Representation Theory Approach to the Polynomial Solutions of q - Difference Equations : U_q(sl(3)) and Beyond,

A new approach to the theory of polynomial solutions of q - difference equations is proposed. The approach is based on the representation theory of simple Lie algebras and their q - deformations and is presented here for U_q(sl(n)). First a q - difference realization of U_q(sl(n)) in terms of n(n-1)/2 commuting variables and depending on n-1 complex representation parameters r_i, is constructed. From this realization lowest weight modules (LWM) are obtained which are studied in detail for the case n=3 (the well known n=2 case is also recovered). All reducible LWM are found and the polynomial bases of their invariant irreducible subrepresentations are explicitly given. This also gives a classification of the quasi-exactly solvable operators in the present setting. The invariant subspaces are obtained as solutions of certain invariant q - difference equations, i.e., these are kernels of invariant q - difference operators, which are also explicitly given. Such operators were not used until now in the theory of polynomial solutions. Finally the states in all subrepresentations are depicted graphically via the so called Newton diagrams.Comment: uuencoded Z-compressed .tar file containing two ps files

Deformations of Multiparameter Quantum gl(N)

Multiparameter quantum gl(N) is not a rigid structure. This paper defines an essential deformation as one that cannot be interpreted in terms of a similarity transformation, nor as a perturbation of the parameters. All the equivalence classes of first order essential deformations are found, as well as a class of exact deformations. This work provides quantization of all the classical Lie bialgebra structures (constant r-matrices) found by Belavin and Drinfeld for sl(n). A special case, that requires the Hecke parameter to be a cubic root of unity, stands out.Comment: 15 pages. Plain Te

Trigeminal sensory pathway function in patients with SUNCT

[IF 2.64] Objective: Short-lasting unilateral neuralgiform headache with conjunctival injection and tearing (SUNCT) is a rare primary headache whose origins are unclear. To seek information on its pathophysiology, we studied the trigeminal Ab and Ad pathways by recording trigeminal reflexes and laser evoked potentials (LEPs) in patients with SUNCT. Methods: Trigeminal reflexes and LEPs were recorded in 11 consecutive patients. Ten patients had neuroimaging evidence documenting idiopathic SUNCT and one had a posterior fossa tumour that compressed the trigeminal nerve thus causing symptomatic SUNCT. Results: Whereas the patients with idiopathic SUNCT had normal trigeminal reflex and LEP responses, the patient with symptomatic SUNCT had abnormal responses. Conclusions: Our neurophysiological findings show that idiopathic SUNCT spares the trigeminal sensory pathways whereas symptomatic SUNCT does not. Significance: Neurophysiological testing can easily differentiate the idiopathic and symptomatic forms of SUNCT. It also suggests that the two forms are pathophysiologically distinct entities

On the stability of quantum holonomic gates

We provide a unified geometrical description for analyzing the stability of holonomic quantum gates in the presence of imprecise driving controls (parametric noise). We consider the situation in which these fluctuations do not affect the adiabatic evolution but can reduce the logical gate performance. Using the intrinsic geometric properties of the holonomic gates, we show under which conditions on noise's correlation time and strength, the fluctuations in the driving field cancel out. In this way, we provide theoretical support to previous numerical simulations. We also briefly comment on the error due to the mismatch between real and nominal time of the period of the driving fields and show that it can be reduced by suitably increasing the adiabatic time.Comment: 7 page

The diagnostic accuracy of the small fiber neuropathy symptoms inventory questionnaire (SFN-SIQ) for identifying pure small fiber neuropathy

A definite diagnosis of pure small fiber neuropathy (SFN) relies on specific diagnostic testing, such as skin biopsy, quantitative sensory testing (QST), and nociceptive evoked potentials, which require considerable resources that may not be widely available. Accordingly, diagnostic tools with easy implementation in non-specialist centers are warranted to identify patients who require second-level diagnostic tests. In this study, we aimed to test the accuracy of the Small Fiber Neuropathy Symptoms Inventory Questionnaire (SFN-SIQ) in diagnosing pure SFN. We enrolled 86 patients with suspected pure SFN. In these patients, we calculated the diagnostic accuracy of the SFN-SIQ using a combination of clinical examination, QST, and skin biopsy as a reference standard. We found that the SFN-SIQ showed an excellent ability to discriminate between patients with and without pure SFN, with 86% sensitivity and 70% specificity in the diagnosis of pure SFN. Our study providing the diagnostic yield of the SFN-SIQ for pure SFN diagnosis suggests that this questionnaire might be used to screen patients with suspected SFN and identify those requiring second-level diagnostic tests such as QST, skin biopsy, or nociceptive evoked potentials

Tools for Assessing Neuropathic Pain

Giorgio Cruccu and Andrea Truini discuss a new pain assessment tool published in PLoS Medicine called Standardized Evaluation of Pain and they review other tools to assess neuropathic pain

Pain associated with COVID-19 vaccination is unrelated to skin biopsy abnormalities

Previous clinical observations raised the possibility that COVID-19 vaccination might trigger a small-fibre neuropathy.Objectives:In this uncontrolled observational study, we aimed to identify small fibre damage in patients complaining of generalized sensory symptoms and pain after COVID-19 vaccination.Methods:We collected clinical data, including a questionnaire for assessing autonomic symptoms (Composite Autonomic Symptom Score-31), and investigated quantitative sensory testing (QST) and skin biopsy in 15 prospectively enrolled patients with generalized sensory symptoms and pain after COVID-19 vaccination. Nine patients complaining of orthostatic intolerance also underwent cardiovascular autonomic tests.Results:We found that all patients experienced widespread pain, and most of them (11 of 15) had a fibromyalgia syndrome. All patients had normal skin biopsy findings, and in the 9 patients with orthostatic intolerance, cardiovascular autonomic tests showed normal findings. Nevertheless, 5 patients had cold and warm detection abnormalities at the QST investigation.Conclusions:In our study, most patients complaining of generalized sensory symptoms and pain after COVID-19 vaccination had clinical and diagnostic test findings compatible with a fibromyalgia syndrome. Although the abnormal QST findings we found in 5 patients might be compatible with a small-fibre neuropathy, they should be cautiously interpreted given the psychophysical characteristics of this diagnostic test. Further larger controlled studies are needed to define precisely the association between small fibre damage and COVID-19 vaccination

Effects of miRNA-15 and miRNA-16 expression replacement in chronic lymphocytic leukemia : implication for therapy

This work was supported by: Associazione Italiana Ricerca sul Cancro (AIRC) Grant 5 x mille n.9980, (to M.F., F.M. A. N., P.T. and M.N.) ; AIRC I.G. n. 14326 (to M.F.), n.10136 and 16722 (A.N.), n.15426 (to F.F.). AIRC and Fondazione CaRiCal co-financed Multi Unit Regional Grant 2014 n.16695 (to F.M.). Italian Ministry of Health 5x1000 funds (to S.Z. and F.F). A.G R. was supported by Associazione Italiana contro le Leucemie-Linfomi-Mielomi (AIL) Cosenza - Fondazione Amelia Scorza (FAS). S.M. C.M., M.C., L.E., S.B. were supported by AIRC.Peer reviewedPostprin