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  • Publication . Article . Preprint . 2021
    Open Access English
    Authors: 
    Anat Ganor; C S Karthik; Dömötör Pálvölgyi;
    Project: EC | COMPECON (740282)

    Brouwer’s fixed point theorem states that any continuous function from a compact convex space to itself has a fixed point. Roughgarden and Weinstein (FOCS 2016) initiated the study of fixed point computation in the two-player communication model, where each player gets a function from [0,1]^n to [0,1]^n , and their goal is to find an approximate fixed point of the composition of the two functions. They left it as an open question to show a lower bound of 2^{\Omega (n)} for the (randomized) communication complexity of this problem, in the range of parameters which make it a total search problem. We answer this question affirmatively. Additionally, we introduce two natural fixed point problems in the two-player communication model. Each player is given a function from [0,1]^n to [0,1]^{n/2} , and their goal is to find an approximate fixed point of the concatenation of the functions. Each player is given a function from [0,1]^n to [0,1]^{n} , and their goal is to find an approximate fixed point of the mean of the functions. We show a randomized communication complexity lower bound of 2^{\Omega (n)} for these problems (for some constant approximation factor). Finally, we initiate the study of finding a panchromatic simplex in a Sperner-coloring of a triangulation (guaranteed by Sperner’s lemma) in the two-player communication model: A triangulation T of the d -simplex is publicly known and one player is given a set S_A\subset T and a coloring function from S_A to \lbrace 0,\ldots ,d/2\rbrace , and the other player is given a set S_B\subset T and a coloring function from S_B to \lbrace d/2+1,\ldots ,d\rbrace , such that S_A\dot{\cup }S_B=T , and their goal is to find a panchromatic simplex. We show a randomized communication complexity lower bound of |T|^{\Omega (1)} for the aforementioned problem as well (when d is large). On the positive side, we show that if d\le 4 then there is a deterministic protocol for the Sperner problem with O((\log |T|)^2) bits of communication.

  • Publication . Article . Presentation . Other literature type . Conference object . Preprint . 2021
    Open Access English

    We investigate the special case of diamond relay comprising a Gaussian channel with identical frequency response from the user to the relays and fronthaul links with limited rate from the relays to the destination. We use the oblivious compress and forward (CF) with distributed compression and decode and forward (DF) where each relay decodes the whole message and sends half of its bits to the destination. We derive achievable rate by using time-sharing between DF and CF. It is proved that optimal CF-DF time sharing is advantageous over superposition of CF and DF. The optimal time sharing proportion between DF and CF and power and rate allocations are different at each frequency and are fully determined.

  • Publication . Article . Preprint . 2021
    Open Access English
    Authors: 
    Miron Amusia; Arkadiy S. Baltenkov;

    In this paper we calculate the elastic scattering cross sections of slow electron by carbon nanotubes. The corresponding electron-nanotube interaction is substituted by a zero-thickness cylindrical potential that neglects the atomic structure of real nanotubes, thus limiting the range of applicability of our approach to sufficiently low incoming electron energies. The strength of the potential is chosen the same that was used in describing scattering of electrons by fullerene C60. We present results for total and partial electron scattering cross sections as well as respective angular distributions, all with account of five lowest angular momenta contributions. In the calculations we assumed that the incoming electron moves perpendicular to the nanotube axis, since along the axis the incoming electron moves freely. 10 pages, 2 figures

  • Publication . Article . Preprint . 2021
    Open Access English
    Authors: 
    Itai Benjamini; David Ellis;
    Country: United Kingdom

    We continue the study of the properties of graphs in which the ball of radius $r$ around each vertex induces a graph isomorphic to the ball of radius $r$ in some fixed vertex-transitive graph $F$, for various choices of $F$ and $r$. This is a natural extension of the study of regular graphs. More precisely, if $F$ is a vertex-transitive graph and $r \in \mathbb{N}$, we say a graph $G$ is {\em $r$-locally $F$} if the ball of radius $r$ around each vertex of $G$ induces a graph isomorphic to the graph induced by the ball of radius $r$ around any vertex of $F$. We consider the following random graph model: for each $n \in \mathbb{N}$, we let $G_n = G_n(F,r)$ be a graph chosen uniformly at random from the set of all unlabelled, $n$-vertex graphs that are $r$-locally $F$. We investigate the properties possessed by the random graph $G_n$ with high probability, for various natural choices of $F$ and $r$. We prove that if $F$ is a Cayley graph of a torsion-free group of polynomial growth, and $r$ is sufficiently large depending on $F$, then the random graph $G_n = G_n(F,r)$ has largest component of order at most $n^{5/6}$ with high probability, and has at least $\exp(n^{\delta})$ automorphisms with high probability, where $\delta>0$ depends upon $F$ alone. Both properties are in stark contrast to random $d$-regular graphs, which correspond to the case where $F$ is the infinite $d$-regular tree. We also show that, under the same hypotheses, the number of unlabelled, $n$-vertex graphs that are $r$-locally $F$ grows like a stretched exponential in $n$, again in contrast with $d$-regular graphs. In the case where $F$ is the standard Cayley graph of $\mathbb{Z}^d$, we obtain a much more precise enumeration result, and more precise results on the properties of the random graph $G_n(F,r)$. Our proofs use a mixture of results and techniques from geometry, group theory and combinatorics. Comment: Full proof of Theorem 7 added. Statement of Proposition 38 has been strengthened slightly. 61 pages

  • Open Access English
    Authors: 
    Homa Nikbakht; Michele Wigger; Shlomo Shamai;
    Publisher: Zenodo
    Project: EC | CloudRadioNet (694630), EC | CTO Com (715111)

    This paper analyzes the multiplexing gains (MG) for simultaneous transmission of delay-sensitive and delay-tolerant data over interference networks. In the considered model, only delay-tolerant data can profit from coordinated multipoint (CoMP) transmission or reception techniques, because delay-sensitive data has to be transmitted without further delay. Transmission of delay-tolerant data is also subject to a delay constraint, which is however less stringent than the one on delay-sensitive data. Different coding schemes are proposed, and the corresponding MG pairs for delay-sensitive and delay-tolerant data are characterized for Wyner's linear symmetric network and for Wyner's two-dimensional hexagonal network with and without sectorization. For Wyner's linear symmetric also an information-theoretic converse is established and shown to be exact whenever the cooperation rates are sufficiently large or the delay-sensitive MG is small or moderate. These results show that on Wyner's symmetric linear network and for sufficiently large cooperation rates, the largest MG for delay-sensitive data can be achieved without penalizing the maximum sum-MG of both delay-sensitive and delay-tolerant data. A similar conclusion holds for Wyner's hexagonal network only for the model with sectorization. In the model without sectorization, a penalty in sum-MG is incurred whenever one insists on a positive delay-sensitive MG. 41 pages, submitted to Transactions on Communications

  • Publication . Article . Other literature type . Preprint . 2021
    Open Access English
    Authors: 
    Marco Piccardo; Vincent Ginis; Andrew Forbes; Simon Mahler; Haoran Ren; Ahmed H. Dorrah; Firehun Tsige Dullo; Antonio Ambrosio; Sylvain Gigan; Markus Hiekkamäki; +28 more
    Publisher: IOP Publishing
    Country: Switzerland
    Project: EC | CHIC (724344), NSERC , NSF | NNCI: The Center for Nano... (1541959), FCT | UIDB/50008/2020 (UIDB/50008/2020)

    Our ability to generate new distributions of light has been remarkably enhanced in recent years. At the most fundamental level, these light patterns are obtained by ingeniously combining different electromagnetic modes. Interestingly, the modal superposition occurs in the spatial, temporal as well as spatio-temporal domain. This generalized concept of structured light is being applied across the entire spectrum of optics: generating classical and quantum states of light, harnessing linear and nonlinear light-matter interactions, and advancing applications in microscopy, spectroscopy, holography, communication, and synchronization. This Roadmap highlights the common roots of these different techniques and thus establishes links between research areas that complement each other seamlessly. We provide an overview of all these areas, their backgrounds, current research, and future developments. We highlight the power of multimodal light manipulation and want to inspire new eclectic approaches in this vibrant research community. Under review in J. Opt

  • Publication . Article . Preprint . 2021
    Open Access English
    Authors: 
    Andrea Guerrieri; Amit Sever;

    We consider a dual $S$-matrix Bootstrap approach in $d\geq 3$ space-time dimensions which relies solely on the rigorously proven analyticity, crossing, and unitarity properties of the scattering amplitudes. As a proof of principle, we provide rigorous upper and lower numerical bounds on the quartic coupling for the scattering of identical scalar particles in four dimensions. 5 + 10 pages, 3 + 6 figures, major revision in the appendices, improved numerics, typos corrected

  • Publication . Article . Conference object . Preprint . 2021
    Open Access English
    Authors: 
    Chengshuai Wu; Lars Grune; Thomas Kriecherbauer; Michael Margaliot;

    A time-varying nonlinear dynamical system is called a totally positive differential system (TPDS) if its Jacobian admits a special sign pattern: it is tri-diagonal with positive entries on the super- and sub-diagonals. If the vector field of a TPDS is T-periodic then every bounded trajectory converges to a T-periodic solution. In particular, when the vector field is time-invariant every bounded trajectory of a TPDS converges to an equlbrium. Here, we use the spectral theory of oscillatory matrices to analyze the behavior near a periodic solution of a TPDS. This yields information on the perturbation directions that lead to the fastest and slowest convergence to or divergence from the periodic solution. We demonstrate the theoretical results using a model from systems biology called the ribosome flow model.

  • Publication . Conference object . Preprint . Article . 2021
    Open Access English
    Authors: 
    Ofir, Ron; Margaliot, Michael; Levron, Yoash; Slotine, Jean-Jacques;

    The flow of contracting systems contracts 1-dimensional polygons (i.e. lines) at an exponential rate. One reason for the usefulness of contracting systems is that many interconnections of contracting sub-systems yield an overall contracting system. A recent generalization of contracting systems is called $k$-contracting systems, where $k\in\{1,\dots,n\}$. The flow of such systems contracts $k$-dimensional polygons at an exponential rate, and in particular they reduce to contracting systems when $k=1$. Here, we analyze serial interconnections of $1$-contracting and $2$-contracting systems. We provide conditions guaranteeing that such interconnections have a well-ordered asymptotic behaviour, and demonstrate the theoretical results using several examples.

  • Publication . Article . Preprint . 2021
    Open Access English
    Authors: 
    Ron Levie; Haim Avron;
    Country: Germany

    AbstractThis paper focuses on signal processing tasks in which the signal is transformed from the signal space to a higher dimensional coefficient space (also called phase space) using a continuous frame, processed in the coefficient space, and synthesized to an output signal. We show how to approximate such methods, termed phase space signal processing methods, using a Monte Carlo method. As opposed to standard discretizations of continuous frames, based on sampling discrete frames from the continuous system, the proposed Monte Carlo method is directly a quadrature approximation of the continuous frame. We show that the Monte Carlo method allows working with highly redundant continuous frames, since the number of samples required for a certain accuracy is proportional to the dimension of the signal space, and not to the dimension of the phase space. Moreover, even though the continuous frame is highly redundant, the Monte Carlo samples are spread uniformly, and hence represent the coefficient space more faithfully than standard frame discretizations.

Advanced search in
Research products
arrow_drop_down
Searching FieldsTerms
Any field
arrow_drop_down
includes
arrow_drop_down
Include:
10,274 Research products, page 1 of 1,028
  • Publication . Article . Preprint . 2021
    Open Access English
    Authors: 
    Anat Ganor; C S Karthik; Dömötör Pálvölgyi;
    Project: EC | COMPECON (740282)

    Brouwer’s fixed point theorem states that any continuous function from a compact convex space to itself has a fixed point. Roughgarden and Weinstein (FOCS 2016) initiated the study of fixed point computation in the two-player communication model, where each player gets a function from [0,1]^n to [0,1]^n , and their goal is to find an approximate fixed point of the composition of the two functions. They left it as an open question to show a lower bound of 2^{\Omega (n)} for the (randomized) communication complexity of this problem, in the range of parameters which make it a total search problem. We answer this question affirmatively. Additionally, we introduce two natural fixed point problems in the two-player communication model. Each player is given a function from [0,1]^n to [0,1]^{n/2} , and their goal is to find an approximate fixed point of the concatenation of the functions. Each player is given a function from [0,1]^n to [0,1]^{n} , and their goal is to find an approximate fixed point of the mean of the functions. We show a randomized communication complexity lower bound of 2^{\Omega (n)} for these problems (for some constant approximation factor). Finally, we initiate the study of finding a panchromatic simplex in a Sperner-coloring of a triangulation (guaranteed by Sperner’s lemma) in the two-player communication model: A triangulation T of the d -simplex is publicly known and one player is given a set S_A\subset T and a coloring function from S_A to \lbrace 0,\ldots ,d/2\rbrace , and the other player is given a set S_B\subset T and a coloring function from S_B to \lbrace d/2+1,\ldots ,d\rbrace , such that S_A\dot{\cup }S_B=T , and their goal is to find a panchromatic simplex. We show a randomized communication complexity lower bound of |T|^{\Omega (1)} for the aforementioned problem as well (when d is large). On the positive side, we show that if d\le 4 then there is a deterministic protocol for the Sperner problem with O((\log |T|)^2) bits of communication.

  • Publication . Article . Presentation . Other literature type . Conference object . Preprint . 2021
    Open Access English

    We investigate the special case of diamond relay comprising a Gaussian channel with identical frequency response from the user to the relays and fronthaul links with limited rate from the relays to the destination. We use the oblivious compress and forward (CF) with distributed compression and decode and forward (DF) where each relay decodes the whole message and sends half of its bits to the destination. We derive achievable rate by using time-sharing between DF and CF. It is proved that optimal CF-DF time sharing is advantageous over superposition of CF and DF. The optimal time sharing proportion between DF and CF and power and rate allocations are different at each frequency and are fully determined.

  • Publication . Article . Preprint . 2021
    Open Access English
    Authors: 
    Miron Amusia; Arkadiy S. Baltenkov;

    In this paper we calculate the elastic scattering cross sections of slow electron by carbon nanotubes. The corresponding electron-nanotube interaction is substituted by a zero-thickness cylindrical potential that neglects the atomic structure of real nanotubes, thus limiting the range of applicability of our approach to sufficiently low incoming electron energies. The strength of the potential is chosen the same that was used in describing scattering of electrons by fullerene C60. We present results for total and partial electron scattering cross sections as well as respective angular distributions, all with account of five lowest angular momenta contributions. In the calculations we assumed that the incoming electron moves perpendicular to the nanotube axis, since along the axis the incoming electron moves freely. 10 pages, 2 figures

  • Publication . Article . Preprint . 2021
    Open Access English
    Authors: 
    Itai Benjamini; David Ellis;
    Country: United Kingdom

    We continue the study of the properties of graphs in which the ball of radius $r$ around each vertex induces a graph isomorphic to the ball of radius $r$ in some fixed vertex-transitive graph $F$, for various choices of $F$ and $r$. This is a natural extension of the study of regular graphs. More precisely, if $F$ is a vertex-transitive graph and $r \in \mathbb{N}$, we say a graph $G$ is {\em $r$-locally $F$} if the ball of radius $r$ around each vertex of $G$ induces a graph isomorphic to the graph induced by the ball of radius $r$ around any vertex of $F$. We consider the following random graph model: for each $n \in \mathbb{N}$, we let $G_n = G_n(F,r)$ be a graph chosen uniformly at random from the set of all unlabelled, $n$-vertex graphs that are $r$-locally $F$. We investigate the properties possessed by the random graph $G_n$ with high probability, for various natural choices of $F$ and $r$. We prove that if $F$ is a Cayley graph of a torsion-free group of polynomial growth, and $r$ is sufficiently large depending on $F$, then the random graph $G_n = G_n(F,r)$ has largest component of order at most $n^{5/6}$ with high probability, and has at least $\exp(n^{\delta})$ automorphisms with high probability, where $\delta>0$ depends upon $F$ alone. Both properties are in stark contrast to random $d$-regular graphs, which correspond to the case where $F$ is the infinite $d$-regular tree. We also show that, under the same hypotheses, the number of unlabelled, $n$-vertex graphs that are $r$-locally $F$ grows like a stretched exponential in $n$, again in contrast with $d$-regular graphs. In the case where $F$ is the standard Cayley graph of $\mathbb{Z}^d$, we obtain a much more precise enumeration result, and more precise results on the properties of the random graph $G_n(F,r)$. Our proofs use a mixture of results and techniques from geometry, group theory and combinatorics. Comment: Full proof of Theorem 7 added. Statement of Proposition 38 has been strengthened slightly. 61 pages

  • Open Access English
    Authors: 
    Homa Nikbakht; Michele Wigger; Shlomo Shamai;
    Publisher: Zenodo
    Project: EC | CloudRadioNet (694630), EC | CTO Com (715111)

    This paper analyzes the multiplexing gains (MG) for simultaneous transmission of delay-sensitive and delay-tolerant data over interference networks. In the considered model, only delay-tolerant data can profit from coordinated multipoint (CoMP) transmission or reception techniques, because delay-sensitive data has to be transmitted without further delay. Transmission of delay-tolerant data is also subject to a delay constraint, which is however less stringent than the one on delay-sensitive data. Different coding schemes are proposed, and the corresponding MG pairs for delay-sensitive and delay-tolerant data are characterized for Wyner's linear symmetric network and for Wyner's two-dimensional hexagonal network with and without sectorization. For Wyner's linear symmetric also an information-theoretic converse is established and shown to be exact whenever the cooperation rates are sufficiently large or the delay-sensitive MG is small or moderate. These results show that on Wyner's symmetric linear network and for sufficiently large cooperation rates, the largest MG for delay-sensitive data can be achieved without penalizing the maximum sum-MG of both delay-sensitive and delay-tolerant data. A similar conclusion holds for Wyner's hexagonal network only for the model with sectorization. In the model without sectorization, a penalty in sum-MG is incurred whenever one insists on a positive delay-sensitive MG. 41 pages, submitted to Transactions on Communications

  • Publication . Article . Other literature type . Preprint . 2021
    Open Access English
    Authors: 
    Marco Piccardo; Vincent Ginis; Andrew Forbes; Simon Mahler; Haoran Ren; Ahmed H. Dorrah; Firehun Tsige Dullo; Antonio Ambrosio; Sylvain Gigan; Markus Hiekkamäki; +28 more
    Publisher: IOP Publishing
    Country: Switzerland
    Project: EC | CHIC (724344), NSERC , NSF | NNCI: The Center for Nano... (1541959), FCT | UIDB/50008/2020 (UIDB/50008/2020)

    Our ability to generate new distributions of light has been remarkably enhanced in recent years. At the most fundamental level, these light patterns are obtained by ingeniously combining different electromagnetic modes. Interestingly, the modal superposition occurs in the spatial, temporal as well as spatio-temporal domain. This generalized concept of structured light is being applied across the entire spectrum of optics: generating classical and quantum states of light, harnessing linear and nonlinear light-matter interactions, and advancing applications in microscopy, spectroscopy, holography, communication, and synchronization. This Roadmap highlights the common roots of these different techniques and thus establishes links between research areas that complement each other seamlessly. We provide an overview of all these areas, their backgrounds, current research, and future developments. We highlight the power of multimodal light manipulation and want to inspire new eclectic approaches in this vibrant research community. Under review in J. Opt

  • Publication . Article . Preprint . 2021
    Open Access English
    Authors: 
    Andrea Guerrieri; Amit Sever;

    We consider a dual $S$-matrix Bootstrap approach in $d\geq 3$ space-time dimensions which relies solely on the rigorously proven analyticity, crossing, and unitarity properties of the scattering amplitudes. As a proof of principle, we provide rigorous upper and lower numerical bounds on the quartic coupling for the scattering of identical scalar particles in four dimensions. 5 + 10 pages, 3 + 6 figures, major revision in the appendices, improved numerics, typos corrected

  • Publication . Article . Conference object . Preprint . 2021
    Open Access English
    Authors: 
    Chengshuai Wu; Lars Grune; Thomas Kriecherbauer; Michael Margaliot;

    A time-varying nonlinear dynamical system is called a totally positive differential system (TPDS) if its Jacobian admits a special sign pattern: it is tri-diagonal with positive entries on the super- and sub-diagonals. If the vector field of a TPDS is T-periodic then every bounded trajectory converges to a T-periodic solution. In particular, when the vector field is time-invariant every bounded trajectory of a TPDS converges to an equlbrium. Here, we use the spectral theory of oscillatory matrices to analyze the behavior near a periodic solution of a TPDS. This yields information on the perturbation directions that lead to the fastest and slowest convergence to or divergence from the periodic solution. We demonstrate the theoretical results using a model from systems biology called the ribosome flow model.

  • Publication . Conference object . Preprint . Article . 2021
    Open Access English
    Authors: 
    Ofir, Ron; Margaliot, Michael; Levron, Yoash; Slotine, Jean-Jacques;

    The flow of contracting systems contracts 1-dimensional polygons (i.e. lines) at an exponential rate. One reason for the usefulness of contracting systems is that many interconnections of contracting sub-systems yield an overall contracting system. A recent generalization of contracting systems is called $k$-contracting systems, where $k\in\{1,\dots,n\}$. The flow of such systems contracts $k$-dimensional polygons at an exponential rate, and in particular they reduce to contracting systems when $k=1$. Here, we analyze serial interconnections of $1$-contracting and $2$-contracting systems. We provide conditions guaranteeing that such interconnections have a well-ordered asymptotic behaviour, and demonstrate the theoretical results using several examples.

  • Publication . Article . Preprint . 2021
    Open Access English
    Authors: 
    Ron Levie; Haim Avron;
    Country: Germany

    AbstractThis paper focuses on signal processing tasks in which the signal is transformed from the signal space to a higher dimensional coefficient space (also called phase space) using a continuous frame, processed in the coefficient space, and synthesized to an output signal. We show how to approximate such methods, termed phase space signal processing methods, using a Monte Carlo method. As opposed to standard discretizations of continuous frames, based on sampling discrete frames from the continuous system, the proposed Monte Carlo method is directly a quadrature approximation of the continuous frame. We show that the Monte Carlo method allows working with highly redundant continuous frames, since the number of samples required for a certain accuracy is proportional to the dimension of the signal space, and not to the dimension of the phase space. Moreover, even though the continuous frame is highly redundant, the Monte Carlo samples are spread uniformly, and hence represent the coefficient space more faithfully than standard frame discretizations.

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