Exact conserved quantities on the cylinder II: off-critical case

With the aim of exploring a massive model corresponding to the perturbation of the conformal model [hep-th/0211094] the nonlinear integral equation for a quantum system consisting of left and right KdV equations coupled on the cylinder is derived from an integrable lattice field theory. The eigenvalues of the energy and of the transfer matrix (and of all the other local integrals of motion) are expressed in terms of the corresponding solutions of the nonlinear integral equation. The analytic and asymptotic behaviours of the transfer matrix are studied and given.Comment: enlarged version before sending to jurnal, second part of hep-th/021109

From finite geometry exact quantities to (elliptic) scattering amplitudes for spin chains: the 1/2-XYZ

Initially, we derive a nonlinear integral equation for the vacuum counting function of the spin 1/2-XYZ chain in the {\it disordered regime}, thus paralleling similar results by Kl\"umper \cite{KLU}, achieved through a different technique in the {\it antiferroelectric regime}. In terms of the counting function we obtain the usual physical quantities, like the energy and the transfer matrix (eigenvalues). Then, we introduce a double scaling limit which appears to describe the sine-Gordon theory on cylindrical geometry, so generalising famous results in the plane by Luther \cite{LUT} and Johnson et al. \cite{JKM}. Furthermore, after extending the nonlinear integral equation to excitations, we derive scattering amplitudes involving solitons/antisolitons first, and bound states later. The latter case comes out as manifestly related to the Deformed Virasoro Algebra of Shiraishi et al. \cite{SKAO}. Although this nonlinear integral equations framework was contrived to deal with finite geometries, we prove it to be effective for discovering or rediscovering S-matrices. As a particular example, we prove that this unique model furnishes explicitly two S-matrices, proposed respectively by Zamolodchikov \cite{ZAMe} and Lukyanov-Mussardo-Penati \cite{LUK, MP} as plausible scattering description of unknown integrable field theories.Comment: Article, 41 pages, Late

Exact conserved quantities on the cylinder I: conformal case

The nonlinear integral equations describing the spectra of the left and right (continuous) quantum KdV equations on the cylinder are derived from integrable lattice field theories, which turn out to allow the Bethe Ansatz equations of a twisted ``spin -1/2'' chain. A very useful mapping to the more common nonlinear integral equation of the twisted continuous spin $+1/2$ chain is found. The diagonalization of the transfer matrix is performed. The vacua sector is analysed in detail detecting the primary states of the minimal conformal models and giving integral expressions for the eigenvalues of the transfer matrix. Contact with the seminal papers \cite{BLZ, BLZ2} by Bazhanov, Lukyanov and Zamolodchikov is realised. General expressions for the eigenvalues of the infinite-dimensional abelian algebra of local integrals of motion are given and explicitly calculated at the free fermion point.Comment: Journal version: references added and minor corrections performe

Reliable Peer-to-Peer Access for Italian Citizens to Digital Government Services on the Internet

In the delivery of e-government services to citizens it should be clear that the viewpoint cannot simply be the standard one of client-supplier commonly used to provide services on the Internet. In a modern society it has rather to be the peer-to-peer approach which is typical of democracies, where institutions are equal to citizens in front of the law. But this is not yet a widely accepted standpoint in digital government efforts going on in many advanced countries in the world. Italian government, in its ever increasing effort to provide citizens with easier access to online government services, has instead adopted and is pursuing this symmetric approach, which is going to represent a fundamental tool in the ongoing march towards e-democracy. In this paper we describe the organizations involved in the process and the Information Technology (IT) infrastructure enabling the effective management of the whole process while ensuring the mandatory security functions in a democratic manner. Organizational complexity lies in the distribution of responsibilities for the management of people’s personal data among the more than 8000 Italian Municipalities and the need of keeping a centralized control on all processes dealing with identity of people. Technical complexity stems from the need of efficiently supporting this distribution of responsibilities while ensuring, at the same time, interoperability of IT-based systems independent of technical choices of the organizations involved, and fulfillment of privacy constraints. The IT architecture defined for this purpose features a clear separation between security services, provided at an infrastructure level, and application services, exposed on the Internet as Web Services

Scaling Functions in the Odd Charge Sector of Sine-Gordon/Massive Thirring Theory

A non-linear integral equation (NLIE) governing the finite size effects of excited states of even topological charge in the sine-Gordon (sG) / massive Thirring (mTh) field theory, deducible from a light-cone lattice formulation of the model, has been known for some time. In this letter we conjecture an extension of this NLIE to states with odd topological charge, thus completing the spectrum of the theory. The scaling functions obtained as solutions to our conjectured NLIE are compared successfully with Truncated Conformal Space data and the construction is shown to be compatible with all other facts known about the local Hilbert spaces of sG and mTh models. With the present results we have achieved a full control over the finite size behaviour of energy levels of sG/mTh theory.Comment: LaTeX2e, 12 pp., 3 eps figs. Remarks on locality adde

On Uniquely Closable and Uniquely Typable Skeletons of Lambda Terms

Uniquely closable skeletons of lambda terms are Motzkin-trees that predetermine the unique closed lambda term that can be obtained by labeling their leaves with de Bruijn indices. Likewise, uniquely typable skeletons of closed lambda terms predetermine the unique simply-typed lambda term that can be obtained by labeling their leaves with de Bruijn indices. We derive, through a sequence of logic program transformations, efficient code for their combinatorial generation and study their statistical properties. As a result, we obtain context-free grammars describing closable and uniquely closable skeletons of lambda terms, opening the door for their in-depth study with tools from analytic combinatorics. Our empirical study of the more difficult case of (uniquely) typable terms reveals some interesting open problems about their density and asymptotic behavior. As a connection between the two classes of terms, we also show that uniquely typable closed lambda term skeletons of size $3n+1$ are in a bijection with binary trees of size $n$.Comment: Pre-proceedings paper presented at the 27th International Symposium on Logic-Based Program Synthesis and Transformation (LOPSTR 2017), Namur, Belgium, 10-12 October 2017 (arXiv:1708.07854

MRI correlates of Parkinson's disease progression: A voxel based morphometry study

We investigated structural brain differences between a group of early-mild PD patients at different phases of the disease and healthy subjects using voxel-based morphometry (VBM). 20 mild PD patients compared to 15 healthy at baseline and after 2 years of follow-up. VBM is a fully automated technique, which allows the identification of regional differences in the gray matter enabling an objective analysis of the whole brain between groups of subjects. With respect to controls, PD patients exhibited decreased GM volumes in right putamen and right parietal cortex. After 2 years of disease, the same patients confirmed GM loss in the putamen and parietal cortex; a significant difference was also observed in the area of pedunculopontine nucleus (PPN) and in the mesencephalic locomotor region (MLR). PD is associated with brain morphological changes in cortical and subcortical structures. The first regions to be affected in PD seem to be the parietal cortex and the putamen. A third structure that undergoes atrophy is the part of the inferior-posterior midbrain, attributable to the PPN and MLR. Our findings provide new insight into the brain involvement in PD and could contribute to a better understanding of the sequence of events occurring in these patients

Primary antiphospholipid syndrome during aromatase inhibitors therapy: A case report and review of the literature

RATIONALE: Aromatase inhibitors (AIs) are a class of drugs widely used in the treatment of estrogen sensitive breast and ovarian cancer which convert testosterone to estradiol and androstenedione to estrogen. The AIs of third generation, including anastrazole, letrozole and exemestane, have actually become the standard of care of estrogen-receptor-positive breast cancer in menopausal women and are recommended as adjuvant treatment after surgery in place of/or following tamoxifen. Their main side-effects include reduction in bone mineral density, occurrence of menopausal manifestations and development of musculoskeletal symptoms which are, usually, transient, but sometimes evolve into a typical form of arthritis, such as rheumatoid arthritis (RA). Recently, a pathogenic linkage with other autoimmunity diseases, such as Sjogren syndrome (SjS), anti-synthetase antibody syndrome (ASAS), systemic sclerosis (SS) and subacute cutaneous lupus erythematosus (SCLE), was also described. PATIENT CONCERNS: Here, we report the first case of a patient with primary antiphospholipid syndrome (APS) developed during treatment with anastrazole. DIAGNOSIS: The patient developed a sudden onset of speech disturbance and disorientation, due to ischemic lesions, after 6 months of AIs therapy and the laboratory examination showed the positivity of anti-Cardiolipin antibodies, anti-\u3b22 Glycoprotein 1 antibodies and Lupus Anticoagulant, so a certain diagnosis of APS was achieved. INTERVENTIONS: The patient was treated with warfarin associated to hydroxychloroquine and monthly cycles of low doses intravenous immunoglobulins. OUTCOMES: A good control of the disease was obtained despite the continuation of anastrazole; the patient's clinical and laboratory situation remained not modified after AIs withdrawal. LESSONS: We discussed the possible role of anastrazole treatment in inducing APS in our patient, reporting the available literature data about the association between AIs treatment and autoimmune diseases. Furthermore, we analyzed the mechanism of action of estrogens in the pathophysiology of autoimmune rheumatic disorder