Factorizing a String into Squares in Linear Time

A square factorization of a string w is a factorization of w in which each factor is a square. Dumitran et al. [SPIRE 2015, pp. 54-66] showed how to find a square factorization of a given string of length n in O(n log n) time, and they posed a question whether it can be done in O(n) time. In this paper, we answer their question positively, showing an O(n)-time algorithm for square factorization in the standard word RAM model with machine word size omega = Omega(log n). We also show an O(n + (n log^2 n) / omega)-time (respectively, O(n log n)-time) algorithm to find a square factorization which contains the maximum (respectively, minimum) number of squares

ベタヒスチンが一側内耳破壊後のラットの前庭代償に与える影響

Background: Vestibular compensation (VC) after unilateral labyrinthectomy (UL) consists of the initial and late processes. These processes can be evaluated based on the decline in the frequency of spontaneous nystagmus (SN) and the number of MK801-induced Fos-positive neurons in the contralateral medial vestibular nucleus (contra-MVe) in rats. Histamine H3 receptors (H3R) are reported to be involved in the development of VC. Objective: We examined the effects of betahistine, an H3R antagonist, on the initial and late processes of VC in UL rats. Methods: Betahistine dihydrochloride was continuously administered to the UL rats at doses of 100 and 200 mg/kg/day using an osmotic minipump. MK801 (1.0 mg/kg) was intraperitoneally administered on days 7, 10, 12, and 14 after UL, while Fos-positive neurons were immunohistochemically stained in the contra-MVe. Results: The SN disappeared after 42 h, and continuous infusion of betahistine did not change the decline in the frequency of SN. The number of MK801-induced Fos-positive neurons in contra-MVe significantly decreased on days 7, 10, and 12 after UL in a dose-dependent manner in the betahistine-treated rats, more so than in the saline-treated rats. Conclusion: These findings suggest that betahistine facilitated the late, but not the initial, process of VC in UL rats

Minor Contribution of Quasars to Ionizing Photon Budget at z~6: Update on Quasar Luminosity Function at the Faint-end with Subaru/Suprime-Cam

We constrain the quasar contribution to cosmic reionization based on our deep optical survey of z~6 quasars down to z_R=24.15 using Subaru/Suprime-Cam in three UKIDSS-DXS fields covering 6.5 deg^2. In Kashikawa et al. (2015), we select 17 quasar candidates and report our initial discovery of two low-luminosity quasars (M_1450~ -23) from seven targets, one of which might be a Lyman alpha emitting galaxy. From an additional optical spectroscopy, none of the four candidates out of the remaining ten turn out to be genuine quasars. Moreover, the deeper optical photometry provided by the Hyper Suprime-Cam Subaru Strategic Program (HSC-SSP) shows that, unlike the two already-known quasars, the i-z and z-y colors of the last six candidates are consistent with M- or L-type brown dwarfs. Therefore, the quasar luminosity function (QLF) in the previous paper is confirmed. Compiling QLF measurements from the literature over a wide magnitude range, including an extremely faint AGN candidate from Parsa et al. (2017}, to fit them with a double power-law, we find that the best-fit faint-end slope is alpha=-2.04^+0.33_-0.18 (-1.98^+0.48_-0.21) and characteristic magnitude is M_1450^*=-25.8^+1.1_-1.9 (-25.7^+1.0_-1.8) in the case of two (one) quasar detection. Our result suggests that, if the QLF is integrated down to M_1450=-18, quasars produce ~1-12% of the ionizing photons required to ionize the whole universe at z~6 with 2sigma confidence level, assuming that the escape fraction is f_esc=1 and the IGM clumpy factor is C=3. Even when the systematic uncertainties are taken into account, our result supports the scenario that quasars are the minor contributors of reionization.Comment: 8 pages, 3 figures, ApJL accepte