Massive Scaling Limit of beta-Deformed Matrix Model of Selberg Type

We consider a series of massive scaling limits m_1 -> infty, q -> 0, lim m_1 q = Lambda_{3} followed by m_4 -> infty, Lambda_{3} -> 0, lim m_4 Lambda_{3} = (Lambda_2)^2 of the beta-deformed matrix model of Selberg type (N_c=2, N_f=4) which reduce the number of flavours to N_f=3 and subsequently to N_f=2. This keeps the other parameters of the model finite, which include n=N_L and N=n+N_R, namely, the size of the matrix and the "filling fraction". Exploiting the method developed before, we generate instanton expansion with finite g_s, epsilon_{1,2} to check the Nekrasov coefficients (N_f =3,2 cases) to the lowest order. The limiting expressions provide integral representation of irregular conformal blocks which contains a 2d operator lim frac{1}{C(q)} : e^{(1/2) \alpha_1 \phi(0)}: (int_0^q dz : e^{b_E phi(z)}:)^n : e^{(1/2) alpha_2 phi(q)}: and is subsequently analytically continued.Comment: LaTeX, 21 pages; v2: a reference adde

Rational Design of Novel Anticancer Small-Molecule RNA m6A Demethylase ALKBH5 Inhibitors

The RNA 6-N-methyladenosine (m6A) demethylase ALKBH5 has been shown to be oncogenic in several cancer types, including leukemia and glioblastoma. We present here the target-tailored development and first evaluation of the antiproliferative effects of new ALKBH5 inhibitors. Two compounds, 2-[(1-hydroxy-2-oxo-2-phenylethyl)sulfanyl]acetic acid (3) and 4-{[(furan-2-yl)methyl]amino}-1,2-diazinane-3,6-dione (6), with IC50 values of 0.84 mu M and 1.79 mu M, respectively, were identified in high-throughput virtual screening of the library of 144 000 preselected compounds and subsequent verification of hits in an m6A antibody-based enzyme-linked immunosorbent assay (ELISA) enzyme inhibition assay. The effect of these compounds on the proliferation of selected target cancer cell lines was then measured. In the case of three leukemia cell lines (HL-60, CCRF-CEM, and K562) the cell proliferation was suppressed at low micromolar concentrations of inhibitors, with IC50 ranging from 1.38 to 16.5 mu M. However, the effect was low or negligible in the case of another leukemia cell line, Jurkat, and the glioblastoma cell line A-172. These results demonstrate the potential of ALKBH5 inhibition as a cancer-cell-type-selective antiproliferative strategy.Peer reviewe

Random matrix theory, the exceptional Lie groups, and L-functions

There has recently been interest in relating properties of matrices drawn at random from the classical compact groups to statistical characteristics of number-theoretical L-functions. One example is the relationship conjectured to hold between the value distributions of the characteristic polynomials of such matrices and value distributions within families of L-functions. These connections are here extended to non-classical groups. We focus on an explicit example: the exceptional Lie group G_2. The value distributions for characteristic polynomials associated with the 7- and 14-dimensional representations of G_2, defined with respect to the uniform invariant (Haar) measure, are calculated using two of the Macdonald constant term identities. A one parameter family of L-functions over a finite field is described whose value distribution in the limit as the size of the finite field grows is related to that of the characteristic polynomials associated with the 7-dimensional representation of G_2. The random matrix calculations extend to all exceptional Lie groupsComment: 14 page

The nonrelativistic limit of the Magueijo-Smolin model of deformed special relativity

We study the nonrelativistic limit of the motion of a classical particle in a model of deformed special relativity and of the corresponding generalized Klein-Gordon and Dirac equations, and show that they reproduce nonrelativistic classical and quantum mechanics, respectively, although the rest mass of a particle no longer coincides with its inertial mass. This fact clarifies the meaning of the different definitions of velocity of a particle available in DSR literature. Moreover, the rest mass of particles and antiparticles differ, breaking the CPT invariance. This effect is close to observational limits and future experiments may give indications on its effective existence.Comment: 10 pages, plain TeX. Discussion of generalized Dirac equation and CPT violation adde

Wigner quantization of some one-dimensional Hamiltonians

Recently, several papers have been dedicated to the Wigner quantization of different Hamiltonians. In these examples, many interesting mathematical and physical properties have been shown. Among those we have the ubiquitous relation with Lie superalgebras and their representations. In this paper, we study two one-dimensional Hamiltonians for which the Wigner quantization is related with the orthosymplectic Lie superalgebra osp(1|2). One of them, the Hamiltonian H = xp, is popular due to its connection with the Riemann zeros, discovered by Berry and Keating on the one hand and Connes on the other. The Hamiltonian of the free particle, H_f = p^2/2, is the second Hamiltonian we will examine. Wigner quantization introduces an extra representation parameter for both of these Hamiltonians. Canonical quantization is recovered by restricting to a specific representation of the Lie superalgebra osp(1|2)

Quantum Limits of Eisenstein Series and Scattering states

We identify the quantum limits of scattering states for the modular surface. This is obtained through the study of quantum measures of non-holomorphic Eisenstein series away from the critical line. We provide a range of stability for the quantum unique ergodicity theorem of Luo and Sarnak.Comment: 12 pages, Corrects a typo and its ramification from previous versio

The trace of the heat kernel on a compact hyperbolic 3-orbifold

The heat coefficients related to the Laplace-Beltrami operator defined on the hyperbolic compact manifold H^3/\Ga are evaluated in the case in which the discrete group \Ga contains elliptic and hyperbolic elements. It is shown that while hyperbolic elements give only exponentially vanishing corrections to the trace of the heat kernel, elliptic elements modify all coefficients of the asymptotic expansion, but the Weyl term, which remains unchanged. Some physical consequences are briefly discussed in the examples.Comment: 11 page

The Partition Function of Multicomponent Log-Gases

We give an expression for the partition function of a one-dimensional log-gas comprised of particles of (possibly) different integer charge at inverse temperature {\beta} = 1 (restricted to the line in the presence of a neutralizing field) in terms of the Berezin integral of an associated non- homogeneous alternating tensor. This is the analog of the de Bruijn integral identities [3] (for {\beta} = 1 and {\beta} = 4) ensembles extended to multicomponent ensembles.Comment: 14 page

Periodic Orbits in Polygonal Billiards

We review some properties of periodic orbit families in polygonal billiards and discuss in particular a sum rule that they obey. In addition, we provide algorithms to determine periodic orbit families and present numerical results that shed new light on the proliferation law and its variation with the genus of the invariant surface. Finally, we deal with correlations in the length spectrum and find that long orbits display Poisson fluctuations.Comment: 30 pages (Latex) including 11 figure

Numerical Study of Length Spectra and Low-lying Eigenvalue Spectra of Compact Hyperbolic 3-manifolds

In this paper, we numerically investigate the length spectra and the low-lying eigenvalue spectra of the Laplace-Beltrami operator for a large number of small compact(closed) hyperbolic (CH) 3-manifolds. The first non-zero eigenvalues have been successfully computed using the periodic orbit sum method, which are compared with various geometric quantities such as volume, diameter and length of the shortest periodic geodesic of the manifolds. The deviation of low-lying eigenvalue spectra of manifolds converging to a cusped hyperbolic manifold from the asymptotic distribution has been measured by $\zeta-$ function and spectral distance.Comment: 19 pages, 18 EPS figures and 2 GIF figures (fig.10) Description of cusped manifolds in section 2 is correcte