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We study the quantum nature of non-Bunch-Davies states in de Sitter space by evaluating CHSH inequality on a localized two-atom system. We show that quantum nonlocality can be generated through the Markovian evolution of two-atom, witnessed by a violation of CHSH inequality on its final equilibrium state. We find that the upper bound of inequality violation is determined by different choices of de Sitter-invariant vacua sectors. In particular, with growing Gibbons-Hawking temperature, the CHSH bound degrades monotonously for Bunch-Davies vacuum sector. Due to the intrinsic correlation of non-Bunch-Davies vacua, we find that the related violation of inequality can however drastically increase after certain turning point, and may persist for arbitrarily large environment decoherence. This implies that the CHSH inequality is useful to classify the initial quantum state of the Universe. Finally, we clarify that the witnessed intrinsic correlation of non-Bunch-Davies vacua can be utilized for quantum information applications, e.g., surpassing the Heisenberg uncertainty bound of quantum measurement in de Sitter space., Comment: 9 pages, 4 figures, final version to appear in Physics Letters B

p53 encodes a transcription factor that transactivates downstream target genes involved in tumour suppression. Although osteosarcoma frequently has p53 mutations, the role of p53 in osteosarcomagenesis is not fully understood. To explore p53-target genes comprehensively in calvarial bone and find out novel druggable p53 target genes for osteosarcoma, we performed RNA sequencing using the calvarial bone and 23 other tissues from p53+/+ and p53−/− mice after radiation exposure. Of 23,813 genes, 69 genes were induced more than two-fold in irradiated p53+/+ calvarial bone, and 127 genes were repressed. Pathway analysis of the p53-induced genes showed that genes associated with cytokine-cytokine receptor interactions were enriched. Three genes, CD137L, CDC42 binding protein kinase gamma and Follistatin, were identified as novel direct p53 target genes that exhibited growth-suppressive effects on osteosarcoma cell lines. Of the three genes, costimulatory molecule Cd137l was induced only in calvarial bone among the 24 tissues tested. CD137L-expressing cells exhibited growth-suppressive effects in vivo. In addition, recombinant Fc-fusion Cd137l protein activated the immune response in vitro and suppressed osteosarcoma cell growth in vivo. We clarified the role of CD137L in osteosarcomagenesis and its potential therapeutic application. Our transcriptome analysis also indicated the regulation of the immune response through p53.

// Takafumi Miyamoto 1 , Chizu Tanikawa 1 , Varalee Yodsurang 5 , Yao-Zhong Zhang 2 , Seiya Imoto 3 , Rui Yamaguchi 2 , Satoru Miyano 2 , Hidewaki Nakagawa 4 and Koichi Matsuda 5 1 Laboratory of Genome Technology, Human Genome Center, Institute of Medical Science, The University of Tokyo, Tokyo, Japan 2 Laboratory of DNA Information Analysis, Human Genome Center, Institute of Medical Science, The University of Tokyo, Tokyo, Japan 3 Division of Health Medical Data Science, Health Intelligence Center, Institute of Medical Science, The University of Tokyo, Tokyo, Japan 4 Laboratory for Genome Sequencing Analysis, RIKEN Center for Integrative Medical Sciences, Tokyo, Japan 5 Laboratory of Clinical Genome Sequencing, Department of Computational Biology and Medical Sciences, Graduate School of Frontier Sciences, The University of Tokyo, Tokyo, Japan Correspondence to: Koichi Matsuda, email: // Keywords : p53, breast cancer, transcriptome analysis, adriamycin, gene module Received : January 27, 2017 Accepted : May 28, 2017 Published : July 26, 2017 Abstract The p53 protein is a sophisticated transcription factor that regulates dozens of target genes simultaneously in accordance with the cellular circumstances. Although considerable efforts have been made to elucidate the functions of p53-induced genes, a holistic understanding of the orchestrated signaling network repressed by p53 remains elusive. Here, we performed a systematic analysis to identify simultaneously regulated p53-repressed genes in breast cancer cells. Consequently, 28 genes were designated as the p53-repressed gene module, whose gene components were simultaneously suppressed in breast cancer cells treated with Adriamycin. A ChIP-seq database showed that p53 does not preferably bind to the region around the transcription start site of the p53-repressed gene module elements compared with that of p53-induced genes. Furthermore, we demonstrated that p21/CDKN1A plays a pivotal role in the suppression of the p53-repressed gene module in breast cancer cells. Finally, we showed that appropriate suppression of some genes belonging to the p53-repressed gene module contributed to a better prognosis of breast cancer patients. Taken together, these findings disentangle the gene regulatory network underlying the built-in p53-mediated tumor suppression system.

Although recent cancer genomics studies have identified a large number of genes that were mutated in human cancers, p53 remains as the most frequently mutated gene. To further elucidate the p53-signalling network, we performed transcriptome analysis on 24 tissues in p53+/+ or p53−/− mice after whole-body X-ray irradiation. Here we found transactivation of a total of 3551 genes in one or more of the 24 tissues only in p53+/+ mice, while 2576 genes were downregulated. p53 mRNA expression level in each tissue was significantly associated with the number of genes upregulated by irradiation. Annotation using TCGA (The Cancer Genome Atlas) database revealed that p53 negatively regulated mRNA expression of several cancer therapeutic targets or pathways such as BTK, SYK, and CTLA4 in breast cancer tissues. In addition, stomach exhibited the induction of Krt6, Krt16, and Krt17 as well as loricrin, an epidermal differentiation marker, after the X-ray irradiation only in p53+/+ mice, implying a mechanism to protect damaged tissues by rapid induction of differentiation. Our comprehensive transcriptome analysis elucidated tissue specific roles of p53 and its signalling networks in DNA-damage response that will enhance our understanding of cancer biology., Highlights • Transcriptome analysis across 24 mouse tissues identified a total of 3551 p53-induced genes and 2576 p53-repressed genes. • p53 mRNA in each tissue was associated with the numbers of p53-induced/repressed genes. • p53 would protect gastric epithelial cells from X-ray irradiation through the induction of differentiation and keratinization p53 is the most frequently mutated tumor-suppressor that functions as a transcription factor. Transcriptome analysis of 280 samples from 24 tissues identified 3551 p53-induced and 2576 p53-repressed genes. p53 negatively regulated several cancer therapeutic targets, BTK, SYK, and CTLA4 in breast cancer tissues. Majority of X-ray responsive genes were regulated by p53 and p53 mRNA expression in each tissue was associated with the numbers of p53-induced and repressed genes, demonstrating its crucial roles in damage response. The whole-body transcriptome analysis revealed that p53 would protect gastric epithelial cells from X-ray irradiation through the induction of differentiation and keratinization.

We construct the coherent states and Schr\"odinger cat states associated with new types of ladder operators for a particular case of a rationally extended harmonic oscillator involving type III Hermite exceptional orthogonal polynomials. In addition to the coherent states of the annihilation operator, $c$, we form the linearised version, \tilde{c}, and obtain its coherent states. We find that while the coherent states defined as eigenvectors of the annihilation operator $c$ display only quantum behaviour, those of the linearised version, \tilde{c}, have position probability densities displaying distinct wavepackets oscillating and colliding in the potential. The collisions are certainly quantum, as interference fringes are produced, but the remaining evolution indicates a classical analogue., Comment: 15 pages, 10 figures

Bethe ansatz solutions of the two-axis countertwisting Hamiltonian for any (integer and half-integer) $J$ are derived based on the Jordan-Schwinger (differential) boson realization of the $SU(2)$ algebra after desired Euler rotations, where $J$ is the total angular momentum quantum number of the system. It is shown that solutions to the Bethe ansatz equations can be obtained as zeros of the extended Heine-Stieltjes polynomials. Two sets of solutions, with solution number being $J+1$ and $J$ respectively when $J$ is an integer and $J+1/2$ each when $J$ is a half-integer, are obtained. Properties of the zeros of the related extended Heine-Stieltjes polynomials for half-integer $J$ cases are discussed. It is clearly shown that double degenerate level energies for half-integer $J$ are symmetric with respect to the $E=0$ axis. It is also shown that the excitation energies of the `yrast' and other `yrare' bands can all be asymptotically given by quadratic functions of $J$, especially when $J$ is large., LaTex 12 pages, 3 figures. Major cosmetic type revision. arXiv admin note: text overlap with arXiv:1609.05581

We revisit the MIC-harmonic oscillator in flat space with monopole interaction and derive the polynomial algebra satisfied by the integrals of motion and its energy spectrum using the ad hoc recurrence approach. We introduce a superintegrable monopole system in generalized Taub-NUT space. The Schr\"{o}dinger equation of this model is solved in spherical coordinates in the framework of St\"{a}ckel transformation. It is shown that wave functions of the quantum system can be expressed in terms of the product of Laguerre and Jacobi polynomials. We construct ladder and shift operators based on the corresponding wave functions and obtain the recurrence formulas. By applying these recurrence relations, we construct higher order algebraically independent integrals of motion. We show the integrals form a polynomial algebra. We construct the structure functions of the polynomial algebra and obtain the degenerate energy spectra of the model., Comment: 19 pages

We explore the entropic uncertainty relation in the curved background outside a Schwarzschild black hole, and find that Hawking radiation introduces a nontrivial modification on the uncertainty bound for particular observer, therefore it could be witnessed by proper uncertainty game experimentally. We first investigate an uncertainty game between a free falling observer and his static partner holding a quantum memory initially entangled with the quantum system to be measured. Due to the information loss from Hawking decoherence, we find an inevitable increase of the uncertainty on the outcome of measurements in the view of static observer, which is dependent on the mass of the black hole, the distance of observer from event horizon, and the mode frequency of quantum memory. To illustrate the generality of this paradigm, we relate the entropic uncertainty bound with other uncertainty probe, e.g., time-energy uncertainty. In an alternative game between two static players, we show that quantum information of qubit can be transferred to quantum memory through a bath of fluctuating quantum fields outside the black hole. For a particular choice of initial state, we show that the Hawking decoherence cannot counteract entanglement generation after the dynamical evolution of system, which triggers an effectively reduced uncertainty bound that violates the intrinsic limit $-\log_2c$. Numerically estimation for a proper choice of initial state shows that our result is comparable with possible real experiments. Finally, a discussion on the black hole firewall paradox in the context of entropic uncertainty relation is given., 11 pages, 2figures. Minor typos corrected, references and comment on the black hole firewall added. Matches the version to appear in Physics Letters B

We present (exact) solutions of the Dirac equation with equally mixed interactions for a single fermion bounded by the family of fractional power singular potentials. Closed-form expressions as well as numerical values for the energies were obtained. The wave functions and the allowed values of the potential parameters for the first two members of the family are obtained in terms of a set of algebraic equations. The non relativistic limit is also discussed and using the Hellmann-Feynmann theorem, some useful expectation values are obtained., 15 Pages, 16 Figures, 2 Tables. In press JPA

We obtain the determinant representations of the scalar products for the XXZ Gaudin model with generic non-diagonal boundary terms., Latex file, 17 pages

The Drinfeld twists or factorizing F-matrices for the open XXZ spin chain with non-diagonal boundary terms are constructed. It is shown that in the F-basis the two sets of pseudo-particle creation operators simultaneously take completely symmetric and polarization free form. The explicit and completely symmetric expressions of the two sets of Bethe states of the model are obtained., Latex file, 25 pages

We present higher order polynomial algebras which are the dynamical symmetry algebras of a wide class of multi-mode boson systems in non-linear optics. We construct their unitary representations and the corresponding single-variable differential operator realizations. We then use the results to obtain exact (Bethe ansatz) solutions to the multi-mode boson systems, including the BEC models as special cases., LaTex 14 pages, no figure; Version 2, to appear in J. Phys. A: Math. Theor

We introduce higher order polynomial deformations of $A_1$ Lie algebra. We construct their unitary representations and the corresponding single-variable differential operator realizations. We then use the results to obtain exact (Bethe ansatz) solutions to a class of 2-mode boson systems, including the Boson-Einstein Condensate models as special cases. Up to an overall factor, the eigenfunctions of the 2-mode boson systems are given by polynomials whose roots are solutions of the associated Bethe ansatz equations. The corresponding eigenvalues are expressed in terms of these roots. We also establish the spectral equivalence between the BEC models and certain quasi-exactly solvable Sch\"ordinger potentials., Comment: 20 pages, final version to appear in J. Phys. A: Math. Theor.

We derive the recursive relations of the partition function for the eight-vertex model on an $N\times N$ square lattice with domain wall boundary condition. Solving the recursive relations, we obtain the explicit expression of the domain wall partition function of the model. In the trigonometric/rational limit, our results recover the corresponding ones for the six-vertex model., Latex file, 20 pages; V2, references added

We construct the free field representation of the affine currents, energy-momentum tensor and screening currents of the first kind of the current superalgebra $gl(m|n)_k$ uniformly for $m=n$ and $m\neq n$. The energy-momentum tensor is given by a linear combination of two Sugawara tensors associated with the two independent quadratic Casimir elements of $gl(m|n)$., Latex file, 15 pages

Bethe ansatz formulation is presented for several explicit examples of quasi exactly solvable difference equations of one degree of freedom which are introduced recently by one of the present authors. These equations are deformation of the well-known exactly solvable difference equations of the Meixner-Pollaczek, continuous Hahn, continuous dual Hahn, Wilson and Askey-Wilson polynomials. Up to an overall factor of the so-called pseudo ground state wavefunction, the eigenfunctions within the exactly solvable subspace are given by polynomials whose roots are solutions of the associated Bethe ansatz equations. The corresponding eigenvalues are expressed in terms of these roots.

The quiver Hopf algebras are classified by means of ramification systems with irreducible representations. This leads to the classification of Nichols algebras over group algebras and pointed Hopf algebras of type one., 19 pages; To appear in Bulletin of the Australian Mathematical Society

The multiple reference state structure of the $\Z_n$ Belavin model with non-diagonal boundary terms is discovered. It is found that there exist $n$ reference states, each of them yields a set of eigenvalues and Bethe Ansatz equations of the transfer matrix. These $n$ sets of eigenvalues together constitute the complete spectrum of the model. In the quasi-classic limit, they give the complete spectrum of the corresponding Gaudin model., Latex file, 24 pages

With the help of the factorizing $F$-matrix, the scalar products of the $U_q(gl(1|1))$ free fermion model are represented by determinants. By means of these results, we obtain the determinant representations of correlation functions of the model., Latex File, 20 pages, V.3: some discussions are added, V.4 Reference update, this version will appear in J. Math. Phys

The $A^{(1)}_{n-1}$ trigonometric vertex model with {\it generic non-diagonal} boundaries is studied. The double-row transfer matrix of the model is diagonalized by algebraic Bethe ansatz method in terms of the intertwiner and the corresponding face-vertex relation. The eigenvalues and the corresponding Bethe ansatz equations are obtained., Latex file, 25 pages; V2: minor typos corrected, the version appears in JHEP

We obtain a class of non-diagonal solutions of the reflection equation for the trigonometric $A^{(1)}_{n-1}$ vertex model. The solutions can be expressed in terms of intertwinner matrix and its inverse, which intertwine two trigonometric R-matrices. In addition to a {\it discrete} (positive integer) parameter $l$, $1\leq l\leq n$, the solution contains $n+2$ {\it continuous} boundary parameters., Latex file, 14 pages; V2, minor typos corrected and a reference added

The XXZ Gaudin model with {\it generic} integerable boundaries specified by generic {\it non-diagonal} K-matrices is studied. The commuting families of Gaudin operators are diagonalized by the algebraic Bethe ansatz method. The eigenvalues and the corresponding Bethe ansatz equations are obtained., Latex file, 17 pages;V2:minor typos corrected, references updated and a discussion added

Representations of the superalgebra $osp(2|2)$ and current superalgebra $osp(2|2)^{(1)}_k$ in the standard basis are investigated. All finite-dimensional typical and atypical representations of $osp(2|2)$ are constructed by the vector coherent state method. Primary fields of the non-unitary conformal field theory associated with $osp(2|2)^{(1)}_k$ in the standard basis are constructed for arbitrary level $k$., 12 pages, cosmetic changes, to appear in Phys. Lett. A

Braided m-Lie algebras induced by multiplication are introduced, which generalize Lie algebras, Lie color algebras and quantum Lie algebras. The necessary and sufficient conditions for the braided m-Lie algebras to be strict Jacobi braided Lie algebras are given. Two classes of braided m-Lie algebras are given, which are generalized matrix braided m-Lie algebras and braided m-Lie subalgebras of $End_F M$, where $M$ is a Yetter-Drinfeld module over $B$ with dim $B< \infty $ . In particular, generalized classical braided m-Lie algebras $sl_{q, f}(GM_G(A), F)$ and $osp_{q, t} (GM_G(A), M, F)$ of generalized matrix algebra $GM_G(A)$ are constructed and their connection with special generalized matrix Lie superalgebra $sl_{s, f}(GM_{{\bf Z}_2}(A^s), F)$ and orthosymplectic generalized matrix Lie super algebra $osp_{s, t} (GM_{{\bf Z}_2}(A^s), M^s, F)$ are established. The relationship between representations of braided m-Lie algebras and their associated algebras are established., 14 pages

Based on Haldane's spherical geometrical formalism of two-dimensional quantum Hall fluids, the relation between the noncommutative geometry of $S^2$ and the two-dimensional quantum Hall fluids is exhibited. If the number of particles $N$ is infinitely large, two-dimensional quantum Hall physics can be precisely described in terms of the noncommutative U(1) Chern-Simons theory proposed by Susskind, like in the case of plane. However, for the finite number of particles on two-sphere, the matrix-regularized version of noncommutative U(1) Chern-Simons theory involves in spinor oscillators. We establish explicitly such a finite matrix model on two-sphere as an effective description of fractional quantum Hall fluids of finite extent. The complete sets of physical quantum states of this matrix model are determined, and the properties of quantum Hall fluids related to them are discussed. We also describe how the low-lying excitations are constructed in terms of quasiparticle and quasihole excitations in the matrix model. It is shown that there consistently exists a Haldane's hierarchical structure of two-dimensional quantum Hall fluid states in the matrix model. These hierarchical fluid states are generated by the parent fluid state for particles by condensing the quasiparticle and quasihole excitations level by level, without any requirement of modifications of the matrix model., LaTex file, 19 pages

Motivated by application of current superalgebras in the study of disordered systems such as the random XY and Dirac models, we investigate $gl(2|2)$ current superalgebra at general level $k$. We construct its free field representation and corresponding Sugawara energy-momentum tensor in the non-standard basis. Three screen currents of the first kind are also presented., LaTex file 11 pages

We study the conformal field theories corresponding to current superalgebras $osp(2|2)^{(1)}_k$ and $osp(2|2)^{(2)}_k$. We construct the free field realizations, screen currents and primary fields of these current superalgebras at general level $k$. All the results for $osp(2|2)^{(2)}_k$ are new, and the results for the primary fields of $osp(2|2)^{(1)}_k$ also seem to be new. Our results are expected to be useful in the supersymmetric approach to Gaussian disordered systems such as random bond Ising model and Dirac model., LaTex file 20 pages; Title changed and modifications made

Supersymmetric t-J Gaudin models with both periodic and open boundary conditions are constructed and diagonalized by means of the algebraic Bethe ansatz method. Off-shell Bethe ansatz equations of the Gaudin systems are derived, and used to construct and solve the KZ equations associated with $sl(2|1)^{(1)}$ superalgebra., LaTex 21 pages

Motivated by applications of twisted current algebras in description of the entropy of $Ads_3$ black hole, we investigate the simplest twisted current algebra $sl(3,{\bf C})^{(2)}_k$. Free field representation of the twisted algebra and the corresponding twisted Sugawara energy-momentum tensor are obtained by using three $(\beta,\gamma)$ pairs and two scalar fields. Primary fields and two screening currents of the first kind are presented., Comment: LaTex file 12 pages; Final version for publication in Phys. Letts. B (a couple of typos on page 7 have been corrected in this version)

The q-deformed supersymmetric t-J model on a semi-infinite lattice is diagonalized by using the level-one vertex operators of the quantum affine superalgebra $U_q[\hat{sl(2|1)}]$. We give the bosonization of the boundary states. We give an integral expression of the correlation functions of the boundary model, and derive the difference equations which they satisfy., LaTex file 18 pages

We study the level-one irreducible highest weight representations of the quantum affine superalgebra $U_q[\hat{sl(N|1)}]$, and calculate their characters and supercharacters. We obtain bosonized q-vertex operators acting on the irreducible $U_q[\hat{sl(N|1)}]$-modules and derive the exchange relations satisfied by the vertex operators. We give the bosonization of the multi-component super $t-J$ model by using the bosonized vertex operators., LaTex file 21 pages

Bosonized q-vertex operators related to the 4-dimensional evaluation modules of the quantum affine superalgebra $U_q[\hat{sl(2|1)}]$ are constructed for arbitrary level $k=\alpha$, where $\alpha\neq 0, -1$ is a complex parameter appearing in the 4-dimensional evaluation representations. They are intertwiners among the level-$\alpha$ highest weight Fock-Wakimoto modules. Screen currents which commute with the action of $U_q[\hat{sl(2|1)}]$ up to total differences are presented. Integral formulae for N-point functions of type I and type II q-vertex operators are proposed., Comment: Latex file 18 pages

A class of integrable boundary terms for the eight-state supersymmtric $U$ model are presented by solving the graded reflection equations. The boundary model is solved by using the coordinate Bethe ansatz method and the Bethe ansatz equations are obtained., 5 pages, RevTex