Integer Networks

Inspired by Pythagoras's belief that numbers are the absolute reality, we obtain some demonstrational results about topological properties of integer networks, in which the vertices represent integers and two vertices are neighbors if and only if there exists a divisibility relation between them. We strictly prove that the diameter of networks has a constant upper bound independent to the network size $N$, which is completely different from the extensively studied real-life networks with their average distance increasing logarithmically to $N$ as $L\sim \texttt{ln}N$ or $L\sim \texttt{lnln}N$. Further more, the integer networks is high clustered, with clustered coefficient $C\approx 0.34$, and display power-law degree distribution of exponent $\gamma\approx 2.4$.Comment: 3 pages, 4 figure

The relationship between mitochondrial function and walking performance in older adults with a wide range of physical function.

Age related declines in walking performance may be partly attributable to skeletal muscle mitochondrial dysfunction as mitochondria produce over 90% of ATP needed for movement and the capacity for oxidative phosphorylation decreases with age. Participants were from two studies: an ancillary to the Lifestyle Interventions and Independence for Elders (LIFE) Study (n=33), which recruited lower functioning participants (Short Physical Performance Battery [SPPB], 7.8±1.2), and the Study of Energy and Aging-Pilot (SEA, n=29), which enrolled higher functioning (SPPB, 10.8±1.4). Physical activity was measured objectively using the Actigraph accelerometer (LIFE) and SenseWear Pro armband (SEA). Phosphocreatine recovery following muscle contraction of the quadriceps was measured using (31)P magnetic resonance spectroscopy and ATPmax (mM ATP/s) was calculated. Walking performance was defined as time (s) to walk 400m at a usual-pace. The cross-sectional association between mitochondrial function and walking performance was assessed using multivariable linear regression. Participants were 77.6±5.3years, 64.2% female and 67.2% white. ATPmax was similar in LIFE vs. SEA (0.52±0.14 vs. 0.55±0.14, p=0.31), despite different function and activity levels (1.6±2.2 vs.77.4±73.3min of moderate activity/day, p<0.01). Higher ATPmax was related to faster walk-time in SEA (r(2)=0.19, p=0.02,); but not the LIFE (r(2)<0.01, p=0.74) cohort. Mitochondrial function was associated with walking performance in higher functioning, active older adults, but not lower functioning, sedentary older adults

Moments of the Virtual Photon Structure Function

The photon structure function is a useful testing ground for QCD. It is perturbatively computable apart from a contribution from what is usually called the hadronic component of the photon. There have been many proposals for this nonperturbative part of the real photon structure function. By studying moments of the virtual photon structure function, we explore the extent to which these proposed nonperturbative contributions can be identified experimentally.Comment: LaTeX, 16 pages + 14 compressed and uuencoded postscript figures, UMN-TH-1111/9

Instream and riparian implications of weed cutting in a chalk river

Macrophyte growth is extensive in the iconic chalk streams that are concentrated in southern and eastern England. Widespread and frequent weed cutting is undertaken to maintain their key functions (e.g. flood water conveyance and maintenance of viable fisheries). In this study, a multidisciplinary approach was adopted to quantify coincident physico-chemical responses (instream and riparian) that result from weed cutting and to discuss their potential implications. Three weed cuts were monitored at a site on the River Lambourn (The CEH River Lambourn Observatory) and major instream and riparian impacts were observed. Measurements clearly demonstrated how weed cutting enhanced flood flow conveyance, reduced water levels (river and wetland), increased river velocities, and mobilised suspended sediment (with associated chemicals) and reduced the capacity for its retention within the river channel. Potential implications in relation to flood risk, water resources, downstream water quality, instream and riparian ecology, amenity value of the river, and wetland greenhouse gas emissions were considered. Provided the major influence of macrophytes on instream and riparian environments is fully understood then the manipulation of macrophytes represents an effective management tool that demonstrates the great potential of working with nature

On Spectra of Linearized Operators for Keller-Segel Models of Chemotaxis

We consider the phenomenon of collapse in the critical Keller-Segel equation (KS) which models chemotactic aggregation of micro-organisms underlying many social activities, e.g. fruiting body development and biofilm formation. Also KS describes the collapse of a gas of self-gravitating Brownian particles. We find the fluctuation spectrum around the collapsing family of steady states for these equations, which is instrumental in derivation of the critical collapse law. To this end we develop a rigorous version of the method of matched asymptotics for the spectral analysis of a class of second order differential operators containing the linearized Keller-Segel operators (and as we argue linearized operators appearing in nonlinear evolution problems). We explain how the results we obtain are used to derive the critical collapse law, as well as for proving its stability.Comment: 22 pages, 1 figur

Distributed flow optimization and cascading effects in weighted complex networks

We investigate the effect of a specific edge weighting scheme $\sim (k_i k_j)^{\beta}$ on distributed flow efficiency and robustness to cascading failures in scale-free networks. In particular, we analyze a simple, yet fundamental distributed flow model: current flow in random resistor networks. By the tuning of control parameter $\beta$ and by considering two general cases of relative node processing capabilities as well as the effect of bandwidth, we show the dependence of transport efficiency upon the correlations between the topology and weights. By studying the severity of cascades for different control parameter $\beta$, we find that network resilience to cascading overloads and network throughput is optimal for the same value of $\beta$ over the range of node capacities and available bandwidth

Dynamics of systems with isotropic competing interactions in an external field: a Langevin approach

We study the Langevin dynamics of a ferromagnetic Ginzburg-Landau Hamiltonian with a competing long-range repulsive term in the presence of an external magnetic field. The model is analytically solved within the self consistent Hartree approximation for two different initial conditions: disordered or zero field cooled (ZFC), and fully magnetized or field cooled (FC). To test the predictions of the approximation we develop a suitable numerical scheme to ensure the isotropic nature of the interactions. Both the analytical approach and the numerical simulations of two-dimensional finite systems confirm a simple aging scenario at zero temperature and zero field. At zero temperature a critical field $h_c$ is found below which the initial conditions are relevant for the long time dynamics of the system. For $h < h_c$ a logarithmic growth of modulated domains is found in the numerical simulations but this behavior is not captured by the analytical approach which predicts a $t^1/2$ growth law at $T = 0$

Aberrant behaviours of reaction diffusion self-organisation models on growing domains in the presence of gene expression time delays

Turing’s pattern formation mechanism exhibits sensitivity to the details of the initial conditions suggesting that, in isolation, it cannot robustly generate pattern within noisy biological environments. Nonetheless, secondary aspects of developmental self-organisation, such as a growing domain, have been shown to ameliorate this aberrant model behaviour. Furthermore, while in-situ hybridisation reveals the presence of gene expression in developmental processes, the influence of such dynamics on Turing’s model has received limited attention. Here, we novelly focus on the Gierer–Meinhardt reaction diffusion system considering delays due the time taken for gene expression, while incorporating a number of different domain growth profiles to further explore the influence and interplay of domain growth and gene expression on Turing’s mechanism. We find extensive pathological model behaviour, exhibiting one or more of the following: temporal oscillations with no spatial structure, a failure of the Turing instability and an extreme sensitivity to the initial conditions, the growth profile and the duration of gene expression. This deviant behaviour is even more severe than observed in previous studies of Schnakenberg kinetics on exponentially growing domains in the presence of gene expression (Gaffney and Monk in Bull. Math. Biol. 68:99–130, 2006). Our results emphasise that gene expression dynamics induce unrealistic behaviour in Turing’s model for multiple choices of kinetics and thus such aberrant modelling predictions are likely to be generic. They also highlight that domain growth can no longer ameliorate the excessive sensitivity of Turing’s mechanism in the presence of gene expression time delays. The above, extensive, pathologies suggest that, in the presence of gene expression, Turing’s mechanism would generally require a novel and extensive secondary mechanism to control reaction diffusion patterning

The role of a matchmaker in buyer-vendor interactions

We consider a simple market where a vendor offers multiple variants of a certain product and preferences of both the vendor and potential buyers are heterogeneous and possibly even antagonistic. Optimization of the joint benefit of the vendor and the buyers turns the toy market into a combinatorial matching problem. We compare the optimal solutions found with and without a matchmaker, examine the resulting inequality between the market participants, and study the impact of correlations on the system.Comment: 7 pages, 5 figures, minor modification

Using Simulation to Assess the Opportunities of Dynamic Waste Collection

In this paper, we illustrate the use of discrete event simulation to evaluate how dynamic planning methodologies can be best applied for the collection of waste from underground containers. We present a case study that took place at the waste collection company Twente Milieu, located in The Netherlands. Even though the underground containers are already equipped with motion sensors, the planning of container emptying’s is still based on static cyclic schedules. It is expected that the use of a dynamic planning methodology, that employs sensor information, will result in a more efficient collection process with respect to customer satisfaction, profits, and CO2 emissions. In this research we use simulation to (i) evaluate the current planning methodology, (ii) evaluate various dynamic planning possibilities, (iii) quantify the benefits of switching to a dynamic collection process, and (iv) quantify the benefits of investing in fill‐level sensors. After simulating all scenarios, we conclude that major improvements can be achieved, both with respect to logistical costs as well as customer satisfaction