The Bishop-Phelps-Bollob\'{a}s property deals with simultaneous approximation of an operator $T$ and a vector $x$ at which $T$ nearly attains its norm by an operator $T_0$ and a vector $x_0$, respectively, such that $T_0$ attains its norm at $x_0$. In this note we extend the already known results about {the} Bishop-Phelps-Bollob\'{a}s property for Asplund operators to a wider class of Banach spaces and to a wider class of operators. Instead of proving a BPB-type theorem for each space separately we isolate two main notions: $\Gamma$-flat operators and Banach spaces with ACK$_\rho$ structure. In particular, we prove a general BPB-type theorem for $\Gamma$-flat operators acting to a space with ACK$_\rho$ structure and show that uniform algebras and spaces with the property $\beta$ have ACK$_\rho$ structure. We also study the stability of the ACK$_\rho$ structure under some natural Banach space theory operations. As a consequence, we discover many new examples of spaces $Y$ such that the Bishop-Phelps-Bollob\'{a}s property for Asplund operators is valid for all pairs of the form ($X,Y$).

Bernardo Cascales Antonio J. Guirao Vladimir Kadets Mariia Soloviova

Consider a processor having access only to meta-data consisting of the timings of data packets and acknowledgment (ACK) packets from all nodes in a network. The meta-data report the source node of each packet, but not the destination nodes or the contents of the packets. The goal of the processor is to infer the network topology based solely on such information. Prior work leveraged causality metrics to identify which links are active. If the data timings and ACK timings of two nodes -- say node 1 and node 2, respectively -- are causally related, this may be taken as evidence that node 1 is communicating to node 2 (which sends back ACK packets to node 1). This paper starts with the observation that packet losses can weaken the causality relationship between data and ACK timing streams. To obviate this problem, a new Expectation Maximization (EM)-based algorithm is introduced -- EM-causality discovery algorithm (EM-CDA) -- which treats packet losses as latent variables. EM-CDA iterates between the estimation of packet losses and the evaluation of causality metrics. The method is validated through extensive experiments in wireless sensor networks on the NS-3 simulation platform.

Wenbo Du Tao Tan Haijun Zhang Xianbin Cao Gang Yan Osvaldo Simeone

We have analysed the chemical photospheric composition of 24 Herbig Ae/Be and Vega-type stars in search for the lambda Bootis phenomenon. We present the results of the elemental abundances of the sample stars. Some of the stars were never before studied spectroscopically at optical wavelengths. We have determined the projected rotational velocities of our sample stars. Furthermore, we discuss stars that depict a (selective) depletion pattern in detail. HD 4881 and HD 139614 seem to display an overall deficiency. AB Aur and possibly HD 126367 have subsolar values for the iron abundance, but are almost solar in silicon. HD 100546 is the only clear lambda Bootis star in our sample.

Bram Acke Christoffel Waelkens

In this paper the sum of an orthogonal matrix and an outer product is studied, and a relation between the norms of the vectors forming the outer product and the singular values of the resulting matrix is presented. The main result may be found in Theorem 1.

Mårten Wadenbäck

We discuss a new concept of definitizability of a normal operator on Krein spaces. For this new concept we develop a functional calculus $\phi \mapsto \phi(N)$ which is the proper analogue of $\phi \mapsto \int \phi \, dE$ in the Hilbert space situation.

Michael Kaltenbäck

In the present note a spectral theorem for normal definitizable linear operators on Krein spaces is derived by developing a functional calculus $\phi \mapsto \phi(N)$ which is the proper analogue of $\phi \mapsto \int \phi \, dE$ in the Hilbert space situation.

Michael Kaltenbäck

In traditional communication system, information of APP (Application) layer, transport layer and MAC (Media Access Control)layer has not been fully interacted,which inevitably leads to inconsistencies among TCP congestion state, clients'requirements and resource allocation. To solve the problem, we propose a joint optimization framework, which consists of APP layer, transport layer and MAC layer, to improve the video clients'playback experience and system throughput. First, a client requirement aware autonomous packet drop strategy, based on packet importance, channel condition and playback status, is developed to decrease the network load and the probability of rebuffering events. Further, TCP (Transmission Control Protocol) state aware downlink and uplink resource allocation schemes are proposed to achieve smooth video transmission and steady ACK (Acknowledgement) feedback respectively. For downlink scheme, maximum transmission capacity requirement for each client is calculated based on feedback ACK information from transport layer to avoid allocating excessive resource to the client, whose ACK feedback is blocked due to bad uplink channel condition. For uplink scheme, information of RTO (Retransmission Timeout) and TCP congestion window are utilized to indicate ACK scheduling priority. The simulation results show that our algorithm can signficantly improve the system throughput and the clients'playback continuity with acceptable video quality.

Xinyu Huang Lijun He

It is well-known that cross-layer scheduling which adapts power, rate and user allocation can achieve significant gain on system capacity. However, conventional cross-layer designs all require channel state information at the base station (CSIT) which is difficult to obtain in practice. In this paper, we focus on cross-layer resource optimization based on ACK/NAK feedback flows in OFDM systems without explicit CSIT. While the problem can be modeled as Markov Decision Process (MDP), brute force approach by policy iteration or value iteration cannot lead to any viable solution. Thus, we derive a simple closed-form solution for the MDP cross-layer problem, which is asymptotically optimal for sufficiently small target packet error rate (PER). The proposed solution also has low complexity and is suitable for realtime implementation. It is also shown to achieve significant performance gain compared with systems that do not utilize the ACK/NAK feedbacks for cross-layer designs or cross-layer systems that utilize very unreliable CSIT for adaptation with mismatch in CSIT error statistics. Asymptotic analysis is also provided to obtain useful design insights.

Zuleita Ka Ming Ho Vincent K. N. Lau Roger S. K. Cheng

To combat the detrimental effects of the variability in wireless channels, we consider cross-layer rate adaptation based on limited feedback. In particular, based on limited feedback in the form of link-layer acknowledgements (ACK) and negative acknowledgements (NAK), we maximize the physical-layer transmission rate subject to an upper bound on the expected packet error rate. \textr{We take a robust approach in that we do not assume} any particular prior distribution on the channel state. We first analyze the fundamental limitations of such systems and derive an upper bound on the achievable rate for signaling schemes based on uncoded QAM and random Gaussian ensembles. We show that, for channel estimation based on binary ACK/NAK feedback, it may be preferable to use a separate training sequence at high error rates, rather than to exploit low-error-rate data packets themselves. We also develop an adaptive recursive estimator, which is provably asymptotically optimal and asymptotically efficient.

C. Emre Koksal Philip Schniter

In this paper, we consider the problem of joint scheduling and resource allocation in the OFDMA downlink, with the goal of maximizing an expected long-term goodput-based utility subject to an instantaneous sum-power constraint, and where the feedback to the base station consists only of ACK/NAKs from recently scheduled users. We first establish that the optimal solution is a partially observable Markov decision process (POMDP), which is impractical to implement. In response, we propose a greedy approach to joint scheduling and resource allocation that maintains a posterior channel distribution for every user, and has only polynomial complexity. For frequency-selective channels with Markov time-variation, we then outline a recursive method to update the channel posteriors, based on the ACK/NAK feedback, that is made computationally efficient through the use of particle filtering. To gauge the performance of our greedy approach relative to that of the optimal POMDP, we derive a POMDP performance upper-bound. Numerical experiments show that, for slowly fading channels, the performance of our greedy scheme is relatively close to the upper bound, and much better than fixed-power random user scheduling (FP-RUS), despite its relatively low complexity.

Rohit Aggarwal C. Emre Koksal Philip Schniter