We study the space of all kinematically allowed four photon and four graviton S-matrices, polynomial in scattering momenta. We demonstrate that this space is the permutation invariant sector of a module over the ring of polynomials of the Mandelstam invariants s, t and u. We construct these modules for every value of the spacetime dimension D, and so explicitly count and parameterize the most general four photon and four graviton S-matrix at any given derivative order. We also explicitly list the local Lagrangians that give rise to these S-matrices. We then conjecture that the Regge growth of S-matrices in all physically acceptable classical theories is bounded by s 2 at fixed t. A four parameter subset of the polynomial photon S-matrices constructed above satisfies this Regge criterion. For gravitons, on the other hand, no polynomial addition to the Einstein S-matrix obeys this bound for D ≤ 6. For D ≥ 7 there is a single six derivative polynomial Lagrangian consistent with our conjectured Regge growth bound. Our conjecture thus implies that the Einstein four graviton S-matrix does not admit any physically acceptable polynomial modifications for D ≤ 6. A preliminary analysis also suggests that every finite sum of pole exchange contributions to four graviton scattering also such violates our conjectured Regge growth bound, at least when D ≤ 6, even when the exchanged particles have low spin.

Our aim was to find out the association between nasal smear eosinophil count and allergic rhinitis (AR) and to determine a cutoff value that is significant for a diagnosis of AR. We also wanted to determine whether this count is related to the predominant symptoms, duration, or type and severity of AR, or to the presence of coexisting asthma. We selected 100 patients with a clinical diagnosis of allergic rhinitis across all age groups and an equal number of age-and sex-matched controls for the study. Their nasal smear eosinophil counts were recorded in terms of the number of eosinophils per high-power field (HPF). All patients were then clinically assessed for asthma and underwent spirometry. The data were recorded and appropriate statistical analysis done. The difference in the mean eosinophil counts of patients with AR and controls was found to be statistically significant (p = 0.000). A nasal smear eosinophil count of >0.3 per HPF had a 100% specificity and a 100% positive predictive value for AR. Asthma was associated with allergic rhinitis in 40% of patients; an association was not found between nasal smear eosinophil count and the symptoms, duration, type, and severity of allergic rhinitis or coexistent asthma. We conclude that an eosinophil count of >0.3 per HPF in nasal smears is a highly specific criterion for the diagnosis of AR. However, nasal smear eosinophil counts are poor indicators of the degree, duration, or type of upper or associated lower airway inflammation due to allergy.

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