Possible thermodynamic structure underlying the laws of Zipf and Benford

We show that the laws of Zipf and Benford, obeyed by scores of numerical data generated by many and diverse kinds of natural phenomena and human activity are related to the focal expression of a generalized thermodynamic structure. This structure is obtained from a deformed type of statistical mechanics that arises when configurational phase space is incompletely visited in a severe way. Specifically, the restriction is that the accessible fraction of this space has fractal properties. The focal expression is an (incomplete) Legendre transform between two entropy (or Massieu) potentials that when particularized to first digits leads to a previously existing generalization of Benford's law. The inverse functional of this expression leads to Zipf's law; but it naturally includes the bends or tails observed in real data for small and large rank. Remarkably, we find that the entire problem is analogous to the transition to chaos via intermittency exhibited by low-dimensional nonlinear maps. Our results also explain the generic form of the degree distribution of scale-free networks.Comment: To be published in European Physical Journal

Phase Space Models for Stochastic Nonlinear Parabolic Waves: Wave Spread and Singularity

We derive several kinetic equations to model the large scale, low Fresnel number behavior of the nonlinear Schrodinger (NLS) equation with a rapidly fluctuating random potential. There are three types of kinetic equations the longitudinal, the transverse and the longitudinal with friction. For these nonlinear kinetic equations we address two problems: the rate of dispersion and the singularity formation. For the problem of dispersion, we show that the kinetic equations of the longitudinal type produce the cubic-in-time law, that the transverse type produce the quadratic-in-time law and that the one with friction produces the linear-in-time law for the variance prior to any singularity. For the problem of singularity, we show that the singularity and blow-up conditions in the transverse case remain the same as those for the homogeneous NLS equation with critical or supercritical self-focusing nonlinearity, but they have changed in the longitudinal case and in the frictional case due to the evolution of the Hamiltonian

Micro-CT Characterization of Human Trabecular Bone in Osteogenesis Imperfecta

Osteogenesis imperfecta (OI) is a genetic syndrome affecting collagen synthesis and assembly. Its symptoms vary widely but commonly include bone fragility, reduced stature, and bone deformity. Because of the small size and paucity of human specimens, there is a lack of biomechanical data for OI bone. Most literature has focused on histomorphometric analyses, which rely on assumptions to extrapolate 3-D properties. In this study, a micro-computed tomography (μCT) system was used to directly measure structural and mineral properties in pediatric OI bone collected during routine surgical procedures. Surface renderings suggested a poorly organized, plate-like orientation. Patients with a history of bone-augmenting drugs exhibited increased bone volume fraction (BV/TV), trabecular number (Tb.N), and connectivity density (Eu.Conn.D). The latter two parameters appeared to be related to OI severity. Structural results were consistently higher than those reported in a previous histomorphometric study, but these differences can be attributed to factors such as specimen collection site, drug therapy, and assumptions associated with histomorphometry. Mineral testing revealed strong correlations with several structural parameters, highlighting the importance of a dual approach in trabecular bone testing. This study reports some of the first quantitative μCT data of human OI bone, and it suggests compelling possibilities for the future of OI bone assessment

A Case of Reactive Cervical Lymphadenopathy with Fat Necrosis Impinging on Adjacent Vascular Structures.

A tender neck mass in adults can be a diagnostic challenge due to a wide differential diagnosis, which ranges from reactive lymphadenopathy to malignancy. In this report, we describe a case of a young female with an unusually large and tender reactive lymph node with fat necrosis. The diagnostic imaging findings alone mimicked that of scrofula and malignancy, which prompted a complete workup. Additionally, the enlarged lymph node was compressing the internal jugular vein in the setting of oral contraceptive use by the patient, raising concern for Lemierre's syndrome or internal jugular vein thrombosis. This report shows how, in the appropriate clinical context, and especially with the involvement of adjacent respiratory or neurovascular structures, aggressive diagnostic testing can be indicated

Recent Topics on Very High Energy Gamma-ray Astronomy

With the advent of imaging atmospheric Cherenkov telescopes in late 1980's, ground-based observation of TeV gamma-rays came into reality after struggling trials by pioneers for twenty years, and the number of gamma-ray sources detected at TeV energies has increased to be over seventy now. In this review, recent findings from ground-based very-high-energy gamma-ray observations are summarized (as of 2008 March), and up-to-date problems in this research field are presented.Comment: 6 pages, 4 figures, Proceedings of the International Workshop on Advances in Cosmic Ray Science, March 17-19, 2008, Waseda University, Tokyo, Japan; to be published in Journal of the Physical Society of Japan (supplement

Revealing hidden symmetries and gauge invariance of the massive Carroll-Field-Jackiw model

In this paper we have analyzed the improved version of the Gauge Unfixing (GU) formalism of the massive Carroll-Field-Jackiw model, which breaks both the Lorentz and gauge invariances, to disclose hidden symmetries to obtain gauge invariance, the key stone of the Standard Model. In this process, as usual, we have converted this second-class system into a first-class one and we have obtained two gauge invariant models. We have verified that the Poisson brackets involving the gauge invariant variables, obtained through the GU formalism, coincide with the Dirac brackets between the original second-class variables of the phase space. Finally, we have obtained two gauge invariant Lagrangians where one of them represents the Stueckelberg form.Comment: revised version. To appear in Europhysics Letter

Avalanche-Induced Current Enhancement in Semiconducting Carbon Nanotubes

Semiconducting carbon nanotubes under high electric field stress (~10 V/um) display a striking, exponential current increase due to avalanche generation of free electrons and holes. Unlike in other materials, the avalanche process in such 1D quantum wires involves access to the third sub-band, is insensitive to temperature, but strongly dependent on diameter ~exp(-1/d^2). Comparison with a theoretical model yields a novel approach to obtain the inelastic optical phonon emission length, L_OP,ems ~ 15d nm. The combined results underscore the importance of multi-band transport in 1D molecular wires