Novel method for one-way local distinguishability of generalized Bell states in arbitrary dimension

In this paper the local distinguishability of generalized Bell states in arbitrary dimension is investigated. We firstly study the decomposition of a basis which consists of $d^{2}$ number of generalized Pauli matrices. We discover that this basis is equal to the union of $D$ number of different sets, where $D=\frac{2}{\phi(d)}\sum_{t\in \mathbb{Z}_{d} \atop gcd(t,d)=1}\sum_{i=2}^{\lfloor\frac{d}{t}\rfloor}\phi(i)+1$ and $\phi$ is Euler $\phi$-function. Then we define the generator of the matrices in this decomposition, and exhibit an algorithm to calculate generators of a given set of matrices. This algorithm shows that generators of a given set can be calculated simply and efficiently. Secondly, we show that a set $\mathcal {L}$ of GBSs can be distinguished by one-way LOCC if the cardinality of $\mathcal {G}_{\mathcal {L}}$ is less than $D\phi(d)$, where $\mathcal {G}_{\mathcal {L}}$ is a set of generators of all the elements in difference set of a set $\mathcal {L}$ of GBSs. The previous results in [2004 Phys. Rev. Lett. \textbf{92} 177905; 2019 Phys. Rev. A \textbf{99} 022307; 2021 Quant. Info. Proc. \textbf{20} 52] can be covered by our result. Finally, for the uncovered cases in [2021 Quant. Info. Proc. \textbf{20} 52], we give a new result to partly solve that problem.

The Pintz–Steiger–Szemerédi estimate for intersective quadratic polynomials in function fields

Let [Formula: see text] be the polynomial ring over the finite field [Formula: see text] of [Formula: see text] elements. For a natural number [Formula: see text] let [Formula: see text] be the set of all polynomials in [Formula: see text] of degree less than [Formula: see text] Let [Formula: see text] be a quadratic polynomial over [Formula: see text] Suppose that [Formula: see text] is intersective, that is, which satisfies [Formula: see text] for any [Formula: see text] with [Formula: see text] where [Formula: see text] denotes the difference set of [Formula: see text] Let [Formula: see text] Suppose that [Formula: see text] and that the characteristic of [Formula: see text] is not divisible by 2. It is proved that [Formula: see text] for any [Formula: see text] where [Formula: see text] is a constant depending only on [Formula: see text] and [Formula: see text]

Symmetric Channel Hopping algorithm for a Cognitive Radio Network in Asynchronous environment

<div>Rendezvous is a critical step in Cognitive Radio Network (CRN) prior to transmission for establishing communication links between secondary users (SUs). Due to the long-term blocking, channel saturation, and scalability issues encountered by dedicated common control channels (CCC) in a distributed CRN, rendezvous is preferable on the available idle channels of the primary users (PUs). In fact, each SU is unaware of the other SUs’ available channel sets, and the blind rendezvous is performed through the channel hopping (CH) process. As a result, ensuring a rendezvous between two SUs in a finite period in an asynchronous environment remains a challenging problem. In this work, a disjoint difference set based CH (DDSCH) method is developed that ensures the highest degree of rendezvous in comparatively less time. </div>

Symmetric Channel Hopping algorithm for a Cognitive Radio Network in Asynchronous environment

<div>Rendezvous is a critical step in Cognitive Radio Network (CRN) prior to transmission for establishing communication links between secondary users (SUs). Due to the long-term blocking, channel saturation, and scalability issues encountered by dedicated common control channels (CCC) in a distributed CRN, rendezvous is preferable on the available idle channels of the primary users (PUs). In fact, each SU is unaware of the other SUs’ available channel sets, and the blind rendezvous is performed through the channel hopping (CH) process. As a result, ensuring a rendezvous between two SUs in a finite period in an asynchronous environment remains a challenging problem. In this work, a disjoint difference set based CH (DDSCH) method is developed that ensures the highest degree of rendezvous in comparatively less time. </div>

Knowledge, attitudes and perceptions of radiology healthcare workers during the COVID-19 pandemic

Background: Medical imaging is vital in the diagnostic workup and evaluation of patients suspected or confirmed to have COVID-19; hence, radiology healthcare workers (HCWs) were an essential part of the early containment response to the pandemic. Radiology services are facing rising demands to introduce stricter infection control measures, and staff are expected to adhere to the new protocols while coping with a surge in patients. Objectives: This study aims to identify the knowledge, attitudes and perceptions (KAPs) of radiology HCWs at a single site with regard to workplace preparedness during the COVID-19 pandemic. Methods: A 26-item questionnaire was conducted with radiographers, radiology nurses, and support staff who had direct patient contact. Questions were concerned with involvement in managing suspected or positive COVID-19 patients, knowledge of infection control measures, and attitudes and perceptions in relation to working during the pandemic. Results were analysed using t-tests, chi-square tests, and Spearman’s rank-order correlation, with statistical difference set at p<0.05. Results: Radiology HCWs self-reported significantly better knowledge of infection control measures and positive work attitudes. Those who had received the flu vaccine had significantly better perceptions of working during the pandemic. Suggested improvements included better organisational structure and more resources, better staff compliance and vigilance, better education, and a clearer focus on staff wellbeing. Conclusion: The findings indicate favourable KAPs among radiology HCWs in Singapore with regard to workplace preparedness during the pandemic, but efforts towards sustainability must be considered. Formulating policies to nurture motivated and resilient HCWs during a pandemic is advocated to foster a resilient workforce that is prepared for the next pandemic.

On Computational Hardness of Multidimensional Subtraction Games

We study the algorithmic complexity of solving subtraction games in a fixed dimension with a finite difference set. We prove that there exists a game in this class such that solving the game is EXP-complete and requires time 2Ω(n), where n is the input size. This bound is optimal up to a polynomial speed-up. The results are based on a construction introduced by Larsson and Wästlund. It relates subtraction games and cellular automata.

Appropriate Data Quality Checks Improve the Reliability of Values Predicted from Milk Mid-Infrared Spectra

The use of abnormal milk mid-infrared (MIR) spectrum strongly affects prediction quality, even if the prediction equations used are accurate. So, this record must be detected after or before the prediction process to avoid erroneous spectral extrapolation or the use of poor-quality spectral data by dairy herd improvement (DHI) organizations. For financial or practical reasons, adapting the quality protocol currently used to improve the accuracy of fat and protein contents is unfeasible. This study proposed three different statistical methods that would be easy to implement by DHI organizations to solve this issue: the deletion of 1% of the extreme high and low predictive values (M1), the deletion of records based on the Global-H (GH) distance (M2), and the deletion of records based on the absolute fat residual value (M3). Additionally, the combinations of these three methods were investigated. A total of 346,818 milk samples were analyzed by MIR spectrometry to predict the contents of fat, protein, and fatty acids. Then, the same traits were also predicted externally using their corresponded standardized MIR spectra. The interest in cleaning procedures was assessed by estimating the root mean square differences (RMSDs) between those internal and external predicted phenotypes. All methods allowed for a decrease in the RMSD, with a gain ranging from 0.32% to 41.39%. Based on the obtained results, the “M1 and M2” combination should be preferred to be more parsimonious in the data loss, as it had the higher ratio of RMSD gain to data loss. This method deleted the records based on the 2% extreme predictions and a GH threshold set at 5. However, to ensure the lowest RMSD, the “M2 or M3” combination, considering a GH threshold of 5 and an absolute fat residual difference set at 0.30 g/dL of milk, was the most relevant. Both combinations involved M2 confirming the high interest of calculating the GH distance for all samples to predict. However, if it is impossible to estimate the GH distance due to a lack of relevant information to compute this statistical parameter, the obtained results recommended the use of M1 combined with M3. The limitation used in M3 must be adapted by the DHI, as this will depend on the spectral data and the equation used. The methodology proposed in this study can be generalized for other MIR-based phenotypes.

A Recursive Construction for Skew Hadamard Difference Sets

A major conjecture on the existence of abelian skew Hadamard difference sets is: if an abelian group $G$ contains a skew Hadamard difference set, then $G$ must be elementary abelian. This conjecture remains open in general. In this paper, we give a recursive construction for skew Hadamard difference sets in abelian (not necessarily elementary abelian) groups. The new construction can be considered as a result on the aforementioned conjecture: if there exists a counterexample to the conjecture, then there exist infinitely many counterexamples to it.