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This paper considers near-equilibrium systems of ordinary differential equations with explicit separation of the slow and stable manifolds. Formal B-series like those previously used to analyze highly oscillatory systems or to construct modified equations are employed here to construct expansions of the change of variables, the center invariant manifold and the reduced model. The new approach may be seen as a process of reduction to a normal form, with the surprising advantage, as compared to the standard view conveyed by the celebrated center manifold theorem, that it is possible to recover the complete solution at any time through an explicitly computable way. [ABSTRACT FROM AUTHOR]

A shadowable point for a flow is a point where the shadowing lemma holds for pseudo-orbits passing through it. We prove that this concept satisfies the following properties: the set of shadowable points is invariant and a Gδ set. A flow has the pseudo-orbit tracing property if and only if every point is shadowable. The chain recurrent and nonwandering sets coincide when every chain recurrent point is shadowable. The chain recurrent points which are shadowable are exactly those that can be are approximated by periodic points when the flow is expansive. These results extends those presented in Morales (Dyn Syst. 2016;31(3):347-356). We study the relations between shadowable points of a homeomorphism and the shadowable points of its suspension flow. We characterize the set of forward shadowable points for transitive flows and chain transitive flows. We prove that the geometric Lorenz attractor does not have shadowable points. We show that in the presence of shadowable points chain transitive flows are transitive and that transitivity is a necessary condition for chain recurrent flows with shadowable points whenever the phase space is connected. Finally, as an application, these results we give concise proofs of some well known theorems establishing that flows with POTP admitting some kind of recurrence are minimal. [ABSTRACT FROM AUTHOR]

In this paper we investigate the quasi-shadowing property for C1 random dynamical systems on their random partially hyperbolic sets. It is shown that for any pseudo orbit {xk}−∞+∞ on a random partially hyperbolic set there exists a “center” pseudo orbit {yk}−∞+∞ shadowing it in the sense that yk+1 is obtained from the image of yk by a motion along the center direction. Moreover, when the random partially hyperbolic set has a local product structure, the above “center” pseudo orbit {yk}−∞+∞ can be chosen such that yk+1 and the image of yk lie in their common center leaf. [ABSTRACT FROM AUTHOR]

We define topological pseudo orbital specification, topological weak specification, topological ergodic shadowing, topological d̲-shadowing for a continuous map on a uniform space and show that they are equivalent for a uniformly continuous map with topological shadowing on a totally bounded uniform space. [ABSTRACT FROM AUTHOR]

Prior work has addressed the effects of multipath fading and path loss separately for broadcast and multiple-access channels. It has been shown that the number of simultaneously active users are of the order $$\Theta (\ln (\ln (n)))$$ for random channel gains with exponentially-decaying tails, where n is the total number of users. Furthermore, it has been shown that assuming path loss is dominant and ignoring multipath fading, the user capacity (i.e. the maximum number of simultaneously active users in a wireless system) of multi-user channels is of the order $$\Theta (\ln (n))$$ when the users are spatially distributed on the plane with a Gaussian or Uniform distribution. In this paper, we study the shadowing effects on the number of active users for broadcast and multiple-access channels in which the users are randomly distributed on the plane. It is shown that as the total number of users in the multi-user channel goes to infinity, the number of active users is of the order $$\Theta (\sqrt{\ln (n)}).$$ [ABSTRACT FROM AUTHOR]

We introduce and study here the notion of specification property termed as topological specification property for homeomorphisms on non-compact non-metrizable spaces. We prove that if a self homeomorphism on a totally bounded uniform space is mixing, topologically expansive and topologically shadowing then the map has topological specification property. [ABSTRACT FROM AUTHOR]

We call that a vector field has the oriented shadowing property if for any $$\varepsilon >0$$ there is $$d>0$$ such that each $$d$$ -pseudo orbit is $$\varepsilon $$ -oriented shadowed by some real orbit. In this paper, we show that the $$C^1$$ -interior of the set of vector fields with the oriented shadowing property is contained in the set of vector fields with the $$\Omega $$ -stability. [ABSTRACT FROM AUTHOR]

Although electronic gaming machine (EGM) jackpots are widespread, little research has yet considered the impact of this feature on gamblers' behaviour. We present the results of an in-venue shadowing study, which provided measures of player investment and persistence (e.g. number of spins, time-on-machine) from participants undertaking one or more EGM sessions on their choice of machines. 234 participants (162 female) were recruited in-venue, with half (stratified by age and gender) primed by answering questions encouraging 'big-win' oriented ideation. Primed participants were more likely to select jackpot-oriented EGMs, and primed at-risk [Problem Gambling Severity Index (PGSI) > 4] gamblers tended to select machines with a higher median jackpot prize amount than others ([Formula: see text]). Neither PGSI nor priming was associated with the rate at which participants switched machines. EGM jackpots were associated with great spend overall, and PGSI score was associated with a greater spend per play. Positive interactions were found between jackpots and PGSI, and PGSI and priming in terms of predicting greater persistence. Finally a structural model of session level variables is presented, that incorporates positive feedback between money won and number of plays in an EGM session. [ABSTRACT FROM AUTHOR]

We consider shadowing properties for vector fields corresponding to different type of reparametrizations. We give an example of a vector field which has the oriented shadowing properties, but does not have the standard shadowing property. [ABSTRACT FROM AUTHOR]

In this paper, we study the connectivity of multihop wireless networks with the log-normal shadowing model by investigating the critical transmission power required by each node for asymptotic vanishing of the isolated nodes, and the precise distribution of the number of isolated nodes. The vanishing of isolated nodes is not only a prerequisite but also a good indication of network connectivity. Most of the known works on network connectivity under such a shadowing model were obtained only based on simulation studies or ignoring the important boundary effect to avoid the challenging technical analysis, and thus hardly applied to practical wireless networks. It is extremely challenging to take the complicated boundary effect into consideration under such a realistic shadowing model because the transmission area of each node is an irregular region other than a circular area. Assume the wireless nodes are represented by a Poisson point process with density $$n$$ over a unit-area disk. With the boundary effect taken into consideration, we first obtain an explicit formula for the expected number of isolated nodes, we then derive an upper and a lower bounds of the critical transmission power for asymptotic vanishing of the isolated nodes. The tightness of the upper and lower bounds for the critical transmission power are analyzed via numerical analysis by using the software engineering approach. When a wireless network consists of $$n$$ nodes distributed independently and uniformly over a unit-area disk, we derive the precise distribution of the number of the isolated nodes under such a realistic shadowing model with the linear power assignment, taking the boundary effect into consideration. [ABSTRACT FROM AUTHOR]

We consider a linear skew product with the full shift in the base and nonzero Lyapunov exponent in the fiber. We provide a sharp estimate for the precision of shadowing for a typical pseudotrajectory of finite length. This result indicates that the high-dimensional analog of the Hammel-Yorke-Grebogi conjecture concerning the interval of shadowability for a typical pseudotrajectory is not correct. The main technique is the reduction of the shadowing problem to the ruin problem for a simple random walk. [ABSTRACT FROM AUTHOR]

In many papers dealing with connections between the theory of shadowing of pseudotrajectories of dynamical systems and the theory of structural stability, the authors apply the Mañé theorem on the characterization of structural stability in terms of the analytic strong transversality condition. The original proof of this theorem contains a proof of the implication (the analytic strong transversality condition) ⇒ (density of periodic points in the nonwandering set), which is based on the nontrivial theory of hyperbolic limit sets. In this short note, we show that the proof of this implication can be substantially simplified in the case of a diffeomorphism having the shadowing property. [ABSTRACT FROM AUTHOR]

Relay deployments promise to alleviate the limitations of conventional macrocell networks, such as poor indoor penetration and coverage holes in a cost-efficient way. In this context, the capacity of the wireless relay link between a relay node (RN) and its serving base station has a crucial impact on the end-to-end performance. The deployment flexibility of RNs, which mainly stems from the wireless relay link, compact physical characteristics, and low-power consumption, can be exploited by relay site planning (RSP) to overcome the limitations of the relay link and, thus, enhance the system performance. To this end, RSP is carried out via selecting an RN deployment location from a discrete set of alternatives considering the signal-to-interference-plus-noise ratio (SINR) on the relay link as the selection criterion. In practice, the so-called coarse RSP takes into account only large-scale fading due to shadowing. Nevertheless, as RNs are stationary, the wireless channels pertaining to relay deployments are subject to simultaneous impairments by both shadowing and multi-path fading, i.e., composite fading/shadowing. In this paper, we present the performance of coarse RSP that can be used for planning and dimensioning of two-hop cellular relay networks in composite fading/shadowing environments, where co-channel interference is also present. The relay link is modeled by Nakagami-lognormal distribution while the access link between a mobile terminal and its serving RN is modeled by Rician-lognormal distribution. Further, we provide an accurate analytical framework through closed-form expressions for relay link SINR, link rates, and end-to-end rate. Results show that coarse RSP can still yield high performance improvements in terms of both SINR and rate considering composite fading/shadowing channels. Moreover, coarse RSP is shown to effectively decrease the amount of fading on the relay link and, thus, mitigate the detrimental effects of composite fading/shadowing. [ABSTRACT FROM AUTHOR]

We study the screening effect for the multiparton interactions (MPI) for proton-deuteron collisions in the kinematics where one parton belonging to the deuteron has small $$x_1$$ , so the leading twist shadowing is present, while the second parton ( $$x_2$$ ) is involved in the interaction in the kinematics where shadowing effects are small. We find that the ratio of the shadowing and the impulse approximation terms is approximately a factor of 2 larger for MPI than for the single parton distributions. We also calculate the double parton antishadowing (DPA) contribution to the cross section due to the independent interactions of the partons of the projectile proton with two nucleons of the deuteron and find that shadowing leads to a strong reduction of the DPA effect. For example, for the resolution scale $$Q_1^2 \sim 4$$ $$\text{ GeV }^2$$ of the interaction with parton $$x_1$$ we find that shadowing reduces the DPA effect by $$\sim $$ 30 %. It is argued that in the discussed kinematics the contribution of the interference diagrams, which correspond to the interchange of partons between the proton and neutron, constitutes only a small correction to the shadowing contributions. [ABSTRACT FROM AUTHOR]

We analyse the derivative of the reduced cross-section $\frac {{\partial }{\sigma ^{s}_{r}}}{{\partial }{\ln }y}|_{x}$, using the nonlinear Dokshitzer-Gribov-Lipatov-Altarelli-Parisi (NLDGLAP) evolution equation at small x. The small x behaviour of the structure functions are obtained by solving the Gribov, Levin, Ryskin, Mueller and Qiu (GLR-MQ) evolution equation with the nonlinear shadowing term incorporated. We show that the strong rise corresponding to the linear QCD evolution equations, can be tamed by screening effects. [ABSTRACT FROM AUTHOR]

For a parabolic equation, we consider the problem of constructing a feedback control synthesis algorithm ensuring that the solution of a given equation shadows the solution of another equation with unknown right-hand side. We suggest a noise-immune algorithm based on the extremal shift method well known in guaranteed control theory. [ABSTRACT FROM AUTHOR]

Let M be a closed smooth manifold M, and let f: M → M be a diffeomorphism. In this paper, we consider a nontrivial transitive set Λ of f. We show that if f has the C-stably average shadowing property on Λ, then Λ admits a dominated splitting. [ABSTRACT FROM AUTHOR]

We have carried out a wide study of shadowing and antishadowing effects on J/ ψ production in dAu collisions at $${\sqrt{s_{N N}} = 200}$$ GeV. We have studied the effects of three different gluon nPDF sets, using the exact kinematics for a 2 → 2 process, namely g + g → J/ ψ + g as expected from LO pQCD. We have computed the rapidity dependence of R and R for the different centrality classes of the PHENIX data. For mid rapidities, we have also computed the transverse-momentum dependence of the nuclear modification factor, which cannot be predicted with the usual 2 → 1 simplified kinematics. All these observables have been compared to the PHENIX data in dAu collisions. [ABSTRACT FROM AUTHOR]

We present a shadowing theorem on the existence of hyperbolic trajectories on finite time intervals based on the EPH partition by George Haller and apply it to an example which is inspired by the problem of two-dimensional symmetric vortex merger. [ABSTRACT FROM AUTHOR]

In this paper two aspects of numerical dynamics are used for an artificial neural network (ANN) analysis. It is shown that topological conjugacy of gradient dynamical systems and both the shadowing and inverse shadowing properties have nontrivial implications in the analysis of a perceptron learning process. The main result is that, generically, any such process is stable under numerics and robust. Implementation aspects are discussed as well. The analysis is based on the theorem concerning global topological conjugacy of cascades generated by a gradient flow on a compact manifold without a boundary. [ABSTRACT FROM AUTHOR]

We give a characterization of structurally stable diffeomorphisms by making use of the notion of L-shadowing property. More precisely, we prove that the set of structurally stable diffeomorphisms coincides with the C-interior of the set of diffeomorphisms having L-shadowing property. [ABSTRACT FROM AUTHOR]

This paper presents a high-quality high-performance algorithm to compute plausible soft shadows for complex dynamic scenes. Given a rectangular light source, the scene is rendered from the viewpoint placed at the center of the light source, and discretized into a layered depth map. For each scene point sampled in the depth map, the occlusion degree is computed, and stored in a layered occlusion map. When the scene is rendered from the camera's viewpoint, the occlusion degree of a scene point is computed by filtering the layered occlusion map. The proposed algorithm produces soft shadows the quality of which is quite close to that of the ground truth reference. As it runs very fast, a scene with a million polygons can be rendered in real-time. The proposed method does not require pre-processing and is easy to implement in contemporary graphic hardware. [ABSTRACT FROM AUTHOR]

A general model with multiple input flows (classes) and several flexible multi-server pools is considered. We propose a robust, generic scheme for routing new arrivals, which optimally balances server pools’ loads, without the knowledge of the flow input rates and without solving any optimization problem. The scheme is based on Shadow routing in a virtual queueing system. We study the behavior of our scheme in the Halfin–Whitt (or, QED) asymptotic regime, when server pool sizes and the input rates are scaled up simultaneously by a factor r growing to infinity, while keeping the system load within $O(\sqrt{r}\,)$ of its capacity. The main results are as follows. (i) We show that, in general, a system in a stationary regime has at least $O(\sqrt{r}\,)$ average queue lengths, even if the so called null-controllability (Atar et al., Ann. Appl. Probab. 16, 1764–1804, ) on a finite time interval is possible; strategies achieving this $O(\sqrt{r}\,)$ growth rate we call order-optimal. (ii) We show that some natural algorithms, such as MaxWeight, that guarantee stability, are not order-optimal. (iii) Under the complete resource pooling condition, we prove the diffusion limit of the arrival processes into server pools, under the Shadow routing. (We conjecture that result (iii) leads to order-optimality of the Shadow routing algorithm; a formal proof of this fact is an important subject of future work.) Simulation results demonstrate good performance and robustness of our scheme. [ABSTRACT FROM AUTHOR]

The aim of this paper is to derive estimates for the accuracy of the Viability Kernel Algorithm for systems which have shadowing properties. Recently developed shadowing results are applied in order to prove for a certain class of right hand sides that the algorithm has the same convergence properties as fully discretized numerical methods on a finite time interval. [ABSTRACT FROM AUTHOR]

The shadowing property is to find an exact solution to an iterated map that remains close to an approximate solution. In this article, using shadowing property, we show the stability of the following equation in normed group: 4n-2Cn/2-1r2f(Σnj=1(xj/r)) + nΣikΣ(0,1),Σn k-1 ik=n/2 r2(Σni=1 (-1)ik(xi/r)) + 4n∙n-2Cn/2-1Σn i=1 f(xi), where n ⩾ 2, r Σ R (r2≠n) and f is a mapping. And we prove that the even mapping which satisfies the above equation is quadratic and also the Hyers-Ulam stability of the functional equation in Banach spaces. [ABSTRACT FROM AUTHOR]

In this paper, we consider the shadowing and the inverse shadowing properties for C 1 endomorphisms. We show that near a hyperbolic set a C 1 endomorphism has the shadowing property, and a hyperbolic endomorphism has the inverse shadowing property with respect to a class of continuous methods. Moreover, each of these shadowing properties is also “uniform” with respect to C 1 perturbation. [ABSTRACT FROM AUTHOR]

We briefly discuss the observational evidence for linear features in diffuse astronomical sources. We then discuss their formation either by radiation shadowing or by hydrodynamic processes. [ABSTRACT FROM AUTHOR]

The effect of patton shadowing on the distributions of global observables (total transverse energy E[sub T] and charged-particle multiplicity n[sub ch]) is investigated on the basis of the HIJING model of nucleus-nucleus interactions. It is shown that, for the interaction of lead nuclei at √s = 5 TeV per nucleon, the shadowing effect results in a considerable reduction of the cross section for (mini)jet production (approximately by a factor of 4); this in turn reduces the total transverse energy and the charged-particle multiplicity by a factor of 2.7. Upon taking into account the QCD evolution of nuclear structure functions in Q², the shadowing effect becomes less pronounced (by a factor of 1.9 for PbPb interactions). It is shown that global observables can be used to test models of patton shadowing. [ABSTRACT FROM AUTHOR]

We study the accuracy of the Regge behavior of the gluon distribution function for an approximate relation that is frequently used to extract the logarithmic slopes of the structure function from the gluon distribution at small x. We show that the Regge behavior analysis results are comparable with HERA data and are also better than other methods that expand the gluon density at distinct points of expansion. We also show that for Q = 22.4 GeV, the x dependence of the data is well described by gluon shadowing corrections to the GLR-MQ equation. The resulting analytic expression allows us to predict the logarithmic derivative ∂ F( x, Q)/∂ln Q and to compare the results with the H1 data and a QCD analysis fit with the MRST parameterization input. [ABSTRACT FROM AUTHOR]