Symmetric Path Research Articles

Finitely Repeated Voluntary Provision of a Public Good

This paper theoretically explores the voluntary provision of a public good in a finitely repeated setting. Agents' utility is the sum of their monetary earnings and a non-material psychological component that can be interpreted as a taste for efficiency and/or fairness. An arbitrarily small degree of such non-material payoffs can generate large contributions in the repeated game, even if the incentive to free-ride on others' contributions calls for negligible public good provision in the static game. The payoff dominant symmetric perfect equilibrium path is characterized by a sharp decline in contributions toward the end of the game. Several comparative results regarding group size and technology are consistent with laboratory data obtained by Isaac and Walker (1988) and Isaac et al. (1994). The model also predicts the puzzling restart effect observed by Andreoni (1988) in an experimental study. It is therefore possible to reconcile previous experimental observations with fully rational behavior, using only mild assumptions on preferences and the standard tools of repeated games.

A Switched-Capacitor DC–DC Converter With High Voltage Gain and Reduced Component Rating and Count

This paper proposes a bidirectional switched-capacitor dc-dc converter for applications that require high voltage gain. Some of conventional switched-capacitor dc-dc converters have diverse voltage or current stresses for the switching devices in the circuit, not suitable for modular configuration or for high efficiency demand; some suffer from relatively high power loss or large device count for high voltage gain, even if the device voltage stress could be low. By contrast, the proposed dc-dc converter features low component (switching device and capacitor) power rating, small switching device count, and low output capacitance requirement. In addition to its low current stress, the combination of two short symmetric paths of charge pumps further lowers power loss. Therefore, a small and light converter with high voltage gain and high efficiency can be achieved. Simulation and experimental results of a 450-W prototype with a voltage conversion ratio of six validate the principle and features of this topology.

Relativistic potential energy surfaces of initial oxidations of Si(100) by atomic oxygen: The importance of surface dimer triplet state

The non-relativistic and relativistic potential energy surfaces (PESs) of the symmetric and asymmetric reaction paths of Si(100)-2×1 oxidations by atomic oxygen were theoretically explored. Although only the singlet PES turned out to exist as a major channel leading to "on-dimer" product, both the singlet and triplet PESs leading to "on-top" products are attractive. The singlet PESs leading to the two surface products were found to be the singlet combinations (open-shell singlet) of the low-lying triplet state of surface silicon dimer and the ground (3)P state of atomic oxygen. The triplet state of the "on-top" product can also be formed by the ground singlet state of the surface silicon dimer and the same (3)P oxygen. The attractive singlet PESs leading to the "on-dimer" and "on-top" products made neither the intersystem crossings from triplet to singlet PES nor high energy (1)D of atomic oxygen necessary. Rather, the low-lying triplet state of surface silicon dimer plays an important role in the initial oxidations of silicon surface.

Performance Metrics of Multipath State Aware Concurrent Multipath Transfer using Redundant Transfer in Stream Control Transmission Protocol Multihoming for Symmetric Paths

Problem statement: In multihomed host, if data transfer starts using CMT, unaware of paths status causes delay in data transfer or packet loss due to path failure. Transmission Path (one or more paths) failures result in out-of-order data delivery causing receiver buffer blocking and preventing sender from transmitting further data. Approach: Multipath State Aware Concurrent Multipath Transfer using Redundant Transfer (MSACMT-RT), status of multipath is determined, initially and periodically before transmission. Data transfer begins immediately after determining the path status, for a particular interval of time and later transfers with CMT only for predefined period. Results: We discuss MSACMT-RT performance in symmetric paths with the constrained receiver buffer (rbuf) value of 128 and 256KB’s. Our simulation result shows Percentage of throughput Increase between 5-15% for transfer of 20 and 40MB file sizes. Conclusion: By using MSACMT-RT we infer that our algorithm outperforms on par or better but never worse than Concurrent Multipath Transfer Potentially Failed (CMT-PF). MSACMT-RT mechanism in alternate paths increases the throughput during aggressive failures and Non-failure scenarios. Larger the file sizes of file transfer, greater the degree of throughput with less transfer time is achieved.

LDU decomposition of an extension matrix of the Pascal matrix

Let Ω m , n ( α , β , γ ) denote a set of all elements of weighted lattice paths with weight ( α , β , γ ) in the xy-plane from ( 0 , 0 ) to ( m , n ) such that a vertical step V = ( 0 , 1 ) , a horizontal step H = ( 1 , 0 ) , and a diagonal step D = ( 1 , 1 ) are endowed with weights α , β , and γ respectively and let ω ( Ω m , n ( α , β , γ ) ) denote the weight of Ω m , n ( α , β , γ ) defined by ω ( Ω m , n ( α , β , γ ) ) = ∑ p ∈ Ω m , n ( α , β , γ ) ega ( p ) where ω ( p ) is the product of the weights of all its steps in p . A matrix A = [ a ij ] is called a lattice path matrix with weight ( α , β , γ ) if a ij = ω ( Ω i , j ( α , β , γ ) ) for a triple α , β , and γ of real numbers . In this paper, we present LDU decomposition of lattice path matrices with weight ( α , β , γ ) and related properties for every triple α , β , and γ of real numbers, and a necessary and sufficient condition in which the symmetric lattice path matrices are positive definite. We also investigate the relationship between the lattice path matrices and generalized Pascal matrices.

Traffic grooming in bidirectional WDM ring networks

AbstractWe study the minimization of ADMs (Add‐Drop Multiplexers) in optical WDM bidirectional rings considering symmetric shortest path routing and all‐to‐all unitary requests. We precisely formulate the problem in terms of graph decompositions, and state a general lower bound for all the values of the grooming factor C and N, the size of the ring. We first study exhaustively the cases C = 1, C = 2, and C = 3, providing improved lower bounds, optimal constructions for several infinite families, as well as asymptotically optimal constructions and approximations. We then study the case C > 3, focusing specifically on the case C = k(k + 1)/2 for some k ≥ 1. We give optimal decompositions for several congruence classes of N using the existence of some combinatorial designs. We conclude with a comparison of the cost functions in unidirectional and bidirectional WDM rings. © 2010 Wiley Periodicals, Inc. NETWORKS, Vol. 58(1), 20–35 2011

Breaking Path Symmetries on 4-Connected Grid Maps

Pathfinding systems that operate on regular grids are common in the AI literature and often used in real-time video games. Typical speed-up enhancements include reducing the size of the search space using abstraction, and building more informed heuristics. Though effective each of these strategies has shortcomings. For example, pathfinding with abstraction usually involves trading away optimality for speed. Meanwhile, improving on the accuracy of the well known Manhattan heuristic usually requires significant extra memorWe present a different kind of speedup technique based on the idea of identifying and eliminating symmetric path segments in 4-connected grid maps (which allow straight but not diagonal movement). Our method identifies rectangular rooms with no obstacles and prunes all interior nodes, leaving only a boundary perimeter. This process eliminates many symmetric path segments and results in grid maps which are often much smaller and consequently much faster to search than the original. We evaluate our technique on a range of different grid maps including a well known set from the popular video game Baldur's Gate II. On our test data, A* can run up to 3.5 times faster on average. We achieve this without using any significant extra memory or sacrificing solution optimality.

Design Considerations For Pulsed-Flow Comprehensive Two-Dimensional GC: Dynamic Flow Model Approach

A dynamic flow model, which maps carrier gas pressures and carrier gas flow rates through the first dimension separation column, the modulator sample loop, and the second dimension separation column(s) in a pulsed-flow modulation comprehensive two-dimensional gas chromatography (PFM-GCxGC) system is described. The dynamic flow model assists design of a PFM-GCxGC modulator and leads to rapid determination of pneumatic conditions, timing parameters, and the dimensions of the separation columns and connecting tubing used to construct the PFM-GCxGC system. Three significant innovations are introduced in this manuscript, which were all uncovered by using the dynamic flow model. A symmetric flow path modulator improves baseline stability, appropriate selection of the flow restrictors in the first dimension column assembly provides a generally more stable and robust system, and these restrictors increase the modulation period flexibility of the PFM-GCxGC system. The flexibility of a PFM-GCxGC system resulting from these innovations is illustrated using the same modulation interface to analyze Special Antarctic Blend (SAB) diesel using 3 s and 9 s modulation periods.

Smooth partitions and Chebyshev polynomials

A partition of the set [n]={1, 2, …, n} is a collection {B1, …, Bk} of nonempty disjoint subsets of [n] (called blocks) whose union equals [n]. A partition of [n] is said to be smooth if i ∈ Bs implies that i + 1 ∈ Bs−1 ∪ Bs ∪ Bs+1 for all i ∈ [n − 1] (B0 = Bk + 1 = ∅). This paper presents the generating function for the number of k-block, smooth partitions of [n], written in terms of Chebyshev polynomials of the second kind. There follows a formula for the number of k-block, smooth partitions of [n] written in terms of trigonometric sums. Also, by first establishing a bijection between the set of smooth partitions of [n] and a class of symmetric Dyck paths of semilength 2n − 1, we prove that the counting sequence for smooth partitions of [n] is Sloane's A005773.

Identification and inversion of converted shear waves: case studies from the European North Atlantic continental margins

Wide-angle shear wave arrivals, converted from compressional to shear waves at crustal interfaces, enable crustal Vp/Vs ratios to be determined which provide valuable constraint on geological interpretations. Analysis of the converted shear wave phases represents the next logical step in characterizing the crustal structure and composition following multichannel seismic structural imaging and tomographic inversion of the wide-angle compressional wave phases. In this offshore study across two passive margins extending from stretched continental to fully oceanic crust, the high-data density (2–10 km ocean bottom seismometer, OBS, spacing) and a consistent, efficient conversion interface produced shear wave data sets suitable for traveltime inversion. The shear waves were recorded by three orthogonal geophones in each OBS. Arrival phases, visible to 180 km offset, were identified using their arrival times, moveout velocities and particle motions. Across the North Atlantic volcanic rifted continental margins studied, breakup was accompanied by the eruption of large volumes of basalts of the North Atlantic Igneous Province. The interface between post-volcanic sediments and the top of the basalts provides the dominant conversion boundary across the oceanic crust and the continent—ocean transition. However, the shear wave data quality was significantly diminished at the continental ends of the profiles where the thick basalt flows and hence this conversion interface feathers out and crustal attenuation increases. Initial modelling of the converted shear wave phases was carried out using a layer-based approach with arrivals converted on the way up used to constrain the Vp/Vs ratio of the post-volcanic sedimentary sequence beneath each OBS. To produce a model with continuous crustal S-wave velocities, the compressional wave velocities beneath the sediment-top basalt interface were transformed into starting shear wave velocities using a constant value of Vp/Vs and the inversion carried out by specifying the appropriate ray path. Once the data set had been fully interpreted, correction of the traveltimes to effective symmetric ray paths enabled us to apply a regularized grid inversion. Such inversions are less subjective than the layer-based approach and yield more robust minimum structure results with quantifiable errors, except in the vicinity of a known subbasalt low-velocity zone encountered on the Faroes margin. Monte Carlo analyses were performed for this approach; the average model from multiple inversions using randomized starting models and traveltimes shows the structure required by the traveltimes and the model standard deviation gives an estimate of uncertainty. Model and inversion parametrizations were fully tested and optimum parameters chosen for compressional and shear wave inversions. This allows, after appropriate model smoothing, an estimate to be made of the spatial variation of the Vp/Vs ratio within the crust. There are marked gradients in Vp, Vs and Vp/Vs ratio across the continent—ocean transition, which may result from intrusion of high magnesium mafic igneous material into the crystalline continental crust. The Vp/Vs ratio, used in conjunction with Vp, also provides constraints on the subbasalt lithologies forming the low-velocity zone. We conclude from such an analysis that this zone is unlikely to be composed entirely of igneous hyaloclastite material; some proportion of clastic sedimentary rocks is likely to be present. The Vp/Vs and Vp properties of the units underlying the low-velocity zone are inconsistent with crystalline continental basement and this unit is likely to represent a sill-intruded Mesozoic sedimentary sequence from a pre-breakup sedimentary basin.

Bargaining with nonanonymous disagreement: Monotonic rules

We analyze bargaining situations where the agents' payoffs from disagreement depend on who among them breaks down the negotiations. We model such problems as a superset of the standard domain of Nash [Nash, J.F., 1950. The bargaining problem. Econometrica 18, 155–162]. On our extended domain, we analyze the implications of two central properties which, on the Nash domain, are known to be incompatible: strong monotonicity [Kalai, E., 1977. Proportional solutions to bargaining situations: Interpersonal utility comparisons. Econometrica 45, 1623–1630] and scale invariance [Nash, J.F., 1950. The bargaining problem. Econometrica 18, 155–162]. We first show that a class of monotone path rules uniquely satisfy strong monotonicity, scale invariance, weak Pareto optimality, and “continuity”. We also show that dropping scale invariance from this list characterizes the whole class of monotone path rules. We then introduce a symmetric monotone path rule that we call the Cardinal Egalitarian rule and show that it is weakly Pareto optimal, strongly monotonic, scale invariant, symmetric and that it is the only rule to satisfy these properties on a class of two-agent problems.

FISSION OF SUPER-HEAVY NUCLEI EXPLORED WITH SKYRME FORCES

We present a large scale survey of life-times for spontaneous fission in the regime of super-heavy elements (SHE), i.e. nuclei with Z =104-122. This is done on the basis of the Skyrme-Hartree-Fock model. The axially symmetric fission path is computed using a quadrupole constraint. Self-consistent cranking is used for the collective masses and associated quantum corrections. The actual tunneling probability is estimated by the WKB approximation. Three typical Skyrme forces are used to explore the sensitivity of the results. Benchmarks in the regime Z =104-108 show an acceptable agreement. The general systematics reflects nicely the islands of shell stabilization and the crossover from α-decay to fission for the decay chains from the region of Z / N =118/176.

Design of Grip-and-Move Manipulators Using Symmetric Path Generating Compliant Mechanisms

This paper presents the problem formulation and design of compliant grip-and-move manipulators. Each manipulator is composed of two identical path generating compliant mechanisms such that it can grip an object and convey it from one point to another. The integration of both gripping and moving behaviors within a simple mechanism is accomplished by the use of compliant mechanisms, which generate paths that are symmetric. The automated synthesis of these symmetric path generating mechanisms is by a structural topology optimization approach. The problem of topology optimization of continuum structures is solved using a multiobjective genetic algorithm coupled with a morphological representation of geometry that efficiently defines the variable structural geometry upon a finite element grid. A graph-theoretic chromosome encoding together with compatible crossover and mutation operators are then applied to form an effective evolutionary optimization procedure. Two designs have been created and are presented in this paper, and some concluding remarks and future work are put forward.

Relative Morse index and multiple brake orbits of asymptotically linear Hamiltonian systems in the presence of symmetries

In this paper, we define a relative Morse index for two continuous symmetric matrices paths in R 2 n satisfying condition (B1) and study its relation with the Maslov-type indices under brake orbit boundary value of these two symmetric matrices paths. As applications, using this relation we obtain a multiple existence of periodic brake orbit solutions of asymptotically linear Hamiltonian system in the presence of symmetries.

Existence and minimizing properties of retrograde orbits to the three-body problem with various choices of masses

Poincare made the first attempt in 1896 on applying variational calculus to the three-body problem and observed that collision orbits do not necessarily have higher values of action than classical solutions. Little progress had been made on resolving this difficulty until a recent breakthrough by Chenciner and Montgomery. Afterward, variational methods were successfully applied to the JV-body problem to construct new classes of solutions. In order to avoid collisions, the problem is confined to symmetric path spaces and all new planar solutions were constructed under the assumption that some masses are equal. A question for the variational approach on planar problems naturally arises: Are minimizing methods useful only when some masses are identical? This article addresses this question for the three-body problem. For various choices of masses, it is proved that there exist infinitely many solutions with a certain topological type, called retrograde orbits, that minimize the action functional on certain path spaces. Cases covered in our work include triple stars in retrograde motions, double stars with one outer planet, and some double stars with one planet orbiting around one primary mass. Our results largely complement the classical results by the Poincare continuation method and Conley's geometric approach.

Conditions for symmetric, antisymmetric, and zero-stiffness bifurcation in view of imperfection sensitivity and insensitivity

In general, it is not clear how to design structures such that they are ab initio imperfection insensitive, i.e., without modifications of the original design after the diagnosis of imperfection sensitivity. Symmetry and antisymmetry of bifurcation paths, representing qualitative properties of a structure, not only simplify the postbuckling analysis, but also have an influence on the behavior of real, i.e., imperfect structures. The special case of a zero-stiffness postbuckling path incorporates both, symmetry and antisymmetry. Mathematical definitions of the three categories symmetric, antisymmetric, and zero-stiffness equilibrium paths are given. It is shown that symmetry as well as antisymmetry causes the vanishing of specific coefficients in an asymptotic series expansion, following from Koiter’s initial postbuckling analysis. Thereupon, methods of checking for the three categories of bifurcation behavior are discussed. Finally, the three categories are investigated in terms of necessary and/or sufficient conditions for imperfection insensitivity. For instance, a horizontal tangent of the postbuckling path at the bifurcation point is required for imperfection insensitivity. Four examples illustrate non-symmetric, symmetric, and antisymmetric bifurcation as well as zero-stiffness postbuckling behavior. For the first two examples, the approach of increasing the stiffness results in the conversion of the system from imperfection sensitivity into insensitivity. Remarkably, this happens without changing the prebuckling behavior and the buckling load of the structure. The third example demonstrates that imperfection sensitivity is an inevitable implication of antisymmetric bifurcation.

Performance analysis of multi-homed transport protocols with network failure tolerance

The performance of multi-homed transport protocols tolerant of network failure is studied. It evaluates the performance of different retransmission policies combined with path failure detection thresholds, infinite or finite receive buffers for various path bandwidths, delays and loss rate conditions through stream control transmission protocol simulation. The results show that retransmission policies perform differently with different path failure detection threshold configurations. It identifies that retransmission of all data on an alternate path with the path failure detection threshold set to zero performs the best in symmetric path conditions but its performance degrades acutely in asymmetric path conditions even when the alternate path delay is shorter than the primary path delay. It illustrates that retransmission of all data on the same path with the path failure detection threshold set to one or zero gives the most stable performance in all path configurations.

Postbuckling behavior of symmetrically laminated thin shallow circular arches

Abstract The large deflection behavior of a symmetrically laminated thin shallow circular arch subjected to a central concentrated load is studied using the Rayleigh–Ritz finite element method. The shape functions used in the finite element method maintain C1-continuity of the radial displacement (deflection) and C0-continuity of the tangential displacement, respectively. The nonlinear algebraic equations of equilibrium are solved to a high degree of accuracy using Taylor’s expansion technique in conjunction with the Newton–Raphson method. Nonlinear stability analysis provides accurate solutions for the symmetric and antisymmetric buckling of both pin-ended and fixed shallow arches. The stability of the symmetric deformation path is investigated for both pinned and fixed arches, and a detailed analysis is carried out at the point of bifurcation onto an asymmetric deformation path for a pinned symmetrically laminated shallow arch. The slope of this post-buckled path is also computed, and is shown to be accurate for deformations well beyond the point of bifurcation.

Statistics of Illuminated Sea Wave Crests as Observed Over Symmetric Radio Paths at Small Grazing Angles

Statistics of Illuminated Sea Wave Crests as Observed Over Symmetric Radio Paths at Small Grazing Angles

Current-mode variable-frequency control architecture for high-current low-voltage DC–DC converters [Letters

For controlling high-current low-voltage dc–dc converters, the control methods with variable switching frequency have the potential to achieve fast transient response and high efficiency. However, some issues in practical design limit the usefulness of the conventional variable-frequency control methods, such as the voltage-mode hysteretic control. This letter presents a novel implementation of current-mode variable-frequency control. The system architecture features a dual-loop feedback and a unique structure with symmetric signal paths for voltage and current signals. The symmetric structure provides practical advantages for integrated controller design to achieve accurate control on the droop resistance (or the load-line resistance). The system dynamics are analyzed with the small-signal model. Design guidelines are derived for simple compensation circuits to achieve constant output impedance. With variable switching frequency, the system achieves good dynamic response without requiring high switching frequency at steady-state. The system performance was verified by a two-channel interleaved controller chip implemented with CMOS technology.