Weak local rules for planar octagonal tilings

We provide an effective characterization of the planar octagonal tilings which admit weak local rules. As a corollary, we show that they are all based on quadratic irrationalities, as conjectured by Thang Le in the 90s.Comment: 23 pages, 6 figure

On the resource allocation for D2D underlaying uplink cellular networks

Device-to-Device (D2D) communications has attracted research interests as an emerging technology towards 5G and beyond cellular networks. In this paper, we investigate the power allocation in D2D underlaying cellular networks with uplink channel reuse. We first develop an optimization problem to minimize the total power consumption subject to per- user Quality-of-Service (QoS) constraints. A distributed power allocation algorithm is proposed to allocate the power for both D2D and cellular users by exploiting the property of strictly non-negative inverse of a Z-matrix. It is shown that the power allocated for users can be considerably saved for low QoS requirements, especially with a large number of D2D users. The proposed algorithm is validated through simulation to realize the impacts of noise power, distance between D2D users and the number of D2D pairs in the network

An optimal power allocation for D2D communications over multi-user cellular uplink channels

Device-to-Device (D2D) communications has emerged as a promising technology for optimizing spectral efficiency, reducing latency, improving data rate and increasing system capacity in cellular networks. Power allocation in D2D communication to maintain Quality-of-Service (QoS) remains as a challenging task. In this paper, we investigate the power allocation in D2D underlaying cellular networks with multi-user cellular uplink channel reuse. Specifically, this paper aims at minimizing the total transmit power of D2D users and cellular users (CUs) sub- ject to QoS requirement at each user in terms of the required signal-to- interference-plus-noise ratio (SINR) at D2D users and base station (BS) over uplink channel as well as their limited transmit power. We first derive expressions of SINR at the D2D users and BS based on which an optimization framework for power allocation is developed. We then propose an optimal power allocation algorithm for all D2D users and CUs by taking into account the property of non-negative inverse of a Z- matrix. The proposed algorithm is validated through simulation results which show the impacts of noise power, distance between D2D users, the number of D2D pairs and the number of CUs on the power allocation in the D2D underlaying cellular networks

Kontsevich integral for knots and Vassiliev invariants

We review quantum field theory approach to the knot theory. Using holomorphic gauge we obtain the Kontsevich integral. It is explained how to calculate Vassiliev invariants and coefficients in Kontsevich integral in a combinatorial way which can be programmed on a computer. We discuss experimental results and temporal gauge considerations which lead to representation of Vassiliev invariants in terms of arrow diagrams. Explicit examples and computational results are presented.Comment: 25 pages, 17 figure

Two applications of elementary knot theory to Lie algebras and Vassiliev invariants

Using elementary equalities between various cables of the unknot and the Hopf link, we prove the Wheels and Wheeling conjectures of [Bar-Natan, Garoufalidis, Rozansky and Thurston, arXiv:q-alg/9703025] and [Deligne, letter to Bar-Natan, January 1996, http://www.ma.huji.ac.il/~drorbn/Deligne/], which give, respectively, the exact Kontsevich integral of the unknot and a map intertwining two natural products on a space of diagrams. It turns out that the Wheeling map is given by the Kontsevich integral of a cut Hopf link (a bead on a wire), and its intertwining property is analogous to the computation of 1+1=2 on an abacus. The Wheels conjecture is proved from the fact that the k-fold connected cover of the unknot is the unknot for all k. Along the way, we find a formula for the invariant of the general (k,l) cable of a knot. Our results can also be interpreted as a new proof of the multiplicativity of the Duflo-Kirillov map S(g)-->U(g) for metrized Lie (super-)algebras g.Comment: Published by Geometry and Topology at http://www.maths.warwick.ac.uk/gt/GTVol7/paper1.abs.htm

A new root-knot nematode, Meloidogyne moensi n. sp. (Nematoda : Meloidogynidae), parasitizing Robusta coffee from Western Highlands, Vietnam

A new root-knot nematode, parasitizing Robusta coffee in Dak Lak Province, Western Highlands of Vietnam, is described as Meloidogyne moensi n. sp. Morphological and molecular analyses demonstrated that this species differs clearly from other previously described root-knot nematodes. Morphologically, the new species is characterized by a swollen body of females with a small posterior protuberance that elongated from ovoid to saccate; perineal patterns with smooth striae, continuous and low dorsal arch; lateral lines marked as a faint space or linear depression at junction of the dorsal and ventral striate; distinct phasmids; perivulval region free of striae; visible and wide tail terminus surrounding by concentric circles of striae; medial lips of females in dumbbell-shaped and slightly raised above lateral lips; female stylet is normally straight with posteriorly sloping stylet knobs; lip region of second stage juvenile (J2) is not annulated; medial lips and labial disc of J2 formed dumbbell shape; lateral lips are large and triangular; tail of J2 is conoid with rounded unstriated tail tip; distinct phasmids and hyaline; dilated rectum. Meloidogyne moensi n. sp. is most similar to M. africana, M. ottersoni by prominent posterior protuberance. Results of molecular analysis of rDNA sequences including the D2-D3 expansion regions of 28S rDNA, COI, and partial COII/16S rRNA of mitochondrial DNA support for the new species status

Fundamental Limits of Low-Density Spreading NOMA with Fading

Spectral efficiency of low-density spreading non-orthogonal multiple access channels in the presence of fading is derived for linear detection with independent decoding as well as optimum decoding. The large system limit, where both the number of users and number of signal dimensions grow with fixed ratio, called load, is considered. In the case of optimum decoding, it is found that low-density spreading underperforms dense spreading for all loads. Conversely, linear detection is characterized by different behaviors in the underloaded vs. overloaded regimes. In particular, it is shown that spectral efficiency changes smoothly as load increases. However, in the overloaded regime, the spectral efficiency of low- density spreading is higher than that of dense spreading

Words are Malleable: Computing Semantic Shifts in Political and Media Discourse

Recently, researchers started to pay attention to the detection of temporal shifts in the meaning of words. However, most (if not all) of these approaches restricted their efforts to uncovering change over time, thus neglecting other valuable dimensions such as social or political variability. We propose an approach for detecting semantic shifts between different viewpoints--broadly defined as a set of texts that share a specific metadata feature, which can be a time-period, but also a social entity such as a political party. For each viewpoint, we learn a semantic space in which each word is represented as a low dimensional neural embedded vector. The challenge is to compare the meaning of a word in one space to its meaning in another space and measure the size of the semantic shifts. We compare the effectiveness of a measure based on optimal transformations between the two spaces with a measure based on the similarity of the neighbors of the word in the respective spaces. Our experiments demonstrate that the combination of these two performs best. We show that the semantic shifts not only occur over time, but also along different viewpoints in a short period of time. For evaluation, we demonstrate how this approach captures meaningful semantic shifts and can help improve other tasks such as the contrastive viewpoint summarization and ideology detection (measured as classification accuracy) in political texts. We also show that the two laws of semantic change which were empirically shown to hold for temporal shifts also hold for shifts across viewpoints. These laws state that frequent words are less likely to shift meaning while words with many senses are more likely to do so.Comment: In Proceedings of the 26th ACM International on Conference on Information and Knowledge Management (CIKM2017

Gamma-Ray Bursts as a Probe of the Very High Redshift Universe

We show that, if many GRBs are indeed produced by the collapse of massive stars, GRBs and their afterglows provide a powerful probe of the very high redshift (z > 5) universe.Comment: To appear in Proc. of the 5th Huntsville Gamma-Ray Burst Symposium, 5 pages, LaTe