Decomposable Subspaces, Linear Sections of Grassmann Varieties, and Higher Weights of Grassmann Codes

Given a homogeneous component of an exterior algebra, we characterize those subspaces in which every nonzero element is decomposable. In geometric terms, this corresponds to characterizing the projective linear subvarieties of the Grassmann variety with its Plucker embedding. When the base field is finite, we consider the more general question of determining the maximum number of points on sections of Grassmannians by linear subvarieties of a fixed (co)dimension. This corresponds to a known open problem of determining the complete weight hierarchy of linear error correcting codes associated to Grassmann varieties. We recover most of the known results as well as prove some new results. In the process we obtain, and utilize, a simple generalization of the Griesmer-Wei bound for arbitrary linear codes.Comment: 16 page

Specific and non-specific biomarkers in neuroendocrine gastroenteropancreatic tumors

The diagnosis of neuroendocrine tumors (NETs) is a challenging task: Symptoms are rarely specific, and clinical manifestations are often evident only when metastases are already present. However, several bioactive substances secreted by NETs can be included for diagnostic, prognostic, and predictive purposes. Expression of these substances differs between different NETs according to the tumor hormone production. Gastroenteropancreatic (GEP) NETs originate from the diffuse neuroendocrine system of the gastrointestinal tract and pancreatic islets cells: These tumors may produce many non-specific and specific substances, such as chromogranin A, insulin, gastrin, glucagon, and serotonin, which shape the clinical manifestations of the NETs. To provide an up-to-date reference concerning the different biomarkers, as well as their main limitations, we reviewed and summarized existing literature

Epidemiology of simultaneous medullary and papillary thyroid carcinomas (MTC/PTC): An Italian multicenter study

Background: The concomitant presence of papillary thyroid cancer (PTC) and medullary TC (MTC) is rare. In this multicentric study, we documented the epidemiological characteristics, disease conditions and clinical outcome of patients with simultaneous MTC/PTC. Methods: We collected data of patients with concomitant MTC/PTC at 14 Italian referral centers. Results: In total, 183 patients were enrolled. Diagnosis was mostly based on cytological examination (n = 58, 32%). At diagnosis, in the majority of cases, both PTC (n = 142, 78%) and MTC (n = 100, 54%) were at stage I. However, more cases of stage II\u2013IV were reported with MTC (stage IV: n = 27, 15%) compared with PTC (n = 9, 5%). Information on survival was available for 165 patients: 109 patients (66%) were disease-free for both PTC and MTC at the last follow-up. Six patients died from MTC. Median time to progression was 123 months (95% confidence interval (CI): 89.3\u2013156.7 months). Overall, 45% of patients were disease-free after >10 years from diagnosis (125 months); this figure was 72.5% for PTC and 51.1% for MTC. Conclusions: When MTC and PTC are concurrent, the priority should be given to the management of MTC since this entity appears associated with the most severe impact on prognosis

An Algebra of Pieces of Space -- Hermann Grassmann to Gian Carlo Rota

We sketch the outlines of Gian Carlo Rota's interaction with the ideas that Hermann Grassmann developed in his Ausdehnungslehre of 1844 and 1862, as adapted and explained by Giuseppe Peano in 1888. This leads us past what Rota variously called 'Grassmann-Cayley algebra', or 'Peano spaces', to the Whitney algebra of a matroid, and finally to a resolution of the question "What, really, was Grassmann's regressive product?". This final question is the subject of ongoing joint work with Andrea Brini, Francesco Regonati, and William Schmitt. The present paper was presented at the conference "The Digital Footprint of Gian-Carlo Rota: Marbles, Boxes and Philosophy" in Milano on 17 Feb 2009. It will appear in proceedings of that conference, to be published by Springer Verlag.Comment: 28 page

A rare case of pituitary melanoma metastasis: a dramatic and prolonged response to dabrafenib-trametinib therapy

Introduction: Pituitary metastases (PM) are rare events and to date only very few cases of melanoma PM have been described in literature up to now. Case Presentation: We describe the clinical history of a 33-year-old male patient who underwent surgical excision of an inter-scapular melanoma in 2008. The subsequent follow-up was negative for ~10 years. In September 2018, due to the onset of a severe headache, the patient underwent a brain magnetic resonance imaging, which showed an expansive mass in the saddle and suprasellar region with a maximum diameter of 17 mm. Pituitary function tests and visual field were normal. Worsening of the headache and the appearance of a left eye ptosis led the patient to surgical removal of the lesion in October 2018. The histological examination unexpectedly showed metastasis of the melanoma. Post-operative hormonal assessment showed secondary hypothyroidism and hypoadrenalism, which were both promptly treated, and a mild hypogonadism. Three months after surgery, a sellar MRI showed a persistent, increased pituitary mass (3 cm of diameter); fluorine-18-fluorodeoxyglucose positron emission tomography/computed tomography (18F-FDG PET/CT) detected an increased radiopharmaceutical uptake in the sellar region. Due to the persistence of the disease and the evidence of a BRAF V600E mutation, in February 2019, the patient underwent a combined treatment with dabrafenib (a BRAF inhibitor) and trametinib (mitogen-activated extracellular signal-regulate kinase inhibitor). Sellar MRI performed 6 months later showed no evidence of mass in the sellar region. The patient was in a good clinical condition and did not complain of headaches or other symptoms; there were no significant side-effects from the anticancer therapy. After 13 months of treatment, the patient showed no recurrence of the disease on morphological imaging. Anticancer therapy was confirmed, replacement therapies with hydrocortisone and levothyroxine continued and the pituitary-gonadal axis was restored. Conclusion: This is a very interesting case, both for the rarity of the pituitary melanoma metastasis and for the singular therapeutic course carried out by the patient. This is the first case of a pituitary melanoma metastasis with BRAF mutation, successfully treated with the combination of dabrafenib and trametinib after incomplete surgical removal

Case Report: Ipilimumab-Induced Panhypophysitis: An Infrequent Occurrence and Literature Review

BackgroundImmune checkpoint inhibitors (ICIs), by unleashing the anticancer response of the immune system, can improve survival of patients affected by several malignancies, but may trigger a broad spectrum of adverse events, including autoimmune hypophysitis. ICI-related hypophysitis mainly manifests with anterior hypopituitarism, while the simultaneous involvement of both anterior and posterior pituitary (i.e., panhypophysitis) has rarely been described.Case PresentationIn June 2015, a 64-year-old man affected by liver metastases of a uveal melanoma was referred to us due to polyuria and polydipsia. Two months prior, he had started ipilimumab therapy (3 mg/kg iv every 21 days). The treatment was well-tolerated (only mild asthenia and diarrhea were reported). A few days before the fourth cycle, the patient complained of intense headaches, profound fatigue, nocturia, polyuria (up to 10 L urine/daily), and polydipsia. Laboratory tests were consistent with adrenal insufficiency, hypothyroidism, and transient central diabetes insipidus. The pituitary MRI showed an enlarged gland with microinfarcts, while the hypophyseal stalk was normal, and the neurohypophyseal 'bright signal' in T1 sequences was not detected. The treatment included dexamethasone (then cortisone acetate at replacement dose), desmopressin, and levothyroxine. Within the next five days, the symptoms resolved, and blood pressure, electrolytes, glucose, and urinalysis were stable within the normal ranges; desmopressin was discontinued while cortisone acetate and levothyroxine were maintained. The fourth ipilimumab dose was entirely administered in the absence of further side effects.ConclusionAs ICIs are increasingly used as anticancer agents, the damage to anterior and/or posterior pituitary can be progressively encountered by oncologists and endocrinologists in their clinical practice. Patients on ICIs and their caregivers should be informed about that risk and be empowered to alert the referring specialists early, at the onset of panhypopituitarism symptoms, including polyuria/polydipsia

Indirect basal metabolism estimation in tailoring recombinant human TSH administration in patients affected by differentiated thyroid cancer: A hypothesis-generating study

Purpose: Recombinant human TSH (rhTSH) is currently used in follow-up of patients affected by differentiated thyroid cancer (DTC). Age, sex, weight, body mass index, body surface area (BSA) and renal function are known factors affecting serum TSH peak levels, but the proper rhTSH dose to deliver to single patient remains elusive. In this study, the correlations of basal metabolic rates with serum TSH peak following rhTSH administration were investigated.Methods: We evaluated 221 patients affected by thyroid cancer that received a standard dose rhTSH. Blood samples were collected at pre-established time points. Data on body weight, height, and BSA were collected. The Mifflin-St Jeor and Fleisch equations were used to assess basal metabolism.Results: The median value (range) of serum TSH peaks was 142 +/- 53 mu U/ml. Serum TSH peaks were significantly lower in males than in females (p = 0.04). TSH values also increased with age. Data showed a significant decrease of TSH peak levels at day 3 from the administration of rhTSH when basal metabolic rates increased (p = 0.002 and p = 0.009, respectively). Similar findings were observed at day 5 (p = 0.004 and p = 0.04, respectively). A multivariate analysis of several factors revealed that patients' basal metabolism (obtained using the Mifflin-St Jeor but not Fleisch equation) predicts serum TSH level peak at day 3 (p < 0.001). These results were used to generate a new formula based on Mifflin-StJeor equation which reveals as a promising tool in tailoring rhTSH dose.Conclusion: Basal metabolism appears an improving factor in tailoring diagnostic rhTSH dose in patients affected by DTC

A Grassmann integral equation

The present study introduces and investigates a new type of equation which is called Grassmann integral equation in analogy to integral equations studied in real analysis. A Grassmann integral equation is an equation which involves Grassmann integrations and which is to be obeyed by an unknown function over a (finite-dimensional) Grassmann algebra G_m. A particular type of Grassmann integral equations is explicitly studied for certain low-dimensional Grassmann algebras. The choice of the equation under investigation is motivated by the effective action formalism of (lattice) quantum field theory. In a very general setting, for the Grassmann algebras G_2n, n = 2,3,4, the finite-dimensional analogues of the generating functionals of the Green functions are worked out explicitly by solving a coupled system of nonlinear matrix equations. Finally, by imposing the condition G[{\bar\Psi},{\Psi}] = G_0[{\lambda\bar\Psi}, {\lambda\Psi}] + const., 0<\lambda\in R (\bar\Psi_k, \Psi_k, k=1,...,n, are the generators of the Grassmann algebra G_2n), between the finite-dimensional analogues G_0 and G of the (``classical'') action and effective action functionals, respectively, a special Grassmann integral equation is being established and solved which also is equivalent to a coupled system of nonlinear matrix equations. If \lambda \not= 1, solutions to this Grassmann integral equation exist for n=2 (and consequently, also for any even value of n, specifically, for n=4) but not for n=3. If \lambda=1, the considered Grassmann integral equation has always a solution which corresponds to a Gaussian integral, but remarkably in the case n=4 a further solution is found which corresponds to a non-Gaussian integral. The investigation sheds light on the structures to be met for Grassmann algebras G_2n with arbitrarily chosen n.Comment: 58 pages LaTeX (v2: mainly, minor updates and corrections to the reference section; v3: references [4], [17]-[21], [39], [46], [49]-[54], [61], [64], [139] added

Renormalization of total sets of states into generalized bases with a resolution of the identity

YesA total set of states for which we have no resolution of the identity (a `pre-basis'), is considered in a finite dimensional Hilbert space. A dressing formalism renormalizes them into density matrices which resolve the identity, and makes them a `generalized basis', which is practically useful. The dresssing mechanism is inspired by Shapley's methodology in cooperative game theory, and it uses Mobius transforms. There is non-independence and redundancy in these generalized bases, which is quantifi ed with a Shannon type of entropy. Due to this redundancy, calculations based on generalized bases, are sensitive to physical changes and robust in the presence of noise. For example, the representation of an arbitrary vector in such generalized bases, is robust when noise is inserted in the coeffcients. Also in a physical system with ground state which changes abruptly at some value of the coupling constant, the proposed methodology detects such changes, even when noise is added to the parameters in the Hamiltonian of the system