Entanglement and criticality in translational invariant harmonic lattice systems with finite-range interactions

We discuss the relation between entanglement and criticality in translationally invariant harmonic lattice systems with non-randon, finite-range interactions. We show that the criticality of the system as well as validity or break-down of the entanglement area law are solely determined by the analytic properties of the spectral function of the oscillator system, which can easily be computed. In particular for finite-range couplings we find a one-to-one correspondence between an area-law scaling of the bi-partite entanglement and a finite correlation length. This relation is strict in the one-dimensional case and there is strog evidence for the multi-dimensional case. We also discuss generalizations to couplings with infinite range. Finally, to illustrate our results, a specific 1D example with nearest and next-nearest neighbor coupling is analyzed.Comment: 4 pages, one figure, revised versio

Diffusion on non exactly decimable tree-like fractals

We calculate the spectral dimension of a wide class of tree-like fractals by solving the random walk problem through a new analytical technique, based on invariance under generalized cutting-decimation transformations. These fractals are generalizations of the NTD lattices and they are characterized by non integer spectral dimension equal or greater then 2, non anomalous diffusion laws, dynamical dimension splitting and absence of phase transitions for spin models.Comment: 5 pages Latex, 3 figures (figures are poscript files

Percolation model for nodal domains of chaotic wave functions

Nodal domains are regions where a function has definite sign. In recent paper [nlin.CD/0109029] it is conjectured that the distribution of nodal domains for quantum eigenfunctions of chaotic systems is universal. We propose a percolation-like model for description of these nodal domains which permits to calculate all interesting quantities analytically, agrees well with numerical simulations, and due to the relation to percolation theory opens the way of deeper understanding of the structure of chaotic wave functions.Comment: 4 pages, 6 figures, Late

Numerical indications of a q-generalised central limit theorem

We provide numerical indications of the $q$-generalised central limit theorem that has been conjectured (Tsallis 2004) in nonextensive statistical mechanics. We focus on $N$ binary random variables correlated in a {\it scale-invariant} way. The correlations are introduced by imposing the Leibnitz rule on a probability set based on the so-called $q$-product with $q \le 1$. We show that, in the large $N$ limit (and after appropriate centering, rescaling, and symmetrisation), the emerging distributions are $q_e$-Gaussians, i.e., $p(x) \propto [1-(1-q_e) \beta(N) x^2]^{1/(1-q_e)}$, with $q_e=2-\frac{1}{q}$, and with coefficients $\beta(N)$ approaching finite values $\beta(\infty)$. The particular case $q=q_e=1$ recovers the celebrated de Moivre-Laplace theorem.Comment: Minor improvements and corrections have been introduced in the new version. 7 pages including 4 figure

The Counterpart Principle of Analogical Support by Structural Similarity

We propose and investigate an Analogy Principle in the context of Unary Inductive Logic based on a notion of support by structural similarity which is often employed to motivate scientific conjectures

Uniqueness of the solution to inverse scattering problem with scattering data at a fixed direction of the incident wave

Let $q(x)$ be real-valued compactly supported sufficiently smooth function. It is proved that the scattering data $A(\beta,\alpha_0,k)$ $\forall \beta\in S^2$, $\forall k>0,$ determine $q$ uniquely. Here $\alpha_0\in S^2$ is a fixed direction of the incident plane wave

An insurance value modeling approach that captures the wider value of a novel antimicrobial to health systems, patients, and the population.

Background: Traditional health economic evaluations of antimicrobials currently underestimate their value to wider society. They can be supplemented by additional value elements including insurance value, which captures the value of an antimicrobial in preventing or mitigating impacts of adverse risk events. Despite being commonplace in other sectors, constituents of the impacts and approaches for estimating insurance value have not been investigated. Objectives: This study assessed the insurance value of a novel gram-negative antimicrobial from operational healthcare, wider population health, productivity, and informal care perspectives. Methods: A novel mixed-methods approach was used to model insurance value in the United Kingdom: (1) literature review and multidisciplinary expert workshops to identify risk events for 4 relevant scenarios: ward closures, unavoidable shortage of conventional antimicrobials, viral respiratory pandemics, and catastrophic antimicrobial resistance (AMR); (2) parameterizing mitigable costs and frequencies of risk events across perspectives and scenarios; (3) estimating insurance value through a Monte Carlo simulation model for extreme events and a dynamic disease transmission model. Results: The mean insurance value across all scenarios and perspectives over 10 years in the UK was £718 million, should AMR remain unchanged, where only £134 million related to operational healthcare costs. It would be 50%-70% higher if AMR steadily increased or if a more risk-averse view (1-in-10 year downside) of future events is taken. Discussion: The overall insurance value if AMR remains at current levels (a conservative projection), is over 5 times greater than insurance value from just the operational healthcare costs perspective, traditionally the sole perspective used in health budgeting. Insurance value was generally larger for nationwide or universal (catastrophic AMR, pandemic, and conventional antimicrobial shortages) rather than localized (ward closure) scenarios, across perspectives. Components of this insurance value match previously published estimates of operational costs and mortality impacts. Conclusions: Insurance value of novel antimicrobials can be systematically modeled and substantially augments their traditional health economic value in normal circumstances. These approaches are generalizable to similar health interventions and form a framework for health systems and governments to capture broader value in health technology assessments, improve healthcare access, and increase resilience by planning for adverse scenarios

Phase transitions with four-spin interactions

Using an extended Lee-Yang theorem and GKS correlation inequalities, we prove, for a class of ferromagnetic multi-spin interactions, that they will have a phase transition(and spontaneous magnetization) if, and only if, the external field $h=0$ (and the temperature is low enough). We also show the absence of phase transitions for some nonferromagnetic interactions. The FKG inequalities are shown to hold for a larger class of multi-spin interactions

Random walks on graphs: ideas, techniques and results

Random walks on graphs are widely used in all sciences to describe a great variety of phenomena where dynamical random processes are affected by topology. In recent years, relevant mathematical results have been obtained in this field, and new ideas have been introduced, which can be fruitfully extended to different areas and disciplines. Here we aim at giving a brief but comprehensive perspective of these progresses, with a particular emphasis on physical aspects.Comment: LateX file, 34 pages, 13 jpeg figures, Topical Revie