Asymptotics of block Toeplitz determinants and the classical dimer model

We compute the asymptotics of a block Toeplitz determinant which arises in the classical dimer model for the triangular lattice when considering the monomer-monomer correlation function. The model depends on a parameter interpolating between the square lattice ($t=0$) and the triangular lattice ($t=1$), and we obtain the asymptotics for $0<t\le 1$. For $0<t<1$ we apply the Szeg\"o Limit Theorem for block Toeplitz determinants. The main difficulty is to evaluate the constant term in the asymptotics, which is generally given only in a rather abstract form

Potts Model On Random Trees

We study the Potts model on locally tree-like random graphs of arbitrary degree distribution. Using a population dynamics algorithm we numerically solve the problem exactly. We confirm our results with simulations. Comparisons with a previous approach are made, showing where its assumption of uniform local fields breaks down for networks with nodes of low degree.Comment: 10 pages, 3 figure

BKT-like transition in the Potts model on an inhomogeneous annealed network

We solve the ferromagnetic q-state Potts model on an inhomogeneous annealed network which mimics a random recursive graph. We find that this system has the inverted Berezinskii--Kosterlitz--Thouless (BKT) phase transition for any $q \geq 1$, including the values $q \geq 3$, where the Potts model normally shows a first order phase transition. We obtain the temperature dependences of the order parameter, specific heat, and susceptibility demonstrating features typical for the BKT transition. We show that in the entire normal phase, both the distribution of a linear response to an applied local field and the distribution of spin-spin correlations have a critical, i.e. power-law, form.Comment: 7 pages, 3 figure

Abcesso Hepático Amebiano na Criança: Caso Clínico

A infecção humana por Entamoeba histolytica tem uma distribuição mundial, com zonas endémicas situadas nos trópicos. A manifestação mais comum é a colite amebiana. O fígado é o órgão extra-intestinal mais frequentemente envolvido. Descreve-se o caso clínico de uma criança do sexo masculino, com nove anos de idade, internada no decurso de quadro clínico de febre alta e dor abdominal, com nove dias de evolução; referia a ingestão de água não canalizada e contacto com cães. Ao exame físico destacava-se a presença de hepatomegalia e dor à palpação no hipocôndrio direito. Analiticamente apresentava parâmetros sugestivos de infecção com leucocitose e proteína C reactiva elevada. A ecografia hepática revelou lesão ocupando espaço. A serologia positiva para Entamoeba histolytica e o exame parasitológico das fezes com quistos deste mesmo parasita permitiram o diagnóstico etiológico. Após terapêutica com metronidazol, seguido de paramomicina, assistiu-se a uma boa evolução clínica. No inquérito epidemiológico, apesar de referência a ingestão de água não canalizada, não foi possível a demonstração inequívoca da fonte de infecção. A amebíase é uma entidade patológica pouco frequente em Portugal, mas não pode ser esquecida, principalmente se houver contexto epidemiológico (ingestão de alimentos e/ou água contaminados com quistos amebianos).info:eu-repo/semantics/publishedVersio

Phenomenological Models of Socio-Economic Network Dynamics

We study a general set of models of social network evolution and dynamics. The models consist of both a dynamics on the network and evolution of the network. Links are formed preferentially between 'similar' nodes, where the similarity is defined by the particular process taking place on the network. The interplay between the two processes produces phase transitions and hysteresis, as seen using numerical simulations for three specific processes. We obtain analytic results using mean field approximations, and for a particular case we derive an exact solution for the network. In common with real-world social networks, we find coexistence of high and low connectivity phases and history dependence.Comment: 11 pages, 8 figure

Correlations in interacting systems with a network topology

We study pair correlations in cooperative systems placed on complex networks. We show that usually in these systems, the correlations between two interacting objects (e.g., spins), separated by a distance $\ell$, decay, on average, faster than $1/(\ell z_\ell)$. Here $z_\ell$ is the mean number of the $\ell$-th nearest neighbors of a vertex in a network. This behavior, in particular, leads to a dramatic weakening of correlations between second and more distant neighbors on networks with fat-tailed degree distributions, which have a divergent number $z_2$ in the infinite network limit. In this case, only the pair correlations between the nearest neighbors are observable. We obtain the pair correlation function of the Ising model on a complex network and also derive our results in the framework of a phenomenological approach.Comment: 5 page

Non-locking screw insertion:No benefit seen if tightness exceeds 80% of the maximum torque

Screws are the most commonly used orthopaedic implant, however they are frequently overtightened when inserted. Using screw, bone and screw hole characteristics, maximum torque for a screw hole is predicted prior to insertion. Using this, optimum tightness as a percentage of the maximum torque is investigated as functions of compression and pullout forces. This data set provides the raw data for these investigations. The methodology is described in detail in the related manuscript: Fletcher, J., Ehrhardt, B., MacLeod, A., Whitehouse, M., Gill, H. & Preatoni, E. 2019. Non-locking screw insertion: No benefit seen if tightness exceeds 80% of the maximum torque. Clinical Biomechanics. https://doi.org/10.1016/j.clinbiomech.2019.07.009Biomechanical testing using juvenile bovine bone'R' software, v3.3.3 (R: A language and environment for statistical computing. R Foundation for Statistical Computing)

An inventory model with random replenishment quantities.

A single-period random demand inventory model is analysed under the assumption that the replenishment quantity is a random function of the amount ordered. The structure of optimal policies is characterized for linear ordering cost functions, both with and without a setup cost. Generalizations of base-stock policies and (s, S) policies are shown to be optimal. Closed form analytic expressions for optimal policies are obtained for the special ease of linear ordering cost and uniformly distributed demand. Optimal policies are compared with two heuristics in a more general demand environment. It is shown that a very simple heuristic policy performs quite well

Integral operators with the generalized sine-kernel on the real axis

The asymptotic properties of integral operators with the generalized sine kernel acting on the real axis are studied. The formulas for the resolvent and the Fredholm determinant are obtained in the large x limit. Some applications of the results obtained to the theory of integrable models are considered.Comment: 17 pages, 2 Postscript figures, submitted to Theor. Math. Phy

Enhancing joint reconstruction and segmentation with non-convex Bregman iteration

All imaging modalities such as computed tomography (CT), emission tomography and magnetic resonance imaging (MRI) require a reconstruction approach to produce an image. A common image processing task for applications that utilise those modalities is image segmentation, typically performed posterior to the reconstruction. We explore a new approach that combines reconstruction and segmentation in a unified framework. We derive a variational model that consists of a total variation regularised reconstruction from undersampled measurements and a Chan-Vese based segmentation. We extend the variational regularisation scheme to a Bregman iteration framework to improve the reconstruction and therefore the segmentation. We develop a novel alternating minimisation scheme that solves the non-convex optimisation problem with provable convergence guarantees. Our results for synthetic and real data show that both reconstruction and segmentation are improved compared to the classical sequential approach