The infimum, supremum and geodesic length of a braid conjugacy class

Algorithmic solutions to the conjugacy problem in the braid groups B_n were given by Elrifai-Morton in 1994 and by the authors in 1998. Both solutions yield two conjugacy class invariants which are known as `inf' and `sup'. A problem which was left unsolved in both papers was the number m of times one must `cycle' (resp. `decycle') in order to increase inf (resp. decrease sup) or to be sure that it is already maximal (resp. minimal) for the given conjugacy class. Our main result is to prove that m is bounded above by n-2 in the situation of the second algorithm and by ((n^2-n)/2)-1 in the situation of the first. As a corollary, we show that the computation of inf and sup is polynomial in both word length and braid index, in both algorithms. The integers inf and sup determine (but are not determined by) the shortest geodesic length for elements in a conjugacy class, as defined by Charney, and so we also obtain a polynomial-time algorithm for computing this geodesic length.Comment: 15 pages. Journa

Deep Learning Framework for Wireless Systems: Applications to Optical Wireless Communications

Optical wireless communication (OWC) is a promising technology for future wireless communications owing to its potentials for cost-effective network deployment and high data rate. There are several implementation issues in the OWC which have not been encountered in radio frequency wireless communications. First, practical OWC transmitters need an illumination control on color, intensity, and luminance, etc., which poses complicated modulation design challenges. Furthermore, signal-dependent properties of optical channels raise non-trivial challenges both in modulation and demodulation of the optical signals. To tackle such difficulties, deep learning (DL) technologies can be applied for optical wireless transceiver design. This article addresses recent efforts on DL-based OWC system designs. A DL framework for emerging image sensor communication is proposed and its feasibility is verified by simulation. Finally, technical challenges and implementation issues for the DL-based optical wireless technology are discussed.Comment: To appear in IEEE Communications Magazine, Special Issue on Applications of Artificial Intelligence in Wireless Communication

Particle-in-cell and weak turbulence simulations of plasma emission

The plasma emission process, which is the mechanism for solar type II and type III radio bursts phenomena, is studied by means of particle-in-cell and weak turbulence simulation methods. By plasma emission, it is meant as a loose description of a series of processes, starting from the solar flare associated electron beam exciting Langmuir and ion-acoustic turbulence, and subsequent partial conversion of beam energy into the radiation energy by nonlinear processes. Particle-in-cell (PIC) simulation is rigorous but the method is computationally intense, and it is difficult to diagnose the results. Numerical solution of equations of weak turbulence (WT) theory, termed WT simulation, on the other hand, is efficient and naturally lends itself to diagnostics since various terms in the equation can be turned on or off. Nevertheless, WT theory is based upon a number of assumptions. It is, therefore, desirable to compare the two methods, which is carried out for the first time in the present paper with numerical solutions of the complete set of equations of the WT theory and with two-dimensional electromagnetic PIC simulation. Upon making quantitative comparisons it is found that WT theory is largely valid, although some discrepancies are also found. The present study also indicates that it requires large computational resources in order to accurately simulate the radiation emission processes, especially for low electron beam speeds. Findings from the present paper thus imply that both methods may be useful for the study of solar radio emissions as they are complementary.Comment: 21 pages, 9 figure

Optimal Remote Qubit Teleportation Using Node2vec

Much research work is done on implementing quantum teleportation and entanglement swapping for remote entanglement. Due to dynamical topological changes in quantum networks, nodes have to construct the shortest paths every time they want to communicate with a remote neighbour. But due to the entanglement failures remote entanglement establishment is still a challenging task. Also as the nodes know only about their neighbouring nodes computing optimal paths between source and remote nodes is time consuming too. In finding the next best neighbour in the optimal path between a given source and remote nodes so as to decrease the entanglement cost, deep learning techniques can be applied. In this paper we defined throughput of the quantum network as the maximum qubits transmitted with minimum entanglement cost. Much of research work is done to improve the throughput of the quantum network using the deep learning techniques. In this paper we adopted deep learning techniques for implementing remote entanglement between two non-neighbour nodes using remote qubit teleportation and entanglement swapping. The proposed method called Optimal Remote Qubit Teleportation outperforms the throughput obtained by the state of art approach

Children’s Use of Geometry for Reorientation

Research on navigation has shown that humans and laboratory animals recover their sense of orientation primarily by detecting geometric properties of large-scale surface layouts (e.g. room shape), but the reasons for the primacy of layout geometry have not been clarified. In four experiments, we tested whether 4-year-old children reorient by the geometry of extended wall-like surfaces because such surfaces are large and perceived as stable, because they serve as barriers to vision or to locomotion, or because they form a single, connected geometric figure. Disoriented children successfully reoriented by the shape of an arena formed by surfaces that were short enough to see and step over. In contrast, children failed to reorient by the shape of an arena defined by large and stable columns or by connected lines on the floor. We conclude that preschool children's reorientation is not guided by the functional relevance of the immediate environmental properties, but rather by a specific sensitivity to the geometric properties of the extended three-dimensional surface layout.Psycholog

A Modular Geometric Mechanism for Reorientation in Children

Although disoriented young children reorient themselves in relation to the shape of the surrounding surface layout, cognitive accounts of this ability vary. The present paper tests three theories of reorientation: a snapshot theory based on visual image-matching computations, an adaptive combination theory proposing that diverse environmental cues to orientation are weighted according to their experienced reliability, and a modular theory centering on encapsulated computations of the shape of the extended surface layout. Seven experiments test these theories by manipulating four properties of objects placed within a cylindrical space: their size, motion, dimensionality, and distance from the space’s borders. Their findings support the modular theory and suggest that disoriented search behavior centers on two processes: a reorientation process based on the geometry of the 3D surface layout, and a beacon-guidance process based on the local features of objects and surface markings.Psycholog

Histamine and Histamine H4 Receptor Promotes Osteoclastogenesis in Rheumatoid Arthritis.

Histamine H4 receptor (H4R) has immune-modulatory and chemotaxic effects in various immune cells. This study aimed to determine the osteoclastogenic role of H4R in rheumatoid arthritis (RA). The concentration of histamine in synovial fluid (SF) and sera in patients with RA was measured using ELISA. After RA SF and peripheral blood (PB) CD14+ monocytes were treated with histamine, IL-17, IL-21 and IL-22, and a H4R antagonist (JNJ7777120), the gene expression H4R and RANKL was determined by real-time PCR. Osteoclastogenesis was assessed by counting TRAP-positive multinucleated cells in PB CD14+ monocytes cultured with histamine, Th17 cytokines and JNJ7777120. SF and serum concentration of histamine was higher in RA, compared with osteoarthritis and healthy controls. The expression of H4R was increased in PB monocytes in RA patients. Histamine, IL-6, IL-17, IL-21 and IL-22 induced the expression of H4R in monocytes. Histamine, IL-17, and IL-22 stimulated RANKL expression in RA monocytes and JNJ7777120 reduced the RANKL expression. Histamine and Th17 cytokines induced the osteoclast differentiation from monocytes and JNJ7777120 decreased the osteoclastogenesis. H4R mediates RANKL expression and osteoclast differentiation induced by histamine and Th17 cytokines. The blockage of H4R could be a new therapeutic modality for prevention of bone destruction in RA

Start-Up Success Factors Perceived as Important by USA and Korean Consultants

This study evaluates the determinants for  the start-up process  of successful  businesses in the USA and Korea. In particular, this study focuses on  the personal background of the consultants for start-up businesses from the two countries. How consultants perceive the determinants for start-up and the different factors between the two countries are examined

Deep Learning for Distributed Optimization: Applications to Wireless Resource Management

This paper studies a deep learning (DL) framework to solve distributed non-convex constrained optimizations in wireless networks where multiple computing nodes, interconnected via backhaul links, desire to determine an efficient assignment of their states based on local observations. Two different configurations are considered: First, an infinite-capacity backhaul enables nodes to communicate in a lossless way, thereby obtaining the solution by centralized computations. Second, a practical finite-capacity backhaul leads to the deployment of distributed solvers equipped along with quantizers for communication through capacity-limited backhaul. The distributed nature and the nonconvexity of the optimizations render the identification of the solution unwieldy. To handle them, deep neural networks (DNNs) are introduced to approximate an unknown computation for the solution accurately. In consequence, the original problems are transformed to training tasks of the DNNs subject to non-convex constraints where existing DL libraries fail to extend straightforwardly. A constrained training strategy is developed based on the primal-dual method. For distributed implementation, a novel binarization technique at the output layer is developed for quantization at each node. Our proposed distributed DL framework is examined in various network configurations of wireless resource management. Numerical results verify the effectiveness of our proposed approach over existing optimization techniques.Comment: to appear in IEEE J. Sel. Areas Commu

Learning Autonomy in Management of Wireless Random Networks

This paper presents a machine learning strategy that tackles a distributed optimization task in a wireless network with an arbitrary number of randomly interconnected nodes. Individual nodes decide their optimal states with distributed coordination among other nodes through randomly varying backhaul links. This poses a technical challenge in distributed universal optimization policy robust to a random topology of the wireless network, which has not been properly addressed by conventional deep neural networks (DNNs) with rigid structural configurations. We develop a flexible DNN formalism termed distributed message-passing neural network (DMPNN) with forward and backward computations independent of the network topology. A key enabler of this approach is an iterative message-sharing strategy through arbitrarily connected backhaul links. The DMPNN provides a convergent solution for iterative coordination by learning numerous random backhaul interactions. The DMPNN is investigated for various configurations of the power control in wireless networks, and intensive numerical results prove its universality and viability over conventional optimization and DNN approaches.Comment: to appear in IEEE TW