Byzantine Vector Consensus in Complete Graphs

Consider a network of n processes each of which has a d-dimensional vector of reals as its input. Each process can communicate directly with all the processes in the system; thus the communication network is a complete graph. All the communication channels are reliable and FIFO (first-in-first-out). The problem of Byzantine vector consensus (BVC) requires agreement on a d-dimensional vector that is in the convex hull of the d-dimensional input vectors at the non-faulty processes. We obtain the following results for Byzantine vector consensus in complete graphs while tolerating up to f Byzantine failures: * We prove that in a synchronous system, n >= max(3f+1, (d+1)f+1) is necessary and sufficient for achieving Byzantine vector consensus. * In an asynchronous system, it is known that exact consensus is impossible in presence of faulty processes. For an asynchronous system, we prove that n >= (d+2)f+1 is necessary and sufficient to achieve approximate Byzantine vector consensus. Our sufficiency proofs are constructive. We show sufficiency by providing explicit algorithms that solve exact BVC in synchronous systems, and approximate BVC in asynchronous systems. We also obtain tight bounds on the number of processes for achieving BVC using algorithms that are restricted to a simpler communication pattern

Canonical structure of the E10 model and supersymmetry

A coset model based on the hyperbolic Kac-Moody algebra E10 has been conjectured to underly eleven-dimensional supergravity and M theory. In this note we study the canonical structure of the bosonic model for finite- and infinite-dimensional groups. In the case of finite-dimensional groups like GL(n) we exhibit a convenient set of variables with Borel-type canonical brackets. The generalisation to the Kac-Moody case requires a proper treatment of the imaginary roots that remains elusive. As a second result, we show that the supersymmetry constraint of D=11 supergravity can be rewritten in a suggestive way using E10 algebra data. Combined with the canonical structure, this rewriting explains the previously observed association of the canonical constraints with null roots of E10. We also exhibit a basic incompatibility between local supersymmetry and the K(E10) `R symmetry', that can be traced back to the presence of imaginary roots and to the unfaithfulness of the spinor representations occurring in the present formulation of the E10 worldline model, and that may require a novel type of bosonisation/fermionisation for its resolution. This appears to be a key challenge for future progress with E10.Comment: 1+39 pages. v2: small corrections. Version to appear in PR

Simulations Show that Vortex Flows could Heat the Chromosphere in Solar Plage

The relationship between vortex flows at different spatial scales and their contribution to the energy balance in the chromosphere is not yet fully understood. We perform three-dimensional (3D) radiation-magnetohydrodynamic (MHD) simulations of a unipolar solar plage region at a spatial resolution of 10 km using the MURaM code. We use the swirling-strength criterion that mainly detects the smallest vortices present in the simulation data. We additionally degrade our simulation data to smooth-out the smaller vortices, so that also the vortices at larger spatial scales can be detected. Vortex flows at various spatial scales are found in our simulation data for different effective spatial resolutions. We conclude that the observed large vortices are likely clusters of much smaller ones that are not yet resolved by observations. We show that the vertical Poynting flux decreases rapidly with reduced effective spatial resolutions and is predominantly carried by the horizontal plasma motions rather than vertical flows. Since the small-scale horizontal motions or the smaller vortices carry most of the energy, the energy transported by vortices deduced from low resolution data is grossly underestimated. In full resolution simulation data, the Poynting flux contribution due to vortices is more than adequate to compensate for the radiative losses in plage, indicating their importance for chromospheric heating.Comment: 8 pages, 5 figures, accepted in ApJ

Research options for controlling Zoonotic disease in India, 2010-2015

BACKGROUND: Zoonotic infections pose a significant public health challenge for low- and middle-income countries and have traditionally been a neglected area of research. The Roadmap to Combat Zoonoses in India (RCZI) initiative conducted an exercise to systematically identify and prioritize research options needed to control zoonoses in India. METHODS AND FINDINGS: Priority setting methods developed by the Child Health and Nutrition Research Initiative were adapted for the diversity of sectors, disciplines, diseases and populations relevant for zoonoses in India. A multidisciplinary group of experts identified priority zoonotic diseases and knowledge gaps and proposed research options to address key knowledge gaps within the next five years. Each option was scored using predefined criteria by another group of experts. The scores were weighted using relative ranks among the criteria based upon the feedback of a larger reference group. We categorized each research option by type of research, disease targeted, factorials, and level of collaboration required. We analysed the research options by tabulating them along these categories. Seventeen experts generated four universal research themes and 103 specific research options, the majority of which required a high to medium level of collaboration across sectors. Research options designated as pertaining to 'social, political and economic' factorials predominated and scored higher than options focussing on ecological, genetic and biological, or environmental factors. Research options related to 'health policy and systems' scored highest while those related to 'research for development of new interventions' scored the lowest. CONCLUSIONS: We methodically identified research themes and specific research options incorporating perspectives of a diverse group of stakeholders. These outputs reflect the diverse nature of challenges posed by zoonoses and should be acceptable across diseases, disciplines, and sectors. The identified research options capture the need for 'actionable research' for advancing the prevention and control of zoonoses in India

Performance analysis of FSO using relays and spatial diversity under log-normal fading channel

The performance analysis of free space optical communication (FSO) system using relays and spatial diversity at the source is studied in this paper. The effect of atmospheric turbulence and attenuation, caused by different weather conditions and geometric losses, has also been considered for analysis. The exact closed-form expressions are presented for bit error rate (BER) of M-ary quadrature amplitude modulation (M-QAM) technique for multi-hop multiple-input single-output (MISO) FSO system under log-normal fading channel. Furthermore, the link performance of multi-hop MISO and multi-hop single-input and single-output (SISO) FSO systems are compared to the different systems using on-off keying (OOK), repetition codes (RCs) and M-ary pulse amplitude modulation (M-PAM) techniques. A significant performance enhancement in terms of BER analysis and SNR gains is shown for multi-hop MISO and multi-hop SISO FSO systems with M-QAM over other existing systems with different modulation schemes. Moreover, Monte-Carlo simulations are used to validate the accuracy and consistency of the derived analytical results. Numerical results show that M-QAM modulated multi-hop MISO and multi-hop SISO FSO system with relays and spatial diversity outperforms other systems while having the same spectral efficiency of each system.Comment: 4 pages, 4 figures, 4th International Conference on Electrical Energy Systems (ICEES), Feb. 7-9, 2018, SSNCE, Chennai, TN, INDI

Trapping and sorting active particles: motility-induced condensation & smectic defects

We present an experimental realization of the collective trapping phase transition [Kaiser et al., PRL 108, 268307 (2012)], using motile polar granular rods in the presence of a V-shaped obstacle. We offer a theory of this transition based on the interplay of motility-induced condensation and liquid-crystalline ordering and show that trapping occurs when persistent influx overcomes the collective expulsion of smectic defect structures. In agreement with the theory, our experiments find that a trap fills to the brim when the trap angle $\theta$ is below a threshold $\theta_c$, while all particles escape for $\theta > \theta_c$. Our simulations support a further prediction, that $\theta_c$ goes down with increasing rotational noise. We exploit the sensitivity of trapping to the persistence of directed motion to sort particles based on the statistical properties of their activityComment: 6 pages, 5 figures, for supplementary mpg files, see "https://www.dropbox.com/sh/3cmswfoysdn0sb6/AACpEp-G3768B6Y62nDFj_Hea?dl=0". This paper supersedes our earlier version arXiv:1603.08535 and contains substantial new results including revised theoretical treatmen