Analytical results for the distribution of cover times of random walks on random regular graphs

We present analytical results for the distribution of cover times of random walks (RWs) on random regular graphs consisting of N nodes of degree c (c ≥ 3). Starting from a random initial node at time t = 1, at each time step t ≥ 2 an RW hops into a random neighbor of its previous node. In some of the time steps the RW may visit a new, yet-unvisited node, while in other time steps it may revisit a node that has already been visited before. The cover time TCis the number of time steps required for the RW to visit every single node in the network at least once. We derive a master equation for the distribution Pt(S = s) of the number of distinct nodes s visited by an RW up to time t and solve it analytically. Inserting s = N we obtain the cumulative distribution of cover times, namely the probability P (TC ≤ t) = Pt(S = N) that up to time t an RW will visit all the N nodes in the network. Taking the large network limit, we show that P (TC ≤ t) converges to a Gumbel distribution. We calculate the distribution of partial cover (PC) times P (TPC,k = t), which is the probability that at time t an RW will complete visiting k distinct nodes. We also calculate the distribution of random cover (RC) times P (TRC,k = t), which is the probability that at time t an RW will complete visiting all the nodes in a subgraph of k randomly pre-selected nodes at least once. The analytical results for the distributions of cover times are found to be in very good agreement with the results obtained from computer simulations.

Textile-Reinforced Mortar (TRM) Strengthened One-Way Reinforced Concrete Slabs

The issue of upgrading and strengthening the reinforced concrete (RC) infrastructure has become of great importance. Recently, textile-reinforced mortar (TRM) was used in the field of structural strengthening. In the current study, using of TRM for flexural retrofitting of one-way reinforced concrete (RC) slabs was experimentally and theoretically investigated. The parameters examined included; the number of TRM layers (1, 3, 5 layers) and the strengthening configuration fully and partially). For this purpose, eight specimens were prepared and tested under three points- loading up to failure. The result showed that the TRM increases substantially the flexural capacity of RC slabs. The highest flexural capacity increase recorded was 103 %. It was also noted that increasing the number of retrofitting layers resulted in different increases in the flexural capacity. It was also shown that the strengthening configuration plays an important role in the effectiveness of the technique. The fully covered approach showed higher loading capacity than the partial cover technique provided that the same TRM layer is applied. Finally, the ultimate moment of the strengthened specimens was calculated theoretically and compared with that obtained experimentally. The results of calculations showed a good agreement between the theoretical and experimental results.

A mechanistic model for bedrock undercut from saltating bedload particle impacts

<p>Bedrock walls can be undercut by saltating bedload particle impacts that are deflected by alluvial cover. Continued undercutting of the lower wall creates an imbalance on the wall and may cause the upper part to collapse and to widen the whole channel. Compared with vertical erosion rates, less is known about lateral erosion (undercutting) rates that are thought to dominate when river beds are alluviated. Here, we derive an analytical model for lateral erosion by saltating bedload particle impacts. The analytical model is a simplification of the Li et al. (2020) numerical model of the same process. The analytical model predicts a nonlinear dependence of lateral erosion rate on sediment supply, shear stress and grain size, revealing the same behaviour observed in the numerical model, but without tracking particle movements through time and space. The analytical model considers both uniformly distributed cover and patchy partial cover that is implemented with a fully alluviated patch along one bank and a bare bedrock along the other. The model predicts that lateral erosion rate peaks when the bed is ~70% covered for uniformly distributed alluvium and when the bed is fully covered for patchy alluvium. Vertical erosion dominates over lateral erosion for ~75% and >90% of sediment supply and transport conditions for uniformly distributed cover and patchy cover, respectively. We use the model to derive a phase diagram of channel responses (steepening, flattening, narrowing, widening) for various combinations of transport stage and relative sediment supply. Application of our model to Boulder Creek, CA captures the observed channel widening in response to increased sediment supply and steepening in response to larger grain size.</p>

To feed or flee: early life-history behavioural strategies of juvenile lake sturgeon (Acipenser fulvescens) during risk-sensitive foraging

Balancing foraging opportunities with predation risk can promote complex behavioural strategies in juvenile fishes, particularly in northern temperate environments with short growing seasons. To test how predation experience may influence foraging effort and risk assessment of juvenile lake sturgeon (Acipenser fulvescens Rafinesque, 1817), flight response and substrate preference behavioural measurements were taken during critical life periods of early exogenous feeding (∼60 days post fertilization (dpf)) and pre-winter (∼160 dpf). Lake sturgeon were placed in arenas with partial cover and exposed white plastic bottom. Chemical alarm cue (AC) was introduced to predator naïve individuals in the presence or absence of food over the exposed portion of the arena to simulate risk sensitive foraging over diurnal and seasonal periods. The same protocol was run on predator-experienced individuals, which were classically conditioned to predator cue (PC) prior to the trials. Whole-body cortisol measures were also taken to determine the physiological response to predation experience. Results suggest a propensity to forage in spite of predation risk during the naïve ∼60 dpf trials and highlight context-specific anti-predator responses of naïve and experienced lake sturgeon. Elevated basal whole-body cortisol levels and reduced body condition (p < 0.05) were observed with increased predator experience.

Dynamics of Host-Parasite Models with Harvesting of Parasites and Partial Cover for Host

Modeling might be viewed like a knowledge concerning with the communication among other topics and mathematics, theoretical discipline on a number of elements of the daily world. Mathematical models take to be crucial resources in iterative methods and biological investigations of info collection. Mathematical models take to be crucial resources in bioticsurveys with an iterative process of info collection. The experimental investigation as well as the theoretical model is usually a crucial element in developing tests and in the interpretation of information. Parasites are actually the organisms which feed on their hosts or host immediately upon it, at some point resulting in the death of host species.

Ultrasound evaluation of the variants position of the femoral artery and vein in surgical practice

Aim. Clarify common variant of the relationship of the initial parts of the femoral artery and vein among outpatients Orel. Methods. In the observation, 138 patients were examined on an outpatient basis using a Samsung Medison R7 ultrasound scanner using a 7-12 MHz linear transducer when examining the arteries and veins of the lower limbs [4]. 81 women and 57 men, aged 21 to 91 years (mean age 57.3 ± 9.9 years) were examined. Results. As a result of the observation, 6 main types of mutual relations of the initial sections of the femoral vein were distinguished on the basis of a possible cover of the anterior wall of the vein of the femoral artery among the 138 outpatients. The results are grouped by type of vascular arrangement, patients' sex, and visualization of structures. The most common option was the close non-intersecting location of the vascular trunks, and the rarest - a partial cover of the surface of the femoral vein by 1/3 and 3/4 of the femoral artery trunk. Conclusion. Knowledge of the characteristics of the relationship of large arterial and venous highways at “key points” allows us to develop the most optimal techniques for minimally invasive surgical interventions, reducing the likelihood of complications.

Combining Satellite and UAV Imagery to Delineate Forest Cover and Basal Area after Mixed-Severity Fires

In northern Argentina, the assessment of degraded forests is a big challenge for both science and practice, due to their heterogeneous structure. However, new technologies could contribute to mapping post-disturbance canopy cover and basal area in detail. Therefore, this research assesses whether or not the inclusion of partial cover unmanned aerial vehicle imagery could reduce the classification error of a SPOT6 image used in an area-based inventory. BA was calculated from 77 ground inventory plots over 3944 ha of a forest affected by mixed-severity fires in the Argentinian Yungas. In total, 74% of the area was covered with UAV flights, and canopy height models were calculated to estimate partial canopy cover at three tree height classes. Basal area and partial canopy cover were used to formulate the adjusted canopy cover index, and it was calculated for 70 ground plots and an additional 20 image plots. Four classes of fire severity were created based on basal area and adjusted canopy cover index, and were used to run two supervised classifications over a segmented (algorithm multiresolution) wall-to-wall SPOT6 image. The comparison of the Cohan’s Kappa coefficient of both classifications shows that they are not significantly different (p-value: 0.43). However, the approach based on the adjusted canopy cover index achieved more homogeneous strata (Welch t-test with 95% of confidence). Additionally, UAV-derived canopy height model estimates of tree height were compared with field measurements of 71 alive trees. The canopy height models underestimated tree height with an RMSE ranging from 2.8 to 8.3 m. The best accuracy of the canopy height model was achieved using a larger pixel size (10 m), and for lower stocked plots due to high fire severity.