Search Results (29)

The continual production of long wavelength gravitons during primordial inflation endows graviton loop corrections with secular growth factors. During a prolonged period of inflation, these factors eventually overwhelm the small loop-counting parameter of $G{H}^2$, causing perturbation theory to break down. A technique was recently developed for summing the leading secular effects at each order in non-linear sigma models, which possess the same kind of derivative interactions as gravity. This technique combines a variant of Starobinsky’s stochastic formalism with a variant of the renormalization group. Generalizing the technique to quantum gravity is a two-step process, the first of which is the determination of the gauge fixing condition that will allow this summation to be realized; this is the subject of this paper. Moreover, we briefly discuss the second step, which shall obtain the Langevin equation, in which secular changes in gravitational phenomena are driven by stochastic fluctuations of the graviton field. Full article

We consider application of the self-similarity principle in approximation theory under the conditions of asymptotic scale-invariance. For the effective summation of the asymptotic series methods, an iterative Borel summation with self-similar iterated roots is applied. The approximants follow from the self-similarity considerations and behave asymptotically as a power-law satisfying the asymptotic scale invariance. Optimal conditions on convergence of the sequence of approximants are imposed through the critical indices defined from the approximants. The indices are understood as control parameters for the optimal convergence of the asymptotic series. Such interpretation of the indices leads to an overall improvement of accuracy in calculations of the indices. The statement is supported by fifteen examples from condensed matter physics, quantum mechanics and field theory. Full article

Spinors are important objects in physics, which have found their place more and more after the discovery that particles have an intrinsic angular momentum shape and Cartan’s mathematical expression of this situation. Recent studies using special number sequences have also revealed a new approach to the use of spinors in mathematics and have provided a different perspective for spinor research that can be used as a source for future physics studies. The purpose of this work is to expand the generalized Fibonacci quaternion polynomials to the generalized Fibonacci polynomial spinors by associating spinors with quaternions, and to introduce and investigate a new polynomial sequence that can be used to benefit from the potential advantages of spinors in physical applications, and thus, to provide mathematical arguments, such as new polynomials, for studies using spinors and quaternions in quantum mechanics. Starting from this point of view, in this paper we introduce and investigate a new family of sequences called generalized Fibospinomials (or generalized Fibonacci polynomial spinors or Horadam polynomial spinors). Being particular cases, we use $(r,s)$-Fibonacci and $(r,s)$-Lucas polynomial spinors. We present Binet’s formulas, generating functions and the summation formulas for these polynomials. In addition, we obtain some special identities of these new sequences and matrices related to these polynomials. The importance of this study is that generalized Fibospinomials are currently the most generalized sequence in the literature when moving from Fibonacci quaternions to spinor structure, and that a wide variety of new spinor sequences can be obtained from this particular polynomial sequence. Full article

Quantum secure multi-party summation (QSMS) is a fundamental problem in quantum secure multi-party computation (QSMC), wherein multiple parties compute the sum of their data without revealing them. This paper proposes a novel QSMS protocol based on graph state, which offers enhanced security, usability, and flexibility compared to existing methods. The protocol leverages the structural advantages of graph state and employs random graph state structures and random encryption gate operations to provide stronger security. Additionally, the stabilizer of the graph state is utilized to detect eavesdroppers and channel noise without the need for decoy bits. The protocol allows for the arbitrary addition and deletion of participants, enabling greater flexibility. Experimental verification is conducted to demonstrate the security, effectiveness, and practicality of the proposed protocols. The correctness and security of the protocols are formally proven. The QSMS method based on graph state introduces new opportunities for QSMC. It highlights the potential of leveraging quantum graph state technology to securely and efficiently solve various multi-party computation problems. Full article

Cardiovascular diseases (CVDs) represent a significant challenge in global health, demanding advancements in diagnostic modalities. This review delineates the progressive and restrictive facets of nanomaterial-based biosensors in the context of detecting N-terminal pro-B-type natriuretic peptide (NT-proBNP), an indispensable biomarker for CVD prognosis. It scrutinizes the escalation in diagnostic sensitivity and specificity attributable to the incorporation of novel nanomaterials such as graphene derivatives, quantum dots, and metallic nanoparticles, and how these enhancements contribute to reducing detection thresholds and augmenting diagnostic fidelity in heart failure (HF). Despite these technological strides, the review articulates pivotal challenges impeding the clinical translation of these biosensors, including the attainment of clinical-grade sensitivity, the substantial costs associated with synthesizing and functionalizing nanomaterials, and their pragmatic deployment across varied healthcare settings. The necessity for intensified research into the synthesis and functionalization of nanomaterials, strategies to economize production, and amelioration of biosensor durability and ease of use is accentuated. Regulatory hurdles in clinical integration are also contemplated. In summation, the review accentuates the transformative potential of nanomaterial-based biosensors in HF diagnostics and emphasizes critical avenues of research requisite to surmount current impediments and harness the full spectrum of these avant-garde diagnostic instruments. Full article

Random pulse computing (RPC), the third paradigm along with digital and quantum computing, draws inspiration from biology, particularly the functioning of neurons. Here, we study information processing in random pulse computing circuits intended for the summation of numbers. Based on the information-theoretic merits of entropy budget and relative Kolmogorov–Sinai entropy, we investigate the prior art and propose new circuits: three deterministic adders with significantly improved output entropy and one exact nondeterministic adder that requires much less additional entropy than the previous art. All circuits are realized and tested experimentally, using quantum entropy sources and reconfigurable logic devices. Not only the proposed circuits yield a precise mathematical result and have output entropy near maximum, which satisfies the need for building a programmable random pulse computer, but also they provide affordable hardware options for generating additional entropy. Full article

Measurement of the intracellular pH is particularly crucial for the detection of numerous diseases, such as carcinomas, that are characterised by a low intracellular pH. Therefore, pH-responsive nanosensors have been developed by many researchers due to their ability to non-invasively detect minor changes in the pH of many biological systems without causing significant biological damage. However, the existing pH-sensitive nanosensors, such as the polyacrylamide, silica, and quantum dots-based nanosensors, require large quantities of organic solvents that could cause detrimental damage to the ecosystem. As a result, this research is aimed at developing a new generation of pH-responsive nanosensors comprising alginate natural polymers and pH-sensitive fluorophores using an organic, solvent-free, and ecologically friendly method. Herein, we successfully synthesised different models of pH-responsive alginate nanoparticles by varying the method of fluorophore conjugation. The synthesised pH nanosensors demonstrated a low MHD with a relatively acceptable PDI when using the lowest concentration of the cross-linker Ca⁺² (1.25 mM). All the pH nanosensors showed negative zeta potential values, attributed to the free carboxylate groups surrounding the nanoparticles’ surfaces, which support the colloidal stability of the nanosensors. The synthesised models of pH nanosensors displayed a high pH-responsiveness with various correlations between the pH measurements and the nanosensors’ fluorescence signal. In summation, pH-responsive alginate nanosensors produced using organic, solvent-free, green technology could be harnessed as potential diagnostics for the intracellular and extracellular pH measurements of various biological systems. Full article

In this review, our goal is to design and test quantum-like algorithms for Artificial Intelligence (AI) in open systems to structure a human–machine team to be able to reach its maximum performance. Unlike the laboratory, in open systems, teams face complexity, uncertainty and conflict. All task domains have complexity levels—some low, and others high. Complexity in this new domain is affected by the environment and the task, which are both affected by uncertainty and conflict. We contrast individual and interdependence approaches to teams. The traditional and individual approach focuses on building teams and systems by aggregating the best available information for individuals, their thoughts, behaviors and skills. Its concepts are characterized chiefly by one-to-one relations between mind and body, a summation of disembodied individual mental and physical attributes, and degrees of freedom corresponding to the number of members in a team; however, this approach is characterized by the many researchers who have invested in it for almost a century with few results that can be generalized to human–machine interactions; by the replication crisis of today (e.g., the invalid scale for self-esteem); and by its many disembodied concepts. In contrast, our approach is based on the quantum-like nature of interdependence. It allows us theorization about the bistability of mind and body, but it poses a measurement problem and a non-factorable nature. Bistability addresses team structure and performance; the measurement problem solves the replication crisis; and the non-factorable aspect of teams reduces the degrees of freedom and the information derivable from teammates to match findings by the National Academies of Science. We review the science of teams and human–machine team research in the laboratory versus in the open field; justifications for rejecting traditional social science while supporting our approach; a fuller understanding of the complexity of teams and tasks; the mathematics involved; a review of results from our quantum-like model in the open field (e.g., tradeoffs between team structure and performance); and the path forward to advance the science of interdependence and autonomy. Full article

As a powerful tool for models of quantum computing, q-calculus has drawn the attention of many researchers in the discipline of special functions. In this paper, we present new properties and characterize q-Bessel functions of the first kind using some identities of q-calculus. The results presented in this article help us to obtain new expression results related to q-special functions. New summation and integral representations for q-Bessel functions of the first kind are also established. A few examples are also provided to demonstrate the effectiveness of the proposed strategy. Full article

In quantum secure multi-party summation protocols, some attackers can impersonate legitimate participants in the summation process, and easily steal the summation results from the participants. This is often overlooked for existing secure multi-party summation protocols, thus rendering them insecure. Based on commutative encryption, a quantum secure multi-party summation protocol with identity authentication is proposed in this paper. In the protocol, each participant encodes a secret integer on photons via unitary operations. At the same time, a one-way hash function technique with a key is utilized to perform identity authentication operations for each participant. Finally, the summation is calculated with the help of a semi-trusted third party. The analysis of the protocol shows that the proposed protocol is correct and resistant to common and impersonation attacks. Compared to related protocols, the use and measurement of single photons makes the protocol easier to implement into existing technology. Furthermore, the simulation experiments on the IBM Q Experience cloud platform demonstrate the effectiveness of the presented protocol. Full article

In this paper, we propose a secure multi-party summation based on single photons. With the help of a semi-honest third party, n participants can simultaneously obtain the summation result without revealing their secret inputs. Our protocol uses single photon states as the information carriers. In addition, each participant with secret input only performs simple single-particle operators rather than particle preparation and any complex quantum measurements. These features make our protocol more feasible to implement. We demonstrate the correctness and security of the proposed protocol, which is resistant to participant attack and outside attack. In the end, we compare in detail the performance of the quantum summation protocol in this paper with other schemes in terms of different indicators. By comparison, our protocol is efficient and easy to implement. Full article

Quantum summation is one of the various applications in secure multi-party computation. However, most of the existing quantum summation protocols assume that the participants possess all the quantum devices. Considering future applications, the capability of the participants must be adjusted before it can be put into practical use. Although Boyer et al. proposed that the semi-quantum environment could be used to solve this problem; another practical problem is the interference by noise. In 2022, Ye et al. proposed a two-party semi-quantum summation (SQS) protocol resistant to the interference of collective noise, in which two classical participants can accomplish the summation of their private binary sequences with the assistance of a quantum semi-honest third party. They proved that their SQS protocol is resistant to various eavesdropping attacks. This paper unveils two risks of information leakage in Ye et al.’s SQS protocol. If the aforementioned security issues are not resolved, Ye et al.’s SQS protocol may not be able to perform private quantum computations securely. Fortunately, the SQS protocol against the collective-dephasing noise proposed in this study is free from the issue of information leakage as well as resistant to various quantum attacks. In addition, the quantum efficiency of the SQS protocol proposed in this study is four times higher than that of Ye et al.’s SQS protocol, which can effectively improve the quantum utilization rate. Full article

In this paper, we develop theorems on finite and infinite summation formulas by utilizing the $\mathfrak{q}$ and $(\mathfrak{q},\mathfrak{h})$ anti-difference operators, and also we extend these core theorems to ${\mathfrak{q}}_{\left(\alpha \right)}$ and ${(\mathfrak{q},\mathfrak{h})}_{\alpha }$ difference operators. Several integer order theorems based on $\mathfrak{q}$ and ${\mathfrak{q}}_{\left(\alpha \right)}$ difference operator have been published, which gave us the idea to derive the fractional order anti-difference equations for $\mathfrak{q}$ and ${\mathfrak{q}}_{\left(\alpha \right)}$ difference operators. In order to develop the fractional order anti-difference equations for $\mathfrak{q}$ and ${\mathfrak{q}}_{\left(\alpha \right)}$ difference operators, we construct a function known as the quantum geometric and alpha-quantum geometric function, which behaves as the class of geometric series. We can use this function to convert an infinite summation to a limited summation. Using this concept and by the gamma function, we derive the fractional order anti-difference equations for $\mathfrak{q}$ and ${\mathfrak{q}}_{\left(\alpha \right)}$ difference operators for polynomials, polynomial factorials, and logarithmic functions that provide solutions for symmetric difference operator. We provide appropriate examples to support our results. In addition, we extend these concepts to the $(\mathfrak{q},\mathfrak{h})$ and ${(\mathfrak{q},\mathfrak{h})}_{\alpha }$ difference operators, and we derive several integer and fractional order theorems that give solutions for the mixed symmetric difference operator. Finally, we plot the diagrams to analyze the $(\mathfrak{q},\mathfrak{h})$ and ${(\mathfrak{q},\mathfrak{h})}_{\alpha }$ difference operators for verification. Full article

Air traffic controller (ATC) fatigue has become a major cause of air traffic accidents. Speech-based fatigue-state detection is proposed in this paper. The speech signal is preprocessed to further extract the Mel frequency cepstrum coefficient (MFCC) from speech discourse. The machine learning method is used in fatigue detection. However, single machine learning fatigue detection methods often have low detection accuracy. To solve this problem, an ensemble learning method based on self-adaption quantum genetic algorithm (SQGA) heterogeneous learning methods is proposed. Pattern-level and feature-level resampling are used to increase the differences in the base learner’s training dataset. To enlarge the diversity of single learners, k-nearest neighbor (KNN), Bayesian network (BN), back propagation neural network (BPNN) and support vector machine (SVM) are adopted for the heterogeneous ensemble. On this basis, finally, the detection result is obtained by weighted summation. The weight of each base learner was determined by SQGA. The SQGA method combines the quantum genetic algorithm with the adaptive strategy. The adaptive strategy includes adaptive adjustment of the quantum rotation gate, adaptive generation of crossover probability and adaptive generation of mutation probability. The experiments on real civil aviation radio land–air communication show that the proposed method can obtain 98.5% detection accuracy, with a 1.2% false and 3.0% missing report rate, whereas the SVM only obtains 94.0% detection accuracy, with a 5.4% false and 9.0% missing report rate. Full article

This is an unconventional review article on spectral problems in black hole perturbation theory. Our purpose is to explain how to apply various known techniques in quantum mechanics to such spectral problems. The article includes analytical/numerical treatments, semiclassical perturbation theory, the (uniform) WKB method and useful mathematical tools: Borel summations, Padé approximants, and so forth. The article is not comprehensive, but rather looks into a few examples from various points of view. The techniques in this article are widely applicable to many other examples. Full article