Symmetry Lie Algebras of Varieties with Applications to Algebraic Statistics

The motivation for this paper is to detect when an irreducible projective variety V is not toric. We do this by analyzing a Lie group and a Lie algebra associated to V. If the dimension of V is strictly less than the dimension of the above mentioned objects, then V is not a toric variety. We provide an algorithm to compute the Lie algebra of an irreducible variety and use it to provide examples of non-toric statistical models in algebraic statistics.Comment: 18 pages. Code attached. Comments welcome

Effect of building gap to improve pedestrian comfort levels and ventilation

Rapid rates of urbanization have resulted into increased concerns of urban environment. Amongst them, wind and thermal comfort levels for pedestrians have attracted research interest. In this regards, urban wind environment is seen as a crucial components that can lead to improved thermal comfort levels for pedestrian population. High rise building in modern urban setting causes high levels of turbulence that renders discomfort to pedestrians. Additionally, a higher frequency of high ris e buildings at a particular region acts as a shield against the wind flow to the lower buildings beyond them resulting into higher levels of discomfort to users or residents. Studies conducted on developing wind flow models using Computational Fluid Dynami cs (CFD) simulations have revealed improvement in interval to height ratios can results into improved wind flow within the simulation grid. However, high value and demand for land in urban areas renders expansion to be an impractical solution. Nonetheless, innovative utilization of architectural concepts can be imagined to improve the pedestrian comfort levels through improved wind permeability. This paper assesses the possibility of through-building gaps being a solution to improve pedestrian comfort levels

Recognition of Characters from Streaming Videos

Non

Worldline effective field theory of inspiralling black hole binaries in presence of dark photon and axionic dark matter

We investigate the correction to the potential that gives rise to the bound orbits and radiation from non-spinning inspiralling binary black holes in a dark matter environment consisting of axion-like particles and dark photons using the techniques of Worldline Effective Field Theory. We compute the conservative dynamics up to $1$PN order for gravitational, electromagnetic, and Proca fields and up to $2$PN order for the scalar field. The effect of axion-electromagnetic coupling ($g_{a\gamma\gamma}$) arises to the conservative dynamics at $2.5$PN order and the kinetic mixing constant ($\gamma$) at $1$PN order. Furthermore, we calculate the radiation due to the various fields present in our theory. We find that the contribution of $g_{a\gamma\gamma}$ to the gravitational radiation appears at $N^{(7)}LO$ and to the scalar radiation appears at $N^{(5)}LO$. We also find that these radiative corrections due to the coupling $g_{a\gamma\gamma}$ vanishes for any orbit confined to a plane because of the existence of a binormal like term in effective radiative action but give rise to non-zero contributions for any orbit that lies in three dimensions. Last but not the least, $\gamma$ contributes to the gravitational radiation at $N^{(2)}LO$ and $N^{(4)}LO$.Comment: 80 pages, 19 figures, 4 tables, improvements in wording, reference updated, v2: accepted for publication in JHE

Concise tensors of minimal border rank

We determine defining equations for the set of concise tensors of minimal border rank in $C^m\otimes C^m\otimes C^m$ when $m=5$ and the set of concise minimal border rank $1_*$-generic tensors when $m=5,6$. We solve this classical problem in algebraic complexity theory with the aid of two recent developments: the 111-equations defined by Buczy\'{n}ska-Buczy\'{n}ski and results of Jelisiejew-\v{S}ivic on the variety of commuting matrices. We introduce a new algebraic invariant of a concise tensor, its 111-algebra, and exploit it to give a strengthening of Friedland's normal form for $1$-degenerate tensors satisfying Strassen's equations. We use the 111-algebra to characterize wild minimal border rank tensors and classify them in $C^5\otimes C^5\otimes C^5$.Comment: v2, fina

2 x 2 Phased Array Consisting of Square Loop Antennas for High Gain Wide Angle Scanning With Low Grating Lobes

A 2 × 2 array antenna comprised of conventional hybrid high impedance surface-based reconfigurable square loop antennas (SLAs) as elements is presented. The SLA element has four conducting arms and each arm is fed at the middle by vertical probes, which is connected to a 50 Ω port at the bottom of antenna ground plane. Thus, the SLA element has four feeding ports and it is capable of generating five distinct radiation patterns by using a combination of its feeding ports. Depending upon which of its four ports are excited it can provide four high gain off-boresight tilted beams (8.9 dBi at θmax= 36°) in four different quadrants of the space (tilted beam mode). When all the four ports are simultaneously excited with phases of 0°, 0°, 180°, and 180°, it provides an axial beam (6.5 dBi) at boresight (axial beam mode). By combining these two modes the 2 × 2 array of SLAs can provide a scanning range of-60° to +60° in the elevation plane with high-gain beams (14-11.2 dBi)