Strongly Polynomial Primal-Dual Algorithms for Concave Cost Combinatorial Optimization Problems

We introduce an algorithm design technique for a class of combinatorial optimization problems with concave costs. This technique yields a strongly polynomial primal-dual algorithm for a concave cost problem whenever such an algorithm exists for the fixed-charge counterpart of the problem. For many practical concave cost problems, the fixed-charge counterpart is a well-studied combinatorial optimization problem. Our technique preserves constant factor approximation ratios, as well as ratios that depend only on certain problem parameters, and exact algorithms yield exact algorithms. Using our technique, we obtain a new 1.61-approximation algorithm for the concave cost facility location problem. For inventory problems, we obtain a new exact algorithm for the economic lot-sizing problem with general concave ordering costs, and a 4-approximation algorithm for the joint replenishment problem with general concave individual ordering costs

Separable Concave Optimization Approximately Equals Piecewise-Linear Optimization

We study the problem of minimizing a nonnegative separable concave function over a compact feasible set. We approximate this problem to within a factor of 1+epsilon by a piecewise-linear minimization problem over the same feasible set. Our main result is that when the feasible set is a polyhedron, the number of resulting pieces is polynomial in the input size of the polyhedron and linear in 1/epsilon. For many practical concave cost problems, the resulting piecewise-linear cost problem can be formulated as a well-studied discrete optimization problem. As a result, a variety of polynomial-time exact algorithms, approximation algorithms, and polynomial-time heuristics for discrete optimization problems immediately yield fully polynomial-time approximation schemes, approximation algorithms, and polynomial-time heuristics for the corresponding concave cost problems. We illustrate our approach on two problems. For the concave cost multicommodity flow problem, we devise a new heuristic and study its performance using computational experiments. We are able to approximately solve significantly larger test instances than previously possible, and obtain solutions on average within 4.27% of optimality. For the concave cost facility location problem, we obtain a new 1.4991+epsilon approximation algorithm.Comment: Full pape

Traditional approaches to foreign aid versus innovative ways to tackle development at international level

The history of foreign aid starts in colonial times when the dominant empires provided grants for infrastructure development or food aid to their colonies. The aid flows intensified after the World War II, with the successful implementation of the Marshal Plan in Europe. Despite huge amounts of money that were given especially to the African continent, results have failed to appear, leaving the continent even poorer than before. Therefore, the objective of the thesis is to understand what are the typical approaches to foreign aid and to explore the alternatives, putting an emphasis on microfinance. With the help of statistical indicators from the World Bank and Mix Market data base, an analysis was made about microfinance´ impact in four countries, namely: Bangladesh, India, Kenya and Uganda. We find that microfinance is important for the economy of all countries analyzed in the thesis. The sector outreaches directly and indirectly a significant part of the population. Besides loans, savings seem to be more significant to the African countries, rather than to the Asian ones. The Net ODA received, as a percentage of the Gross National Income is heavier for Kenya and Uganda than for Bangladesh and India; and it grew at a higher CAGR than the average loan per borrower. In the latest countries, the reverse situation is observable. In what concerns poverty reduction, all indicators decreased for the period of analysis. In Bangladesh and India, women are the main microfinance clients, with a proportion of 90%, while in Kenya and Uganda the proportion is equal to approximately 50% with a tendency to decline. The results suggest that microfinance doesn’t necessary help women enter the labor market or secure jobs. In what concerns the business sector, the number of microenterprises financed by microfinance institutions grew at higher CAGR´s than the countries´ total number of new businesses registered (with the exception of Kenya). All countries of analysis were downgraded in the World Bank Doing Business Index, when compared to their position in 2006. However, the business sector undergone significant positive changes.A história da ajuda internacional começa nos tempos coloniais, quando os impérios dominantes forneciam às suas colónias bolsas/subsídios para o desenvolvimento da infraestrutura ou ajuda alimentar. Os fluxos de ajuda intensificaram-se depois da Segunda Guerra Mundial, com o sucesso da implementação do Plano Marshall na Europa. Apesar das enormes quantias de dinheiro que foram dadas especialmente ao continente Africano, os resultados deixaram de aparecer, deixando o continente ainda mais pobre do que antes. Por esse motivo, o objetivo desta tese é perceber quais são as abordagens típicas à ajuda internacional e explorar as alternativas, destacando a “microfinance”. Com a ajuda de dados estatísticos da base de dados do Banco Mundial e Mix Market, foi feita uma análise sobre o impacto da microfinance em quatro países, nomeadamente: Bangladesh, Índia, Quénia e Uganda. Descobrimos que a microfinance é importante para a economia de todos os países analisados na tese. O sector alcança diretamente e indiretamente uma parte significativa da população. Além de empréstimos, as poupanças parecem ser mais importantes para os países Africanos do que para os países Asiáticos. A ajuda oficial ao desenvolvimento recebida em termos líquidos e como percentagem do Rendimento Nacional Bruto é mais pesada/significativa para Quénia e Uganda do que para Bangladesh e índia, crescendo a uma taxa de crescimento anual maior do que o empréstimo médio por devedor. Nos últimos países, observa-se uma situação inversa. No que diz respeito à redução da pobreza, todos os indicadores decresceram durante o período de análise. No Bangladesh e Índia, as mulheres são o principal cliente da microfinance, com uma proporção de 90%, enquanto no Quénia e Uganda esta proporção é aproximadamente 50%, com uma tendência para decrescer. Os resultados sugerem que microfinance não ajuda necessariamente as mulheres a entrar no mercado de trabalho ou assegurar os seus postos de emprego. No que diz respeito ao sector empresarial, o número de pequenas empresas financiadas pelas instituições de microfinance aumentou a uma taxa anual de crescimento maior do que o número total de empresas registadas no país (com a exceção do Quénia). Todos os países analisados decresceram de acordo com o Doing Business Index desenvolvido pelo Banco Mundial, quando comparados com a sua posição em 2006. Contudo, o sector empresarial atravessou mudanças significativas positivas

Uretrocistografia micțională retrogradă ca metodă de diagnostic a refluxului vezico-ureteral și vezico-renal

Catedra de Radiologie și Imagistică, Universitatea de Stat de Medicină şi Farmacie “Nicolae Testemiţanu” Chișinău, Republica Moldova The IVth Congress of Radiology and Medical Imaging of the Republic of Moldova with international participation, Chisinau, May 31 – June 2, 2018Introducere: Uretrocistografia micţională retrogradă este utilizată pentru confirmarea diagnosticului de reflux vezico-ureteral (RVU) sau vezico-renal (RVR). Scopul tratamentului constă în prevenirea injuriilor parenchimatoase renale, deși mulţi pacienţi au deja cicatrici renale la momentul diagnosticului. Material și metode: Studiul a inclus 180 de copii (105 fete și 75 de băieți) care au fost supravegheați pentru depistarea unui reflux pe o perioadă de 4 ani. Stabilirea diagnosticului de reflux vezico-ureteral a fost efectuată prin intermediul uretrocistografiei micționale retrograde. A fost evaluat tipul și gradul refluxului, precum și indicațiile și rezultatele terapeutice. Vârsta medie în lotul de diagnostic a fost de 26,8 luni. Rezultate: Pielonefrita acută a fost primul indiciu care a inițiat investigațiile pentru diagnosticul refluxului la 139 (77%) de copii. Diagnosticul prenatal de reflux după detectarea dilatației pielicei a fost înregistrat la 29 (16%) copii. Refluxul a implicat un tract urinar simplu la 163 de copii și duplicitate a tractului urinar – la 17 copii. Refluxul a fost bilateral în 43% cazuri. La circa 1/3 pacienți refluxul a fost mai mic de gradul II, proporția fiind inversată însă pentru refluxul antenatal (62% cazuri ≥ gradul II). Tratamentul chirurgical a fost efectuat în 55% din cazuri, la restul pacienților (45%) fiindu-le administrat doar tratamentul terapeutic. Urmărirea în dinamică a pacienților a relevat o rată scăzută de pielonefrită recurentă, echivalentă în ambele grupuri. Concluzii: Pielonefrita acută rămâne cauza principală a investigațiilor pentru diagnosticul refluxului vezico-ureteral și vezico-renal. Ultrasonografia renală cu cistografie retrogradă reprezintă investigațiile de primă intenție după un prim episod de infecție renală. Descoperirea refluxului în timpul diagnosticului antenatal este efectuat prin screening

Combinatorial optimization problems with concave costs

Thesis (Ph. D.)--Massachusetts Institute of Technology, Sloan School of Management, Operations Research Center, 2009.Includes bibliographical references (p. 83-89).In the first part, we study the problem of minimizing a separable concave function over a polyhedron. We assume the concave functions are nonnegative nondecreasing on R+, and the polyhedron is in RI' (these assumptions can be relaxed further under suitable technical conditions). We show how to approximate this problem to 1+ E precision in optimal value by a piecewise linear minimization problem so that the number of resulting pieces is polynomial in the input size of the original problem and linear in 1/c. For several concave cost problems, the resulting piecewise linear problem can be reformulated as a classical combinatorial optimization problem. As a result of our bound, a variety of polynomial-time heuristics, approximation algorithms, and exact algorithms for classical combinatorial optimization problems immediately yield polynomial-time heuristics, approximation algorithms, and fully polynomial-time approximation schemes for the corresponding concave cost problems. For example, we obtain a new approximation algorithm for concave cost facility location, and a new heuristic for concave cost multi commodity flow. In the second part, we study several concave cost problems and the corresponding combinatorial optimization problems. We develop an algorithm design technique that yields a strongly polynomial primal-dual algorithm for a concave cost problem whenever such an algorithm exists for the corresponding combinatorial optimization problem.(cont.) Our technique preserves constant-factor approximation ratios as well as ratios that depend only on certain problem parameters, and exact algorithms yield exact algorithms. For example, we obtain new approximation algorithms for concave cost facility location and concave cost joint replenishment, and a new exact algorithm for concave cost lot-sizing. In the third part, we study a real-time optimization problem arising in the operations of a leading internet retailer. The problem involves the assignment of orders that arrive via the retailer's website to the retailer's warehouses. We model it as a concave cost facility location problem, and employ existing primal-dual algorithms and approximations of concave cost functions to solve it. On past data, we obtain solutions on average within 1.5% of optimality, with running times of less than 100ms per problem.by Dan Stratila.Ph.D

Diagonalization and representation results for nonpositive sesquilinear form measures

We study decompositions of operator measures and more general sesquilinear form measures $E$ into linear combinations of positive parts, and their diagonal vector expansions. The underlying philosophy is to represent $E$ as a trace class valued measure of bounded variation on a new Hilbert space related to $E$. The choice of the auxiliary Hilbert space fixes a unique decomposition with certain properties, but this choice itself is not canonical. We present relations to Naimark type dilations and direct integrals.Comment: J. Math. Anal. Appl., in pres

Lagrangian Grassmannian in Infinite Dimension

Given a complex structure $J$ on a real (finite or infinite dimensional) Hilbert space $H$, we study the geometry of the Lagrangian Grassmannian $\Lambda(H)$ of $H$, i.e. the set of closed linear subspaces $L\subset H$ such that $$J(L)=L^\perp.$$ The complex unitary group $U(H_J)$, consisting of the elements of the orthogonal group of $H$ which are complex linear for the given complex structure, acts transitively on $\Lambda(H)$ and induces a natural linear connection in $\Lambda(H)$. It is shown that any pair of Lagrangian subspaces can be joined by a geodesic of this connection. A Finsler metric can also be introduced, if one regards subspaces $L$ as projections $p_L$ (=the orthogonal projection onto $L$) or symmetries \e_L=2p_L-I, namely measuring tangent vectors with the operator norm. We show that for this metric the Hopf-Rinow theorem is valid in $\Lambda(H)$: a geodesic joining a pair of Lagrangian subspaces can be chosen to be of minimal length. We extend these results to the classical Banach-Lie groups of Schatten.Comment: 23 page

The relationship between the number of Streptococcus mutans in the saliva and the influence of dental caries in children with congenital heart defects

Universitatea de Stat de Medicină şi Farmacie „Nicolae Testemiţanu”, Chişinău, Republica MoldovaIntroducere. Caria dentară (CD) este una dintre cele mai frecvente boli, în etiologia căreia este recunoscut impactul agentului microbian. Asocierea CD cu bolile sistemice precum maladiile cardiovasculare, inclusiv, malformațiile cardiace congenitale (MCC), poate provoca complicații severe la copii, deoarece focarele cronice de infecție odontogenă pot majora riscul de dezvoltare a endocarditei bacteriene. Scopul lucrării. Evaluarea relației dintre numărul Streptococcus mutans în salivă și afectarea prin caria dentară a copiilor cu malformații cardiace congenitale. Materiale și metode. Studiul clinic de tip caz-martor a fost efectuat pe un eșantion de 46 de copii repartizați în 2 loturi identice după structură. Lotul de cercetare a fost constituit din 23 de copii cu MCC și vârstele de 7-18 ani (L 1 = 23). Lotul martor (L 0 = 23) a fost format din 23 de copii convențional sănătoși. S-au estimat indicatorii de afectare prin carie dentară: indicele de prevalență (IP) și indicii COA și COAS. Pentru evaluarea numărului Streptococcus mutans a fost utilizat kit-ul Saliva-Check Mutans, GC. Rezultate. IP la copiii cu MCC a costituit 73,91%, fiind de 1,42 ori mai crescut comparativ cu subiecții convențional sănătoși. Valorile indicilor COA și COAS la copiii din lotul de cercetare (3,22±0,14 și respectiv, 7,16±0,39) au fost crescute statistic semnificativ, în raport cu L 0. Numărul crescut (> 5x105 UFC/ml) de Streptococcus mutans în salivă s-a depistat la 69,57% dintre copiii din L 1 și 17,39% dintre subiecții din L 0. Prin estimarea coeficientului de corelație Spearman (ρ) s-a stabilit o relație directă semnificativă între indicatorii COA (ρ = 0,56, p 5x10 5 CFU/ml) of Streptococcus mutans in saliva were detected in 69.57% of L 1 children and 17.39% of L 0 subjects. By estimating Spearman correlation coefficient (ρ), a significant direct relationship was established between DMFT (ρ = 0.56, p<0.05) and DMFS (ρ = 0.67, p<0.01) indicators and the number of Streptococcus mutans in the saliva of children with CHD. Conclusion. The significant direct relationship between indicators of DC damage and the number of Streptococcus mutans in the saliva of children with CHD demonstrates the importance of assessing the number of Streptococcus mutans in saliva and dental biofilm for the development of effective methods to prevent DC and Streptococcus mutans invasion of the bloodstream, and finally, prevention of bacterial endocarditis

On unbounded p-summable Fredholm modules

We prove that odd unbounded p-summable Fredholm modules are also bounded p-summable Fredholm modules (this is the odd counterpart of a result of A. Connes for the case of even Fredholm modules)