Elad Cohen | Freie Universität Berlin (original) (raw)

Papers by Elad Cohen

Electronic Notes in Discrete Mathematics, 2011

Information Processing Letters, 2008

An (h,s,t)-representation of a graph G consists of a collection of subtrees {S v | v ∈ V(G)} of a... more An (h,s,t)-representation of a graph G consists of a collection of subtrees {S v | v ∈ V(G)} of a tree T, such that (i) the maximum degree of T is at most h, (ii) every subtree has maximum degree at most s, and (iii) there is an edge between two vertices in the graph if and only if the corresponding subtrees in T have at least t vertices in common. For example, chordal graphs correspond to [ ∞ , ∞ ,1] = [3,3,1] = [3,3,2] graphs (notation of ∞ here means that no restriction is imposed). We investigate the complete bipartite graph K 2,n and prove new theorems characterizing those K 2,n graphs that have an (h,s,2)-representation and those that have an (h,s,3)-representation. We characterize [3,2,4] graphs as equivalent to the 4-flower-free [2,4,4] graphs and give a recognition algorithm for [2,3,4] graphs. Based on these characterizations, we present new results that confirm that weakly chordal graphs, as opposed to chordal graphs, can not be characterized within the [h,s,t] framework. Furthermore, we show a hierarchy of families of graphs between chordal and weakly chordal within the [h,s,t] framework.

Electronic Notes in Discrete Mathematics, 2011

Information Processing Letters, 2008

An (h,s,t)-representation of a graph G consists of a collection of subtrees {S v | v ∈ V(G)} of a... more An (h,s,t)-representation of a graph G consists of a collection of subtrees {S v | v ∈ V(G)} of a tree T, such that (i) the maximum degree of T is at most h, (ii) every subtree has maximum degree at most s, and (iii) there is an edge between two vertices in the graph if and only if the corresponding subtrees in T have at least t vertices in common. For example, chordal graphs correspond to [ ∞ , ∞ ,1] = [3,3,1] = [3,3,2] graphs (notation of ∞ here means that no restriction is imposed). We investigate the complete bipartite graph K 2,n and prove new theorems characterizing those K 2,n graphs that have an (h,s,2)-representation and those that have an (h,s,3)-representation. We characterize [3,2,4] graphs as equivalent to the 4-flower-free [2,4,4] graphs and give a recognition algorithm for [2,3,4] graphs. Based on these characterizations, we present new results that confirm that weakly chordal graphs, as opposed to chordal graphs, can not be characterized within the [h,s,t] framework. Furthermore, we show a hierarchy of families of graphs between chordal and weakly chordal within the [h,s,t] framework.

Physical Review E, 2007

We analyze the time resolved spike statistics of a solitary and two mutually interacting chaotic ... more We analyze the time resolved spike statistics of a solitary and two mutually interacting chaotic semiconductor lasers whose chaos is characterized by apparently random, short intensity spikes. Repulsion between two successive spikes is observed, resulting in a refractory period which is largest at laser threshold. For time intervals between spikes greater than the refractory period, the distribution of the intervals follows a Poisson distribution. The spiking pattern is highly periodic over time windows corresponding to the optical length of the external cavity, with a slow change of the spiking pattern as time increases. When zero-lag synchronization between the two lasers is established, the statistics of the nearly perfectly matched spikes are not altered. The similarity of these features to those found in complex interacting neural networks, suggests the use of laser systems as simpler physical models for neural networks.

Journal of Physics: Conference Series, 2010

Random bit generators (RBGs) are important in many aspects of statistical physics and crucial in ... more Random bit generators (RBGs) are important in many aspects of statistical physics and crucial in Monte-Carlo simulations, stochastic modeling and quantum cryptography. The quality of a RBG is measured by the unpredictability of the bit string it produces and the speed at which the truly random bits can be generated. Deterministic algorithms generate pseudo-random numbers at high data rates as they are only limited by electronic hardware speed, but their unpredictability is limited by the very nature of their deterministic origin. It is widely accepted that the core of any true RBG must be an intrinsically non-deterministic physical process, e.g. measuring thermal noise from a resistor. Owing to low signal levels, such systems are highly susceptible to bias, introduced by amplification, and to small nonrandom external perturbations resulting in a limited generation rate, typically less than 100M bit/s. We present a physical random bit generator, based on a chaotic semiconductor laser, having delayed optical feedback, which operates reliably at rates up to 300Gbit/s. The method uses a high derivative of the digitized chaotic laser intensity and generates the random sequence by retaining a number of the least significant bits of the high derivative value. The method is insensitive to laser operational parameters and eliminates the necessity for all external constraints such as incommensurate sampling rates and laser external cavity round trip time. The randomness of long bit strings is verified by standard statistical tests.

Electronic Notes in Discrete Mathematics, 2011

Information Processing Letters, 2008

An (h,s,t)-representation of a graph G consists of a collection of subtrees {S v | v ∈ V(G)} of a... more An (h,s,t)-representation of a graph G consists of a collection of subtrees {S v | v ∈ V(G)} of a tree T, such that (i) the maximum degree of T is at most h, (ii) every subtree has maximum degree at most s, and (iii) there is an edge between two vertices in the graph if and only if the corresponding subtrees in T have at least t vertices in common. For example, chordal graphs correspond to [ ∞ , ∞ ,1] = [3,3,1] = [3,3,2] graphs (notation of ∞ here means that no restriction is imposed). We investigate the complete bipartite graph K 2,n and prove new theorems characterizing those K 2,n graphs that have an (h,s,2)-representation and those that have an (h,s,3)-representation. We characterize [3,2,4] graphs as equivalent to the 4-flower-free [2,4,4] graphs and give a recognition algorithm for [2,3,4] graphs. Based on these characterizations, we present new results that confirm that weakly chordal graphs, as opposed to chordal graphs, can not be characterized within the [h,s,t] framework. Furthermore, we show a hierarchy of families of graphs between chordal and weakly chordal within the [h,s,t] framework.

Electronic Notes in Discrete Mathematics, 2011

Information Processing Letters, 2008

An (h,s,t)-representation of a graph G consists of a collection of subtrees {S v | v ∈ V(G)} of a... more An (h,s,t)-representation of a graph G consists of a collection of subtrees {S v | v ∈ V(G)} of a tree T, such that (i) the maximum degree of T is at most h, (ii) every subtree has maximum degree at most s, and (iii) there is an edge between two vertices in the graph if and only if the corresponding subtrees in T have at least t vertices in common. For example, chordal graphs correspond to [ ∞ , ∞ ,1] = [3,3,1] = [3,3,2] graphs (notation of ∞ here means that no restriction is imposed). We investigate the complete bipartite graph K 2,n and prove new theorems characterizing those K 2,n graphs that have an (h,s,2)-representation and those that have an (h,s,3)-representation. We characterize [3,2,4] graphs as equivalent to the 4-flower-free [2,4,4] graphs and give a recognition algorithm for [2,3,4] graphs. Based on these characterizations, we present new results that confirm that weakly chordal graphs, as opposed to chordal graphs, can not be characterized within the [h,s,t] framework. Furthermore, we show a hierarchy of families of graphs between chordal and weakly chordal within the [h,s,t] framework.

Physical Review E, 2007

We analyze the time resolved spike statistics of a solitary and two mutually interacting chaotic ... more We analyze the time resolved spike statistics of a solitary and two mutually interacting chaotic semiconductor lasers whose chaos is characterized by apparently random, short intensity spikes. Repulsion between two successive spikes is observed, resulting in a refractory period which is largest at laser threshold. For time intervals between spikes greater than the refractory period, the distribution of the intervals follows a Poisson distribution. The spiking pattern is highly periodic over time windows corresponding to the optical length of the external cavity, with a slow change of the spiking pattern as time increases. When zero-lag synchronization between the two lasers is established, the statistics of the nearly perfectly matched spikes are not altered. The similarity of these features to those found in complex interacting neural networks, suggests the use of laser systems as simpler physical models for neural networks.

Journal of Physics: Conference Series, 2010

Random bit generators (RBGs) are important in many aspects of statistical physics and crucial in ... more Random bit generators (RBGs) are important in many aspects of statistical physics and crucial in Monte-Carlo simulations, stochastic modeling and quantum cryptography. The quality of a RBG is measured by the unpredictability of the bit string it produces and the speed at which the truly random bits can be generated. Deterministic algorithms generate pseudo-random numbers at high data rates as they are only limited by electronic hardware speed, but their unpredictability is limited by the very nature of their deterministic origin. It is widely accepted that the core of any true RBG must be an intrinsically non-deterministic physical process, e.g. measuring thermal noise from a resistor. Owing to low signal levels, such systems are highly susceptible to bias, introduced by amplification, and to small nonrandom external perturbations resulting in a limited generation rate, typically less than 100M bit/s. We present a physical random bit generator, based on a chaotic semiconductor laser, having delayed optical feedback, which operates reliably at rates up to 300Gbit/s. The method uses a high derivative of the digitized chaotic laser intensity and generates the random sequence by retaining a number of the least significant bits of the high derivative value. The method is insensitive to laser operational parameters and eliminates the necessity for all external constraints such as incommensurate sampling rates and laser external cavity round trip time. The randomness of long bit strings is verified by standard statistical tests.