Complex numbers are an intrinsic part of the mathematical formalism of quantum theory and are perhaps its most characteristic feature. In this article, we show that the complex nature of the quantum formalism can be derived directly from the assumption that a pair of real numbers is associated with each sequence of measurement outcomes, with the probability of this sequence being a real-valued ...

While the ALP may involve only a small number of variables, there is a potentially intractable number of constraints — one per state-action pair. As such, we cannot in general expect to solve the ALP exactly. The focus of this paper is on a tractable approximation to the ALP: the reduced linear program (RLP). Generation of an RLP relies on three objects: (1) a constraint sample size m, (2) a pr...

We investigate the all-pairs shortest paths problem in weighted graphs. We present an algorithm|the Hidden Paths Algorithm|that nds these paths in time O(m n+n 2 log n), where m is the number of edges participating in shortest paths. Our algorithm is a practical substitute for Dijkstra's algorithm. We argue that m is likely to be small in practice, since m = O(n logn) with high probability for ...

This paper focuses on the probability density function of the Euclidean distance between node pairs in rectangular random graphs. As the main achievement of the paper, a closed analytic formula of the probability density function of the Euclidean distance between node pairs in rectangular random graphs was obtained basing on combinatorial theory and asymptotic concept. Some lemmas, such as numb...

Using recent results from coding theory, it is shown how to break block ciphers operating on GF(q) where the ciphertext is expressible as evaluations of an unknown univariate polynomial of low degree m over the plaintext with a typically low but non-negligible probability μ. The method employed is essentially Sudan’s algorithm for decoding Reed-Solomon codes beyond the error-correction diameter...

Quantum communication typically involves a linear chain of repeater stations, each capable of reliable local quantum computation and connected to their nearest neighbors by unreliable communication links. The communication rate of existing protocols is low as two-way classical communication is used. By using a surface code across the repeater chain and generating Bell pairs between neighboring ...

To assess the impact of thalamic synchronization on cortical responsiveness, we used conditional cross-correlation analysis to measure the probability of neuronal discharges in somatosensory cortex as a function of the time between discharges in pairs of simultaneously recorded neurons in the ventrobasal thalamus. Among 26 neuronal trios, we found that thalamocortical efficacy after synchronous...

We propose a method for extracting semantic orientations of phrases (pairs of an adjective and a noun): positive, negative, or neutral. Given an adjective, the semantic orientation classification of phrases can be reduced to the classification of words. We construct a lexical network by connecting similar/related words. In the network, each node has one of the three orientation values and the n...

Social networks and interactions in social media involve both positive and negative relationships. Signed graphs capture both types of relationships: positive edges correspond to pairs of “friends”, and negative edges to pairs of “foes”. The edge sign prediction problem is an important graph mining task for which many heuristics have recently been proposed [LHK10a; LHK10b]. In this paper we mod...

Although signaling between neurons is central to the functioning of the brain, we still do not understand how the code used in signaling depends on the properties of synaptic transmission. Theoretical analysis combined with patch clamp recordings from pairs of neocortical pyramidal neurons revealed that the rate of synaptic depression, which depends on the probability of neurotransmitter releas...