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Katona's intersection theorem states that every intersecting family F ⊆ [ n ] (k) satisfies | ∂ F | ⩾ | F | , where ∂ F = { F \ { x } : x ∈ F ∈ F } is the shadow of F . Frankl conjectured that for n > 2 k and every intersecting family F ⊆ [ n ] (k) , there is some i ∈ [ n ] such that | ∂ F (i) | ⩾ | F (i) | , where F (i) = { F \ { i } : i ∈ F ∈ F } is the link of F at i. Here, we prove this conjecture in a very strong form for n > k + 1 2 . In particular, our result implies that for any j ∈ [ k ] , there is a j-set { a 1 , ⋯ , a j } ∈ [ n ] (j) such that | ∂ F (a 1 , ⋯ , a j) | ⩾ | F (a 1 , ⋯ , a j) | . A similar statement is also obtained for cross-intersecting families. [ABSTRACT FROM AUTHOR]

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]

Shadow fading is one of the least investigated factors of received signal power in a typical wireless communication system. Variations in the received power caused by shadowing events can impose some serious changes in the communication. This paper, proposes a new multiuser cognitive radio system in shadowing environment and its design optimization using cuckoo search algorithm. The transmission parameters of multiple secondary users in the purposed CR model are considered on the basis of IEEE 802.22 WRAN standard. An attempt to optimize these parameters in shadowing environment to achieve multiple objectives for desired quality of service have been made using a relatively newer and simpler cuckoo search algorithm. The optimization results have been compared with another efficient biogeography based optimization technique and the traditional simulated annealing. [ABSTRACT FROM AUTHOR]

In this work, we derive the closed-form expressions of channel capacity with maximal ratio combining, equal gain combining and selection combining schemes under different transmission policies such as optimal power and rate adaptation, optimal rate adaptation, channel inversion with fixed rate (CIFR) and truncated CIFR. Various approximations to the intractable integrals have been proposed using methods such as Holtzman and Gauss-Hermite approximations and simpler expressions are suggested. Moreover, as an application, the channel capacity of lognormally distributed fading channel in the interference-limited environment is discussed. The obtained closed-form expressions have been validated with the exact numerical results. [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]

For opportunistic relaying, different relays are distributed in different locations, so the shadowing between different links is likely to be different and correlated. In this letter, we investigate the effect of correlated log-normal shadowing on the outage probability of opportunistic decode-and-forward relaying. Since there is no closed-form expression for the outage probability, we present a decorrelating transformation and then use Gaussian-Hermite integration technique to evaluate this outage probability. The numerical and simulation results verify that our proposed approach is accurate, and show that the correlation coefficients and standard deviations of shadowing have a significant impact on the outage performance. [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]

The McKay density function has been cited in the study of wireless channels in connection with the analysis of diversity. It is also a forerunner of the $$\upeta $$ - $$\upmu $$ and $$\upeta $$ - $$\uplambda $$ - $$\upmu $$ distributions in wireless channels. Starting with a physical description of fading in terms of clustering and using the existing results from the original work of Nakagami, the probability density function of the signal-to-noise ratio has been shown to match the three parameter McKay distribution. It is demonstrated that the McKay density also allows for the modeling of wireless channels exhibiting fading levels far worse than what is seen in Nakagami channels, allowing the amount of fading to vary from 0 to $$\infty $$ . The shadowing in wireless channels is then incorporated in the model using the cascading concept to describe the shadowing. The error rates in such a McKay-Meijer G model are studied using the example of a coherent binary shift keying modem. With the availability of closed form expressions for the density, cumulative distribution function, error rates and outage probabilities, the McKay-Meijer G model offers a very flexible means to study the performance of modems in composite shadowed fading channels. [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]