Open Problems Presented at SCG'98

A subset of the problems presented at the open-problem session of the 14th Annual ACM Symposium on Computational Geometry, held on June 7–10, 1998, is listed.     

Dynamics of algae blooming: effects of budget allocation and time delay

Algal blooms are increasing in coastal waters worldwide. The study on the features of algal pollution in water bodies and the ways to eliminate them is of vital importance. Preventing, treating, and monitoring algal blooms can be an unanticipated cost for a water system. To tame algal bloom in a lake, the government provides funds through budget allocation. In this paper, we propose a mathematical model to investigate the effect of budget allocation on the control of algal bloom in a lake. We assume that the growth of budget follows logistic law and also increases in proportion to the algal density in the lake. A part of the budget is utilized for the control of inflow of nutrients, while the remaining is used in the removal of algae from the lake. Our results show that algal bloom can be mitigated from the lake by reducing the inflow rate of nutrients to a very low value, which can be achieved for very high efficacy of budget allocation for the control of nutrients inflow from outside sources. Also, increasing the efficacy of budget allocation for the removal of algae helps to control the algal bloom. Further, more budget should be used on the control of nutrient’s inflow than on the removal of algae, as the presence of nutrients in high concentration will immediately proliferate the growth of algae. Moreover, the combined effects of controlling the inflow of nutrients and removing algae at high rates will result in nutrients and algae-free aquatic environment. Further, we modify the model by considering a discrete time delay involved in the increment of budget due to increased density of algae in the lake. We observe that chaotic oscillations may arise via equilibrium destabilization on increasing the values of time delay. We apply basic tools of nonlinear dynamics such as Poincaré section and maximum Lyapunov exponent to confirm the chaotic behavior of the system.

     

Hydrothermal Synthesis of g‐C3N4/NiFe2O4 Nanocomposite and Its Enhanced Photocatalytic Activity

Herein, for the first time, a direct Z‐scheme g‐C₃N₄/NiFe₂O₄ nanocomposite photocatalyst was prepared using facile one‐pot hydrothermal method and characterized using XRD, FT‐IR, DRS, PL, SEM, EDS, TEM, HRTEM, XPS, BET and VSM characterized techniques. The result reveals that the NiFe₂O₄ nanoparticles are loaded on the g‐C₃N₄ sheets successfully. The photocatalytic activities of the as‐prepared photocatalysts were evaluated for the degradation of methyl orange (MO) under visible light irradiation. It was shown that the photocatalytic activity of the g‐C₃N₄/NiFe₂O₄ nanocomposite is about 4.4 and 3 times higher than those of the pristine NiFe₂O₄ and g‐C₃N₄ respectively. The enhanced photocatalytic activity could be ascribed to the formation of g‐C₃N₄/NiFe₂O₄ direct Z‐scheme photocatalyst, which results in efficient space separation of photogenerated charge carriers. More importantly, the as‐prepared Z‐scheme photocatalyst can be recoverable easily from the solution by an external magnetic field and it shows almost the same activity for three consecutive cycles. Considering the simplicity of preparation method, this work will provide new insights into the design of high‐performance magnetic Z‐scheme photocatalysts for organic contaminate removal.     

Early Time Solvation Dynamics Probed by Spectrally Resolved Degenerate Pump-Probe Spectroscopy

The dynamic role of solvent in influencing the rates of physico-chemical processes (for example, polar solvation and electron transfer) has been extensively studied using time-resolved fluorescence spectroscopy. Here we study ultrafast excited state relaxation dynamics of three different fluorescent probes (DNTTCI, IR-140 and IR-144) in two polar solvents, ethanol and ethylene glycol, using spectrally resolved degenerate pump-probe spectroscopy. We discuss how time-resolved emission spectra can be directly used for constructing relaxation correlation function, obviating spectral reconstruction and estimation of time-zero spectrum in non-polar solvents. We show that depending on the specific probe used, the relaxation dynamics is governed either by intramolecular vibrational relaxation (for IR140) or by intermolecular solvation (for DNTTCI) or by both (for IR144). We further show (using DNTTCI as a probe) that major differences in solvation by ethanol and ethylene glycol is contributed by early time (<1 ps) dynamics.     

Compositional dependence of optical parameters in Se–Bi–Te–Ag thin films

Compositional dependence of optical parameters in thermally evaporated amorphous Se_80.5Bi_1.5Te_18 ? yAg_y (for y = 0, 1.0, 1.5 and 2.0 at.%) quaternary thin films has been studied using well established Swanepoel method. The optical properties like, refractive index (n), extinction coefficient (k), absorption coefficient (α) and optical band gap (E_g) have been determined from the transmission spectra in the spectral range from 500 to 2500 nm. The optical band gap (E_g) has been estimated by using Tauc's extrapolation method and is found to increase with an increase in the Ag concentration. Present study shows that the refractive index, extinction coefficient and optical band gap increase with the increasing Ag content which is in agreement with the earlier studies. While the increase in the refractive index with Ag content over the entire spectral range can be attributed to the increased polarizability of larger Ag atomic radius (153 pm) compared to the Te atomic radius (135 pm), the increase in the optical band gap with increasing Ag concentration is correlated to an increase in the cohesive energy and decrease in the electronegativity of the films under study. The dielectric constant and optical conductivity (σ) of the thin films under study are also found to increase with the Ag concentration.     

Asset portfolio optimization using support vector machines and real-coded genetic algorithm

This paper presents an integrated approach for portfolio selection in a multicriteria decision making framework. Firstly, we use Support Vector Machines for classifying financial assets in three pre-defined classes, based on their performance on some key financial criteria. Next, we employ Real-Coded Genetic Algorithm to solve a mathematical model of the multicriteria portfolio selection problem in the respective classes incorporating investor-preferences.     

Electron impact ionisation cross sections derived from total inelastic cross section for CF3X and CF2X2 (X = H,Cl, Br and I) molecules

We report here the total ionisation cross sections for CF₃X and CF₂X₂ (X = H, Cl, Br and I) molecules by electron impact from ionisation threshold to 5 keV. The total inelastic cross section is obtained employing a quantum mechanical approach called spherical complex optical potential formalism. Then, using a semi-empirical complex scattering potential-ionisation contribution method, the ionisation cross section is derived from the inelastic cross section. The results obtained are compared with previous measurements and theoretical values, wherever available and a satisfactorily agreement is observed. The ionisation cross section values for CF₂I₂ molecule are reported for the first time.     

On the phase-space analysis of photon mediated quantum state transfer in nanophotonic waveguidance

A cavity quantum electrodynamics (QED) based approach for transferring quantum state between quantum nodes has been proposed, wherein a rubidium (⁸⁷Rb) atom trapped inside a two-mode optical cavity forms the quantum node and photons serve as the information carrier between two such nodes. Information is encoded into polarized photon states generated through the application of a system of lasers. The focus is made on the phase-space analysis of the approach, wherein two subspaces of the hyperfine energy levels with magnetic sub-levels of rubidium (⁸⁷Rb) atom represent the logic states ‘0’ and ‘1’. The system of lasers initiates a cavity assisted Raman process which, in turn, generates a right- or left-circularly polarized photon depending on the logic state of the transmit node. Once the photon is received (at the receive node), the logic state of the transmit node is restored into the receive node through a cavity QED process.     

Design of peptide affinity ligands for S-protein: a comparison of combinatorial and de novo design strategies

Design of peptide affinity ligands against biological targets is important for a broad range of applications. Here, we report on de novo and combinatorial strategies for the design of high-affinity and high-specificity peptides against S-protein as a target. The peptide libraries employed in this study contain (1) consensus motif (CM) sequences identified from high-throughput phage combinatorial screening, (2) point mutations of CM sequences, and (3) de novo sequences rationally designed based on stereo-chemical information of the complex between S-protein and its natural ligand, S-peptide. In general, point mutations to CM allowed for modulating peptide affinity and specificity over a broad range. This is particularly useful in designing peptides with varying affinities and specificities for the target. De novo sequences, especially those based on the S-protein binding pocket, on average bound with higher affinities within a narrow range (10–100 nM) as compared to point mutations to CM (1 nM–2 $\mu $ M). As such, the approaches described here serve as a general guide for optimizing the design of peptide affinity ligands for a wide range of target proteins or applications.