Type Ia supernovae as tools for cosmology

Includes abstract. Includes bibliographical references (leaves 95-100)

Type Ia supernovae as tools for cosmology

Includes abstract. Includes bibliographical references (leaves 95-100)

Is the Dynamics of Tracking Dark Energy Detectable?

We highlight the unexpected impact of nucleosynthesis and other early universe constraints on the detectability of tracking quintessence dynamics at late times, showing that such dynamics may well be invisible until the unveiling of the Stage-IV dark energy experiments (DUNE, JDEM, LSST, SKA). Nucleosynthesis forces |w'(0)| < 0.2 for the models we consider and strongly limits potential deviations from LCDM. Surprisingly, the standard CPL parametrisation, w(z) = w_0 + w_a z/(1+z), cannot match the nucleosynthesis bound for minimally coupled tracking scalar fields. Given that such models are arguably the best-motivated alternatives to a cosmological constant these results may significantly impact future cosmological survey design and imply that dark energy may well be dynamical even if we do not detect any dynamics in the next decade.Comment: 5 pages, 2 figures. Updated to match published versio

A New and Deterministic Scheme for Characterizing The Organization of Prime Numbers

The fundamental theorem of arithmetic states that any composite natural integer can be expressed in one and only one way as a product of prime numbers. This sets the understanding of the organization of prime numbers at the core of number theory. In this work we present a simple, self-consistent and deterministic scheme allowing to investigate further the intrinsic organization of prime numbers. Using this scheme, we establish an algorithm that yields the complete list of prime numbers below any preassigned limit x. Counting the latter yields π(x), the number of prime numbers below x. Based on preliminary tests on computing clusters available, a considerable gain in computational speed and algorithmic simplicity towards producing complete lists of large prime numbers is observed. At the core of the new scheme lays its ability to provide, in a deterministic way, complete lists of consecutive and composite odd numbers below any preassigned limit x. The complete list of prime numbers below x is deduced from the latter. The two key ingredients of the scheme are a set of eleven generic tables, coupled with a three-criteria test applied on the differences between pairs of the consecutive composite odd numbers initially obtained. Since it leads to counting all the elements of a complete list of prime numbers up to x, our deterministic scheme provides a new approach to the long standing problem of " how many prime numbers are there below any preassigned limit x ". The said scheme therefore potentially contributes towards studies aimed at unveiling the organization of prime numbers. We illustrate the latter in a follow-up paper, Paper II [3], where we propose a new perspective on the Riemann hypothesis

Novel Aspects Of The Global Regularity Of Primes

For any $m = 3 \left( 2n + 1 \right) with \ n \in \mathbb{N^*} ,$ the prime counting function $\pi(m) = 4 + \left \vert A_4(m) \right \vert + 2 \left \vert A_6(m) \right \vert$ where $A_6(m)$ and $A_4(m)$ are the sets of Twin Primes and "Isolated" Primes, below $m$, respectively. $T(m) = 1 + \left \vert A_2(m) \right \vert + \left \vert A_4(m) \right \vert + \left \vert A_6(m) \right \vert$ is the number of consecutive odd composite numbers (COCONs) below $m.$ $A_2(m)$ is the set of COCONs, below $m$ and distant by 2. With $m$ odd, $\pi(m)$, $T(m)$ and $\left \vert A_2(m) \right \vert = \frac{m - 9}{2} - 3 \left \vert A_6(m) \right \vert - 2 \left \vert A_4(m) \right \vert$ lead to $4 \left \vert A_6(m) \right \vert + 7 = m - 2 \left( T(m) + \left \vert A_4(m) \right \vert \right). \ Hence \ 0 < 1 - \frac{ 2 }{m} \left( T(m) + \left \vert A_4(m) \right \vert \right) < 1.$ Thus the non-empty unique set S \equiv \left\lbrace 1 - \frac{ 2 }{l} \left( T(l) + \left \vert A_4(l) \right \vert \right) \ \mbox{such that} \ l = 3 \left( 2k + 1 \right) with \ k \in \mathbb{N^*} \right\rbrace \subset \mathbb{R} is bounded. Therefore $Inf \left( S \right)$ exists, is unique and finite. By definition, $Inf(S) > 0.$ $\mathbb{Q}$ dense in $\mathbb{R}$ also guarantees the latter. S and $Inf(S)$ are independent of $m.$ We then introduce $\alpha = Inf \left( S \right):$ $\alpha$ is independent of $m.$ We then have $0 < \alpha \leq 1 - \frac{ 2 }{m} \left( T(m) + \left \vert A_4(m) \right \vert \right)$ for any m as above. Therefore, $4 \left \vert A_6(m) \right \vert + 7 \geq \alpha m,$ with $\alpha > 0$ and independent of $m.$ Hence $\displaystyle \lim_{ m \longrightarrow + \infty } \left \vert 2 A_6(m) \right \vert = + \infty.$ Similarly, $\displaystyle \lim_{ m \longrightarrow + \infty } \left \vert A_4(m) \right \vert = + \infty .$Comment: 10 pages, 1 figure, 2 tables, typos corrected, strengthened argument in section III, results unchanged, comments welcom

Intelligent Systems Using Sensors and/or Machine Learning to Mitigate Wildlife&ndash;Vehicle Collisions: A Review, Challenges, and New Perspectives

Worldwide, the persistent trend of human and animal life losses, as well as damage to properties due to wildlife&ndash;vehicle collisions (WVCs) remains a significant source of concerns for a broad range of stakeholders. To mitigate their occurrences and impact, many approaches are being adopted, with varying successes. Because of their increased versatility and increasing efficiency, Artificial Intelligence-based methods have been experiencing a significant level of adoption. The present work extensively reviews the literature on intelligent systems incorporating sensor technologies and/or machine learning methods to mitigate WVCs. Included in our review is an investigation of key factors contributing to human&ndash;wildlife conflicts, as well as a discussion of dominant state-of-the-art datasets used in the mitigation of WVCs. Our study combines a systematic review with bibliometric analysis. We find that most animal detection systems (excluding autonomous vehicles) are relying neither on state-of-the-art datasets nor on recent breakthrough machine learning approaches. We, therefore, argue that the use of the latest datasets and machine learning techniques will minimize false detection and improve model performance. In addition, the present work covers a comprehensive list of associated challenges ranging from failure to detect hotspot areas to limitations in training datasets. Future research directions identified include the design and development of algorithms for real-time animal detection systems. The latter provides a rationale for the applicability of our proposed solutions, for which we designed a continuous product development lifecycle to determine their feasibility

Radio Astronomical Antennas in the Central African Region to Improve the Sampling Function of the VLBI Network in the SKA Era?

On the African continent, South Africa has world-class astronomical facilities for advanced radio astronomy research. With the advent of the Square Kilometre Array project in South Africa (SA SKA), six countries in Africa (SA SKA partner countries) have joined South Africa to contribute towards the African Very Long Baseline Interferometry (VLBI) Network (AVN). Each of the AVN countries aims to construct a single-dish radio telescope that will be part of the AVN, the European VLBI Network, and the global VLBI network. The SKA and the AVN will enable very high sensitivity VLBI in the southern hemisphere. In the current AVN, there is a gap in the coverage in the central African region. This work analyses the increased scientific impact of having additional antennas in each of the six countries in central Africa, i.e., Cameroon, Gabon, Congo, Equatorial Guinea, Chad, and the Central African Republic. A number of economic human capital impacts of having a radio interferometer in central Africa are also discussed. This work also discusses the recent progress on the AVN project and shares a few lessons from some past successes in ground stations retrofitting

Error Correction Based Deep Neural Networks for Modeling and Predicting South African Wildlife–Vehicle Collision Data

The seasonal autoregressive integrated moving average with exogenous factors (SARIMAX) has shown promising results in modeling small and sparse observed time-series data by capturing linear features using independent and dependent variables. Long short-term memory (LSTM) is a promising neural network for learning nonlinear dependence features from data. With the increase in wildlife roadkill patterns, the SARIMAX-only and LSTM-only models would likely fail to learn the precise endogenous and/or exogenous variables driven by this wildlife roadkill data. In this paper, we design and implement an error correction mathematical framework based on LSTM-only. The framework extracts features from the residual error generated by a SARIMAX-only model. The learned residual features correct the output time-series prediction of the SARIMAX-only model. The process combines SARIMAX-only predictions and LSTM-only residual predictions to obtain a hybrid SARIMAX-LSTM. The models are evaluated using South African wildlife–vehicle collision datasets, and the experiments show that compared to single models, SARIMAX-LSTM increases the accuracy of a taxon whose linear components outweigh the nonlinear ones. In addition, the hybrid model fails to outperform LSTM-only when a taxon contains more nonlinear components rather than linear components. Our assumption of the results is that the collected exogenous and endogenous data are insufficient, which limits the hybrid model’s performance since it cannot accurately detect seasonality on residuals from SARIMAX-only and minimize the SARIMAX-LSTM error. We conclude that the error correction framework should be preferred over single models in wildlife time-series modeling and predictions when a dataset contains more linear components. Adding more related data may improve the prediction performance of SARIMAX-LSTM