On moments of the integrated exponential Brownian motion

We present new exact expressions for a class of moments for the geometric Brownian motion, in terms of determinants, obtained using a recurrence relation and combinatorial arguments for the case of a Ito's Wiener process. We then apply the obtained exact formulas to computing averages of the solution of the logistic stochastic differential equation via a series expansion, and compare the results to the solution obtained via Monte Carlo

"Spectrally gapped" random walks on networks: a Mean First Passage Time formula

We derive an approximate but explicit formula for the Mean First Passage Time of a random walker between a source and a target node of a directed and weighted network. The formula does not require any matrix inversion, and it takes as only input the transition probabilities into the target node. It is derived from the calculation of the average resolvent of a deformed ensemble of random sub-stochastic matrices H = ⟨ H ⟩ + δ H, with ⟨ H ⟩ rank- 1 and non-negative. The accuracy of the formula depends on the spectral gap of the reduced transition matrix, and it is tested numerically on several instances of (weighted) networks away from the high sparsity regime, with an excellent agreement

Technical-economic comparison of chemical precipitation and ion exchange processes for the removal of phosphorus from wastewater

Chemical precipitation with the addition of ferric chloride is commonly used to remove phosphorus from wastewater. However, since its application also involves several disadvantages, alternative solutions are required. The present paper shows the results of a full-scale experimental work aimed at evaluating the efficiency of the ion exchange process using a polymeric anion exchange resin impregnated with aluminum ions in the removal of phosphorus from wastewater. The study compared the results obtained through this process with chemical precipitation, considering both technical and economic issues. At the same dosage of 6 L/hour and influent concentration (about 6 mg/L), total removal efficiency of 95% and 78% (including also that occurring in the mechanical and biological processes) was achieved by means of the anion exchange process and chemical precipitation, respectively. However, in the latter case, this value was insufficient to ensure consistent compliance with the limit of 2 mg/L Ptot set on the effluent; to achieve this goal, the ferric chloride dosage had to be raised to 12 L/hour, thus increasing the related costs. Furthermore, the anion exchange process generated a lower sludge production. Therefore, the ion exchange process represents a valid alternative to chemical precipitation for P removal from wastewater

Quantum Bose-Hubbard model with an evolving graph as a toy model for emergent spacetime

We present a toy model for interacting matter and geometry that explores quantum dynamics in a spin system as a precursor to a quantum theory of gravity. The model has no a priori geometric properties; instead, locality is inferred from the more fundamental notion of interaction between the matter degrees of freedom. The interaction terms are themselves quantum degrees of freedom so that the structure of interactions and hence the resulting local and causal structures are dynamical. The system is a Hubbard model where the graph of the interactions is a set of quantum evolving variables. We show entanglement between spatial and matter degrees of freedom. We study numerically the quantum system and analyze its entanglement dynamics. We analyze the asymptotic behavior of the classical model. Finally, we discuss analogues of trapped surfaces and gravitational attraction in this simple model

Clinical radiographical outcomes and complications after a brand-new total ankle replacement design through an anterior approach: A retrospective at a short-term follow up

Recently, the progress in techniques and in projecting new prosthetic designs has allowed increasing indications for total ankle replacement (TAR) as treatment for ankle osteoarthritis. This retrospective work comprehended 39 subjects aged between 47 and 79 years old. The patients, observed for at least 12 months (mean follow up of 18.2 ± 4.1 months), have been evaluated according to clinical and radiological parameters, both pre-and post-operatively. The AOFAS and VAS score significantly improved, respectively, from 46.2 ± 4.8 to 93.9 ± 4.1 and from 7.1 ± 1.1 to 0.7 ± 0.5 (p value < 0.05). At the final evaluation, the mean plantarflexion passed from 12.2◦ ± 2.3◦ to 18.1◦ ± 2.4◦ (p value < 0.05) and dorsiflexion from a pre-operative mean value of 8.7◦ ± 4.1◦ to 21.7◦ ± 5.4◦ post-operatively (p value < 0.05). This study found that this new total ankle replacement design is a safe and effective procedure for patients effected by end-stage ankle osteoarthritis. Improvements have been demonstrated in terms of range of motion, radiographic parameters and patient-reported outcomes. However, further studies are needed to assess the long-term performance of these prostheses

A note on entropic force and brane cosmology

Recently Verlinde proposed that gravity is an entropic force caused by information changes when a material body moves away from the holographic screen. In this note we apply this argument to brane cosmology, and show that the cosmological equation can be derived from this holographic scenario.Comment: 5 pages, no figures;references adde

Evaluation of proprioception and postural control at a minimum 1 year follow-up after ankle capsuloligamentous lateralplasty with Brostrom technique: A cohort study

Recovery of postural control and proprioception in patients affected by chronic ankle instability (CAI) and operated on capsulo-ligaments reconstructive surgery lacks of objective assessment. The aim of this study was to evaluate long-term post-surgical postural and proprioceptive control through the DPPS device in a cohort of patients operated on ligaments reconstruction through the modified Brostrom procedure at a minimum follow up of 12 months.Eleven patients with post-traumatic lateral CAI, operated of external capsulo-ligamentous complex repair according to Brostrom technique at a minimum follow-up of 1 year were enrolled. Physical examination and American Orthopaedics Foot and Ankle Society (AOFAS) ankle-hindfoot score. Proprioceptive and postural stability was assessed by DPPS - Delos Postural Proprioceptive System, linked to a computer with a specific software and including a flat table, an electronic unstable proprioceptive board, a Delos Vertical Controller, a monitor and a horizontal bar fitted with an infra-red sensor for hand support.Patients were 5 males and 6 females, mean age of 38.4 ± 12 years. Mean BMI of the patients was 26.8 ± 4.4. Mean follow up was 13.4 ± 2.1. The mean value of (AOFAS) clinical score was 90.3/100. Mean Static Stability Index (SSI) with open eyes was 87.7% (±7.6) in the operated leg and 90.4% (±6.1) in the contra-lateral. SSI with closed eyes was 64.5% (±11.2) in the operated leg and 61.6% (±16.8) in the contra-lateral. Mean Dynamic Stability Index (DSI) without restrictions was 56.2% (±14.6) in the operated leg and 56.8% (±10.6) in the contra-lateral. DSI with restricted upper limbs, had a mean value of 56.3% (±11.4) in the operated leg and 58.1% (±11.9) in the contra-lateral.Re-tensioning capsular-ligamentous surgery of the external compartment for CAI allow to recovery proprioceptive and postural control on the operated side, comparable with data from the contralateral limb and from the healthy population of the same age and sex

Weight bearing versus conventional CT for the measurement of patellar alignment and stability in patients after surgical treatment for patellar recurrent dislocation

Purpose: To compare weight-bearing cone-beam computer tomography (CBCT) and conventional computer tomography (CT)-based measurements of patellofemoral alignment and stability in patients surgically treated for recurrent patellar dislocation. These scans implied respectively single-leg up-right posture, the knee flexed, and lower limb muscles activation, versus supine position with the knee extended. Methods: A total of 17 patients (11 males/6 females) after surgical reconstruction with fascia lata allograft for recurrent patellofemoral dislocation were analyzed at 60-month follow-up. Tilt and congruence angles and tibial tuberosity–trochlear groove (TT-TG) offset were measured on images obtained from CBCT and conventional CT scans by three independent and expert radiologists. Paired t tests were performed to compare measurements obtained from the two scans. Inter-rater reliability was assessed using a two-way mixed-effects model intra-class correlation coefficient (ICC). Results: Only TT-TG offset was found significantly smaller (p < 0.001) in CBCT (mean 9.9 ± 5.3 mm) than in conventional CT (mean 15.9 ± 4.9 mm) scans. ICC for tilt and congruence angles and for TT-TG offset ranged between 0.80–0.94 with measurements in CBCT scans, between 0.52 and0.78 in conventional CT. Conclusion: In patients surgically treated for recurrent patellar dislocation, TT-TG offset was found overestimated with conventional CT. All measurements of patellofemoral stability and alignment were found more consistent when obtained with weight-bearing CBCT compared to conventional CT

A quantum Bose-Hubbard model with evolving graph as toy model for emergent spacetime

We present a toy model for interacting matter and geometry that explores quantum dynamics in a spin system as a precursor to a quantum theory of gravity. The model has no a priori geometric properties, instead, locality is inferred from the more fundamental notion of interaction between the matter degrees of freedom. The interaction terms are themselves quantum degrees of freedom so that the structure of interactions and hence the resulting local and causal structures are dynamical. The system is a Hubbard model where the graph of the interactions is a set of quantum evolving variables. We show entanglement between spatial and matter degrees of freedom. We study numerically the quantum system and analyze its entanglement dynamics. We analyze the asymptotic behavior of the classical model. Finally, we discuss analogues of trapped surfaces and gravitational attraction in this simple model.Comment: 23 pages, 6 figures; updated to published versio

Rotation and twist regular modes for trapped ghosts

A parameter-independent notion of stationary slow motion is formulated then applied to the case of stationary rotation of massless trapped ghosts. The excitations correspond to a rotation mode with angular momentum $J\neq 0$ and twist modes. It is found that the rotation mode, which has no parity, causes excess in the angular velocity of dragged distant coordinate frames in one sheet of the wormhole while in the other sheet the angular velocity of the ghosts is that of rotating stars: $2J/r^3$. As to the twist modes, which all have parity, they cause excess in the angular velocity of one of the throat's poles with respect to the other.Comment: 11 pages, 3 figures; General Relativity and Gravitation - 201