Abstract:
In the IPCC Intergovernmental Panel on Climate Change Special Report on Emission Scenarios (SRES), it was projected that the number of CO2 emission sources from the electric power and industrial sectors will increase significantly until 2050. Because fossil fuel-fired power plants are responsible for around one-third of total global CO2 emissions, they are prime candidates for the application of CO2 capture and storage techniques. The aim of this work is to mitigate the impact of climate change by reducing the amount of CO2 emitted to the atmosphere in Mulla Abdulla and Taza power plants in Kirkuk/ Iraq using CCS techniques, and to calculate the cost of the system components.

Abstract:
The discrete memoryless interference channel is modelled as a conditional probability distribution with two outputs depending on two inputs and has widespread applications in practical communication scenarios. In this paper, we introduce and study the quantum interference channel, a generalization of a two-input, two-output memoryless channel to the setting of quantum Shannon theory. We discuss three different coding strategies and obtain corresponding achievable rate regions for quantum interference channels. We calculate the capacity regions in the special cases of "very strong" and "strong" interference. The achievability proof in the case of "strong" interference exploits a novel quantum simultaneous decoder for two-sender quantum multiple access channels. We formulate a conjecture regarding the existence of a quantum simultaneous decoder in the three-sender case and use it to state the rates achievable by a quantum Han-Kobayashi strategy.

Abstract:
Calculating the capacity of interference channels is a notorious open problem in classical information theory. Such channels have two senders and two receivers, and each sender would like to communicate with a partner receiver. The capacity of such channels is known exactly in the settings of "very strong" and "strong" interference, while the Han-Kobayashi coding strategy gives the best known achievable rate region in the general case. Here, we introduce and study the quantum interference channel, a natural generalization of the interference channel to the setting of quantum information theory. We restrict ourselves for the most part to channels with two classical inputs and two quantum outputs in order to simplify the presentation of our results (though generalizations of our results to channels with quantum inputs are straightforward). We are able to determine the exact classical capacity of this channel in the settings of "very strong" and "strong" interference, by exploiting Winter's successive decoding strategy and a novel two-sender quantum simultaneous decoder, respectively. We provide a proof that a Han-Kobayashi strategy is achievable with Holevo information rates, up to a conjecture regarding the existence of a three-sender quantum simultaneous decoder. This conjecture holds for a special class of quantum multiple access channels with average output states that commute, and we discuss some other variations of the conjecture that hold. Finally, we detail a connection between the quantum interference channel and prior work on the capacity of bipartite unitary gates.

Abstract:
We study distance properties of a general class of random directed acyclic graphs (DAGs). In a DAG, many natural notions of distance are possible, for there exists multiple paths between pairs of nodes. The distance of interest for circuits is the maximum length of a path between two nodes. We give laws of large numbers for the typical depth (distance to the root) and the minimum depth in a random DAG. This completes the study of natural distances in random DAGs initiated (in the uniform case) by Devroye and Janson (2009+). We also obtain large deviation bounds for the minimum of a branching random walk with constant branching, which can be seen as a simplified version of our main result.

Abstract:
In the presence of multiple senders, one of the simplest decoding strategies that can be employed by a receiver is successive decoding. In a successive decoding strategy, the receiver decodes the messages one at a time using the knowledge of the previously decoded messages as side information. Recently, there have been two separate attempts to construct codes for the interference channel using successive decoding based on the idea of rate-splitting. In this note, we highlight a difficulty that arises when a rate-splitting codebook is to be decoded by multiple receivers. The main issue is that the rates of the split codebook are tightly coupled to the properties of the channel to the receiver, thus, rates chosen for one of the receivers may not be decodable for the other. We illustrate this issue by scrutinizing two recent arguments claiming to achieve the Han-Kobayashi rate region for the interference channel using rate-splitting and successive decoding.

Abstract:
We study the encoding complexity for quantum error correcting codes with large rate and distance. We prove that random Clifford circuits with $O(n \log^2 n)$ gates can be used to encode $k$ qubits in $n$ qubits with a distance $d$ provided $\frac{k}{n} < 1 - \frac{d}{n} \log_2 3 - h(\frac{d}{n})$. In addition, we prove that such circuits typically have a depth of $O( \log^3 n)$.

Abstract:
In the context of network information theory, one often needs a multiparty probability distribution to be typical in several ways simultaneously. When considering quantum states instead of classical ones, it is in general difficult to prove the existence of a state that is jointly typical. Such a difficulty was recently emphasized and conjectures on the existence of such states were formulated. In this paper, we consider a one-shot multiparty typicality conjecture. The question can then be stated easily: is it possible to smooth the largest eigenvalues of all the marginals of a multipartite state {\rho} simultaneously while staying close to {\rho}? We prove the answer is yes whenever the marginals of the state commute. In the general quantum case, we prove that simultaneous smoothing is possible if the number of parties is two or more generally if the marginals to optimize satisfy some non-overlap property.

Abstract:
A central question in information theory is to determine the maximum success probability that can be achieved in sending a fixed number of messages over a noisy channel. This was first studied in the pioneering work of Shannon who established a simple expression characterizing this quantity in the limit of multiple independent uses of the channel. Here we consider the general setting with only one use of the channel. We observe that the maximum success probability can be expressed as the maximum value of a submodular function. Using this connection, we establish the following results: 1. There is a simple greedy polynomial-time algorithm that computes a code achieving a (1-1/e)-approximation of the maximum success probability. Moreover, for this problem it is NP-hard to obtain an approximation ratio strictly better than (1-1/e). 2. Shared quantum entanglement between the sender and the receiver can increase the success probability by a factor of at most 1/(1-1/e). In addition, this factor is tight if one allows an arbitrary non-signaling box between the sender and the receiver. 3. We give tight bounds on the one-shot performance of the meta-converse of Polyanskiy-Poor-Verdu.

Abstract:
The goal of this paper is to analyze an intriguing phenomenon recently discovered in deep networks, that is their instability to adversarial perturbations (Szegedy et. al., 2014). We provide a theoretical framework for analyzing the robustness of classifiers to adversarial perturbations, and establish fundamental limits on the robustness of some classifiers in terms of a distinguishability measure that captures the notion of difficulty of the classification task. Our result implies that in tasks involving small distinguishability, no classifier in the considered set will be robust to adversarial perturbations, even if a good accuracy is achieved. Our theoretical framework moreover suggests that the phenomenon of adversarial instability is due to the low flexibility of classifiers, compared to the difficulty of the classification task (captured mathematically by the distinguishability measure). Moreover, we show the existence of a clear distinction between the robustness of a classifier to random noise and its robustness to adversarial perturbations. Specifically, the former is shown to be larger than the latter by a factor that is proportional to \sqrt{d} (with d being the signal dimension) for linear classifiers. This result gives a theoretical explanation for the discrepancy between the two robustness properties in high dimensional problems, which was empirically observed in (Szegedy et. al., 2014) in the context of neural networks. To the best of our knowledge, this is the first theoretical work that addresses the phenomenon of adversarial instability recently observed for deep networks. Our analysis is complemented by experimental results on controlled and real-world data.

Abstract:
Context and Objective: Hamstring strain is a common injury in football and it causes a significant amount of time lost from competition and training. Since poor flexibility is thought to predispose to muscle strain, stretching is routinely recommended during warm-up routines by coaches to prevent injuries. However, available evidence suggests that pre-exercise stretching (PES), especially static stretching, has no benefit on injury rates and may even reduce performance in explosive type activities. We designed this study to assess the attitudes, beliefs and practices of football coaches regarding stretching in the prevention of hamstring strains. Design: A cross-sectional survey. Setting: Mauritius Football Association (MFA). Participants: 26 football coaches registered with the MFA. Intervention: Questionnaires were distributed to football coaches of the MFA via sports officers. Questionnaires were then collected two weeks after distribution. Main Outcome Measures: Attitudes, beliefs and practices of football coaches regarding stretching in the prevention of ham-string strains. Results: MFA coaches held generally positive attitudes and beliefs towards stretching. 88% of coaches felt that PES is beneficial and 93% believed that PES prevents hamstring strains. The majority of coaches recommended stretching after warming up (81%) and after the training session (93%). 76% of coaches also advised stretching outside the training sessions. 96% of coaches used static stretching to stretch the hamstrings. The hamstrings were stretched on average for 4 times at each training session and the mean duration of a static stretch was 12 seconds. Conclusions: Nearly all coaches believed that PES prevents hamstring strains although evidence is limited. Some of the coaches’ beliefs and practices were not in line with current recommendations. Coaches reported that their stretching practices would be most likely influenced by scientific research. Thus there is an urgent need to devise awareness and training programmes in this area.