On the complexity of branching proofs

We consider the task of proving integer infeasibility of a bounded convex K in Rn using a general branching proof system. In a general branching proof, one constructs a branching tree by adding an integer disjunction ax ≤ b or ax ≥ b + 1, a ∈ Zn, b ∈ Z, at each node, such that the leaves of the tree correspond to empty sets (i.e., K together with the inequalities picked up from the root to leaf is empty). Recently, Beame et al (ITCS 2018), asked whether the bit size of the coefficients in a branching proof, which they named stabbing planes (SP) refutations, for the case of polytopes derived from SAT formulas, can be assumed to be polynomial in n. We resolve this question in the affirmative, by showing that any branching proof can be recompiled so that the normals of the disjunctions have coefficients of size at most (nR)O(n2), where R ∈ N is the radius of an `1 ball containing K, while increasing the number of nodes in the branching tree by at most a factor O(n). Our recompilation techniques works by first replacing each disjunction using an iterated Diophantine approximation, introduced by Frank and Tardos (Combinatorica 1986), and proceeds by “fixing up” the leaves of the tree using judiciously added Chvátal-Gomory (CG) cuts. As our second contribution, we show that Tseitin formulas, an important class of infeasible SAT instances, have quasi-polynomial sized cutting plane (CP) refutations. This disproves a conjecture that Tseitin formulas are (exponentially) hard for CP. Our upper bound follows by recompiling the quasi-polynomial sized SP refutations for Tseitin formulas due to Beame et al, which have a special enumerative form, into a CP proof of the same length using a serialization technique of Cook et al (Discrete Appl. Math. 1987). As our final contribution, we give a simple family of polytopes in [0, 1]n requiring exponential sized branching proofs

Relativistic Electromagnetic Mass Models: Charged Dust Distribution in Higher Dimensions

Electromagnetic mass models are proved to exist in higher dimensional theory of general relativity corresponding to charged dust distribution. Along with the general proof a specific example is also sited as a supporting candidate.Comment: Latex, 7 pages. Accepted in Astrophysics and Space Scienc

Five Dimensional Cosmological Models in General Relativity

A Five dimensional Kaluza-Klein space-time is considered in the presence of a perfect fluid source with variable G and $\Lambda$. An expanding universe is found by using a relation between the metric potential and an equation of state. The gravitational constant is found to decrease with time as $G \sim t^{-(1-\omega)}$ whereas the variation for the cosmological constant follows as $\Lambda \sim t^{-2}$, $\Lambda \sim (\dot R/R)^2$ and $\Lambda \sim \ddot R/R$ where $\omega$ is the equation of state parameter and $R$ is the scale factor.Comment: 13 pages, 4 figures, accepted in Int. J. Theor. Phy

Some anisotropic universes in the presence of imperfect fluid coupling with spatial curvature

We consider Bianchi VI spacetime, which also can be reduced to Bianchi types VI0-V-III-I. We initially consider the most general form of the energy-momentum tensor which yields anisotropic stress and heat flow. We then derive an energy-momentum tensor that couples with the spatial curvature in a way so as to cancel out the terms that arise due to the spatial curvature in the evolution equations of the Einstein field equations. We obtain exact solutions for the universes indefinetly expanding with constant mean deceleration parameter. The solutions are beriefly discussed for each Bianchi type. The dynamics of the models and fluid are examined briefly, and the models that can approach to isotropy are determined. We conclude that even if the observed universe is almost isotropic, this does not necessarily imply the isotropy of the fluid (e.g., dark energy) affecting the evolution of the universe within the context of general relativity.Comment: 17 pages, no figures; to appear in International Journal of Theoretical Physics; in this version (which is more concise) an equation added, some references updated and adde

Statefinder Parameters for Different Dark Energy Models with Variable G Correction in Kaluza-Klein Cosmology

In this work, we have calculated the deceleration parameter, statefinder parameters and EoS parameters for different dark energy models with variable $G$ correction in homogeneous, isotropic and non-flat universe for Kaluza-Klein Cosmology. The statefinder parameters have been obtained in terms of some observable parameters like dimensionless density parameter, EoS parameter and Hubble parameter for holographic dark energy, new agegraphic dark energy and generalized Chaplygin gas models.Comment: 9 pages, no figure, accepted for publication in IJTP. arXiv admin note: text overlap with arXiv:1104.2366 by other author

Resource mobilization and organizational support in irrigation system management: Experience from Kulariya Jamara, and Rani Kulos of Kailai District

In IIMI, Irrigation management in Nepal: Research papers from a National Seminar, Bharatpur, Nepal, 4-6 June 1987. Kathmandu, Nepal: IIM

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Not AvailableCellular levels of specific transcripts or proteins are often measured in relation to a variety of biological events, using a selection of qualitative and quantitative methodologies. Changes in expression levels, measured in a native sentinel species may serve as biomarkers for the effects of environmental perturbations. A quantitative real-time reverse-transcriptase polymerase chain reaction study was conducted using freshwater air-breathing fish, Channa punctata (Bloch) as a test model for observing metallothionein mRNA expression pattern under the influence of varied concentrations of heavy metal, cadmium for an exposure span of 14 days. The findings revealed that metallothionein gene expression is a tissue specific phenomenon in C. punctata and liver is a prominent site for first-line defence during early exposure phase to cadmium, whereas kidney metallothionein mRNA indicates prolong presence of metal in the body.University Grants Commission, New Delhi, Indi

On the integrality gap of binary integer programs with Gaussian data

For a binary integer program (IP) max cTx, Ax≤ b, x∈ { 0, 1 } n, where A∈ Rm × n and c∈ Rn have independent Gaussian entries and the right-hand side b∈ Rm satisfies that its negative coordinates have ℓ2 norm at most n/10, we prove that the gap between the value of the linear programming relaxation and the IP is upper bounded by poly (m) (log n) 2/ n with probability at least 1 - 1 / n7- 2 - poly ( m ). Our results give a Gaussian analogue of the classical integrality gap result of Dyer and Frieze (Math. of O.R., 1989) in the case of random packing IPs. In constrast to the packing case, our integrality gap depends only polynomially on m instead of exponentially. By recent breakthrough work of Dey, Dubey and Molinaro (SODA, 2021), the bound on the integrality gap immediately implies that branch and bound requires npoly ( m ) time on random Gaussian IPs with good probability, which is polynomial when the number of constraints m is fixed

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Not AvailableThe present study was undertaken to investigate the acute toxicity of cadmium, a heavy metal widely detected in the aquatic environment due to natural effects and anthropogenic activities, in freshwater teleost, Channa punctata (Bloch). The experiments for the bioassay were performed in semi-static test condition according to the standard guidelines. The behavioural changes in the fish were observed for all tested concentrations of the metal. The data obtained for bioassay were analyzed for median lethal concentrations (LC50) of the metal by SPSS computer software, Finneyʼs Probit analysis and Trimmed Spearman-Karberʼs method. The LC50 values, estimated by SPSS, with 95% confidence level were found to be: 26.88 (21.69-71.68), 18.76 (17.13-20.81), 16.70 (14.77-17.96) and 14.95 (13.13-15.88) mg l-1 for dissolved metal concentrations, at 24, 48, 72 and 96 h exposure durations respectively. All three methods showed good agreement among the estimates. Furthermore, the exposed specimens showed dose and duration dependent abnormal behaviour and hyperactivity.University Grants Commission, New Delhi, Indi