Branch-and-lift algorithm for deterministic global optimization in nonlinear optimal control

This paper presents a branch-and-lift algorithm for solving optimal control problems with smooth nonlinear dynamics and potentially nonconvex objective and constraint functionals to guaranteed global optimality. This algorithm features a direct sequential method and builds upon a generic, spatial branch-and-bound algorithm. A new operation, called lifting, is introduced, which refines the control parameterization via a Gram-Schmidt orthogonalization process, while simultaneously eliminating control subregions that are either infeasible or that provably cannot contain any global optima. Conditions are given under which the image of the control parameterization error in the state space contracts exponentially as the parameterization order is increased, thereby making the lifting operation efficient. A computational technique based on ellipsoidal calculus is also developed that satisfies these conditions. The practical applicability of branch-and-lift is illustrated in a numerical example. © 2013 Springer Science+Business Media New York

Mathematics of Gravitational Lensing: Multiple Imaging and Magnification

The mathematical theory of gravitational lensing has revealed many generic and global properties. Beginning with multiple imaging, we review Morse-theoretic image counting formulas and lower bound results, and complex-algebraic upper bounds in the case of single and multiple lens planes. We discuss recent advances in the mathematics of stochastic lensing, discussing a general formula for the global expected number of minimum lensed images as well as asymptotic formulas for the probability densities of the microlensing random time delay functions, random lensing maps, and random shear, and an asymptotic expression for the global expected number of micro-minima. Multiple imaging in optical geometry and a spacetime setting are treated. We review global magnification relation results for model-dependent scenarios and cover recent developments on universal local magnification relations for higher order caustics.Comment: 25 pages, 4 figures. Invited review submitted for special issue of General Relativity and Gravitatio

Generalized pustular psoriasis : A global Delphi consensus on clinical course, diagnosis, treatment goals and disease management

Generalized pustular psoriasis (GPP) is a rare and highly heterogeneous skin disease, characterized by flares of neutrophilic pustules and erythema. As a rare disease with few clinical studies and no standardized management approaches, there is a paucity of knowledge regarding GPP. Conduct a Delphi panel study to identify current evidence and gain advanced insights into GPP. A systematic literature review was used to identify published literature and develop statements categorized into four key domains: clinical course and flare definition; diagnosis; treatment goals; and holistic management. Statements were rated on a Likert scale by a panel of dermatologists in two rounds of online questionnaires; the threshold for consensus was agreement by ≥80%. Twenty-one panellists reached consensus on 70.9%, 61.8%, 100.0% and 81.8% of statements in the 'clinical course and flare definition', 'diagnosis', 'treatment goals' and 'holistic management of GPP' domains, respectively. There was clear consensus on GPP being phenotypically, genetically and immunologically distinct from plaque psoriasis. Clinical course is highly variable, with an extensive range of complications. Clinical and histologic features supporting GPP diagnosis reached high levels of agreement, and although laboratory evaluations were considered helpful for diagnosis and monitoring disease severity, there was uncertainty around the value of individual tests. All acute and long-term treatment goals reached consensus, including rapid and sustained clearance of pustules, erythema, scaling and crust, clearance of skin lesions and prevention of new flares. Potential triggers, associated comorbidities and differential diagnoses achieved low rates of consensus, indicating that further evidence is needed. Global consensus between dermatologists was reached on clinically meaningful goals for GPP treatment, on key features of GPP flares and on approaches for assessing disease severity and multidisciplinary management of patients. On this basis, we present a management algorithm for patients with GPP for use in clinical practice

Efficacy and safety of apremilast, an oral phosphodiesterase 4 inhibitor, in patients with moderate‐to‐severe plaque psoriasis over 52 weeks: a phase III, randomized controlled trial (ESTEEM 2)

SummaryBackground Apremilast, an oral phosphodiesterase 4 inhibitor, regulates immune responses associated with psoriasis. Objectives ESTEEM 2 evaluated the efficacy and safety of apremilast 30 mg twice daily for moderate-to-severe plaque psoriasis. Methods This phase III, double-blind, placebo-controlled trial randomized adults to apremilast or placebo (2 : 1). At week 16, placebo patients switched to apremilast. At week 32, apremilast patients achieving ≥ 50% reduction in Psoriasis Area and Severity Index (PASI 50) were rerandomized (1 : 1) to continue apremilast or receive placebo. Upon loss of 50% of PASI improvement obtained at week 32, patients rerandomized to placebo resumed apremilast. Results The modified intention-to-treat population (full analysis set) included 137 placebo and 274 apremilast patients. At week 16, significantly more apremilast patients achieved PASI 75 (28·8%), PASI 50 (55·5%) and static Physician's Global Assessment score of 0 or 1 (20·4%) vs. placebo (5·8%, 19·7%, 4·4%, respectively; P < 0·001). Most patients rerandomized to apremilast at week 32 had a PASI 50 response at week 52 (80%). Patients treated with apremilast showed significant improvements in quality of life (as assessed by the Dermatology Life Quality Index) and pruritus at week 16 compared with placebo (P < 0·001). The exposure-adjusted incidence of adverse events did not increase with continued apremilast treatment for up to 52 weeks. The most common adverse events were nausea, diarrhoea, nasopharyngitis and upper respiratory tract infection. Conclusions Apremilast was effective in the treatment of moderate-to-severe plaque psoriasis over 52 weeks

Treatment-emergent Candida infections in patients with psoriasis, psoriatic arthritis, and axial spondyloarthritis treated with ixekizumab : an integrated safety analysis of 25 clinical studies

This safety analysis investigates treatment-emergent mucosal/cutaneous Candida infections in patients treated with ixekizumab (IXE), an anti-interleukin-17A monoclonal antibody, across the approved indications: psoriasis (PsO), psoriatic arthritis (PsA), and axial spondyloarthritis (axSpA). Safety data were pooled from 25 clinical studies. Incidence rates (IRs) are expressed as per 100 patient-years (PY), using the entire duration of exposure. Candida infections had an IR of 1.9 per 100 PY in patients with PsO (N = 6892; total PY = 18025.7), 2.0 per 100 PY in patients with PsA (N = 1401; total PY = 2247.7), and 1.2 per 100 PY in patients with axSpA (N = 932; total PY = 2097.7). The majority of treatment-emergent Candida infections were: (i) experienced only once by patients (IR = 1.3;IR = 1.6;IR = 1.0), (ii) mild/moderate in severity (IR = 0.8/0.9;IR = 1.5/0.4;IR = 0.8/0.5) as opposed to severe (IR = 0.0; IR = 0.0; IR = 0.0), (iii) oral Candida or genital Candida (IR = 0.9/0.6;IR = 1.0/0.7;IR = 0.4/0.6), (iv) marked as recovered/resolved during the studies (89.3%;93.8%;90.3%), (v) not leading to IXE discontinuation (0.0%;0.0%;0.1% discontinued), (vi) managed with topical (34.7%;22.2%;11.5%) or no anti-fungal medications (63.5%;77.8%;80.8%) as opposed to systemic therapies (1.5%;0.0%;7.7%), (vii) typically resolved before next visit. This integrated safety analysis shows that the risk of developing Candida infections is low with IXE, and the severity is mild-to-moderate in most instances across the approved IXE indications. A comprehensive list of the clinical trials and their registration numbers is reported in Table S1 of the supplemental material

Benefit-risk profile of tofacitinib in patients with moderate-to-severe chronic plaque psoriasis : pooled analysis across six clinical trials

Altres ajuts: This study was funded by Pfizer Inc. The authors would like to thank Maryam Asgari and Charlie Quesenberry, principal investigators of the KPNC database cohort study, and Kevin Winthrop and Jeffrey Curtis, principal investigators of the Medicare database cohort. This study was supported by Pfizer Inc. Medical writing support under the guidance of the authors was provided by Sandrine M. Dupré, PhD, and Carole Evans, PhD, at and on behalf of Complete Medical Communications, Manchester, U.K., and was funded by Pfizer Inc., New York, NY, U.S.A., in accordance with the Good Publication Practice (GPP3) guidelines.Background: Although existing psoriasis treatments are effective and well tolerated in many patients, there is still a need for new effective targeted treatment options. Tofacitinib is an oral Janus kinase inhibitor that has been investigated in patients with moderate-to-severe chronic plaque psoriasis. Objectives: To consider the benefits and risks of tofacitinib in patients with moderate-to-severe psoriasis. Methods: Data were pooled from one phase II, four phase III and one long-term extension study comprising 5204 patient-years of tofacitinib treatment. Efficacy end points included patients achieving Physician's Global Assessments of 'clear' or 'almost clear', ≥ 75% and ≥ 90% reduction in Psoriasis Area and Severity Index (coprimary end points) and improvements in Dermatology Life Quality Index score, Hospital Anxiety and Depression Scale depression score and Itch Severity Item score, at weeks 16 and 52. Safety data were summarized for 3 years of tofacitinib exposure. Results: Tofacitinib 5 and 10 mg twice daily (BID) showed superiority over placebo for all efficacy end points at week 16, with response maintained for 52 weeks of continued treatment. Tofacitinib improved patients' quality of life and was well tolerated. Rates of safety events of interest (except herpes zoster) were similar to those in the published literature and healthcare databases for other systemic psoriasis therapies. Tofacitinib 10 mg BID demonstrated greater efficacy than 5 mg BID. Conclusions: Tofacitinib has a benefit-risk profile in moderate-to-severe psoriasis consistent with that of other systemic treatments

Efficacy of secukinumab and adalimumab in psoriatic arthritis patients with concomitant moderate to severe plaque psoriasis: results from the EXCEED, a randomised, double‐blind head‐to‐head monotherapy study

Background: Secukinumab [an interleukin (IL)‐17A inhibitor] has demonstrated significantly higher efficacy vs. etanercept (a tumour necrosis factor inhibitor) and ustekinumab (an IL‐12/23 inhibitor) in patients with moderate‐to‐severe plaque psoriasis. Objectives: To report 52‐week results from a prespecified analysis of patients with active psoriatic arthritis (PsA) having concomitant moderate‐to‐severe plaque psoriasis from the head‐to‐head EXCEED monotherapy study comparing secukinumab with adalimumab. Methods: Patients were randomized to receive secukinumab 300 mg via subcutaneous injection at baseline, week 1–4, and then every 4 weeks until week 48 or adalimumab 40 mg via subcutaneous injection every 2 weeks from baseline until week 50. Assessments in patients with concomitant moderate‐to‐severe psoriasis, defined as having affected body surface area &gt; 10% or Psoriasis Area and Severity Index (PASI) ≥ 10 at baseline, included musculoskeletal, skin and quality‐of‐life outcomes. Missing data were handled using multiple imputation. Results: Of the 853 patients [secukinumab (N = 426), adalimumab (N = 427)], 211 (24·7%) had concomitant moderate‐to‐severe psoriasis [secukinumab (N = 110, 25·8%), adalimumab (N = 101, 23·7%)]. Up to week 50, 5·5% of patients discontinued secukinumab vs.17·8% in the adalimumab group. The proportion of patients who achieved American College of Rheumatology (ACR) 20 response was 76·4% with secukinumab vs. 68·3% with adalimumab (P = 0·175), PASI 100 response was 39·1% vs. 23·8% (P = 0·013), and simultaneous improvement in ACR 50 and PASI 100 response at week 52 was 28·2% vs. 17·7%, respectively (P = 0·06). Secukinumab demonstrated consistently higher responses vs. adalimumab across skin endpoints. Conclusions: This prespecified analysis in PsA patients with concomitant moderate‐to‐severe plaque psoriasis in the EXCEED study provides further evidence that IL‐17 inhibitors offer a comprehensive biological treatment to manage the concomitant features of psoriasis and PsA

A core domain set for hidradenitis suppurativa trial outcomes: an international Delphi process

Background There is no consensus on core outcome domains for hidradenitis suppurativa (HS). Heterogeneous outcome measure instruments in clinical trials likely leads to outcome reporting bias and limits the ability to synthesise evidence. Objectives To achieve global multi‐stakeholder consensus on a Core Outcome Set (COS) of domains regarding what to measure in clinical trials for HS. Methods Six stakeholder groups participated in a Delphi process which included five anonymous e‐Delphi rounds and four face‐to‐face consensus meetings to reach consensus on the final COS. The aim was for a 1:1 ratio of patients: Health Care Professionals (HCPs). Results A total of 41 patients and 52 HCPs from 19 countries in four continents participated in the consensus process which yielded a final COS that included five domains: pain, physical signs, HS specific quality of life, global assessment and progression of course. A sixth domain, symptoms, was highly supported by patients and not by healthcare professionals but is recommended for the core domain set. Conclusions Routine adoption of the COS in future HS trials should ensure that core outcomes of importance to both patients and HCPs are collected

Patient-reported outcome measures for health-related quality of life in patients with psoriasis: a systematic review

Importance  Multiple patient-reported outcome measures (PROMs) for health-related quality of life (HRQL) exist for patients with psoriasis. Evidence for the content validity and other measurement properties of these PROMs is critical to determine which HRQL PROMs could be recommended for use.Objective  To systematically review the validity of HRQL-focused PROMs used in patients with psoriasis.Evidence Review  Using PubMed and Embase, full-text articles published in English or Spanish on development or validation studies for psoriasis-specific, dermatology-specific, or generic HRQL PROMs were included. Development studies included original development studies, even if not studied in psoriasis patients per Consensus-Based Standards for the Selection of Health Measurement Instruments (COSMIN) recommendations. If a study included multiple diagnoses, more than 50% of patients had to have psoriasis or psoriasis-specific subgroup analyses available. Data extraction and analysis followed the COSMIN guidelines. Two independent reviewers extracted and analyzed the data, including PROM characteristics, quality of measurement properties (structural validity, internal consistency, cross-cultural validity, reliability, measurement error, criterion validity, construct validity, and responsiveness), and level of evidence. PROMs were classified into 3 levels of recommendations: (1) PROM recommended for use; (2) PROM requires further validation; and (3) PROM not recommended for use.Findings  Overall, 97 articles were identified for extraction. This included 19 psoriasis-specific, 8 skin-specific, and 6 generic PROMs. According to COSMIN standards, most measures identified received a B recommendation for use, indicating their potential but requiring further validation. Only the Rasch reduced version of the Impact of Psoriasis Questionnaire (IPSO-11 Rasch) received an A recommendation for use given that it had sufficient content validity, structural validity, and internal consistency.Conclusions and Relevance  This study identified a significant lack of information concerning the quality of HRQL measures in psoriasis. This gap in knowledge can be attributed to the fact that traditional measures were developed using validation criteria that differ from the current standards in use. Consequently, additional validation studies in accordance with contemporary standards will be useful in aiding researchers and clinicians in determining the most suitable measure for assessing HRQL in patients with psoriasis.Dermatology-oncolog