Leadership Statistics in Random Structures

The largest component (``the leader'') in evolving random structures often exhibits universal statistical properties. This phenomenon is demonstrated analytically for two ubiquitous structures: random trees and random graphs. In both cases, lead changes are rare as the average number of lead changes increases quadratically with logarithm of the system size. As a function of time, the number of lead changes is self-similar. Additionally, the probability that no lead change ever occurs decays exponentially with the average number of lead changes.Comment: 5 pages, 3 figure

Formal [4 + 2] cycloaddition of alkoxy-substituted donor-acceptor cyclobutanes and aldehydes catalyzed by Yb(OTf)3.

The cycloaddition between 2-alkoxy-1,1-cyclobutane diesters and aromatic, heteroaromatic, or aliphatic aldehydes under Yb(OTf)(3) catalysis generates tetrahydropyrans in high yields with exclusive cis-stereochemistry

Kaposi sarcoma in an HIV-negative Tunisian patient: A rare cause of metatarsalgia

AbstractBackgroundKaposi sarcoma (KS) is an angioproliferative neoplasm that is commonly associated with human herpes virus-8 (HHV-8) and human immunodeficiency virus (HIV)/acquired immunodeficiency syndrome (AIDS). KS with osseous involvement is a rare occurrence, and is far more common in acquired immunodeficiency syndrome (AIDS)-related KS.Case presentationWe present a 32-year-old Tunisian man, HIV negative, who presented with a 4-year history of atraumatic mechanical metatarsalgia that progressively worsened with a limping gait. Physical examination revealed marked symmetrical forefoot lymphedema and a painful restricted left knee joint movement. Physical examination showed purple-blue plaques and nodules on the feet and ankles. Serologic tests for HIV and syphilis were negative. Plain radiography of the feet revealed numerous small lytic lesions. There were also scattered lytic lesions in the metaphysis of the proximal tibia and fibula. Osteolysis was predominantly left. Magnetic resonance imaging of the feet showed abnormal bone marrow signal of metatarsals and phalanges. Skin lesion biopsy yielded the diagnosis of Kaposi sarcoma. The disease was managed with chemotherapy including vinblastine.ConclusionIn a patient presenting with metatarsalgia without a commonly detected cause, it is mandatory to search for other lesions that may point to a rare diagnosis as KS which is famous for involvement of the metatarsal bone

Robustness of Local Predictions in Atomistic Machine Learning Models

Machine learning (ML) models for molecules and materials commonly rely on a decomposition of the global target quantity into local, atom-centered contributions. This approach is convenient from a computational perspective, enabling large-scale ML-driven simulations with a linear-scaling cost and also allows for the identification and posthoc interpretation of contributions from individual chemical environments and motifs to complicated macroscopic properties. However, even though practical justifications exist for the local decomposition, only the global quantity is rigorously defined. Thus, when the atom-centered contributions are used, their sensitivity to the training strategy or the model architecture should be carefully considered. To this end, we introduce a quantitative metric, which we call the local prediction rigidity (LPR), that allows one to assess how robust the locally decomposed predictions of ML models are. We investigate the dependence of the LPR on the aspects of model training, particularly the composition of training data set, for a range of different problems from simple toy models to real chemical systems. We present strategies to systematically enhance the LPR, which can be used to improve the robustness, interpretability, and transferability of atomistic ML models

Robustness of Local Predictions in Atomistic Machine Learning Models

Machine learning (ML) models for molecules and materials commonly rely on a decomposition of the global target quantity into local, atom-centered contributions. This approach is convenient from a computational perspective, enabling large-scale ML-driven simulations with a linear-scaling cost, and also allow for the identification and post-hoc interpretation of contributions from individual chemical environments and motifs to complicated macroscopic properties. However, even though there exist practical justifications for these decompositions, only the global quantity is rigorously defined, and thus it is unclear to what extent the atomistic terms predicted by the model can be trusted. Here, we introduce a quantitative metric, which we call the local prediction rigidity (LPR), that allows one to assess how robust the locally decomposed predictions of ML models are. We investigate the dependence of LPR on the aspects of model training, particularly the composition of training dataset, for a range of different problems from simple toy models to real chemical systems. We present strategies to systematically enhance the LPR, which can be used to improve the robustness, interpretability, and transferability of atomistic ML models

Addition-Deletion Networks

We study structural properties of growing networks where both addition and deletion of nodes are possible. Our model network evolves via two independent processes. With rate r, a node is added to the system and this node links to a randomly selected existing node. With rate 1, a randomly selected node is deleted, and its parent node inherits the links of its immediate descendants. We show that the in-component size distribution decays algebraically, c_k ~ k^{-beta}, as k-->infty. The exponent beta=2+1/(r-1) varies continuously with the addition rate r. Structural properties of the network including the height distribution, the diameter of the network, the average distance between two nodes, and the fraction of dangling nodes are also obtained analytically. Interestingly, the deletion process leads to a giant hub, a single node with a macroscopic degree whereas all other nodes have a microscopic degree.Comment: 8 pages, 5 figure

Ertapenem Once a Day Versus Piperacillin–Tazobactam Every 6 Hours for Treatment of Acute Pelvic Infections: A Prospective, Multicenter, Randomized, Double-Blind Study

Objective: To compare ertapenem therapy with piperacillin–tazobactam therapy for the management of acute pelvic infections. Methods: In a multicenter, double-blind study, 412 women with acute pelvic infection were assigned to one of two strata, namely obstetric/postpartum infection or gynecologic/postoperative infection, and were then randomized to ertapenem, 1 g once a day, or piperacillin–tazobactam, 3.375 g every 6 hours, both administered intravenously. Results: In total, 163 patients in the ertapenem group and 153 patients in the piperacillin–tazobactam group were clinically evaluable. The median duration of therapy was 4.0 days in both treatment groups. The most common single pathogen was Escherichia coli . At the primary efficacy endpoint 2–4 weeks post therapy, 93.9% of patients who received ertapenem and 91.5% of those who received piperacillin–tazobactam were cured (95% confidence interval for the difference, adjusting for strata, –4% to 8.8%), indicating that cure rates for both treatment groups were equivalent. Cure rates for both treatment groups were also similar when compared by stratum and severity of infection. The frequency and severity of drug-related adverse events were generally similar in both groups. Conclusions: In this study, ertapenem was as effective as piperacillin–tazobactam for the treatment of acute pelvic infection, was generally well tolerated, and had an overall safety profile similar to that of piperacillin–tazobactam

Understanding Search Trees via Statistical Physics

We study the random m-ary search tree model (where m stands for the number of branches of a search tree), an important problem for data storage in computer science, using a variety of statistical physics techniques that allow us to obtain exact asymptotic results. In particular, we show that the probability distributions of extreme observables associated with a random search tree such as the height and the balanced height of a tree have a traveling front structure. In addition, the variance of the number of nodes needed to store a data string of a given size N is shown to undergo a striking phase transition at a critical value of the branching ratio m_c=26. We identify the mechanism of this phase transition, show that it is generic and occurs in various other problems as well. New results are obtained when each element of the data string is a D-dimensional vector. We show that this problem also has a phase transition at a critical dimension, D_c= \pi/\sin^{-1}(1/\sqrt{8})=8.69363...Comment: 11 pages, 8 .eps figures included. Invited contribution to STATPHYS-22 held at Bangalore (India) in July 2004. To appear in the proceedings of STATPHYS-2

Spondylodiscite tuberculeuse : 12 ans d'expérience dans un centre hospitalier en Tunisie

Objectifs : Décrire les particularités épidémiologiques, cliniques et paracliniques des spondylodiscites tuberculeuses et déterminer les facteurs prédictifs d’une évolution défavorable. Patients et Méthode: Etude rétrospective sur une période de 12 ans. Le diagnostic a été porté sur des preuves bactériologiques, anatomopathologiques ou sur un faisceau d’arguments. Résultats : Il s’agissait de 49 patients (26F/23H), âgés en moyenne de 51,84 ans. Le délai moyen de diagnostic était de 6,65 mois. Un facteur prédisposant à l’infection a été relevé chez 38,7% des patients. L’étage lombaire était le plus touché (67,3%). L’imagerie par résonnance magnétique était pathologique dans tous les cas où elle a été effectuée. Le diagnostic de certitude a été porté dans 9 cas sur une preuve histologique. La ponction biopsie disco-vertébrale a permis de confirmer le diagnostic dans 6/36 cas. Tous les patients ont reçu un traitement anti-tuberculeux d’une durée moyenne de 13,59 mois associé à un geste interventionnel dans 8 cas. L’évolution était favorable dans 84,2% des cas. Nous avons identifiés quatre facteurs prédictifs d’une évolution défavorable: une hyperleucocytose initiale ≥11500 éléments/mm3 (p=0,031), la présence d’abcès ou de collection à l’imagerie (p=0,018); un tassement vertébral à l’IRM (p=0,018) et l’existence de déformation osseuse avant correction chirurgicale (p<0,001). Conclusion: La spondylodiscite tuberculeuse devrait être suspectée devant toute rachialgie inflammatoire. Une prise en charge précoce est la clé pour éviter les complications neurologiques et ostéo-articulaires