Partner orbits and action differences on compact factors of the hyperbolic plane. Part I: Sieber-Richter pairs

Physicists have argued that periodic orbit bunching leads to universal spectral fluctuations for chaotic quantum systems. To establish a more detailed mathematical understanding of this fact, it is first necessary to look more closely at the classical side of the problem and determine orbit pairs consisting of orbits which have similar actions. In this paper we specialize to the geodesic flow on compact factors of the hyperbolic plane as a classical chaotic system. We prove the existence of a periodic partner orbit for a given periodic orbit which has a small-angle self-crossing in configuration space which is a `2-encounter'; such configurations are called `Sieber-Richter pairs' in the physics literature. Furthermore, we derive an estimate for the action difference of the partners. In the second part of this paper [13], an inductive argument is provided to deal with higher-order encounters.Comment: to appear on Nonlinearit

Estradiol, Progesterone, and Transforming Growth Factor α Regulate Insulin-Like Growth Factor Binding Protein-3 (IGFBP3) Expression in Mouse Endometrial Cells

Insulin-like growth factor 1 (IGF1) Is Involved in the proliferation of mouse and rat endometrial cells in a paracrine or autocrine manner. Insulin-like growth factor binding protein-3 (IGFBP3) modulates actions of IGFs directly or indirectly. The present study aimed to determine whether IGFBP3 is Involved In the regulation of proliferation of mouse endometrial cells. Mouse endometrial epithelial cells and stromal cells were isolated, and cultured In a serum free medium. IGF1 stimulated DNA synthesis by endometrial epithelial and stromal cells, and IGFBP3 Inhibited IGF1-induced DNA synthesis. Estradiol-17 beta (E2) decreased the Igfbp3 mRNA level in endometrial stromal cells, whereas It Increased the Igf1 mRNA level. Transforming growth factor alpha (TGF alpha) significantly decreased IGFBP3 expression at both the mRNA and secreted protein levels in endometrial stromal cells. Progesterone (134) did not affect the E2-induced down-regulation of Igfbp3 mRNA expression in endometrial stromal cells, although P4 alone increased Igfbp3 mRNA levels. The present findings suggest that in mouse endometrial stromal cells E2 enhances IGF1 action through enhancement of IGF1 synthesis and reduction of IGFBP3 synthesis, and that TGF alpha affects IGF1 actions through modulation of IGFBP3 levels

Spitzer 70 Micron Source Counts in GOODS-North

We present ultradeep Spitzer 70 μm observations of GOODS-North (Great Observatories Origins Deep Survey). For the first time, the turnover in the 70 μm Euclidean-normalized differential source counts is observed. We derive source counts down to a flux density of 1.2 mJy. From the measured source counts and fluctuation analysis, we estimate a power-law approximation of the faint 70 μm source counts of dN/dS ∝ S^−1.6, consistent with that observed for the faint 24 μm sources. An extrapolation of the 70 μm source counts to zero flux density implies a total extragalactic background light (EBL) of 7.4 ± 1.9 nW m^−2 sr^−1. The source counts above 1.2 mJy account for about 60% of the estimated EBL. From fluctuation analysis, we derive a photometric confusion level of σc = 0.30 ± 0.15 mJy (q = 5) for the Spitzer 70 μm band

Trabecular bone structure correlates with hand posture and use in hominoids

Bone is capable of adapting during life in response to stress. Therefore, variation in locomotor and manipulative behaviours across extant hominoids may be reflected in differences in trabecular bone structure. The hand is a promising region for trabecular analysis, as it is the direct contact between the individual and the environment and joint positions at peak loading vary amongst extant hominoids. Building upon traditional volume of interest-based analyses, we apply a whole-epiphysis analytical approach using high-resolution microtomographic scans of the hominoid third metacarpal to investigate whether trabecular structure reflects differences in hand posture and loading in knuckle-walking (Gorilla, Pan), suspensory (Pongo, Hylobates and Symphalangus) and manipulative (Homo) taxa. Additionally, a comparative phylogenetic method was used to analyse rates of evolutionary changes in trabecular parameters. Results demonstrate that trabecular bone volume distribution and regions of greatest stiffness (i.e., Young's modulus) correspond with predicted loading of the hand in each behavioural category. In suspensory and manipulative taxa, regions of high bone volume and greatest stiffness are concentrated on the palmar or distopalmar regions of the metacarpal head, whereas knuckle-walking taxa show greater bone volume and stiffness throughout the head, and particularly in the dorsal region; patterns that correspond with the highest predicted joint reaction forces. Trabecular structure in knuckle-walking taxa is characterised by high bone volume fraction and a high degree of anisotropy in contrast to the suspensory brachiators. Humans, in which the hand is used primarily for manipulation, have a low bone volume fraction and a variable degree of anisotropy. Finally, when trabecular parameters are mapped onto a molecular-based phylogeny, we show that the rates of change in trabecular structure vary across the hominoid clade. Our results support a link between inferred behaviour and trabecular structure in extant hominoids that can be informative for reconstructing behaviour in fossil primates

Unary Pushdown Automata and Straight-Line Programs

We consider decision problems for deterministic pushdown automata over a unary alphabet (udpda, for short). Udpda are a simple computation model that accept exactly the unary regular languages, but can be exponentially more succinct than finite-state automata. We complete the complexity landscape for udpda by showing that emptiness (and thus universality) is P-hard, equivalence and compressed membership problems are P-complete, and inclusion is coNP-complete. Our upper bounds are based on a translation theorem between udpda and straight-line programs over the binary alphabet (SLPs). We show that the characteristic sequence of any udpda can be represented as a pair of SLPs---one for the prefix, one for the lasso---that have size linear in the size of the udpda and can be computed in polynomial time. Hence, decision problems on udpda are reduced to decision problems on SLPs. Conversely, any SLP can be converted in logarithmic space into a udpda, and this forms the basis for our lower bound proofs. We show coNP-hardness of the ordered matching problem for SLPs, from which we derive coNP-hardness for inclusion. In addition, we complete the complexity landscape for unary nondeterministic pushdown automata by showing that the universality problem is $\Pi_2 \mathrm P$-hard, using a new class of integer expressions. Our techniques have applications beyond udpda. We show that our results imply $\Pi_2 \mathrm P$-completeness for a natural fragment of Presburger arithmetic and coNP lower bounds for compressed matching problems with one-character wildcards

Fuzzy controller for better tennis ball robot

This paper aims at designing a tennis ball robot as a training facility for tennis players. The robot is built with fuzzy controller which provides proper techniques for the players to gain practical experience as well as technical skills; thus, it can effectively serve the community and train athletes in the high-performance sport. It is found that it is more economically efficient by using the sensorless fuzzy control algorithm to replace the high-resolution optical encoders traditionally used in two main servo motors. From our simulation and practical experiment, the tennis ball robot can provide accurate speed and various directions as expected

Integer Vector Addition Systems with States

This paper studies reachability, coverability and inclusion problems for Integer Vector Addition Systems with States (ZVASS) and extensions and restrictions thereof. A ZVASS comprises a finite-state controller with a finite number of counters ranging over the integers. Although it is folklore that reachability in ZVASS is NP-complete, it turns out that despite their naturalness, from a complexity point of view this class has received little attention in the literature. We fill this gap by providing an in-depth analysis of the computational complexity of the aforementioned decision problems. Most interestingly, it turns out that while the addition of reset operations to ordinary VASS leads to undecidability and Ackermann-hardness of reachability and coverability, respectively, they can be added to ZVASS while retaining NP-completness of both coverability and reachability.Comment: 17 pages, 2 figure

Secrecy outage probability of a NOMA scheme and impact imperfect channel state information in underlay cooperative cognitive networks

Security performance and the impact of imperfect channel state information (CSI) in underlay cooperative cognitive networks (UCCN) is investigated in this paper. In the proposed scheme, relay R uses non-orthogonal multiple access (NOMA) technology to transfer messages e1, e2 from the source node S to User 1 (U1) and User 2 (U2), respectively. An eavesdropper (E) is also proposed to wiretap the messages of U1 and U2. The transmission’s security performance in the proposed system was analyzed and performed over Rayleigh fading channels. Through numerical analysis, the results showed that the proposed system’s secrecy performance became more efficient when the eavesdropper node E was farther away from the source node S and the intermediate cooperative relay R. The secrecy performance of U1 was also compared to the secrecy performance of U2. Finally, the simulation results matched the Monte Carlo simulations well