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  • Publication . Article . Preprint . Conference object . 2022
    Open Access
    Authors: 
    Yair Bartal; Ora Nova Fandina; Ofer Neiman;
    Publisher: Elsevier BV

    A tree cover of a metric space (X,d) is a collection of trees, so that every pair x,y in X has a low distortion path in one of the trees. If it has the stronger property that every point x in X has a single tree with low distortion paths to all other points, we call this a Ramsey tree cover. Tree covers and Ramsey tree covers have been studied by [Yair Bartal et al., 2005; Anupam Gupta et al., 2004; T-H. Hubert Chan et al., 2005; Gupta et al., 2006; Mendel and Naor, 2007], and have found several important algorithmic applications, e.g. routing and distance oracles. The union of trees in a tree cover also serves as a special type of spanner, that can be decomposed into a few trees with low distortion paths contained in a single tree; Such spanners for Euclidean pointsets were presented by [S. Arya et al., 1995]. In this paper we devise efficient algorithms to construct tree covers and Ramsey tree covers for general, planar and doubling metrics. We pay particular attention to the desirable case of distortion close to 1, and study what can be achieved when the number of trees is small. In particular, our work shows a large separation between what can be achieved by tree covers vs. Ramsey tree covers.

  • Publication . Article . Preprint . 2022
    Open Access
    Authors: 
    Michael Larsen; Aner Shalev; Pham Huu Tiep;
    Publisher: Springer Science and Business Media LLC
    Project: NSF | Group Representations and... (1840702)

    We show that, if $w_1, \ldots , w_6$ are words which are not an identity of any (non-abelian) finite simple group, then $w_1(G)w_2(G) \cdots w_6(G) = G$ for all (non-abelian) finite simple groups $G$. In particular, for every word $w$, either $w(G)^6 = G$ for all finite simple groups, or $w(G)=1$ for some finite simple groups. These theorems follow from more general results we obtain on characteristic collections of finite groups and their covering numbers, which are of independent interest and have additional applications. Comment: 20 pages

  • Open Access English
    Authors: 
    Alexander Tarnavsky Eitan; Shirly Someck; Mario Zajac; Eran Socher; Eran Stark;

    In the intact brain, neural activity can be recorded using sensing electrodes and manipulated using light stimulation. Silicon probes with integrated electrodes and micro-LEDs enable the detection and control of neural activity using a single implanted device. Miniaturized solutions for recordings from small freely moving animals are commercially available, but stimulation is driven by large, stationary current sources. We designed and fabricated a current source chip and integrated it into a headstage PCB that weighs 1.37 g. The proposed system provides 10-bit resolution current control for 32 channels, driving micro-LEDs with up to 4.6 V and sourcing up to 0.9 mA at a refresh rate of 5 kHz per channel. When calibrated against a micro-LED probe, the system allows linear control of light output power, up to 10 micro-W per micro-LED. To demonstrate the capabilities of the system, synthetic sequences of neural spiking activity were produced by driving multiple micro-LEDs implanted in the hippocampal CA1 area of a freely moving mouse. The high spatial, temporal, and amplitude resolution of the system provides a rich variety of stimulation patterns. Combined with commercially available sampling headstages, the system provides an easy to use back-end, fully utilizing the bi-directional potential of integrated opto-electronic arrays. 11 pages, 9 figures

  • Publication . Preprint . Article . 2022
    Open Access
    Authors: 
    Tuvia Gefen; Alex Retzker; Jan Kolodynski; Yink Loong Len;
    Publisher: Springer Science and Business Media LLC

    The impact of measurement imperfections on quantum metrology protocols has not been approached in a systematic manner so far. In this work, we tackle this issue by generalising firstly the notion of quantum Fisher information to account for noisy detection, and propose tractable methods allowing for its approximate evaluation. We then show that in canonical scenarios involving $N$ probes with local measurements undergoing readout noise, the optimal sensitivity depends crucially on the control operations allowed to counterbalance the measurement imperfections -- with global control operations, the ideal sensitivity (e.g.~the Heisenberg scaling) can always be recovered in the asymptotic $N$ limit, while with local control operations the quantum-enhancement of sensitivity is constrained to a constant factor. We illustrate our findings with an example of NV-centre magnetometry, as well as schemes involving spin-$1/2$ probes with bit-flip errors affecting their two-outcome measurements, for which we find the input states and control unitary operations sufficient to attain the ultimate asymptotic precision. Comment: v2. 33 pages, 14 figures. Comments are welcome

  • Publication . Article . Preprint . 2022 . Embargo End Date: 01 Jan 2022
    Open Access
    Authors: 
    Serge Galam; Yuval Gefen; Yonathan Shapir;
    Publisher: arXiv

    A new approach to the understanding of sociological collective behaviour, based on the framework of critical phenomena in physics, is presented. The first step consists of constructing a simple mean-behaviour model and applying it to a strike process in a plant. The model comprises only a limited number of parameters characteristic of the plant considered and of the society. A dissatisfaction function is introduced with a basic principle stating that the stable state of the plant is a state, which minimizes this function. It is found that the plant can be in one of two phases: the "collective phase" and the "individual phase". These two phases are separated by a critical point, in the neighbourhood of which the system is very sensitive to small changes in the parameters. The collective phase includes a region of parameters for which the system has two possible states: a "work state" and a "strike state". The actual state of the system depends on the parameters and on the "history of the system". The irreversibility of the transition between these two states indicates the existence of metastable states. For these particular states, the effect of small groups of workers or of a small perturbation in the system results in drastic changes in the state of the plant. Other non-trivial implications of the model, as well as possible extensions and refinements of the approach, are discussed. Comment: First paper coining the term sociophysics to launch a new field of research (submitted in 1980, published in 1982), retyped in its original format, 13 pages, 4 figures

  • Publication . Conference object . Preprint . Contribution for newspaper or weekly magazine . Article . 2022 . Embargo End Date: 01 Jan 2022
    Open Access
    Authors: 
    Anton Tsitsulin; Davide Mottin; Panagiotis Karras; Alexander M. Bronstein; Emmanuel Müller;
    Publisher: arXiv

    We introduce a spectral notion of graph complexity derived from the Weyl's law. We experimentally demonstrate its correlation to how well the graph can be embedded in a low-dimensional Euclidean space. Comment: BigNet workshop at the Web conferece'2019

  • Open Access English
    Authors: 
    Itay Glazer; Dan Mikulincer;
    Project: EC | PATHWISE (803084)

    We study random variables of the form $f(X)$, when $f$ is a degree $d$ polynomial, and $X$ is a random vector on $\mathbb{R}^{n}$, motivated towards a deeper understanding of the covariance structure of $X^{\otimes d}$. For applications, the main interest is to bound $\mathrm{Var}(f(X))$ from below, assuming a suitable normalization on the coefficients of $f$. Our first result applies when $X$ has independent coordinates, and we establish dimension-free bounds. We also show that the assumption of independence can be relaxed and that our bounds carry over to uniform measures on isotropic $L_{p}$ balls. Moreover, in the case of the Euclidean ball, we provide an orthogonal decomposition of $\mathrm{Cov}(X^{\otimes d})$. Finally, we utilize the connection between anti-concentration and decay of Fourier coefficients to prove a high-dimensional analogue of the van der Corput lemma, thus partially answering a question posed by Carbery and Wright. 28 pages. Lemma 8 is updated in Version 2

  • Open Access English
    Authors: 
    Boris Aronov; Esther Ezra; Micha Sharir;

    We present subquadratic algorithms, in the algebraic decision-tree model of computation, for detecting whether there exists a triple of points, belonging to three respective sets $A$, $B$, and $C$ of points in the plane, that satisfy a certain polynomial equation or two equations. The best known instance of such a problem is testing for the existence of a collinear triple of points in $A\times B\times C$, a classical 3SUM-hard problem that has so far defied any attempt to obtain a subquadratic solution, whether in the (uniform) real RAM model, or in the algebraic decision-tree model. While we are still unable to solve this problem, in full generality, in subquadratic time, we obtain such a solution, in the algebraic decision-tree model, that uses only roughly $O(n^{28/15})$ constant-degree polynomial sign tests, for the special case where two of the sets lie on two respective one-dimensional curves and the third is placed arbitrarily in the plane. Our technique is fairly general, and applies to many other problems where we seek a triple that satisfies a single polynomial equation, e.g., determining whether $A\times B\times C$ contains a triple spanning a unit-area triangle. This result extends recent work by Barba \etal~(2017) and by Chan (2018), where all three sets $A$,~$B$, and~$C$ are assumed to be one-dimensional. As a second application of our technique, we again have three $n$-point sets $A$, $B$, and $C$ in the plane, and we want to determine whether there exists a triple $(a,b,c) \in A\times B\times C$ that simultaneously satisfies two independent real polynomial equations. For example, this is the setup when testing for collinearity in the complex plane, when each of the sets $A$, $B$, $C$ lies on some constant-degree algebraic curve. We show that problems of this kind can be solved with roughly $O(n^{24/13})$ constant-degree polynomial sign tests.

  • Open Access English
    Authors: 
    Hengxin Tan; Daniel Kaplan; Binghai Yan;
    Project: EC | NonlinearTopo (815869)

    Magnetic topological insulators (MnBi$_2$Te$_4$)(Bi$_2$Te$_3$)$_n$ were anticipated to exhibit magnetic energy gaps while recent spectroscopic studies did not observe them. Thus, magnetism on the surface is under debate. In this work, we propose another symmetry criterion to probe the surface magnetism. Because of both time-reversal symmetry-breaking and inversion symmetry-breaking, we demonstrate that the surface band structure violates momentum-inversion symmetry and leads to a three-fold rather than six-fold rotational symmetry on the Fermi surface if corresponding surface states couple strongly to the surface magnetism. Such a momentum-inversion symmetry violation is significant along the $\Gamma-K$ direction for surface bands on the (0001) plane. Comment: 4 pages, 3 figures

  • Publication . Article . Preprint . Conference object . 2022
    Open Access
    Authors: 
    Edelstein, Michal; Peleg, Hila; Itzhaky, Shachar; Ben-Chen, Mirela;
    Publisher: ACM
    Project: EC | OPREP (714776)

    We propose an approach for generating crochet instructions (patterns) from an input 3D model. We focus on Amigurumi, which are knitted stuffed toys. Given a closed triangle mesh, and a single point specified by the user, we generate crochet instructions, which when knitted and stuffed result in a toy similar to the input geometry. Our approach relies on constructing the geometry and connectivity of a Crochet Graph, which is then translated into a crochet pattern. We segment the shape automatically into chrochetable components, which are connected using the join-as-you-go method, requiring no additional sewing. We demonstrate that our method is applicable to a large variety of shapes and geometries, and yields easily crochetable patterns. Comment: 11 pages, 10 figures, SCF 2022

Advanced search in
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arrow_drop_down
Searching FieldsTerms
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arrow_drop_down
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Include:
11,732 Research products, page 1 of 1,174
  • Publication . Article . Preprint . Conference object . 2022
    Open Access
    Authors: 
    Yair Bartal; Ora Nova Fandina; Ofer Neiman;
    Publisher: Elsevier BV

    A tree cover of a metric space (X,d) is a collection of trees, so that every pair x,y in X has a low distortion path in one of the trees. If it has the stronger property that every point x in X has a single tree with low distortion paths to all other points, we call this a Ramsey tree cover. Tree covers and Ramsey tree covers have been studied by [Yair Bartal et al., 2005; Anupam Gupta et al., 2004; T-H. Hubert Chan et al., 2005; Gupta et al., 2006; Mendel and Naor, 2007], and have found several important algorithmic applications, e.g. routing and distance oracles. The union of trees in a tree cover also serves as a special type of spanner, that can be decomposed into a few trees with low distortion paths contained in a single tree; Such spanners for Euclidean pointsets were presented by [S. Arya et al., 1995]. In this paper we devise efficient algorithms to construct tree covers and Ramsey tree covers for general, planar and doubling metrics. We pay particular attention to the desirable case of distortion close to 1, and study what can be achieved when the number of trees is small. In particular, our work shows a large separation between what can be achieved by tree covers vs. Ramsey tree covers.

  • Publication . Article . Preprint . 2022
    Open Access
    Authors: 
    Michael Larsen; Aner Shalev; Pham Huu Tiep;
    Publisher: Springer Science and Business Media LLC
    Project: NSF | Group Representations and... (1840702)

    We show that, if $w_1, \ldots , w_6$ are words which are not an identity of any (non-abelian) finite simple group, then $w_1(G)w_2(G) \cdots w_6(G) = G$ for all (non-abelian) finite simple groups $G$. In particular, for every word $w$, either $w(G)^6 = G$ for all finite simple groups, or $w(G)=1$ for some finite simple groups. These theorems follow from more general results we obtain on characteristic collections of finite groups and their covering numbers, which are of independent interest and have additional applications. Comment: 20 pages

  • Open Access English
    Authors: 
    Alexander Tarnavsky Eitan; Shirly Someck; Mario Zajac; Eran Socher; Eran Stark;

    In the intact brain, neural activity can be recorded using sensing electrodes and manipulated using light stimulation. Silicon probes with integrated electrodes and micro-LEDs enable the detection and control of neural activity using a single implanted device. Miniaturized solutions for recordings from small freely moving animals are commercially available, but stimulation is driven by large, stationary current sources. We designed and fabricated a current source chip and integrated it into a headstage PCB that weighs 1.37 g. The proposed system provides 10-bit resolution current control for 32 channels, driving micro-LEDs with up to 4.6 V and sourcing up to 0.9 mA at a refresh rate of 5 kHz per channel. When calibrated against a micro-LED probe, the system allows linear control of light output power, up to 10 micro-W per micro-LED. To demonstrate the capabilities of the system, synthetic sequences of neural spiking activity were produced by driving multiple micro-LEDs implanted in the hippocampal CA1 area of a freely moving mouse. The high spatial, temporal, and amplitude resolution of the system provides a rich variety of stimulation patterns. Combined with commercially available sampling headstages, the system provides an easy to use back-end, fully utilizing the bi-directional potential of integrated opto-electronic arrays. 11 pages, 9 figures

  • Publication . Preprint . Article . 2022
    Open Access
    Authors: 
    Tuvia Gefen; Alex Retzker; Jan Kolodynski; Yink Loong Len;
    Publisher: Springer Science and Business Media LLC

    The impact of measurement imperfections on quantum metrology protocols has not been approached in a systematic manner so far. In this work, we tackle this issue by generalising firstly the notion of quantum Fisher information to account for noisy detection, and propose tractable methods allowing for its approximate evaluation. We then show that in canonical scenarios involving $N$ probes with local measurements undergoing readout noise, the optimal sensitivity depends crucially on the control operations allowed to counterbalance the measurement imperfections -- with global control operations, the ideal sensitivity (e.g.~the Heisenberg scaling) can always be recovered in the asymptotic $N$ limit, while with local control operations the quantum-enhancement of sensitivity is constrained to a constant factor. We illustrate our findings with an example of NV-centre magnetometry, as well as schemes involving spin-$1/2$ probes with bit-flip errors affecting their two-outcome measurements, for which we find the input states and control unitary operations sufficient to attain the ultimate asymptotic precision. Comment: v2. 33 pages, 14 figures. Comments are welcome

  • Publication . Article . Preprint . 2022 . Embargo End Date: 01 Jan 2022
    Open Access
    Authors: 
    Serge Galam; Yuval Gefen; Yonathan Shapir;
    Publisher: arXiv

    A new approach to the understanding of sociological collective behaviour, based on the framework of critical phenomena in physics, is presented. The first step consists of constructing a simple mean-behaviour model and applying it to a strike process in a plant. The model comprises only a limited number of parameters characteristic of the plant considered and of the society. A dissatisfaction function is introduced with a basic principle stating that the stable state of the plant is a state, which minimizes this function. It is found that the plant can be in one of two phases: the "collective phase" and the "individual phase". These two phases are separated by a critical point, in the neighbourhood of which the system is very sensitive to small changes in the parameters. The collective phase includes a region of parameters for which the system has two possible states: a "work state" and a "strike state". The actual state of the system depends on the parameters and on the "history of the system". The irreversibility of the transition between these two states indicates the existence of metastable states. For these particular states, the effect of small groups of workers or of a small perturbation in the system results in drastic changes in the state of the plant. Other non-trivial implications of the model, as well as possible extensions and refinements of the approach, are discussed. Comment: First paper coining the term sociophysics to launch a new field of research (submitted in 1980, published in 1982), retyped in its original format, 13 pages, 4 figures

  • Publication . Conference object . Preprint . Contribution for newspaper or weekly magazine . Article . 2022 . Embargo End Date: 01 Jan 2022
    Open Access
    Authors: 
    Anton Tsitsulin; Davide Mottin; Panagiotis Karras; Alexander M. Bronstein; Emmanuel Müller;
    Publisher: arXiv

    We introduce a spectral notion of graph complexity derived from the Weyl's law. We experimentally demonstrate its correlation to how well the graph can be embedded in a low-dimensional Euclidean space. Comment: BigNet workshop at the Web conferece'2019

  • Open Access English
    Authors: 
    Itay Glazer; Dan Mikulincer;
    Project: EC | PATHWISE (803084)

    We study random variables of the form $f(X)$, when $f$ is a degree $d$ polynomial, and $X$ is a random vector on $\mathbb{R}^{n}$, motivated towards a deeper understanding of the covariance structure of $X^{\otimes d}$. For applications, the main interest is to bound $\mathrm{Var}(f(X))$ from below, assuming a suitable normalization on the coefficients of $f$. Our first result applies when $X$ has independent coordinates, and we establish dimension-free bounds. We also show that the assumption of independence can be relaxed and that our bounds carry over to uniform measures on isotropic $L_{p}$ balls. Moreover, in the case of the Euclidean ball, we provide an orthogonal decomposition of $\mathrm{Cov}(X^{\otimes d})$. Finally, we utilize the connection between anti-concentration and decay of Fourier coefficients to prove a high-dimensional analogue of the van der Corput lemma, thus partially answering a question posed by Carbery and Wright. 28 pages. Lemma 8 is updated in Version 2

  • Open Access English
    Authors: 
    Boris Aronov; Esther Ezra; Micha Sharir;

    We present subquadratic algorithms, in the algebraic decision-tree model of computation, for detecting whether there exists a triple of points, belonging to three respective sets $A$, $B$, and $C$ of points in the plane, that satisfy a certain polynomial equation or two equations. The best known instance of such a problem is testing for the existence of a collinear triple of points in $A\times B\times C$, a classical 3SUM-hard problem that has so far defied any attempt to obtain a subquadratic solution, whether in the (uniform) real RAM model, or in the algebraic decision-tree model. While we are still unable to solve this problem, in full generality, in subquadratic time, we obtain such a solution, in the algebraic decision-tree model, that uses only roughly $O(n^{28/15})$ constant-degree polynomial sign tests, for the special case where two of the sets lie on two respective one-dimensional curves and the third is placed arbitrarily in the plane. Our technique is fairly general, and applies to many other problems where we seek a triple that satisfies a single polynomial equation, e.g., determining whether $A\times B\times C$ contains a triple spanning a unit-area triangle. This result extends recent work by Barba \etal~(2017) and by Chan (2018), where all three sets $A$,~$B$, and~$C$ are assumed to be one-dimensional. As a second application of our technique, we again have three $n$-point sets $A$, $B$, and $C$ in the plane, and we want to determine whether there exists a triple $(a,b,c) \in A\times B\times C$ that simultaneously satisfies two independent real polynomial equations. For example, this is the setup when testing for collinearity in the complex plane, when each of the sets $A$, $B$, $C$ lies on some constant-degree algebraic curve. We show that problems of this kind can be solved with roughly $O(n^{24/13})$ constant-degree polynomial sign tests.

  • Open Access English
    Authors: 
    Hengxin Tan; Daniel Kaplan; Binghai Yan;
    Project: EC | NonlinearTopo (815869)

    Magnetic topological insulators (MnBi$_2$Te$_4$)(Bi$_2$Te$_3$)$_n$ were anticipated to exhibit magnetic energy gaps while recent spectroscopic studies did not observe them. Thus, magnetism on the surface is under debate. In this work, we propose another symmetry criterion to probe the surface magnetism. Because of both time-reversal symmetry-breaking and inversion symmetry-breaking, we demonstrate that the surface band structure violates momentum-inversion symmetry and leads to a three-fold rather than six-fold rotational symmetry on the Fermi surface if corresponding surface states couple strongly to the surface magnetism. Such a momentum-inversion symmetry violation is significant along the $\Gamma-K$ direction for surface bands on the (0001) plane. Comment: 4 pages, 3 figures

  • Publication . Article . Preprint . Conference object . 2022
    Open Access
    Authors: 
    Edelstein, Michal; Peleg, Hila; Itzhaky, Shachar; Ben-Chen, Mirela;
    Publisher: ACM
    Project: EC | OPREP (714776)

    We propose an approach for generating crochet instructions (patterns) from an input 3D model. We focus on Amigurumi, which are knitted stuffed toys. Given a closed triangle mesh, and a single point specified by the user, we generate crochet instructions, which when knitted and stuffed result in a toy similar to the input geometry. Our approach relies on constructing the geometry and connectivity of a Crochet Graph, which is then translated into a crochet pattern. We segment the shape automatically into chrochetable components, which are connected using the join-as-you-go method, requiring no additional sewing. We demonstrate that our method is applicable to a large variety of shapes and geometries, and yields easily crochetable patterns. Comment: 11 pages, 10 figures, SCF 2022

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