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On the asymptotic risk of ridge regression with many predictors
No full textThis work is concerned with the properties of the ridge regression where the number of predictors p is proportional to the sample size n. Asymptotic properties of the means square error (MSE) of the estimated mean vector using ridge regression is investigated when the design matrix X may be non-random or random. Approximate asymptotic expression of the MSE is derived under fairly general conditions on the decay rate of the eigenvalues of XTX when the design matrix is nonrandom. The value of the optimal MSE provides conditions under which the ridge regression is a suitable method for estimating the mean vector. In the random design case, similar results are obtained when the eigenvalues of E[XTX] satisfy a similar decay condition as in the non-random case
Oncometabolites in pancreatic cancer: Strategies and its implications
No full textPancreatic cancer (PanCa) is a catastrophic disease, being third lethal in both the genders around the globe. The possible reasons are extreme disease invasiveness, highly fibrotic and desmoplastic stroma, dearth of confirmatory diagnostic approaches and resistance to chemotherapeutics. This inimitable tumor microenvironment (TME) or desmoplasia with excessive extracellular matrix accumulation, create an extremely hypovascular, hypoxic and nutrient-deficient zone inside the tumor. To survive, grow and proliferate in such tough TME, pancreatic tumor and stromal cells transform their metabolism. Transformed glucose, glu-tamine, fat, nucleotide metabolism and inter-metabolite communication between tumor and TME in synergism, impart therapy resistance, and immunosuppression in PanCa. Thus, a finer knowledge of altered metabolism would uncover its metabolic susceptibilities. These unique metabolic targets may help to device novel diagnostic/prognostic markers and therapeutic strategies for better management of PanCa. In this review, we sum up reshaped metabolic pathways in PanCa to formulate detection and remedial strategies of this devastating disease
Optimizing machine learning for water safety: A comparative analysis with dimensionality reduction and classifier performance in potability prediction
No full textIn this study, we investigated the effectiveness of machine learning techniques in predicting water potability based on water quality attributes. Initially, we applied seven classification-based methods directly to the original dataset, yielding varying accuracy scores. Notably, the Support Vector Machine (SVM) achieved the highest accuracy of 69%, while other methods such as XGBoost, k-Nearest Neighbors, Gaussian Naive Bayes, and Random Forest demonstrated competitive performance with scores ranging from 62% to 68%. Subsequently, we employed Principal Component Analysis (PCA) to reduce the dataset’s dimensionality to six principal components, followed by reapplication of the machine learning techniques. The results showed an increase in accuracy across all classifiers, increasing to nearly 100%. This study provides insights into the impact of dimensionality reduction on predictive accuracy and underscores the importance of selecting appropriate techniques for water potability prediction
PERTURBED BAYESIAN BEST RESPONSE DYNAMIC IN CONTINUUM GAMES
No full textThe notion of perturbed Bayesian best response dynamic for continuum strategy Bayesian population games is introduced. Fundamental properties of the dynamic such as existence of perturbed equilibrium, convergence of the perturbed equilibrium to the Bayesian equilibrium of the underlying game, as well as existence, uniqueness, and continuity of solutions from arbitrary initial conditions is established. As applications to the theory, convergence of solutions to the perturbed equilibria is shown to hold for two classes of games, namely, Bayesian potential games and Bayesian negative semidefinite games
Phase synchronization in cryptocurrency network and its features
No full textInvestigating the time-frequency-based phase synchronization between nonstationary time series of the cryptocurrencies\u27 prices can be a suitable tool to reveal their complicated interactions at different frequencies. In this work, the phase synchronization between 25 cryptocurrencies with the highest capitalization from December 1, 2021 to June 1, 2022 is calculated using the phase-locking value method based on wavelet transform. Then, utilizing the graph theory, the cryptocurrency networks are constructed, and their topological features like path length (PL), clustering coefficient (CC) and node strength are evaluated in various frequencies. This research indicates a strong phase synchronization between the investigated cryptocurrencies, especially in low frequencies. Also, the networks\u27 high average CC and short PL compared to their equivalent regular and random networks display the small-worldness of the networks. We observe from the obtained results that Bitcoin, Ethereum and Binance currencies, among the most popular cryptocurrencies, have the highest average node strengths at different frequencies. Also, TRON shows the lowest CC and node strength among all currencies, representing its limited phase interaction with other currencies
Post-inflationary leptogenesis and dark matter production: metric versus Palatini formalism
No full textWe investigate production of non-thermal dark matter particles and heavy sterile neutrinos from inflaton during the reheating era, which is preceded by a slow-roll inflationary epoch with a quartic potential and non-minimal coupling (ξ) between inflaton and gravity. We compare our analysis between metric and Palatini formalism. For the latter, the tensor-to-scalar ratio, r, decreases with ξ. We find that for ξ = 0.5 and number of e-folds ~ 60, r can be as small as ~ O (10−3) which may be validated at future reaches of upcoming CMB observation such as CMB-S4 etc. We identify the permissible range of Yukawa coupling yχ between inflaton and fermionic DM χ, to be O (10−3.5) ≳ yχ ≳ O (10−20) for metric formalism and O (10−4) ≳ yχ ≳ O (10−11) for Palatini formalism which is consistent with current PLANCK data and also within the reach of future CMB experiments. For the scenario of leptogenesis via the decay of sterile neutrinos produced from inflaton decay, we also investigate the parameter space involving heavy neutrino mass MN1 and Yukawa coupling yN1 of sterile neutrino with inflaton, which are consistent with current CMB data and successful generation of the observed baryon asymmetry of the universe via leptogenesis. In contrast to metric formalism, in the case of Palatini formalism, for successful leptogenesis to occur, we find that yN1 has a very narrow allowable range and is severely constrained from the consistency with CMB predictions
Quadrant analysis of turbulence over a degraded channel-bed of bimodal sediment, with a definition framework for averaging methods
No full textThis study focuses on the conditional turbulence characteristics in a flow through a degraded channel bed with a mixture of two sediment sizes. After achieving an equilibrium scour condition in a laboratory experiment, three components of instantaneous velocity were recorded for sufficient duration using a Vectrino velocimeter; vertical profiles were measured at three stream-wise locations along the flume axis. An in-depth analysis was performed of conditional statistics for stream-wise and vertical velocity components, Reynolds stresses, turbulent kinetic energy fluxes, along with the percentage occurrence, persistence and frequency of flow in any quadrant. Importantly, the experiment served as a platform for definition of different conditional means: two different approaches, namely total- and quadrant-averaging, were used and the results were systematically compared. The experimental results demonstrate the presence of a top layer where the properties of the flow do not differ much from those of the incoming flow, and of a mixing layer at around the original bed elevation. Sweeps and ejections are the dominant events close to the bed and for higher elevation, respectively. While the percentage occurrence of the sweeps and ejections is higher than that of other events, the frequency of all the events is similar, corresponding to that of the burst cycle. Turbulence is stronger at the locations with flow expansion than at that with flow contraction. Arguments are proposed on the relevance of the two conditional means for phenomenological interpretation of the interactions between a flow and surrounded bodies like sediment, plants and fish. The systematic analysis was performed without applying a hole, that is instead sometimes used in literature works. In this respect, the definition framework is extended to show that, when a hole is applied, four conditional means may be defined, whose variation with the hole size is not always straightforward. The definition framework may give impulse to considering these multiple averaging options in quadrant-based analyses of turbulent flows