Towards Tighter Space Bounds for Counting Triangles and Other Substructures in Graph Streams

We revisit the much-studied problem of space-efficiently estimating the number of triangles in a graph stream, and extensions of this problem to counting fixed-sized cliques and cycles. For the important special case of counting triangles, we give a 4-pass, (1 +/- epsilon)-approximate, randomized algorithm using O-tilde(epsilon^(-2) m^(3/2) / T) space, where m is the number of edges and T is a promised lower bound on the number of triangles. This matches the space bound of a recent algorithm (McGregor et al., PODS 2016), with an arguably simpler and more general technique. We give an improved multi-pass lower bound of Omega(min{m^(3/2)/

Long-range and short-range magnetic correlations, and microscopic origin of net magnetization in the spin-1 trimer chain compound CaNi3P4O14

Spin-spin correlations and microscopic origin of net magnetization in the spin-1 trimer chain compound CaNi3P4O14 have been investigated by powder neutron diffraction. The present study reveals a 3D long-range magnetic ordering below 16 K where the magnetic structure consists of ferromagnetic trimers that are coupled ferromagnetically along the spin-chain. The moment components along the a and c axes arrange antiferromagnetically. Our study establishes that the uncompensated moment components along the b axis result in a net magnetization per unit cell. The magnetic structure, determined in the present study, is in agreement with the results of recent first principles calculation; however, it is in contrast to a fascinating experimental prediction of ferrimagnetic ordering based on the periodicity of the exchange interactions in CaNi3P4O14. Our study also confirms the presence of broad diffuse magnetic scattering, due to 1D short-range spin-spin correlations, over a wide temperature range below ~50 K down to a temperature well below the Tc. Total neutron scattering analysis by the RMC method reveals that the dominating spin-spin correlation above Tc is ferromagnetic and along the b axis. The nearest neighbour spin-spin correlations along the a and c axes are found to be weakly antiferromagnetic. The nature of the trimer spin structure of the short-range state is similar to that of the 3D long-range ordered state. The present investigation of microscopic nature of the magnetic ground state also explains the condition required for the 1/3 magnetization plateau to be observed in the trimer spin-chains. In spite of the S=1 trimer chain system, the present compound CaNi3P4O14 is found to be a good realization of 3D magnet below the Tc=16 K with full ordered moment values of ~2 mu_B/Ni2+ (1.98 and 1.96 mu_B/Ni2+ for two Ni sites, respectively) at 1.5 K.Comment: 10 pages, 8 figure

Graph Coloring via Degeneracy in Streaming and Other Space-Conscious Models

We study the problem of coloring a given graph using a small number of colors in several well-established models of computation for big data. These include the data streaming model, the general graph query model, the massively parallel computation (MPC) model, and the CONGESTED-CLIQUE and the LOCAL models of distributed computation. On the one hand, we give algorithms with sublinear complexity, for the appropriate notion of complexity in each of these models. Our algorithms color a graph $G$ using about $\kappa(G)$ colors, where $\kappa(G)$ is the degeneracy of $G$: this parameter is closely related to the arboricity $\alpha(G)$. As a function of $\kappa(G)$ alone, our results are close to best possible, since the optimal number of colors is $\kappa(G)+1$. On the other hand, we establish certain lower bounds indicating that sublinear algorithms probably cannot go much further. In particular, we prove that any randomized coloring algorithm that uses $\kappa(G)+1$ many colors, would require $\Omega(n^2)$ storage in the one pass streaming model, and $\Omega(n^2)$ many queries in the general graph query model, where $n$ is the number of vertices in the graph. These lower bounds hold even when the value of $\kappa(G)$ is known in advance; at the same time, our upper bounds do not require $\kappa(G)$ to be given in advance.Comment: 26 page

Novel Hydrothermal Synthesis of CoS₂/MWCNT Nanohybrid Electrode for Supercapacitor: A Systematic Investigation on the Influence of MWCNT

Here we report a novel hydrothermal method to synthesize hybrid nanostructures based on single phase cobalt disulfide (CoS2) nanoparticles decorated on multiwalled carbon nanotubes (MWCNT) for application as supercapacitor electrode. This is also the first report on systematic investigation of the influence of MWCNTs on the electrochemical properties of CoS2 nanoparticle based electrode for supercapacitor. The X-ray diffraction and electron microscopic analyses revealed that incorporation of CNTs promotes the growth of only the CoS2 phase in the form of spherical nanoparticles with an average diameter of ∼9 nm. CoS2-MWCNT nanohybrid electrode containing 20 wt % MWCNT showed the highest specific capacitance of 1486 F/g at 1 A/g discharge current density along with excellent reversibility. It also showed high cycle stability with ∼80% retention of specific capacitance even after 10,000 cycles. Thus, we show a low cost and simple method to synthesize a CoS2-MWCNT nanohybrid that has great promise as electrode material for supercapacitor applications. Incorporation of CNT not only provides a conducting network for fast charge diffusion but (due to large surface area) also allows more CoS2 molecules to be readily available for redox reaction resulting in the reduction of the charge transfer resistance consistent with the data obtained from electrochemical impedance spectroscopy

Understanding the multiple magnetic structures of the intermetallic compound NdMn1.4Co0.6Si2

Magnetic phases for the intermetallic compound NdMn1.4Co0.6Si2 have been investigated at various temperatures by dc magnetization, neutron diffraction and neutron depolarization. Our study shows multiple magnetic phase transitions with temperature (T) over 1.5-300 K. In agreement with dc-magnetization and neutron depolarization results, the temperature dependence of the neutron diffraction patterns shows five distinct regions with different magnetic phases. These temperature regions are (i) T >= 215 K, (ii) 215 K > T >= 50 K, (iii) 50 K > T >= 40 K, (iv) 40 K > T > 15 K, and (v) T =< 15 K. The corresponding magnetic structures are paramagnetic, commensurate collinear antiferromagnetic (AFM-I), incommensurate AFM (AFM-II), mixed ferromagnetic and AFM (FM+AFM-II), and incommensurate AFM (AFM-II), respectively.Comment: 26 pages, 10 figure

Search for gravitational-lensing signatures in the full third observing run of the LIGO-Virgo network

Gravitational lensing by massive objects along the line of sight to the source causes distortions of gravitational wave-signals; such distortions may reveal information about fundamental physics, cosmology and astrophysics. In this work, we have extended the search for lensing signatures to all binary black hole events from the third observing run of the LIGO--Virgo network. We search for repeated signals from strong lensing by 1) performing targeted searches for subthreshold signals, 2) calculating the degree of overlap amongst the intrinsic parameters and sky location of pairs of signals, 3) comparing the similarities of the spectrograms amongst pairs of signals, and 4) performing dual-signal Bayesian analysis that takes into account selection effects and astrophysical knowledge. We also search for distortions to the gravitational waveform caused by 1) frequency-independent phase shifts in strongly lensed images, and 2) frequency-dependent modulation of the amplitude and phase due to point masses. None of these searches yields significant evidence for lensing. Finally, we use the non-detection of gravitational-wave lensing to constrain the lensing rate based on the latest merger-rate estimates and the fraction of dark matter composed of compact objects

A Depth-Five Lower Bound for Iterated Matrix Multiplication

We prove that certain instances of the iterated matrix multiplication (IMM) family of polynomials with N variables and degree n require N^(Omega(sqrt(n))) gates when expressed as a homogeneous depth-five Sigma Pi Sigma Pi Sigma arithmetic circuit with the bottom fan-in bounded by N^(1/2-epsilon). By a depth-reduction result of Tavenas, this size lower bound is optimal and can be achieved by the weaker class of homogeneous depth-four Sigma Pi Sigma Pi circuits. Our result extends a recent result of Kumar and Saraf, who gave the same N^(Omega(sqrt(n))) lower bound for homogeneous depth-four Sigma Pi Sigma Pi circuits computing IMM. It is analogous to a recent result of Kayal and Saha, who gave the same lower bound for homogeneous Sigma Pi Sigma Pi Sigma circuits (over characteristic zero) with bottom fan-in at most N^(1-epsilon), for the harder problem of computing certain polynomials defined by Nisan-Wigderson designs

A multi-attribute decision making approach of mix design based on experimental soil characterization

The clay mineral composition is one of the major factors that governs the physical properties of silty sand subgrade. Therefore, a thorough knowledge of mineral composition is essential to predict the optimum engineering properties of the soil, which is generally characterized by different indices like maximum dry density (MDD), California bearing ratio (CBR), unconfined compressive strength (UCS) and free swelling index (FSI). In this article, a novel multiattribute decision making (MADM) based approach of mix design has been proposed for silty sand–artificial clay mix to improve the characteristic strength of a soil subgrade. Experimental investigation has been carried out in this study to illustrate the proposed approach of selecting appropriate proportion for the soil mix to optimize all the above mentioned engineering properties simultaneously. The results show that a mix proportion containing approximately 90% silty sand plus 10% bentonite soil is the optimal combination in context to the present study. The proposed methodology for optimal decision making to choose appropriate combination of bentonite and silty sand is general in nature and therefore, it can be extended to other problems of selecting mineral compositions.</p