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In this paper, we propose a regional dynamic traffic assignment framework for macroscopic fundamental diagram (MFD) models that explicitly accounts for trip length distributions. The proposed framework considers stochasticity on both the trip lengths and the regional mean speed. Consequently, we can define utility functions to assess the cost on alternatives, depending on which terms are considered stochastic. We propose a numerical resolution scheme based on Monte Carlo simulations and use the method of successive averages to solve the network equilibrium. Based on our test scenarios, we show that the variability of trip lengths inside the regions cannot be neglected. Moreover, it is also important to consider the stochasticity on the regional mean speeds to account for correlation between regional paths. We also discuss an implementation of the proposed dynamic traffic assignment framework on the sixth district of the Lyon network, where trip lengths are explicitly calculated. The traffic states are modeled by considering the accumulation-based MFD model. The results highlight the influence of the variability of trip lengths on the predicted traffic states.

A critical challenge in neuromorphic computing is to present computationally efficient algorithms of learning. When implementing gradient-based learning, error information must be routed through the network, such that each neuron knows its contribution to output, and thus how to adjust its weight. This is known as the credit assignment problem. Exactly implementing a solution like backpropagation involves weight sharing, which requires additional bandwidth and computations in a neuromorphic system. Instead, models of learning from neuroscience can provide inspiration for how to communicate error information efficiently, without weight sharing. Here we present a novel dendritic event-based processing (DEP) algorithm, using a two-compartment leaky integrate-and-fire neuron with partially segregated dendrites that effectively solves the credit assignment problem. In order to optimize the proposed algorithm, a dynamic fixed-point representation method and piecewise linear approximation approach are presented, while the synaptic events are binarized during learning. The presented optimization makes the proposed DEP algorithm very suitable for implementation in digital or mixed-signal neuromorphic hardware. The experimental results show that spiking representations can rapidly learn, achieving high performance by using the proposed DEP algorithm. We find the learning capability is affected by the degree of dendritic segregation, and the form of synaptic feedback connections. This study provides a bridge between the biological learning and neuromorphic learning, and is meaningful for the real-time applications in the field of artificial intelligence.

Let $f:2^X \\rightarrow \\cal R_+$ be a monotone submodular set function, and let $(X,\\cal I)$ be a matroid. We consider the problem ${\\rm max}_{S \\in \\cal I} f(S)$. It is known that the greedy algorithm yields a $1/2$-approximation [M. L. Fisher, G. L. Nemhauser, and L. A. Wolsey, Math. Programming Stud., no. 8 (1978), pp. 73-87] for this problem. For certain special cases, e.g., ${\\rm max}_{|S| \\leq k} f(S)$, the greedy algorithm yields a $(1-1/e)$-approximation. It is known that this is optimal both in the value oracle model (where the only access to f is through a black box returning $f(S)$ for a given set S) [G. L. Nemhauser and L. A. Wolsey, Math. Oper. Res., 3 (1978), pp. 177-188] and for explicitly posed instances assuming $P \\neq NP$ [U. Feige, J. ACM, 45 (1998), pp. 634-652]. In this paper, we provide a randomized $(1-1/e)$-approximation for any monotone submodular function and an arbitrary matroid. The algorithm works in the value oracle model. Our main tools are a variant of the pipage rounding technique of Ageev and Sviridenko [J. Combin. Optim., 8 (2004), pp. 307-328], and a continuous greedy process that may be of independent interest. As a special case, our algorithm implies an optimal approximation for the submodular welfare problem in the value oracle model [J. Vondrák, Proceedings of the $38$th ACM Symposium on Theory of Computing, 2008, pp. 67-74]. As a second application, we show that the generalized assignment problem (GAP) is also a special case; although the reduction requires $|X|$ to be exponential in the original problem size, we are able to achieve a $(1-1/e-o(1))$-approximation for GAP, simplifying previously known algorithms. Additionally, the reduction enables us to obtain approximation algorithms for variants of GAP with more general constraints. [PUBLICATION ABSTRACT]

Minimization with orthogonality constraints (e.g., ) and/or spherical constraints (e.g., ) has wide applications in polynomial optimization, combinatorial optimization, eigenvalue problems, sparse PCA, p-harmonic flows, 1-bit compressive sensing, matrix rank minimization, etc. These problems are difficult because the constraints are not only non-convex but numerically expensive to preserve during iterations. To deal with these difficulties, we apply the Cayley transform—a Crank-Nicolson-like update scheme—to preserve the constraints and based on it, develop curvilinear search algorithms with lower flops compared to those based on projections and geodesics. The efficiency of the proposed algorithms is demonstrated on a variety of test problems. In particular, for the maxcut problem, it exactly solves a decomposition formulation for the SDP relaxation. For polynomial optimization, nearest correlation matrix estimation and extreme eigenvalue problems, the proposed algorithms run very fast and return solutions no worse than those from their state-of-the-art algorithms. For the quadratic assignment problem, a gap 0.842 % to the best known solution on the largest problem “tai256c” in QAPLIB can be reached in 5 min on a typical laptop.

The engagement of a group of autonomous air vehicles against several targets is a major challenge in mission planning. This paper addresses the problem of cooperative flight path planning where the air vehicles should arrive at the destinations simultaneously or sequentially with specified time delays, while minimizing the total mission time. This involves finding an optimal assignment of air vehicles to targets and generating trajectories in compliance with the kinematic constraints of the vehicles. The trajectories have to avoid nofly-areas, threats and other obstacles, and must prevent the air vehicles from colliding with each other. The presented algorithm for simultaneous arrival first calculates shortest flight paths between all pairs of air vehicles and targets using a network-based routing model. An optimal assignment and a critical path is found by solving a linear bottleneck assignment problem with costs corresponding to the lengths of the shortest paths. The other flight paths are prolongated to the length of the critical path by automatic insertion of waypoints. This is achieved by concatenating subpaths stored in different shortest-path-trees. Due to the special structure of the network, all concatenated flight paths are flyable and feasible. Sequential arrival at a target is realized by sorting the flight paths according to their lengths and prolongating them whenever necessary to accomplish the desired time delays. The capability of the approach is demonstrated by simulation results.

Wireless communication supports various real-world applications, such as aeronautical navigation, satellite and TV broadcasting, wireless LANs, and mobile communications. The inherent characteristics of the electromagnetic spectrum impose constraints on telecommunication channels and their frequency bandwidths within mobile networks. A persistent challenge in these applications is providing high-demand services to mobile users, where frequency assignment problems, also known as channel assignment problems, assume significance. Researchers have developed several modeling approaches to address different facets of this problem, including the management of interfering radio signals, the assessment of available frequencies, and optimization criteria. In this paper, we present improved algorithms for solving the Minimum Span Frequency Assignment Problem in mobile communication systems using the greedy optimization approach known as F/DR. We solved and evaluated twenty well-known benchmark cases to assess the efficacy of our algorithms. Our findings consistently demonstrate that the modified algorithms outperform the F/DR approach with comparable computational complexity. The proposed algorithm notably achieves the following benchmarks: The modified algorithms consistently produce at least one local optimum better than the traditional algorithm in all benchmark tests. In 95% of the benchmarks evaluated, the probability of discovering a local optimum value (calculated by the modified algorithm) that is better than or equal to the one found by the conventional algorithm exceeds 50%.

Several school districts use assignment systems that give students an incentive to misrepresent their preferences. We find evidence consistent with strategic behavior in Cambridge. Such strategizing can complicate preference analysis. This paper develops empirical methods for studying random utility models in a new and large class of school choice mechanisms. We show that preferences are nonparametrically identified under either sufficient variation in choice environments or a preference shifter. We then develop a tractable estimation procedure and apply it to Cambridge. Estimates suggest that while 83% of students are assigned to their stated first choice, only 72% are assigned to their true first choice because students avoid ranking competitive schools. Assuming that students behave optimally, the Immediate Acceptance mechanism is preferred by the average student to the Deferred Acceptance mechanism by an equivalent of 0.08 miles. The estimated difference is smaller if beliefs are biased, and reversed if students report preferences truthfully.

Causal effects are defined as comparisons of potential outcomes under different treatments on a common set of units. Observed values of the potential outcomes are revealed by the assignment mechanism-a probabilistic model for the treatment each unit receives as a function of covariates and potential outcomes. Fisher made tremendous contributions to causal inference through his work on the design of randomized experiments, but the potential outcomes perspective applies to other complex experiments and nonrandomized studies as well. As noted by Kempthorne in his 1976 discussion of Savage's Fisher lecture, Fisher never bridged his work on experimental design and his work on parametric modeling, a bridge that appears nearly automatic with an appropriate view of the potential outcomes framework, where the potential outcomes and covariates are given a Bayesian distribution to complete the model specification. Also, this framework crisply separates scientific inference for causal effects and decisions based on such inference, a distinction evident in Fisher's discussion of tests of significance versus tests in an accept/reject framework. But Fisher never used the potential outcomes framework, originally proposed by Neyman in the context of randomized experiments, and as a result he provided generally flawed advice concerning the use of the analysis of covariance to adjust for posttreatment concomitants in randomized trials.

Administrative structure can shape bureaucratic process, performance, and responsiveness and is a particularly important consideration when new bureaucratic functions and programs are being established. However, the factors that influence the assignment of these functions to specific government agencies or departments are understudied, particularly at the local level. The absence of empirical evidence regarding bureaucratic assignment in local government limits understanding of institutional design and the organizational choices available, particularly as they relate to specific policy areas. As an initial step in developing a theory of agency assignment at the local level, we examine the placement of sustainability programs in 401 US cities and assess explanations for assignment based on policy scope, interest group support, governmental capacity, policy characteristics, and institutional structures that shape the incentives of local decision makers. Although it is not a traditional function of local government, sustainability is becoming an increasingly common objective. Because of its newness and cross-cutting nature, local policy makers have an array of institutional units to which they can assign the primary responsibility for sustainability. We focus on two dimensions of assignment of bureaucratic responsibility: whether the locus of responsibility lies within the executive or a line department and whether there is a specialized unit within the city government that is explicitly responsible for sustainability. The scope and maturity of cities' sustainability policies and the structure of local representation (i.e., whether council representatives are elected by district, at-large, or via a mixed system) have the greatest influence on shaping administrative placement. The latter suggests potential distributive outcomes from local sustainability efforts.