To develop decision rules regarding acceptance or rejection of production lots based on sample data is the purpose of acceptance sampling inspection plan. Dependent sampling procedures cumulate results from several preceding production lots when testing is expensive or destructive. This chaining of past lots reduce the sizes of the required samples, essential for acceptance or rejection of production lots. In this article, a new approach for chaining the past lot(s) results proposed, named as modified chain group acceptance sampling inspection plan, requires a smaller sample size than the commonly used sampling inspection plan, such as group acceptance sampling inspection plan and single acceptance sampling inspection plan. A comparison study has been done between the proposed and group acceptance sampling inspection plan as well as single acceptance sampling inspection plan. A example has been given to illustrate the proposed plan in a good manner.

The recent developments in the study of topological multi-boundary entanglement in the context of 3d Chern-Simons theory (with gauge group $G$ and level $k$) suggest a strong interplay between entanglement measures and number theory. The purpose of this note is twofold. First, we conjecture that the 'sum of the negative powers of the quantum dimensions of all integrable highest weight representations at level $k$' is an integer multiple of the Witten zeta function of $G$ when $k \to \infty$. This provides an alternative way to compute these zeta functions, and we present some examples. Next, we use this conjecture to investigate number-theoretic properties of the Rényi entropies of the quantum state associated with the $S^3$ complement of torus links of type $T_{p,p}$. In particular, we show that in the semiclassical limit of $k \to \infty$, these entropies converge to a finite value. This finite value can be written in terms of the Witten zeta functions of the group $G$ evaluated at positive even integers.

The World Wide Web is the most wide known information source that is easily available and searchable. It consists of billions of interconnected documents Web pages are authored by millions of people. Accesses made by various users to pages are recorded inside web logs. These log files exist in various formats. Because of increase in usage of web, size of web log files is increasing at a much faster rate. Web mining is application of data mining technique to these log files. It can be of three types Web usage mining, Web structure mining and Web content mining. Web Usage mining is mining of usage patterns of users which can then be used to personalize web sites and create attractive web sites. It consists of three main phases: Preprocessing, Pattern discovery and Pattern analysis. In this paper we focus on Data cleaning and IP Address identification stages of preprocessing. Methodology has been proposed for both the stages. At the end conclusion is made about number of users left after IP address identification.

We obtain a quiver representation for a family of knots called double twist knots $K(p,-m)$. Particularly, we exploit the reverse engineering of Melvin-Morton-Rozansky(MMR) formalism to deduce the pattern of the charge matrix for these quivers.

The non-Hermitian systems exhibit extreme sensitivity to the boundary conditions. The change in the eigenspectrum with tunning boundary parameter is intimately connected to the non-Hermitian skin effect. The single-particle systems are affected by the boundary perturbations; however the interplay of a random disorder potential and non-reciprocal hopping under boundary perturbations of an interacting many-body system is not yet clear. In this work, we examine the boundary sensitivity of a non-Hermitian interacting fermionic system in the presence of a random disorder potential. A non-zero boundary parameter results in real-complex spectral transitions with non-reciprocal (or unidirectional) hopping at weak disorder. While the many-body localization at strong disorder washes away real-complex transitions leading to dynamical stability and real eigenvalue spectrum. We show that the boundary-driven real-complex spectral transitions of the non-Hermitian chain are accompanied by the corresponding changes in the level statistics and nearest level-spacing distributions. The intriguing features of non-reciprocity and boundary sensitivity are further revealed using the averaged inverse participation ratios. Finally, we find distinct behaviour in the quench dynamics of local particle density, population imbalance, and entanglement entropy of charge-density-wave ordered state that corroborate the real-complex and localization transitions. Our results provide a route to understanding disordered many-body systems under a generalized boundary.

The commuting graph ${\Gamma(G)}$ of a group $G$ is the simple undirected graph with group elements as a vertex set and two elements $x$ and $y$ are adjacent if and only if $xy=yx$ in $G$. By eliminating the identity element of $G$ and all the dominant vertices of $\Gamma(G)$, the resulting subgraphs of $\Gamma(G)$ are $\Gamma^*(G)$ and $\Gamma^{**}(G)$, respectively. In this paper, we classify all the finite groups $G$ such that the graph $\Delta(G) \in \{\Gamma(G), \Gamma^*(G), \Gamma^{**}(G)\}$ is the line graph of some graph. We also classify all the finite groups $G$ whose graph $\Delta(G) \in \{\Gamma(G), \Gamma^*(G), \Gamma^{**}(G)\}$ is the complement of line graph.

The ultracold atoms are an ideal platform to implement atomtronics and Josephson junctions analogous to superconducting circuits. The collective modes of a Bose gas split by a potential barrier have been known. However, the role of barriers on the collective excitation spectra of ultracold atomic mixtures has not been examined. Here, we examine the low-lying collective modes of (an)harmonically trapped quasi-one-dimensional Bose-Einstein condensates in a Josephson barrier by employing the variational approach and Bogoliubov theory. We first show that the anharmonicity of the external potential leads to an increase in the critical barrier strength of mode softening in a single-species condensate. The Josephson barrier drives the softening of in-phase and out-of-phase dipole modes of two-species Bose-Einstein condensates, and consequently leads to two additional zero-energy Goldstone modes in the miscible phase, in agreement with the variational approach. Furthermore, the sandwich immiscible state results in an additional Goldstone mode due to the barrier, in contrast to the spatially symmetry-broken side-by-side profile. Our results unveil the distinct collective response of the Josephson barrier in binary mixtures owing to interspecies atomic correlations.

People have recently begun communicating their thoughts and viewpoints through user-generated multimedia material on social networking websites. This information can be images, text, videos, or audio. Recent years have seen a rise in the frequency of occurrence of this pattern. Twitter is one of the most extensively utilized social media sites, and it is also one of the finest locations to get a sense of how people feel about events that are linked to the Monkeypox sickness. This is because tweets on Twitter are shortened and often updated, both of which contribute to the platform's character. The fundamental objective of this study is to get a deeper comprehension of the diverse range of reactions people have in response to the presence of this condition. This study focuses on finding out what individuals think about monkeypox illnesses, which presents a hybrid technique based on CNN and LSTM. We have considered all three possible polarities of a user's tweet: positive, negative, and neutral. An architecture built on CNN and LSTM is utilized to determine how accurate the prediction models are. The recommended model's accuracy was 94% on the monkeypox tweet dataset. Other performance metrics such as accuracy, recall, and F1-score were utilized to test our models and results in the most time and resource-effective manner. The findings are then compared to more traditional approaches to machine learning. The findings of this research contribute to an increased awareness of the monkeypox infection in the general population.

A description of the endomorphisms of semidirect products of two groups as a group of $2\times 2$ matrices of maps is already known. Using this description, we have studied the concept of determinant for the endomorphisms of semidirect product of two groups. A characterization of the invertible endomorphisms is given with the help of the tools developed using the determinants.

Hidden attractors are present in many nonlinear dynamical systems and are not associated with equilibria, making them difficult to locate. Recent studies have demonstrated methods of locating hidden attractors, but the route to these attractors is still not fully understood. In this letter, we present the route to hidden attractors in systems with stable equilibrium points and in systems without any equilibrium points. We show that hidden attractors emerge as a result of the saddle-node bifurcation of stable and unstable periodic orbits. Real-time hardware experiments were performed to demonstrate the existence of hidden attractors in these systems. Despite the difficulties in identifying the suitable initial conditions from the appropriate basin of attraction, we performed experiments to detect hidden attractors in nonlinear electronic circuits. Our results provide new insights into the generation of hidden attractors in nonlinear dynamical systems.

Finding an exact solution for a realistic interacting quantum many-body problem is often challenging. There are only a few problems where an exact solution can be found, usually in a narrow parameter space. Here, we propose a spin-$1/2$ Heisenberg model on a square lattice with spatial anisotropy and bond depletion for the nearest-neighbor antiferromagnetic interactions but not for the next-nearest-neighbor interactions. This model has an \emph{exact} and \emph{unique} dimer ground state at $J_2/J_1=1/2$; a dimer state is a product state of spin-singlets on dimers (here, staggered nearest-neighbor bonds). We examine this model by employing the bond-operator mean-field theory and exact diagonalization. These analytical and numerical methods precisely affirm the correctness of the dimer ground state at the exact point ($J_2/J_1=1/2$). As one moves away from the exact point, the dimer order melts and vanishes when the spin gap becomes zero. The mean-field theory with harmonic approximation indicates that the dimer order persists for $-0.35\lesssim J_2/J_1\lesssim 1.35$. However, in non-harmonic approximation, the upper critical point lowers by $0.28$ to $1.07$, but the lower critical point remains intact. The exact diagonalization results suggest that the latter approximation fares better. The model reveals N\'eel order below the lower critical point and stripe magnetic order above the upper critical point. It has a topologically equivalent model on a honeycomb lattice where the nearest-neighbor interactions are still spatial anisotropic, but the bond depletion shifts into the isotropic next-neighbor interactions. Moreover, these models can also be generalized in the three dimensions.

A detailed investigation of the structural and magnetic properties, including magnetocaloric effect, re-entrant spin-glass behavior at low temperature, and critical behavior in polycrystalline Al$_2$MnFe Heusler alloy is reported. The prepared alloy crystallizes in a cubic CsCl-type crystal structure with Pm-3m space group. The temperature-dependent magnetization data reveals a second-order paramagnetic to ferromagnetic phase transition ($\sim$ 122.9 K), which is further supported by the analysis of the magnetocaloric effect. The isothermal magnetization loops show a soft ferromagnetic behavior of the studied alloy and also reveal an itinerant character of the underlying exchange interactions. In order to understand the nature of magnetic interactions, the critical exponents for spontaneous magnetization, initial magnetic susceptibility, and critical MH isotherm are determined using Modified Arrott plots, Kouvel-Fisher plots, and critical isotherm analysis. The derived critical exponents $\beta$ = 0.363(2), $\gamma$ = 1.384(3), and $\delta$ = 4.81(3) confirm the critical behavior similar to that of a 3D-Heisenberg-type ferromagnet with short-range exchange interactions that are found to decay with distance as J(r) $\approx$ r$^{-4.936}$. Moreover, the detailed analysis of the AC susceptibility data suggests that the frequency-dependent shifting of the peak temperatures is well explained using standard dynamic scaling laws such as the critical slowing down model and Vogel-Fulcher law, and confirms the signature of re-entrant spin-glass features in Al$_2$MnFe Heusler alloy. Furthermore, maximum magnetic entropy change of $\sim$ 1.92 J/kg-K and relative cooling power of $\sim$ 496 J/kg at 50 kOe applied magnetic field are determined from magnetocaloric studies that are comparable to those of other Mn-Fe-Al systems.

Mechanical systems exhibit complex dynamical behavior from harmonic oscillations to chaotic motion. The dynamics undergo qualitative changes due to changes to internal system parameters like stiffness and changes to external forcing. Mapping out complete bifurcation diagrams numerically or experimentally is resource-consuming, or even infeasible. This study uses a data-driven approach to investigate how bifurcations can be learned from a few system response measurements. Particularly, the concept of reservoir computing (RC) is employed. As proof of concept, a minimal training dataset under the resource constraint problem of a Duffing oscillator with harmonic external forcing is provided as training data. Our results indicate that the RC not only learns to represent the system dynamics for the external forcing seen during training, but it also provides qualitatively accurate and robust system response predictions for completely unknown multi-parameter regimes outside the training data. Particularly, while being trained solely on regular period-2 cycle dynamics, the proposed framework correctly predicts higher-order periodic and even chaotic dynamics for out-of-distribution forcing signals.

Security issues related to the cloud computing are relevant to various stakeholders for an informed cloud adoption decision. Apart from data breaches, the cyber security research community is revisiting the attack space for cloud-specific solutions as these issues affect budget, resource management, and service quality. Distributed Denial of Service (DDoS) attack is one such serious attack in the cloud space. In this paper, we present developments related to DDoS attack mitigation solutions in the cloud. In particular, we present a comprehensive survey with a detailed insight into the characterization, prevention, detection, and mitigation mechanisms of these attacks. Additionally, we present a comprehensive solution taxonomy to classify DDoS attack solutions. We also provide a comprehensive discussion on important metrics to evaluate various solutions. This survey concludes that there is a strong requirement of solutions, which are designed keeping utility computing models in mind. Accurate auto-scaling decisions, multi-layer mitigation, and defense using profound resources in the cloud, are some of the key requirements of the desired solutions. In the end, we provide a definite guideline on effective solution building and detailed solution requirements to help the cyber security research community in designing defense mechanisms. To the best of our knowledge, this work is a novel attempt to identify the need of DDoS mitigation solutions involving multi-level information flow and effective resource management during the attack.

Most previous studies on coupled dynamical systems assume that all interactions between oscillators take place uniformly in time, but in reality, this does not necessarily reflect the usual scenario. The heterogeneity in the timings of such interactions strongly influences the dynamical processes. Here, we introduce a time-evolving state-space dependent coupling among an ensemble of identical coupled oscillators, where individual units are interacting only when the mean state of the system lies within a certain proximity of the phase space. They interact globally with mean-field diffusive coupling in a certain vicinity and behave like uncoupled oscillators with self-feedback in the remaining complementary subspace. Interestingly due to this occasional interaction, we find that the system shows an abrupt explosive transition from oscillatory to death state. Further, in the explosive death transitions, the oscillatory state and the death state coexist over a range of coupling strengths near the transition point. We explore our claim using Van der pol, FitzHughNagumo and Lorenz oscillators with dynamic mean field interaction. The dynamic interaction mechanism can explain sudden suppression of oscillations and concurrence of oscillatory and steady state in biological as well as technical systems.

An extensive experimental investigation on the structural, static magnetic, and non-equilibrium dynamical properties of polycrystalline Mn$_2$CuGe Heusler alloy using powder X-ray diffraction, DC magnetization, magnetic relaxation, magnetic memory effect, and specific heat measurements is presented. Structural studies reveal that the alloy crystallizes in a mixed hexagonal crystal structure (space groups P3c1 (no. 158) and P6$_3$/mmc (no. 194)) with lattice parameters a = b = 7.18(4) $\mathring{A}$ and c = 13.12(4) $\mathring{A}$ for the majority phase. The DC magnetization analysis reveals a paramagnetic to ferrimagnetic phase transition around T$_C$ $\approx$ 682 K with a compensation of magnetization at $\approx$ 250 K, and a spin-glass transition around T$_P$ $\approx$ 25.6 K. The Néel theory of ferrimagnets supports the ferrimagnetic nature of the studied alloy and the estimated T$_C$ ($\approx$ 687 K) from this theory is consistent with that obtained from the DC magnetization data. A detailed study of non-equilibrium spin dynamics via magnetic relaxation and memory effect experiments shows the evolution of the system through a number of intermediate states and striking magnetic memory effect. Furthermore, heat capacity measurements suggest a large electronic contribution to the specific heat capacity suggesting strong spin fluctuations, due to competing magnetic interactions. All the observations render a spin-glass behavior in Mn$_2$CuGe, attributed to the magnetic frustration possibly arising out of the competing ferromagnetic and antiferromagnetic interactions.

Misinformation about vaccination poses a significant public health threat by reducing vaccination rates and increasing disease burden. Understanding population heterogeneity can aid in recognizing and mitigating the effects of such misinformation, especially when vaccine effectiveness is low. Our research quantifies the impact of misinformation on vaccination uptake and explores its effects in heterogeneous versus homogeneous populations. We employed a dual approach combining ordinary differential equations (ODE) and complex network models to analyze how different epidemiological parameters influence disease spread and vaccination behaviour. Our results indicate that misinformation significantly lowers vaccination rates, particularly in homogeneous populations, while heterogeneous populations demonstrate greater resilience. Among network topologies, small-world networks achieve higher vaccination rates under varying vaccine efficacies, while scale-free networks experience reduced vaccine coverage with higher misinformation amplification. Notably, cumulative infection remains independent of disease transmission rate when the vaccine is partially effective. In small-world networks, cumulative infection shows high stochasticity across vaccination rates and misinformation parameters, while cumulative vaccination is highest with higher and lower misinformation. To control disease spread, public health efforts should address misinformation, particularly in homogeneous populations and scale-free networks. Building resilience by promoting reliable vaccine information can boost vaccination rates. Focusing campaigns on small-world networks can result in higher vaccine uptake.

In this paper, we classify all the finite groups $G$ such that the commuting graph $\Gamma_C(G)$, order-sum graph $\Gamma_{OS}(G)$ and non-inverse graph $\Gamma_{NI}(G)$ are minimally edge connected graphs. We also classify all the finite groups $G$ for that, these graphs are minimally connected. We also classify some groups for that the co-prime graph $\Gamma_{CP}(G)$ has minimal edge connectedness. In final part, we classify all the finite groups $G$ for that co-prime graph $\Gamma_{CP}(G)$ is minimally connected.

In this paper, we introduce a new generalization of geometric distribution which can also viewed as discrete analogue of weighted exponential distribution introduced by Gupta and Kundu(2009). We study some basic distributional properties like moments, generating functions, hazard function followed by different methods of estimation of the parameters. Characterization of Geometric distribution have also been presented. Finally, we examine the model with real data sets.