Airport departure operations constitute an important source of airline delays and passenger frustration. Excessive surface traffic is the cause of increased controller and pilot workload; It is also the source of increased emissions; It worsens traffic safety and often does not yield improved runway throughput. Acknowledging this fact, this paper explores some of the feedback mechanisms by whic...

We study the Price of Anarchy (PoA) of the competitive cascade game following the framework proposed by Goyal and Kearns in [11]. Our main insight is that a reduction to a Linear Threshold Model in a time-expanded graph establishes the submodularity of the social utility function. From this observation, we deduce that the game is a valid utility game, which in turn implies an upper bound of 2 o...

A linear threshold element computes a function that is a sign of a weighted sum of the input variables. The best known lower bounds on the size of threshold circuits are for depth-2 circuits with small (polynomial-size) weights. However, in general, the weights are arbitrary integers and can be of exponential size in the number of input variables. Namely, obtaining progress in lower bounds for ...

In this paper, we consider a biologically-inspired Boolean function P D that models a simple task of detecting global spatial patterns on a twodimensional map. We prove that P D is computable by a threshold circuit of size (i.e., number of gates) O( √ n logn), which is an improvement on the previous upper bound O(n), while our circuit has larger depth O( √ n) and total wire length O(n log n). M...

Optimal stopping problems require people to choose from a sequence of values, under the constraint that they cannot return to an earlier option once it is rejected. We study how people solve optimal stopping problems when the distribution of values they must choose from is not uniform, but is constructed to contain many high values or many low values. We present empirical evidence that people a...

We find the threshold between avoidable and unavoidable repetitions in circular words over k letters for any k > 6. Namely, we show that the number CRT(k) = ⌈k/2⌉+1 ⌈k/2⌉ satisfies the following properties. For any n there exists a k-ary circular word of length n containing no repetition of exponent greater than CRT(k). On the other hand, k-ary circular words of some lengths must have a repetit...

An integer polynomial p of n variables is called a threshold gate for a Boolean function f of n variables if for all x ∈ {0, 1} f(x) = 1 if and only if p(x) > 0. The weight of a threshold gate is the sum of its absolute values. In this paper we study how large a weight might be needed if we fix some function and some threshold degree. We prove 2 ) lower bound on this value. The best previous bo...

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In 1987-2001 unemployment and inßation have the opposite inßuences on the popularities of Finnish and Swedish leftist and rightist parties. The popularities of the Finnish right-wing (left-wing) parties decrease (increase) when unemployment and inßation increase but in Sweden the opposite happens although the countries experience simultaneously an economic crisis. Fitting a threshold model in t...

We investigate opinion spreading by a threshold model in a situation in which the influence of people is heterogeneously distributed. We assume that there is a coupling between the influence of an individual (measured by the out-degree) and the threshold for accepting a new opinion or habit. We find that if the coupling is strongly positive, the final state of the system will be a mix of differ...