Symmetry-breaking in cumulative measures of shapes of polymer models.

Using numerical simulations we investigate shapes of random equilateral open and closed chains, one of the simplest models of freely fluctuating polymers in a solution. We are interested in the 3D density distribution of the modeled polymers where the polymers have been aligned with respect to their three principal axes of inertia. This type of approach was pioneered by Theodorou and Suter in 1985. While individual configurations of the modeled polymers are almost always nonsymmetric, the approach of Theodorou and Suter results in cumulative shapes that are highly symmetric. By taking advantage of asymmetries within the individual configurations, we modify the procedure of aligning independent configurations in a way that shows their asymmetry. This approach reveals, for example, that the 3D density distribution for linear polymers has a bean shape predicted theoretically by Kuhn. The symmetry-breaking approach reveals complementary information to the traditional, symmetrical, 3D density distributions originally introduced by Theodorou and Suter.

Mise en oeuvre de protocoles spatiaux pour analyser la modulation de processus cognitifs en fonction de la dimension émotionnelle chez le rongeur

Résumé : Emotion et cognition sont deux termes généralement employés pour désigner des processus psychiques de nature opposée. C'est ainsi que les sciences cognitives se sont longtemps efforcées d'écarter la composante «chaude »des processus «froids »qu'elles visaient, si ce n'est pour montrer l'effet dévastateur de la première sur les seconds. Pourtant, les processus cognitifs (de collecte, maintien et utilisation d'information) et émotioAnels (d'activation subjective, physiologique et comportementale face à ce qui est attractif ou aversif) sont indissociables. Par l'approche neuro-éthologique, à l'interface entre le substrat biologique et les manifestations comportementales, nous nous sommes intéressés à une fonction cognitive essentielle, la fonction mnésique, classiquement exprimée chez le rongeur par l'orientation spatiale. Au niveau du substrat, McDonald et White (1993) ont montré la dissociation de trois systèmes de mémoire, avec les rôles de l'hippocampe, du néostriatum et de l'amygdale dans l'encodage des informations respectivement épisodiques, procédurales et émotionnelles. Nous nous sommes penchés sur l'interaction entre ces systèmes en fonction de la dimension émotionnelle par l'éclairage du comportement. L'état émotionnel de l'animal dépend de plusieurs facteurs, que nous avons tenté de contrôler indirectement en comparant leurs effets sur l'acquisition, dans diverses conditions, de la tâche de Morris (qui nécessite la localisation dans un bassin de la position d'une plate-forme submergée), ainsi que sur le style d'exploration de diverses arènes, ouvertes ou fermées, plus ou moins structurées par la présence de tunnels en plexiglas transparent. Nous avons d'abord exploré le rôle d'un composant du système adrénergique dans le rapport à la difficulté et au stress, à l'aide de souris knock-out pour le récepteur à la noradrénaline a-1 B dans un protocole avec 1 ou 4 points de départ dans un bassin partitionné. Ensuite, nous nous sommes penchés, chez le rat, sur les effets de renforcement intermittent dans différentes conditions expérimentales. Dans ces conditions, nous avons également tenté d'analyser en quoi la situation du but dans un paysage donné pouvait interférer avec les effets de certaines formes de stress. Finalement, nous avons interrogé les conséquences de perturbations passées, y compris le renforcement partiel, sur l'organisation des déplacements sur sol sec. Nos résultats montrent la nécessité, pour les souris cont~ô/es dont l'orientation repose sur l'hippocampe, de pouvoir varier les trajectoires, ce qui favoriserait la constitution d'une carte cognitive. Les souris a->B KO s'avèrent plus sensibles au stress et capables de bénéficier de la condition de route qui permet des réponses simples et automatisées, sous-tendues par l'activité du striatum. Chez les rats en bassin 100% renforcé, l'orientation apparaît basée sur l'hippocampe, relayée par le striatum pour le développement d'approches systématiques et rapides, avec réorientation efficace en nouvelle position par réactivation dépendant de l'hippocampe. A 50% de renforcement, on observe un effet du type de déroulement des sessions, transitoirement atténué par la motivation Lorsque les essais s'enchaînent sans pause intrasession, les latences diminuent régulièrement, ce qui suggère une prise en charge possible par des routines S-R dépendant du striatum. L'organisation des mouvements exploratoires apparaît dépendante du niveau d'insécurité, avec différents profils intermédiaires entre la différentiation maximale et la thigmotaxie, qui peuvent être mis en relation avec différents niveaux d'efficacité de l'hippocampe. Ainsi, notre travail encourage à la prise en compte de la dimension émotionnelle comme modulatrice du traitement d'information, tant en phase d'exploration de l'environnement que d'exploitation des connaissances spatiales. Abstract : Emotion and cognition are terms widely used to refer to opposite mental processes. Hence, cognitive science research has for a long time pushed "hot" components away from "cool" targeted processes, except for assessing devastating effects of the former upon the latter. However, cognitive processes (of information collection, preservation, and utilization) and emotional processes (of subjective, physiological, and behavioral activation roue to attraction or aversion) are inseparable. At the crossing between biological substrate and behavioral expression, we studied a chief cognitive function, memory, classically shown in animals through spatial orientation. At the substrate level, McDonald et White (1993) have shown a dissociation between three memory systems, with the hippocampus, neostriatum, and amygdala, encoding respectively episodic, habit, and emotional information. Through the behavior of laboratory rodents, we targeted the interaction between those systems and the emotional axis. The emotional state of an animal depends on different factors, that we tried to check in a roundabout way by the comparison of their effects on acquisition, in a variety of conditions, of the Morris task (in which the location of a hidden platform in a pool is required), as well as on the exploration profile in different apparatus, open-field and closed mazes, more or less organized by clear Plexiglas tunnels. We first tracked the role, under more or less difficult and stressful conditions, of an adrenergic component, with knock-out mice for the a-1 B receptor in a partitioned water maze with 1 or 4 start positions. With rats, we looked for the consequences of partial reinforcement in the water maze in different experimental conditions. In those conditions, we further analyzed how the situation of the goal in the landscape could interfere with the effect of a given stress. At last, we conducted experiments on solid ground, in an open-field and in radial mazes, in order to analyze the organization of spatial behavior following an aversive life event, such as partial reinforcement training in the water maze. Our results emphasize the reliance of normal mice to be able to vary approach trajectories. One of our leading hypotheses is that such strategies are hippocampus-dependent and are best developed for of a "cognitive map like" representation. Alpha-1 B KO mice appear more sensitive to stress and able to take advantage of the route condition allowing simple and automated responses, most likely striatum based. With rats in 100% reinforced water maze, the orientation strategy is predominantly hippocampus dependent (as illustrated by the impairment induced by lesions of this structure) and becomes progressively striatum dependent for the development of systematic and fast successful approaches. Training towards a new platform position requires a hippocampus based strategy. With a 50% reinforcement rate, we found a clear impairment related to intersession disruption, an effect transitorily minimized by motivation enhancement (cold water). When trials are given without intrasession interruption, latencies consistently diminish, suggesting a possibility for striatum dependent stimulus-response routine to occur. The organization of exploratory movements is shown to depend on the level of subjective security, with different intermediary profiles between maximum differentiation and thigmotaxy, which can be considered in parallel with different efficiency levels of the hippocampus dependent strategies. Thus, our work fosters the consideration of emotion as a cognitive treatment modulator, during spatial exploration as well as spatial learning. It leads to a model in which the predominance of hippocampus based exploration is challenged by training conditions of various nature.

Closure of large intrathoracic airway defects using extrathoracic muscle flaps.

BACKGROUND: Prospective assessment of pedicled extrathoracic muscle flaps for the closure of large intrathoracic airway defects after noncircumferential resection in situations where an end-to-end reconstruction seemed risky (defects of > 4-cm length, desmoplastic reactions after previous infection or radiochemotherapy). METHODS: From 1996 to 2001, 13 intrathoracic muscle transpositions (6 latissimus dorsi and 7 serratus anterior muscle flaps) were performed to close defects of the intrathoracic airways after noncircumferential resection for tumor (n = 5), large tracheoesophageal fistula (n = 2), delayed tracheal injury (n = 1) and bronchopleural fistula (n = 5). In 2 patients, the extent of the tracheal defect required reinforcement of the reconstruction by use of a rib segment embedded into the muscle flap followed by temporary tracheal stenting. Patient follow-up was by clinical examination bronchoscopy and biopsy, pulmonary function tests, and dynamic virtual bronchoscopy by computed tomographic (CT) scan during inspiration and expiration. RESULTS: The airway defects ranged from 2 x 1 cm to 8 x 4 cm and involved up to 50% of the airway circumference. They were all successfully closed using muscle flaps with no mortality and all patients were extubated within 24 hours. Bronchoscopy revealed epithelialization of the reconstructions without dehiscence, stenosis, or recurrence of fistulas. The flow-volume loop was preserved in all patients and dynamic virtual bronchoscopy revealed no significant difference in the endoluminal cross surface areas of the airway between inspiration and expiration above (45 +/- 21 mm(2)), at the site (76 +/- 23 mm(2)) and below the reconstruction (65 +/- 40 mm(2)). CONCLUSIONS: Intrathoracic airway defects of up to 50% of the circumference may be repaired using extrathoracic muscle flaps when an end-to-end reconstruction is not feasible.

Le déterminisme linguistique en Russie actuelle

Résumé : Depuis la fin de la perestroïka s'est mis en place en Russie un discours identitaire qui, en linguistique, prend des formes extrêmes, reposant sur un strict déterminisme de la pensée par la langue. Les organismes de financement de la recherche scientifique soutiennent des projets qui étudient le rapport entre la grammaire russe et le « caractère national russe ». Des objets nouveaux apparaissent : « l'image linguistique russe du monde », « la personnalité linguistique », la « linguoculturologie ». Cet ensemble discursif construit dans l'imaginaire une identité collective rassurante, reposant sur l'idée que 1) tous les gens qui parlent la même langue pensent de la même façon; 2) les langues, donc les pensées collectives, sont imperméables entre elles, et donc intraduisibles. Cette tendance néo-humboldtienne dans la linguistique russe actuelle se déploie en toute méconnaissance de ses origines historiques : le Romantisme allemand dans son opposition à la philosophie des Lumières, le positivisme évolutionnisme d'Auguste Comte et la linguistique déterministe de l'Allemagne des années 1930.AbstractSince the end of perestroika, in linguistics in Russia, a new form of discourse has taken place, which stresses a very tight determinism of thought by language. The funding organizations of scientific research back up projects studying the relationship between Russiangrammar and the « Russian national character ». New objects of knowledge come to light : « the Russian linguistic image of the world », « linguistic personnality », « culturology ». This kind of discourse builds up an imaginary comforting collective identity, which relies on the principle that 1) all the people who speak the same language think the same way; 2) languages, hence collective kinds of thought, are hermetically closed to each other, and untranslatable. This neo-humboldtian trend in contemporary Russian linguistics has no knowledge of its historical origins : German Romanticism in its Anti-Enlightenment trend, evolutionnist positivism of Auguste Comte, and deterministic linguistics in Germany in the 1930s.

Esophageal leaks repaired by a muscle onlay approach in the presence of mediastinal sepsis.

BACKGROUND: Nineteen patients were evaluated after closure of intrathoracic esophageal leaks by a pediculated muscle flap onlay repair in the presence of mediastinal and systemic sepsis. METHODS: Intrathoracic esophageal leaks with mediastinitis and systemic sepsis occurred after delayed spontaneous perforations (n = 7) or surgical and endoscopic interventions (n = 12). Six patients presented with fulminant anastomotic leaks. Seven patients had previous attempts to close the leak by surgery (n = 4) or stenting (2) or both (n = 1). The debrided defects measured up to 2 x 12 cm or involved three quarters of the anastomotic circumference and were closed either by a full thickness diaphragmatic flap (n = 13) or a pediculated intrathoracically transposed extrathoracic muscle flap (n = 6). All patients had postoperative contrast esophagography between days 7 and 10 and an endoscopic evaluation 4 to 6 months after surgery. RESULTS: There was no 30-day mortality. During follow-up (4 to 42 months), 16 patients (84%) revealed functional and morphological restoration of the esophagointestinal integrity without further interventions. One patient required serial dilatations for a stricture, and 1 underwent temporary stenting for a persistent fistula; both patients had normal control endoscopy during follow-up. A third patient requiring permanent stenting for stenosis died from gastrointestinal bleeding due to stent erosion during follow-up. CONCLUSIONS: Intrathoracic esophageal leaks may be closed efficiently by a muscle flap onlay approach in the presence of mediastinitis and where a primary repair seems risky. The same holds true for fulminant intrathoracic anastomotic leaks after esophagectomy or other surgical interventions at the gastroesophageal junction.

Endoscopic off-pump aortic valve replacement: does the pericardial cuff improve the sutureless closure of left ventricular access?

OBJECTIVE: Off-pump trans left ventricular approach provides more precise deployment of stented aortic valve of any size with respect to the endovascular replacement. One of the key steps of this procedure is the ventricle repair after catheter withdrawing. We designed an animal study to compare the consistency of a sutureless repair of the left ventricle access using nitinol occluder with and without pericardial cuff on the ventricular side. METHODS: Material description: The Amplatz-nitinol occluder consists of two square heads squeezing ventricle wall in between them, sealing the defect. To improve its sealing property, a pericardial patch was sutured to the ventricular head of the occluder. Animal study setup: In adult pigs, a 30F sheath was inserted into the epigastric area through the cardiac apex, up to the left ventricle, simulating the approach for off-pump aortic valve replacement. The sheath was then removed and the ventricle closed with standard occluder in half of the animals, and cuffed occluder in the other half. Animals were followed-up for 3h, collecting haemodynamics data and pericardial bleeding. RESULTS: Device was successfully deployed in 12 animals in less than 1min. In the group where the standard occluder was used, bleeding during the deployment was 80+/-20ml and after the deployment was 800+/-20ml over 3h. In the group where the cuffed occluder was used, bleeding during the deployment was 85+/-20ml and after the deployment was 100+/-5ml over 3h. In the cuffed group, bleeding was significantly lower than the standard group, p-value being <0.001. CONCLUSIONS: The occluder is easy to use and the pericardial cuff dramatically increases its efficacy as demonstrated by a significant reduction of blood loss. The cuffed occluder opens the way for endoscopic, off-pump, transventricular aortic valve replacement.

Simultaneous EEG-fMRI at ultra-high field: Artifact prevention and safety assessment.

The simultaneous recording of scalp electroencephalography (EEG) and functional magnetic resonance imaging (fMRI) can provide unique insights into the dynamics of human brain function, and the increased functional sensitivity offered by ultra-high field fMRI opens exciting perspectives for the future of this multimodal approach. However, simultaneous recordings are susceptible to various types of artifacts, many of which scale with magnetic field strength and can seriously compromise both EEG and fMRI data quality in recordings above 3T. The aim of the present study was to implement and characterize an optimized setup for simultaneous EEG-fMRI in humans at 7T. The effects of EEG cable length and geometry for signal transmission between the cap and amplifiers were assessed in a phantom model, with specific attention to noise contributions from the MR scanner coldheads. Cable shortening (down to 12cm from cap to amplifiers) and bundling effectively reduced environment noise by up to 84% in average power and 91% in inter-channel power variability. Subject safety was assessed and confirmed via numerical simulations of RF power distribution and temperature measurements on a phantom model, building on the limited existing literature at ultra-high field. MRI data degradation effects due to the EEG system were characterized via B0 and B1(+) field mapping on a human volunteer, demonstrating important, although not prohibitive, B1 disruption effects. With the optimized setup, simultaneous EEG-fMRI acquisitions were performed on 5 healthy volunteers undergoing two visual paradigms: an eyes-open/eyes-closed task, and a visual evoked potential (VEP) paradigm using reversing-checkerboard stimulation. EEG data exhibited clear occipital alpha modulation and average VEPs, respectively, with concomitant BOLD signal changes. On a single-trial level, alpha power variations could be observed with relative confidence on all trials; VEP detection was more limited, although statistically significant responses could be detected in more than 50% of trials for every subject. Overall, we conclude that the proposed setup is well suited for simultaneous EEG-fMRI at 7T.

Glutathione Precursor, N-Acetyl-Cysteine, Modulates EEG Synchronization in Schizophrenia Patients

Background: Glutathione (GSH) dysregulation at the gene, protein and functional levels observed in schizophrenia patients, and schizophrenia-like anomalies in GSH deficit experimental models, suggest that genetic glutathione synthesis impairments represent one major risk factor for the disease (Do et al., 2009). In a randomized, double blind, placebo controlled, add-on clinical trial of 140 patients, the GSH precursor N-Acetyl-Cysteine (NAC, 2g/day, 6 months) significantly improved the negative symptoms and reduced sideeffects due to antipsychotics (Berk et al., 2008). In a subset of patients (n=7), NAC (2g/day, 2 months, cross-over design) also improved auditory evoked potentials, the NMDA-dependent mismatch negativity (Lavoie et al, 2008). Methods: To determine whether increased GSH levels would modulate the topography of functional brain connectivity, we applied a multivariate phase synchronization (MPS) estimator (Knyazeva et al, 2008) to dense-array EEGs recorded during rest with eyes closed at the protocol onset, the point of crossover, and at its end. Results: The whole-head imaging revealed a specific synchronization landscape in NAC compared to placebo condition. In particular, NAC increased MPS over frontal and left temporal regions in a frequency-specific manner. The topography and direction of MPS changes were similar and robust in all 7 patients. Moreover, these changes correlated with the changes in the Liddle's score of disorganization, thus linking EEG synchronization to the improvement of the clinical picture. Conclusions: The data suggest an important pathway towards new therapeutic strategies that target GSH dysregulation in schizophrenia. They also show the utility of MPS mapping as a marker of treatment efficacy.

Medial femoral condyle fracture as a complication of antegrade intramedullary nailing.

A 49-year-old man suffered a closed oblique fracture of the middle third of his left femur. Closed reduction and internal fixation by intramedullary (IM) nailing were performed. Per-operative fluoroscopic imaging and initial postoperative X-rays were judged normal and the patient followed the usual rehabilitation protocol. At 3-month follow-up the patient still demonstrated poor knee function and pain. A plain X-ray and a CT scan of the left knee revealed a displaced fracture of the medial femoral condyle. Analysis of the postoperative imaging suggests that the fracture occurred during the insertion of the IM nail. The nail possibly hit the Steinmann traction pin in the distal femur causing the medial condyle fracture. The patient was reoperated; open reduction and internal plate and screw fixation were performed with satisfactory clinical progress postoperatively. The description and illustration of this case is intended to make trauma surgeons aware of this rare but serious complication of IM femoral nailing.

Validity of the "Drift without pronation" sign in conversion disorder.

BACKGROUND: Conversion disorder (CD) is a psychiatric disorder, yet the diagnosis cannot be established without the expertise of a neurologist, as distinguishing a functional from an organic symptom relies on careful bedside examination. Joseph Babinski considered the absence of pronator drift as a 'positive sign' for hysterical paresis but the validity of this sign has never been evaluated. The aim of this study was to examine the sensitivity and specificity of the "drift without pronation" sign. METHODS: Twenty-six patients with unilateral functional upper limb paresis diagnosed with CD (DSM-IV) and a control group of 28 patients with an organic neurological condition were consecutively included. The arm stabilisation test was performed with arms stretched out in full supination, fingers adducted, eyes closed for 10 seconds. A positive "drift without pronation" sign was defined by the presence of a downward drift without pronation. RESULTS: All CD subjects (100%) displayed a positive sign when only 7.1% of organic subjects did (Fisher's p < 0.001). The sign yielded a sensitivity of 100% (95% CI:84%-100%) and a specificity of 93% (95% CI:76%-98%). CONCLUSION: The observation of a "drift without pronation" sign is specific for Conversion Disorder and can be of help in making a quick distinction between organic and functional paresis at the bedside.

Effective size of two feral domestic cat populations (Felis catus L): effect of the mating system.

A variety of behavioural traits have substantial effects on the gene dynamics and genetic structure of local populations. The mating system is a plastic trait that varies with environmental conditions in the domestic cat (Felis catus) allowing an intraspecific comparison of the impact of this feature on genetic characteristics of the population. To assess the potential effect of the heterogenity of males' contribution to the next generation on variance effective size, we applied the ecological approach of Nunney & Elam (1994) based upon a demographic and behavioural study, and the genetic 'temporal methods' of Waples (1989) and Berthier et al. (2002) using microsatellite markers. The two cat populations studied were nearly closed, similar in size and survival parameters, but differed in their mating system. Immigration appeared extremely restricted in both cases due to environmental and social constraints. As expected, the ratio of effective size to census number (Ne/N) was higher in the promiscuous cat population (harmonic mean = 42%) than in the polygynous one (33%), when Ne was calculated from the ecological method. Only the genetic results based on Waples' estimator were consistent with the ecological results, but failed to evidence an effect of the mating system. Results based on the estimation of Berthier et al. (2002) were extremely variable, with Ne sometimes exceeding census size. Such low reliability in the genetic results should retain attention for conservation purposes.

Peritalar dislocations: a retrospective study of 18 cases.

The purpose of this study is to retrospectively evaluate 18 consecutive cases of peritalar dislocations referred to our department during a period of 25 years and to delineate the factors influencing long-term prognosis. There were 13 (73%) medial and 5 (27%) lateral dislocations. Six patients (33%) suffered an open injury, including 2 of 13 (15%) medial and 4 of 5 (80%) lateral dislocations. Associated fractures involving the hindfoot or forefoot were noted in 7 feet, including 3 of 5 lateral dislocation cases. Reduction was accomplished under general anesthesia; in no case was open reduction necessary. In 4 of 6 open injuries with associated fractures, temporary fixation with Kirschner wires was performed. Patients were immobilized in a plaster cast for 4 weeks, or for 6 weeks in the presence of fracture, followed by weightbearing as tolerated. At a mean follow-up of 10.2 years (range, 4 to 26 years), 10 patients (56%) showed excellent results; all had sustained a closed medial low-energy dislocation. There were 3 cases (17%) with fair results and 5 cases (28%) with poor results. Forty-five percent of patients showed a restriction of activity, a reduction of subtalar range of motion, and moderate or severe radiographic signs of hindfoot degenerative arthritis. There were no cases of talar avascular necrosis, and in no case was secondary surgery necessary. Lateral dislocation and open medial dislocations with concomitant fractures showed a greater potential for poor prognosis. The results were independent from period of cast immobilization, suggesting that 4 to 6 weeks of immobilization provides acceptable long-term results.

Indicazioni e risultati della laparostomia retroperitoneale nel trattamento della pancreatite acuta necrotizzante infetta [Indications and results of retroperitoneal laparostomy in the treatment of infected acute necrotizing pancreatitis]

The aim of this study is to describe personal experience with retroperitoneal laparostomy in the management of infected acute necrotizing pancreatitis. The presence of an infected phlegmon requires surgical debridement and drainage. The surgical approach can be either an anterior laparotomy with irrigation and drainage (which can be either an open or closed laparotomy) or a posterior laparostomy. Three patients (2 men and 1 woman) presented with an unfavourable course of their acute necrotizing pancreatitis despite the administration of broad spectrum antibiotics. A posterior laparostomy with necrosectomy and drainage was performed. The postoperative course was slowly favorable in all 3 cases. Abdominal CT is the best modality for the detection and follow-up of pancreatic necrosis. CT-guided fine needle aspiration can detect superinfection of areas of necrosis. Posterior laparostomy presents several advantages compared to an anterior approach. There is no contamination of the peritoneal cavity; the integrity of the abdominal wall is respected. The necrosectomy is equally complete and the drainage is better as it is direct and posterior.

Questioni di pulizia: rappresentazioni e valori

In the framework of social representation, this research explores how the concept of cleanness does not refer solely to individual hygienic praxes and thoughts, but it is also linked to social and cultural aspects. In this way, the definitions of what is dirty and what is clean, what is pure and what is impure, are linked to social discrimination attitudes, based for example on the fear for contamination. Our general hypothesis is that the representations of dirt/cleanness and purity/impurity define ideas and praxes linked to personal hygiene, but refer also to the way people interact with the world and the others. Hence, we hypothesize that the representations of dirt/cleanness and purity/impurity are linked to values and political and religious orientations. A questionnaire with closed-answer questions and a free association task were distributed to 450 subjects. Results show how, in effects, the concepts of dirt/cleanness, purity/ impurity skip from their daily praxis connotations and assume a symbolic function for discriminating between individuals and social groups.

Predicting optimal lengths of random knots

In a thermally fluctuating long linear polymeric chain in a solution, the ends, from time to time, approach each other. At such an instance, the chain can be regarded as closed and thus will form a knot or rather a virtual knot. Several earlier studies of random knotting demonstrated that simpler knots show a higher occurrence for shorter random walks than do more complex knots. However, up to now there have been no rules that could be used to predict the optimal length of a random walk, i.e. the length for which a given knot reaches its highest occurrence. Using numerical simulations, we show here that a power law accurately describes the relation between the optimal lengths of random walks leading to the formation of different knots and the previously characterized lengths of ideal knots of a corresponding type.