On the classification of plane graphs representing structurally stable rational Newton flows

We study certain plane graphs, called Newton graphs, representing a special class of dynamical systems which are closely related to Newton's iteration method for finding zeros of (rational) functions defined on the complex plane. These Newton graphs are defined in terms of nonvanishing angles between edges at the same vertex. We derive necessary and sufficient conditions -of purely combinatorial nature- for an arbitrary plane graph in order to be topologically equivalent with a Newton graph. Finally, we analyse the structure of Newton graphs and prove the existence of a polynomial algorithm to recognize such graphs

Semi-infinite optimization: Structure and stability of the feasible set

The problem of the minimization of a functionf: ℝn→ℝ under finitely many equality constraints and perhaps infinitely many inequality constraints gives rise to a structural analysis of the feasible setM[H, G]={x∈ℝn¦H(x)=0,G(x, y)≥0,y∈Y} with compactY⊂ℝr. An extension of the well-known Mangasarian-Fromovitz constraint qualification (EMFCQ) is introduced. The main result for compactM[H, G] is the equivalence of the topological stability of the feasible setM[H, G] and the validity of EMFCQ. As a byproduct, we obtain under EMFCQ that the feasible set admits local linearizations and also thatM[H, G] depends continuously on the pair (H, G). Moreover, EMFCQ is shown to be satisfied generically

Critical sets in parametric optimization

We deal with one-parameter families of optimization problems in finite dimensions. The constraints are both of equality and inequality type. The concept of a ‘generalized critical point’ (g.c. point) is introduced. In particular, every local minimum, Kuhn-Tucker point, and point of Fritz John type is a g.c. point. Under fairly weak (even generic) conditions we study the set∑ consisting of all g.c. points. Due to the parameter, the set∑ is pieced together from one-dimensional manifolds. The points of∑ can be divided into five (characteristic) types. The subset of ‘nondegenerate critical points’ (first type) is open and dense in∑ (nondegenerate means: strict complementarity, nondegeneracy of the corresponding quadratic form and linear independence of the gradients of binding constraints). A nondegenerate critical point is completely characterized by means of four indices. The change of these indices along∑ is presented. Finally, the Kuhn-Tucker subset of∑ is studied in more detail, in particular in connection with the (failure of the) Mangasarian-Fromowitz constraint qualification

One-parameter families of optimization problems: equality constraints

In this paper, we introduce generalized critical points and discuss their relationship with other concepts of critical points [resp., stationary points]. Generalized critical points play an important role in parametric optimization. Under generic regularity conditions, we study the set of generalized critical points, in particular, the change of the Morse index. We focus our attention on problems with equality constraints only and provide an indication of how the present theory can be extended to problems with inequality constraints as well

A solvable model of the genesis of amino-acid sequences via coupled dynamics of folding and slow genetic variation

We study the coupled dynamics of primary and secondary structure formation (i.e. slow genetic sequence selection and fast folding) in the context of a solvable microscopic model that includes both short-range steric forces and and long-range polarity-driven forces. Our solution is based on the diagonalization of replicated transfer matrices, and leads in the thermodynamic limit to explicit predictions regarding phase transitions and phase diagrams at genetic equilibrium. The predicted phenomenology allows for natural physical interpretations, and finds satisfactory support in numerical simulations.Comment: 51 pages, 13 figures, submitted to J. Phys.

Organization and functioning of liberalized electricity markets: An overview of the Dutch market

Abstract In this paper, we examine the organization and the functioning of the Dutch electricity market. First we describe the organization of the Dutch electricity supply chain and the role of the main market participants including the transmission system operator, distribution system operators, program responsible parties and metering companies. We then describe the organization of financial trading and clearing mechanism of electricity through the organized futures exchange (The European Energy Derivatives Exchange), and the spot market (Amsterdam Power Exchange) which includes the day-ahead market and intra-day markets. We also detail the functioning of the imbalance market and reserve capacity management in the Netherlands. Through a set of numerical analysis, we provide an exploratory analysis of the APX day-ahead spot prices and the real-time imbalance prices using electricity price data from 2002 to 2013. We observe the price spikes both in the day-ahead and imbalance markets usually occur around 6-10 AM and 5-7 PM. We also observe that in the imbalance market system overages happen significantly more often than shortages pointing out that the market tends to buy more than what is demanded. This could be explained by the risk attitude of the market participants in the imbalance market. © 2015 Elsevier Ltd

An Open-Label, Noncomparative, Multicenter Study to Evaluate Efficacy and Safety of NASHA/Dx Gel as a Bulking Agent for the Treatment of Fecal Incontinence

Fecal incontinence (FI) is the involuntary loss of rectal contents through the anal canal. Reports of its prevalence vary from 1–21%. Studies, have demonstrated a positive effect on FI symptoms with injectable bulking agents. This study evaluated the safety and efficacy of NASHA/Dx gel in the treatment of FI. One hundred fifteen eligible patients suffering from FI received 4 injections of 1 mL NASHA/Dx gel. Primary efficacy was based on data from 86 patients that completed the study. This study demonstrated a ≥50% reduction from baseline in the number of FI episodes in 57.1% of patients at 6 months, and 64.0% at 12 months. Significant improvements (P < .001) were also noted in total number of both solid and loose FI episodes, FI free days, CCFIS, and FIQL scores in all 4 domains. The majority of the treatment related AEs (94.9%) were mild or moderate intensity, and (98.7%) of AEs resolved spontaneously, or following treatment, without sequelae. Results of this study indicate NASHA/Dx gel was efficacious in the treatment of FI. Treatment effect was significant both in reduction of number of FI episodes and disease specific quality of life at 6 months and lasted up to 12 months after treatment

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Hervorming Sociale Regelgevin

Ligament reconstruction in thumb carpometacarpal joint instability:A systematic review

In thumb carpometacarpal (CMC) instability, laxity of the ligaments surrounding the joint leads to pain and weakness in grip and pinch strength, which predisposes the patient to developing CMC joint arthritis. Recent advancements in joint anatomy and kinematics have led to the development of various surgical reconstructive procedures. This systematic review outlines the available ligament reconstruction techniques and their efficacy in treating nontraumatic and nonarthritic CMC instability. Additionally, we aimed to provide evidence which specific ligament reconstruction technique demonstrates the best results. Four databases (Embase, MEDLINE, Web of Science, and Cochrane Central) were searched for studies that reported on surgical techniques and their clinical outcomes in patients with nontraumatic and nonarthritic CMC instability. Twelve studies were analyzed for qualitative review, including nine different surgical ligament reconstruction techniques involving two hundred and thirty thumbs. All but one of the reported techniques improved postoperative pain scores and showed substantial improvement in pinch and grip strength. Complication rates varied between 0% and 25%. The included studies showed that ligament reconstruction effectively alleviated the patients’ complaints regarding pain and instability, resulting in overall high patient satisfaction. Nevertheless, drawing definitive conclusions regarding the superiority of any ligament reconstruction technique remains challenging owing to the limited availability of homogeneous data in the current literature.</p