Computing cliques and cavities in networks

Complex networks contain complete subgraphs such as nodes, edges, triangles, etc., referred to as simplices and cliques of different orders. Notably, cavities consisting of higher-order cliques play an important role in brain functions. Since searching for maximum cliques is an NP-complete problem, we use k-core decomposition to determine the computability of a given network. For a computable network, we design a search method with an implementable algorithm for finding cliques of different orders, obtaining also the Euler characteristic number. Then, we compute the Betti numbers by using the ranks of boundary matrices of adjacent cliques. Furthermore, we design an optimized algorithm for finding cavities of different orders. Finally, we apply the algorithm to the neuronal network of C. elegans with data from one typical dataset, and find all of its cliques and some cavities of different orders, providing a basis for further mathematical analysis and computation of its structure and function.

Experimental Investigations of the Ignitability of Several Coal Dust Qualities

The ignition characteristics of coal dust is of high importance for the flame stability in coal-fired power plants. We investigate the ignitability of six lignite dust qualities and one hard coal using dust explosion tests and an ignitability characteristic number. The paper aims to identify the degree of impact of the properties of coals, such as the moisture content, the ash content etc., on the ignition characteristics and ultimately to compare the identified relevant ignition parameters to the ignition performance of the dust qualities in an industrially relevant environment. The minimum cloud ignition temperature (MCIT), the maximum rate of pressure rise ((dp/dt)max), the maximum explosion pressure (pmax), the deflagration index (Kst-value) and the modified ignitability characteristic number (ZWZmod.) were determined and were attributed to the moisture content, the ash content and the median particle size. The MCIT was largely influenced by the volatile content, whereas the variations of moisture and ash contents within the range of 10% to 20% did not have a significant impact on the MCIT. The maximum explosion pressure did not differ considerably and stayed in a narrow range among the tested dust qualities. The deflagration index showed a higher sensitivity to the dust properties. The deflagration index and the modified ignitability characteristics number dropped as the moisture content increased and the volatile content reduced. The Kst and ZWZmod. values showed the highest susceptibility to the coal dust properties. Hence, they were used as representative parameters for further comparison with the ignition performance of coal dust in a pilot-scale testing. The results showed that both parameters predicted the ignition performance relatively well and can be used as indicators for the prediction of the ignition performance.

Computing Cliques and Cavities in Networks

Complex networks have complete subgraphs such as nodes, edges, triangles, etc., referred to as cliques of different orders. Notably, cavities consisting of higher-order cliques have been found playing an important role in brain functions. Since searching for the maximum clique in a large network is an NP-complete problem, we propose using k-core decomposition to determine the computability of a given network subject to limited computing resources. For a computable network, we design a search algorithm for finding cliques of different orders, which also provides the Euler characteristic number. Then, we compute the Betti number by using the ranks of the boundary matrices of adjacent cliques. Furthermore, we design an optimized algorithm for finding cavities of different orders. Finally, we apply the algorithm to the neuronal network of C. elegans in one dataset, and find all of its cliques and some cavities of different orders therein, providing a basis for further mathematical analysis and computation of the structure and function of the C. elegans neuronal network.

Studies on Clarification of Coal Washery Effluent Using Polymeric Flocculants and Settling Kinetics

Settling tests were conducted on the washery effluent using three types of flocculants namely cationic (Telfloc-3674F), anionic (Magna-1011) and non-ionic (Nalco-83370+). For the study purpose coal washery effluent (having pH of 8.72) was collected from a newly commissioned plant-thickener. Tests were conducted by varying the pH of the pulp at three levels of acidic (4.0), alkaline (11.0) and the natural pH (8.72) of the as collected effluent, besides the flocculent dosages varied at four levels (2, 4, 6 and 8 gpt) for each of the flocculants stated. The results of these tests, estimated in terms of initial settling rate and turbidity indicated that; among the three flocculants tested Telfloc-3674F and Magna-1011 gave best results as compared to Nalco-83370+ flocculent at a washery water pH 8.72. The effect of molecular weight of the flocculants on settling of solids in effluent has been established in terms of the kinetics with a characteristic number for each of the type of flocculants used.

The evolution of the UV luminosity and stellar mass functions of Lyman-α emitters from z ∼ 2 to z ∼ 6

We measure the evolution of the rest-frame UV luminosity function (LF) and the stellar mass function (SMF) of Lyman-α (Lyα) emitters (LAEs) from z ∼ 2 to z ∼ 6 by exploring ∼4000 LAEs from the SC4K sample. We find a correlation between Lyα luminosity (LLyα) and rest-frame UV (MUV), with best-fit M$_{\rm UV}=-1.6_{-0.3}^{+0.2}\log _{10} (\rm L_{Ly\alpha }/erg\, s^{-1})+47_{-11}^{+12}$ and a shallower relation between LLyα and stellar mass (M⋆), with best-fit $\log _{10} (\rm M_\star /{\rm M}_\odot )=0.9_{-0.1}^{+0.1}\log _{10} (\rm L_{Ly\alpha }/erg\, s^{-1})-28_{-3.8}^{+4.0}$. An increasing LLyα cut predominantly lowers the number density of faint MUV and low M⋆ LAEs. We estimate a proxy for the full UV LFs and SMFs of LAEs with simple assumptions of the faint end slope. For the UV LF, we find a brightening of the characteristic UV luminosity (M$_{\rm UV}^*$) with increasing redshift and a decrease of the characteristic number density (Φ*). For the SMF, we measure a characteristic stellar mass (${\rm M_\star ^*/{\rm M}_\odot }$) increase with increasing redshift, and a Φ* decline. However, if we apply a uniform luminosity cut of $\log _{10} (\rm L_{Ly\alpha }/erg\, s^{-1}) \ge 43.0$, we find much milder to no evolution in the UV and SMF of LAEs. The UV luminosity density (ρUV) of the full sample of LAEs shows moderate evolution and the stellar mass density (ρM) decreases, with both being always lower than the total ρUV and ρM of more typical galaxies but slowly approaching them with increasing redshift. Overall, our results indicate that both ρUV and ρM of LAEs slowly approach the measurements of continuum-selected galaxies at z > 6, which suggests a key role of LAEs in the epoch of reionisation.

Studies on Clarification of Coal Washery Effluent Using Polymeric Flocculants and Settling Kinetics

Settling tests were conducted on the washery effluent using three types of flocculants namely cationic (Telfloc-3674F), anionic (Magna-1011) and non-ionic (Nalco-83370 + ). For the study purpose coal washery effluent (having pH of 8.72) was collected from a newly commissioned plant-thickener. Tests were conducted by varying the pH of the pulp at three levels of acidic (4.0), alkaline (11.0) and the natural pH (8.72) of the as collected effluent, besides the flocculent dosages varied at four levels (2, 4, 6 and 8gpt) for each of the flocculants stated. The results of these tests, estimated in terms of initial settling rate and turbidity indicated that; among the three flocculants tested Telfloc-3674F and Magna-1011 gave best results as compared to Nalco-83370 + flocculent at a washery water pH 8.72. The effect of molecular weight of the flocculants on settling of solids in effluent has been established in terms of the kinetics with a characteristic number for each of the type of flocculants used.

Determining the Topology and Deflection Angle of Ringholes via Gauss-Bonnet Theorem

In this letter, we use a recent wormhole metric known as a ringhole [Gonzalez-Diaz, Phys. Rev. D 54, 6122, 1996] to determine the surface topology and the deflection angle of light in the weak limit approximation using the Gauss-Bonnet theorem (GBT). We apply the GBT and show that the surface topology at the wormhole throat is indeed a torus by computing the Euler characteristic number. As a special case of the ringhole solution, one can find the Ellis wormhole which has the surface topology of a 2-sphere at the wormhole throat. The most interesting results of this paper concerns the problem of gravitational deflection of light in the spacetime of a ringhole geometry by applying the GBT to the optical ringhole geometry. It is shown that, the deflection angle of light depends entirely on the geometric structure of the ringhole geometry encoded by the parameters b0 and a, being the ringhole throat radius and the radius of the circumference generated by the circular axis of the torus, respectively. As special cases of our general result, the deflection angle by Ellis wormhole is obtained. Finally, we work out the problem of deflection of relativistic massive particles and show that the deflection angle remains unaltered by the speed of the particles.

Rational cuspidal curves in a moving family of ℙ2

In this paper we obtain a formula for the number of rational degree d curves in ℙ3 having a cusp, whose image lies in a ℙ2 and that passes through r lines and s points (where r + 2s = 3 d + 1). This problem can be viewed as a family version of the classical question of counting rational cuspidal curves in ℙ2, which has been studied earlier by Z. Ran ([13]), R. Pandharipande ([12]) and A. Zinger ([16]). We obtain this number by computing the Euler class of a relevant bundle and then finding out the corresponding degenerate contribution to the Euler class. The method we use is closely based on the method followed by A. Zinger ([16]) and I. Biswas, S. D’Mello, R. Mukherjee and V. Pingali ([1]). We also verify that our answer for the characteristic numbers of rational cuspidal planar cubics and quartics is consistent with the answer obtained by N. Das and the first author ([2]), where they compute the characteristic number of δ-nodal planar curves in ℙ3 with one cusp (for δ ≤ 2).

THE STANDARDIZATION OF QUQLITY ASSESMENT OF SPECIAL METALLURGICAL CRANES BASED ON DESIGN RISK ANALYSIS

The article critically analyzes the standards for assessing the quality of the supporting structures of special bridge metallurgical cranes. At the present stage, more than 80% of such cranes are operated outside the warranty period. The standards are aimed either at a finite number of operating cycles, or at objects of low complexity, in particular FMEA. To estimate the resource, the characteristic number, a generalized indicator of the supporting structure, is used. Risk analysis is a promising and recommended one today. The structural risk analysis is considered as an integral indicator for assessing the quality of the actual technical condition of a special metallurgical crane. The article is a continuation of a series on the study of the use of structural risk analysis for assessing the quality of structures of a metallurgical enterprise. Models of quality are given according to the following risk criteria: normal, maximum permissible, critical (catastrophic). The largest catastrophic events of a metallurgical enterprise have been studied for 70 years. The statement of the problem is formulated as follows: it is necessary to critically assess the current state of the standards and find their joint optimal parameters or put forward new requirements to create a draft of a new standard for assessing the quality of special metallurgical cranes operating outside the warranty period. An algorithm is presented that includes and refines modern standards, including FMEA. Quality is calculated as a function that changes over time, inversely proportional to the risk, taking into account the damage. The calculated values of the quality are obtained, which make it possible to relate the number of worked cycles, the acting stresses and deformations.

Shape Factor Asymptotic Analysis I

We proposed using shape factor to distinguish probability distributions, and using relative minimum or maximum values of shape factor to locate distribution parameter allowable ranges for distribution fitting in our previous study. In this paper, the shape factor asymptotic analysis is employed to study such conditional minimum or maximum, to cross validate results found from numerical study and empirical formula we obtained and published earlier. The shape factor defined as kurtosis divided by skewness squared is characterized as the unique maximum choice of among all factors that is greater than or equal to 1 for all probability distributions. For all distributions from a specific distribution family, there may exists such that. The least upper bound of all such is defined as the distribution family’s characteristic number. The useful extreme values of the shape factor for various distributions that are found numerically before, the Beta, Kumaraswamy, Weibull, and GB2 distributions are derived using asymptotic analysis. The match of the numerical and the analytical results may arguably be considered proof of each other. The characteristic numbers of these distributions are also calculated. The study of the extreme value of the shape factor, or the shape factor asymptotic analysis, help reveal properties of the original shape factor, and reveal relationship between distributions, such as that between the Kumaraswamy distribution and the Weibull distribution.