From In-Out Duality to the Foundation of Social Quantum Mechanics

This paper introduces a framework of in-out duality, merging insights from quantum mechanics with social sciences to illuminate the complex interplay between internal potentialities and external manifestations. It articulates foundational, mathematical axioms (Entanglement, Homogeneity, Emergence, and Measurement) that underpin the dynamics of systems, emphasizing the interconnectedness and emergent behaviors resulting from internal and external interactions. By exploring quantum concepts like coherence, entanglement, and superposition, the paper proposes an interdisciplinary approach termed Quantum Social Mechanics. This approach challenges classical paradigms, advocating for a reevaluation of conventional notions through the lens of quantum principles. The paper argues that understanding the universe’s complexities requires a synthesis of motion states and potential states, suggesting a paradigm shift towards integrating quantum mechanics into the philosophical foundation of social theory. Through this comprehensive framework, the paper aims to foster a deeper understanding of the universe’s interconnected nature and the dynamic processes that govern the emergence of complex systems and behaviors.

核转录因子Yin-Yang1与中医阴阳学说

Yin- Yang 1 ( YY1 )是一种具有双重转录活性的核转录因子 ,广泛存在于真核细胞中 ,自被发现十余年来 ,国外对其研究报道逐年增多 ,对其在基因转录调控、分子信号转导中所表现出的关键作用的认识日益引起重视。本文综述了近年来 YY1研究的部分相关文献 ,分析了 YY1与中医阴阳的关系 ,以期为中医阴阳学说的现代研究带来新的思路。

Duality theorem for smash coproduct over quantum groupoids

The duality theorem of generalized weak smash coproducts of weak module coalgebras and comodule coalgebras over quantum groupoids is studied.Let H be a weak Hopf algebra,C a left weak H-comodule coalgebra and D a left weak H-module coalgebra.First,a weak generalized smash coproduct C×lH D over quantum groupoids is defined and the module and comodule structures on it are constructed.The weak generalized right smash coproduct C×rL D is similar.Then some isomorph-isms between them are obtained.Secondly,by introducing some concepts of a weak convolution invertible element,a weak co-inner coaction and a strongly relative co-inner coaction,a sufficient condition for C×rH D to be isomorphic to Cv D is obtained,where v∈WC（C,H）and the coaction of H on D is right strongly relative co-inner.Finally,the duality theorem for a generalized smash coproduct over quantum groupoids,（C×lH H）×lH H≌Cv（H×lH H）,is obtained.

APPROXIMATE DUALITY OF g-FRAMES IN HILBERT SPACES

In this article, we introduce and characterize approximate duality for g-frames. We get some important properties and applications of approximate duals. We also obtain some new results in approximate duality of frames, and generalize some of the known results in approximate duality of frames to g-frames. We also get some results for fusion frames, and perturbation of approximately dual g-frames. We show that approximate duals are stable under small perturbations and they are useful for erasures and reconstruction.

Duality Computing in Quantum Computers

In this letter,we propose a duality computing mode,which resembles particle-wave duality property whena quantum system such as a quantum computer passes through a double-slit.In this mode,computing operations arenot necessarily unitary.The duality mode provides a natural link between classical computing and quantum computing.In addition,the duality mode provides a new tool for quantum algorithm design.

Elementary analysis of interferometers for wave particle duality test and the prospect of going beyond the complementarity principle

A distinct method to show a quantum object behaving both as wave and as particle is proposed and described in some detail. We make a systematic analysis using the elementary methodology of quantum mechanics upon Young＇s two-slit interferometer and the Mach-Zehnder two-arm interferometer with the focus placed on how to measure the interference pattern （wave nature） and the which-way information （particle nature） of quantum objects. We design several schemes to simultaneously acquire the which-way information for an individual quantum object and the high-contrast interference pattern for an ensemble of these quantum objects by placing two sets of measurement instruments that are well separated in space and whose perturbation of each other is negligibly small within the interferometer at the same time. Yet, improper arrangement and cooperation of these two sets of measurement instruments in the interferometer would lead to failure of simultaneous observation of wave and particle behaviors. The internal freedoms of quantum objects could be harnessed to probe both the which-way information and the interference pattern for the center-of-mass motion. That quantum objects can behave beyond the wave-particle duality and the complementarity principle would stimulate new conceptual examination and exploration of quantum theory at a deeper level.

General Quantum Interference Principle and Duality Computer

In this article, we propose a general principle of quantum interference for quantum system, and based on this we propose a new type of computing machine, the duality computer, that may outperform in principle both classical computer and the quantum computer. According to the general principle of quantum interference, the very essence of quantum interference is the interference of the sub-waves of the quantum system itself A quantum system considered here can be any quantum system： a single microscopic particle, a composite quantum system such as an atom or a molecule, or a loose collection of a few quantum objects such as two independent photons. In the duality computer, the wave of the duality computer is split into several sub-waves and they pass through different routes, where different computing gate operations are performed. These sub-waves are then re-combined to interfere to give the computational results. The quantum computer, however, has only used the particle nature of quantum object. In a duality computer, it may be possible to find a marked item from an unsorted database using only a single query, and all NP-complete problems may have polynomial algorithms. Two proof-of-the-principle designs of the duality computer are presented： the giant molecule scheme and the nonlinear quantum optics scheme. We also propose thought experiment to check the related fundamental issues, the measurement efficiency of a partial wave function.

An Improved Dynamic Core for a Non-hydrostatic Model System on the Yin-Yang Grid

A 3D dynamic core of the non-hydrostatic model GRAPES（Global/Regional Assimilation and Prediction System） is developed on the Yin-Yang grid to address the polar problem and to enhance the computational efficiency. Three-dimensional Coriolis forcing is introduced to the new core, and full representation of the Coriolis forcing makes it straightforward to share code between the Yin and Yang subdomains. Similar to that in the original GRAPES model, a semi-implicit semi-Lagrangian scheme is adopted for temporal integration and advection with additional arrangement for cross-boundary transport. Under a non-centered second-order temporal and spatial discretization, the dry nonhydrostatic frame is summarized as the solution of an elliptical problem. The resulting Helmholtz equation is solved with the Generalized Conjugate Residual solver in cooperation with the classic Schwarz method. Even though the coefficients of the equation are quite different from those in the original model, the computational procedure of the new core is just the same. The bi-cubic Lagrangian interpolation serves to provide Dirichlet-type boundary conditions with data transfer between the subdomains. The dry core is evaluated with several benchmark test cases, and all the tests display reasonable numerical stability and computing performance. Persistency of the balanced flow and development of both the mountain-induced Rossby wave and Rossby–Haurwitz wave confirms the appropriate installation of the 3D Coriolis terms in the semi-implicit semi-Lagrangian dynamic core on the Yin-Yang grid.

UHPLC-MS/MS analysis of cAMP and cGMP in rat plasma as potential biomarkers of Yin-Yang disharmony in traditional Chinese medicine

Cyclic 3’,5’-adenosine monophosphate(cAMP)and cyclic 3’,5’-guanosine monophosphate(cGMP)are considered as potential biomarkers for Yin-Yang disharmony in traditional Chinese medicine.However,phosphodiesterase-mediated ex vivo degradation of these molecules in biological samples may result in their underestimation.In the present study,a ultra-high performance liquid chromatography-tandem mass spectrometry(UHPLC-MS/MS)method was developed for determination of cAMP and cGMP in rat plasma,with special consideration of their stability ex vivo.Following precipitation of proteins from plasma samples with 0.4 M perchloric acid,the analytes were chromatographed on a Shimadzu Shimpack-XR-ODS II column with 2.5 mM ammonium acetate and methanol in gradient mode.The MS/MS detection was performed using multiple reaction monitoring in the positive electrospray ionization mode.The lower limit of quantification was 0.27 ng/mL for cAMP and 0.37 ng/mL for cGMP.The method was used to determine the plasma cAMP and cGMP levels in normal and Yin deficiency diabetic rats treated with or without Rehmannia glutinosa.The developed method may be useful for evaluating the regulatory effects of Chinese herbal medicine on the levels of cAMP and cGMP in the body.

DUALITY OF WEIGHTED MULTIPARAMETER TRIEBEL-LIZORKIN SPACES

In this paper, we reintroduce the weighted multi-parameter Triebel-Lizorkin spaces Fp^a,q（w;R^n1×R^n2） based on the Frazier and Jawerth＇ method in [11]. This space was firstly introduced in [18]. Then we establish its dual space and get that （Fp＇q）＊ = CMOp^-a,q＇ for 0 ~p≤ 1.

KUHN-TUCKER CONDITION AND WOLFE DUALITY OF PREINVEX SET-VALUED OPTIMIZATION

The optimality Kuhn-Tucker condition and the wolfe duality for the preinvex set-valued optimization are investigated. Firstly, the concepts of alpha-order G-invex set and the alpha-order S-preinvex set-valued function were introduced, from which the properties of the corresponding contingent cone and the alpha-order contingent derivative were studied. Finally, the optimality Kuhn-Tucker condition and the Wolfe duality theorem for the alpha-order S-preinvex set-valued optimization were presented with the help of the alpha-order contingent derivative.

Prime Factorization in the Duality Computer

We give algorithms to factorize large integers in the duality computer. We provide three duality algorithms for factorization based on a naive factorization method, the Shor algorithm in quantum computing, and the Fermat＇s method in classical computing. All these algorithms may be polynomial in the input size.

The Wave-Particle Duality—Does the Concept of Particle Make Sense in Quantum Mechanics? Should We Ask the Second Quantization?

The quantum object is in general considered as displaying both wave and particle nature. By particle is understood an item localized in a very small volume of the space, and which cannot be simultaneously in two disjoint regions of the space. By wave, to the contrary, is understood a distributed item, occupying in some cases two or more disjoint regions of the space. The quantum formalism did not explain until today the so-called “collapse” of the wave-function, i.e. the shrinking of the wave-function to one small region of the space, when a macroscopic object is encountered. This seems to happen in “which-way” experiments. A very appealing explanation for this behavior is the idea of a particle, localized in some limited part of the wave-function. The present article challenges the concept of particle. It proves in the base of a variant of the Tan, Walls and Collett experiment, that this concept leads to a situation in which the particle has to be simultaneously in two places distant from one another—situation that contradicts the very definition of a particle. Another argument is based on a modified version of the Afshar experiment, showing that the concept of particle is problematic. The concept of particle makes additional difficulties when the wave-function passes through fields. An unexpected possibility to solve these difficulties seems to arise from the cavity quantum electrodynamics studies done recently by S. Savasta and his collaborators. It involves virtual particles. One of these studies is briefly described here. Though, experimental results are needed, so that it is too soon to conclude whether it speaks in favor, or against the concept of particle.

Influence of TBX21 T-1993C variant on autoimmune hepatitis development by Yin-Yang 1 binding

AIM To investigated the mechanism of the association between the TBX21 T-1993 C promoter polymorphism and autoimmune hepatitis type 1(AIH-1) development.METHODS In vivo,In vivo,and reporter analyses were performed to determine the function of transcription factors binding to the T-1993 C element of the TBX21 promoter in human CD4+ T and B cell lines. Flow cytometry and quantitative real-time PCR were used to analyze T-box transcription factor(T-bet) and interferon-γ(IFN-γ) expressions in CD4+ T cells,B cells and monocytes from the peripheral blood of AIH-1 patients including 5-1993 TC and 15-1993 TT genotype carriers,and healthy controls including 10-1993 TC and 25-1993 TT genotype carriers. Furthermore,a range of biochemical indices was measured simultaneously in the blood of AIH-1 patients.RESULTS TBX21-1993 C allele created a strong Yin-Yang 1(YY1)-binding site and decreased transcriptional activity of TBX21 promoter in human CD4+ T and B cells.Higher levels of T-bet and IFN-γ were detected in the circulating CD4+ T cells and B cells of AIH-1 patients carrying the TBX21-1993 TT genotype compared with the patients carrying the-1993 TC genotype and controls with the-1993 TC genotype. T-bet expression levels of circulating T cells and B cells were positively correlated with AIH-1 disease activity. Knockdown of YY1 with si RNA caused increased expression of T-bet and IFN-γ in peripheral blood mononuclear cells in AIH-1 patients. CONCLUSION The repression of TBX21 expression by high-affinity binding of YY1 to the-1993 C allele may contribute to a decreased development of AIH-1 via suppression of type 1 immunity.

Duality theorem for weak L-R smash products

This paper gives a duality theorem for weak L-R smash products, which extends the duality theorem for weak smash products given by Nikshych.

Wave–particle duality in a Raman atom interferometer

We theoretically investigate the wave–particle duality based on a Raman atom interferometer, via the interaction between the atom and Raman laser, which is similar to the optical Mach–Zehnder interferometer. The wave and which-way information are stored in the atomic internal states. For the φ- π- π /2 type of atom interferometer, we find that the visibility(V) and predictability(P) still satisfy the duality relation, P2+ V2≤ 1.

Sufficiency and Duality for Nondif ferentiable Multiobjective Fractional Programming Problems with (Φ,ρ,α)-V-Invexity

A new concept of(Φ,ρ,α)-V-invexity for differentiable vector-valued functions is introduced,which is a generalization of differentiable scalar-valued(Φ,ρ)-invexity.Based upon the(Φ,ρ,α)-V-invex functions,sufficient optimality conditions and MondWeir type dual theorems are derived for a class of nondifferentiable multiobjective fractional programming problems in which every component of the objective function and each constraint function contain a term involving the support function of a compact convex set.

Long Non-coding RNA ANRIL in Gene Regulation and Its Duality in Atherosclerosis

The antisense transcript long non-coding RNA（lnc RNA）（antisense non-coding RNA in the INK4 locus, ANRIL） is an antisense of the cyclin-dependent kinase inhibitor 2 B（CDKN2B） gene on chromosome 9 p21 that contains an overlapping 299-bp region and shares a bidirectional promoter with alternate open reading frame（ARF）. In the context of gene regulation, ANRIL is responsible for directly recruiting polycomb group（Pc G） proteins, including polycomb repressive complex-1（PRC-1） and polycomb repressive complex-2（PRC-2）, to modify the epigenetic chromatin state and subsequently inhibit gene expression in cis-regulation. On the other hand, previous reports have indicated that ANRIL is capable of binding to a specific site or sequence, including the Alu element, E2 F transcription factor 1（E2F1）, and CCCTC-binding factor（CTCF）, to achieve trans-regulation functions. In addition to its function in cell proliferation, adhesion and apoptosis, ANRIL is very closely associated with atherosclerosis-related diseases. The different transcripts and the SNPs that are related to atherosclerotic vascular diseases（ASVD-SNPs） are inextricably linked to the development and progression of atherosclerosis. Linear transcripts have been shown to be a risk factor for atherosclerosis, whereas circular transcripts are protective against atherosclerosis. Furthermore, ANRIL also acts as a component of the inflammatory pathway involved in the regulation of inflammation, which is considered to be one of the causes of atherosclerosis. Collectively, ANRIL plays an important role in the formation of atherosclerosis, and the artificial modification of ANRIL transcripts should be considered following the development of this disease.

OPTIMALITY CONDITIONS AND DUALITY RESULTS FOR NONSMOOTH VECTOR OPTIMIZATION PROBLEMS WITH THE MULTIPLE INTERVAL-VALUED OBJECTIVE FUNCTION

In this paper, both Fritz John and Karush-Kuhn-Tucker necessary optimality conditions are established for a （weakly） LU-efficient solution in the considered nonsmooth multiobjective programming problem with the multiple interval-objective function. Further, the sufficient optimality conditions for a （weakly） LU-efficient solution and several duality results in Mond-Weir sense are proved under assumptions that the functions constituting the considered nondifferentiable multiobjective programming problem with the multiple interval- objective function are convex.

SYMPLECTIC DUALITY SYSTEM ON PLANE MAGNETOELECTROELASTIC SOLIDS

By means of the generalized variable principle of magnetoelectroelastic solids, the plane magnetoelectroelastic solids problem was derived to Hamiltonian system. In symplectic geometry space, which consists of original variables, displacements, electric potential and magnetic potential, and their duality variables, lengthways stress, electric displacement and magnetic induction, the effective methods of separation of variables and symplectic eigenfunction expansion were applied to solve the problem. Then all the eigen-solutions and the eigen-solutions in Jordan form on eigenvalue zero can be given, and their specific physical significations were shown clearly. At last, the special solutions were presented with uniform loader, constant electric displacement and constant magnetic induction on two sides of the rectangle domain.