We present the critical behavior of a model for a magnetic polymer under an external magnetic field on the three-dimensional Sierpińsky gasket. Our findings reveal that, at zero magnetic field, the polymer-collapse transition occurs first, followed by a magnetic transition as the temperature is lowered. The first is signaled by a nonzero polymer density with zero magnetization while the second by a spontaneous magnetization. In the presence of a magnetic field the polymer collapses into a magnetized state and there is only one transition. We have mapped the exact phase diagram, identifying the various phases and phase transitions. The model predicts the existence of a reentrance of paramagnetic collapse phase observed even in the absence of a magnetic field. In a limit where only even numbers of spins of each type on an elementary tetrahedron is permitted, we see a stabilization of a paramagnetic-collapsed polymer state against the addition of moderate ferromagnetic field.

We conducted atomistic Molecular Dynamics (MD) simulations of DNA-Hairpin molecules encapsulated within Single-Walled Carbon Nanotubes (SWCNTs) at a temperature of 300 K. Our investigation revealed that the structural integrity of the DNA-Hairpin can be maintained within SWCNTs, provided that the diameter of the SWCNT exceeds a critical threshold value. Conversely, when the SWCNT diameter falls below this critical threshold, the DNA-Hairpin undergoes denaturation, even at a temperature of 300 K. The DNA-Hairpin model we employed consisted of a 12-base pair stem and a 3-base loop, and we studied various SWCNTs with different diameters. Our analyses identified a critical SWCNT diameter of 3.39 nm at 300 K. Examination of key structural features, such as hydrogen bonds (H-bonds), van der Waals (vdW) interactions, and other inter-base interactions, demonstrated a significant reduction in the number of H-bonds, vdW energy, and electrostatic energies among the DNA hairpin's constituent bases when confined within narrower SWCNTs (with diameters of 2.84 nm and 3.25 nm). However, it was observed that the increased interaction energy between the DNA-Hairpin and the inner surface of narrower SWCNTs promoted the denaturation of the DNA-Hairpin. In-depth analysis of electrostatic mapping and hydration status further revealed that the DNA-Hairpin experienced inadequate hydration and non-uniform distribution of counter ions within SWCNTs having diameters below the critical value of 3.39 nm. Our inference is that the inappropriate hydration of counter ions, along with their non-uniform spatial distribution around the DNA hairpin, contributes to the denaturation of the molecule within SWCNTs of smaller diameters. For DNA-Hairpin molecules that remained undenatured within SWCNTs, we investigated their mechanical properties, particularly the elastic properties. Our findings demonstrated an increase in the persistence length of the DNA-Hairpin with increasing SWCNT diameter. Additionally, the stretch modulus and torsional stiffness of the DNA-Hairpin were observed to increase as a function of SWCNT diameter, indicating that confinement within SWCNTs enhances the mechanical flexibility of the DNA-Hairpin.

An estimate of the location of a distribution is the most fundamental type of inference about a population. Consequently, obtaining more accurate estimators of the population mean of interest is essential in every statistical estimating technique. Survey statisticians most often use priori information at an estimation stage to form an estimator for estimating parameters. In this study, we suggested an estimator for the population mean in the presence of non-response utilizing information from the past surveys along with information available from the current surveys in the form of a hybrid exponentially weighted moving average. We obtained the expressions of the suggested estimator's mean and variance and established the mathematical conditions to demonstrate the efficiency of the suggested estimator. We supported the theoretical outcomes with the help of a simulation study and a real-life example. The results show that the utilization of information from past surveys along with the current surveys improves the efficiency of the suggested estimator. For example: in the simulation study, for a sample size n (= 50,100) at the non-response rate W-2 (= 0.20, 0.15) and weights alpha(1) (0.10)and alpha(2) (0.15) to the current and past observations, variances of the suggested estimator were (0.000683, 0.000559;0.000635, 0.000309), which were less than (0.020944, 0.009756; 0.020024, 0.008920) of the existing Hansen and Hurwitz (1946) estimator. Similarly, in the empirical study of the real-life dataset, for the sample number delta(= 6) having size n (=12) at W-2 (=0.30,0.2 5 ) , alpha(1) ( = 0.1 0 )and alpha(2) (= 0.15), variances of the suggested estimator were (0.74, 0.71), which were significantly less than (95.12, 90.65) of the existing Hansen and Hurwitz (1946) estimator. The suggested work is limited to the homogeneous population only.

The nonequilibrium behavior of many bio-materials under classical jump experiments, in which the system is subject to an instantaneous increase of controlled intensive variables, is poorly studied. Here, we study the response to such jumps of a short DNA hairpin, that possesses a bubble-generating block, in which we assume an initially equilibrated DNA. In particular, we impose temperature-jump (T-jump) and force-jump (F-jump) at various strengths and follow the DNA denaturation in time. We show how partial opening states, which can be also detected in equilibrium at various temperatures and forces, are transiently populated during the equilibration process. In combined large T- and F-jumps, we demonstrate an overshoot in the opening process, in which the middle bubble re-closes transiently after its initial opening, before opening up again permanently. Such an oscillatory behavior has been previously observed in soft-matter systems, but not in DNA, and can have consequences on the intracellular opening processes of DNA.

We study the influence of confinement on the dynamics of translocation of a linear polymer chain in a good solvent through a cone-shaped pore. Using the Langevin dynamics simulations, we calculate both the first attempt time and translocation time as a function of the position of the back wall and apex angle alpha. As the in vivo confining environment is inherently dynamic, we extended the present study to explore the consequences of a periodically driven back wall and apex angles on the translocation dynamics. Our findings reveal that the translocation time initially decreases as the driving frequency increases, but increases after a certain frequency. The frequency at which the translocation time is found to be minimum is referred to as the resonance activation. Analyzing the distribution of translocation times around this frequency renders interesting information about the translocation process. We further explore the translocation dynamics by calculating the residence time of individual monomers, shedding light on the microscopic aspects of the process. We study the influence of periodically driven confinement on the dynamics of translocation of a linear polymer chain in a good solvent through a cone-shaped pore.

Using auxiliary information at an estimation stage has an important role in forming estimators with better precision. This precision can further be increased using prior information available in any other forms. In this paper, we utilized a hybrid exponentially weighted moving average statistic to form new generalized ratio-and product-type estimators for a population mean in simple random sampling without replacement. This statistics utilizes information from current surveys and past surveys in the form of a hybrid exponentially weighted moving average. We derived expressions of mean square errors and biases for the suggested estimators. Further, we obtained mathematical conditions under which the suggested estimators will perform better than the existing estimators. We supported our results through a simulation and an empirical study.

In the field of data science, the performance of a least square estimator is highly affected if the variable under study departs from normality or has the presence of outliers. This study proposes robust HEWMA-type estimators for the population mean by considering some auxiliary information under a non-normality assumption for a time-based survey. The proposed estimators are found to have the minimum mean square errors and biases compared to other relevant estimators for the long-tailed symmetric family. We have investigated the robustness properties of the proposed estimator in presence of the outliers. Finally, the authors provide a simulation study and a real-life application to support the theoretical outcomes of the proposed estimators over the relevant estimators.

In sample surveys, when information on two auxiliary characters is available, several authors prefer chain-typeestimators to improve the performance of estimators of the population mean. These authors have assumed that the information(population mean, total, etc.) on the first auxiliary or auxiliary character is not available but on the second or additionalauxiliary character. However, there are instances where the latter and former may also be unavailable. In such cases, we havesuggested a novel modified regression-type estimator that uses the data from the auxiliary character and the auxiliaryattribute in double sampling to estimate the population mean. We have derived the expressions for bias and mean square errorof the suggested estimator using the large sample approximation. After mathematical comparisons, we have obtainedmathematical conditions under which the suggested estimator has lower mean square error than the existing estimators.Further, we supported these theoretical comparisons using a numerical analysis with a real-life dataset

We investigate the influence of varying confinement on the dynamics of polymer translocation through a cone-shaped channel. For this, a linear polymer chain is modeled using self-avoiding walks on a square lattice. The cis side of a cone-shaped channel has a finite volume, while the trans side has a semi-infinite space. The confining environment is varied either by changing the position of the back wall while keeping the apex angle fixed or altering the apex angle while keeping the position of the back wall fixed. In both cases, the effective space ϕ, which represents the number of monomers in a chain relative to the total number of accessible sites within the cone, is reduced due to the imposed confinement. Consequently, the translocation dynamics are affected. We analyze the entropy of the confined system as a function of ϕ, which exhibits nonmonotonic behavior. We also calculate the free energy associated with the confinement as a function of a virtual coordinate for different positions of the back wall (base of the cone) along the conical axis for various apex angles. Employing the Fokker-Planck equation, we calculate the translocation time as a function of ϕ for different solvent conditions across the channel. Our findings indicate that the translocation time decreases as ϕ increases, but it eventually reaches a saturation point at a certain value of ϕ. Moreover, we highlight the possibility of controlling the translocation dynamics by manipulating the solvent quality across the channel. Furthermore, our investigation delves into the intricacies of polymer translocation through a cone-shaped channel, considering both repulsive and neutral interactions with the channel wall. This exploration unveils nuanced dynamics and sheds light on the factors that significantly impact translocation within confined channels.

We present the (numerically) exact phase diagram of a magnetic polymer on the Sierpińsky gasket embedded in three dimensions using the renormalization group method. We report distinct phases of the magnetic polymer, including paramagnetic swollen, ferromagnetic swollen, paramagnetic collapsed, and ferromagnetic collapsed states. By evaluating critical exponents associated with phase transitions, we located the phase boundaries between different phases. If the model is extended to include a four-site interaction which disfavors configurations with a single spin of a given type, we find a rich variety of critical behaviors. Notably, we uncovered a phenomenon of reentrance, where the system transitions from a collapsed (paramagnetic) state to a swollen (paramagnetic) state followed by another collapse (paramagnetic) and ultimately reaching a ferromagnetic collapsed state. These findings shed new light on the complex behavior of (lattice) magnetic polymers.

It is of great interest for researchers to assess the COVID-19 pandemic in Europe. Grouping of COVID-19-affected regions is an effective way to monitor and optimize planning to combat the disease. This paper applied hierarchical clustering based on principal components analysis (HCPCA) to COVID-19 data from affected European countries. Considering several attribute indices, we obtained a new set of indicators using principal components analysis to aggregate and reduce the dimension of attribute indices of affected countries. Further, we obtained groups of affected countries subject to their similarity using hierarchical clustering to the reduced observations of new attributes indices of these countries. This study aims to group European countries with similar epidemic severity using some presumed attribute indices. The study is limited up to 24 May 2020, to assess if the outputs of the study could help governments, administrators, World Health Organization (WHO), healthcare service professionals, and other decision-makers to optimize their policies and plan their regulations in the country level requirements so that transmission of infections, deaths, critical conditions of patients could be minimized. For this purpose, we used hierarchical clustering using principal components analysis to obtain better clusters of countries with similar epidemic severity.

Using Langevin dynamic simulations, a simple coarse-grained model of a DNA protein construct is used to study the DNA rupture and the protein unfolding. We identify three distinct states: (i) zipped DNA and collapsed protein, (ii) unzipped DNA and stretched protein, and (iii) unzipped DNA and collapsed protein. Here, we find a phase diagram that shows these states depending on the size of the DNA handle and the protein. For a less stable protein, unfolding is solely governed by the size of the linker DNA, whereas if the protein's stability increases, complete unfolding becomes impossible because the rupture force for DNA has reached a saturation regime influenced by the de Gennes length. We show that unfolding occurs via a few intermediate states by monitoring the force-extension curve of the entire protein. We extend our study to a heterogeneous protein system, where similar intermediate states in two systems can lead to different protein unfolding paths.

Background: For skewed datasets, the mode is utilized as a more appropriate measure of location. We formed chain ratio and product estimators for the population mode using two types of auxiliary information under the two-phase sampling scheme. Methods: Expressions for biases and mean square errors for the formed estimators up to the first order of approximation are obtained. The confidence intervals of the estimators are obtained and the aspects related to fixed cost and fixed variance are also studied. A simulation study is performed to support the theoretical outcomes. A real dataset is also provided which was collected from the department of agriculture, United States. Results: The simulation results for the fixed first-phase sample size and the second-phase sample size show that the mean square error is 0.035, the bias is 0.012, the confidence interval is 2.67-3.15, and the cost of the survey under the fixed variance is ₹ 194.67 of the proposed estimator , which is lower than 0.039, 0.055, 2.70-3.20, and ₹ 247.37 of the ratio estimator and 0.078, 0.041, 2.57-3.31, and ₹ 268.73 of the naive estimator . Conclusions: The simulation results show that the proposed estimator performs better than the ratio estimator and the naive estimator .

In this paper, we consider the situation where the underlying distribution of the study variable is not normally distributed. Under such situations, we propose ratio and product based estimators for the finite population mean in simple random sampling using known auxiliary information based on order statistics. We obtain the expressions for biases and mean square errors (MSEs) of the proposed estimators, which show that the proposed estimators have less MSEs and biases than other existing estimators. Simulations have been studied under various super-population models. A real life application is also provided. Robustness properties of the proposed estimators have been studied via simulations. Confidence intervals (CIs) show that the proposed estimators have shorter CIs of estimates than those of the existing estimators.

Using the exact enumeration technique, we have studied the force-induced melting of a DNA hairpin on the face centered cubic lattice for two different sequences which differ in terms of loop closing base pairs. The melting profiles obtained from the exact enumeration technique is consistent with the Gaussian network model and Langevin dynamics simulations. Probability distribution analysis based on the exact density of states revealed the microscopic details of the opening of the hairpin. We showed the existence of intermediate states near the melting temperature. We further showed that different ensembles used to model single-molecule force spectroscopy setups may give different force-temperature diagrams. We delineate the possible reasons for the observed discrepancies.

Use of a priori information is very common at an estimation stage to form an estimator of a population parameter. Estimation problems can lead to more accurate and efficient estimates using prior information. In this study, we utilized the information from the past surveys along with the information available from the current surveys in the form of a hybrid exponentially weighted moving average to suggest the estimator of the population mean using a known coefficient of variation of the study variable for time-based surveys. We derived the expression of the mean square error of the suggested estimator and established the mathematical conditions to prove the efficiency of the suggested estimator. The results showed that the utilization of information from past surveys and current surveys excels the estimator's efficiency. A simulation study and a real-life example are provided to support using the suggested estimator.

The self avoiding walk (SAW) model of the polymer has been extended to study the equilibrium properties of double stranded DNA (dsDNA) where two strands of the dsDNA are modeled by two mutually attracting self-avoiding walks (MASAWs) in the presence of an attractive surface. We study simultaneous adsorption and force induced melting transitions and explore different phases of DNA. It is observed that melting is entropically dominated, which can be substantially reduced under the application of an applied force. We consider three scenarios, where the surface is weakly, moderately and highly attractive. For both weakly and moderately attractive surfaces, the DNA desorbs from the surface in a zipped form and acquires the conformation of a melted state with the rise in temperature. However, for a strongly attractive surface, the force applied at one end of the strand (strand-II) results in unzipping, while the other strand (strand-I) remains adsorbed on the surface. We identify this as adsorption-induced unzipping, where the force applied on a single strand (strand-II) can unzip the dsDNA if the surface interaction energy exceeds a specific threshold. We also note that at a moderate surface attraction, the desorbed-zipped DNA melts with an increase in temperature and the free strand (strand-I) gets re-adsorbed onto the surface.

This article introduces a technique of improving the link performance of the underwater wireless optical communication (UWOC) system in terms of signal-to-noise ratio (SNR) by incorporating a novel ratiometric signal processing (RSP) scheme at the receiver node. In addition, the temporal fluctuations in the attenuation coefficient information (ACI) of the UWOC channel in the nonuniform turbulent regime are analyzed, and the corresponding distribution function is analytically derived. The consistency of the obtained statistical distribution of the ACI parameter is analyzed by simulating the experimental data in a UWOC prototype link within a laboratory-controlled turbulent regime. The experimental outcomes indicate a relative improvement in the SNR by 1.70 to 3.23 dB in the nonuniform turbulent conditions upon incorporating the proposed RSP technique at the receiver node. It is also observed that the mean square error and an average difference of the received images that are processed by incorporating the RSP technique are lower as compared to that of the images without processing at the receiver node in the UWOC prototype link. The approach of implementing the proposed RSP technique is observed to improve the performance of the UWOC link.

Statisticians often use auxiliary information at an estimation stage to increase efficiencies of estimators. In this article, we suggest modified ratio- and product-type estimators utilizing the known value of the coefficient of variation of the auxiliary variable for a time-based survey. Further, to excel the performance of the suggested estimators, we utilize information from the past surveys along with the current surveys through hybrid exponentially weighted average. We obtain expressions for biases and mean square errors of the suggested estimators. The conditions, under which the suggested estimators have less mean square errors than that of other existing estimators, are also obtained. The results obtained through an empirical analysis examine the use of information from past surveys along with current surveys and show that the mean square errors and biases of the suggested estimators are less than that of the existing estimators. For example: for a sample size 5, mean square error and bias of the suggested ratio-type estimator are (0.0414,0.0065) which are less than (0.5581,0.0944) of the existing Cochran (1940) estimator, (0.4788,0.0758), of Sisodia and Dwivedi (1981) estimator and (0.0482,0.0082) of Muhammad Noor-ul-Amin (2020) estimator. Similarly, mean square error and bias of the suggested product- type estimator are (0.0025,−0.0006) which are less than (0.0612,−0.0096) of the existing Murthy (1964) estimator, (0.0286,−0.0071), of Pandey and Dubey (1988) estimator and (0.0053,−0.0008) of Muhammad Noor-ul-Amin (2020) estimator.