Infinite Duration Research Articles

Responses of soil organic carbon decomposition to warming depend on the natural warming gradient

Inconsistent responses of soil organic carbon (SOC) decomposition to climate warming have been observed in field experiments. Responses vary with the duration of experimental warming; however, even the longest warming experiment could not account for possible future climate-driven changes in SOC decomposition. Here, we investigated the responses of SOC decomposition to natural warming in soil samples (at soil depths of 0–10, 10–20, and 20–30 cm) collected at two altitudes (lower-elevation, warm points; higher-elevation, cool points) with an approximate 1 °C difference in mean soil temperature, representing an infinite natural warming duration in the Qinghai–Tibetan Plateau. We incubated these soil samples at three temperatures (i.e., 5, 10, and 15 °C) and analyzed the CO2 emission rate to assess the responses of SOC decomposition to warming. The results revealed higher CO2 emission rates from topsoil (0–10 and 10–20 cm) samples collected at lower-elevation (warm points) than higher-elevation (cool points). By contrast, subsoil (20–30 cm) samples showed higher CO2 emission rates at higher-elevation points. Soil microbial biomass carbon (MBC) exhibited similar patterns in topsoil and subsoil, indicative of the regulation SOC decomposition by MBC. Overall, CO2 emission rates were higher in subsoil, possible the result of the high vulnerability of carbon and decreased microbial carbon use efficiency in subsoil. For all sampling points, the largest CO2 emission rates and MBC increases were observed at 5 °C incubation temperature, demonstrating that cold-tolerant microbes may undergo adaptations that enable their tolerance to cold conditions. Taken together, our findings provide evidence of the natural warming gradient using a climosequence approach to illustrate the importance of microbial-mediation in controlling SOC decomposition. Moreover, models should consider different mechanisms of soil carbon dynamics in topsoil and subsoil when predicting carbon–climate feedback.

Color induction in equiluminant flashed stimuli.

Color induction is the influence of the surrounding color (inducer) on the perceived color of a central region. There are two different types of color induction: color contrast (the color of the central region shifts away from that of the inducer) and color assimilation (the color shifts towards the color of the inducer). Several studies on these effects have used uniform and striped surrounds, reporting color contrast and color assimilation, respectively. Other authors [J. Vis.12(1), 22 (2012)1534-736210.1167/12.12.1] have studied color induction using flashed uniform surrounds, reporting that the contrast is higher for shorter flash duration. Extending their study, we present new psychophysical results using both flashed and static (i.e., non-flashed) equiluminant stimuli for both striped and uniform surrounds. Similarly to them, for uniform surround stimuli we observed color contrast, but we did not obtain the maximum contrast for the shortest (10ms) flashed stimuli, but for 40ms. We only observed this maximum contrast for red, green, and lime inducers, while for a purple inducer we obtained an asymptotic profile along the flash duration. For striped stimuli, we observed color assimilation only for the static (infinite flash duration) red-green surround inducers (red first inducer, green second inducer). For the other inducers' configurations, we observed color contrast or no induction. Since other studies showed that non-equiluminant striped static stimuli induce color assimilation, our results also suggest that luminance differences could be a key factor to induce it.

On Solving Mean Payoff Games Using Pivoting Algorithms

Two classical pivoting algorithms, due to Lemke and Cottle–Dantzig, are studied on linear complementarity problems (LCPs) and their generalizations that arise from infinite duration two-person mean payoff games (MPGs) under zero-mean partition problem. Lemke’s algorithm was studied in solving MPGs via reduction to discounted payoff games or to simple stochastic games. We provide an alternative and efficient approach for studying the LCPs arising from the MPGs without any reduction. A binary MPG can easily be formulated as an LCP which has always terminated in a complementary solution in numerical experiments, but has not yet been proven either the processability of MPG’s by Lemke’s algorithm or a counter example that it will not terminate with a solution. Till now, the processability of MPG’s by Lemke’s algorithm remains open. A general MPG (with arbitrary outgoing arcs) naturally reduces to a generalized linear complementarity problem (GLCP) involving a rectangular matrix where the vertices are represented by the columns and the outgoing arcs from each vertex are represented by rows in a particular block. The noteworthy result in this paper is that the GLCP obtained from an MPG is processable by Cottle–Dantzig principal pivoting algorithm which terminates with a solution. Several properties of the matrix which arise in this context are also discussed.

Initialization Algorithms for Convolutional Network Coding

We present algorithms for initializing a convolutional network coding (CNC) scheme in networks that may contain cycles. An initialization process for finding global encoding kernels (GEK) is needed if the network is unknown or if local encoding kernels are chosen randomly. During the initialization process every source node transmits basis vectors and every sink node gets the impulse response of the network. The impulse response is then used to find the GEK, which are needed for a decoding algorithm and to find the set of all achievable rates. We present two initialization algorithms that find the GEK and one algorithm that finds achievable rates from the GEK. In the first initialization algorithm it is assumed that we can perform a reset operation on the network at some fixed times, while the second algorithm does not operate under this assumption. Unlike acyclic networks, for which it is sufficient to transmit basis vectors one after another, the initialization of cyclic networks is more involved, as test symbols from different times interfere with each other and the impulse response is of infinite duration. Our algorithms use only a finite number of the initial values of the impulse response to find the full GEK. This is possible because a CNC scheme can be described by a state space representation and, using the Cayley-Hamilton theorem, it is possible to find its full impulse response from its initial values.

Phase Transition in Protocols Minimizing Work Fluctuations.

For two canonical examples of driven mesoscopic systems-a harmonically trapped Brownian particle and a quantum dot-we numerically determine the finite-time protocols that optimize the compromise between the standard deviation and the mean of the dissipated work. In the case of the oscillator, we observe a collection of protocols that smoothly trade off between average work and its fluctuations. However, for the quantum dot, we find that as we shift the weight of our optimization objective from average work to work standard deviation, there is an analog of a first-order phase transition in protocol space: two distinct protocols exchange global optimality with mixed protocols akin to phase coexistence. As a result, the two types of protocols possess qualitatively different properties and remain distinct even in the infinite duration limit: optimal-work-fluctuation protocols never coalesce with the minimal-work protocols, which therefore never become quasistatic.

Periodic solutions of a two-degree-of-freedom autonomous vibro-impact oscillator with sticking phases

This contribution explores the free dynamics of a simple two-degree-of-freedom vibro-impact oscillator. One degree-of-freedom is unilaterally constrained by the presence of a rigid obstacle and periodic solutions involving one sticking phase per period (1-SPP) are targeted. A solution method to obtain such orbits is proposed: it provides conditions on the existence of 1-SPP as well as closed-form solutions. It is shown that 1-SPP might not exist for a given combination of masses and stiffnesses. The set of 1-SPP is at most a countable set of isolated periodic orbits. The construction of 1-SPP requires numerical developments that are illustrated on a few relevant examples. Comparison with nonlinear modes of vibration involving one impact per period (1-IPP) is also considered. Interestingly, an equivalence between 1-SPP and a special set of isolated 1-IPP is established. It is also demonstrated that the prestressed system features sticking phases of infinite duration.

Memoryless determinacy of finite parity games: Another simple proof

Memoryless determinacy of (infinite) parity games is an important result with numerous applications. It was first independently established by Emerson and Jutla [1] and Mostowski [2] but their proofs involve elaborate developments. The elegant and simpler proof of Zielonka [3] still requires a nested induction on the finite number of priorities and on ordinals for sets of vertices. There are other proofs for finite games like the one of Björklund, Sandberg and Vorobyovin [4] that relies on relating infinite and finite duration games. We present here another simple proof that finite parity games are determined with memoryless strategies using induction on the number of relevant states. The closest proof that relies on induction over non absorbing states is the one of Grädel [5]. However instead of focusing on a single appropriate vertex for induction as we do here, he considers two reduced games per vertex, for all the vertices of the game. The idea of reasoning about a single state has been inspired to me by the analysis of finite stochastic priority games by Karelovic and Zielonka [6].

Looking at mean payoff through foggy windows

Mean-payoff games (MPGs) are infinite duration two-player zero-sum games played on weighted graphs. Under the hypothesis of perfect information, they admit memoryless optimal strategies for both players and can be solved in Open image in new window . MPGs are suitable quantitative models for open reactive systems. However, in this context the assumption of perfect information is not always realistic. For the partial-observation case, the problem that asks if the first player has an observation-based winning strategy that enforces a given threshold on the mean-payoff, is undecidable. In this paper, we study the window mean-payoff objectives introduced recently as an alternative to the classical mean-payoff objectives. We show that, in sharp contrast to the classical mean-payoff objectives, some of the window mean-payoff objectives are decidable in games with partial-observation.

Modeling Economic Growth: Domar on Moving Equilibrium

This essay makes use of archival material to examine Evsey Domar's role in the introduction of the rate of growth as a variable in economics in the 1940s and 1950s. Domar investigated the nature of what he called the “moving equilibrium” of economic processes with infinite duration. Reactions to Domar's approach at the time brought about methodological assertions on the distinction between models and theories. Domar's model was an open one, in the sense that his growth equation allowed different closures. A main feature of the model was its relatively stable capital-output ratio, which reflected the terms of the debate about A. H. Hansen's stagnation thesis in the 1940s. The real economy was supposed to be stable, although the model itself was not perfectly consistent with that. The estimation of the “Residual” by Solow and others led Domar to rethink aspects of his original model.

How Much Lookahead is Needed to Win Infinite Games?

Delay games are two-player games of infinite duration in which one player may delay her moves to obtain a lookahead on her opponent's moves. For $\omega$-regular winning conditions it is known that such games can be solved in doubly-exponential time and that doubly-exponential lookahead is sufficient. We improve upon both results by giving an exponential time algorithm and an exponential upper bound on the necessary lookahead. This is complemented by showing EXPTIME-hardness of the solution problem and tight exponential lower bounds on the lookahead. Both lower bounds already hold for safety conditions. Furthermore, solving delay games with reachability conditions is shown to be PSPACE-complete. This is a corrected version of the paper https://arxiv.org/abs/1412.3701v4 published originally on August 26, 2016.

Analysis of Residence Time in the Measurement of Radon Activity by Passive Diffusion in an Open Volume: A Micro-Statistical Approach

Residence time in a flow measurement of radioactivity is the time spent by a pre-determined quantity of radioactive sample in the flow cell. In a recent report of the measurement of indoor radon by passive diffusion in an open volume (i.e. no flow cell or control volume), the concept of residence time was generalized to apply to measurement conditions with random, rather than directed, flow. The generalization, leading to a quantity Δtr, involved use of a) a phenomenological alpha-particle range function to calculate the effective detection volume, and b) a phenomenological description of diffusion by Fick’s law to determine the effective flow velocity. This paper examines the residence time in passive diffusion from the micro-statistical perspective of single-particle continuous Brownian motion. The statistical quantity “mean residence time” Tr is derived from the Green’s function for unbiased single-particle diffusion and is shown to be consistent with Δtr. The finite statistical lifetime of the randomly moving radioactive atom plays an essential part. For stable particles, Tr is of infinite duration, whereas for an unstable particle (such as 222Rn), with diffusivity D and decay rate λ, Tr is approximately the effective size of the detection region divided by the characteristic diffusion velocity . Comparison of the mean residence time with the time of first passage (or exit time) in the theory of stochastic processes shows the conditions under which the two measures of time are equivalent and helps elucidate the connection between the phenomenological and statistical descriptions of radon diffusion.

Fee Simple Absolute in the US Real Estate Law

The article discusses the nature and analyzes the features of fee simple absolute as a key, fundamental title in the system of real property law in the United States. It is noted that this title is the closest to continental (incl. Russian) proprietary structures. The author examines the characteristics of this title: its potentially infinite duration, alienability, completeness of powers given to the owner, the absence of encumbrances, etc. The article explores the requirements on the use of certain reservations and phraseological units in agreements and unilateral contracts, on the basis of which property is transferred due to the fee simple absolute. The author examines controversial provisions of the doctrine, legislation and case practice of the United States that define the principles of application of the rules on fee simple absolute. Particular attention is given to the special statutory rules, which contribute to the interpretation of the party's intent to transfer ownership based on fee simple absolute and/or to obtain such a right. In conclusion, the author summarizes the analysis of the Anglo-American approach to defining fee simple absolute as a subjective civil right, as well as evaluates the risks of artificial delineation of property rights and objects which these rights can be applied to.

Experimental simulation of blast loading on structural elements using rarefaction waves – theoretical analysis

An experimental approach aiming at producing blast loading on structural elements without using either an explosive charge or an impact load, shock waves or compression waves, was investigated theoretically. The transient pressure pulse loading is produced by a transient differential pressure gradient created by a timely sudden pressure release from two connected chambers in between which a target plate is placed. It was shown that this test facility is capable of producing uniform pulse loading on the face of the tested element. An effective model with lumped parameters has been developed to simulate the problem and calculate the resulting blast pulses. The model allows analysis of the basic characteristics of the blast pulses depending on a predefined initial pressure, on the chambers volumes and on the exit air release opening areas. The following characteristics of a blast pulse are studied with that model: peak pressure, built-up duration and pressure drop to zero duration. Both short pulses and pulses with a plateau segment and with an infinite duration are considered.The effect of the filling gas properties on the resulting blast pressures acting on the target was investigated including a diatomic (air) and monatomic (helium) gases. The analytical results are compared with computational results obtained from simulations using the AUTODYN software. Comparisons are also made with experimental data. Excellent agreement is obtained between the calculated pressure time histories predicted by the proposed model and the computational and measured experimental pressure signals. The new presented model with lumped parameters allows an effective analysis of any experiment using that experimental system and definitely will help in planning experiments with specific blast characteristics through proper selection of the suitable parameters to achieve the planned experiment goal.

On Exact Solutions of Rarefaction-Rarefaction Interactions in Compressible Isentropic Flow

Consider the interaction of two centered rarefaction waves in one-dimensional, compressible gas flow with pressure function \(p(\rho )=a^2\rho ^\gamma \) with \(\gamma >1\). The classic hodograph approach of Riemann provides linear 2nd order equations for the time and space variables t, x as functions of the Riemann invariants r, s within the interaction region. It is well known that t(r, s) can be given explicitly in terms of the hypergeometric function. We present a direct calculation (based on works by Darboux and Martin) of this formula, and show how the same approach provides an explicit formula for x(r, s) in terms of Appell functions (two-variable hypergeometric functions). Motivated by the issue of vacuum and total variation estimates for 1-d Euler flows, we then use the explicit t-solution to monitor the density field and its spatial variation in interactions of two centered rarefaction waves. It is found that the variation is always non-monotone, and that there is an overall increase in density variation if and only if \(\gamma >3\). We show that infinite duration of the interaction is characterized by approach toward vacuum in the interaction region, and that this occurs if and only if the Riemann problem defined by the extreme initial states generates a vacuum. Finally, it is verified that the minimal density in such interactions decays at rate O(1)/t.

Reactive synthesis without regret

Two-player zero-sum games of infinite duration and their quantitative versions are used in verification to model the interaction between a controller (Eve) and its environment (Adam). The question usually addressed is that of the existence (and computability) of a strategy for Eve that can maximize her payoff against any strategy of Adam. In this work, we are interested in strategies of Eve that minimize her regret, i.e. strategies that minimize the difference between her actual payoff and the payoff she could have achieved if she had known the strategy of Adam in advance. We give algorithms to compute the strategies of Eve that ensure minimal regret against an adversary whose choice of strategy is (1) unrestricted, (2) limited to positional strategies, or (3) limited to word strategies, and show that the two last cases have natural modelling applications. These results apply for quantitative games defined with the classical payoff functions $$\mathsf {Inf}$$Inf, $$\mathsf {Sup}$$Sup, $${\mathsf {LimInf}}$$LimInf, $$\mathsf {LimSup}$$LimSup, and mean-payoff. We also show that our notion of regret minimization in which Adam is limited to word strategies generalizes the notion of good for games introduced by Henzinger and Piterman, and is related to the notion of determinization by pruning due to Aminof, Kupferman and Lampert.

Delay Games with WMSO+U Winning Conditions

Delay games are two-player games of infinite duration in which one player may delay her moves to obtain a lookahead on her opponent’s moves. We consider delay games with winning conditions expressed in weak monadic second order logic with the unbounding quantifier, which is able to express (un)boundedness properties. We show that it is decidable whether the delaying player has a winning strategy using bounded lookahead and give a doubly-exponential upper bound on the necessary lookahead. In contrast, we show that bounded lookahead is not always sufficient: we present a game that can be won with unbounded lookahead, but not with bounded lookahead. Then, we consider such games with unbounded lookahead and show that the exact evolution of the lookahead is irrelevant: the winner is always the same, as long as the initial lookahead is large enough and the lookahead is unbounded.

Spontaneous excitation of an accelerated atom: (i) Acceleration of infinite duration (the Unruh effect), (ii) acceleration of finite duration

We consider a proton and an electron bound by scalar electrodynamics with the proton forced by an external agency to move along an asymptotically inertial trajectory. We apply previously developed methods for atoms constrained to move relativistically (Barton and Calogeracos, 2005) to examine spontaneous excitation of the atom accompanied by photon emission. In the limit where the asymptotically inertial trajectory tends to the well-known hyperbolic trajectory we do recover the constant transition rate first obtained by Unruh a long time ago: the atom radiates as if it is found in a bath of photons at the Unruh temperature (Barton and Calogeracos, 2008 [7]). In the case of a truncated hyperbolic trajectory and for small accelerations we obtain a transition probability proportional to the square of the acceleration scaled by the acceleration at the Bohr orbit. On the other hand it is to be noted that the Unruh transition rate is exponentially small for small accelerations. Hence accelerations of finite duration provide a more promising context for the observation of spontaneous excitation.

On refinements of subgame perfect $$\epsilon $$ ϵ -equilibrium

The concept of subgame perfect $$\epsilon $$ -equilibrium ( $$\epsilon $$ -SPE), where $$\epsilon $$ is an error-term, has in recent years emerged as a prominent solution concept for perfect information games of infinite duration. We propose two refinements of this concept: continuity $$\epsilon $$ -SPE and $$\phi $$ -tolerance equilibrium. A continuity $$\epsilon $$ -SPE is an $$\epsilon $$ -SPE in which, in any subgame, the induced play is a continuity point of the payoff functions. We prove that continuity $$\epsilon $$ -SPE exists for each $$\epsilon > 0$$ if the payoff functions are bounded and lower semicontinuous. A loss tolerance function $$\phi $$ is a function that assigns to each history $$h$$ a positive real number $$\phi (h)$$ . A strategy profile is said to be a $$\phi $$ -tolerance equilibrium if for each history $$h$$ it is a $$\phi (h)$$ -equilibrium in the subgame starting at $$h$$ . We prove that, for each loss tolerance function $$\phi $$ , there exists a $$\phi $$ -tolerance equilibrium provided that the payoff functions are bounded and continuous. We give counterexamples to show the sharpness of the existence results.

Tarapur atomic power station: analysis of station blackout scenario

Abstract India is currently operating two BWR built by General Electric Company. The design features of these reactors are similar to the Fukushima's BWR except some better containment features in Indian BWR. This paper discusses the enveloping scenario of station blackout of infinite duration with no operator action and no component failure. The paper describes the details of modelling the TAPS-BWR plant model including SCDAP modelling of reactor core in system code RELAP5 and further thermal hydraulic safety assessment of station blackout scenario. The analysis brought out effectively the response of the plant to this high-pressure severe accident scenario. The time line of the severe accident progression will give details of various stages of accident progression along with hydrogen generation, which will be useful in evolving suitable severe accident management guidelines.

Modeling Economic Growth: Domar on Moving Equilibrium

The paper makes use of archive material to examine Evsey Domar’s role in the introduction of the rate of growth as a variable in economics in the 1940s and 1950s. Domar investigated the nature of what he called the “moving equilibrium” of economic processes with infinite duration. Reactions to Domar’s approach at the time brought about methodological assertions on the distinction between models and theories. Domar’s model was an open one, in the sense that his growth equation allowed different closures. A main feature of the model was its relatively stable capital-output ratio, which reflected the terms of the debate about A.H. Hansen’s stagnation thesis in the 1940s. The real economy was supposed to be stable, although the model itself was not perfectly consistent with that. The estimation of the “residual” by Solow and others led Domar to rethink aspects of his original model.