Infinite Duration Research Articles

Hasdai Crescas, Gianfrancesco Pico, Giordano Bruno: On Infinite Space and Time

This article examines the conception of infinite space and time in Hasdai Crescas, Gianfrancesco Pico della Mirandola and Giordano Bruno. If Crescas’ presence is explicit in Gianfrancesco Pico’s Examen vanitatis (1520), the reception by Bruno, who never mentions him, was postulated by Harry A. Wolfson in 1929. More recently, David Harari and Mauro Zonta posited the intermediary role of an unknown Jewish author. However, a comparison of the critique of Aristotle by Crescas and Bruno shows that, apart from two points, Bruno was able to reach his positions, independently of Crescas, from his own critical reading of Aristotle and from his knowledge of the developments in medieval scholasticism and the Neoplatonic concept of time. Significantly, Crescas qualifies space and time as attributes of God in a purely metaphorical sense, a question that Pico leaves aside, while Bruno conceives of infinite space and duration, together with matter, as real attributes of God, who, as an indifferent unity of opposites, is both mind and intellect as well as space and matter.

A coalitional differential game of vaccine producers

The paper proposes a game-theoretic model of competition and cooperation of vaccine producers. Various versions of players' cooperation (partial and full) have been studied. The differential game has an infinite duration. For each possible coalition of players, the profits and production quantities of its members are determined. An stability analysis of possible coalition structures, as well as coalitions that are most attractive to customers has been made.

A Coalitional Differential Game of Vaccine Producers

The paper proposes a game-theoretic model of competition and cooperation, including partial cooperation, of vaccine producers. Various versions of players’ cooperation (partial and full) have been studied. The differential game has an infinite duration. For each possible coalition of players, the profits and production quantities of its members are determined. An stability analysis of possible coalition structures, as well as coalitions that are most attractive to customers has been made.

Non-local linear response in anomalous transport

The anomalous heat transport observed in low-dimensional classical systems is associated with super-diffusive spreading of the space–time correlation of the conserved fields in the system. This leads to a non-local linear response relation between the heat current and the local temperature gradient in the non-equilibrium steady state. This relation provides a generalization of Fourier’s law of heat transfer and is characterized by a non-local kernel operator related to the fractional operators describing super-diffusion. The kernel is essentially proportional, in an appropriate hydrodynamic scaling limit, to the time integral of the space–time correlations of local currents in equilibrium. In finite-size systems, the time integral of correlation of microscopic currents at different locations over an infinite duration is independent of the locations. On the other hand, the kernel operator is space-dependent. We demonstrate that the resolution of this apparent puzzle becomes evident when we consider an appropriate combination of the limits of a large system size and a long integration time. Our study shows the importance of properly handling these limits, even when dealing with (open) systems connected to reservoirs. In particular, we reveal how to extract the kernel operator from simulated microscopic current–current correlation data. For two model systems exhibiting anomalous transport, we provide a direct and detailed numerical verifications of the kernel operators.

Subgame-perfect Equilibria in Mean-payoff Games (journal version)

In this paper, we provide an effective characterization of all the subgame-perfect equilibria in infinite duration games played on finite graphs with mean-payoff objectives. To this end, we introduce the notion of requirement, and the notion of negotiation function. We establish that the plays that are supported by SPEs are exactly those that are consistent with a fixed point of the negotiation function. Finally, we use that characterization to prove that the SPE threshold problem, who status was left open in the literature, is decidable.

Collapse mechanisms of a Neimark–Sacker torus

Two examples of collapse of a Neimark–Sacker torus in the Rössler system are studied. Their stability is evaluated by measuring the rotation number, defined as the long-term average value of the angular phase shift that occurs in the Poincaré map on each pass, and by theoretically calculating the same angular shift within the context of a normalized cubic model. The parameters of the cubic model are evaluated using perturbation theory applied to a limit cycle, which involves first evaluating the response after a fixed time, the known period of the limit cycle, and then calculating the additional effect due to variations in time of flight to reach a fixed plane perpendicular to velocity.For the first example of collapse, the above two methods yield the same result, namely that the collapse is characterized by a constant rotation number as we move away from the bifurcation, leading to a torus that usually coalesces into discrete branches and then collapses due to turning points. This mechanism allows us to define a simple criterion that the parameters of the cubic model must satisfy, which is related to stability. The second example of collapse is more complex: the normalized cubic model suggests correctly that the collapse will be associated with the calculated radius of the torus becoming complex, which leads to a second criterion for the cubic parameters. However, the predicted point of collapse is significantly premature. The actual torus continues to survive until the rotation number approaches zero, leading to a single wave packet of infinite duration that travels between the two known equilibrium points of the system.

Characterizing Positionality in Games of Infinite Duration over Infinite Graphs

We study turn-based quantitative games of infinite duration opposing two antagonistic players and played over graphs. This model is widely accepted as providing the adequate framework for formalizing the synthesis question for reactive systems. This important application motivates the question of strategy complexity: which valuations (or payoff functions) admit optimal positional strategies (without memory)? Valuations for which both players have optimal positional strategies have been characterized by Gimbert and Zielonka for finite graphs and by Colcombet and Niwi\'nski for infinite graphs. However, for reactive synthesis, existence of optimal positional strategies for the opponent (which models an antagonistic environment) is irrelevant. Despite this fact, not much is known about valuations for which the protagonist admits optimal positional strategies, regardless of the opponent. In this work, we characterize valuations which admit such strategies over infinite game graphs. Our characterization uses the vocabulary of universal graphs, which has also proved useful in understanding recent breakthrough results regarding the complexity of parity games. More precisely, we show that a valuation admitting universal graphs which are monotone and well-ordered is positional over all game graphs, and -- more surprisingly -- that the converse is also true for valuations admitting neutral colors. We prove the applicability and elegance of the framework by unifying a number of known positionality results, proving new ones, and establishing closure under lexicographical products. Finally, we discuss a class of prefix-independent positional objectives which is closed under countable unions.

The Theory of Universal Graphs for Infinite Duration Games

We introduce the notion of universal graphs as a tool for constructing algorithms solving games of infinite duration such as parity games and mean payoff games. In the first part we develop the theory of universal graphs, with two goals: showing an equivalence and normalisation result between different recently introduced related models, and constructing generic value iteration algorithms for any positionally determined objective. In the second part we give four applications: to parity games, to mean payoff games, to a disjunction between a parity and a mean payoff objective, and to disjunctions of several mean payoff objectives. For each of these four cases we construct algorithms achieving or improving over the best known time and space complexity.

Physical implementation of optimal control over a direct current

In the next manuscript we will show an interesting physical application of the technique of optimal control over a direct current, more exactly on a direct current motor. For this, the mathematical support or scaffolding that allows to establish the model of the problem will be presented in the development of the document, which contains a basic structure supported in a general dynamic system (linear or non-linear) and an objective function that will depend on the system. Although in essence the optimal control problems correspond to infinite spaces, the finite-dimensional case will be analyzed initially and then made an extension to the case of a quadratic linear regulator for an interval of infinite duration. The results of the implementation of this optimal control technique on a direct current motor will be analyzed by means of Bole diagrams that will represent the frequency response of the system and a follow-up diagram of set points and rejection of disturbances.

Axonal excitability changes in children with spinal muscular atrophy treated with nusinersen.

Spinal muscular atrophy (SMA) is associated with developmental disruption of motor axons in ventral roots of the spinal cord alongside motor axon degeneration. The pathogenesis of peripheral axonal change during development is pertinent to understand treatment response. Nerve excitability techniques, stimulating the median motor nerve at the wrist, were utilised to investigate axonal change during neurodevelopment in 24 children with SMA, compared with 71 age-matched controls. Longitudinal axonal response to nusinersen treatment in 18 children was also investigated. Significant differences in axonal development were noted in the youngest children with SMA, signified by reduced compound muscle action potential (CMAP) (P=0.030), higher axonal threshold (P=0.016), rheobase (minimal current amplitude of infinite duration, required to generate an action potential) (P=0.012) and greater changes in depolarising and hyperpolarising threshold electrotonus. Subexcitability increased in all children with SMA, compared to controls. With treatment, nerve excitability changes were observed prominently in young children, with increases in CMAP, reduction in axonal threshold, fanning-in of threshold electrotonus, increase in resting current-threshold slope and reduction in subexcitability. Whilst motor axons continue to mature in SMA, developmental delays in passive and active membrane properties occur especially in early childhood. Concurrently, motor axons actively undergo degeneration. Nusinersen restores the developmental trajectory of motor axons reducing degeneration, especially in children with early treatment initiation. Our findings move the field forward in understanding the developmental aspect of childhood-onset motor neurone diseases and changes in axonal function associated with disease modification. KEY POINTS: Pathomechanisms in spinal muscular atrophy involve concurrent neurodevelopmental and neurodegenerative processes. The greatest delays in maturation of the passive and active properties of the peripheral motor axon are seen in early childhood. Nusinersen facilitates developmental recovery of the motor axon whilst also reducing neurodegeneration. Axonal dysfunction is reversed with SMN repletion particularly when intervention occurs early in development.

A novel methodology for large strain under intermediate strain rate loading

Hopkinson bar has already worked to measure mechanical properties of materials under high strain rates, but it fails to conduct intermediate strain rates loading with considerable deformation. Thereby, a methodology is proposed for achieving enough large strains under intermediate strain rates. The experimental system based on it is then constructed: a striker bar with same length as incident bar is selected to generate continuous stress wave loading, and a long polymethylmethacrylate bar is preferred as the transmitted bar to guide and record transmitted signals. Thus, loading stress wave is achievable with a nearly constant amplitude and an infinite loading duration. The involved data interpretations are deduced, and verified both theoretically and experimentally. Its measurement capacity is confirmed by loading a thermoplastic polyurethane, and maximum strains up to 12% and 65% under strain rates of 40/s and 270/s, respectively. Finally, the involved influences and factor sensitivities are analyzed for enough experimental accuracy and extensive measurements.

Forced vibration analysis of laminated composite stiffened plates

The extensive parametric study on the forced vibration characteristics of laminated composite stiffened plates using finite element method (FEM) is investigated in this paper. A nine noded isoparametric plate element with five degrees of freedom and a three noded isoparametric beam element with four degrees of freedom as stiffener element are appropriately combined together to obtain stiffened plate element. Newmark's method is applied to obtain the dynamic response of stiffened plates and is investigated for three different types of transient loads: uniformly distributed step load of infinite duration, uniformly distributed step load of finite duration (1 s) and uniformly distributed half sine load of finite duration (1 s). The dynamic response analysis of laminated stiffened plate is conducted with respect to boundary conditions of the plate, number, type and orientation of stiffeners, stiffener depth to plate thickness ratio and types of dynamic loading. Significant effects of the above parameters are observed on the dynamic responses of the laminated stiffened plates. Reduction of displacement response of the laminated composite plate is noticed to a large extent with introduction of stiffeners.

Dynamic Stability Critical State of Pin-Ended Arches under Sudden Central Concentrated Load

The dynamic in-plane instability process of extreme point type for pin-ended arches when a central radial load applied suddenly with infinite duration is analyzed with finite element method in this study. The state of arch can be determined by the crown’s vertical displacement varied with time and the critical load can be obtained by repeating trial-calculation. When the arch structure reaches the dynamically stable critical state, the kinetic energy of the structure is very small or even zero. The dynamic critical load of elastic arch calculated with the theoretical analysis method which is based on energy principle is proved accuracy enough by comparing with the finite element calculation results and the percentage of the differences between them are no more than 4.5 %. The maximal elastic strain energy is certain for the elastic-plastic arch in certain geometry under both a sudden load and static load. The maximal elastic strain energy in static calculation can be used in determining the state of the elastic-plastic arch under dynamic sudden loads applied and this method is more accurate which errors won’t exceed 3.5 %. The accuracy of dynamic critical load calculation method for elastic arch is verified by numerical calculation in this study, and based on the characteristic of elastic strain energy in critical state, a method for determining the stability of elastic-plastic arch is presented.

Infinite aggregation: expanded addition

How might we extend aggregative moral theories to compare infinite worlds? In particular, how might we extend them to compare worlds with infinite spatial volume, infinite temporal duration, and infinitely many morally valuable phenomena? When doing so, we face various impossibility results from the existing literature. For instance, the view we adopt can endorse the claim that (1) worlds are made better if we increase the value in every region of space and time, or (2) that they are made better if we increase the value obtained by every person. But they cannot endorse both claims, so we must choose. In this paper I show that, if we choose the latter, our view will face serious problems such as generating incomparability in many realistic cases. Opting instead to endorse the first claim, I articulate and defend a spatiotemporal, expansionist view of infinite aggregation. Spatiotemporal views such as this do face some difficulties, but I show that these can be overcome. With modification, they can provide plausible comparisons in cases that we care about most.

Comment on “Nondispersive analytical solutions to the Dirac equation”

In our Comment we question the validity of the claim made by Campos and Cabrera [Phys. Rev. Res. 2, 013051 (2020)] that their solutions of the Dirac equation in an external time-dependent electromagnetic field describe beams of electrons. In every time-dependent field, no matter how weak, which has an infinite time duration, there is continuous electron-positron pair creation and annihilation. Without the proper accounting for these processes, the mathematical solutions of the Dirac equation are not directly applicable to realistic physical situations. In particular, the time evolution of the average values $\ensuremath{\langle}x\ensuremath{\rangle}$ and $\ensuremath{\langle}y\ensuremath{\rangle}$ does not describe the electron trajectory but the motion of some combination of the electron and positron charge distributions with pathological properties (zitterbewegung).

Multiparameter control modeling of electrical signal in a medium voltage network by Markov random approach

In this paper, the electrical signals coupled to the fields present in a medium voltage network are analyzed by the randomMarkov approach. This approach with the contribution of the “Yakam Matrix” is studied to establish the quantitative approximationsof the current I and the voltage V in non-steady state conditions in order to efficiently deduct the error percent between theexperimental and the simulated results. Also, the aim was to determine the functional constant with infinite duration through multivariablestabilization in commandability and controllability process. The development of the transition and observability matrices ofthe electrical signals behavior to establish the initialization’s system of Dirichlet is presented where the vector  by the hidden Markovapproach revealed to be almost stable. The multiparameter analysis in non-steady state conditions is conducted to show the maximumprobability of the injected signals. The comparison of the experimental results with the simulation is presented with a 4% errorobtained by using MATLAB. Since the function current I(t) remains in (0  I  20)A conditions in case of phase disconnection.However, the application of the Markov random approach in electrical networks control modeling still require further studies andclarifications.

Теорема отсчетов во временной области для инфинитного сигнала: аналитическое выражение и геометрическая иллюстрация

Теорема отсчетов во временной области для инфинитного сигнала: аналитическое выражение и геометрическая иллюстрация

Optimization algorithms, an effective tool for the design of digital filters; a review

Nowadays, optimal and intelligent design approaches are vital in almost all areas of engineering. Scientists and engineers are attempting to make frameworks and models more proficient and intelligent. This paper deals with a detailed investigation on design of various digital filters using optimization algorithms. Generally digital filters are classified into two types which are FIR and IIR filters and are again classified into one dimensional, two dimensional and three dimensional filters for signal, image and video respectively. The design of a digital filter that satisfies all the required conditions perfectly is a challenging factor. So, apart from the conventional mathematical methods, optimization algorithms can be used to design optimal digital filters. IIR Filters are infinite impulse response filter; they have impulse response of infinite duration. FIR Filters are finite impulse response filters; they have impulse response of finite duration. In this paper we have discussed the design of various optimal digital filters based on various optimization algorithms, for processing of signal, image and video. The design of digital filters based on Evolutionary algorithms and swarm intelligence algorithms like Genetic Algorithm, Particle Swarm Optimization, Artificial Bee Colony Optimization, Cuckoo Search Algorithm, Differential Evolution, Gravitational Search, Harmony Search, Spiral Optimization, teaching–learning based optimization, wind driven optimization, hybridization of optimization algorithm are presented.

Tensor stability in Born-Infeld determinantal gravity

We consider the transverse-traceless tensor perturbation of a spatial flat homogeneous and isotropic spacetime in Born-Infeld determinantal gravity, and investigate the evolution of the tensor mode for two solutions in the early universe. For the first solution where the initial singularity is replaced by a regular geometric de Sitter inflation of infinite duration, the evolution of the tensor mode is stable for the parameter spaces alpha <-1, omega ge -1/3 and alpha =-1, omega >0. For the second solution where the initial singularity is replaced by a primordial brusque bounce, which suffers a sudden singularity at the bouncing point, the evolution of the tensor mode is stable for all regions of the parameter space. Our calculation suggests that the tensor evolution can hold stability in large parameter spaces, which is a remarkable property of Born-Infeld determinantal gravity. We also constrain the theoretical parameter |lambda |ge 10^{-38} text {m}^{-2} by resorting to the current bound on the speed of the gravitational waves.

Critical current formula of perpendicularly magnetized magnetic random access memory revisited

A theoretical formula of the current necessary to reverse a perpendicular magnetization by the spin torque effect is derived by solving the Landau–Lifshitz–Gilbert equation. Our formula reproduces the critical current formulas in previous works under several limiting conditions such as an infinite pulse duration of current and low damping. On the other hand, our formula gives a different estimation of the critical current when the pulse duration and/or damping are finite. The comparison with numerical simulation confirms that the derived formula provides a highly accurate estimation of the critical current for a wide range of pulse durations and damping constants.