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In this paper, we investigate the general properties and structure of $C^*$-extreme points within the $C^*$-convex set $\mathrm{UCP}(\mathcal{A},B(\mathcal{H}))$ of all unital completely positive (UCP) maps from a unital real $C^*$-algebra $\mathcal{A}$ to the algebra $B(\mathcal{H})$ of all bounded real linear maps on a real Hilbert space $\mathcal{H}$. We analyze the differences in the structure of $C^*$-extreme points between the real and complex $C^*$-algebra cases. In particular, we show that the necessary and sufficient conditions for a UCP map between matrix algebras to be a $C^*$-extreme point are identical in both the real and complex matrix algebra cases. We also observe significant differences in the structure of $C^*$-extreme points when $\mathcal{A}$ is a commutative real $C^*$-algebra compared to when $\mathcal{A}$ is a commutative complex $C^*$-algebra. We provide a complete classification of the $C^*$-extreme points of $\mathrm{UCP}(\mathcal{A},B(\mathcal{H}))$, where $\mathcal{A}$ is a unital commutative real $C^*$-algebra and $\mathcal{H}$ is a finite-dimensional real Hilbert space. As an application, we classify all $C^*$-extreme points in the $C^*$-convex set of all contractive skew-symmetric real matrices in $M_n(\mathbb{R})$.

Given a nonnegative noncommutative polynomial $f$, equivalently a sum of Hermitian squares (SOHS), there exists a positive semidefinite Gram matrix that encrypts all essential information of $f$. There are no available methods for extending a noncommutative polynomial to a SOHS keeping the Gram matrices unperturbed. As a remedy, we introduce an equally significant notion of Gram-like matrices and provide linear algebraic techniques to get the desired extensions. We further use positive semidefinite completion problem to get SOHS and provide criteria in terms of chordal graphs and 2-regular projective algebraic sets., Comment: All comments are welcome

One of the key characteristics of secure quantum communication is quantum secure multiparty computation. In this paper, we propose a quantum secure multiparty summation (QSMS) protocol that can be applied to many complex quantum operations. It is based on the $(t, n)$ threshold approach. We combine the classical and quantum phenomena to make this protocol realistic and secure. Because the current protocols employ the $(n, n)$ threshold approach, which requires all honest players to execute the quantum multiparty summation protocol, they have certain security and efficiency problems. However, we employ a $(t, n)$ threshold approach, which requires the quantum summation protocol to be computed only by $t$ honest players. Our suggested protocol is more economical, practical, and secure than alternative protocols.

One crucial and basic method for disclosing a secret to every participant in quantum cryptography is quantum secret sharing. Numerous intricate protocols, including secure multiparty summation, multiplication, sorting, voting, and more, can be designed with it. A quantum secret sharing protocol with a $(t,n)$ threshold approach and modulo d, where t and n represent the threshold number of participants and the total number of participants, respectively was recently discussed by Song et al. Kao et al. notes that without the information of other participants, the secret in Song {\em et al.'s}protocol cannot be reconstructed. We address a protocol that solves this issue in this paper.

The entanglement spectrum serves as a powerful tool for probing the structure and dynamics of quantum many-body systems, revealing key information about symmetry, topology, and excitations. While the entanglement entropy (EE) of ground states typically follows an area law, highly excited states obey a volume law, leading to a striking contrast in their scaling behavior. In this paper, we investigate the crossover between these two regimes, focusing on the role of quasi-particles (QPs) in mediating this transition. By analyzing the energy dependence of EE in various many-body systems, we explore how the presence of long-lived QPs influences the entanglement structure of excited states. We present numerical results for spinless fermions, a spin chain near a many-body localization transition, and the Sachdev-Ye-Kitaev (SYK) model, which lacks a conventional QP description. Our findings are complemented by a theoretical model based on Fermi liquid theory, providing insight into the interaction-dependent scaling of EE and its consistency with numerical simulations. We find that a hallmark of QPs is a linear dependence of the eigenstate EE on energy, which breaks down at high energy and in the limit of strong interaction. The slope of this linear dependence reflects the QP weight, which reduces with interaction strength., Comment: 8 pages, 6 figures

Hepatitis B virus (HBV) is considered as etiological agent of the lethal liver disease hepatitis B. Globally, hepatitis B is recognized as one of the prevailing infectious diseases with a significant impact on human health. In spite of being non-infectious in nature, sub-viral particles (SVPs) , composed with mainly viral surface proteins, play critical roles in the persistence and progression of the infection. Although the understanding on the functions of these non-infectious SVPs remains limited and incomplete. In this study, a mathematical model is proposed for the first time by incorporating the roles of SVPs and including the effects of capsids recycling. The impacts of spatial mobility of capsids, viruses, SVPs and antibodies are also taken into account in this model. Overall, this model carry unique characteristics in the context of this viral infection. This study investigates the changes in the dynamics of infection considering both single-point as well as multi-point infection initial condition. As a result, it is observed that SVPs can significantly enhance intracellular viral replication and gene expression by reducing the neutralization of virus particles by antibodies. The recycling of capsids substantially increase the concentration of SVPs. The experiments which are carried out on single-point as well as multi-point infection initial conditions show that if the liver is infected at more than one point, infection propagates rapidly. The outcomes of the proposed model strongly recommend that it is imperative to consider the diffusion term while HBV infection dynamics are illustrated.

This paper addresses the limitations of traditional keyword-based search in understanding user intent and introduces a novel hybrid search approach that leverages the strengths of non-semantic search engines, Large Language Models (LLMs), and embedding models. The proposed system integrates keyword matching, semantic vector embeddings, and LLM-generated structured queries to deliver highly relevant and contextually appropriate search results. By combining these complementary methods, the hybrid approach effectively captures both explicit and implicit user intent.The paper further explores techniques to optimize query execution for faster response times and demonstrates the effectiveness of this hybrid search model in producing comprehensive and accurate search outcomes.

The electron-electron and electron-phonon coupling in complex materials can be more complicated than simple density-density interactions, involving intertwined dynamics of spin, charge, and spatial symmetries. This motivates studying universal models with complex interactions, and studying whether in this case BCS-type singlet pairing is still the ``natural'' fate of the system. To this end, we construct a Yukawa-SYK model with nonlocal couplings in both spin and charge channels. Furthermore, we provide for time-reversal-symmetry breaking dynamics by averaging over the Gaussian Unitary ensemble rather than the Orthogonal ensemble. We find that the ground state of the system can be an orbitally nonlocal superconducting state arising from incoherent fermions with no BCS-like analog. The superconductivity has an equal tendency to triplet and singlet pairing states separated by a non-Fermi liquid phase. We further study the fate of the system within the superconducting phase and find that the expected ground state, away from the critical point, is a mixed singlet/triplet state. Finally, we find that while at $T_c$ the triplet and singlet transitions are dual to one another, below $T_c$ the duality is broken, with the triplet state more susceptible to orbital fluctuations just by virtue of its symmetry. Our results indicate that such fluctuation-induced mixed states may be an inherent feature of strongly correlated materials., Comment: 4 pages, 3 figures

In this paper, we investigate the dynamics of hepatitis B virus infection taking into account the implementation of combination therapy through mathematical modeling. This model is established considering the interplay between uninfected cells, infected cells, capsids, and viruses. Three drugs are considered for specific roles (i) pegylated interferon (PEG IFN) for immune modulation, (ii) lamivudine (LMV) as a reverse-transcriptase inhibitor, and (iii) entecavir (ETV) to block capsid recycling. Using these drugs, three combination therapies are introduced, specifically CT PEG IFN plus LMV, CT PEG IFN plus ETV, and CT PEG IFN plus LMV plus ETV. As a result, when LMV is used in combination therapy with PEG IFN and ETV, the impacts of ETV become insignificant. In conclusion, if the appropriate drug effectively inhibits reverse transcription, there is no need for an additional inhibitor to block capsid recycling.

In this work, a hepatitis B virus infection dynamics model is proposed including the spatial dependence of viruses. The existence of traveling waves for the proposed model is established through the application of the celebrated Gersgorin theorem. The procedure followed to establish the existence of a traveling wave solution is innovative and probably the first attempt of this particular approach. The elasticity of basic reproduction number with respect to some model parameters are also shown. Furthermore, the effects of spatial diffusivity of the viruses on infection are studied, and it is noticed that due to the diffusion, viruses spread rapidly throughout the liver.

Proliferation of uninfected as well as infected hepatocytes and recycling of DNA-containing capsids are two major mechanisms playing significant roles in the clearance of hepatitis B virus (HBV) infection. In this study, the temporal dynamics of this infection are investigated through two in silico bio-mathematical models considering both proliferation of hepatocytes and the recycling of capsids. Both models are formulated on the basis of a key finding in the existing literature: mitosis of infected yields in two uninfected progenies. In the first model, we examine regular proliferation (occurs continuously), while the second model deals with the irregular proliferation (happens when the total number of liver cells decreases to less than 70% of its initial volume). The models are calibrated with the experimental data obtained from an adult chimpanzee. Results of this study suggest that when both hepatocytes proliferate with equal rate, proliferation aids the individual in a rapid recovery from the acute infection whereas in the case of chronic infection, the severity of the infection increases if the proliferation occurs frequently. On the other hand, if the infected cells proliferate at a slower rate than uninfected cells, the proliferation of uninfected hepatocytes contributes to increase the infection, but the proliferation of infected hepatocytes acts to reduce the infection from the long-term perspective. Furthermore, it is also observed that the differences between the outcomes of regular and irregular proliferations are substantial and noteworthy.

Recently many body localized systems have been treated as a hopping problem on a Fock space lattice with correlated disorder, where the many-body eigenstates exhibit multi-fractal character. The many-body propagator in Fock space has been shown to be useful for capturing this multifractality and extracting a Fock-space localization length for systems with random disorder in real space. Here we study a one-dimensional interacting system of spinless Fermions in the presence of a deterministic quasiperiodic potential using the Fock-space propagator. From the system-size scaling of the self-energy associated with the diagonal elements and the scaling of the off-diagonal elements of the propagator, we extract fractal characteristics and FS localization lengths, respectively, which behave similarly to that in the random system. We compute the sample-to-sample fluctuations of the typical self-energy and the off-diagonal propagator over different realizations of the potential and show that the fluctuations in the self-energy distinguish quasiperiodic and random systems, whereas the fluctuations of the off-diagonal elements cannot demarcate the two types of potential., Comment: 13 pages, 13 figures

Spectral flow was first studied by Atiyah and Lusztig, and first appeared in print in the work of Atiyah-Patodi-Singer (APS). For a norm-continuous path of self-adjoint Fredholm operators in the multiplier algebra $\mathcal{M}(\mathcal{B})$ with $\mathcal{B}$ separable and stable, spectral flow roughly measures the ``net mass" of spectrum that passes through zero in the positive direction, as we move along the continuous path. As the index of a Fredholm operator has had many fruitful and important generalizations to general operator algebras, generalizing the spectral flow of a path of self-adjoint Fredholm operators would also be of great interest to operator theory. We develop a notion of spectral flow which works for arbitrary separable stable canonical ideals -- including stably projectionless C*-algebras (which depends on a quite general notion of essential codimension). We show that, under appropriate hypotheses, spectral flow induces a group isomorphism $\pi_1(Fred_{SA,\infty},pt)\cong K_0(\mathcal{B})$, generalizing a result of APS. We also provide an axiomatization of spectral flow., Comment: Lemma 2.18, addressing Question 2.21 (older version), introduces a simpler spectral flow definition in 2.27, equivalent to the older one. Most changes occur in Introduction and Section 2. Main theorems and their proofs, such as the Spectral Flow Isomorphism Theorem and axiomatization, remain unaltered. (69 Pages)

Improper disposal of e-waste poses global environmental and health risks, raising serious concerns. The accurate classification of e-waste images is critical for efficient management and recycling. In this paper, we have presented a comprehensive dataset comprised of eight different classes of images of electronic devices named the E-Waste Vision Dataset. We have also presented EWasteNet, a novel two-stream approach for precise e-waste image classification based on a data-efficient image transformer (DeiT). The first stream of EWasteNet passes through a sobel operator that detects the edges while the second stream is directed through an Atrous Spatial Pyramid Pooling and attention block where multi-scale contextual information is captured. We train both of the streams simultaneously and their features are merged at the decision level. The DeiT is used as the backbone of both streams. Extensive analysis of the e-waste dataset indicates the usefulness of our method, providing 96% accuracy in e-waste classification. The proposed approach demonstrates significant usefulness in addressing the global concern of e-waste management. It facilitates efficient waste management and recycling by accurately classifying e-waste images, reducing health and safety hazards associated with improper disposal., Comment: 6 pages

Hepatitis B virus infection is a deadly liver disease. A part of newly produced HBV DNA-containing capsids are reused as a core particle in HBV replication. It is investigated that the recycling of HBV capsids greatly affects the intracellular dynamics of HBV infection. The main purpose of the present work is to study the recycling effects of HBV DNA-containing capsids in the HBV infection. Incorporating recycling effects of capsids, a four-compartment mathematical model is proposed for the first time in order to understand the dynamics of HBV infection in a better way. The well-posedness of the model is obtained by showing non-negativity, boundedness, and uniqueness of the solution. The explicit formula for the basic reproduction number is determined by applying the next-generation approach method. The proposed model is solved with help of fourth-order explicit Runge-Kutta method. Through a rigorous comparison with experimental data obtained from four chimpanzees, the proposed model demonstrates a strong correspondence with the dynamics of HBV infection. Global sensitivity analysis is also conducted to identify the most positively as well as negatively sensitive parameters for each compartment in the model. In the context of biology, depending on the value of basic reproduction number, the present model possesses two global asymptotically stable steady states: disease-free and endemic. The present study shows that the consideration of recycling of capsids reverses the existing mechanism of infection dynamics. This study also reveals that the accumulation of capsids within the infected hepatocytes is a key factor for exacerbating the disease. Moreover, another major finding of our study is that due to recycling of capsids, the number of released virus increases in spite of low virus production rate. The recycling of capsids acts as a positive feedback loop in the viral infection.

False news has received attention from both the general public and the scholarly world. Such false information has the ability to affect public perception, giving nefarious groups the chance to influence the results of public events like elections. Anyone can share fake news or facts about anyone or anything for their personal gain or to cause someone trouble. Also, information varies depending on the part of the world it is shared on. Thus, in this paper, we have trained a model to classify fake and true news by utilizing the 1876 news data from our collected dataset. We have preprocessed the data to get clean and filtered texts by following the Natural Language Processing approaches. Our research conducts 3 popular Machine Learning (Stochastic gradient descent, Na\"ive Bayes, Logistic Regression,) and 2 Deep Learning (Long-Short Term Memory, ASGD Weight-Dropped LSTM, or AWD-LSTM) algorithms. After we have found our best Naive Bayes classifier with 56% accuracy and an F1-macro score of an average of 32%.

This study compares the performance of a causal and a predictive model in modeling travel mode choice in three neighborhoods in Chicago. A causal discovery algorithm and a causal inference technique were used to extract the causal relationships in the mode choice decision making process and to estimate the quantitative causal effects between the variables both directly from observational data. The model results reveal that trip distance and vehicle ownership are the direct causes of mode choice in the three neighborhoods. Artificial neural network models were estimated to predict mode choice. Their accuracy was over 70%, and the SHAP values obtained measure the importance of each variable. We find that both the causal and predictive modeling approaches are useful for the purpose they serve. We also note that the study of mode choice behavior through causal modeling is mostly unexplored, yet it could transform our understanding of the mode choice behavior. Further research is needed to realize the full potential of these techniques in modeling mode choice.

Analysis of cell population can reveal the average information about the viral infection in host whereas single-cell analysis can capture the individual consideration. Single-cell analysis can also provide new ways to explore viral diversities and identify the intrinsic extreme phenotype of the cells. In this study, a single-cell hepatitis B virus (HBV) infection model is proposed by considering all possible intracellular steps which are observed in the viral life cycle. To the best of our knowledge, it is the most generalized model to date. The effects of newly introduced factors or components such as, cccDNA, HBx proteins, surface proteins, and double-stranded linear DNA-containing capsids are explained very well by this model. The intracellular delay is also incorporated into the proposed model, and it is seen that it has no significant impact on the persistence of infection. The global sensitivity analysis of the parameters is also performed using partial rank correlation coefficients based on Latin hypercube sampling method. According to PRCC values, the most positive and most negative sensitive parameters are identified. Moreover, it is observed that the availability of viral surface proteins switches the replication pattern from acute to chronic, whereas there is no considerable contribution of HBx proteins to the progression of HBV infection. Another striking result is that the recycling of capsids appears to act as a positive feedback loop throughout the infection.

DNA has been discussed as a potential medium for data storage. Potentially it could be denser, could consume less energy, and could be more durable than conventional storage media such as hard drives, solid-state storage, and optical media. However, computing on data stored in DNA is a largely unexplored challenge. This paper proposes an integrated circuit (IC) based on microfluidics that can perform complex operations such as artificial neural network (ANN) computation on data stored in DNA. It computes entirely in the molecular domain without converting data to electrical form, making it a form of in-memory computing on DNA. The computation is achieved by topologically modifying DNA strands through the use of enzymes called nickases. A novel scheme is proposed for representing data stochastically through the concentration of the DNA molecules that are nicked at specific sites. The paper provides details of the biochemical design, as well as the design, layout, and operation of the microfluidics device. Benchmarks are reported on the performance of neural network computation., Comment: 24 pages, 11 figures

ChatGPT is a conversational artificial intelligence that is a member of the generative pre-trained transformer of the large language model family. This text generative model was fine-tuned by both supervised learning and reinforcement learning so that it can produce text documents that seem to be written by natural intelligence. Although there are numerous advantages of this generative model, it comes with some reasonable concerns as well. This paper presents a machine learning-based solution that can identify the ChatGPT delivered text from the human written text along with the comparative analysis of a total of 11 machine learning and deep learning algorithms in the classification process. We have tested the proposed model on a Kaggle dataset consisting of 10,000 texts out of which 5,204 texts were written by humans and collected from news and social media. On the corpus generated by GPT-3.5, the proposed algorithm presents an accuracy of 77%.