Randomness in completeness and space-bounded computations

The study of computational complexity investigates the role of various computational resources such as processing time, memory requirements, nondeterminism, randomness, nonuniformity, etc. to solve different types of computational problems. In this dissertation, we study the role of randomness in two fundamental areas of computational complexity: NP-completeness and space-bounded computations. The concept of completeness plays an important role in defining the notion of \u27hard\u27 problems in Computer Science. Intuitively, an NP-complete problem captures the difficulty of solving any problem in NP. Polynomial-time reductions are at the heart of defining completeness. However, there is no single notion of reduction; researchers identified various polynomial-time reductions such as many-one reduction, truth-table reduction, Turing reduction, etc. Each such notion of reduction induces a notion of completeness. Finding the relationships among various NP-completeness notions is a significant open problem. Our first result is about the separation of two such polynomial-time completeness notions for NP, namely, Turing completeness and many-one completeness. This is the first result that separates completeness notions for NP under a worst-case hardness hypothesis. Our next result involves a conjecture by Even, Selman, and Yacobi [ESY84,SY82] which states that there do not exist disjoint NP-pairs all of whose separators are NP-hard via Turing reductions. If true, this conjecture implies that a certain kind of probabilistic public-key cryptosystems is not secure. The conjecture is open for 30 years. We provide evidence in support of a variant of this conjecture. We show that if there exist certain secure one-way functions, then the ESY conjecture for the bounded-truth-table reduction holds. Now we turn our attention to space-bounded computations. We investigate probabilistic space-bounded machines that are allowed to access their random bits {\em multiple times}. Our main conceptual contribution here is to establish an interesting connection between derandomization of such probabilistic space-bounded machines and the derandomization of probabilistic time-bounded machines. In particular, we show that if we can derandomize a multipass machine even with a small number of passes over random tape and only O(log^2 n) random bits to deterministic polynomial-time, then BPTIME(n) ⊆ DTIME(2^{o(n)}). Note that if we restrict the number of random bits to O(log n), then we can trivially derandomize the machine to polynomial time. Furthermore, it can be shown that if we restrict the number of passes to O(1), we can still derandomize the machine to polynomial time. Thus our result implies that any extension beyond these trivialities will lead to an unknown derandomization of BPTIME(n). Our final contribution is about the derandomization of probabilistic time-bounded machines under branching program lower bounds. The standard method of derandomizing time-bounded probabilistic machines depends on various circuit lower bounds, which are notoriously hard to prove. We show that the derandomization of low-degree polynomial identity testing, a well-known problem in co-RP, can be obtained under certain branching program lower bounds. Note that branching programs are considered weaker model of computation than the Boolean circuits

Separating Cook Completeness from Karp-Levin Completeness Under a Worst-Case Hardness Hypothesis

We show that there is a language that is Turing complete for NP but not many-one complete for NP, under a worst-case hardness hypothesis. Our hypothesis asserts the existence of a non-deterministic, double-exponential time machine that runs in time O(2^2^n^c) (for some c > 1) accepting Sigma^* whose accepting computations cannot be computed by bounded-error, probabilistic machines running in time O(2^2^{beta * 2^n^c) (for some beta > 0). This is the first result that separates completeness notions for NP under a worst-case hardness hypothesis

Measuring Technical Efficiency and Returns to Scale in Indian Agriculture Using Panel Data: A Case Study of West Bengal

The study investigates farm level technical efficiency (TE) and its determinants in the state of West Bengal in India. A stochastic production frontier model has been applied for determining technical efficiency by using panel data on 17 agricultural production units over a period of 23 years. Maximum-likelihood estimates of the Cobb-Douglas stochastic frontier production function in a time-variant truncated normal distribution is appropriate for the measurement of technical efficiency of West Bengal agriculture in India. The estimated variance ratio indicates that 48.90 percent of the differences between the observed and the estimated output is caused by differences in farms’ technical inefficiencies. However, the remaining variation is due to factors beyond farmers’ control. The study shows that the agricultural farms in West Bengal exhibit increasing returns to scale in production. The study finds that farmers’ education and agricultural extension are important determinants of technical efficiency. Other prominent determinants that have a significant contribution are farm size, crop diversification, number of available agricultural markets, the proportion of small landholders and input intensity. All these determinants, excluding the proportion of small landholders, have a largely positive impact on technical efficiency. The maximum-likelihood estimation (MLE) and principal component analysis (PCA) are applied to determine the effects of determinants on TE. Both methods give similar results

The Impact of Price and Non-Price Factors on Area Allocated to Oilseeds in India: An Application of ARDL Model

The study attempts to investigate the dynamic relationship between acreage allocation of oilseeds and price (own price and prices of competitive crops) and also search for the link between area allocation and other non-price factors including productivity, irrigation, rainfall, technology and a policy-making variable (economic liberalization). The dynamic panel data for the year 1976-77 to 2017-18 have been used in the analysis. The study has used the autoregressive distributive lag (ARDL) model to understand the relationship between the dependent and the independent variables and to investigate the long-run equilibrium relationship between them. To estimate the model, both PMG (Pooled Mean Group) and MG (Mean group) estimation methods have been used. The Hausman test has been conducted to see the difference between the PMG and the MG results. The outcomes show that PMG serves as an efficient estimator here. The error correction terms are negative and significant. The results show strong evidence of area allocation towards oilseed crops, indicate a strong co-integration among their determinants in the long run. The ARDL results indicate that the speed of adjustment towards long-run equilibrium varies from 14.8 to 40.6 percent

EFFECTIVENESS OF SOLAR THERMOELECTRIC COOLER FOR FISH PRESERVATION: EXPERIMENTAL STUDY ON QUALITY CHARACTERISTICS OF Pangasius bocourti FISH FILLETS DURING STORAGE

Preservation of fish products is a big issue where inconsistent electricity supply. In the current study, a solar thermoelectric cooler (STC) was fabricated by exploiting the solar energy and its cooling potential for fish preservation was evaluated. The STC consists of a photovoltaic (PV) panel, battery, PV charge controller, thermoelectric cooling system, and cooler box. The temperature of the STC decreased to 7.4ºC within 90 minutes and then reached 5±0.2ºC in 150 min. The cooling capacity and coefficient of performance of the STC were 23.8 W and 0.44, respectively, at an input electric current of 3.5 A. The Pangasius bocourti fish fillets were stored in the STC for 10 days and tested its quality at 2 days intervals. On day 10, thiobarbituric acid, peroxide, pH, water binding ability, total plate count values were 1.65mg MDA/kg, 5.04 mEqO2/kg, 7.16, 26.18%, and 4.26 log CFU/g, respectively. A significant reduction in hardness, springiness, and chewiness values was observed, whereas no cohesiveness changes. The color values L* and a* decreased significantly, whereas b* and ΔE increased. The sensory attributes were found in the range of 5.2-6.0 on the 10th day. As the quality parameters showing an acceptable level, STC could be an alternate green option for fish preservation

Synthesis of Reconfigurable Multiple Shaped Beams of a Concentric Circular Ring Array Antenna Using Evolutionary Algorithms, Journal of Telecommunications and Information Technology, 2023, nr 1

The approach described in this paper uses evolutionary algorithms to create multiple-beam patterns for a concentric circular ring array (CCRA) of isotropic antennas using a common set of array excitation amplitudes. The flat top, cosec2, and pencil beam patterns are examples of multiple-beam patterns. All of these designs have an upward angle of θ = 0◦. All the patterns are further created in three azimuth planes (φ = 0◦, 5◦, and 10◦). To create the necessary patterns, non-uniform excitations are used in combination with evenly spaced isotropic components. For the flat top and cosecant-squared patterns, the best combination of common components, amplitude and various phases is applied, whereas the pencil beam pattern is produced using the common amplitude only. Differential evolutionary algorithm (DE), genetic algorithm (GA), and firefly algorithm (FA) are used to generate the best 4-bit discrete magnitudes and 5-bit discrete phases. These discrete excitations aid in lowering the feed network design complexity and the dynamic range ratio (DRR). A variety of randomly selected azimuth planes are used to verify the excitations as well. With small modifications in the desired parameters, the patterns are formed using the same excitation. The results proved both the efficacy of the suggested strategy and the dominance of DE over GA as well as FA

Immobilization of Ruthenium Benzylidene on Thermoresponsive Polymer : Methodology and Application

Attachment of metal complex on polymer has direct implication for the development of novel catalyst with recyclability, reusability and water solubility in the context environmental concern. In this paper, we illustrate a simple strategy to immobilize ruthenium benzylidene organometallic complex on thermoresponsive polymer. For this, pyridine-substituted poly (N-isopropylacrylamide) has been synthesized by atom transfer radical polymerization from a suitable initiator. Then, ruthenium benzylidene has been conjugated by binding with pyridine part of the polymer. Polymer conjugated ruthenium benzylidene is shown to have thermoresponsive characteristic in water (soluble below lower critical solution temperature (LCST) but precipitates out above LCST in water). Hence it can act as smart catalyst for metathesis reaction in water. For instance, it can be used as homogeneous metathesis catalyst for allyl alcohol in aqueous medium below lower critical solution temperature (LCST), that can be recovered as heterogeneous catalyst above LCST and recycled again as homogeneous catalyst. This is the first example of water-soluble recyclable metathesis catalyst. It is further demonstrated that steric crowding in the ligand play an important role in the superior performance of the catalyst

Nanoscale Functionalization of Surfaces by Graft-Through Sonogashira Polymerization

Graft through Sonogashira polymerization was used to functionalize various surfaces with conjugate polymers in a dimension of less than 100 nm. Atomic force microscopy measurement revealed a dense surface coverage with several closely packed islands. UV-vis spectroscopy and cyclic voltametry measurements suggested a moderate band gap, which is important for various applications in material science. A device was fabricated using polymer functionalized ITO and deposited aluminium as cathode to determine the current-voltage (I-V) characteristics and charge carrier mobility. Space charge limited current method indicated moderate charge carrier mobility while I-V characteristic data indicated its behaviour as semiconducting material

Green synthesized silver nanoparticles destroy multidrug resistant bacteria via reactive oxygen species mediated membrane damage

AbstractThe growing need of antimicrobial agent for novel therapies against multi-drug resistant bacteria has drawn researchers to green nanotechnology. Especially, eco-friendly biosynthesis of silver nanoparticles (Ag NPs) has shown its interesting impact against bacterial infection in laboratory research. In this study, a simple method was developed to form Ag NPs at room temperature, bio-reduction of silver ions from silver nitrate salt by leaf extract from Ocimum gratissimum. The Ag NPs appear to be capped with plant proteins, but are otherwise highly crystalline and pure. The Ag NPs have a zeta potential of −15mV, a hydrodynamic diameter of 31nm with polydispersity index of 0.65, and dry sizes of 18±3nm and 16±2nm, based on scanning and transmission electron microscopy respectively. The minimum inhibitory concentration (MIC) of the Ag NPs against a multi-drug resistant Escherichia coli was 4μg/mL and the minimum bactericidal concentration (MBC) was 8μg/mL, while the MIC and MBC against a resistant strain of Staphylococcus aureus were slightly higher at 8μg/mL and 16μg/mL respectively. Further, the Ag NPs inhibited biofilm formation by both Escherichia coli and S. aureus at concentrations similar to the MIC for each strain. Treatment of E. coli and S. aureus with Ag NPs resulted in damage to the surface of the cells and the production of reactive oxygen species. Both mechanisms likely contribute to bacterial cell death. In summary, this new method appears promising for green biosynthesis of pure Ag NPs with potent antimicrobial activity