Improving randomness characterization through Bayesian model selection

Nowadays random number generation plays an essential role in technology with important applications in areas ranging from cryptography, which lies at the core of current communication protocols, to Monte Carlo methods, and other probabilistic algorithms. In this context, a crucial scientific endeavour is to develop effective methods that allow the characterization of random number generators. However, commonly employed methods either lack formality (e.g. the NIST test suite), or are inapplicable in principle (e.g. the characterization derived from the Algorithmic Theory of Information (ATI)). In this letter we present a novel method based on Bayesian model selection, which is both rigorous and effective, for characterizing randomness in a bit sequence. We derive analytic expressions for a model's likelihood which is then used to compute its posterior probability distribution. Our method proves to be more rigorous than NIST's suite and the Borel-Normality criterion and its implementation is straightforward. We have applied our method to an experimental device based on the process of spontaneous parametric downconversion, implemented in our laboratory, to confirm that it behaves as a genuine quantum random number generator (QRNG). As our approach relies on Bayesian inference, which entails model generalizability, our scheme transcends individual sequence analysis, leading to a characterization of the source of the random sequences itself.Comment: 25 page

An Improved Upper Bound for the Ground State Energy of Fermion Lattice Models

We present an improved upper bound for the ground state energy of lattice fermion models with sign problem. The bound can be computed by numerical simulation of a recently proposed family of deformed Hamiltonians with no sign problem. For one dimensional models, we expect the bound to be particularly effective and practical extrapolation procedures are discussed. In particular, in a model of spinless interacting fermions and in the Hubbard model at various filling and Coulomb repulsion we show how such techniques can estimate ground state energies and correlation function with great accuracy.Comment: 5 pages, 5 figures; to appear in Physical Review

A Straightforward approach to multifunctional graphene

Graphene has been covalently functionalized through a one‐pot reductive pathway using graphite intercalation compounds (GICs), in particular KC8, with three different orthogonally protected derivatives of 4‐aminobenzylamine. This novel multifunctional platform exhibits excellent bulk functionalization homogeneity (Hbulk) and degree of addition while preserving the chemical functionalities of the organic addends through different protecting groups, namely: tert‐butyloxycarbonyl (Boc), benzyloxycarbonyl (Cbz) and phthalimide (Pht). We have employed (temperature‐dependent) statistical Raman spectroscopy (SRS), X‐ray photoelectron spectroscopy (XPS), magic angle spinning solid state 13C NMR (MAS‐NMR), and a characterization tool consisting of thermogravimetric analysis coupled with gas chromatography and mass spectrometry (TG‐GC‐MS) to unambiguously demonstrate the covalent binding and the chemical nature of the different molecular linkers. This work paves the way for the development of smart graphene‐based materials of great interest in biomedicine or electronics, to name a few, and will serve as a guide in the design of new 2D multifunctional materials

Phase diagram of the lattice Wess-Zumino model from rigorous lower bounds on the energy

We study the lattice N=1 Wess-Zumino model in two dimensions and we construct a sequence $\rho^{(L)}$ of exact lower bounds on its ground state energy density $\rho$, converging to $\rho$ in the limit $L\to\infty$. The bounds $\rho^{(L)}$ can be computed numerically on a finite lattice with $L$ sites and can be exploited to discuss dynamical symmetry breaking. The transition point is determined and compared with recent results based on large-scale Green Function Monte Carlo simulations with good agreement.Comment: 32 pages, 12 figure

Intratumoral Gold Nanoparticle-Enhanced CT Imaging: An in Vivo Investigation of Biodistribution and Retention

This study aims to evaluate the in vivo distribution of Gold Nanoparticles (GNPs) at different time points after intratumoral (IT) injection, exploiting their properties as contrast agents for Computed Tomography (CT). GNPs approximately 40 nm in diameter were synthesized with a surface plasmon peak at ~530 nm, capped with Bovine Serum Albumin (BSA) to improve colloidal stability, and characterized with standard methods. CT phantom imaging was performed to quantify X-ray attenuation as a function of GNP concentration and surface functionalization and to determine the appropriate particle dose for in vivo studies. Concentrated GNPs were intratumorally (IT) injected into Lewis Lung Carcinoma (LLC) solid tumors grown on the right flank of 6-week old female C57BL/6 mice. Ten days post-injection, follow up CT imaging was performed to assess the distribution and retention of the particles in the tumor. Using the CT attenuation quantification, images for each timepoint were segmented, and 3D volumes rendered, to conduct biodistribution analyses. The successful retention and permanence of the GNPs into the solid tumor after ten days suggests the significance of GNPs as a potential theranostic agent

Adaptive Optimization of Wave Functions for Fermion Lattice Models

We present a simulation algorithm for Hamiltonian fermion lattice models. A guiding trial wave function is adaptively optimized during Monte Carlo evolution. We apply the method to the two dimensional Gross-Neveu model and analyze systematc errors in the study of ground state properties. We show that accurate measurements can be achieved by a proper extrapolation in the algorithm free parameters.Comment: 4 pages, 6 figures (Encapsulated PostScript

Bayesian network analysis reveals the interplay of intracranial aneurysm rupture risk factors

Clinical decision making regarding the treatment of unruptured intracranial aneurysms (IA) benefits from a better understanding of the interplay of IA rupture risk factors. Probabilistic graphical models can capture and graphically display potentially causal relationships in a mechanistic model. In this study, Bayesian networks (BN) were used to estimate IA rupture risk factors influences. From 1248 IA patient records, a retrospective, single-cohort, patient-level data set with 9 phenotypic rupture risk factors (n=790 complete entries) was extracted. Prior knowledge together with score-based structure learning algorithms estimated rupture risk factor interactions. Two approaches, discrete and mixed-data additive BN, were implemented and compared. The corresponding graphs were learned using non-parametric bootstrapping and Markov chain Monte Carlo, respectively. The BN models were compared to standard descriptive and regression analysis methods. Correlation and regression analyses showed significant associations between IA rupture status and patient’s sex, familial history of IA, age at IA diagnosis, IA location, IA size and IA multiplicity. BN models confirmed the findings from standard analysis methods. More precisely, they directly associated IA rupture with familial history of IA, IA size and IA location in a discrete framework. Additive model formulation, enabling mixed-data, found that IA rupture was directly influenced by patient age at diagnosis besides additional mutual influences of the risk factors. This study establishes a data-driven methodology for mechanistic disease modelling of IA rupture and shows the potential to direct clinical decision-making in IA treatment, allowing personalised prediction

A Study of the Antiferromagnetic Phase in the Hubbard Model by means of the Composite Operator Method

We have investigated the antiferromagnetic phase of the 2D, the 3D and the extended Hubbard models on a bipartite cubic lattice by means of the Composite Operator Method within a two-pole approximation. This approach yields a fully self-consistent treatment of the antiferromagnetic state that respects the symmetry properties of both the model and the algebra. The complete phase diagram, as regards the antiferromagnetic and the paramagnetic phases, has been drawn. We firstly reported, within a pole approximation, three kinds of transitions at half-filling: Mott-Hubbard, Mott-Heisenberg and Heisenberg. We have also found a metal-insulator transition, driven by doping, within the antiferromagnetic phase. This latter is restricted to a very small region near half filling and has, in contrast to what has been found by similar approaches, a finite critical Coulomb interaction as lower bound at half filling. Finally, it is worth noting that our antiferromagnetic gap has two independent components: one due to the antiferromagnetic correlations and another coming from the Mott-Hubbard mechanism.Comment: 20 pages, 37 figures, RevTeX, submitted to Phys. Rev.

Vertebral Augmentation: Is It Time to Get Past the Pain? A Consensus Statement from the Sardinia Spine and Stroke Congress

Vertebral augmentation has been used to treat painful vertebral compression fractures and metastatic lesions in millions of patients around the world. An international group of subject matter experts have considered the evidence, including but not limited to mortality. These considerations led them to ask whether it is appropriate to allow the subjective measure of pain to so dominate the clinical decision of whether to proceed with augmentation. The discussions that ensued are related below

Electro-optical sampling of single-cycle Thz fields with single-photon detectors

Electro-optical sampling of Terahertz fields with ultrashort pulsed probes is a well-established approach for directly measuring the electric field of THz radiation. This technique usually relies on balanced detection to record the optical phase shift brought by THz-induced birefringence. The sensitivity of electro-optical sampling is, therefore, limited by the shot noise of the probe pulse, and improvements could be achieved using quantum metrology approaches using, e.g., NOON states for Heisenberg-limited phase estimation. We report on our experiments on THz electro-optical sampling using single-photon detectors and a weak squeezed vacuum field as the optical probe. Our approach achieves field sensitivity limited by the probe state statistical properties using phase-locked single-photon detectors and paves the way for further studies targeting quantum-enhanced THz sensing