competition the ones against the others. For example there are contexts in which we deal with an even paired competition, in the sense the pairings are evenly matched: if we think for example of a national soccer championship, each team is paired with every other team the same number of times. Sometimes we may deal with an uneven paired competition: think for example of the UEFA Champions League, in which the pairings are not fully covered, but just some pairings are set, by means of a random selection process for example. Mathematically based ranking schemes can be used and may show interesting connections between the ranking problems and classical theoretical results. In this working paper we first show how a linear scheme in the ranking process directly takes to some fundamental Linear Algebra concepts and results, mainly the eigenvalues and eigenvectors of linear transformations and Perron\u2013Frobenius theorem. We apply also the linear ranking model to a numerical simulation taking the data from the Italian soc- cer championship 2015-2016. We finally point out some interesting differences in the final ranking by comparing the actual placements of the teams at the end of the contest with the mathematical scores provided to teams by the theoretical model

Un criterio generale di divisibilit\ue0 di due interi

In the secondary school textbooks some classical divisibility criteria between two integer numbers are considered. These criteria, while showing some common aspects, are very different though in terms of other characteristics. In this paper we state and prove a general divisibility criterion, initially given for two digit divisors, written in binomial decimal form. The criterion is based on the determinant of the coefficient matrix of the binomial form and also on a further algebraic condition. Some examples are provided. Finally some generalizations are considered, in particular some cases in which the additional condition is always true. We give a general characterization of these cases

On linear problems with complementarity constraints

A mathematical program with complementarity constraints (MPCC) is an optimization problem with equality/inequality constraints in which a complementarity type constraint is considered in addition. This complementarity condition modifies the feasible region so as to remove many of those properties that are usually important to obtain the standard optimality conditions, e.g., convexity and constraint qualifications. In the literature, these problems have been tackled in many different ways: methods that introduce a parameter in order to relax the complementarity constraint, modified simplex methods that use an appropriate rule for choosing the non basic variable in order to preserve complementarity. We introduce a decomposition method of the given problem in a sequence of parameterized problems, that aim to force complementarity. Once we obtain a feasible solution, by means of duality results, we are able to eliminate a set of parameterized problems which are not worthwhile to be considered. Furthermore, we provide some bounds for the optimal value of the objective function and we present an application of the proposed technique in a non trivial example

The importance of Perron-Frobenius Theorem in ranking problems

The problem of ranking a set of elements, namely giving a ``rank'' to the elements of the set, may be tackled in many different ways. In particular a mathematically based ranking scheme can be used and sometimes it may be interesting to see how different can be the results of a mathematically based method compared with some more heuristic ways. In this working paper some remarks are presented about the importance, in a mathematical approach to ranking schemes, of a classical result from Linear Algebra, the Perron--Frobenius theorem. To give a motivation of such an importance two different contexts are taken into account, where a ranking problem arises: the example of ranking football/soccer teams and the one of ranking webpages in the approach proposed and implemented by Google's PageRank algorithm

A linear model for a ranking problem

We apply a linear ranking model to the Italian soccer championship. We consider the simulation taking the data from the final results of the 2016-2017 championship. The problem of ranking a set of elements, namely giving a \u201crank\u201d to the elements of the set, may arise in very different contexts and may be handled in some possible different ways, depending on the ways these elements are set in competition the ones against the others. In this working paper we deal with a so called even paired competition, where the pairings are evenly matched: in a national soccer championship actually each team is paired with every other team the same number of times. A mathematically based ranking scheme can be defined in order to get the scores for all the teams. The underlined structure of the model depends on the existence and uniqueness of a particular eigenvalue of the preference matrix. At this point the Perron\u2013 Frobenius theorem is involved, together with the dominant eigenvalue and a corresponding positive eigenvector. The linear ranking model is also used for a numerical simulation. This gives evidence of some discrepancies between the actual final placements of teams and the ones provided by the model. We want to go here into a more detailed study about this aspect

On the mathematical background of Google PageRank algorithm

The PageRank algorithm, the kernel of the method used by Google Search to give us the answer of a search we are asking in the web, contains a lot of mathematics. Maybe one could say that graphs and Markov chains theories are in the background, while the crucial steps are in a linear algebra context, as the eigenvalues of a matrix are involved. In this working paper we deal with all the mathematics we need to explain how the PageRank method works

Estudios tafonómicos del nivel Auriñaciense Arcaico de la cueva de El Castillo (Pueste Visgo, Cantabria) : los microdesechos líticos

En este trabajo se analizan los microdesechos líticos del nivel Auriñaciense Arcaico de la Cueva de El Castillo. En el mismo se presenta la metodología y técnica para efectuar este tipo de análisis. Los resultados obtenidos permiten identificar: 1) que se han llevado a cabo actividades de manufactura, uso, modificación y mantenimiento de los utensilios; 2) se han priorizado estrategias tecnológicas conservadoras en detrimento de las expeditivas; 3) se han localizado posibles áreas de actividad de talla in situ; 4) utilización preferencial de percutores blandos con relación a los duros; 5) selección preferencial de materias primas Ifticas; 6) finalmente, se han reconocido acumulaciones primarias y secundarias que podrían responder a los procesos postdeposicionales del depósito arqueológico.In this paper we have studied the lithic microdebitage of the Earliest Aurignacian Level of the El Castillo Cave. The methodology and technique to perform this type of analysis also is presented. The results obtained allow to identify: 1) Manufacture, use, modification and maintenance activities of tools that have been implemented; 2) Curated technological strategies have been developed in a bigger vjay than the expedient ones; 3) Some possible flintworking activity áreas have been located; 4) Preferential utilization of soft hammers over tfie hard ones; 5) Raw material selection; 6) flnally, it is been recognized priman/ and secondary clusters that could fiave fiad ttieir origin in tfie postdepositional formation processes of ttie arcfiaeological deposit

A performance evaluation of oscillation based test in continuous time filters

This work evaluates the ability of OBT for detecting parametric faults in continuous-time filters. To this end, we adopt two filters with quite different topologies as cases of study and a previously reported statistical fault model. In addition, we explore the behavior of the test schemes when a particular test condition is changed. The new data reported here, obtained from a fault simulation process, reveal a lower performance of OBT not observed in previous work using single-deviation faults, even under the change in the test condition.publishedVersionFil: Romero, Eduardo Abel. Universidad Tecnológica Nacional. Facultad Regional Villa María; Argentina.Fil: Romero, Eduardo Abel. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física; Argentina.Fil: Costamagna, Marcelo. Universidad Tecnológica Nacional. Facultad Regional Villa María; Argentina.Fil: Peretti, Gabriela Marta. Universidad Tecnológica Nacional. Facultad Regional Villa María; Argentina.Fil: Peretti, Gabriela Marta. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física; Argentina.Fil: Marqués, Carlos Alberto. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física; Argentina.Otras Ingeniería Eléctrica, Ingeniería Electrónica e Ingeniería de la Informació

Virus-like particle vaccines against BK and JC polyomaviruses

Nearly all healthy adults are asymptomatically infected with human polyomaviruses. In immunosuppressed individuals, the infection can reactivate and cause disease. BK polyomavirus (BKV) frequently damages transplanted kidneys and causes severe bladder disease in bone marrow transplant patients. JC polyomavirus (JCV) causes a lethal brain disease, PML, in individuals on various immunosuppressive therapies. PML also affects immunodeficient individuals, including AIDS patients. The outer capsid proteins of polyomaviruses are structurally similar to the capsids of human papillomaviruses (HPVs). Building on the success of the NCI’s HPV virus-like particle (VLP) vaccine technologies, we have developed VLP vaccines targeting BKV and JCV. Preclinical testing in a monkey model indicates that the BKV and JCV VLP vaccines share the HPV vaccines’ exceptionally potent immunogenicity. Given our knowledge of the role that antibodies play in ameliorating polyomavirus pathologies, the new VLP vaccines are likely to protect at-risk patients against the development of BKV-induced urinary tract disease and JCV-induced brain disease. Each year, roughly 30,000 Americans join wait-lists for kidney transplantation. Additionally, roughly 300,000 Americans per year are diagnosed with diseases that might be treated with bone marrow transplantation. Emerging evidence indicates that antibody-producing plasma cells elicited by the BKV vaccine will persist after bone marrow transplantation and the vaccine should thus provide protection against post-transplant hemorrhagic cystitis. The highly effective multiple sclerosis therapy Tysabri (natalizumab) is associated with up to 2% risk of PML side effects. Rituxan (rituximab), which is used for treatment of rheumatoid arthritis and certain types of lymphoma, carries a black box warning for PML and a dozen additional immunosuppressive therapies are also known or suspected to have PML side effects. The JCV vaccine should be a useful preventive adjunct for these popular immunotherapies. Since there are currently no effective treatments for BKV or JCV diseases, the candidate vaccines seem likely to qualify for FDA’s Accelerated Approval Program. The NCI is currently seeking industry partners