In the context of evaluating physical function in individuals with stroke, the 3-meter backward walk test (3MBWT) emerges as a potential tool of interest. The purpose of this study was to assess the test-retest reliability and construct validity of the 3MBWT and its correlation with falling incidents. Conducted in a neurological rehabilitation center, 35 ambulatory individuals with stroke were enrolled within a month post-stroke onset. These participants, with a Functional Ambulation Category score of ≥4, underwent the 3MBWT, Functional Gait Assessment (FGA), 10-Meter Walk Test (10MWT), and 6-Minute Walk Test (6MWT) three times by different physiotherapists. Results indicated the 3MBWT displayed high reliability (r=0.97-0.98) and showed significant construct validity with other established walking tests like the 6MWT (r=-0.78) and 10MWT (r=0.71), with a moderate correlation to the FGA (r=-0.54). No marked differences in test outcomes were observed between participants based on their fall history. Conclusively, the 3MBWT proves to be highly reliable and validates well with existing walking function assessments for stroke patients, suggesting its potential as a time-efficient alternative.

Background: The 6-minute walk test (6MWT) is a simple and low-cost method that allows assessment of functional capacity in patients with heart failure (HF). However, the prognostic role of 6MWT in HF remains uncertain. Objectives: We aimed to evaluate the 6MWT as a predictor of mid-term adverse outcomes in patients with HF with mid-range and reduced ejection fraction. Methods: Prospective single-center cohort study that included patients with HF with an ejection fraction under 50% at a specialized outpatient HF service. Patients underwent the 6MWT on admission and were compared according to the distance walked: Group I walked ≥350 meters and group II <350 meters. The primary outcome was a composite of death from any cause or hospitalization for HF decompensation in one-year follow-up. Secondary outcomes were the components of the primary outcome in an isolated analysis. Results: Sixty patients were included, 43.3% male, with a mean age of 61.1 ± 12.9 years and ejection fraction 34.3 ± 10.1%. 52 patients (86.7%) were on guideline-directed triple therapy for HF. The average distance walked in the 6MWT was 395.1 ± 98.8 meters, with 40 patients (66.7%) in group I and 20 (33.3%) in group II. The primary outcome in groups I and II were, respectively, 15,0% and 35,0% (p=0.05). One-year mortality was 5.0% vs 15.0% (p=0.18) and the hospitalization rate was 10.0% vs 20.0% (p=0.28). Conclusions: There was no association of distance <350 meters in the 6MWT with the primary outcome in patients with HF. Despite the higher occurrence of outcomes in group II, the difference was not statistically significant in this analysis. On a selective basis, the 6MWT may be a useful tool for prognostic stratification in HF, if combined with other methods.

We consider a discrete-time random walk (xt) which at random times is reset to the starting position and performs a deterministic motion between them. We show that the quantity Prxt+1=n+1|xt=n,n→∞ determines if the system is averse, neutral or inclined towards resetting. It also classifies the stationary distribution. Double barrier probabilities, first passage times and the distribution of the escape time from intervals are determined.

Discovery of stable and broad frequency combs in monochromatically pumped high-Q optical Kerr microresonators caused by generation of temporal solitons can be regarded as one of the major breakthroughs in nonlinear optics during the last two decades. Transfer of the soliton-comb concept to χ(2) microresonators promises lowering of the pump power, new operation regimes, and entering new spectral ranges; scientifically, it is of a big challenge. Here we represent an overview of stable and accessible soliton-comb regimes in monochromatically pumped χ(2) microresonators discovered during the last several years. The main stress is made on lithium niobate based resonators. The overview pretends to be rather simple, complete, and comprehensive: It incorporates the main factors affecting the soliton-comb generation, such as the choice of the pumping scheme (pumping to the first or second harmonic), the choice of phase matching scheme (natural or artificial), the effects of temporal walk-off and dispersion coefficients, and also the influence of frequency detunings and Q-factors. Most of discovered nonlinear regimes are self-starting – they can be accessed from noise upon a not very abrupt increase of the pump power. The soliton-comb generation scenarios are not universal – they can be realized only under proper combinations of the above mentioned factors. We indicate what kind of restrictions on the experimental conditions have to be imposed to get the soliton-comb generation.

This paper proposes an encryption scheme for high pixel density images. Based on the application of the quantum random walk algorithm, the Long short-term memory (LSTM) can effectively solve the problem of low efficiency of the quantum random walk algorithm in generating large-scale pseudorandom matrices, and further improve the statistical properties of the pseudorandom matrices required for encryption. The LSTM is then divided into columns and fed into the LSTM in order for training. Due to the randomness of the input matrix, the LSTM cannot be trained effectively, so the output matrix is predicted to be highly random. The LSTM prediction matrix of the same size as the key matrix is generated based on the pixel density of the image to be encrypted, which can effectively complete the encryption of the image. In the statistical performance test, the proposed encryption scheme achieves an average information entropy of 7.9992, an average number of pixels changed rate (NPCR) of 99.6231%, an average uniform average change intensity (UACI) of 33.6029% and an average correlation of 0.0032. Finally, various noise simulation tests are also conducted to verify its robustness in real-world applications where common noise and attack interference are encountered.

Information is physically measurable as a selection from a set of possibilities, the domain of information. This defines the term "information". The domain of the information must be known together reproducibly beforehand. As a practical consequence, digital information exchange can be made globally efficient, interoperable and searchable to a large extent by online definition of application-optimized domains of information. There are even more far-reaching consequences for physics. The purpose of this article is to present prerequisites and possibilities for a physical approach that is consistent with the precise definition of information. This concerns not only the discretization of the sets of possible experimental results, but also the order of their definition along time. The access to or comparison with the domain of information is the more frequent, the earlier it was defined. The geometrical appearance of our space is apparently a delayed statistical consequence of a very frequent connection with the common primary domain of information.

. 1) Background: Intersectionality contests that individuals have multiple characteristics in their identity that cannot be siloed or deemed exclusive to each other. Understanding and utilising an intersectional lens in organisations can increase inclusion of individuals and organisational performance. An educational package known as the Intersectionality Walk (IW) was developed by the authors, piloted, and evaluated in order to break down the commonly held descriptors of diversity silos that fragments inclusion, and to understand how various identity characteristics compound disadvantage. The paper outlines the need to transition from siloed views of diversity to a more intrinsic view of identity to achieve inclusivity. 2) Methods: The IW was developed and trialled with a series of work-based scenarios and realistic multifaceted personas. Data collection occurred pre- and post- IW utilising a mixed methods approach. Responses to Likert scale surveys and open-ended questions were captured and analysed via inductive and ground theory perspectives. 3) Results: An improved awareness and understanding of individual knowledge, reflectivity and positionality relating to intersectionality and intersectional approaches was reported on completion of the IW. Further, responses reported how and why organisations can approach and improve inclusivity via using intersectional approaches. 4) Conclusions: The IW as an educational package has a positive impact and is a key linkage for all employers to build an inclusive culture and to harness the talent of all employees. Further research will occur to measure the implemented change in organisations following the IW.

The Universe, rather than being homogeneous, displays an almost infinite topological genus, because it is punctured with a countless number of gravitational vortexes, i.e., black holes. Starting from this view, we aim to show that the occurrence of black holes is constrained by geometric random walks taking place during cosmic inflationary expansion. At first, we introduce a visual model, based on the Pascal’s triangle and linear and nonlinear arithmetic octahedrons, which describes three-dimensional cosmic random walks. In case of nonlinear 3D paths, trajectories in an expanding Universe can be depicted as the operation of filling the numbers of the octahedrons in the form of “islands of numbers”: this leads to separate cosmic structures (standing for matter/energy), spaced out by empty areas (constituted by black holes and dark matter). These procedures allow us to describe the topology of an universe of infinite genus, to assess black hole formation in terms of infinite Betti numbers, to highlight how non-linear random walks might provoke gravitational effects also in absence of mass/energy, and to propose a novel interpretation of Beckenstein-Hawking entropy: it is proportional to the surface, rather than the volume, of a black hole, because the latter does not contain information.

We present the design and overall development of an eight degrees of freedom (DOF) based Bioinspired Quadruped Robot (BiQR). The robot is designed with a skeleton made of cedar wood. The wooden skeleton is based on exploring the potential of cedar wood to be a choice for legged robots’ design. With a total weight of 1.19 kg, the robot uses eight servo motors that run the position control. Relying on the inverse kinematics, the control design enables the robot to perform the walk gait-based locomotion in a controlled environment. The robot has two main aspects: 1) the initial wooden skeleton development of the robot showing it to be an acceptable choice for robot design, 2) the robot’s applicability as a low-cost legged platform to test the locomotion in a laboratory or a classroom setting.

Investigating the network response to node removal and the efficacy of the node removal strategies are related and fundamental questions in network science. Research studies proposed many node centralities based on the network structure ranking node to remove. The random walk (RW) on networks describes a stochastic process in which a walker travels among nodes. RW can be a model of transport, diffusion, and search on networks, and an essential tool for studying the importance of network nodes. In this manuscript, we propose four new measures of node centrality based on RW. Then, we compare the efficacy of the new RW node removal strategies to network dismantle with effective node removal strategies from the literature, such as betweenness and closeness node removal over synthetic and real-world networks. We evaluate the network dismantle along node removal using the size of the largest connected component (LCC). We find that, hence the betweenness nodes attack is the best strategy overall, the new node removal strategies based on RW show the highest efficacy in peculiar network topology. Specifically, RW strategies based on covering times emerge as the most effective strategy on a synthetic lattice network and two real-world road networks. Our results may be useful in selecting the best node attack strategies in a specific class of networks and in building more robust network structures.

Information and communication technologies play an increasingly important role in the process of acquiring knowledge from a territory and managing it at different scales. ICTs allow a rapid diffusion of data not only through institutional channels but also through social networks where the smart community share experiences and perceptions. In this sense, ICTs become strategic to support the promotion of sustainable tourism development of territories. An important tool to implement it, can be a circular smart dashboard, a decision support system in which the digital data are organized and processed to produce an information output, to be used, after the evaluation by the decision makers, as a new input for the system. The present paper deals with a wider research the authors are involved in, related to the reconversion and valorization of a former mining area towards slow tourism, as the Santa Barbara Walk (SBW), an ancient mining route in the Sulcis Iglesiente area (Sardinia, Italy) . In particular, we here focus on the design proposal of a dashboard, capable of organizing information concerning the main features of the walk, in order to facilitate a shared governance for an effective tourism promotion. The paper is based on a thorough recognition of the main characteristics of the Walk, both the material ones and the digital, immaterial ones. The SBW represents in fact a network connecting the main points of interest along the Walk. On the contrary, its digital network – consisting of intangible infrastructure and flows - is however fragmented in terms of policies and contents Also a state of disorganization in slow tourism promotion activities can be observed. The goal of this paper is to present and analysis of the area, and to propose an evaluation and planning tool as the design of a circular dashboard of the SBW.

A swarm based nature-inspired optimization algorithm namely fruit fly optimization algorithm (FOA) has simple structure and ease of implementation. However, FOA has a low success rate and a slow convergence because FOA generates new positions around the best location using fixed search radius. Several improved FOAs have been proposed. But their exploration ability is questionable. To make the search process to transit from the exploration phase to the exploitation phase smoothly, this paper proposes a new FOA constructed from a cooperation of the multileader and the probabilistic random walk strategies (CPFOA). It has two population types working together. CPFOA's performance is evaluated by 18 well-known standard benchmark, and 30 CEC’2017 functions. The results showed that CPFOA outperforms both the original FOA and its variants in terms of convergence speed and performance accuracy. The results base on CEC’2017 show that CPFOA can achieve a very promising accuracy when compared with the well-known competitive algorithms. CPFOA is applied to optimize two applications; the MLPs classifying real datasets and extracting parameters of T-S fuzzy system for modelling Box and Jenkins gas furnace data set. CPFOA can find parameters having a very high quality compared with the best known competitive algorithms.

The nonlocality (superdiffusion) of turbulence is expressed in the empiric Richardson t3 scaling law for the mean square of the mutual separation of a pair of particles in a fluid or gaseous medium. The development of the theory of nonlocality of various processes in physics and other sciences based on the concept of Lévy flights resulted in the idea of Shlesinger and colleagues about the possibility of describing the nonlocality of turbulence using a linear integro-differential equation with a slowly falling kernel. The close approach developed by us made it possible to establish the closeness of the superdiffusion parameter of plasma density fluctuations moving across a strong magnetic field in a tokamak to the Richardson law. In this paper, we show the possibility of a universal description of the characteristics of nonlocality of transfer in a stochastic medium (including turbulence of gases and fluids) using the Biberman-Holstein approach to the transfer of excitation of a medium by photons, generalized to take into account the finiteness of the velocity of excitation carriers. This approach enables us to propose a scaling that generalizes Richardson's t3 scaling law to the combined regime of Lévy flights and Lévy walks.

The paper presents a modeling framework to analyze the effect of episodic rainfall supply on groundwater dynamics in the Ionian coastal plain multilayered aquifer. The focus is essentially on the short-term behavior of the shallowest layer, with a specific analysis on episodic rainfall events. In the studied aquifer, groundwater level responds sensitively to rainfall events, highlighting the presence of preferential recharge zones. The hydraulic head peak is a function of groundwater level antecedent to the rainfall event. A kinematic dispersion wave model was used to model infiltration processes via preferential pathways. A one-dimensional and non-linear particle based numerical model was developed. Particles with constant water volume travel according to celerity and hydraulic dispersion to simulate the infiltration rate wave through the vadose zone. The flow rate that reaches the water table represents the input function to determine groundwater level fluctuations along groundwater flow direction and according to the lithological features of the surficial levels of the multilayered aquifer, its storage capacity changes passing from unconfined to confined conditions. The model was validated with high time resolution time series of precipitation and groundwater level coming from Terra Montonata meteo-climatic and groundwater level monitoring station. The developed model represents a basis for evaluating and predicting groundwater discharge of the shallowest layers of the Ionian coastal multilayered aquifer under natural conditions including episodic rainfall.

Polymers in highly confined geometries can display complex morphologies including ordered phases. A basic component of a theoretical analysis of their phase behavior in confined geometries is the knowledge of the number of possible single-chain conformations compatible with the geometrical restrictions and the established crystalline morphology. While the statistical properties of unrestricted self-avoiding random walks (SAWs) both on and off-lattice are very well known, the same is not true for SAWs in confined geometries. The purpose of this contribution is a) to enumerate the number of SAWs on the simple cubic (SC) and face-centered cubic (FCC) lattices under confinement for moderate SAW lengths, and b) to obtain an approximate expression for their behavior as a function of chain length, type of lattice, and degree of confinement. This information is an essential requirement for the understanding and prediction of entropy-driven phase transitions of model polymer chains under confinement. In addition, a simple geometric argument is presented that explains, to first order, the dependence of the number of restricted SAWs on the type of SAW origin.

Recent simulation studies have revealed a wealth of distinct crystal polymorphs encountered in the self-organization of polymer systems driven by entropy or free energy. The present analysis, based on the concept of self-avoiding random walks on crystal lattices, is useful to calculate upper bounds for the entropy difference of the crystals that are formed during polymer crystallization and thus provide predictions on polymorph thermodynamic stability. Here, we compare two pairs of crystals sharing the same coordination number, ncoord: hexagonal close packed (HCP) and face centered cubic (FCC), both having ncoord = 12 and the same packing density, and the less dense hexagonal (HEX) and body centered cubic (BCC) lattices, with ncoord = 8. In both cases, once a critical step length is reached, one of the crystals shows a higher number of SAWs compatible with the crystal. We explain the observed trends in terms of the bending and torsion angles corresponding to the different chain geometry as imposed by the geometric constraints of the crystal lattice.

We present a model of infection dynamics that might explain slower approaching the herd immunity during the covid-19 epidemy in Sweden than it was predicted by a variety of other models; see graphs Fig. \ref{GROWTH2}. The new model takes into account the hierarchic structure of social clusters in the human society. We apply the well developed theory of random walk on the energy landscapes represented mathematically with ultrametric spaces. This theory was created for applications to spin glasses and protein dynamics. To move from one social cluster (valley) to another, the virus should cross a social barrier between them. The magnitude of a barrier depends on the number of social hierarchy's levels composing this barrier. As the most appropriate for the recent situation in Sweden, we consider linearly increasing (with respect to hierarchy's levels) barriers. This structure of barriers matches with a rather soft regulations imposed in Sweden in March 2020. In this model, the infection spreads rather easily inside a social cluster (say working collective), but jumps to other clusters are constrained by social barriers. This model's feature matches with the real situation during the covid-19 epidemy, with its cluster spreading structure. Clusters need not be determined solely geographically, they are based on a number of hierarchically ordered social coordinates. The model differs crucially from the standard models of spread of disease, such as the SIR-model. Our model describes such a specialty of spread of covid-19 virus as the presence of ``super-infectors'' who by performing a kind of random walk on a hierarchic landscape of social clusters spreads infection. In future, this model will be completed by adding the SIR-type counterpart. But, the latter is not a specialty of covid-19 spreading.

We present results on the spontaneous crystallization of freely-jointed polymers of hard spheres obtained in an unprecedentedly long Monte Carlo (MC) simulation on a system of 54 chains of 1000 monomers. Starting from a purely amorphous configuration and after a transitory dominance of the hexagonal closed packed (HCP) polymorph, the system crystallizes in a final, stable, face centered cubic (FCC) crystal of very high perfection. Through refined metrics we gauge the degree of ordering and identify the regions of the phase transition and the corresponding morphologies. An analysis of chain conformational characteristics, of the spatial distribution of monomers and of the volume accessible to them shows that the phase transition is caused by an increase in translational entropy that is larger than the loss of conformational entropy of the chains in the crystal compared to the amorphous state. Polymer chains in the crystal adopt ideal random walk statistics as their great length renders local conformational details, imposed by the geometry of the FCC crystal, irrelevant.