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

Generalized iterated wreath products of symmetric groups and generalized rooted trees correspondence

Consider the generalized iterated wreath product $S_{r_1}\wr \ldots \wr S_{r_k}$ of symmetric groups. We give a complete description of the traversal for the generalized iterated wreath product. We also prove an existence of a bijection between the equivalence classes of ordinary irreducible representations of the generalized iterated wreath product and orbits of labels on certain rooted trees. We find a recursion for the number of these labels and the degrees of irreducible representations of the generalized iterated wreath product. Finally, we give rough upper bound estimates for fast Fourier transforms.Comment: 18 pages, to appear in Advances in the Mathematical Sciences. arXiv admin note: text overlap with arXiv:1409.060

Regulation of mammary gland branching morphogenesis by the extracellular matrix and its remodeling enzymes.

A considerable body of research indicates that mammary gland branching morphogenesis is dependent, in part, on the extracellular matrix (ECM), ECM-receptors, such as integrins and other ECM receptors, and ECM-degrading enzymes, including matrix metalloproteinases (MMPs) and their inhibitors, tissue inhibitors of metalloproteinases (TIMPs). There is some evidence that these ECM cues affect one or more of the following processes: cell survival, polarity, proliferation, differentiation, adhesion, and migration. Both three-dimensional culture models and genetic manipulations of the mouse mammary gland have been used to study the signaling pathways that affect these processes. However, the precise mechanisms of ECM-directed mammary morphogenesis are not well understood. Mammary morphogenesis involves epithelial 'invasion' of adipose tissue, a process akin to invasion by breast cancer cells, although the former is a highly regulated developmental process. How these morphogenic pathways are integrated in the normal gland and how they become dysregulated and subverted in the progression of breast cancer also remain largely unanswered questions

Defining the Differences Between Episodic Migraine and Chronic Migraine

Chronic migraine (CM) and episodic migraine (EM) are part of the spectrum of migraine disorders, but they are distinct clinical entities. Population-based studies have shown that those with CM demonstrate higher individual and societal burden because they are significantly more disabled than those with EM and have greater impaired quality of life both inside and outside the home. Proper diagnosis of both conditions requires clearly defined clinical criteria. Diagnosis enables the initiation of appropriate treatments and risk-factor modification, which ultimately improve functional status and quality of life for persons with migraine. Recognizing that both disorders are on the spectrum of migraine, this review serves as a guide to define the disease state of CM as distinct from EM in terms of clinical, epidemiological, sociodemographic, and comorbidity profiles

Chronic migraine plus medication overuse headache: two entities or not?

Chronic migraine (CM) represents migraine natural evolution from its episodic form. It is realized through a chronicization phase that may require months or years and varies from patient to patient. The transition to more frequent attacks pattern is influenced by lifestyle, life events, comorbid conditions and personal genetic terrain, and it often leads to acute drugs overuse. Medication overuse headache (MOH) may complicate every type of headache and all the drugs employed for headache treatment can cause MOH. The first step in the management of CM complicated by medication overuse must be the withdrawal of the overused drugs and a detoxification treatment. The goal is not only to detoxify the patient and stop the chronic headache but also to improve responsiveness to acute or prophylactic drugs. Different methods have been suggested: gradual or abrupt withdrawal; home treatment, hospitalization, or a day-hospital setting; re-prophylaxes performed immediately or at the end of the wash-out period. Up to now, only topiramate and local injection of onabotulinumtoxinA have shown efficacy as therapeutic agents for re-prophylaxis after detoxification in patients with CM with and without medication overuse. Although the two treatments showed similar efficacy, onabotulinumtoxinA is associated with a better adverse events profile. Recently, the Phase III Research Evaluating Migraine Prophylaxis Therapy (PREEMPT) clinical program proved that patients with CM, even those with MOH, are the ones most likely to benefit from onabotulinumtoxinA treatment. Furthermore, it provided an injection paradigm that can be used as a guide for a correct administration of onabotulinumtoxinA

The role of aerodynamic resistance in thermal remote sensing-based evapotranspiration models

&amp;lt;p&amp;gt;&amp;amp;#8216;Aerodynamic resistance&amp;amp;#8217; (hereafter r&amp;lt;sub&amp;gt;a&amp;lt;/sub&amp;gt;) is a preeminent variable in the modelling of evapotranspiration (ET), and its accurate quantification plays a critical role in determining the performance and consistency of thermal remote sensing-based surface energy balance (SEB) models for estimating ET at local to regional scales. Atmospheric stability links r&amp;lt;sub&amp;gt;a&amp;lt;/sub&amp;gt; with land surface temperature (LST) and the representation of their interactions in the SEB models determines the accuracy of ET estimates.&amp;lt;/p&amp;gt;&amp;lt;p&amp;gt;The present study investigates the influence of r&amp;lt;sub&amp;gt;a&amp;lt;/sub&amp;gt; and its relation to LST uncertainties on the performance of three structurally different SEB models by combining nine OzFlux eddy covariance datasets from 2011 to 2019 from sites of different aridity in Australia with MODIS Terra and Aqua LST and leaf area index (LAI) products. Simulations of the latent heat flux (LE, energy equivalent of ET in W/m&amp;lt;sup&amp;gt;2&amp;lt;/sup&amp;gt;) from the SPARSE (Soil Plant Atmosphere and Remote Sensing Evapotranspiration), SEBS (Surface Energy Balance System) and STIC (Surface Temperature Initiated Closure) models forced with MODIS LST, LAI, and in-situ meteorological datasets were evaluated using observed flux data across water-limited (semi-arid and arid) and radiation-limited (mesic) ecosystems.&amp;lt;/p&amp;gt;&amp;lt;p&amp;gt;Our results revealed that the three models tend to overestimate instantaneous LE in the water-limited shrubland, woodland and grassland ecosystems by up to 60% on average, which was caused by an underestimation of the sensible heat flux (H). LE overestimation was associated with discrepancies in r&amp;lt;sub&amp;gt;a&amp;lt;/sub&amp;gt; retrievals under conditions of high atmospheric instability, during which errors in LST (expressed as the difference between MODIS LST and in-situ LST) apparently played a minor role. On the other hand, a positive bias in LST coincides with low r&amp;lt;sub&amp;gt;a&amp;lt;/sub&amp;gt; and causes slight underestimation of LE at the water-limited sites. The impact of r&amp;lt;sub&amp;gt;a&amp;lt;/sub&amp;gt; on the LE residual error was found to be of the same magnitude as the influence of errors in LST in the semi-arid ecosystems as indicated by variable importance in projection (VIP) coefficients from partial least squares regression above unity. In contrast, our results for mesic forest ecosystems indicated minor dependency on r&amp;lt;sub&amp;gt;a&amp;lt;/sub&amp;gt; for modelling LE (VIP&amp;lt;0.4), which was due to a higher roughness length and lower LST resulting in dominance of mechanically generated turbulence, thereby diminishing the importance of atmospheric stability in the determination of r&amp;lt;sub&amp;gt;a&amp;lt;/sub&amp;gt;.&amp;lt;/p&amp;gt;</jats:p

Basal cutaneous pain threshold in headache patients

The aim of this study was to analyze cutaneous pain threshold (CPT) during the interictal phase in headache patients, and the relationships between headache frequency and analgesic use. A consecutive series of 98 headache patients and 26 sex- and age-balanced controls were evaluated. Acute allodynia (AA) was assessed by Jakubowski questionnaire, and interictal allodynia (IA) by a skin test with calibrated monofilaments. AA is widely known as a symptom more present in migraine than in TTH spectrum: in our study this was confirmed only in cases of episodic attacks. When headache index rises towards chronicization, the prevalence of AA increases in both headache spectrums (χ2 13.55; p < 0.01). AA was associated with IA only in cases of chronic headache. When headache becomes chronic, mostly in presence of medication overuse, interictal CPT decreases and IA prevalence increases (χ2 20.44; p < 0.01), with closer association than AA. In MOH patients there were no significant differences depending on the diagnosis of starting headache (migraine or tension type headache) and, in both groups, we found the overuse of analgesics plays an important role: intake of more than one daily drug dramatically reduces the CPT (p < 0.05). Thus, when acute allodynia increases frequency, worsens or appears for the first time in patients with a long-standing history of chronic headache, it could reasonably suggest that the reduction of CPT had started, without using a specific practical skin test but simply by questioning clinical headache history. In conclusion, these results indicate that the role of medication overuse is more important than chronicization in lowering CPT, and suggest that prolonged periods of medication overuse can interfere with pain perception by a reduction of the pain threshold that facilitates the onset of every new attack leading to chronicization

Chronic migraine classification: current knowledge and future perspectives

In the field of so-called chronic daily headache, it is not easy for migraine that worsens progressively until it becomes daily or almost daily to find a precise and universally recognized place within the current international headache classification systems. In line with the 2006 revision of the second edition of the International Classification of Headache Disorders (ICHD-2R), the current prevailing opinion is that this headache type should be named chronic migraine (CM) and be characterized by the presence of at least 15 days of headache per month for at least 3 consecutive months, with headache having the same clinical features of migraine without aura for at least 8 of those 15 days. Based on much evidence, though, a CM with the above characteristics appears to be a heterogeneous entity and the obvious risk is that its definition may be extended to include a variety of different clinical entities. A proposal is advanced to consider CM a subtype of migraine without aura that is characterized by a high frequency of attacks (10–20 days of headache per month for at least 3 months) and is distinct from transformed migraine (TM), which in turn should be included in the classification as a complication of migraine. Therefore, CM should be removed from its current coding position in the ICHD-2 and be replaced by TM, which has more restrictive diagnostic criteria (at least 20 days of headache per month for at least 1 year, with no more than 5 consecutive days free of symptoms; same clinical features of migraine without aura for at least 10 of those 20 days)