Factorized finite-size Ising model spin matrix elements from Separation of Variables

Using the Sklyanin-Kharchev-Lebedev method of Separation of Variables adapted to the cyclic Baxter--Bazhanov--Stroganov or $\tau^{(2)}$-model, we derive factorized formulae for general finite-size Ising model spin matrix elements, proving a recent conjecture by Bugrij and Lisovyy

An immunotherapy survivor population: health-related quality of life and toxicity in patients with metastatic melanoma treated with immune checkpoint inhibitors

© The Author(s) 2019. This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.Purpose The immune checkpoint inhibitors (ICIs) have resulted in subgroups of patients with metastatic melanoma achievinghigh-quality durable responses. Metastatic melanoma survivors are a new population in the era of cancer survivorship. The aimofthis study was to evaluate metastatic melanoma survivors in terms of health-related quality of life (HRQoL), immune-relatedadverse events (irAEs) and exposure to immunosuppressive agents in a large single centre in the UK.Methods We defined the survivor population as patients with a diagnosis of metastatic melanoma who achieved a durableresponse to an ICI and had been followed-up for a minimum of 12 months from initiation of ICI without disease progression.HRQoL was assessed using SF-36. Electronic health records were accessed to collect data on demographics, treatments, irAEsand survival. HRQoL data was compared with two norm-based datasets.Results Eighty-four metastatic melanoma survivors were eligible and 87% (N = 73) completed the SF-36. ICI-related toxicity ofany grade occurred in 92%of patients and 43%had experienced a grade 3 or 4 toxicity. Almost half (49%) of the patients requiredsteroids for the treatment of ICI-related toxicity, whilst 14% required treatment with an immunosuppressive agent beyondsteroids.Melanoma survivors had statistically significant lower HRQoL scores with regard to physical, social and physical rolefunctioning and general health compared with the normative population. There was a trend towards inferior scores in patientswith previous exposure to ipilimumab compared with those never exposed to ipilimumab.Conclusions Our results show that metastatic melanoma survivors have potentially experienced significant ICI-related toxicityand experience significant impairments in specific HRQoL domains. Future service planning is required to meet this population’sunique survivorship needs.Peer reviewe

Logarithmic perturbation theory for quasinormal modes

Logarithmic perturbation theory (LPT) is developed and applied to quasinormal modes (QNMs) in open systems. QNMs often do not form a complete set, so LPT is especially convenient because summation over a complete set of unperturbed states is not required. Attention is paid to potentials with exponential tails, and the example of a Poschl-Teller potential is briefly discussed. A numerical method is developed that handles the exponentially large wavefunctions which appear in dealing with QNMs.Comment: 24 pages, 4 Postscript figures, uses ioplppt.sty and epsfig.st

Duality and Symmetry in Chiral Potts Model

We discover an Ising-type duality in the general $N$-state chiral Potts model, which is the Kramers-Wannier duality of planar Ising model when N=2. This duality relates the spectrum and eigenvectors of one chiral Potts model at a low temperature (of small $k'$) to those of another chiral Potts model at a high temperature (of $k'^{-1}$). The $\tau^{(2)}$-model and chiral Potts model on the dual lattice are established alongside the dual chiral Potts models. With the aid of this duality relation, we exact a precise relationship between the Onsager-algebra symmetry of a homogeneous superintegrable chiral Potts model and the $sl_2$-loop-algebra symmetry of its associated spin-$\frac{N-1}{2}$ XXZ chain through the identification of their eigenstates.Comment: Latex 34 pages, 2 figures; Typos and misprints in Journal version are corrected with minor changes in expression of some formula

Radiosurgery for brainstem metastases with and without whole brain radiotherapy: clinical series and literature review

Objective The objective of this study was to investigate outcomes for patients with brainstem metastases treated with stereotactic radiosurgery (SRS). Methods Patients with brainstem metastases treated with SRS between April 2006 and June 2012 were identified from a prospective database. Patient and treatment-related factors were recorded. Kaplan-Meier analysis was used to calculate survival and freedom from local and distant brain progression. Univariate and multivariate Cox regression was used to identify factors important for overall survival. Results In total, 44 patients received SRS for 48 brainstem metastases of whom 33 (75 %) also received whole brain radiotherapy (WBRT): 23 patients (52 %) WBRT prior to SRS, 6 (13.6 %) WBRT concurrently with SRS and 4 (9.0 %) WBRT after SRS. Eight patients received a second course ofWBRTat further progression. Median target volume was 1.33 cc (range 0.04–12.17) and median prescribed marginal dose was 15 Gy (range 10–22). There were four cases of local failure, and 6-month and 1-year freedom from local failure was 84.6 and 76.9 %, respectively. Median overall survival (OS) was 5.4 months. There were four cases of radionecrosis, 2 (4.8 %) of which were symptomatic. The absence of external beam brain radiotherapy (predominantly WBRT) showed a trend towards improved OS on univariate analysis. Neither local nor distant brain failure significantly impacted OS. Conclusion This retrospective series of patients treated with SRS for brainstem metastases, largely in combination with at least one course of WBRT, demonstrates that this approach is safe and results in good local control. In this cohort, no variables significantly impacted OS, including intracranial control

On τ(2)\tau^{(2)}-model in Chiral Potts Model and Cyclic Representation of Quantum Group Uq(sl2)U_q(sl_2)

We identify the precise relationship between the five-parameter $\tau^{(2)}$-family in the $N$-state chiral Potts model and XXZ chains with $U_q (sl_2)$-cyclic representation. By studying the Yang-Baxter relation of the six-vertex model, we discover an one-parameter family of $L$-operators in terms of the quantum group $U_q (sl_2)$. When $N$ is odd, the $N$-state $\tau^{(2)}$-model can be regarded as the XXZ chain of $U_{\sf q} (sl_2)$ cyclic representations with ${\sf q}^N=1$. The symmetry algebra of the $\tau^{(2)}$-model is described by the quantum affine algebra $U_{\sf q} (\hat{sl}_2)$ via the canonical representation. In general for an arbitrary $N$, we show that the XXZ chain with a $U_q (sl_2)$-cyclic representation for $q^{2N}=1$ is equivalent to two copies of the same $N$-state $\tau^{(2)}$-model.Comment: Latex 11 pages; Typos corrected, Minor changes for clearer presentation, References added and updated-Journal versio

Isomonodromic deformation theory and the next-to-diagonal correlations of the anisotropic square lattice Ising model

In 1980 Jimbo and Miwa evaluated the diagonal two-point correlation function of the square lattice Ising model as a $\tau$-function of the sixth Painlev\'e system by constructing an associated isomonodromic system within their theory of holonomic quantum fields. More recently an alternative isomonodromy theory was constructed based on bi-orthogonal polynomials on the unit circle with regular semi-classical weights, for which the diagonal Ising correlations arise as the leading coefficient of the polynomials specialised appropriately. Here we demonstrate that the next-to-diagonal correlations of the anisotropic Ising model are evaluated as one of the elements of this isomonodromic system or essentially as the Cauchy-Hilbert transform of one of the bi-orthogonal polynomials.Comment: 11 pages, 1 figur

Form factors and complete spectrum of XXX antiperiodic higher spin chains by quantum separation of variables

The antiperiodic transfer matrix associated to higher spin representations of the rational 6-vertex Yang-Baxter algebra is analyzed by generalizing the approach introduced recently in [1], for the cyclic representations, in [2], for the spin-1/2 highest weight representations, and in [3], for the spin 1/2 representations of the reflection algebra. Here, we derive the complete characterization of the transfer matrix spectrum and we prove its simplicity in the framework of Sklyanin's quantum separation of variables (SOV). Then, the characterization of local operators by Sklyanin's quantum separate variables and the expression of the scalar products of separates states by determinant formulae allow to compute the form factors of the local spin operators by one determinant formulae similar to the scalar product ones. Finally, let us comment that these results represent the SOV analogous in the antiperiodic higher spin XXX quantum chains of the results obtained for the periodic chains in [4] in the framework of the algebraic Bethe ansatz.Comment: 20 pages, introduction improved by taking into account some relevant references on the spectrum of the model under general boundary conditions, no further relevant modification