The weak Stratonovich integral with respect to fractional Brownian motion with Hurst parameter 1/6

Let $B$ be a fractional Brownian motion with Hurst parameter $H=1/6$. It is known that the symmetric Stratonovich-style Riemann sums for $\int g(B(s))\,dB(s)$ do not, in general, converge in probability. We show, however, that they do converge in law in the Skorohod space of c\`adl\`ag functions. Moreover, we show that the resulting stochastic integral satisfies a change of variable formula with a correction term that is an ordinary It\^o integral with respect to a Brownian motion that is independent of $B$.Comment: 45 page

Haar projection numbers and failure of unconditional convergence in Sobolev spaces

For $1<p<\infty$ we determine the precise range of $L_p$ Sobolev spaces for which the Haar system is an unconditional basis. We also consider the natural extensions to Triebel-Lizorkin spaces and prove upper and lower bounds for norms of projection operators depending on properties of the Haar frequency set

POWER-SUPPLaY: Leaking Data from Air-Gapped Systems by Turning the Power-Supplies Into Speakers

It is known that attackers can exfiltrate data from air-gapped computers through their speakers via sonic and ultrasonic waves. To eliminate the threat of such acoustic covert channels in sensitive systems, audio hardware can be disabled and the use of loudspeakers can be strictly forbidden. Such audio-less systems are considered to be \textit{audio-gapped}, and hence immune to acoustic covert channels. In this paper, we introduce a technique that enable attackers leak data acoustically from air-gapped and audio-gapped systems. Our developed malware can exploit the computer power supply unit (PSU) to play sounds and use it as an out-of-band, secondary speaker with limited capabilities. The malicious code manipulates the internal \textit{switching frequency} of the power supply and hence controls the sound waveforms generated from its capacitors and transformers. Our technique enables producing audio tones in a frequency band of 0-24khz and playing audio streams (e.g., WAV) from a computer power supply without the need for audio hardware or speakers. Binary data (files, keylogging, encryption keys, etc.) can be modulated over the acoustic signals and sent to a nearby receiver (e.g., smartphone). We show that our technique works with various types of systems: PC workstations and servers, as well as embedded systems and IoT devices that have no audio hardware at all. We provide technical background and discuss implementation details such as signal generation and data modulation. We show that the POWER-SUPPLaY code can operate from an ordinary user-mode process and doesn't need any hardware access or special privileges. Our evaluation shows that using POWER-SUPPLaY, sensitive data can be exfiltrated from air-gapped and audio-gapped systems from a distance of five meters away at a maximal bit rates of 50 bit/sec

Spectral Efficient and Energy Aware Clustering in Cellular Networks

The current and envisaged increase of cellular traffic poses new challenges to Mobile Network Operators (MNO), who must densify their Radio Access Networks (RAN) while maintaining low Capital Expenditure and Operational Expenditure to ensure long-term sustainability. In this context, this paper analyses optimal clustering solutions based on Device-to-Device (D2D) communications to mitigate partially or completely the need for MNOs to carry out extremely dense RAN deployments. Specifically, a low complexity algorithm that enables the creation of spectral efficient clusters among users from different cells, denoted as enhanced Clustering Optimization for Resources' Efficiency (eCORE) is presented. Due to the imbalance between uplink and downlink traffic, a complementary algorithm, known as Clustering algorithm for Load Balancing (CaLB), is also proposed to create non-spectral efficient clusters when they result in a capacity increase. Finally, in order to alleviate the energy overconsumption suffered by cluster heads, the Clustering Energy Efficient algorithm (CEEa) is also designed to manage the trade-off between the capacity enhancement and the early battery drain of some users. Results show that the proposed algorithms increase the network capacity and outperform existing solutions, while, at the same time, CEEa is able to handle the cluster heads energy overconsumption