Invex nonsmooth alternative theorem and applications

An invex constrained nonsmooth optimization problem is considered, in which the presence of an abstract constraint set is possibly allowed. Necessary and sufficient conditions of optimality are provided and weak and strong duality results established. Following Geoffrion's approach an invex nonsmooth alternative theorem of Gordan type is then derived. Subsequently, some applications on multiobjective programming are then pursued. © 2000 OPA (Overseas Publishers Association) N.V. Published by license under the Gordon and Breach Science Publishers imprint.

An algorithmic Friedman-Pippenger theorem on tree embeddings and applications

An (n, d)-expander is a graph G = (V, E) such that for every X subset of V with vertical bar X vertical bar <= 2n - 2 we have vertical bar Gamma(G)(X) vertical bar >= (d + 1) vertical bar X vertical bar. A tree T is small if it has at most n vertices and has maximum degree at most d. Friedman and Pippenger (1987) proved that any ( n; d)- expander contains every small tree. However, their elegant proof does not seem to yield an efficient algorithm for obtaining the tree. In this paper, we give an alternative result that does admit a polynomial time algorithm for finding the immersion of any small tree in subgraphs G of (N, D, lambda)-graphs Lambda, as long as G contains a positive fraction of the edges of Lambda and lambda/D is small enough. In several applications of the Friedman-Pippenger theorem, including the ones in the original paper of those authors, the (n, d)-expander G is a subgraph of an (N, D, lambda)-graph as above. Therefore, our result suffices to provide efficient algorithms for such previously non-constructive applications. As an example, we discuss a recent result of Alon, Krivelevich, and Sudakov (2007) concerning embedding nearly spanning bounded degree trees, the proof of which makes use of the Friedman-Pippenger theorem. We shall also show a construction inspired on Wigderson-Zuckerman expander graphs for which any sufficiently dense subgraph contains all trees of sizes and maximum degrees achieving essentially optimal parameters. Our algorithmic approach is based on a reduction of the tree embedding problem to a certain on-line matching problem for bipartite graphs, solved by Aggarwal et al. (1996).

Alternative positional FEM applied to thermomechanical impact of truss structures

This paper presents a formulation to deal with dynamic thermomechanical problems by the finite element method. The proposed methodology is based on the minimum potential energy theorem written regarding nodal positions, not displacements, to solve the mechanical problem. The thermal problem is solved by a regular finite element method. Such formulation has the advantage of being simple and accurate. As a solution strategy, it has been used as a natural split of the thermomechanical problem, usually called isothermal split or isothermal staggered algorithm. Usual internal variables and the additive decomposition of the strain tensor have been adopted to model the plastic behavior. Four examples are presented to show the applicability of the technique. The results are compared with other authors` numerical solutions and experimental results. (C) 2010 Elsevier B.V. All rights reserved.

World-line condition and the noninteraction theorem

A 6N-dimensional alternative formulation is proposed for constrained Hamiltonian systems. In this context the noninteraction theorem is derived from the world-line conditions. A model of two interacting particles is exhibited where physical coordinates are canonical.

User interaction widgets for interactive theorem proving

Matita (that means pencil in Italian) is a new interactive theorem prover under development at the University of Bologna. When compared with state-of-the-art proof assistants, Matita presents both traditional and innovative aspects. The underlying calculus of the system, namely the Calculus of (Co)Inductive Constructions (CIC for short), is well-known and is used as the basis of another mainstream proof assistant—Coq—with which Matita is to some extent compatible. In the same spirit of several other systems, proof authoring is conducted by the user as a goal directed proof search, using a script for storing textual commands for the system. In the tradition of LCF, the proof language of Matita is procedural and relies on tactic and tacticals to proceed toward proof completion. The interaction paradigm offered to the user is based on the script management technique at the basis of the popularity of the Proof General generic interface for interactive theorem provers: while editing a script the user can move forth the execution point to deliver commands to the system, or back to retract (or “undo”) past commands. Matita has been developed from scratch in the past 8 years by several members of the Helm research group, this thesis author is one of such members. Matita is now a full-fledged proof assistant with a library of about 1.000 concepts. Several innovative solutions spun-off from this development effort. This thesis is about the design and implementation of some of those solutions, in particular those relevant for the topic of user interaction with theorem provers, and of which this thesis author was a major contributor. Joint work with other members of the research group is pointed out where needed. The main topics discussed in this thesis are briefly summarized below. Disambiguation. Most activities connected with interactive proving require the user to input mathematical formulae. Being mathematical notation ambiguous, parsing formulae typeset as mathematicians like to write down on paper is a challenging task; a challenge neglected by several theorem provers which usually prefer to fix an unambiguous input syntax. Exploiting features of the underlying calculus, Matita offers an efficient disambiguation engine which permit to type formulae in the familiar mathematical notation. Step-by-step tacticals. Tacticals are higher-order constructs used in proof scripts to combine tactics together. With tacticals scripts can be made shorter, readable, and more resilient to changes. Unfortunately they are de facto incompatible with state-of-the-art user interfaces based on script management. Such interfaces indeed do not permit to position the execution point inside complex tacticals, thus introducing a trade-off between the usefulness of structuring scripts and a tedious big step execution behavior during script replaying. In Matita we break this trade-off with tinycals: an alternative to a subset of LCF tacticals which can be evaluated in a more fine-grained manner. Extensible yet meaningful notation. Proof assistant users often face the need of creating new mathematical notation in order to ease the use of new concepts. The framework used in Matita for dealing with extensible notation both accounts for high quality bidimensional rendering of formulae (with the expressivity of MathMLPresentation) and provides meaningful notation, where presentational fragments are kept synchronized with semantic representation of terms. Using our approach interoperability with other systems can be achieved at the content level, and direct manipulation of formulae acting on their rendered forms is possible too. Publish/subscribe hints. Automation plays an important role in interactive proving as users like to delegate tedious proving sub-tasks to decision procedures or external reasoners. Exploiting the Web-friendliness of Matita we experimented with a broker and a network of web services (called tutors) which can try independently to complete open sub-goals of a proof, currently being authored in Matita. The user receives hints from the tutors on how to complete sub-goals and can interactively or automatically apply them to the current proof. Another innovative aspect of Matita, only marginally touched by this thesis, is the embedded content-based search engine Whelp which is exploited to various ends, from automatic theorem proving to avoiding duplicate work for the user. We also discuss the (potential) reusability in other systems of the widgets presented in this thesis and how we envisage the evolution of user interfaces for interactive theorem provers in the Web 2.0 era.

A Median Voter Theorem for Postelection Politics

We analyze a model of 'postelection politics', in which (unlike in the more common Downsian models of 'preelection politics') politicians cannot make binding commitments prior to elections. The game begins with an incumbent politician in office, and voters adopt reelection strategies that are contingent on the policies implemented by the incumbent. We generalize previous models of this type by introducing heterogeneity in voters' ideological preferences, and analyze how voters' reelection strategies constrain the policies chosen by a rent-maximizing incumbent. We first show that virtually any policy (and any feasible level of rent for the incumbent) can be sustained in a Nash equilibrium. Then, we derive a 'median voter theorem': the ideal point of the median voter, and the minimum feasible level of rent, are the unique outcomes in any strong Nash equilibrium. We then introduce alternative refinements that are less restrictive. In particular, Ideologically Loyal Coalition-proof equilibrium also leads uniquely to the median outcome.

Chitosan/tripolyphosphate Nanoparticles Loaded With Paraquat Herbicide: An Environmentally Safer Alternative For Weed Control.

Paraquat is a fast acting nonselective contact herbicide that is extensively used worldwide. However, the aqueous solubility and soil sorption of this compound can cause problems of toxicity in nontarget organisms. This work investigates the preparation and characterization of nanoparticles composed of chitosan and sodium tripolyphosphate (TPP) to produce an efficient herbicidal formulation that was less toxic and could be used for safer control of weeds in agriculture. The toxicities of the formulations were evaluated using cell culture viability assays and the Allium cepa chromosome aberration test. The herbicidal activity was investigated in cultivations of maize (Zea mays) and mustard (Brassica sp.), and soil sorption of the nanoencapsulated herbicide was measured. The efficiency association of paraquat with the nanoparticles was 62.6 ± 0.7%. Encapsulation of the herbicide resulted in changes in its diffusion and release as well as its sorption by soil. Cytotoxicity and genotoxicity assays showed that the nanoencapsulated herbicide was less toxic than the pure compound, indicating its potential to control weeds while at the same time reducing environmental impacts. Measurements of herbicidal activity showed that the effectiveness of paraquat was preserved after encapsulation. It was concluded that the encapsulation of paraquat in nanoparticles can provide a useful means of reducing adverse impacts on human health and the environment, and that the formulation therefore has potential for use in agriculture.

Uv-vis Spectra As An Alternative To The Lowry Method For Quantify Hair Damage Induced By Surfactants.

It is well known that long term use of shampoo causes damage to human hair. Although the Lowry method has been widely used to quantify hair damage, it is unsuitable to determine this in the presence of some surfactants and there is no other method proposed in literature. In this work, a different method is used to investigate and compare the hair damage induced by four types of surfactants (including three commercial-grade surfactants) and water. Hair samples were immersed in aqueous solution of surfactants under conditions that resemble a shower (38 °C, constant shaking). These solutions become colored with time of contact with hair and its UV-vis spectra were recorded. For comparison, the amount of extracted proteins from hair by sodium dodecyl sulfate (SDS) and by water were estimated by the Lowry method. Additionally, non-pigmented vs. pigmented hair and also sepia melanin were used to understand the washing solution color and their spectra. The results presented herein show that hair degradation is mostly caused by the extraction of proteins, cuticle fragments and melanin granules from hair fiber. It was found that the intensity of solution color varies with the charge density of the surfactants. Furthermore, the intensity of solution color can be correlated to the amount of proteins quantified by the Lowry method as well as to the degree of hair damage. UV-vis spectrum of hair washing solutions is a simple and straightforward method to quantify and compare hair damages induced by different commercial surfactants.

Post Hoc Analysis Of The Patricia Randomized Trial Of The Efficacy Of Human Papillomavirus Type 16 (hpv-16)/hpv-18 As04-adjuvanted Vaccine Against Incident And Persistent Infection With Nonvaccine Oncogenic Hpv Types Using An Alternative Multiplex Type-specific Pcr Assay For Hpv Dna.

The efficacy of the human papillomavirus type 16 (HPV-16)/HPV-18 AS04-adjuvanted vaccine against cervical infections with HPV in the Papilloma Trial against Cancer in Young Adults (PATRICIA) was evaluated using a combination of the broad-spectrum L1-based SPF10 PCR-DNA enzyme immunoassay (DEIA)/line probe assay (LiPA25) system with type-specific PCRs for HPV-16 and -18. Broad-spectrum PCR assays may underestimate the presence of HPV genotypes present at relatively low concentrations in multiple infections, due to competition between genotypes. Therefore, samples were retrospectively reanalyzed using a testing algorithm incorporating the SPF10 PCR-DEIA/LiPA25 plus a novel E6-based multiplex type-specific PCR and reverse hybridization assay (MPTS12 RHA), which permits detection of a panel of nine oncogenic HPV genotypes (types 16, 18, 31, 33, 35, 45, 52, 58, and 59). For the vaccine against HPV types 16 and 18, there was no major impact on estimates of vaccine efficacy (VE) for incident or 6-month or 12-month persistent infections when the MPTS12 RHA was included in the testing algorithm versus estimates with the protocol-specified algorithm. However, the alternative testing algorithm showed greater sensitivity than the protocol-specified algorithm for detection of some nonvaccine oncogenic HPV types. More cases were gained in the control group than in the vaccine group, leading to higher point estimates of VE for 6-month and 12-month persistent infections for the nonvaccine oncogenic types included in the MPTS12 RHA assay (types 31, 33, 35, 45, 52, 58, and 59). This post hoc analysis indicates that the per-protocol testing algorithm used in PATRICIA underestimated the VE against some nonvaccine oncogenic HPV types and that the choice of the HPV DNA testing methodology is important for the evaluation of VE in clinical trials. (This study has been registered at ClinicalTrials.gov under registration no. NCT00122681.).

In vitro evaluation of an alternative method to bond molar tubes

Despite the advances in bonding materials, many clinicians today still prefer to place bands on molar teeth. Molar bonding procedures need improvement to be widely accepted clinically. OBJECTIVE: The purpose of this study was to evaluate the shear bond strength when an additional adhesive layer was applied on the occlusal tooth/tube interface to provide reinforcement to molar tubes. MATERIAL AND METHODS: Sixty third molars were selected and allocated to the 3 groups: group 1 received a conventional direct bond followed by the application of an additional layer of adhesive on the occlusal tooth/tube interface, group 2 received a conventional direct bond, and group 3 received a conventional direct bond and an additional cure time of 10 s. The specimens were debonded in a universal testing machine. The results were analyzed statistically by ANOVA and Tukey's test (α=0.05). RESULTS: Group 1 had a significantly higher (p<0.05) shear bond strength compared to groups 2 and 3. No difference was detected between groups 2 and 3 (p>0.05). CONCLUSIONS: The present in vitro findings indicate that the application of an additional layer of adhesive on the tooth/tube interface increased the shear bond strength of the bonded molar tubes.

T-Bar clasp-retained removable partial denture as an alternative to implant-based prosthetic treatment

This article reports the case of a 55-year-old female patient who presented with unsatisfactory temporary crowns in the right mandibular premolars and molars, and a premolar-to-molar fixed partial denture in the left side. The clinical and radiographic examinations revealed a fracture of the left first premolar that was a retainer of the fixed partial denture and required extraction. Initially, the acrylic resin crowns were replaced by new ones, and a provisional RPD was made using acrylic resin and orthodontic wire clasps to resolve the problem arising from the loss of the fixed partial denture. Considering the patient's high esthetic demands, the treatment options for the definitive prosthetic treatment were discussed with her and rehabilitation with implant-supported dentures was proposed because the clinical conditions of the residual alveolar ridge were suitable for implant installation, and the patient's general health was excellent. However, the patient did not agree because she knew of a failed case of implant-retained denture in a diabetic individual and was concerned. The patient was fully informed that implant installation was the best indication for her case, but the arguments were not sufficient to change her decision. The treatment possibilities were presented and the patient opted for a clasp-retained removable partial denture (RPD) associated with the placement of crowns in the pillar teeth. The temporary RPD was replaced by the definitive RPD constructed subsequently. Although RPD was not the first choice, satisfactory esthetic and functional outcomes were achieved, overcaming the patient's expectations. This case report illustrates that the dentist must be prepared to deal with situations where, for reasons that cannot be managed, the patient does not accept the treatment considered as the most indicated for his/her case. Alternatives must be proposed and the functional and esthetic requirements must be fulfilled in the best possible manner.

Evaluation of follicular lymphoid depletion in the Bursa of Fabricius: an alternative methodology using digital image analysis and artificial neural networks

Fifty Bursa of Fabricius (BF) were examined by conventional optical microscopy and digital images were acquired and processed using Matlab® 6.5 software. The Artificial Neuronal Network (ANN) was generated using Neuroshell® Classifier software and the optical and digital data were compared. The ANN was able to make a comparable classification of digital and optical scores. The use of ANN was able to classify correctly the majority of the follicles, reaching sensibility and specificity of 89% and 96%, respectively. When the follicles were scored and grouped in a binary fashion the sensibility increased to 90% and obtained the maximum value for the specificity of 92%. These results demonstrate that the use of digital image analysis and ANN is a useful tool for the pathological classification of the BF lymphoid depletion. In addition it provides objective results that allow measuring the dimension of the error in the diagnosis and classification therefore making comparison between databases feasible.

Can type of school be used as an alternative indicator of socioeconomic status in dental caries studies? A cross-sectional study

Background: Despite the importance of collecting individual data of socioeconomic status (SES) in epidemiological oral health surveys with children, this procedure relies on the parents as respondents. Therefore, type of school (public or private schools) could be used as an alternative indicator of SES, instead of collecting data individually. The aim of this study was to evaluate the use of the variable type of school as an indicator of socioeconomic status as a substitute of individual data in an epidemiological survey about dental caries in Brazilian preschool children. Methods: This study followed a cross-sectional design, with a random sample of 411 preschool children aged 1 to 5 years, representative of Catalao, Brazil. A calibrated examiner evaluated the prevalence of dental caries and parents or guardians provided information about several individual socioeconomic indicators by means of a semi-structured questionnaire. A multilevel approach was used to investigate the association among individual socioeconomic variables, as well as the type of school, and the outcome. Results: When all significant variables in the univariate analysis were used in the multiple model, only mother's schooling and household income (individual socioeconomic variables) presented significant associations with presence of dental caries, and the type of school was not significantly associated. However, when the type of school was used alone, children of public school presented significantly higher prevalence of dental caries than those enrolled in private schools. Conclusions: The type of school used as an alternative indicator for socioeconomic status is a feasible predictor for caries experience in epidemiological dental caries studies involving preschool children in Brazilian context.

Heteroduplex formation and S1 digestion for mapping alternative splicing sites

The identification of alternatively spliced transcripts has contributed to a better comprehension of developmental mechanisms, tissue-specific physiological processes and human diseases. Polymerase chain reaction amplification of alternatively spliced variants commonly leads to the formation of heteroduplexes as a result of base pairing involving exons common between the two variants. S1 nuclease cleaves single-stranded loops of heteroduplexes and also nicks the opposite DNA strand. In order to establish a strategy for mapping alternative splice-prone sites in the whole transcriptome, we developed a method combining the formation of heteroduplexes between 2 distinct splicing variants and S1 nuclease digestion. For 20 consensuses identified here using this methodology, 5 revealed a conserved splice site after inspection of the cDNA alignment against the human genome (exact splice sites). For 8 other consensuses, conserved splice sites were mapped at 2 to 30 bp from the border, called proximal splice sites; for the other 7 consensuses, conserved splice sites were mapped at 40 to 800 bp, called distal splice sites. These latter cases showed a nonspecific activity of S1 nuclease in digesting double-strand DNA. From the 20 consensuses identified here, 5 were selected for reverse transcription-polymerase chain reaction validation, confirming the splice sites. These data showed the potential of the strategy in mapping splice sites. However, the lack of specificity of the S1 nuclease enzyme is a significant obstacle that impedes the use of this strategy in large-scale studies.

Alternative splicing enriched cDNA libraries identify breast cancer-associated transcripts

Background: Alternative splicing (AS) is a central mechanism in the generation of genomic complexity and is a major contributor to transcriptome and proteome diversity. Alterations of the splicing process can lead to deregulation of crucial cellular processes and have been associated with a large spectrum of human diseases. Cancer-associated transcripts are potential molecular markers and may contribute to the development of more accurate diagnostic and prognostic methods and also serve as therapeutic targets. Alternative splicing-enriched cDNA libraries have been used to explore the variability generated by alternative splicing. In this study, by combining the use of trapping heteroduplexes and RNA amplification, we developed a powerful approach that enables transcriptome-wide exploration of the AS repertoire for identifying AS variants associated with breast tumor cells modulated by ERBB2 (HER-2/neu) oncogene expression. Results: The human breast cell line (C5.2) and a pool of 5 ERBB2 over-expressing breast tumor samples were used independently for the construction of two AS-enriched libraries. In total, 2,048 partial cDNA sequences were obtained, revealing 214 alternative splicing sequence-enriched tags (ASSETs). A subset with 79 multiple exon ASSETs was compared to public databases and reported 138 different AS events. A high success rate of RT-PCR validation (94.5%) was obtained, and 2 novel AS events were identified. The influence of ERBB2-mediated expression on AS regulation was evaluated by capillary electrophoresis and probe-ligation approaches in two mammary cell lines (Hb4a and C5.2) expressing different levels of ERBB2. The relative expression balance between AS variants from 3 genes was differentially modulated by ERBB2 in this model system. Conclusions: In this study, we presented a method for exploring AS from any RNA source in a transcriptome-wide format, which can be directly easily adapted to next generation sequencers. We identified AS transcripts that were differently modulated by ERBB2-mediated expression and that can be tested as molecular markers for breast cancer. Such a methodology will be useful for completely deciphering the cancer cell transcriptome diversity resulting from AS and for finding more precise molecular markers.