Finite-time Convergent Gossiping

Gossip algorithms are widely used in modern distributed systems, with applications ranging from sensor networks and peer-to-peer networks to mobile vehicle networks and social networks. A tremendous research effort has been devoted to analyzing and improving the asymptotic rate of convergence for gossip algorithms. In this work we study finite-time convergence of deterministic gossiping. We show that there exists a symmetric gossip algorithm that converges in finite time if and only if the number of network nodes is a power of two, while there always exists an asymmetric gossip algorithm with finite-time convergence, independent of the number of nodes. For $n=2^m$ nodes, we prove that a fastest convergence can be reached in $nm=n\log_2 n$ node updates via symmetric gossiping. On the other hand, under asymmetric gossip among $n=2^m+r$ nodes with $0\leq r<2^m$, it takes at least $mn+2r$ node updates for achieving finite-time convergence. It is also shown that the existence of finite-time convergent gossiping often imposes strong structural requirements on the underlying interaction graph. Finally, we apply our results to gossip algorithms in quantum networks, where the goal is to control the state of a quantum system via pairwise interactions. We show that finite-time convergence is never possible for such systems.Comment: IEEE/ACM Transactions on Networking, In Pres

Hydraulic Model Study of Waller Creek Tunnel Project for the City of Austin, Texas

This report provides the results of a series of model tests designed to understand the fluid dynamics involved with the Waller Creek Tunnel.Waller Creek is centrally located within the City of Austin, Texas, and has one of the most densely developed watersheds in the locality. The main stem is approximately seven miles in length and generally flows from north to south. The total drainage area for Waller Creek is 5.74 square miles (3700 acres) and the watershed lies entirely within the jurisdictional boundaries of the City of Austin and Travis County as shown in Figure 1 and Figure 2. Flood impacts to development adjacent to the creek have been a concern since the area was developed in the 1950’s. Central Texas (including the City of Austin) is prone to flooding, especially in creeks with highly impervious watersheds. The Waller Creek Tunnel Project (WCTP) will reduce the threat of flood damages to existing infrastructure and development, along the Lower Reach of Waller Creek. In addition to flood control, the proposed design will improve water quality, create ecological benefits, mitigate erosion problems, and provide safety to individuals and businesses located in the downtown Austin Waller Creek area. At the request of Crespo Consulting Service Inc., Austin, Texas (Crespo), Alden Research Laboratory (Alden) conducted a hydraulic model study using Computational Fluid Dynamics (CFD) and physical model studies for the proposed WCTP for the City of Austin, Texas. The objective of the study included evaluation of the flow patterns approaching and in the various hydraulic structures. Additionally, the model study was used to: Establish a rating curve for the morning glory spillway, Evaluate the potential air entrainment in the tunnel and the need for any air bleed structures, Establish junction loss coefficients for the 4th Street and 8th Street lateral junctions, Determine the fluctuating pressures due to flow induced excitations at the tunnel portal to the recirculation pump intake when the valve is closed and, Obtain a rating curve for the outlet spillway/weir. Inlet CFD Model -A CFD model of the inlet at Waterloo Park was used to design and evaluate the approach channel geometry, training wall and bar screens. The intake structure is comprised of a morning glory type inlet and includes six bar screen type trash racks which remove a portion of any debris before entering the vertical drop shaft and the underground tunnel. A training wall was designed to improve flow distribution approaching the structure. Model results show that 80% of the bar screen area has a velocity of less than 4 ft/s. The maximum velocity at any location on the screens is less than 5.5 ft/s. To address concerns that debris may accumulate along the training wall, modifications were made to fill in the backside of the barbs (the barbs were developed as part of the design to improve flow distribution and conditions at the screens). With the modifications the model results show that two screens did not have 80% of the bar screen area velocities of less than 4 ft/s and one screen exceeded the 50 % flow variation from the target flow. The final alternative was evaluated in the physical model. Lateral Junction CFD Models - Lateral junctions at 4th Street and 8th Street were evaluated using CFD models. The models were used to simulate flow conditions where the lateral flow is relatively large and the main conduit flow is relatively small. This condition results in the largest impact of the lateral junctions on the main conduit flow. Model results showed that the lateral junctions are not predicted to cause significant flow separations in the main conduit and cavitation potential is small. Outlet CFD Model -A CFD model of the outlet structure was used to design the riser shaft from the tunnel to the surface, and a flip bucket at the toe of the spillway. Based on the CFD model results, Outlet connection 2 as shown in Figure 17 was selected. The final structure design, based on CFD results, shows uniform flow distribution over the spillway. The flip bucket at the toe of the dam decreased the water velocity near the bed of the discharge channel as compared to a no flip bucket condition. Water velocity near the end of the spillway with the 2.25 ft high flip bucket is not predicted to erode the spillway apron. Inlet/Tunnel/Lateral Junctions/Outlet Physical Model - A 1:33 scale model of the Inlet, Tunnel, Lateral Junctions and Outlet of the Waller Creek Tunnel Project was constructed at Alden. The design flow for the model to simulate the friction losses and the expected Hydraulic Gradient Line (HGL) along the tunnel corresponded to the 100 year flood flow. The rating curves for the inlet spillway and outlet weir and the closed conduit flow loss coefficients for tunnel junctions were obtained from the model by testing a range of flows, as they were not affected by the tunnel HGL. Upon initial model start up, air entrainment at the morning glory vertical shaft was observed. The measured average Volume Fraction of air (VFa) in the model was about 5% for 25 year flow and 4% for the 100 year flow. Maximum Volume Fraction of air (VFa) in the model for the 25 year and 100 year flows were 8% and 6%, respectively. The volume fractions obtained from the model data could be corrected for any scale effects on generation of air entrainment using correction factors available in the literature. Also, as the Volume Fraction of air, VFa, can be a function of pressure and temperature, corrections need to be applied taking into account the expected pressure (from HGL calculations) and temperature in the field. The morning glory rating curve (Figure 64) was established in the physical model using inlet flows for the 2, 5, 10, 25, 50, 100 and 500 peak tunnel/ peak intervening events. During the 500 year event the morning glory spillway was submerged and an air drawing free-surface vortex was observed however it should be noted that 1) the building operations deck, which could interfere with vortex formation, was not included in the model and 2) the emergency spillway was not modeled which would result in lower water levels for the 500 yr event. Data was also recorded for two additional flows to determine the point at which the inlet weir becomes drowned out (approximately at a flow of 9,950 cfs at EL 483.2 ft water level). For the 100 year peak inlet flow condition (8,247 cfs) the average HGL was increased in the inlet shaft to above the morning glory crest elevation (474.0 ft) to elevations 478.2 and 479.7 ft to determine any effect on the inlet rating curve. For these submerged conditions, no change in the head on the morning glory spillway was observed. Therefore, the inlet rating curve is hydraulically disconnected from the inlet shaft tailwater up to at least 479.9 ft. Testing was conducted to determine any fluctuating pressures due to flow induced excitations at the tunnel portal to the recirculation pump intake when the valve is closed using the 100 year peak tunnel/ peak intervening condition. A plot of the prototype pressure versus time fluctuation referenced to EL 427 ft is included in Figure 65. The predicted maximum, minimum and average pressures were 16.9, 15.5 and 13.4 psi, respectively. This range of fluctuating pressure was not of concern to the JV in terms of design criteria for the valve. Tests were conducted using the model to determine the Minor Losses and corresponding junction Loss Coefficients at the 8th Street and 4th Street lateral junctions and the tunnel (tees combining main flow in the tunnel with flow from side inlet weir branch). Results indicating the Loss Coefficients determined from the model for the 100 year flood for both Peak Tunnel-Peak Intervening and Lagging Tunnel-Peak Intervening are shown below: 100 yr Peak Tunnel-Peak Int. 100 yr Lagging Tunnel-Peak Int. Loss Coefficient 8th St. 4th St. 8th St. 4th St. Tunnel: K2-3 0.3 0.2 0.3 0.3 Branch: K1-3 -0.6 -0.7 -0.4 -0.4 The branch loss coefficients (K1-3) are negative due to transfer of energy from the through flow in the tunnel to the flow from the branch as the branch flow is only about 10% or so of the tunnel flow. The outlet spillway rating curve was also established in the physical model using inlet flows for the 2, 5, 10, 25, 50, 100 and 500 year peak tunnel/ peak intervening events. The outlet spillway rating curve is shown in Figure 70.Waller Creek Working Grou

Alloying effect on the ideal tensile strength of ferromagnetic and paramagnetic bcc iron

Using \emph{ab initio} alloy theory formulated within the exact muffin-tin orbitals theory in combination with the coherent potential approximation, we investigate the ideal tensile strength (ITS) in the $[001]$ direction of bcc ferro-/ferrimagnetic (FFM) and paramagnetic (PM) Fe$_{1-x}M_{x}$ ($M=$ Al, V, Cr, Mn, Co, or Ni) random alloys. The ITS of ferromagnetic (FM) Fe is calculated to be $12.6$\,GPa, in agreement with available data, while the PM phase turns out to posses a significantly lower value of $0.7\,$GPa. Alloyed to the FM matrix, we predict that V, Cr, and Co increase the ITS of Fe, while Al and Ni decrease it. Manganese yields a weak non-monotonic alloying behavior. In comparison to FM Fe, the alloying effect of Al and Co to PM Fe is reversed and the relative magnitude of the ITS can be altered more strongly for any of the solutes. All considered binaries are intrinsically brittle and fail by cleavage of the $(001)$ planes under uniaxial tensile loading in both magnetic phases. We show that the previously established ITS model based on structural energy differences proves successful in the PM Fe-alloys but is of limited use in the case of the FFM Fe-based alloys. The different performance is attributed to the specific interplay between magnetism and volume change in response to uniaxial tension. We establish a strong correlation between the compositional effect on the ITS and the one on the shear elastic constant $C'$ for the PM alloys and briefly discuss the relation between hardenability and the ITS.Comment: 6 figure

Remote State Estimation with Smart Sensors over Markov Fading Channels

We consider a fundamental remote state estimation problem of discrete-time linear time-invariant (LTI) systems. A smart sensor forwards its local state estimate to a remote estimator over a time-correlated $M$-state Markov fading channel, where the packet drop probability is time-varying and depends on the current fading channel state. We establish a necessary and sufficient condition for mean-square stability of the remote estimation error covariance as $\rho^2(\mathbf{A})\rho(\mathbf{DM})<1$, where $\rho(\cdot)$ denotes the spectral radius, $\mathbf{A}$ is the state transition matrix of the LTI system, $\mathbf{D}$ is a diagonal matrix containing the packet drop probabilities in different channel states, and $\mathbf{M}$ is the transition probability matrix of the Markov channel states. To derive this result, we propose a novel estimation-cycle based approach, and provide new element-wise bounds of matrix powers. The stability condition is verified by numerical results, and is shown more effective than existing sufficient conditions in the literature. We observe that the stability region in terms of the packet drop probabilities in different channel states can either be convex or concave depending on the transition probability matrix $\mathbf{M}$. Our numerical results suggest that the stability conditions for remote estimation may coincide for setups with a smart sensor and with a conventional one (which sends raw measurements to the remote estimator), though the smart sensor setup achieves a better estimation performance.Comment: The paper has been accepted by IEEE Transactions on Automatic Control. Copyright may be transferred without notice, after which this version may no longer be accessibl

Multi-armed Bandit Learning on a Graph

The multi-armed bandit(MAB) problem is a simple yet powerful framework that has been extensively studied in the context of decision-making under uncertainty. In many real-world applications, such as robotic applications, selecting an arm corresponds to a physical action that constrains the choices of the next available arms (actions). Motivated by this, we study an extension of MAB called the graph bandit, where an agent travels over a graph trying to maximize the reward collected from different nodes. The graph defines the freedom of the agent in selecting the next available nodes at each step. We assume the graph structure is fully available, but the reward distributions are unknown. Built upon an offline graph-based planning algorithm and the principle of optimism, we design an online learning algorithm that balances long-term exploration-exploitation using the principle of optimism. We show that our proposed algorithm achieves $O(|S|\sqrt{T}\log(T)+D|S|\log T)$ learning regret, where $|S|$ is the number of nodes and $D$ is the diameter of the graph, which is superior compared to the best-known reinforcement learning algorithms under similar settings. Numerical experiments confirm that our algorithm outperforms several benchmarks. Finally, we present a synthetic robotic application modeled by the graph bandit framework, where a robot moves on a network of rural/suburban locations to provide high-speed internet access using our proposed algorithm