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196
Stability analysis for kwise intersecting families
"... We consider the following generalization of the seminal Erdős–Ko–Rado theorem, due to Frankl [5]. For some k ≥ 2, let F be a kwise intersecting family of rsubsets of an n element set X, i.e. for any F1,...,Fk ∈ F, ∩k i=1Fi (k − 1)n = ∅. If r ≤, k then F  ≤ ( n−1) r−1. We prove a stability ver ..."
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We consider the following generalization of the seminal Erdős–Ko–Rado theorem, due to Frankl [5]. For some k ≥ 2, let F be a kwise intersecting family of rsubsets of an n element set X, i.e. for any F1,...,Fk ∈ F, ∩k i=1Fi (k − 1)n = ∅. If r ≤, k then F  ≤ ( n−1) r−1. We prove a stability
An ErdősKoRado theorem for cross tintersecting families
, 2013
"... Two families A and B, of ksubsets of an nset, are cross tintersecting if for every choice of subsets A ∈ A and B ∈ B we have A∩B  ≥ t. We address the following conjectured cross tintersecting version of the Erdős– Ko–Rado Theorem: For all n ≥ (t + 1)(k − t + 1) the maximum value of AB for ..."
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Two families A and B, of ksubsets of an nset, are cross tintersecting if for every choice of subsets A ∈ A and B ∈ B we have A∩B  ≥ t. We address the following conjectured cross tintersecting version of the Erdős– Ko–Rado Theorem: For all n ≥ (t + 1)(k − t + 1) the maximum value of A
Pairwise intersections and forbidden configurations
, 2006
"... Let fm(a, b, c, d) denote the maximum size of a family F of subsets of an melement set for which there is no pair of subsets A, B ∈ F with A ∩ B  ≥a, Ā ∩ B  ≥b, A ∩ ¯B  ≥c, and Ā ∩ ¯B  ≥d. By symmetry we can assume a ≥ d and b ≥ c. We show that fm(a, b, c, d) is Θ(m a+b−1) if either b> c ..."
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Cited by 7 (5 self)
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key tool is a strong stability version of the Complete Intersection Theorem of Ahlswede and Khachatrian, which is of independent interest.
CROSS tINTERSECTING INTEGER SEQUENCES FROM WEIGHTED ERDŐS–KO–RADO
, 2013
"... Let m, n and t be positive integers. Consider [m] n as the set of sequences of length n on an mletter alphabet. We say that two subsets A ⊂ [m] n and B ⊂ [m] n cross tintersect if any two sequences a ∈ A and b ∈ B match in at least t positions. In this case it is shown that if m> (1 − 1 t √ 2)− ..."
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)−1 then AB  ≤ (m n−t) 2. We derive this result from a weighted version of the Erdős–Ko–Rado theorem concerning cross tintersecting families of subsets, and we also include the corresponding stability statement. One of our main tools is the eigenvalue method for intersection matrices due to Friedgut [10].
Research Article SelfStabilizing TDMA Algorithms for Dynamic Wireless
"... This document has been downloaded from Chalmers Publication Library (CPL). It is the author´s version of a work that was accepted for publication in: ..."
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This document has been downloaded from Chalmers Publication Library (CPL). It is the author´s version of a work that was accepted for publication in:
1Capacity Theorems for the Fading Interference Channel with a Relay and Feedback Links
"... Abstract—Handling interference is one of the main challenges in the design of wireless networks. One of the key approaches to interference management is node cooperation, which can be classified into two main types: relaying and feedback. In this work we consider simultaneous application of both co ..."
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Abstract—Handling interference is one of the main challenges in the design of wireless networks. One of the key approaches to interference management is node cooperation, which can be classified into two main types: relaying and feedback. In this work we consider simultaneous application of both cooperation types in the presence of interference. We obtain exact characterization of the capacity regions for Rayleigh fading and phase fading interference channels with a relay and with feedback links, in the strong and very strong interference regimes. Four feedback configurations are considered: (1) feedback from both receivers to the relay, (2) feedback from each receiver to the relay and to one of the transmitters (either corresponding or opposite), (3) feedback from one of the receivers to the relay, (4) feedback from one of the receivers to the relay and to one of the transmitters. Our results show that there is a strong motivation for incorporating relaying and feedback into wireless networks. I.
1SubNyquist Radar via Doppler Focusing
"... Abstract—We investigate the problem of a monostatic pulseDoppler radar transceiver trying to detect targets, sparsely populated in the radar’s unambiguous timefrequency region. Several past works employ compressed sensing (CS) algorithms to this type of problem, but either do not address sample ra ..."
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Abstract—We investigate the problem of a monostatic pulseDoppler radar transceiver trying to detect targets, sparsely populated in the radar’s unambiguous timefrequency region. Several past works employ compressed sensing (CS) algorithms to this type of problem, but either do not address sample rate reduction, impose constraints on the radar transmitter, propose CS recovery methods with prohibitive dictionary size, or perform poorly in noisy conditions. Here we describe a subNyquist sampling and recovery approach called Doppler focusing which addresses all of these problems: it performs low rate sampling and digital processing, imposes no restrictions on the transmitter, and uses a CS dictionary with size which does not increase with increasing number of pulses P. Furthermore, in the presence of noise, Doppler focusing enjoys a signaltonoise ratio (SNR) improvement which scales linearly with P, obtaining good detection performance even at SNR as low as25dB. The recovery is based on the Xampling framework, which allows reducing the number of samples needed to accurately represent the signal, directly in the analogtodigital conversion process. After sampling, the entire digital recovery process is performed on the low rate samples without having to return to the Nyquist rate. Finally, our approach can be implemented in hardware using a previously suggested Xampling radar prototype. Index Terms—compressed sensing, rate of innovation, radar, sparse recovery, subNyquist sampling, delayDoppler estimation. I.
Multiloop Position Analysis via Iterated Linear Programming
"... Abstract — This paper presents a numerical method able to isolate all configurations that an arbitrary loop linkage can adopt, within given ranges for its degrees of freedom. The procedure is general, in the sense that it can be applied to single or multiple intermingled loops of arbitrary topology. ..."
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Abstract — This paper presents a numerical method able to isolate all configurations that an arbitrary loop linkage can adopt, within given ranges for its degrees of freedom. The procedure is general, in the sense that it can be applied to single or multiple intermingled loops of arbitrary topology
Results 1  10
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196