The Encoding and Decoding Complexities of Entanglement-Assisted Quantum Stabilizer Codes

Quantum error-correcting codes are used to protect quantum information from decoherence. A raw state is mapped, by an encoding circuit, to a codeword so that the most likely quantum errors from a noisy quantum channel can be removed after a decoding process. A good encoding circuit should have some desired features, such as low depth, few gates, and so on. In this paper, we show how to practically implement an encoding circuit of gate complexity $O(n(n-k+c)/\log n)$ for an $[[n,k;c]]$ quantum stabilizer code with the help of $c$ pairs of maximally-entangled states. For the special case of an $[[n,k]]$ stabilizer code with $c=0$, the encoding complexity is $O(n(n-k)/\log n)$, which is previously known to be $O(n^2/\log n)$. For $c>0,$ this suggests that the benefits from shared entanglement come at an additional cost of encoding complexity. Finally we discuss decoding of entanglement-assisted quantum stabilizer codes and extend previously known computational hardness results on decoding quantum stabilizer codes.Comment: accepted by the 2019 IEEE International Symposium on Information Theory (ISIT2019

A Note on Near-factor-critical Graphs

A near-factor of a finite simple graph $G$ is a matching that saturates all vertices except one. A graph $G$ is said to be near-factor-critical if the deletion of any vertex from $G$ results in a subgraph that has a near-factor. We prove that a connected graph $G$ is near-factor-critical if and only if it has a perfect matching. We also characterize disconnected near-factor-critical graphs.Comment: 4 page

A hybrid brain-computer interface based on motor intention and visual working memory

Non-invasive electroencephalography (EEG) based brain-computer interface (BCI) is able to provide alternative means for people with disabilities to communicate with and control over external assistive devices. A hybrid BCI is designed and developed for following two types of system (control and monitor). Our first goal is to create a signal decoding strategy that allows people with limited motor control to have more command over potential prosthetic devices. Eight healthy subjects were recruited to perform visual cues directed reaching tasks. Eye and motion artifacts were identified and removed to ensure that the subjects\u27 visual fixation to the target locations would have little or no impact on the final result. We applied a Fisher Linear Discriminate (FLD) analysis for single-trial classification of the EEG to decode the intended arm movement in the left, right, and forward directions (before the onsets of actual movements). The mean EEG signal amplitude near the PPC region 271-310 ms after visual stimulation was found to be the dominant feature for best classification results. A signal scaling factor developed was found to improve the classification accuracy from 60.11% to 93.91% in the two-class (left versus right) scenario. This result demonstrated great promises for BCI neuroprosthetics applications, as motor intention decoding can be served as a prelude to the classification of imagined motor movement to assist in motor disable rehabilitation, such as prosthetic limb or wheelchair control. The second goal is to develop the adaptive training for patients with low visual working memory (VWM) capacity to improve cognitive abilities and healthy individuals who seek to enhance their intellectual performance. VWM plays a critical role in preserving and processing information. It is associated with attention, perception and reasoning, and its capacity can be used as a predictor of cognitive abilities. Recent evidence has suggested that with training, one can enhance the VWM capacity and attention over time. Not only can these studies reveal the characteristics of VWM load and the influences of training, they may also provide effective rehabilitative means for patients with low VWM capacity. However, few studies have investigated VWM over a long period of time, beyond 5-weeks. In this study, a combined behavioral approach and EEG was used to investigate VWM load, gain, and transfer. The results reveal that VWM capacity is directly correlated to the reaction time and contralateral delay amplitude (CDA). The approximate magic number 4 was observed through the event-related potentials (ERPs) waveforms, where the average capacity is 2.8-item from 15 participants. In addition, the findings indicate that VWM capacity can be improved through adaptive training. Furthermore, after training exercises, participants from the training group are able to improve their performance accuracies dramatically compared to the control group. Adaptive training gains on non-trained tasks can also be observed at 12 weeks after training. Therefore, we conclude that all participants can benefit from training gains, and augmented VWM capacity can be sustained over a long period of time. Our results suggest that this form of training can significantly improve cognitive function and may be useful for enhancing the user performance on neuroprosthetics device

The anodic dissolution of molybdenum in acid sulfate solutions

The world\u27s resources of metals are decreasing. Due to this and the cost of replacing corroded materials, it has come to be realized that prevention is better than cure. The increasing demand for molybdenum and molybdenum alloys has stimulated a great amount of research into the corrosion characteristics of these materials. The result of such research has assisted in the development of suitable molybdenum alloys and protective coatings to retard corrosion. When a molybdenum anode and a suitable cathode are immersed in an oxygen-free electrolyte and are connected to a direct current power source, molybdenum is dissolved. This process is called anodic dissolution and a study of it is useful for many reasons: (1) The apparent valence of the metal undergoing dissolution can be determined. (2) An empirical expression for the dissolution rate can be established. (3) A dissolution reaction mechanism can be hypothesized that may aid in retarding corrosion and predicting behavior in other environments. The mechanism of the anodic dissolution of molybdenum has been formulated only in very vague terms. The purpose of this investigation was to study the dissolution in sulfuric acid solutions of various pH and if possible to establish a mechanism consistent with the data. Toward this end, experiments were performed to determine the relationships between the current density, potential, pH, and faradaic efficiency during dissolution. The effect of chloride ion on the process was also determined --Introduction, page 1

Learner, customer or ambassador? : identity constructions of overseas students in the discourse of entrepreneurialism

In this thesis, I examine overseas students' identity construction in the context of\ud entrepreneurial discourse in relation to the way that the UK government, UK higher\ud education institutions, and university staff and overseas students interact with one\ud another.\ud Overseas students' identity is multifaceted. I am interested in how overseas\ud students' learner and customer identities are constructed and reconstructed in the\ud process of negotiating entrepreneurialism and its interrelated and competing\ud discourses, such as such as OSs as learners, OSs as customers, OSs as change\ud agents and OSs as ambassadors.\ud My empirical research is carried out as qualitative research drawing on\ud ethnographic approaches, and conducted in four UK universities. I interviewed\ud more than 50 postgraduate overseas students and 22 university staff at different\ud levels across universities. My analytical scope is influenced both by interactionism\ud and poststructural concepts of discourses and ideas, emphasising the micro/macro\ud links, rather than posing a dichotomy between micro/macro analytical levels.\ud My central argument is that the ways in which university staff negotiate the notions\ud of 'learner' and 'customer' influence overseas students' identity constructions. The\ud hidden debates on overseas students' learner and customer identities were latently\ud entwined with the construction of overseas students as victims, as problems and\ud as beneficiaries of the marketisation of higher education. These hidden debates\ud illuminate challenges which overseas students have to overcome, when they resist\ud and negotiate their learner and customer identities. My research should\ud counterbalance the one-sided and distorted perspective of overseas students,\ud particularly made by the media, which portrays them as sources of income as well\ud as sources of problems for the UK universities

Determination of image quality for added noise as a function of spatial frequency

The noise in color images which is referred to as chromatic noise represents a distribution within three spectral bands and contributes to chromatic and achromatic visual effects. The chromatic noise depends very strongly on the spatial frequency response of the visual system. Therefore, this study characterizes the variation in perceived chromatic noise level and generates the noise field to add to the color image samples. From these degraded images, we found that noise in low spatial frequencies is much more disturbing than in the medium and high spatial frequency regions. The perceived quality scales of the modulated chromatic noise images were compared to the subjective quality factor (S.Q.F.) scales. By using category analysis, this quality scale yields the S.Q.F. rating, and determines the dependence of the spatial frequency content of chromatic noise and achromatic effect