Exponential beams of electromagnetic radiation

We show that in addition to well known Bessel, Hermite-Gauss, and Laguerre-Gauss beams of electromagnetic radiation, one may also construct exponential beams. These beams are characterized by a fall-off in the transverse direction described by an exponential function of rho. Exponential beams, like Bessel beams, carry definite angular momentum and are periodic along the direction of propagation, but unlike Bessel beams they have a finite energy per unit beam length. The analysis of these beams is greatly simplified by an extensive use of the Riemann-Silberstein vector and the Whittaker representation of the solutions of the Maxwell equations in terms of just one complex function. The connection between the Bessel beams and the exponential beams is made explicit by constructing the exponential beams as wave packets of Bessel beams.Comment: Dedicated to the memory of Edwin Powe

Explicit MBR All-Symbol Locality Codes

Node failures are inevitable in distributed storage systems (DSS). To enable efficient repair when faced with such failures, two main techniques are known: Regenerating codes, i.e., codes that minimize the total repair bandwidth; and codes with locality, which minimize the number of nodes participating in the repair process. This paper focuses on regenerating codes with locality, using pre-coding based on Gabidulin codes, and presents constructions that utilize minimum bandwidth regenerating (MBR) local codes. The constructions achieve maximum resilience (i.e., optimal minimum distance) and have maximum capacity (i.e., maximum rate). Finally, the same pre-coding mechanism can be combined with a subclass of fractional-repetition codes to enable maximum resilience and repair-by-transfer simultaneously

Generalized Gravi-Electromagnetism

A self consistant and manifestly covariant theory for the dynamics of four charges (masses) (namely electric, magnetic, gravitational, Heavisidian) has been developed in simple, compact and consistent manner. Starting with an invariant Lagrangian density and its quaternionic representation, we have obtained the consistent field equation for the dynamics of four charges. It has been shown that the present reformulation reproduces the dynamics of individual charges (masses) in the absence of other charge (masses) as well as the generalized theory of dyons (gravito - dyons) in the absence gravito - dyons (dyons). key words: dyons, gravito - dyons, quaternion PACS NO: 14.80H

Experience with onabotulinumtoxinA (BOTOX) in chronic refractory migraine: focus on severe attacks

The objective of this study is to analyse our experience in the treatment of refractory chronic migraine (CM) with onabotulinumtoxinA (BTA) and specifically in its effects over disabling attacks. Patients with CM and inadequate response or intolerance to oral preventatives were treated with pericranial injections of 100 U of TBA every 3 months. The dose was increased up to 200 U in case of no response. The patients kept a headache diary. In addition, we specifically asked on the effect of BTA on the frequency of disabling attacks, consumption of triptans and visits to Emergency for the treatment of severe attacks. This series comprises a total of 35 patients (3 males), aged 24–68 years. All except three met IHS criteria for analgesic overuse. The number of sessions with BTA ranged from 2 to 15 (median 4) and nine (26%) responded (reduction of >50% in headache days). However, the frequency of severe attacks was reduced to an average of 46%. Oral triptan consumption (29 patients) was reduced by 50% (from an average of 22 to 11 tablets/month). Those six patients who used subcutaneous sumatriptan reduced its consumption to a mean of 69% (from 4.5 to 1.5 injections per month). Emergency visits went from an average of 3 to 0.4 per trimester (−83%). Six patients complained of mild adverse events, transient local cervical pain being the most common. Although our data must be taken with caution as this is an open trial, in clinical practice treatment of refractory CM with BTA reduces the frequency of disabling attacks, the consumption of triptans and the need of visits to Emergency, which makes this treatment a profitable option both clinically and pharmacoeconomically

Shift-Symmetric Configurations in Two-Dimensional Cellular Automata: Irreversibility, Insolvability, and Enumeration

The search for symmetry as an unusual yet profoundly appealing phenomenon, and the origin of regular, repeating configuration patterns have long been a central focus of complexity science and physics. To better grasp and understand symmetry of configurations in decentralized toroidal architectures, we employ group-theoretic methods, which allow us to identify and enumerate these inputs, and argue about irreversible system behaviors with undesired effects on many computational problems. The concept of so-called configuration shift-symmetry is applied to two-dimensional cellular automata as an ideal model of computation. Regardless of the transition function, the results show the universal insolvability of crucial distributed tasks, such as leader election, pattern recognition, hashing, and encryption. By using compact enumeration formulas and bounding the number of shift-symmetric configurations for a given lattice size, we efficiently calculate the probability of a configuration being shift-symmetric for a uniform or density-uniform distribution. Further, we devise an algorithm detecting the presence of shift-symmetry in a configuration. Given the resource constraints, the enumeration and probability formulas can directly help to lower the minimal expected error and provide recommendations for system's size and initialization. Besides cellular automata, the shift-symmetry analysis can be used to study the non-linear behavior in various synchronous rule-based systems that include inference engines, Boolean networks, neural networks, and systolic arrays.Comment: 22 pages, 9 figures, 2 appendice

Quaternion Analysis for Generalized Electromagnetic Fields of Dyons in Isotropic Medium

Quaternion analysis of time dependent Maxwell's equations in presence of electric and magnetic charges has been developed and the solutions for the classical problem of moving charges (electric and magnetic) are obtained in unique, simple and consistent manner

Key stages in mammary gland development: The mammary end bud as a motile organ

In the rodent, epithelial end buds define the tips of elongating mammary ducts. These highly motile structures undergo repeated dichotomous branching as they aggressively advance through fatty stroma and, turning to avoid other ducts, they finally cease growth leaving behind the open, tree-like framework on which secretory alveoli develop during pregnancy. This review identifies the motility of end buds as a unique developmental marker that represents the successful integration of systemic and local mammotrophic influences, and covers relevant advances in ductal growth regulation, extracellular matrix (ECM) remodeling, and cell adhesion in the inner end bud. An unexpected growth-promoting synergy between insulin-like growth factor-1 and progesterone, in which ducts elongate without forming new end buds, is described as well as evidence strongly supporting self-inhibition of ductal elongation by end-bud-secreted transforming growth factor-β acting on stromal targets. The influence of the matrix metalloproteinase ECM-remodeling enzymes, notably matrix metalloproteinase-2, on end bud growth is discussed in the broader context of enzymes that regulate the polysaccharide-rich glycosaminoglycan elements of the ECM. Finally, a critical, motility-enabling role for the cellular architecture of the end bud is identified and the contribution of cadherins, the netrin/neogenin system, and ErbB2 to the structure and motility of end buds is discussed