Polyhedral study of mixed integer sets arising from inventory problems

“Branch-and-cut” algorithm is one of the most efficient exact approaches to solve mixed integer programs. This algorithm combines the advantages of a pure branch-and-bound approach and cutting planes scheme. Branch-and-cut algorithm computes the linear programming relaxation of the problem at each node of the search tree which is improved by the use of cuts, i.e. by the inclusion of valid inequalities. It should be taken into account that selection of strongest cuts is crucial for their effective use in branch-and-cut algorithm. In this thesis, we focus on the derivation and use of cutting planes to solve general mixed integer problems, and in particular inventory problems combined with other problems such as distribution, supplier selection, vehicle routing, etc. In order to achieve this goal, we first consider substructures (relaxations) of such problems which are obtained by the coherent loss of information. The polyhedral structure of those simpler mixed integer sets is studied to derive strong valid inequalities. Finally those strong inequalities are included in the cutting plane algorithms to solve the general mixed integer problems. We study three mixed integer sets in this dissertation. The first two mixed integer sets arise as a subproblem of the lot-sizing with supplier selection, the network design and the vendor-managed inventory routing problems. These sets are variants of the well-known single node fixed-charge network set where a binary or integer variable is associated with the node. The third set occurs as a subproblem of mixed integer sets where incompatibility between binary variables is considered. We generate families of valid inequalities for those sets, identify classes of facet-defining inequalities, and discuss the separation problems associated with the inequalities. Then cutting plane frameworks are implemented to solve some mixed integer programs. Preliminary computational experiments are presented in this direction.

Integer-valued APARCH processes in the analysis of time series of counts

The Asymmetric Power Arch representation for the volatility was introduced by Ding et al.(1993) in order to account for asymmetric responses in the volatility in the analysis of continuous-valued financial time series like, for instance, the log-return series of foreign exchange rates, stock indices or share prices. As reported by Brannas and Quoreshi (2010), asymmetric responses in volatility are also observed in time series of counts such as the number of intra-day transactions in stocks. In this work, an asymmetric power autoregressive conditional Poisson model is introduced for the analysis of time series of counts exhibiting asymmetric overdispersion. Basic probabilistic and statistical properties are summarized and parameter estimation is discussed. A simulation study is presented to illustrate the proposed model. Finally, an empirical application to a set of data concerning the daily number of stock transactions is also presented to attest for its practical applicability in data analysis.

Preconditioning 2D Integer Data for Fast Convex Hull Computations

In order to accelerate computing the convex hull on a set of n points, a heuristic procedure is often applied to reduce the number of points to a set of s points, s ≤ n, which also contains the same hull. We present an algorithm to precondition 2D data with integer coordinates bounded by a box of size p × q before building a 2D convex hull, with three distinct advantages. First, we prove that under the condition min(p, q) ≤ n the algorithm executes in time within O(n); second, no explicit sorting of data is required; and third, the reduced set of s points forms a simple polygonal chain and thus can be directly pipelined into an O(n) time convex hull algorithm. This paper empirically evaluates and quantifies the speed up gained by preconditioning a set of points by a method based on the proposed algorithm before using common convex hull algorithms to build the final hull. A speedup factor of at least four is consistently found from experiments on various datasets when the condition min(p, q) ≤ n holds; the smaller the ratio min(p, q)/n is in the dataset, the greater the speedup factor achieved.

Optimal scheduling of a renewable micro-grid in an isolated load area using mixed-integer linear programming

In the energy management of the isolated operation of small power system, the economic scheduling of the generation units is a crucial problem. Applying right timing can maximize the performance of the supply. The optimal operation of a wind turbine, a solar unit, a fuel cell and a storage battery is searched by a mixed-integer linear programming implemented in General Algebraic Modeling Systems (GAMS). A Virtual Power Producer (VPP) can optimal operate the generation units, assured the good functioning of equipment, including the maintenance, operation cost and the generation measurement and control. A central control at system allows a VPP to manage the optimal generation and their load control. The application of methodology to a real case study in Budapest Tech, demonstrates the effectiveness of this method to solve the optimal isolated dispatch of the DC micro-grid renewable energy park. The problem has been converged in 0.09 s and 30 iterations.

New insights on integer-programming models for the kidney exchange problem

In recent years several countries have set up policies that allow exchange of kidneys between two or more incompatible patient–donor pairs. These policies lead to what is commonly known as kidney exchange programs. The underlying optimization problems can be formulated as integer programming models. Previously proposed models for kidney exchange programs have exponential numbers of constraints or variables, which makes them fairly difficult to solve when the problem size is large. In this work we propose two compact formulations for the problem, explain how these formulations can be adapted to address some problem variants, and provide results on the dominance of some models over others. Finally we present a systematic comparison between our models and two previously proposed ones via thorough computational analysis. Results show that compact formulations have advantages over non-compact ones when the problem size is large.

Mixed integer non linear programming and artificial neural network based approach to ancillary services dispatch in competitive electricity markets

Ancillary services represent a good business opportunity that must be considered by market players. This paper presents a new methodology for ancillary services market dispatch. The method considers the bids submitted to the market and includes a market clearing mechanism based on deterministic optimization. An Artificial Neural Network is used for day-ahead prediction of Regulation Down, regulation-up, Spin Reserve and Non-Spin Reserve requirements. Two test cases based on California Independent System Operator data concerning dispatch of Regulation Down, Regulation Up, Spin Reserve and Non-Spin Reserve services are included in this paper to illustrate the application of the proposed method: (1) dispatch considering simple bids; (2) dispatch considering complex bids.

Fuzzy, integer and fractional-order control: application on a wind turbine benchmark model

This paper presents a comparison between proportional integral control approaches for variable speed wind turbines. Integer and fractional-order controllers are designed using linearized wind turbine model whilst fuzzy controller also takes into account system nonlinearities. These controllers operate in the full load region and the main objective is to extract maximum power from the wind turbine while ensuring the performance and reliability required to be integrated into an electric grid. The main contribution focuses on the use of fractional-order proportional integral (FOPI) controller which benefits from the introduction of one more tuning parameter, the integral fractional-order, taking advantage over integer order proportional integral (PI) controller. A comparison between proposed control approaches for the variable speed wind turbines is presented using a wind turbine benchmark model in the Matlab/Simulink environment. Results show that FOPI has improved system performance when compared with classical PI and fuzzy PI controller outperforms the integer and fractional-order control due to its capability to deal with system nonlinearities and uncertainties. © 2014 IEEE.

Entropy analysis of integer and fractional dynamical systems

This paper investigates the adoption of entropy for analyzing the dynamics of a multiple independent particles system. Several entropy definitions and types of particle dynamics with integer and fractional behavior are studied. The results reveal the adequacy of the entropy concept in the analysis of complex dynamical systems.

Integer and Fractional Order Entropy Analysis of Earthquake Data-series

This paper studies the statistical distributions of worldwide earthquakes from year 1963 up to year 2012. A Cartesian grid, dividing Earth into geographic regions, is considered. Entropy and the Jensen–Shannon divergence are used to analyze and compare real-world data. Hierarchical clustering and multi-dimensional scaling techniques are adopted for data visualization. Entropy-based indices have the advantage of leading to a single parameter expressing the relationships between the seismic data. Classical and generalized (fractional) entropy and Jensen–Shannon divergence are tested. The generalized measures lead to a clear identification of patterns embedded in the data and contribute to better understand earthquake distributions.

Interaction of malaria parasites with host late endocytic and autophagic pathways is essential for Plasmodium liver stage development

RESUMO: A Malária é causada por parasitas do género Plasmodium, sendo a doença parasitária mais fatal para o ser humano. Apesar de, durante o século passado, o desenvolvimento económico e a implementação de diversas medidas de controlo, tenham permitido erradicar a doença em muitos países, a Malária continua a ser um problema de saúde grave, em particular nos países em desenvolvimento. A Malária é transmitida através da picada de uma fêmea de mosquito do género Anopheles. Durante a picada, os esporozoítos são injetados na pele do hospedeiro, seguindo-se a fase hepática e obrigatória do ciclo de vida. No fígado, os esporozoítos infetam os hepatócitos onde se replicam, dentro de um vacúolo parasitário (VP) e de uma forma imunitária silenciosa, em centenas de merozoitos. Estas novas formas do parasita são as responsáveis por infetar os eritrócitos, iniciando a fase sanguínea da doença, onde se os primeiros sintomas se manifestam, tais como a característica febre cíclica. A fase hepática da doença é a menos estudada e compreendida. Mais ainda, as interações entre o VP e os organelos da células hospedeira estão ainda pouco caracterizados. Assim, neste estudo, as interações entre os organelos endocíticos e autofágicos da célula hospedeira e o VP foram dissecados, observando-se que os anfisomas, que são organelos resultantes da intersecção do dois processos de tráfego intracelular, interagem com o parasita. Descobrimos que a autofagia tem também uma importante função imunitária durante a fase hepática inicial, ao passo, que durante o desenvolvimento do parasita, já numa fase mais tardia, o parasita depende da interação com os endossomas tardios e anfisomas para crescer. Vesiculas de BSA, EGF e LC3, foram, também, observadas dentro do VP, sugerindo que os parasitas são capazes de internalizar material endocítico e autofágico do hospedeiro. Mais ainda, mostramos que esta interação depende da cinase PIKfyve, responsável pela conversão do fosfoinositidio-3-fosfato no fosfoinositidio-3,5-bifosfato, uma vez que inibindo esta cinase o parasita não é capaz de crescer normalmente. Finalmente, mostramos que a proteína TRPML1, uma proteína efetora do fosfoinositidio-3,5-bifosfato, e envolvida no processo de fusão das membranas dos organelos endocíticos e autofágicos, também é necessária para o crescimento do parasita. Desta forma, o nosso estudo sugere que a membrana do VP funde com vesiculas endocíticas e autofágicas tardias, de uma forma dependente do fositidio-3,5-bifosfato e do seu effetor TRPML1, permitindo a troca de material com a célula hospedeira. Concluindo, os nossos resultados evidenciam que o processo autofágico que ocorre na célula hospedeira tem um papel duplo durante a fase hepática da malaria. Enquanto numa fase inicial os hepatócitos usam o processo autofágico como forma de defesa contra o parasita, já durante a fase de replicação o VP funde com vesiculas autofágicas e endocíticas de forma a obter os nutrientes necessários ao seu desenvolvimento.--------- ABSTRACT: Malaria, which is caused by parasites of the genus Plasmodium, is the most deadly parasitic infection in humans. Although economic development and the implementation of control measures during the last century have erradicated the disease from many areas of the world, it remains a serious human health issue, particularly in developing countries. Malaria is transmitted by female mosquitoes of the genus Anopheles. During the mosquito blood meal, Plasmodium spp. sporozoites are injected into the skin dermis of the vertebrate host, followed by an obligatory liver stage. Upon entering the liver, Plasmodium parasites infect hepatocytes and silently replicate inside a host cell-derived parasitophorous vacuole (PV) into thousands of merozoites. These new parasite forms can infect red blood cells initiating the the blood stage of the disease which shows the characteristic febrile malaria episodes. The liver stage is the least characterized step of the malaria infection. Moreover, the interactions between the Plasmodium spp. PV and the host cell trafficking pathways are poorly understood. We dissected the interaction between Plasmodium parasites and the host cell endocytic and autophagic pathways and we found that both pathways intersect and interconnect in the close vicinity of the parasite PV, where amphisomes are formed and accumulate. Interestingly, we observed a clearance function for autophagy in hepatocytes infected with Plasmodium berghei parasites at early infection times, whereas during late liver stage development late endosomes and amphisomes are required for parasite growth. Moreover, we found the presence of internalized BSA, EGF and LC3 inside parasite vacuoles, suggesting that the parasites uptake endocytic and autophagic cargo. Furthermore, we showed that the interaction between the PV and host traffic pathways is dependent on the kinase PIKfyve, which converts the phosphoinositide PI(3)P into PI(3,5)P2, since PIKfyve inhibition caused a reduction in parasite growth. Finally, we showed that the PI(3,5)P2 effector protein TRPML1, which is involved in late endocytic and autophagic membrane fusion, is also required for parasite development. Thus, our studies suggest that the parasite parasitophorous vacuole membrane (PVM) is able to fuse with late endocytic and autophagic vesicles in a PI(3,5)P2- and TRPML1-dependent manner, allowing the exchange of material between the host cell and the parasites, necessary for the rapid development of the latter that is seen during the liver stage of infection. In conclusion, we present evidence supporting a specific and essential dual role of host autophagy during the course of Plasmodium liver infection. Whereas in the initial hours of infection the host cell uses autophagy as a cell survival mechanism to fight the infection, during the replicative phase the PV fuses with host autophagic and endocytic vesicles to obtain nutrients required for parasite growth.

sancti Gregorii Turonensis historiae Francorum libri novem : primus liber integer, secundi sex priora capitula et alia passim desiderantur : ad calcem libri noni subjicitur Fredegarii chronicon ab anno quo desierat Gregorius, deductum ad annum 656. quod quidem à variis authoribus productum fuit ad annum 741. porrò chronicon Fredegarii cum additamentis, decimus Gregorii Turonensis liber in hoc codice inscribitur.

Colbertinus

1.° Marciani Capellae satyricon : primus liber integer, secundi initium, sexti finis et tres reliqui desiderantur. — 2.° A. Manlii Boëtii commentarius in Porphyrii isagogen. — 3.° Servii Honorati de ultimarum syllabarum ratione liber ad Aquilinum. — 4.° Prisciani, Grammatici, liber de nomine et pronomine, de verbo et participio ; passim inter lineas glossae.

Colbertinus