A relaxed constant positive linear dependence constraint qualification and applications

In this work we introduce a relaxed version of the constant positive linear dependence constraint qualification (CPLD) that we call RCPLD. This development is inspired by a recent generalization of the constant rank constraint qualification by Minchenko and Stakhovski that was called RCRCQ. We show that RCPLD is enough to ensure the convergence of an augmented Lagrangian algorithm and that it asserts the validity of an error bound. We also provide proofs and counter-examples that show the relations of RCRCQ and RCPLD with other known constraint qualifications. In particular, RCPLD is strictly weaker than CPLD and RCRCQ, while still stronger than Abadie's constraint qualification. We also verify that the second order necessary optimality condition holds under RCRCQ.

TWO NEW WEAK CONSTRAINT QUALIFICATIONS AND APPLICATIONS

We present two new constraint qualifications (CQs) that are weaker than the recently introduced relaxed constant positive linear dependence (RCPLD) CQ. RCPLD is based on the assumption that many subsets of the gradients of the active constraints preserve positive linear dependence locally. A major open question was to identify the exact set of gradients whose properties had to be preserved locally and that would still work as a CQ. This is done in the first new CQ, which we call the constant rank of the subspace component (CRSC) CQ. This new CQ also preserves many of the good properties of RCPLD, such as local stability and the validity of an error bound. We also introduce an even weaker CQ, called the constant positive generator (CPG), which can replace RCPLD in the analysis of the global convergence of algorithms. We close this work by extending convergence results of algorithms belonging to all the main classes of nonlinear optimization methods: sequential quadratic programming, augmented Lagrangians, interior point algorithms, and inexact restoration.

Programming peculiarities in two cochlear implant users with superficial siderosis of the central nervous system

To report the audiological outcomes of cochlear implantation in two patients with severe to profound sensorineural hearing loss secondary to superficial siderosis of the CNS and discuss some programming peculiarities that were found in these cases. Retrospective review. Data concerning clinical presentation, diagnosis and audiological assessment pre- and post-implantation were collected of two patients with superficial siderosis of the CNS. Both patients showed good hearing thresholds but variable speech perception outcomes. One patient did not achieve open-set speech recognition, but the other achieved 70% speech recognition in quiet. Electrical compound action potentials could not be elicited in either patient. Map parameters showed the need for increased charge. Electrode impedances showed high longitudinal variability. The implants were fairly beneficial in restoring hearing and improving communication abilities although many reprogramming sessions have been required. The hurdle in programming was the need of frequent adjustments due to the physiologic variations in electrical discharges and neural conduction, besides the changes in the impedances. Patients diagnosed with superficial siderosis may achieve limited results in speech perception scores due to both cochlear and retrocochlear reasons. Careful counseling about the results must be given to the patients and their families before the cochlear implantation indication.

Linear matrix inequality-based robust model predictive control for time-delayed systems

This work addresses the solution to the problem of robust model predictive control (MPC) of systems with model uncertainty. The case of zone control of multi-variable stable systems with multiple time delays is considered. The usual approach of dealing with this kind of problem is through the inclusion of non-linear cost constraint in the control problem. The control action is then obtained at each sampling time as the solution to a non-linear programming (NLP) problem that for high-order systems can be computationally expensive. Here, the robust MPC problem is formulated as a linear matrix inequality problem that can be solved in real time with a fraction of the computer effort. The proposed approach is compared with the conventional robust MPC and tested through the simulation of a reactor system of the process industry.

The effect of a Lucia jig for 30 minutes on neuromuscular re-programming, in normal subjects

The Lucia jig is a technique that promotes neuromuscular reprogramming of the masticatory system and allows the stabilization of the mandible without the interference of dental contacts, maintaining the mandible position in harmonic condition with the musculature in normal subjects or in patients with temporomandibular dysfunction (TMD). This study aimed to electromyographically analyze the activity (RMS) of the masseter and temporal muscles in normal subjects (control group) during the use of an anterior programming device, the Lucia jig, in place for 0, 5, 10, 20 and 30 minutes to demonstrate its effect on the stomatognathic system. Forty-two healthy dentate individuals (aged 21 to 40 years) with normal occlusion and without parafunctional habits or ternporomandibular dysfunction (RDC/TMD) were evaluated on the basis of the electromyographic activity of the masseter and temporal muscles before placement of a neuromuscular re-programming device, the Lucia jig, on the upper central incisors. There were no statistically significant differences (p < 0.05) in the electromyographic activity of the masticatory muscles in the different time periods. The Lucia jig changed the electromyographic activity by promoting a neuromuscular reprogramming. In most of the time periods, it decreased the activation of the masticatory muscles, showing that this device has wide applicability in dentistry. The use of a Lucia jig over 0, 5, 10, 15, 20 and 30 minutes did not promote any statistically significant increase in muscle activity despite differences in the data, thus showing that this intra-oral device can be used in dentistry.

Implications of maternal nutrient restriction in transgenerational programming of hypertension and endothelial dysfunction across F1-F3 offspring

Aims: An extensive variety of prenatal insults are associated with an increased incidence of metabolic and cardiovascular disorders in adult life. We previously demonstrated that maternal global nutrient restriction during pregnancy leads to increased blood pressure and endothelial dysfunction in the adult offspring. This study aimed to assess whether prenatal exposure to nutritional insult has transgenerational effects in F-2 and F-3 offspring. Main methods: For this, female Wistar rats were randomly divided into two groups on day 1 of pregnancy: a control group fed standard chow ad libitum and a restricted group fed 50% of the ad libitum intake throughout gestation. At delivery, all animals were fed a standard laboratory chow diet. At 11 weeks of age, one female and one male from each restricted litter were randomly selected and mated with rats from another restricted litters in order to generate the F-2 offspring. The same procedure produced F-3 generation. Similarly, the rats in the control group were bred for each generation. Key Findings: Our findings show that the deleterious effects of maternal nutrient restriction to which the F-0 mothers were exposed may not be limited to the male first generation. In fact, we found that elevated blood pressure, an impaired vasodilatory response to acetylcholine and alterations in NO production were all transferred to the subsequent males from F-2 and F-3 generations. Significance: Our data show that global nutrient restriction during pregnancy results in a specific phenotype that can be passed transgenerationally to a second and third generation. (c) 2012 Elsevier Inc. All rights reserved.

Modified constraint-induced movement therapy and modified forced-use therapy for stroke patients are both effective to promote balance and gait improvements

Background: Previous studies show that chronic hemiparetic patients after stroke, presents inabilities to perform movements in paretic hemibody. This inability is induced by positive reinforcement of unsuccessful attempts, a concept called learned non-use. Forced use therapy (FUT) and constraint induced movement therapy (CIMT) were developed with the goal of reversing the learned non-use. These approaches have been proposed for the rehabilitation of the paretic upper limb (PUL). It is unknown what would be the possible effects of these approaches in the rehabilitation of gait and balance. Objectives: To evaluate the effect of Modified FUT (mFUT) and Modified CIMT (mCIMT) on the gait and balance during four weeks of treatment and 3 months follow-up. Methods: This study included thirty-seven hemiparetic post-stroke subjects that were randomly allocated into two groups based on the treatment protocol. The non-paretic UL was immobilized for a period of 23 hours per day, five days a week. Participants were evaluated at Baseline, 1st, 2nd, 3rd and 4th weeks, and three months after randomization. For the evaluation we used: The Stroke Impact Scale (SIS), Berg Balance Scale (BBS) and Fugl-Meyer Motor Assessment (FM). Gait was analyzed by the 10-meter walk test (T10) and Timed Up & Go test (TUG). Results: Both groups revealed a better health status (SIS), better balance, better use of lower limb (BBS and FM) and greater speed in gait (T10 and TUG), during the weeks of treatment and months of follow-up, compared to the baseline. Conclusion: The results show mFUT and mCIMT are effective in the rehabilitation of balance and gait. Trial Registration ACTRN12611000411943.

Augmented Lagrangian method with nonmonotone penalty parameters for constrained optimization

At each outer iteration of standard Augmented Lagrangian methods one tries to solve a box-constrained optimization problem with some prescribed tolerance. In the continuous world, using exact arithmetic, this subproblem is always solvable. Therefore, the possibility of finishing the subproblem resolution without satisfying the theoretical stopping conditions is not contemplated in usual convergence theories. However, in practice, one might not be able to solve the subproblem up to the required precision. This may be due to different reasons. One of them is that the presence of an excessively large penalty parameter could impair the performance of the box-constraint optimization solver. In this paper a practical strategy for decreasing the penalty parameter in situations like the one mentioned above is proposed. More generally, the different decisions that may be taken when, in practice, one is not able to solve the Augmented Lagrangian subproblem will be discussed. As a result, an improved Augmented Lagrangian method is presented, which takes into account numerical difficulties in a satisfactory way, preserving suitable convergence theory. Numerical experiments are presented involving all the CUTEr collection test problems.

Cochlear Implantation Via the Middle Fossa Approach: Surgical and Programming Considerations

Objectives: To report the results of cochlear implantation via the middle fossa approach in 4 patients, discuss the complications, and present a detailed description of the programming specifications in these cases. Study Design: Retrospective case review. Setting: Tertiary-care referral center with a well-established cochlear implant program. Patients: Four patients with bilateral canal wall down mastoid cavities who underwent the middle fossa approach for cochlear implantation. Interventions: Cochlear implantation and subsequent rehabilitation. A middle fossa approach with cochleostomy was successfully performed on the most superficial part of the apical turn in 4 patients. A Nucleus 24 cochlear implant system was used in 3 patients and a MED-EL Sonata Medium device in 1 patient. The single electrode array was inserted through a cochleostomy from the cochlear apex and occupied the apical, middle, and basal turns. Telemetry and intraoperative impedance recordings were performed at the end of surgery. A CT scan of the temporal bones was performed to document electrode insertion for all of the patients. Main Outcome Measures: Complications, hearing thresholds, and speech perception outcomes were evaluated. Results: Neural response telemetry showed present responses in all but 1 patient, who demonstrated facial nerve stimulation during the test. Open-set speech perception varied from 30% to 100%, despite the frequency allocation order of the MAP. Conclusion: Cochlear implantation via the middle cranial fossa is a safe approach, although it is a challenging procedure, even for experienced surgeons.

A comparison of deterministic, reliability-based and risk-based structural optimization under uncertainty

In this paper, the effects of uncertainty and expected costs of failure on optimum structural design are investigated, by comparing three distinct formulations of structural optimization problems. Deterministic Design Optimization (DDO) allows one the find the shape or configuration of a structure that is optimum in terms of mechanics, but the formulation grossly neglects parameter uncertainty and its effects on structural safety. Reliability-based Design Optimization (RBDO) has emerged as an alternative to properly model the safety-under-uncertainty part of the problem. With RBDO, one can ensure that a minimum (and measurable) level of safety is achieved by the optimum structure. However, results are dependent on the failure probabilities used as constraints in the analysis. Risk optimization (RO) increases the scope of the problem by addressing the compromising goals of economy and safety. This is accomplished by quantifying the monetary consequences of failure, as well as the costs associated with construction, operation and maintenance. RO yields the optimum topology and the optimum point of balance between economy and safety. Results are compared for some example problems. The broader RO solution is found first, and optimum results are used as constraints in DDO and RBDO. Results show that even when optimum safety coefficients are used as constraints in DDO, the formulation leads to configurations which respect these design constraints, reduce manufacturing costs but increase total expected costs (including expected costs of failure). When (optimum) system failure probability is used as a constraint in RBDO, this solution also reduces manufacturing costs but by increasing total expected costs. This happens when the costs associated with different failure modes are distinct. Hence, a general equivalence between the formulations cannot be established. Optimum structural design considering expected costs of failure cannot be controlled solely by safety factors nor by failure probability constraints, but will depend on actual structural configuration. (c) 2011 Elsevier Ltd. All rights reserved.

No-pole condition in Landau gauge: Properties of the Gribov ghost form factor and a constraint on the 2d gluon propagator

We study general properties of the Landau-gauge Gribov ghost form factor sigma(p(2)) for SU(N-c) Yang-Mills theories in the d-dimensional case. We find a qualitatively different behavior for d = 3, 4 with respect to the d = 2 case. In particular, considering any (sufficiently regular) gluon propagator D(p(2)) and the one-loop-corrected ghost propagator, we prove in the 2d case that the function sigma(p(2)) blows up in the infrared limit p -> 0 as -D(0) ln(p(2)). Thus, for d = 2, the no-pole condition sigma(p(2)) < 1 (for p(2) > 0) can be satisfied only if the gluon propagator vanishes at zero momentum, that is, D(0) = 0. On the contrary, in d = 3 and 4, sigma(p(2)) is finite also if D(0) > 0. The same results are obtained by evaluating the ghost propagator G(p(2)) explicitly at one loop, using fitting forms for D(p(2)) that describe well the numerical data of the gluon propagator in two, three and four space-time dimensions in the SU(2) case. These evaluations also show that, if one considers the coupling constant g(2) as a free parameter, the ghost propagator admits a one-parameter family of behaviors (labeled by g(2)), in agreement with previous works by Boucaud et al. In this case the condition sigma(0) <= 1 implies g(2) <= g(c)(2), where g(c)(2) is a "critical" value. Moreover, a freelike ghost propagator in the infrared limit is obtained for any value of g(2) smaller than g(c)(2), while for g(2) = g(c)(2) one finds an infrared-enhanced ghost propagator. Finally, we analyze the Dyson-Schwinger equation for sigma(p(2)) and show that, for infrared-finite ghost-gluon vertices, one can bound the ghost form factor sigma(p(2)). Using these bounds we find again that only in the d = 2 case does one need to impose D(0) = 0 in order to satisfy the no-pole condition. The d = 2 result is also supported by an analysis of the Dyson-Schwinger equation using a spectral representation for the ghost propagator. Thus, if the no-pole condition is imposed, solving the d = 2 Dyson-Schwinger equations cannot lead to a massive behavior for the gluon propagator. These results apply to any Gribov copy inside the so-called first Gribov horizon; i.e., the 2d result D(0) = 0 is not affected by Gribov noise. These findings are also in agreement with lattice data.

An integer linear programming approach for bilinear integer programming

We introduce a new Integer Linear Programming (ILP) approach for solving Integer Programming (IP) problems with bilinear objectives and linear constraints. The approach relies on a series of ILP approximations of the bilinear P. We compare this approach with standard linearization techniques on random instances and a set of real-world product bundling problems. (C) 2011 Elsevier B.V. All rights reserved.

Constraint-based analysis of gene interactions using restricted boolean networks and time-series data

Abstract Background A popular model for gene regulatory networks is the Boolean network model. In this paper, we propose an algorithm to perform an analysis of gene regulatory interactions using the Boolean network model and time-series data. Actually, the Boolean network is restricted in the sense that only a subset of all possible Boolean functions are considered. We explore some mathematical properties of the restricted Boolean networks in order to avoid the full search approach. The problem is modeled as a Constraint Satisfaction Problem (CSP) and CSP techniques are used to solve it. Results We applied the proposed algorithm in two data sets. First, we used an artificial dataset obtained from a model for the budding yeast cell cycle. The second data set is derived from experiments performed using HeLa cells. The results show that some interactions can be fully or, at least, partially determined under the Boolean model considered. Conclusions The algorithm proposed can be used as a first step for detection of gene/protein interactions. It is able to infer gene relationships from time-series data of gene expression, and this inference process can be aided by a priori knowledge available.