Emergence of Lie group symmetric classical spacetimes in canonical tensor model

We analyze a wave function of a tensor model in the canonical formalism, when the argument of the wave function takes Lie group invariant or nearby values. Numerical computations show that there are two phases, which we call the quantum and the classical phases, respectively. In the classical phase, fluctuations are suppressed, and there emerge configurations which are discretizations of the classical geometric spaces invariant under the Lie group symmetries. This is explicitly demonstrated for the emergence of $S^n\ (n=1,2,3)$for$SO(n+1)$ symmetries by checking the topological and the geometric (Laplacian) properties of the emerging configurations. The transition between the two phases has the form of splitting/merging of distributions of variables, resembling a matrix model counterpart, namely, the transition between one-cut and two-cut solutions. However this resemblance is obscured by a difference of the mechanism of the distribution in our setup from that in the matrix model. We also discuss this transition as a replica symmetry breaking. We perform various preliminary studies of the properties of the phases and the transition for such values of the argument.Comment: 32 pages, 17 figure

Canonical tensor model through data analysis -- Dimensions, topologies, and geometries --

The canonical tensor model (CTM) is a tensor model in Hamilton formalism and is studied as a model for gravity in both classical and quantum frameworks. Its dynamical variables are a canonical conjugate pair of real symmetric three-index tensors, and a question in this model was how to extract spacetime pictures from the tensors. We give such an extraction procedure by using two techniques widely known in data analysis. One is the tensor-rank (or CP, etc.) decomposition, which is a certain generalization of the singular value decomposition of a matrix and decomposes a tensor into a number of vectors. By regarding the vectors as points forming a space, topological properties can be extracted by using the other data analysis technique called persistent homology, and geometries by virtual diffusion processes over points. Thus, time evolutions of the tensors in the CTM can be interpreted as topological and geometric evolutions of spaces. We have performed some initial investigations of the classical equation of motion of the CTM in terms of these techniques for a homogeneous fuzzy circle and homogeneous two- and three-dimensional fuzzy spheres as spaces, and have obtained agreement with the general relativistic system obtained previously in a formal continuum limit of the CTM. It is also demonstrated by some concrete examples that the procedure is general for any dimensions and topologies, showing the generality of the CTM.Comment: 44 pages, 16 figures, minor correction

Unruptured Saccular Aneurysm Arising from the Fenestrated A1 Segment of the Anterior Cerebral Artery: Report of 2 Cases

Some cases of aneurysms originating from the fenestrated A1 segment of the anterior cerebral artery (ACA) have been reported, but the pitfalls of the surgical procedure have not been well determined. We herein report 2 cases of a saccular aneurysm arising from the fenestrated A1 segment. Case 1 was a 72-year-old man incidentally diagnosed with an unruptured left ACA aneurysm on magnetic resonance imaging (MRI). Cerebral angiography revealed a saccular aneurysm arising from the proximal end of the left A1 segment. He underwent surgical clipping via the left pterional approach. The aneurysm originated from the proximal bifurcation of the fenestrated left A1 segment. A fenestrated ring clip was applied to obliterate the aneurysmal neck and one small fenestrated trunk, preserving the other fenestrated trunk and perforators around the fenestration. Case 2 was a 73-year-old man incidentally diagnosed with an unruptured ACA aneurysm on MRI. Cerebral angiography revealed a saccular aneurysm arising from the proximal end of the fenestrated left A1 segment. He underwent surgical clipping via the interhemispheric approach. The aneurysm originated from the proximal bifurcation of the fenestrated left A1 segment. A fenestrated ring clip was applied to obliterate the aneurysmal neck and one hypoplastic fenestrated trunk, preserving the other fenestrated trunk and perforators around the aneurysm. Detailed intraoperative evaluations of the anatomical structure and hemodynamics around the fenestration are important. The intentional obliteration of a fenestrated trunk and application of fenestrated clips need to be considered in difficult cases in order to expose the aneurysmal neck

Improvement of the target sensitivity in DECIGO by optimizing its parameters for quantum noise including the effect of diffraction loss

DECIGO is the future Japanese gravitational wave detector in outer space. We previously set the default design parameters to provide a good target sensitivity to detect the primordial gravitational waves (GWs). However, the updated upper limit of the primordial GWs by the Planck observations motivated us for further optimization of the target sensitivity. Previously, we had not considered optical diffraction loss due to the very long cavity length. In this paper, we optimize various DECIGO parameters by maximizing the signal-to-noise ratio (SNR), for the primordial GWs to quantum noise including the effects of diffraction loss. We evaluated the power spectrum density for one cluster in DECIGO utilizing the quantum noise of one differential Fabry-Perot interferometer. Then we calculated the SNR by correlating two clusters in the same position. We performed the optimization for two cases: the constant mirror-thickness case and the constant mirror-mass case. As a result, we obtained the SNR dependence on the mirror radius, which also determines various DECIGO parameters. This result is the first step toward optimizing the DECIGO design by considering the practical constraints on the mirror dimension and implementing other noise sources.Comment: 13 pages, 12 figure

Loud calls in male crested macaques, Macaca nigra: a signal of dominance in a tolerant species

Compared to other mammals, sexual signals occur particularly often within the primate order. Nevertheless, little is known so far about the pressures under which these signals evolved. We studied loud calls in wild crested macaques to examine whether these are used as a sexual signal, particularly as a signal of dominance, in this species. Since the structure of loud calls may be influenced by the context in which they are uttered, we tested for contextual differences in call structure. Only males uttered loud calls and analysis of 194 loud calls given by 15 males showed that call structure encoded the caller's identity as well as his social status. Dominance rank was also reflected in the frequency with which males called with alpha males calling most often. The structure of loud calls, however, was not influenced by context. Our findings consolidate the assumption that, in crested macaques, loud calls serve as a signal of dominance, most probably used to prevent contests between males for mates. We herewith provide the first direct evidence for a signal of dominance in a tolerant primate species and discuss why this signal occurs in only one sex

Current status of space gravitational wave antenna DECIGO and B-DECIGO

Deci-hertz Interferometer Gravitational Wave Observatory (DECIGO) is the future Japanese space mission with a frequency band of 0.1 Hz to 10 Hz. DECIGO aims at the detection of primordial gravitational waves, which could be produced during the inflationary period right after the birth of the universe. There are many other scientific objectives of DECIGO, including the direct measurement of the acceleration of the expansion of the universe, and reliable and accurate predictions of the timing and locations of neutron star/black hole binary coalescences. DECIGO consists of four clusters of observatories placed in the heliocentric orbit. Each cluster consists of three spacecraft, which form three Fabry-Perot Michelson interferometers with an arm length of 1,000 km. Three clusters of DECIGO will be placed far from each other, and the fourth cluster will be placed in the same position as one of the three clusters to obtain the correlation signals for the detection of the primordial gravitational waves. We plan to launch B-DECIGO, which is a scientific pathfinder of DECIGO, before DECIGO in the 2030s to demonstrate the technologies required for DECIGO, as well as to obtain fruitful scientific results to further expand the multi-messenger astronomy.Comment: 10 pages, 3 figure