Adaptive Regularization for Nonconvex Optimization Using Inexact Function Values and Randomly Perturbed Derivatives

A regularization algorithm allowing random noise in derivatives and inexact function values is proposed for computing approximate local critical points of any order for smooth unconstrained optimization problems. For an objective function with Lipschitz continuous $p$-th derivative and given an arbitrary optimality order $q \leq p$, it is shown that this algorithm will, in expectation, compute such a point in at most $O\left(\left(\min_{j\in\{1,\ldots,q\}}\epsilon_j\right)^{-\frac{p+1}{p-q+1}}\right)$ inexact evaluations of $f$ and its derivatives whenever $q\in\{1,2\}$, where $\epsilon_j$ is the tolerance for $j$th order accuracy. This bound becomes at most $O\left(\left(\min_{j\in\{1,\ldots,q\}}\epsilon_j\right)^{-\frac{q(p+1)}{p}}\right)$ inexact evaluations if $q>2$ and all derivatives are Lipschitz continuous. Moreover these bounds are sharp in the order of the accuracy tolerances. An extension to convexly constrained problems is also outlined.Comment: 22 page

Updating constraint preconditioners for KKT systems in quadratic programming via low-rank corrections

This work focuses on the iterative solution of sequences of KKT linear systems arising in interior point methods applied to large convex quadratic programming problems. This task is the computational core of the interior point procedure and an efficient preconditioning strategy is crucial for the efficiency of the overall method. Constraint preconditioners are very effective in this context; nevertheless, their computation may be very expensive for large-scale problems, and resorting to approximations of them may be convenient. Here we propose a procedure for building inexact constraint preconditioners by updating a "seed" constraint preconditioner computed for a KKT matrix at a previous interior point iteration. These updates are obtained through low-rank corrections of the Schur complement of the (1,1) block of the seed preconditioner. The updated preconditioners are analyzed both theoretically and computationally. The results obtained show that our updating procedure, coupled with an adaptive strategy for determining whether to reinitialize or update the preconditioner, can enhance the performance of interior point methods on large problems.Comment: 22 page

Adaptive Regularization Algorithms with Inexact Evaluations for Nonconvex Optimization

A regularization algorithm using inexact function values and inexact derivatives is proposed and its evaluation complexity analyzed. This algorithm is applicable to unconstrained problems and to problems with inexpensive constraints (that is constraints whose evaluation and enforcement has negligible cost) under the assumption that the derivative of highest degree is $\beta$-H\"{o}lder continuous. It features a very flexible adaptive mechanism for determining the inexactness which is allowed, at each iteration, when computing objective function values and derivatives. The complexity analysis covers arbitrary optimality order and arbitrary degree of available approximate derivatives. It extends results of Cartis, Gould and Toint (2018) on the evaluation complexity to the inexact case: if a $q$th order minimizer is sought using approximations to the first $p$ derivatives, it is proved that a suitable approximate minimizer within $\epsilon$ is computed by the proposed algorithm in at most $O(\epsilon^{-\frac{p+\beta}{p-q+\beta}})$ iterations and at most $O(|\log(\epsilon)|\epsilon^{-\frac{p+\beta}{p-q+\beta}})$ approximate evaluations. An algorithmic variant, although more rigid in practice, can be proved to find such an approximate minimizer in $O(|\log(\epsilon)|+\epsilon^{-\frac{p+\beta}{p-q+\beta}})$ evaluations.While the proposed framework remains so far conceptual for high degrees and orders, it is shown to yield simple and computationally realistic inexact methods when specialized to the unconstrained and bound-constrained first- and second-order cases. The deterministic complexity results are finally extended to the stochastic context, yielding adaptive sample-size rules for subsampling methods typical of machine learning.Comment: 32 page

Experimental and Numerical Analysis of Single Phase Flow in a micro T-junction

This paper was presented at the 4th Micro and Nano Flows Conference (MNF2014), which was held at University College, London, UK. The conference was organised by Brunel University and supported by the Italian Union of Thermofluiddynamics, IPEM, the Process Intensification Network, the Institution of Mechanical Engineers, the Heat Transfer Society, HEXAG - the Heat Exchange Action Group, and the Energy Institute, ASME Press, LCN London Centre for Nanotechnology, UCL University College London, UCL Engineering, the International NanoScience Community, www.nanopaprika.eu.In this work the fluid-dynamic behaviour of a micro T-junction has been investigated both numerically and experimentally for low Reynolds numbers (Re<14) with water as working fluid. The velocity profiles within the T-junction has been experimentally determined by using the micro Particle Image Velocimetry (μPIV). The experimental data have been compared with the numerical results obtained by means of a 3D model implemented in Comsol Multiphysics® environment for incompressible, isothermal, laminar flows with constant properties. The comparison between the experimental and the numerical data puts in evidence a perfect agreement among the results. In the central region of the T-junction where the velocity profiles of the inlet branches interact, the maximum difference is less than 5.8% for different flow rates imposed at the inlet (with the ratio 1:2) and less than 4.4% in the case of the same flow rate at the inlets (1:1). Since the estimated uncertainty of the experimental velocity is about 3%, the obtained result can be considered very good and it demonstrates that no significant scaling effects influences the liquid mixing for low Reynolds numbers (Re<14) and the behaviour of the micro T-junction can be considered as conventional. The detailed analysis of the velocity profile evolution within the central region of the mixer has allowed to determine where the fully developed laminar profile is reached (for instance 260 mm far from the centre of the T-junction when a maximum water flow rate of 8 ml/h is considered)

Interfacial cracks in bi-material solids: Stroh formalism and skew-symmetric weight functions

A new general approach for deriving the weight functions for 2D interfacial cracks in anisotropic bimaterials has been developed.For perfect interface conditions, the new method avoid the use of Wiener-Hopf technique and the challenging factorization problem connected. Both symmetric and skew-symmetric weight functions can be derived by means of the new approach. Weight functions can be used for deriving singular integral formulation of interfacial cracks in anisotropic media. The proposed method can be applied for studying interfacial cracks problems in many materials:monoclinic, orthotropic, cubic, piezoelectrics, poroelastics, quasicrystals

Morphological evaluation of fetal membranes and placenta of wild life Mazama gouazoubira deer in the first third of pregnancy

Mazama gouazoubira, o veado-catingueiro, é uma espécie de cervídeo de porte pequeno, que pode ser encontrado na América do Sul, desde o sul do Uruguai até o norte de Mato Grosso, no Brasil. Este estudo teve como objetivo descrever as membranas fetais e a placenta de M. gouazoubira no terço inicial de gestação. As amostras coletadas foram analisadas macroscopicamente e microscopicamente. O exame do útero demonstrou uma gestação univitelina e um embrião com crown-rump de 13mm. Na análise do embrião pode ser observado o olho pigmentado, as saliências auriculares, o mesonefro e e metanefro em desenvolvimento, o fígado e sua proeminência externa, o estômago, os membros torácicos e os brotos dos membros pélvicos. A placenta apresentou-se oligocotiledonária e no útero puderam ser observadas nove carúnculas. O saco gestacional mediu 15cm de comprimento e, como observado no início da gestação dos ruminantes domésticos, os cotilédones não puderam ser identificados macroscopicamente. Uma fraca adesão foi observada entre as carúnculas e a membrana corioalantóica (cotilédones) que formavam os placentônios. A membrana corioalantóica demonstrou um alantóide bem vascularizado composto por uma fina camada de células de núcleos e citoplasmas alongados. Na outra face da membrana, o cório foi composto por células cúbicas, de citoplasmas escassos e núcleos grandes e arredondados, características de células trofoblásticas. Envolvendo o embrião visualizou-se o saco amniótico constituído de duas camadas passíveis de separação mecânica, que apresentaram morfologia similar, sendo formadas por um epitélio pavimentoso avascular. Não foi observado saco vitelino no estágio gestacional do espécime estudado. Conclui-se que a placenta de M. gouazoubira é oligocotiledonária, como observado em outros cervídeos, e que as membranas fetais apresentam semelhanças com a de outros ruminantes, incluindo as características citológicas. Estudos adicionais são necessários para determinar a presença do saco vitelino e quando ocorre sua regressão.Mazama gouazoubira is a small-sized deer, which can be found in South America, from southern Uruguay to the north of Mato Grosso, Brazil. This study aimed to describe the fetal membranes and placenta of M. gouazoubira in the first third of pregnancy. Samples collected were macroscopically and microscopically analyzed. Uterus examination demonstrated univitelinic gestation with an embryo measuring a crown-rump length of 13mm. In the embryo analysis we could identify the pigmented eye, auricular hillocks, mesonephron and early metanephron, liver and its external prominence, stomach, thoracic members and buds of pelvic members. Placenta was oligocotyledonary and nine caruncles were found in the uterus. Gestational sac measured 15cm in length, and, as observed in the early gestation of domestic ruminants, cotyledons could not be identified macroscopically. A weak adhesion was found between caruncles and chorioallantoic membrane (cotyledons) forming the placentomes. The chorioallantoic membrane showed a well-vascularized allantoid composed by a thin layer of cells with stretched nucleus and cytoplasm. On the other side of the membrane, the chorion was composed by cubic cells with scant cytoplasm and large-rounded nuclei, features of trophoblast cells. Involving the embryo we identified a two-layered amniotic sac. Layers could be mechanically separated and had similar morphology, showing a non-vascularized squamous epithelium. There was no yolk sac in the gestational stage of this specimen. We concluded that the placenta of M. gouazoubira is an oligocotyledonary placenta, as observed in others cervids, and that the fetal membranes showed similarities with those from other domestic ruminants, including cytological characteristics. Further studies are required in order to determine the presence of the yolk sac and its regression time

Promyelocytic leukemia (PML) gene expression is a prognostic factor in ampullary cancer patients

BACKGROUND: Promyelocytic leukemia (PML) tumor suppressor gene plays a key role in acute PML pathogenesis but its involvement in pathogenesis and prognosis of solid cancers has not been defined yet. PATIENTS AND METHODS: In all, 62 ampullary adenocarcinoma patients who underwent curative surgery between 1996 and 2005 were included. Expression analysis of PML was carried out by immunohistochemical staining and correlated with disease-free survival (DFS) and overall survival (OS). RESULTS: In 24 tumor specimens (38.7%), PML was classified as absent, in 16 (25.8%) as focally expressed and in 22 (35.5%) as diffusely expressed. By univariate analysis, DFS was significantly influenced by pathological T stage (P=0.03), lymph nodal involvement (P=0.002), and PML expression (P=0.001). DFS in patients without PML expression was 28.0 months versus 45.1 and 75.5 for patients with focal and diffuse expression, respectively. OS in the group of patients without PML expression, with focal expression, and with diffuse expression was 40, 48, and 77 months, respectively (P=0.002). By a multivariate analysis, PML expression was the strongest prognostic factor for DFS (P=0.003) and the only statically significant prognostic factor for OS (P=0.009). CONCLUSIONS: Our preliminary data suggest PML as a novel prognostic tool for ampullary cancer patients

HCI at the boundary of work and life

The idea behind this Special Issue originates in a workshop on HCI and CSCW research related to work and non-work-life balance organized in conjunction with the ECSCW 2013 conference by the issue co-editors. Fifteen papers were originally submitted for possible inclusion in this Special Issue, and four papers were finally accepted for publication after two rounds of rigorous peer review. The four accepted papers explore, in different ways, HCI at the boundary of work and life. In this editorial, we offer a description of the overall theme and rationale for the Special Issue, including an introduction on the topic relevance and background, and a reflection on how the four accepted papers further current research and debate on the topic

Radio pulsar populations

The goal of this article is to summarize the current state of play in the field of radio pulsar statistics. Simply put, from the observed sample of objects from a variety of surveys with different telescopes, we wish to infer the properties of the underlying sample and to connect these with other astrophysical populations (for example supernova remnants or X-ray binaries). The main problem we need to tackle is the fact that, like many areas of science, the observed populations are often heavily biased by a variety of selection effects. After a review of the main effects relevant to radio pulsars, I discuss techniques to correct for them and summarize some of the most recent results. Perhaps the main point I would like to make in this article is that current models to describe the population are far from complete and often suffer from strong covariances between input parameters. That said, there are a number of very interesting conclusions that can be made concerning the evolution of neutron stars based on current data. While the focus of this review will be on the population of isolated Galactic pulsars, I will also briefly comment on millisecond and binary pulsars as well as the pulsar content of globular clusters and the Magellanic Clouds.Comment: 16 pages, 6 figures, to appear in Proceedings of ICREA Workshop on The High-Energy Emission from Pulsars and their Systems, Sant Cugat, Spain, 2010 April 12-16 (Springer