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  • Publication . Article . 2011
    Open Access
    Authors: 
    Janez Bernik; Mitja Mastnak; Heydar Radjavi;
    Publisher: Elsevier BV

    Abstract We study various aspects of how certain positivity assumptions on complex matrix semigroups affect their structure. Our main result is that every irreducible group of complex matrices with nonnegative diagonal entries is simultaneously similar to a group of weighted permutations. We also consider the corresponding question for semigroups and discuss the effect of the assumption that a fixed linear functional has nonnegative values when restricted to a given semigroup.

  • Open Access
    Authors: 
    Georges Aad; Leszek Adamczyk; Jahred Adelman; Tim Adye; Tatjana Agatonovic-Jovin; J. A. Aguilar-Saavedra; Faig Ahmadov; Giulio Aielli; Gian Luigi Alberghi; J. Albert; +599 more
    Publisher: American Physical Society (APS)
    Project: NSERC

    Many extensions of the Standard Model posit the existence of heavy particles with long lifetimes. This article presents the results of a search for events containing at least one long-lived particle that decays at a significant distance from its production point into two leptons or into five or more charged particles. This analysis uses a data sample of proton-proton collisions at root s = 8 TeV corresponding to an integrated luminosity of 20.3 fb(-1) collected in 2012 by the ATLAS detector operating at the Large Hadron Collider. No events are observed in any of the signal regions, and limits are set on model parameters within supersymmetric scenarios involving R-parity violation, split supersymmetry, and gauge mediation. In some of the search channels, the trigger and search strategy are based only on the decay products of individual long-lived particles, irrespective of the rest of the event. In these cases, the provided limits can easily be reinterpreted in different scenarios.

  • Publication . Article . Preprint . 2008 . Embargo End Date: 01 Jan 2008
    Open Access
    Authors: 
    U. Munari; L. Tomasella; M. Fiorucci; O. Bienaymé; J. Binney; J. Bland-Hawthorn; C. Boeche; R. Campbell; K. C. Freeman; B. Gibson; +13 more
    Publisher: arXiv
    Countries: Netherlands, United Kingdom

    We have used spectra of hot stars from the RAVE Survey in order to investigate the visibility and properties of five diffuse interstellar bands previously reported in the literature. The RAVE spectroscopic survey for Galactic structure and kinematics records CCD spectra covering the 8400-8800 Ang wavelength region at 7500 resolving power. The spectra are obtained with the UK Schmidt at the AAO, equipped with the 6dF multi-fiber positioner. The DIB at 8620.4 Ang is by far the strongest and cleanest of all DIBs occurring within the RAVE wavelength range, with no interference by underlying absorption stellar lines in hot stars. It correlates so tightly with reddening that it turns out to be a reliable tool to measure it, following the relation E(B-V) = 2.72 (+/- 0.03) x E.W.(Ang), valid throughout the general interstellar medium of our Galaxy. The presence of a DIB at 8648 Ang is confirmed. Its intensity appears unrelated to reddening, in agreement with scanty and preliminary reports available in the literature, and its measurability is strongly compromised by severe blending with underlying stellar HeI doublet at 8649 Ang. The two weak DIBS at 8531 and 8572 Ang do not appear real and should actually be blends of underlying stellar lines. The very weak DIB at 8439 Ang cannot be resolved within the profile of the much stronger underlying hydrogen Paschen 18 stellar line. Comment: Accepted in press by A&A

  • Closed Access
    Authors: 
    Andrej Prošek; Francesco Saverio D'Auria; David J. Richards; Borut Mavko;
    Publisher: Elsevier BV

    Abstract The RD-14M large LOCA test, characterized by a reliable set of experimental data, was selected for an international standard problem exercise (SPE) entitled “Intercomparison and validation of computer codes for thermal–hydraulics safety analyses”. The activity was performed within the frame of International Atomic Energy Agency's (IAEAs) Technical Working Group on Advanced Technologies for Heavy Water Reactors (TWG-HWR). In this study, the recently improved fast Fourier transform based method (FFTBM) was used for accuracy quantification of RD-14M large LOCA test B9401 calculations of six participants using four different thermal–hydraulic codes. In addition, developing the capability to calculate the accuracy as a function of time-continues-valued accuracy, did further improvement of FFTBM. Namely, in the past only single valued accuracy parameters for selected time windows and time intervals were calculated. The objective of the study was to demonstrate that the new FFTBM is a powerful tool for quantitative assessment of thermal–hydraulic codes. For demonstration, the test from the facility simulating heavy water reactor was used. The blind accuracy analysis was completed based on solely experimental and calculated data. However, short discussions were held with the representative from Italy (co-author, here) regarding phenomenological windows, variables and void fraction weights selection. In general, the open accuracy analysis confirmed the results obtained in blind accuracy analysis. The main conclusions from accuracy analysis agree with the conclusions from the SPE intercomparison report, which was written independently. Finally, the results suggest that the accuracy of the best calculations of the RD-14M test is comparable with the best calculations of light water reactor experiments.

  • Closed Access
    Authors: 
    Nataša Poklar; Jens Völker; Gregor Anderluh; Peter Maček; Tigran V. Chalikian;
    Publisher: Elsevier BV

    Abstract We have investigated the acid- and base-induced conformational transitions of equinatoxin II (EqTxII), a pore-forming protein, by a combination of CD-spectroscopy, ultrasonic velocimetry, high precision densimetry, viscometry, gel electrophoresis, and hemolytic activity assays. Between pH 7 and 2, EqTxII does not exhibit any significant structural changes. Below pH 2, EqTxII undergoes a native-to-partially unfolded transition with a concomitant loss of its rigid tertiary structure and the formation of a non-native secondary structure containing additional α-helix. The acid-induced denatured state of EqTxII exhibits a higher intrinsic viscosity and a lower adiabatic compressibility than the native state. Above 50°C, the acid-induced denatured state of EqTxII reversibly denatures to a more unfolded state as judged by the far UV CD spectrum of the protein. At alkaline pH, EqTxII undergoes two base-induced conformational transitions. The first transition occurs between pH 7 and 10 and results in a partial disruption of tertiary structure, while the secondary structure remains largely preserved. The second transition occurs between pH 11 and 13 and results in the complete loss of tertiary structure and the formation of a non-native, more α-helical secondary structure. The acid- and base-induced partially unfolded states of EqTxII form water-soluble oligomers at low salt, while at high salt (>350 mM NaCl), the acid-induced denatured state precipitates. The hemolytic activity assay shows that the acid- and base-induced denatured states of EqTxII exhibit significantly reduced activity compared to the native state.

  • Publication . Article . Preprint . 2006
    Open Access English
    Authors: 
    Matt DeVos; Luis Goddyn; Bojan Mohar; Robert Šámal;
    Project: NSERC

    Let A be a finite nonempty subset of an additive abelian group G, and let \Sigma(A) denote the set of all group elements representable as a sum of some subset of A. We prove that |\Sigma(A)| >= |H| + 1/64 |A H|^2 where H is the stabilizer of \Sigma(A). Our result implies that \Sigma(A) = Z/nZ for every set A of units of Z/nZ with |A| >= 8 \sqrt{n}. This consequence was first proved by Erd\H{o}s and Heilbronn for n prime, and by Vu (with a weaker constant) for general n. Comment: 12 pages

  • Open Access
    Authors: 
    Schellenberg, D; Armstrong Schellenberg, J R M; Mushi, A; Savigny de, D; Mgalula, L; Mbuya, C; Victoria, C.G.;
    Country: Tanzania (United Republic of)

    Objective was to document the prevalence, age-distribution, and risk factors for anaemia in Tanzanian children less than 5 years old,thereby assisting in the development of effective strategies for controlling anaemia. Cluster sampling was used to identify 2417 households at random from four contiguous districts in south-eastern United Republic of Tanzania in mid-1999. Data on various social and medical parameters were collected and analysed. Blood haemoglobin concentrations (Hb) were available for 1979 of the 2131 (93%) children identified and ranged from 1.7 to 18.6 g/dl. Overall, 87% (1722) of children had an Hb <11 g/dl, 39% (775) had an Hb <8 g/dl and 3% (65) had an Hb <5 g/dl. The highest prevalence of anaemia of all three levels was in children aged 6–11 months, of whom 10% (22/226) had an Hb <5 g/dl. However, the prevalence of anaemia was already high in children aged 1–5 months (85% had an Hb <11 g/dl, 42% had an Hb <8 g/dl, and 6% had an Hb <5 g/dl). Anaemia was usually asymptomatic and when symptoms arose they were nonspecific and rarely identified as a serious illness by the care provider. A recent history of treatment with antimalarials and iron was rare. Compliance with vaccinations delivered through the Expanded Programme of Immunization (EPI) was 82% and was notassociated with risk of anaemia. Anaemia is extremely common in south-eastern United Republic of Tanzania, even in very young infants. Further implementation of the Integrated Management of Childhood Illness algorithm should improve the case management of anaemia. However, the asymptomatic nature of most episodes of anaemia highlights the need for preventive strategies. The EPI has good coverage of the target population and it may be an appropriate channel for delivering tools for controlling anaemia and malaria.

  • Open Access
    Authors: 
    G. Aad; B. Abbott; J. Abdallah; A.A. Abdelalim; A. Abdesselam; O. Abdinov; B. Abi; M. Abolins; H. Abramowicz; H. Abreu; +191 more
    Publisher: Elsevier BV
    Project: NSERC

    The cross section for the production of W bosons with subsequent decay W to tau nu is measured with the ATLAS detector at the LHC. The analysis is based on a data sample that was recorded in 2010 at a proton-proton center-of-mass energy of sqrt(s) = 7 TeV and corresponds to an integrated luminosity of 34 pb^-1. The cross section is measured in a region of high detector acceptance and then extrapolated to the full phase space. The product of the total W production cross section and the W to tau nu branching ratio is measured to be 11.1 +/- 0.3 (stat) +/- 1.7 (syst) +/- 0.4 (lumi) nb.

  • Open Access English
    Authors: 
    Aigars Miezitis; Marika Petrovica;
    Publisher: Ubiquity Press
  • Open Access English
    Authors: 
    Yin Tat Lee; Aaron Sidford; Sam Chiu-wai Wong;
    Project: NSF | Graduate Research Fellows... (1122374), NSF | AF: Medium: Algorithmic R... (0964033), NSF | CAREER: Geometric Techniq... (0843915), NSF | AF: Large: Collaborative ... (1111109), NSF | AF: Medium: Algorithmic E... (1408635)

    We improve upon the running time for finding a point in a convex set given a separation oracle. In particular, given a separation oracle for a convex set $K\subset \mathbb{R}^n$ contained in a box of radius $R$, we show how to either find a point in $K$ or prove that $K$ does not contain a ball of radius $\epsilon$ using an expected $O(n\log(nR/\epsilon))$ oracle evaluations and additional time $O(n^3\log^{O(1)}(nR/\epsilon))$. This matches the oracle complexity and improves upon the $O(n^{\omega+1}\log(nR/\epsilon))$ additional time of the previous fastest algorithm achieved over 25 years ago by Vaidya for the current matrix multiplication constant $\omega<2.373$ when $R/\epsilon=n^{O(1)}$. Using a mix of standard reductions and new techniques, our algorithm yields improved runtimes for solving classic problems in continuous and combinatorial optimization: Submodular Minimization: Our weakly and strongly polynomial time algorithms have runtimes of $O(n^2\log nM\cdot\text{EO}+n^3\log^{O(1)}nM)$ and $O(n^3\log^2 n\cdot\text{EO}+n^4\log^{O(1)}n)$, improving upon the previous best of $O((n^4\text{EO}+n^5)\log M)$ and $O(n^5\text{EO}+n^6)$. Matroid Intersection: Our runtimes are $O(nrT_{\text{rank}}\log n\log (nM) +n^3\log^{O(1)}(nM))$ and $O(n^2\log (nM) T_{\text{ind}}+n^3 \log^{O(1)} (nM))$, achieving the first quadratic bound on the query complexity for the independence and rank oracles. In the unweighted case, this is the first improvement since 1986 for independence oracle. Submodular Flow: Our runtime is $O(n^2\log nCU\cdot\text{EO}+n^3\log^{O(1)}nCU)$, improving upon the previous bests from 15 years ago roughly by a factor of $O(n^4)$. Semidefinite Programming: Our runtime is $\tilde{O}(n(n^2+m^{\omega}+S))$, improving upon the previous best of $\tilde{O}(n(n^{\omega}+m^{\omega}+S))$ for the regime where the number of nonzeros $S$ is small. Comment: 111 pages, FOCS 2015

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Include:
The following results are related to Canada. Are you interested to view more results? Visit OpenAIRE - Explore.
3,186 Research products, page 1 of 319
  • Publication . Article . 2011
    Open Access
    Authors: 
    Janez Bernik; Mitja Mastnak; Heydar Radjavi;
    Publisher: Elsevier BV

    Abstract We study various aspects of how certain positivity assumptions on complex matrix semigroups affect their structure. Our main result is that every irreducible group of complex matrices with nonnegative diagonal entries is simultaneously similar to a group of weighted permutations. We also consider the corresponding question for semigroups and discuss the effect of the assumption that a fixed linear functional has nonnegative values when restricted to a given semigroup.

  • Open Access
    Authors: 
    Georges Aad; Leszek Adamczyk; Jahred Adelman; Tim Adye; Tatjana Agatonovic-Jovin; J. A. Aguilar-Saavedra; Faig Ahmadov; Giulio Aielli; Gian Luigi Alberghi; J. Albert; +599 more
    Publisher: American Physical Society (APS)
    Project: NSERC

    Many extensions of the Standard Model posit the existence of heavy particles with long lifetimes. This article presents the results of a search for events containing at least one long-lived particle that decays at a significant distance from its production point into two leptons or into five or more charged particles. This analysis uses a data sample of proton-proton collisions at root s = 8 TeV corresponding to an integrated luminosity of 20.3 fb(-1) collected in 2012 by the ATLAS detector operating at the Large Hadron Collider. No events are observed in any of the signal regions, and limits are set on model parameters within supersymmetric scenarios involving R-parity violation, split supersymmetry, and gauge mediation. In some of the search channels, the trigger and search strategy are based only on the decay products of individual long-lived particles, irrespective of the rest of the event. In these cases, the provided limits can easily be reinterpreted in different scenarios.

  • Publication . Article . Preprint . 2008 . Embargo End Date: 01 Jan 2008
    Open Access
    Authors: 
    U. Munari; L. Tomasella; M. Fiorucci; O. Bienaymé; J. Binney; J. Bland-Hawthorn; C. Boeche; R. Campbell; K. C. Freeman; B. Gibson; +13 more
    Publisher: arXiv
    Countries: Netherlands, United Kingdom

    We have used spectra of hot stars from the RAVE Survey in order to investigate the visibility and properties of five diffuse interstellar bands previously reported in the literature. The RAVE spectroscopic survey for Galactic structure and kinematics records CCD spectra covering the 8400-8800 Ang wavelength region at 7500 resolving power. The spectra are obtained with the UK Schmidt at the AAO, equipped with the 6dF multi-fiber positioner. The DIB at 8620.4 Ang is by far the strongest and cleanest of all DIBs occurring within the RAVE wavelength range, with no interference by underlying absorption stellar lines in hot stars. It correlates so tightly with reddening that it turns out to be a reliable tool to measure it, following the relation E(B-V) = 2.72 (+/- 0.03) x E.W.(Ang), valid throughout the general interstellar medium of our Galaxy. The presence of a DIB at 8648 Ang is confirmed. Its intensity appears unrelated to reddening, in agreement with scanty and preliminary reports available in the literature, and its measurability is strongly compromised by severe blending with underlying stellar HeI doublet at 8649 Ang. The two weak DIBS at 8531 and 8572 Ang do not appear real and should actually be blends of underlying stellar lines. The very weak DIB at 8439 Ang cannot be resolved within the profile of the much stronger underlying hydrogen Paschen 18 stellar line. Comment: Accepted in press by A&A

  • Closed Access
    Authors: 
    Andrej Prošek; Francesco Saverio D'Auria; David J. Richards; Borut Mavko;
    Publisher: Elsevier BV

    Abstract The RD-14M large LOCA test, characterized by a reliable set of experimental data, was selected for an international standard problem exercise (SPE) entitled “Intercomparison and validation of computer codes for thermal–hydraulics safety analyses”. The activity was performed within the frame of International Atomic Energy Agency's (IAEAs) Technical Working Group on Advanced Technologies for Heavy Water Reactors (TWG-HWR). In this study, the recently improved fast Fourier transform based method (FFTBM) was used for accuracy quantification of RD-14M large LOCA test B9401 calculations of six participants using four different thermal–hydraulic codes. In addition, developing the capability to calculate the accuracy as a function of time-continues-valued accuracy, did further improvement of FFTBM. Namely, in the past only single valued accuracy parameters for selected time windows and time intervals were calculated. The objective of the study was to demonstrate that the new FFTBM is a powerful tool for quantitative assessment of thermal–hydraulic codes. For demonstration, the test from the facility simulating heavy water reactor was used. The blind accuracy analysis was completed based on solely experimental and calculated data. However, short discussions were held with the representative from Italy (co-author, here) regarding phenomenological windows, variables and void fraction weights selection. In general, the open accuracy analysis confirmed the results obtained in blind accuracy analysis. The main conclusions from accuracy analysis agree with the conclusions from the SPE intercomparison report, which was written independently. Finally, the results suggest that the accuracy of the best calculations of the RD-14M test is comparable with the best calculations of light water reactor experiments.

  • Closed Access
    Authors: 
    Nataša Poklar; Jens Völker; Gregor Anderluh; Peter Maček; Tigran V. Chalikian;
    Publisher: Elsevier BV

    Abstract We have investigated the acid- and base-induced conformational transitions of equinatoxin II (EqTxII), a pore-forming protein, by a combination of CD-spectroscopy, ultrasonic velocimetry, high precision densimetry, viscometry, gel electrophoresis, and hemolytic activity assays. Between pH 7 and 2, EqTxII does not exhibit any significant structural changes. Below pH 2, EqTxII undergoes a native-to-partially unfolded transition with a concomitant loss of its rigid tertiary structure and the formation of a non-native secondary structure containing additional α-helix. The acid-induced denatured state of EqTxII exhibits a higher intrinsic viscosity and a lower adiabatic compressibility than the native state. Above 50°C, the acid-induced denatured state of EqTxII reversibly denatures to a more unfolded state as judged by the far UV CD spectrum of the protein. At alkaline pH, EqTxII undergoes two base-induced conformational transitions. The first transition occurs between pH 7 and 10 and results in a partial disruption of tertiary structure, while the secondary structure remains largely preserved. The second transition occurs between pH 11 and 13 and results in the complete loss of tertiary structure and the formation of a non-native, more α-helical secondary structure. The acid- and base-induced partially unfolded states of EqTxII form water-soluble oligomers at low salt, while at high salt (>350 mM NaCl), the acid-induced denatured state precipitates. The hemolytic activity assay shows that the acid- and base-induced denatured states of EqTxII exhibit significantly reduced activity compared to the native state.

  • Publication . Article . Preprint . 2006
    Open Access English
    Authors: 
    Matt DeVos; Luis Goddyn; Bojan Mohar; Robert Šámal;
    Project: NSERC

    Let A be a finite nonempty subset of an additive abelian group G, and let \Sigma(A) denote the set of all group elements representable as a sum of some subset of A. We prove that |\Sigma(A)| >= |H| + 1/64 |A H|^2 where H is the stabilizer of \Sigma(A). Our result implies that \Sigma(A) = Z/nZ for every set A of units of Z/nZ with |A| >= 8 \sqrt{n}. This consequence was first proved by Erd\H{o}s and Heilbronn for n prime, and by Vu (with a weaker constant) for general n. Comment: 12 pages

  • Open Access
    Authors: 
    Schellenberg, D; Armstrong Schellenberg, J R M; Mushi, A; Savigny de, D; Mgalula, L; Mbuya, C; Victoria, C.G.;
    Country: Tanzania (United Republic of)

    Objective was to document the prevalence, age-distribution, and risk factors for anaemia in Tanzanian children less than 5 years old,thereby assisting in the development of effective strategies for controlling anaemia. Cluster sampling was used to identify 2417 households at random from four contiguous districts in south-eastern United Republic of Tanzania in mid-1999. Data on various social and medical parameters were collected and analysed. Blood haemoglobin concentrations (Hb) were available for 1979 of the 2131 (93%) children identified and ranged from 1.7 to 18.6 g/dl. Overall, 87% (1722) of children had an Hb <11 g/dl, 39% (775) had an Hb <8 g/dl and 3% (65) had an Hb <5 g/dl. The highest prevalence of anaemia of all three levels was in children aged 6–11 months, of whom 10% (22/226) had an Hb <5 g/dl. However, the prevalence of anaemia was already high in children aged 1–5 months (85% had an Hb <11 g/dl, 42% had an Hb <8 g/dl, and 6% had an Hb <5 g/dl). Anaemia was usually asymptomatic and when symptoms arose they were nonspecific and rarely identified as a serious illness by the care provider. A recent history of treatment with antimalarials and iron was rare. Compliance with vaccinations delivered through the Expanded Programme of Immunization (EPI) was 82% and was notassociated with risk of anaemia. Anaemia is extremely common in south-eastern United Republic of Tanzania, even in very young infants. Further implementation of the Integrated Management of Childhood Illness algorithm should improve the case management of anaemia. However, the asymptomatic nature of most episodes of anaemia highlights the need for preventive strategies. The EPI has good coverage of the target population and it may be an appropriate channel for delivering tools for controlling anaemia and malaria.

  • Open Access
    Authors: 
    G. Aad; B. Abbott; J. Abdallah; A.A. Abdelalim; A. Abdesselam; O. Abdinov; B. Abi; M. Abolins; H. Abramowicz; H. Abreu; +191 more
    Publisher: Elsevier BV
    Project: NSERC

    The cross section for the production of W bosons with subsequent decay W to tau nu is measured with the ATLAS detector at the LHC. The analysis is based on a data sample that was recorded in 2010 at a proton-proton center-of-mass energy of sqrt(s) = 7 TeV and corresponds to an integrated luminosity of 34 pb^-1. The cross section is measured in a region of high detector acceptance and then extrapolated to the full phase space. The product of the total W production cross section and the W to tau nu branching ratio is measured to be 11.1 +/- 0.3 (stat) +/- 1.7 (syst) +/- 0.4 (lumi) nb.

  • Open Access English
    Authors: 
    Aigars Miezitis; Marika Petrovica;
    Publisher: Ubiquity Press
  • Open Access English
    Authors: 
    Yin Tat Lee; Aaron Sidford; Sam Chiu-wai Wong;
    Project: NSF | Graduate Research Fellows... (1122374), NSF | AF: Medium: Algorithmic R... (0964033), NSF | CAREER: Geometric Techniq... (0843915), NSF | AF: Large: Collaborative ... (1111109), NSF | AF: Medium: Algorithmic E... (1408635)

    We improve upon the running time for finding a point in a convex set given a separation oracle. In particular, given a separation oracle for a convex set $K\subset \mathbb{R}^n$ contained in a box of radius $R$, we show how to either find a point in $K$ or prove that $K$ does not contain a ball of radius $\epsilon$ using an expected $O(n\log(nR/\epsilon))$ oracle evaluations and additional time $O(n^3\log^{O(1)}(nR/\epsilon))$. This matches the oracle complexity and improves upon the $O(n^{\omega+1}\log(nR/\epsilon))$ additional time of the previous fastest algorithm achieved over 25 years ago by Vaidya for the current matrix multiplication constant $\omega<2.373$ when $R/\epsilon=n^{O(1)}$. Using a mix of standard reductions and new techniques, our algorithm yields improved runtimes for solving classic problems in continuous and combinatorial optimization: Submodular Minimization: Our weakly and strongly polynomial time algorithms have runtimes of $O(n^2\log nM\cdot\text{EO}+n^3\log^{O(1)}nM)$ and $O(n^3\log^2 n\cdot\text{EO}+n^4\log^{O(1)}n)$, improving upon the previous best of $O((n^4\text{EO}+n^5)\log M)$ and $O(n^5\text{EO}+n^6)$. Matroid Intersection: Our runtimes are $O(nrT_{\text{rank}}\log n\log (nM) +n^3\log^{O(1)}(nM))$ and $O(n^2\log (nM) T_{\text{ind}}+n^3 \log^{O(1)} (nM))$, achieving the first quadratic bound on the query complexity for the independence and rank oracles. In the unweighted case, this is the first improvement since 1986 for independence oracle. Submodular Flow: Our runtime is $O(n^2\log nCU\cdot\text{EO}+n^3\log^{O(1)}nCU)$, improving upon the previous bests from 15 years ago roughly by a factor of $O(n^4)$. Semidefinite Programming: Our runtime is $\tilde{O}(n(n^2+m^{\omega}+S))$, improving upon the previous best of $\tilde{O}(n(n^{\omega}+m^{\omega}+S))$ for the regime where the number of nonzeros $S$ is small. Comment: 111 pages, FOCS 2015