Statistics of first-passage times in disordered systems using backward master equations and their exact renormalization rules

We consider the non-equilibrium dynamics of disordered systems as defined by a master equation involving transition rates between configurations (detailed balance is not assumed). To compute the important dynamical time scales in finite-size systems without simulating the actual time evolution which can be extremely slow, we propose to focus on first-passage times that satisfy 'backward master equations'. Upon the iterative elimination of configurations, we obtain the exact renormalization rules that can be followed numerically. To test this approach, we study the statistics of some first-passage times for two disordered models : (i) for the random walk in a two-dimensional self-affine random potential of Hurst exponent $H$, we focus on the first exit time from a square of size $L \times L$ if one starts at the square center. (ii) for the dynamics of the ferromagnetic Sherrington-Kirkpatrick model of $N$ spins, we consider the first passage time $t_f$ to zero-magnetization when starting from a fully magnetized configuration. Besides the expected linear growth of the averaged barrier $\bar{\ln t_{f}} \sim N$, we find that the rescaled distribution of the barrier $(\ln t_{f})$ decays as $e^{- u^{\eta}}$ for large $u$ with a tail exponent of order $\eta \simeq 1.72$. This value can be simply interpreted in terms of rare events if the sample-to-sample fluctuation exponent for the barrier is $\psi_{width}=1/3$.Comment: 8 pages, 4 figure

Inspædia: [Almost] Everything About Simplicity, Playfulness and Inspiration

The aim of this paper is to disclose the new research developments and the results from the systematization of experience and user interaction with the Inspædia (a new web knowledge “Agora”), to inspire a dynamic, collaborative, and interactive intelligence among the inspædiers. We will explain in detail and describe the design process and discuss the ultimate design interaction concept & development regarding (almost everything about) simplicity and playfulness of the inspædiers’ experience to transform relevant information (related > meanfull > useful) in productive knowledge (inspiration > insight > foresight) in a very easy and quick way (usability: learnability; understandability; operability; attractiveness...), with a smile in the face (satisfaction) and a wow in the mind (or in the soul).Inspædia is the natural consequence and development of the prototype resulting from the research in Design PhD thesis Innovation, design et cetera (FA/UTL, 2012). Therefore, it is being developed with the Science Without Borders Program (2013-2016) with a Special Visiting Researcher fellowship grant of CAPES (Brazil), and under the post-doctoral in Design at the Faculty of Architecture, University of Lisbon (FA/UL); CIAUD – Reseach Centre of Architecture, Urbanism and Design (FA/UL); Faculty of Sciences and Technology, Nova University of Lisbon (FCT/UNL); NOVA-LINCS (FCT/UNL) and CITAD - Research Centre for Territory, Architecture and Design (FAA/ULL). The Inspædia research project was ranked in first place in Design scientific area and obtained a post-doctoral fellowship by FCT – Foundation for Science and Technology (Portugal). The project has been internationally disseminated at international Design conferences with indexed publications. It was presented and published both at AHFE 2014 (Krakow) and AHFE 2015 (Las Vegas). It was part of the biennial Experimentadesign tangential events in 2013 (EXD'13), 2015 (EXD'15) and was presented, by invitation, at the International Congress DESIGN I-CON (2015). During the last year we prototyped and tested (usability testing) with some inspædiers different approaches to achieve users’ needs > desires > expectations) in a challenging way, in order to provide the most powerful and memorable user experience

Rare region effects at classical, quantum, and non-equilibrium phase transitions

Rare regions, i.e., rare large spatial disorder fluctuations, can dramatically change the properties of a phase transition in a quenched disordered system. In generic classical equilibrium systems, they lead to an essential singularity, the so-called Griffiths singularity, of the free energy in the vicinity of the phase transition. Stronger effects can be observed at zero-temperature quantum phase transitions, at nonequilibrium phase transitions, and in systems with correlated disorder. In some cases, rare regions can actually completely destroy the sharp phase transition by smearing. This topical review presents a unifying framework for rare region effects at weakly disordered classical, quantum, and nonequilibrium phase transitions based on the effective dimensionality of the rare regions. Explicit examples include disordered classical Ising and Heisenberg models, insulating and metallic random quantum magnets, and the disordered contact process.Comment: Topical review, 68 pages, 14 figures, final version as publishe

Dynamical replica analysis of processes on finitely connected random graphs II: Dynamics in the Griffiths phase of the diluted Ising ferromagnet

We study the Glauber dynamics of Ising spin models with random bonds, on finitely connected random graphs. We generalize a recent dynamical replica theory with which to predict the evolution of the joint spin-field distribution, to include random graphs with arbitrary degree distributions. The theory is applied to Ising ferromagnets on randomly diluted Bethe lattices, where we study the evolution of the magnetization and the internal energy. It predicts a prominent slowing down of the flow in the Griffiths phase, it suggests a further dynamical transition at lower temperatures within the Griffiths phase, and it is verified quantitatively by the results of Monte Carlo simulations.Comment: 30 pages, 4 figures, submitted to J.Phys.

Energy cost of ambulation in trans-tibial amputees using a dynamic-response foot with hydraulic versus rigid 'ankle': insights from body centre of mass dynamics.

BACKGROUND:Previous research has shown that use of a dynamic-response prosthetic foot (DRF) that incorporates a small passive hydraulic ankle device (hyA-F), provides certain biomechanical benefits over using a DRF that has no ankle mechanism (rigA-F). This study investigated whether use of a hyA-F in unilateral trans-tibial amputees (UTA) additionally provides metabolic energy expenditure savings and increases the symmetry in walking kinematics, compared to rigA-F. METHODS:Nine active UTA completed treadmill walking trials at zero gradient (at 0.8, 1.0, 1.2, 1.4, and 1.6 of customary walking speed) and for customary walking speed only, at two angles of decline (5° and 10°). The metabolic cost of locomotion was determined using respirometry. To gain insights into the source of any metabolic savings, 3D motion capture was used to determine segment kinematics, allowing body centre of mass dynamics (BCoM), differences in inter-limb symmetry and potential for energy recovery through pendulum-like motion to be quantified for each foot type. RESULTS:During both level and decline walking, use of a hyA-F compared to rigA-F significantly reduced the total mechanical work and increased the interchange between the mechanical energies of the BCoM (recovery index), leading to a significant reduction in the metabolic energy cost of locomotion, and hence an associated increase in locomotor efficiency (p < 0.001). It also increased inter-limb symmetry (medio-lateral and progression axes, particularly when walking on a 10° decline), highlighting the improvements in gait were related to a lessening of the kinematic compensations evident when using the rigA-F. CONCLUSIONS:Findings suggest that use of a DRF that incorporates a small passive hydraulic ankle device will deliver improvements in metabolic energy expenditure and kinematics and thus should provide clinically meaningful benefits to UTAs' everyday locomotion, particularly for those who are able to walk at a range of speeds and over different terrains

A novel method for defining the Greyhound talocrural joint axis of rotation for hinged transarticular external skeletal fixation

SummaryIn order to apply hinged transarticular external skeletal fixation for stabilization of the injured canine tarsal joint, knowledge of the three-dimensional (3D) location and orientation of the transverse axis is necessary. This method of immobilization may be used as a primary or adjunctive method of stabilisation for a large number of traumatic conditions. Using pin-mounted markers in the cadaveric Greyhound crus and talus, a closed-form solution of absolute orientation was used to identify, on radiographs, the lateral and medial locations of the transverse axis by tracking the 3D excursions of the markers during flexion and extension. A line was drawn across the dorsal aspect of the calcaneus from the most dorsal point on the distal articular surface (proximal intertarsal joint: PIJ) to the most dorsal point on its proximal articulation with the body of the talus, and the location of the centre of rotation was expressed in terms of the length of that line. In seven Greyhound tarsal joints, the medial end of the axis was located 73 ± 10% proximal to the PIJ and 11 ± 7% dorsal to the line. The lateral end was 73 ± 9% proximal to the PIJ and -2 ± 3% plantar to the line.</jats:p

Use of a Collar-Mounted Triaxial Accelerometer to Predict Speed and Gait in Dogs

Accelerometry has been used to measure treatment efficacy in dogs with osteoarthritis, although interpretation is difficult. Simplification of the output into speed or gait categories could simplify interpretation. We aimed to determine whether collar-mounted accelerometry could estimate the speed and categorise dogs’ gait on a treadmill. Eight Huntaway dogs were fitted with a triaxial accelerometer and then recorded using high-speed video on a treadmill at a slow and fast walk, trot, and canter. The accelerometer data (delta-G) was aligned with the video data and records of the treadmill speed and gait. Mixed linear and logistic regression models that included delta-G and a term accounting for the dogs’ skeletal sizes were used to predict speed and gait, respectively, from the accelerometer signal. Gait could be categorised (pseudo-R2 = 0.87) into binary categories of walking and faster (trot or canter), but not into the separate faster gaits. The estimation of speed above 3 m/s was inaccurate, though it is not clear whether that inaccuracy was due to the sampling frequency of the particular device, or whether that is an inherent limitation of collar-mounted accelerometers in dogs. Thus, collar-mounted accelerometry can reliably categorise dogs’ gaits into two categories, but finer gait descriptions or speed estimates require individual dog modelling and validation. Nonetheless, this accelerometry method could improve the use of accelerometry to detect treatment effects in osteoarthritis by allowing the selection of periods of activity that are most affected by treatment