On limited-memory quasi-Newton methods for minimizing a quadratic function

The main focus in this paper is exact linesearch methods for minimizing a quadratic function whose Hessian is positive definite. We give two classes of limited-memory quasi-Newton Hessian approximations that generate search directions parallel to those of the method of preconditioned conjugate gradients, and hence give finite termination on quadratic optimization problems. The Hessian approximations are described by a novel compact representation which provides a dynamical framework. We also discuss possible extensions of these classes and show their behavior on randomly generated quadratic optimization problems. The methods behave numerically similar to L-BFGS. Inclusion of information from the first iteration in the limited-memory Hessian approximation and L-BFGS significantly reduces the effects of round-off errors on the considered problems. In addition, we give our compact representation of the Hessian approximations in the full Broyden class for the general unconstrained optimization problem. This representation consists of explicit matrices and gradients only as vector components

Approximate solution of system of equations arising in interior-point methods for bound-constrained optimization

The focus in this paper is interior-point methods for bound-constrained nonlinear optimization, where the system of nonlinear equations that arise are solved with Newton's method. There is a trade-off between solving Newton systems directly, which give high quality solutions, and solving many approximate Newton systems which are computationally less expensive but give lower quality solutions. We propose partial and full approximate solutions to the Newton systems. The specific approximate solution depends on estimates of the active and inactive constraints at the solution. These sets are at each iteration estimated by basic heuristics. The partial approximate solutions are computationally inexpensive, whereas a system of linear equations needs to be solved for the full approximate solution. The size of the system is determined by the estimate of the inactive constraints at the solution. In addition, we motivate and suggest two Newton-like approaches which are based on an intermediate step that consists of the partial approximate solutions. The theoretical setting is introduced and asymptotic error bounds are given. We also give numerical results to investigate the performance of the approximate solutions within and beyond the theoretical framework

A structured modified Newton approach for solving systems of nonlinear equations arising in interior-point methods for quadratic programming

The focus in this work is on interior-point methods for inequality-constrained quadratic programs, and particularly on the system of nonlinear equations to be solved for each value of the barrier parameter. Newton iterations give high quality solutions, but we are interested in modified Newton systems that are computationally less expensive at the expense of lower quality solutions. We propose a structured modified Newton approach where each modified Jacobian is composed of a previous Jacobian, plus one low-rank update matrix per succeeding iteration. Each update matrix is, for a given rank, chosen such that the distance to the Jacobian at the current iterate is minimized, in both 2-norm and Frobenius norm. The approach is structured in the sense that it preserves the nonzero pattern of the Jacobian. The choice of update matrix is supported by results in an ideal theoretical setting. We also produce numerical results with a basic interior-point implementation to investigate the practical performance within and beyond the theoretical framework. In order to improve performance beyond the theoretical framework, we also motivate and construct two heuristics to be added to the method

Multi-objective constrained Bayesian optimization for structural design

The planning and design of buildings and civil engineering concrete structures constitutes a complex problem subject to constraints, for instance, limit state constraints from design codes, evaluated by expensive computations such as finite element (FE) simulations. Traditionally, the focus has been on minimizing costs exclusively, while the current trend calls for good trade-offs of multiple criteria such as sustainability, buildability, and performance, which can typically be computed cheaply from the design parameters. Multi-objective methods can provide more relevant design strategies to find such trade-offs. However, the potential of multi-objective optimization methods remains unexploited in structural concrete design practice, as the expensiveness of structural design problems severely limits the scope of applicable algorithms. Bayesian optimization has emerged as an efficient approach to optimizing expensive functions, but it has not been, to the best of our knowledge, applied to constrained multi-objective optimization of structural concrete design problems. In this work, we develop a Bayesian optimization framework explicitly exploiting the features inherent to structural design problems, that is, expensive constraints and cheap objectives. The framework is evaluated on a generic case of structural design of a reinforced concrete (RC) beam, taking into account sustainability, buildability, and performance objectives, and is benchmarked against the well-known Non-dominated Sorting Genetic Algorithm II (NSGA-II) and a random search procedure. The results show that the Bayesian algorithm performs considerably better in terms of rate-of-improvement, final solution quality, and variance across repeated runs, which suggests it is well-suited for multi-objective constrained optimization problems in structural design

Learning Languages and Complex Subjects with Memory Palaces

A memory palace is an ancient technique of using space as a way of organizing memories. It’s a powerful tool for learning, retaining, and recalling large amounts of complex information quickly and effectively. In the middle ages, these techniques were widely used to learn and compose large texts and works of literature. In this paper, we present the fundamental theory behind memory palaces as the foundation for the project Macunx - a VR platform for building memory palaces to learn huge amounts in short time and with full retention - as well as the initial stages of its development. The paper concludes with a discussion of the future stages over the testing of the package with end-users for its final refinement

Genetic, serological and biochemical characterization of Leishmania tropica from foci in northern Palestine and discovery of zymodeme MON-307

Background Many cases of cutaneous leishmaniasis (CL) have been recorded in the Jenin District based on their clinical appearance. Here, their parasites have been characterized in depth. Methods Leishmanial parasites isolated from 12 human cases of CL from the Jenin District were cultured as promastigotes, whose DNA was extracted. The ITS1 sequence and the 7SL RNA gene were analysed as was the kinetoplast minicircle DNA (kDNA) sequence. Excreted factor (EF) serotyping and multilocus enzyme electrophoresis (MLEE) were also applied. Results This extensive characterization identified the strains as Leishmania tropica of two very distinct sub-types that parallel the two sub-groups discerned by multilocus microsatellite typing (MLMT) done previously. A high degree of congruity was displayed among the results generated by the different analytical methods that had examined various cellular components and exposed intra-specific heterogeneity among the 12 strains. Three of the ten strains subjected to MLEE constituted a new zymodeme, zymodeme MON-307, and seven belonged to the known zymodeme MON-137. Ten of the 15 enzymes in the profile of zymodeme MON-307 displayed different electrophoretic mobilities compared with the enzyme profile of the zymodeme MON-137. The closest profile to that of zymodeme MON-307 was that of the zymodeme MON-76 known from Syria. Strains of the zymodeme MON-307 were EF sub-serotype A2 and those of the zymodeme MON-137 were either A9 or A9B4. The sub-serotype B4 component appears, so far, to be unique to some strains of L. tropica of zymodeme MON-137. Strains of the zymodeme MON-137 displayed a distinctive fragment of 417 bp that was absent in those of zymodeme MON-307 when their kDNA was digested with the endonuclease RsaI. kDNA-RFLP after digestion with the endonuclease MboI facilitated a further level of differentiation that partially coincided with the geographical distribution of the human cases from which the strains came. Conclusions The Palestinian strains that were assigned to different genetic groups differed in their MLEE profiles and their EF types. A new zymodeme, zymodeme MON-307 was discovered that seems to be unique to the northern part of the Palestinian West Bank. What seemed to be a straight forward classical situation of L. tropica causing anthroponotic CL in the Jenin District might be a more complex situation, owing to the presence of two separate sub-types of L. tropica that, possibly, indicates two separate transmission cycles involving two separate types of phlebotomine sand fly vector

In vivo toxicity of cationic micelles and liposomes

AbstractThis study investigated toxicity of nanocarriers comprised of cationic polymer and lipid components often used in gene and drug delivery, formulated as cationic micelles and liposomes. Rats were injected intravenously with 10, 25 or 100mg/kg and sacrificed after 24 or 48h, or 24h after the last of three intravenous injections of 100mg/kg every other day. Histological evaluation of liver, lung and spleen, clinical chemistry parameters, and hematology indicated little effect of treatment. DNA strand breaks were increased in the lung and spleen. Further, in the dose response study we found unaltered expression levels of genes in the antioxidant response (HMOX1) and repair of oxidized nucleobases (OGG1), whereas expression levels of cytokines (IL6, CXCL2 and CCL2) were elevated in lung, spleen or liver. The results indicate that assessment of genotoxicity and gene expression add information on toxicity of nanocarriers, which is not obtained by histology and hematology.From the Clinical EditorThis study investigates the toxicity of cationic micelles and liposomes utilized as nanocarriers in gene and drug delivery, demonstrating its effects on the lungs, spleen and liver

Modeling the actinides with disordered local moments

A first-principles disordered local moment (DLM) picture within the local-spin-density and coherent potential approximations (LSDA+CPA) of the actinides is presented. The parameter free theory gives an accurate description of bond lengths and bulk modulus. The case of $\delta$-Pu is studied in particular and the calculated density of states is compared to data from photo-electron spectroscopy. The relation between the DLM description, the dynamical mean field approach and spin-polarized magnetically ordered modeling is discussed.Comment: 6 pages, 4 figure