Rate Lambda Research Articles

Convolutional neural network-based optimal R-λ intra rate control in Versatile Video Coding

Since intra frame rate control has no prior information to rely on, it is difficult to obtain suitable initial rate control parameters for achieving optimal intra coding. The optimal bit allocation and λ decision are proposed based on a convolutional neural network (CNN) in R-λ intra frame rate control. First, according to the rate distortion (R-D) and rate lambda (R-λ) relationships of the coding tree unit (CTU), a CNN with four outputs is designed to predict the key parameters of R-D and R-λ curves. Second, with the R-D optimization of a frame, the coding optimization equation of the frame λ and the target bit can be built to derive the optimal CTU bit allocation. Last, a suitable CTU λ can be obtained based on the allocated bit and predicted R-λ curve for a CTU to minimize the total distortion of the current frame. The experimental results show that the proposed algorithm can improve the intra frame rate control performance by 0.31 dB with a good rate control accuracy of 4.76%.

Counting generations in birth and death processes with competing Erlang and exponential waiting times

Lymphocyte populations, stimulated in vitro or in vivo, grow as cells divide. Stochastic models are appropriate because some cells undergo multiple rounds of division, some die, and others of the same type in the same conditions do not divide at all. If individual cells behave independently, then each cell can be imagined as sampling from a probability density of times to division and death. The exponential density is the most mathematically and computationally convenient choice. It has the advantage of satisfying the memoryless property, consistent with a Markov process, but it overestimates the probability of short division times. With the aim of preserving the advantages of a Markovian framework while improving the representation of experimentally-observed division times, we consider a multi-stage model of cellular division and death. We use Erlang-distributed (or, more generally, phase-type distributed) times to division, and exponentially distributed times to death. We classify cells into generations, using the rule that the daughters of cells in generation n are in generation n+1. In some circumstances, our representation is equivalent to established models of lymphocyte dynamics. We find the growth rate of the cell population by calculating the proportions of cells by stage and generation. The exponent describing the late-time cell population growth, and the criterion for extinction of the population, differs from what would be expected if N steps with rate lambda were equivalent to a single step of rate lambda /N. We link with a published experimental dataset, where cell counts were reported after T cells were transferred to lymphopenic mice, using Approximate Bayesian Computation. In the comparison, the death rate is assumed to be proportional to the generation and the Erlang time to division for generation 0 is allowed to differ from that of subsequent generations. The multi-stage representation is preferred to a simple exponential in posterior distributions, and the mean time to first division is estimated to be longer than the mean time to subsequent divisions.

Constant payoff in zero-sum stochastic games

In a zero-sum stochastic game, at each stage, two adversary players take decisions and receive a stage payoff determined by them and by a controlled random variable representing the state of nature. The total payoff is the normalized discounted sum of the stage payoffs. In this paper we solve the "constant payoff" conjecture formulated by Sorin, Vigeral and Venel (2010): if both players use optimal strategies, then for any alpha>0, the expected discounted payoff between stage 1 and stage alpha/lambda tends to the limit discounted value of the game, as the discount rate lambda goes to 0.

Modelling COVID 19 in the Basque Country from introduction to control measure response

In March 2020, a multidisciplinary task force (so-called Basque Modelling Task Force, BMTF) was created to assist the Basque health managers and Government during the COVID-19 responses. BMTF is a modelling team, working on different approaches, including stochastic processes, statistical methods and artificial intelligence. Here we describe the efforts and challenges to develop a flexible modeling framework able to describe the dynamics observed for the tested positive cases, including the modelling development steps. The results obtained by a new stochastic SHARUCD model framework are presented. Our models differentiate mild and asymptomatic from severe infections prone to be hospitalized and were able to predict the course of the epidemic, providing important projections on the national health system’s necessities during the increased population demand on hospital admissions. Short and longer-term predictions were tested with good results adjusted to the available epidemiological data. We have shown that the partial lockdown measures were effective and enough to slow down disease transmission in the Basque Country. The growth rate lambda was calculated from the model and from the data and the implications for the reproduction ratio r are shown. The analysis of the growth rates from the data led to improved model versions describing after the exponential phase also the new information obtained during the phase of response to the control measures. This framework is now being used to monitor disease transmission while the country lockdown was gradually lifted, with insights to specific programs for a general policy of “social distancing” and home quarantining.

Twenty-year assessment of Lignum-vitae (Guaiacum sanctum, Zygophyllaceae) in the Palo Verde National Park of Costa Rica

Introduction: The Lignum-vitae (Guaiacum sanctum; Zygophyllaceae) of Mesoamerica and the Greater Antilles, is threatened over much of its range. We evaluated whether a G. sanctum population in the Palo Verde National Park of Costa Rica is viable in the long term. Methods: Using two demographic studies, one in 1997 and the other in 2017, we estimated survival and fecundity rates for each tree age class, population growth rate (lambda), and vital rates elasticities, and we used a density-independent deterministic population model to project the long-term trend of that population. Results: The estimated vital rates during the last 20 years suggested that this population is rapidly decreasing. Although some age classes increased in abundance, seedlings are rare and the plants that recruited in 1997 have not yet reached reproductive maturity. Our results suggest that the current abundance of G. sanctum within the national park may not be a good indicator of its long-term conservation status, and from our population viability analysis, we estimated that the population we studied would decrease to less than 1 % of its current size within the next 200 years. Conclusions: Landscape-scale ecosystem deterioration affecting the greater PVNP region, such as loss of seed dispersers and suppression of disturbances, may offset the passive protection of G. sanctum within park boundaries. Relying on the overall strict protection afforded by the location of the population within the Palo Verde National Park may not be sufficient to conserve this population of G. sanctum. We recommend that more proactive experimental protection and/or restoration measures, possibly including disturbance treatments, be implemented within a research program.

The role of rheology in modelling elastic waves with gas bubbles in granular fluid-saturated media

Elastic waves in fluid-saturated granular media depend on the rheology which includes elements representing the fluid and, if necessary, gas bubbles. We investigated the effect of different rheological schemes, including and excluding the bubbles, on the linear Frenkel–Biot waves of P1 type. For the wave with the bubbles the scheme consists of three segments representing the solid continuum, fluid continuum, and a bubble surrounded by the fluid. We derived the Nikolaevskiy-type equations describing the velocity of the solid matrix in the moving reference system. The equations are linearized to yield the decay rate lambda as a function of the wave number k. We compared the lambda(k)-dependence for the cases with and without the bubbles, using typical values of the input mechanical parameters. For the both cases, the lambda(k)-curve lies entirely below zero, which is in line with the notion of the elastic wave being an essentially passive system. We found that the increase of the radius of the bubbles leads to faster decay, while the increase in the number of the bubbles leads to slower decay of the elastic wave.

Local vs. Long-Range Infection in Unidimensional Epidemics

We study the effects of local and distance interactions in the unidimensional contact process (CP). In the model, each site of a lattice is occupied by an individual, which can be healthy or infected. As in the standard CP, each infected individual spreads the disease to one of its first-neighbors with rate lambda, and with unitary rate, it becomes healthy. However, in our model, an infected individual can transmit the disease to an individual at a distance l apart. This step mimics a vector-mediated transmission. We observe the host-host interactions do not alter the critical exponents significantly in comparison to a process with only Levy-type interactions. Our results confirm, numerically, early field-theoretic predictions.

Asymptotically Optimal Load Balancing Topologies

We consider a system of N ~servers inter-connected by some underlying graph topology~G N . Tasks with unit-mean exponential processing times arrive at the various servers as independent Poisson processes of rate lambda. Each incoming task is irrevocably assigned to whichever server has the smallest number of tasks among the one where it appears and its neighbors in G N . The above model arises in the context of load balancing in large-scale cloud networks and data centers, and has been extensively investigated in the case G N is a clique. Since the servers are exchangeable in that case, mean-field limits apply, and in particular it has been proved that for any lambda < 1, the fraction of servers with two or more tasks vanishes in the limit as N -> ınfty. For an arbitrary graph G N , mean-field techniques break down, complicating the analysis, and the queue length process tends to be worse than for a clique. Accordingly, a graph G N is said to be N -optimal or ∞N-optimal when the queue length process on G N is equivalent to that on a clique on an N -scale or ∞N-scale, respectively. We prove that if G N is an Erdos-Rényi random graph with average degree d(N), then with high probability it is N -optimal and ∞N-optimal if d(N) -> ınfty$ and d(N) / (∞N łog(N)) -> ınfty as N -> ınfty, respectively. This demonstrates that optimality can be maintained at N -scale and ∞N-scale while reducing the number of connections by nearly a factor N and ∞N/ łog(N) compared to a clique, provided the topology is suitably random. It is further shown that if G N contains Θ(N) bounded-degree nodes, then it cannot be N -optimal. In addition, we establish that an arbitrary graph G N is N -optimal when its minimum degree is N - o(N), and may not be N -optimal even when its minimum degree is c N + o(N) for any 0 < c < 1/2. Simulation experiments are conducted for various scenarios to corroborate the asymptotic results.

The Supermarket Model with Bounded Queue Lengths in Equilibrium

In the supermarket model, there are n queues, each with a single server. Customers arrive in a Poisson process with arrival rate lambda n, where lambda = lambda (n) in (0,1). Upon arrival, a customer selects d=d(n) servers uniformly at random, and joins the queue of a least-loaded server amongst those chosen. Service times are independent exponentially distributed random variables with mean 1. In this paper, we analyse the behaviour of the supermarket model in the regime where lambda (n) = 1 - n^{-alpha } and d(n) = lfloor n^beta rfloor , where alpha and beta are fixed numbers in (0, 1]. For suitable pairs (alpha , beta ), our results imply that, in equilibrium, with probability tending to 1 as n rightarrow infty , the proportion of queues with length equal to k = lceil alpha /beta rceil is at least 1-2n^{-alpha + (k-1)beta }, and there are no longer queues. We further show that the process is rapidly mixing when started in a good state, and give bounds on the speed of mixing for more general initial conditions.

Diluted paramagnetic impurities in nonmagnetic Ba2YIrO6

The cubic double perovskite Ba$_2$YIrO$_6$ has been investigated by the local probe techniques nuclear magnetic resonance ($^{89}$Y NMR) and muon spin rotation (muSR). Both methods confirm the absence of magnetic long-range order in this compound but find evidence for diluted localized paramagnetic moments. NMR spin-lattice relaxation rate 1/T1 measurements suggest a slowing down of localized spin moments at low temperatures. An increase of the muSR spin-lattice relaxation rate lambda confirms the presence of weak magnetism in Ba$_2$YIrO$_6$ . However, these findings cannot be explained by the recently suggested excitonic type of magnetism. Instead, they point towards tiny amounts of localized paramagnetic spin centers leading to this magnetic response on the background of a simple nonmagnetic ground state of the 5d$^4$ ($J=0)$ electronic configuration of Ir$^{5+}$.

On a tandem queue with batch service and its applications in wireless sensor networks

We present a tandem network of queues 0,dots , s-1. Customers arrive at queue 0 according to a Poisson process with rate lambda . There are s independent batch service processes at exponential rates mu _0, dots , mu _{s-1}. Service process i, i=0, dots , s-1, at rate mu _i is such that all customers of all queues 0, dots , i simultaneously receive service and move to the next queue. We show that this system has a geometric product-form steady-state distribution. Moreover, we determine the service allocation that minimizes the waiting time in the system and state conditions to approximate such optimal allocations. Our model is motivated by applications in wireless sensor networks, where s observations from different sensors are collected for data fusion. We demonstrate that both optimal centralized and decentralized sensor scheduling can be modeled by our queueing model by choosing the values of mu _i appropriately. We quantify the performance gap between the centralized and decentralized schedules for arbitrarily large sensor networks.

Individual heterogeneity in life histories and eco-evolutionary dynamics.

Individual heterogeneity in life history shapes eco-evolutionary processes, and unobserved heterogeneity can affect demographic outputs characterising life history and population dynamical properties. Demographic frameworks like matrix models or integral projection models represent powerful approaches to disentangle mechanisms linking individual life histories and population-level processes. Recent developments have provided important steps towards their application to study eco-evolutionary dynamics, but so far individual heterogeneity has largely been ignored. Here, we present a general demographic framework that incorporates individual heterogeneity in a flexible way, by separating static and dynamic traits (discrete or continuous). First, we apply the framework to derive the consequences of ignoring heterogeneity for a range of widely used demographic outputs. A general conclusion is that besides the long-term growth rate lambda, all parameters can be affected. Second, we discuss how the framework can help advance current demographic models of eco-evolutionary dynamics, by incorporating individual heterogeneity. For both applications numerical examples are provided, including an empirical example for pike. For instance, we demonstrate that predicted demographic responses to climate warming can be reversed by increased heritability. We discuss how applications of this demographic framework incorporating individual heterogeneity can help answer key biological questions that require a detailed understanding of eco-evolutionary dynamics.

Challenges in the Context of the Development and Application of Risk-informed Regulations in the Domain of Safety Technology

Safety regulations have a long historical perspective. Organizations like DIN, German Institute for Standardization (founded in 1917), ISO, International Organization for Standardization (founded in 1947), IEC, International Electrical Commission (founded in 1906) are promoters in that domain. The new era and the main focus of the paper are the transition of regulations from the descriptive format towards to a proactive format considering prognostic elements like: “what can happen if”. The transition to risk-informed regulations creates numerous challenges for the development and application on both performers, the inventor of the regulation and the user working at the industry. A successful transition is not only a typical technical and organisational achievement but also a legislative and juristic problem which has to be resolved. In the central part of the paper are typical challenges and drawbacks between the wishes of the regulators and the reality in industries representing the various domains of safety technologies. A substantial challenge is to gain the prerequisite for utilizing risk-infirmed regulations, namely to learn from the past for the prediction into the future. The learning from the past must be realised twofold. First, qualitatively based on verbal descriptions, underlined by physical data of abnormal events, incidents and accidents, perceived in the past, and secondly, quantitatively based on statistical evidence of probabilities of the occurrences. A significant category of statistical information needed is the so-called failure rate Lambda (λ) of a specific failure mode of the component of interest. Obviously, to payback lessons learned and to utilise and publish it in failure reports is in contrary to the strategic attitude of traditional industries. Finally, the paper summarizes some recommendations, were the leading focus of the diverse industrial endeavours should be to apply the selected examples of risk-informed regulations successfully.

Empirical Likelihood for Compound Poisson Processes

Let {N(t), t > 0} be a Poisson process with rate lambda > 0, independent of the independent and identically distributed random variables X-1; X-2; ... with mean mu and variance sigma(2). The stochastic process Sigma(N(t))(j=1) X-j is then called a compound Poisson process and has a wide range of applications in, for example, physics, mining, finance and risk management. Among these applications, the average number of objects, which is defined to be lambda mu, is an important quantity. Although many papers have been devoted to the estimation of lambda mu in the literature, in this paper, we use the well-known empirical likelihood method to construct confidence intervals. The simulation results show that the empirical likelihood method often outperforms the normal approximation and Edgeworth expansion approaches in terms of coverage probabilities. A real data set concerning coal-mining disasters is analyzed using these methods.

Spin dynamics and spin freezing in the triangular lattice antiferromagnets FeGa2S4and NiGa2S4

Magnetic susceptibility and muon spin relaxation (muSR) experiments have been carried out on the quasi-2D triangular-lattice spin S = 2 antiferromagnet FeGa2S4. The muSR data indicate a sharp onset of a frozen or nearly-frozen spin state at T* = 31(2) K, twice the spin-glass-like freezing temperature T_f = 16(1) K. The susceptibility becomes field dependent below T*, but no sharp anomaly is observed in any bulk property. A similar transition is observed in muSR data from the spin-1 isomorph NiGa2S4. In both compounds the dynamic muon spin relaxation rate lambda_d(T) above T* agrees well with a calculation of spin-lattice relaxation by Chubukov, Sachdev, and Senthil in the renormalized classical regime of a 2D frustrated quantum antiferromagnet. There is no firm evidence for other mechanisms. At low temperatures lambda_d(T) becomes temperature independent in both compounds, indicating persistence of spin dynamics. Scaling of lambda_d(T) between the two compounds is observed from ~T_f to ~1.5T*. Although the muSR data by themselves cannot exclude a truly static spin component below T*, together with the susceptibility data they are consistent with a slowly-fluctuating "spin gel" regime between T_f and T*. Such a regime and the absence of a divergence in lambda_d(T) at T* are features of two unconventional mechanisms: (1) binding/unbinding of Z_2 vortex excitations, and (2) impurity spins in a nonmagnetic spin-nematic ground state. The absence of a sharp anomaly or history dependence at T* in the susceptibility of FeGa2S4, and the weakness of such phenomena in NiGa2S4, strongly suggest transitions to low-temperature phases with unconventional dynamics.

Variable effects of a generalist parasitoid on a biocontrol seed predator and its target weed

Biological control (the importation of enemies from an invader's native range) is often considered our best chance of controlling the most widespread invaders. Ideally, the agent reduces invader abundance to some acceptably low level, and the two coexist at low density with the agent providing continuous control over the long-term. But the outcome may be complicated when the agent is attacked by native predators and parasites. We used a spatially explicit, discrete-time, individual-based, coupled plant-seed predator-parasitoid model to estimate the impact of the biocontrol agent Eustenopus villosus (a seed predator) on the invasive, annual weed Centaurea solstitialis, both with and without the generalist parasitoid Pyemotes tritici. We estimated the agent's ability to reduce plant density, spread rate, and population growth rate over 50 years. We used long-term demographic data from two sites in central California, USA, to parameterize the model and assess how populations in different climatic zones might respond differently to the agent and the parasitoid. We found that the biocontrol agent reduced plant density (relative to predictions for an uncontrolled invasion), but its impact on the invader's spread rate was modest and inconsistent. The agent had no long-term impact on population growth rate (lambda). Parasitism caused a trophic cascade, the strength of which varied between sites. At our coastal site, the parasitoid entirely eliminated the impact of the agent on the plant. At our Central Valley site, even when parasitized, the agent significantly reduced plant density and spread rate over several decades (although to a lesser degree than when it was not parasitized), but not invader lambda. Surprisingly, we also found that the length of time the invader was allowed to spread across the landscape prior to introducing the agent (5, 25, or 50 years) had little influence over its ability to control the weed in the long-term. This is encouraging news for land managers attempting to control invasive plants that have already established widespread, high-density populations. Unfortunately, our results also show that attack by the native generalist parasitoid had a larger influence over how effectively the agent reduced invader performance.

Demographic heterogeneity, cohort selection, and population growth

Demographic heterogeneity--variation among individuals in survival and reproduction--is ubiquitous in natural populations. Structured population models address heterogeneity due to age, size, or major developmental stages. However, other important sources of demographic heterogeneity, such as genetic variation, spatial heterogeneity in the environment, maternal effects, and differential exposure to stressors, are often not easily measured and hence are modeled as stochasticity. Recent research has elucidated the role of demographic heterogeneity in changing the magnitude of demographic stochasticity in small populations. Here we demonstrate a previously unrecognized effect: heterogeneous survival in long-lived species can increase the long-term growth rate in populations of any size. We illustrate this result using simple models in which each individual's annual survival rate is independent of age but survival may differ among individuals within a cohort. Similar models, but with nonoverlapping generations, have been extensively studied by demographers, who showed that, because the more "frail" individuals are more likely to die at a young age, the average survival rate of the cohort increases with age. Within ecology and evolution, this phenomenon of "cohort selection" is increasingly appreciated as a confounding factor in studies of senescence. We show that, when placed in a population model with overlapping generations, this heterogeneity also causes the asymptotic population growth rate lambda to increase, relative to a homogeneous population with the same mean survival rate at birth. The increase occurs because, even integrating over all the cohorts in the population, the population becomes increasingly dominated by the more robust individuals. The growth rate increases monotonically with the variance in survival rates, and the effect can be substantial, easily doubling the growth rate of slow-growing populations. Correlations between parent and offspring phenotype change the magnitude of the increase in lambda, but the increase occurs even for negative parent-offspring correlations. The effect of heterogeneity in reproductive rate on lambda is quite different: growth rate increases with reproductive heterogeneity for positive parent-offspring correlation but decreases for negative parent-offspring correlation. These effects of demographic heterogeneity on lambda have important implications for population dynamics, population viability analysis, and evolution.

Thresholds for Epidemic Spreading in Networks

We study the threshold of epidemic models in quenched networks with degree distribution given by a power-law. For the susceptible-infected-susceptible model the activity threshold λ(c) vanishes in the large size limit on any network whose maximum degree k(max) diverges with the system size, at odds with heterogeneous mean-field (HMF) theory. The vanishing of the threshold has nothing to do with the scale-free nature of the network but stems instead from the largest hub in the system being active for any spreading rate λ>1/√k(max) and playing the role of a self-sustained source that spreads the infection to the rest of the system. The susceptible-infected-removed model displays instead agreement with HMF theory and a finite threshold for scale-rich networks. We conjecture that on quenched scale-rich networks the threshold of generic epidemic models is vanishing or finite depending on the presence or absence of a steady state.

Interactions between local climate and grazing determine the population dynamics of the small herb Viola biflora

Plants of low stature may benefit from the presence of large herbivores through removal of tall competitive neighbours and increased light availability. Accordingly, removal of grazers has been predicted to disfavour small species. In addition to this indirect beneficial effect, the population dynamics of plants is strongly influenced by variation in external conditions such as temperature and precipitation. However, few studies have examined the interaction between large herbivores and inter-annual variation in climate for the population dynamics of small plant species not preferred by herbivores. We studied three populations of the perennial herb Viola biflora exposed to different sheep densities (high, low and zero) for 6 years in a field experiment. Plants were also impacted by invertebrate and small vertebrate herbivores (rodents). Rates of growth were marginally higher at high sheep densities, and during warm summers both survival and growth were higher when sheep were present. Thus, while the height of tall herbs was positively related to July temperature, it was less so in the treatments with sheep, suggesting that sheep reduce the negative effects of interspecific competition for this small herb. Life table response experiment analyses revealed that the population growth rate (lambda) was slightly lower in the absence of sheep, but between-year variation in lambda was larger than variation among sheep density treatments. lambda was negatively related to July temperature, with an additional negative effect of vertebrate grazing frequency (sheep or rodent grazing). The evidence from this 6-year study suggests that the population dynamics of Viola biflora is determined by a complex interplay between climate and grazing by both large and small herbivores.

Flowering Life‐History Strategies Differ between the Native and Introduced Ranges of a Monocarpic Perennial

Life-history theory makes several key predictions about reproductive strategies on the basis of demographic vital rates, particularly the relationship between juvenile and adult survival. Two such predictions concern the optimal time to begin reproducing and whether semelparity or iteroparity is favored. I tested these life-history predictions and explored how they might differ between the native and introduced ranges of the monocarpic perennial Cynoglossum officinale. I first compared vital rates between ranges. I then used these vital rates to parameterize integral projection models to calculate the population growth rate (lambda) and net reproductive rate (R(0)) as surrogates for fitness to compare strategies within and between ranges. I found that both survival and growth were higher in the introduced range, where size at flowering was larger and iteroparity was much more common than in the native range. The observed and predicted strategies for size at flowering were similar in the native range. In the introduced range, however, even though plants flowered at a larger size, the observed size was not as large as the optimum predicted by lambda or the higher optimum predicted by R(0). Iteroparity conferred higher fitness in both ranges, as measured by both fitness metrics, suggesting that severe constraints, potentially specialist herbivores, prevent this strategy from becoming more common in the native range.