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A linear programming primer: from Fourier to Karmarkar
No full textThe story of linear programming is one with all the elements of a grand historical drama. The original idea of testing if a polyhedron is non-empty by using a variable elimination to project down one dimension at a time until a tautology emerges dates back to a paper by Fourier in 1823. This gets re-invented in the 1930s by Motzkin. The real interest in linear programming happens during World War II when mathematicians ponder best ways of utilising resources at a time when they are constrained. The problem of optimising a linear function over a set of linear inequalities becomes the focus of the effort. Dantzig�s Simplex Method is announced and the Rand Corporation becomes a hot bed of computational mathematics. The range of applications of this modelling approach grows and the powerful machinery of numerical analysis and numerical linear algebra becomes a major driver for the advancement of computing machines. In the 1970s, constructs of theoretical computer science indicate that linear programming may in fact define the frontier of tractable problems that can be solved effectively on large instances. This raised a series of questions and answers: Is the Simplex Method a polynomial-time method and if not can we construct novel polynomial time methods, etc. And that is how the Ellipsoid Method from the Soviet Union and the Interior Point Method from Bell Labs make their way into this story as the heroics of Khachiyan and Karmarkar. We have called this paper a primer on linear programming since it only gives the reader a quick narrative of the grand historical drama. Hopefully it motivates a young reader to delve deeper and add another chapter. © 2019, Springer Science+Business Media, LLC, part of Springer Nature
Superior ductility in magnesium alloy-based nanocomposites: the crucial role of texture induced by nanoparticles
No full textIn an expansive field of metals, magnesium has been trending of late in automobile, aerospace, defense, sports, electronic and biomedical sectors as it offers an advantage in lightweighting. In the realm of Mg-based materials, Mg nanocomposites have a good combination of specific strength, thermal and damping properties, but lack a high ductility and do not typically undergo a large amount of uniform elongation. The current work bridges this gap by reporting a magnesium nanocomposite (Mg�1.8Y/1.5Y 2 O 3 ) that exhibits a significantly high tensile ductility of 36. Microstructural characterization of the nanocomposite revealed that the striking presence of micron-Mg�Y phases and nano-Y 2 O 3 particles in matrix led to a bimodal particle distribution which affected the dynamic recrystallization mechanism. It was also observed that the addition of Y 2 O 3 nanoparticles weakened the texture of nanocomposite. The dominating influence of texture weakening over other mechanisms (grain refinement and alleviated micro-strain) on the plastic deformation/ductility of the nanocomposite is highlighted, and the contribution of nanoparticles toward the enhancement of ductility is ascertained. In contrast to the previous studies where Mg-based nanocomposites are known to have improved strengths, this approach can be used to develop magnesium nanocomposites that are exceptional. © 2019, Springer Science+Business Media, LLC, part of Springer Nature
Fission-fusion dynamics and group-size-dependent composition in heterogeneous populations
No full textMany animal groups are heterogeneous and may even consist of individuals of different species, called mixed-species flocks. Mathematical and computational models of collective animal movement behavior, however, typically assume that groups and populations consist of identical individuals. In this paper, using the mathematical framework of the coagulation-fragmentation process, we develop and analyze a model of merge and split group dynamics, also called fission-fusion dynamics, for heterogeneous populations that contain two types (or species) of individuals. We assume that more heterogeneous groups experience higher split rates than homogeneous groups, forming two daughter groups whose compositions are drawn uniformly from all possible partitions. We analytically derive a master equation for group size and compositions and find mean-field steady-state solutions. We predict that there is a critical group size below which groups are more likely to be homogeneous and contain the abundant type or species. Despite the propensity of heterogeneous groups to split at higher rates, we find that groups are more likely to be heterogeneous but only above the critical group size. Monte Carlo simulation of the model show excellent agreement with these analytical model results. Thus, our model makes a testable prediction that composition of flocks are group-size-dependent and do not merely reflect the population level heterogeneity. We discuss the implications of our results to empirical studies on flocking systems. © 2019 American Physical Society
Probabilistic Characterization of Rock Mass from Limited Laboratory Tests and Field Data: Associated Reliability Analysis and Its Interpretation
No full textProbabilistic methods are the most efficient methods to account for different types of uncertainties encountered in the estimated rock properties required for the stability analysis of rock slopes and tunnels. These methods require estimation of various parameters of probability distributions like mean, standard deviation (SD) and distributions types of rock properties, which requires large amount of data from laboratory and field investigations. However, in rock mechanics, the data available on rock properties for a project are often limited since the extents of projects are usually large and the test data are minimal due to cost constraints. Due to the unavailability of adequate test data, parameters (mean and SD) of probability distributions of rock properties themselves contain uncertainties. Since traditional reliability analysis uses these uncertain parameters (mean and SD) of probability distributions of rock properties, they may give incorrect estimation of the reliability of rock slope stability. This paper presents a method to overcome this limitation of traditional reliability analysis and outlines a new approach of rock mass characterization for the cases with limited data. This approach uses Sobol�s global sensitivity analysis and bootstrap method coupled with augmented radial basis function based response surface. This method is capable of handling the uncertainties in the parameters (mean and SD) of probability distributions of rock properties and can include their effect in the stability estimates of rock slopes. The proposed method is more practical and efficient, since it considers uncertainty in the statistical parameters of most commonly and easily available rock properties, i.e. uniaxial compressive strength and Geological Strength Index. Further, computational effort involved in the reliability analysis of rock slopes of large dimensions is comparatively smaller in this method. Present study also demonstrates this method through reliability analysis of a large rock slope of an open pit gold mine in Karnataka region of India. Results are compared with the results from traditional reliability analysis to highlight the advantages of the proposed method. It is observed that uncertainties in probability distribution type and its parameters (mean and SD) of rock properties have considerable effect on the estimated reliability index of the rock slope and hence traditional reliability methods based on the parameters of probability distributions estimated using limited data can make incorrect estimation of rock slope stability. Further, stability of the rock slope determined from proposed approach based on bootstrap method is represented by confidence interval of reliability index instead of a fixed value of reliability index as in traditional methods, providing more realistic estimates of rock slope stability. © 2019, Springer-Verlag GmbH Austria, part of Springer Nature
A SIR-independent role for cohesin in subtelomeric silencing and organization
No full textCohesin is a key determinant of chromosome architecture due to its DNA binding and tethering ability. Cohesin binds near centromeres and chromosome arms and also close to telomeres, but its role near telomeres remains elusive. In budding yeast, transcription within 20 kb of telomeres is repressed, in part by the histone-modifying silent information regulator (SIR) complex. However, extensive subtelomeric repressed domains lie outside the SIR-binding region, but the mechanism of silencing in these regions remains poorly understood. Here, we report a role for cohesin in subtelomeric silencing that extends even beyond the zone of SIR binding. Clusters of subtelomeric genes were preferentially derepressed in a cohesin mutant, whereas SIR binding was unaltered. Genetic interactions with known telomere silencing factors indicate that cohesin operates independent of the SIR-mediated pathway for telomeric silencing. Mutant cells exhibited Mpk1-dependent Sir3 hyperphosphorylation that contributes to subtelomeric derepression to a limited extent. Compaction of subtelomeric domains and tethering to the nuclear envelope were impaired in mutant cells. Our findings provide evidence for a unique SIR-independent mechanism of subtelomeric repression mediated by cohesin
Epithelial cell functionality on electroconductive Fe/Sr co-doped biphasic calcium phosphate
No full textIn the perspective of dental restorative applications, co-doped bioceramics have not been explored much. From the clinical perspective, a successful dental implant is expected to interact with peri-prosthetic bones, gingival tissue, and surrounding connective tissues. The interaction of implant and implant coating materials with bone tissue is well studied. However, their interaction with surrounding epithelial components needs scientific validation. In this context, the present study aims at quantitative evaluation of the electrical properties of Fe/Sr co-doped biphasic calcium phosphate (BCP) samples and assessment of their cytocompatibility with epithelial (vero) cells. Sr/Fe co-doped BCPs were prepared by sol-gel synthesis technique, with different dopant concentration. Impact of co-doping on conductivity was assessed and interestingly an increase in conductivity with dopant amount was recorded in different co-doped BCPs. Cellular study showed the significant (p = 0.01) increase in both cellular viability and functionality with increasing conductivity of samples. Higher epithelial cell adhesion indicates that (Sr/Fe) co-doped BCP would be favorable for faster epithelial sealing and also would reduce the chances of infection. Real-time PCR and immunofluorescence studies indicated that the expression of the epithelial marker (E-cadherin) significantly (p = 0.01) increased in 10, 30 and 40 mol% co-doped samples in comparison to undoped BCP. In contrast to E-cadherin, fold change of beta-catenin remains unchanged amongst the co-doped ceramics, implying the absence of tumorigenic potential of (Sr/Fe) co-doped BCP. In addition, immune-fluorescence signatures for cellular polarity are established from enhanced expression PARD3 protein, which has major relevance for cellular morphogenesis and cell division. Summarizing, the present study establishes the efficacy of Sr/Fe co-doped BCPs as a dental implant coating material and its ability to modulate vero cell functionality
The fast, luminous ultraviolet transient AT2018cow: extreme supernova, or disruption of a star by an intermediate-mass black hole?
No full textWide-field optical surveys have begun to uncover large samples of fast (t(rise) less than or similar to 5 d), luminous (M-peak < 18), blue transients. While commonly attributed to the breakout of a supernova shock into a dense wind, the great distances to the transients of this class found so far have hampered detailed investigation of their properties. We present photometry and spectroscopy from a comprehensive worldwide campaign to observe AT 2018cow (ATLAS 18qqn), the first fast-luminous optical transient to be found in real time at low redshift. Our first spectra (<2 days after discovery) are entirely featureless. A very broad absorption feature suggestive of near-relativistic velocities develops between 3 and 8 days, then disappears. Broad emission features of H and He develop after >10 days. The spectrum remains extremely hot throughout its evolution, and the photospheric radius contracts with time (receding below R < 10 (14) cm after 1 month). This behaviour does not match that of any known supernova, although a relativistic jet within a fallback supernova could explain some of the observed features. Alternatively, the transient could originate from the disruption of a star by an intermediate-mass black hole, although this would require long-lasting emission of highly super-Eddington thermal radiation. In either case, AT 2018cow suggests that the population of fast luminous transients represents a new class of astrophysical event. Intensive follow-up of this event in its late phases, and of any future events found at comparable distance, will be essential to better constrain their origins
Trinuclear and Hexanuclear Lanthanide(III) Complexes of the Chiral 3+3 Macrocycle: X-ray Crystal Structures and Magnetic Properties
No full textA new triphenolic hexaaza chiral macrocyclic amine L forms trinuclear complexes 1-3 with rare earth metal lanthanide(III) ions (Ln = Dy, Eu, and Y) with the general formula Ln(3)L(mu(3)-OH)(2)(NO3)(4)(H2O)(2)]center dot xCH(3)OH. The crystal structures of the nitrate derivatives of this type reveal the presence of a {Ln(3)(mu(3)-OH)(2)} core within the macrocycle. For the chloride derivative of dysprosium(III) 4, a duplex of the trinuclear compound is formed to give the hexanuclear Dy6L2(mu(3)-OH)(3)(mu-O)(2-Cl)(3)Cl-4(H2O)(2)] compound, in which two trinuclear macrocyclic units are linked by bridging chloride anions, supplemented by a hydrogen bond connecting the central oxo and hydroxo bridges as well as by weak interactions at the periphery of the macrocycle. The nuclear magnetic resonance spectra of these complexes reveal a dynamic behavior in solution related to exchange of axial ligands and hindered rotation of phenyl substituents. Magnetic studies of the nitrate (1-3) and chloride (4) dysprosium(III) complexes suggest the presence of weak ferromagnetic interactions between neighboring metal centers. The interaction is strongest for compound 1, and for the related duplex compound 4, it appears to be somewhat weaker. The ac susceptibility measurements for complexes 1 and 4 confirm their field-induced single-molecule magnet behavior with the following characteristics: Lie ff = 10.6 cm(-1) (15.2 K), ro = 2.05 X 10(-4) s under 2500 Oe dc fields for 1; Ue ff 7.9 cm-' (11.4 K), ao = 1.68 X 10(-4) s under a 3000 Oe dc field for 4
Cationic distribution, exchange interactions, and relaxation dynamics in Zn-diluted MnCo2O4 nanostructures
No full textWe report an experimental investigation of the electronic structure and magnetic properties of bulk and nanosized MnCo2O4 diluted with Zn. The cationic distribution for tetrahedral A-site dilution is (Co1-yA2+ZnyA2+)(A)Mn3+Co3+](B)O-4 +/-delta, whereas B-site dilution results in (Co2+)(A)Mn1-xB3+ZnxB2+Co3+](B)O4-delta. The strength of exchange interaction J(ij) between the magnetic ions in a bulk spinel lattice decreases by similar to 15% for A-site dilution relative to the undiluted compound; however, B-site dilution results in an enhancement in J(ij) by 17%. The frequency and temperature dependence of dynamic-susceptibility chi(ac)(f, T)] studies of nanostructured compounds reveals the existence of spin-glass like behavior below the freezing temperature T-F similar to 125.7 K (for x(B) = 0.2) and 154.3 K (y(A) = 0.1). Relaxation time tau follows the Power-Law variation with a dynamical critical exponent zv = 6.17 and microscopic spin relaxation time tau(o) = 4.4 x 10(-15) s for x(B) = 0.2 (for y(A) = 0.1, zv = 5.2 and tau(o) = 5.4 x 10(-13) s). The amplitude and peak position in chi(ac)(T) decreases with an increase in the DC bias field, which indicates that the spin-glass phase can survive in the presence of low fields forming a critical line with an exponent 2/3. This behavior is similar to the de Almeida-Thouless (AT-line) analysis in the T-H phase diagram which supports the existence of spin-glass like behavior below T-F in these Zn diluted spinels. Published under license by AIP Publishing