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Peter Nelson

Publications and source records attributed to Peter Nelson.

At least 55 records · Page 3Linked to original sources
arXiv2017

Stability and exact Turan numbers for matroids

We consider the Turán-type problem of bounding the size of a set $M \subseteq \mathbb{F}_2^n$ that does not contain a linear copy of a given fixed set $N \subseteq \mathbb{F}_2^k$, where $n$ is large compared to $k$. An Erdős-Stone type theorem [5] in this setting gives a bound that is tight up to a $o(2^n)$ error term; our first main result gives a stability version of this theorem, showing that such an $M$ that is close in size to the upper bound in [5] is close in edit distance to the obvious extremal example. Our second result shows that the error term in [5] is exactly controlled by the solution to one of a class of `sparse' extremal problems, and in many cases eliminates the error term completely to give a sharp upper bound on $|M|$.

math.CO↗
arXiv2017

Doubly exponentially many Ingleton matroids

A matroid is Ingleton if all quadruples of subsets of its ground set satisfy Ingleton's inequality. In particular, representable matroids are Ingleton. We show that the number of Ingleton matroids on ground set $[n]$ is doubly exponential in $n$; it follows that almost all Ingleton matroids are non-representable.

math.CO↗
arXiv2017

Survey of Period Variations of Superhumps in SU UMa-Type Dwarf Novae. IX: The Ninth Year (2016-2017)

Continuing the project described by Kato et al. (2009, arXiv:0905.1757), we collected times of superhump maxima for 127 SU UMa-type dwarf novae observed mainly during the 2016--2017 season and characterized these objects. We provide updated statistics of relation between the orbital period and the variation of superhumps, the relation between period variations and the rebrightening type in WZ Sge-type objects. We obtained the period minimum of 0.05290(2)d and confirmed the presence of the period gap above the orbital period ~0.09d. We note that four objects (NY Her, 1RXS J161659.5+620014, CRTS J033349.8-282244 and SDSS J153015.04+094946.3) have supercycles shorter than 100d but show infrequent normal outbursts. We consider that these objects are similar to V503 Cyg, whose normal outbursts are likely suppressed by a disk tilt. These four objects are excellent candidates to search for negative superhumps. DDE 48 appears to be a member of ER UMa-type dwarf novae. We identified a new eclipsing SU UMa-type object MASTER OT J220559.40-341434.9. We observed 21 WZ Sge-type dwarf novae during this interval and reported 18 out of them in this paper. Among them, ASASSN-16js is a good candidate for a period bouncer. ASASSN-16ia showed a precursor outburst for the first time in a WZ Sge-type superoutburst. ASASSN-16kg, CRTS J000130.5+050624 and SDSS J113551.09+532246.2 are located in the period gap. We have newly obtained 15 orbital periods, including periods from early superhumps.

astro-ph.SR↗
arXiv2016

Return of the King: Time-Series Photometry of FO Aquarii's Initial Recovery from its Unprecedented 2016 Low State

In 2016 May, the intermediate polar FO~Aqr was detected in a low state for the first time in its observational history. We report time-resolved photometry of the system during its initial recovery from this faint state. Our data, which includes high-speed photometry with cadences of just 2 sec, shows the existence of very strong periodicities at 22.5 min and 11.26 min, equivalent to the spin-orbit beat frequency and twice its value, respectively. A pulse at the spin frequency is also present but at a much lower amplitude than is normally observed in the bright state. By comparing our power spectra with theoretical models, we infer that a substantial amount of accretion was stream-fed during our observations, in contrast to the disk-fed accretion that dominates the bright state. In addition, we find that FO~Aqr's rate of recovery has been unusually slow in comparison to rates of recovery seen in other magnetic cataclysmic variables, with an $e$-folding time of 115$\pm7$ days. The recovery also shows irregular variations in the median brightness of as much as 0.2~mag over a 10-day span. Finally, we show that the arrival times of the spin pulses are dependent upon the system's overall brightness.

astro-ph.SR↗
arXiv2016

KELT-17b: A hot-Jupiter transiting an A-star in a misaligned orbit detected with Doppler tomography

We present the discovery of a hot-Jupiter transiting the V=9.23 mag main-sequence A-star KELT-17 (BD+14 1881). KELT-17b is a 1.31 -0.29/+0.28 Mj, 1.525 -0.060/+0.065 Rj hot-Jupiter in a 3.08 day period orbit misaligned at -115.9 +/- 4.1 deg to the rotation axis of the star. The planet is confirmed via both the detection of the radial velocity orbit, and the Doppler tomographic detection of the shadow of the planet over two transits. The nature of the spin-orbit misaligned transit geometry allows us to place a constraint on the level of differential rotation in the host star; we find that KELT-17 is consistent with both rigid-body rotation and solar differential rotation rates (alpha < 0.30 at 2 sigma significance). KELT-17 is only the fourth A-star with a confirmed transiting planet, and with a mass of 1.635 -0.061/+0.066 Msun, effective temperature of 7454 +/- 49 K, and projected rotational velocity v sin I_* = 44.2 -1.3/+1.5 km/s; it is amongst the most massive, hottest, and most rapidly rotating of known planet hosts.

astro-ph.EP↗
arXiv2016

KELT-11b: A Highly Inflated Sub-Saturn Exoplanet Transiting the V=8 Subgiant HD 93396

We report the discovery of a transiting exoplanet, KELT-11b, orbiting the bright ($V=8.0$) subgiant HD 93396. A global analysis of the system shows that the host star is an evolved subgiant star with $T_{\rm eff} = 5370\pm51$ K, $M_{*} = 1.438_{-0.052}^{+0.061} M_{\odot}$, $R_{*} = 2.72_{-0.17}^{+0.21} R_{\odot}$, log $g_*= 3.727_{-0.046}^{+0.040}$, and [Fe/H]$ = 0.180\pm0.075$. The planet is a low-mass gas giant in a $P = 4.736529\pm0.00006$ day orbit, with $M_{P} = 0.195\pm0.018 M_J$, $R_{P}= 1.37_{-0.12}^{+0.15} R_J$, $ρ_{P} = 0.093_{-0.024}^{+0.028}$ g cm$^{-3}$, surface gravity log ${g_{P}} = 2.407_{-0.086}^{+0.080}$, and equilibrium temperature $T_{eq} = 1712_{-46}^{+51}$ K. KELT-11 is the brightest known transiting exoplanet host in the southern hemisphere by more than a magnitude, and is the 6th brightest transit host to date. The planet is one of the most inflated planets known, with an exceptionally large atmospheric scale height (2763 km), and an associated size of the expected atmospheric transmission signal of 5.6%. These attributes make the KELT-11 system a valuable target for follow-up and atmospheric characterization, and it promises to become one of the benchmark systems for the study of inflated exoplanets.

astro-ph.EP↗
arXiv2016

GW Librae: Still Hot Eight Years Post-Outburst

We report continued Hubble Space Telescope (HST) ultraviolet spectra and ground-based optical photometry and spectroscopy of GW Librae eight years after its largest known dwarf nova outburst in 2007. This represents the longest cooling timescale measured for any dwarf nova. The spectra reveal that the white dwarf still remains about 3000 K hotter than its quiescent value. Both ultraviolet and optical light curves show a short period of 364-373 s, similar to one of the non-radial pulsation periods present for years prior to the outburst, and with a similar large UV/optical amplitude ratio. A large modulation at a period of 2 h (also similar to that observed prior to outburst) is present in the optical data preceding and during the HST observations, but the satellite observation intervals did not cover the peaks of the optical modulation so it is not possible to determine its corresponding UV amplitude. The similarity of the short and long periods to quiescent values implies the pulsating, fast spinning white dwarf in GW Lib may finally be nearing its quiescent configuration.

astro-ph.SR↗
arXiv2016

The critical number of dense triangle-free binary matroids

We show that, for each real number $ε> 0$ there is an integer $c$ such that, if $M$ is a simple triangle-free binary matroid with $|M| \ge (\tfrac{1}{4} + ε) 2^{r(M)}$, then $M$ has critical number at most $c$. We also give a construction showing that no such result holds for any real number less than $\tfrac{1}{4}$. This shows that the "critical threshold" for the triangle is $\tfrac 1 4$. We extend the notion of critical threshold to every simple binary matroid $N$ and conjecture that, if $N$ has critical number $c\ge 3$, then $N$ has critical threshold $1-i\cdot 2^{-c}$ for some $i\in \{2,3,4\}$. We give some support for the conjecture by establishing lower bounds.

math.CO↗
arXiv2016

Matroids denser than a clique

The growth-rate function for a minor-closed class $\mathcal{M}$ of matroids is the function $h$ where, for each non-negative integer $r$, $h(r)$ is the maximum number of elements of a simple matroid in $\mathcal{M}$ with rank at most $r$. The Growth-Rate Theorem of Geelen, Kabell, Kung, and Whittle shows, essentially, that the growth-rate function is always either linear, quadratic, exponential, or infinite. Morover, if the growth-rate function is quadratic, then $h(r)\ge \binom{r+1}{2}$, with the lower bound coming from the fact that such classes necessarily contain all graphic matroids. We characterise the classes that satisfy $h(r) = \binom{r+1}{2}$ for all sufficiently large $r$.

math.CO↗
arXiv2016

Matroids denser than a projective geometry

The growth-rate function for a minor-closed class $\mathcal{M}$ of matroids is the function $h$ where, for each non-negative integer $r$, $h(r)$ is the maximum number of elements of a simple matroid in $\mathcal{M}$ with rank at most $r$. The Growth-Rate Theorem of Geelen, Kabell, Kung, and Whittle shows, essentially, that the growth-rate function is always either linear, quadratic, exponential with some prime power $q$ as the base, or infinite. Morover, if the growth-rate function is exponential with base $q$, then the class contains all GF$(q)$-representable matroids, and so $h(r)\ge \frac{q^r-1}{q-1}$ for each $r$. We characterise the classes that satisfy $h(r) = \frac{q^r-1}{q-1}$ for all sufficiently large $r$. As a consequence, we determine the eventual value of the growth rate function for most classes defined by excluding lines, free spikes and/or free swirls.

math.CO↗
arXiv2016

The maximum-likelihood decoding threshold for graphic codes

For a class $\mathcal{C}$ of binary linear codes, we write $θ_{\mathcal{C}}\colon (0,1) \to [0,\frac{1}{2}]$ for the maximum-likelihood decoding threshold function of $\mathcal{C}$, the function whose value at $R \in (0,1)$ is the largest bit-error rate $p$ that codes in $\mathcal{C}$ can tolerate with a negligible probability of maximum-likelihood decoding error across a binary symmetric channel. We show that, if $\mathcal{C}$ is the class of cycle codes of graphs, then $θ_{\mathcal{C}}(R) \le \frac{(1-\sqrt{R})^2}{2(1+R)}$ for each $R$, and show that equality holds only when $R$ is asymptotically achieved by cycle codes of regular graphs.

cs.IT↗
arXiv2016

T Pyxidis: Death by a Thousand Novae

We report a 20-year campaign to track the 1.8 hour photometric wave in the recurrent nova T Pyxidis, using the global telescope network of the Center for Backyard Astrophysics. During 1996-2011, that wave was highly stable in amplitude and waveform, resembling the orbital wave commonly seen in supersoft binaries. The period, however, was found to increase on a timescale P/P-dot=3x10^5 years. This suggests a mass transfer rate in quiescence of ~10^-7 M_sol/yr, in substantial agreement with the accretion rate based on the star's luminosity. This is ~2000x greater than is typical for cataclysmic variables of that orbital period. During the post-eruption quiescence (2012-2016), the star continued on its merry but mysterious way - similar luminosity, similar P/P-dot (2.4x10^5 years). The orbital signal became vanishingly weak (<0.003 mag) near maximum light of the 2011 eruption. By day 170 of the eruption, near V=11, the orbital signal reappeared with an amplitude of 0.005 mag. It then gradually strengthened to its normal 0.08 mag amplitude, as the star declined to its "quiescent" magnitude of 15.7. During the ~1 year of invisibility and low amplitude, the orbital signal had increased in period by 0.0054(7)%. This is probably a measure of the mass ejected in the nova outburst. For a plausible choice of binary parameters, that mass is at least 3x10^-5 M_sol, and probably more. This represents >300 years of accretion at the pre-outburst rate, but the time between outbursts was only 45 years. Thus the erupting white dwarf seems to have ejected at least 6x more mass than it accreted. If this eruption is typical, the white dwarf must be eroding, rather than growing, in mass. Unless the present series of eruptions is a short-lived episode, the binary dynamics appear to be a mutual suicide pact between the eroding white dwarf and the low-mass secondary, excited ... . (etc., abstract continues)

astro-ph.SR↗
arXiv2016

The structure of matroids with a spanning clique or projective geometry

Let $s,n \ge 2$ be integers. We give a qualitative structural description of every matroid $M$ that is spanned by a frame matroid of a complete graph and has no $U_{s,2s}$-minor and no rank-$n$ projective geometry minor, showing that every such matroid is `close' to a frame matroid. We also give a similar description of every matroid $M$ with a spanning projective geometry over a field GF$(q)$ as a restriction and with no $U_{s,2s}$-minor and no PG$(n,q')$-minor for any $q' > q$, showing that such an $M$ is `close' to a GF$(q)$-representable matroid.

math.CO↗
arXiv2015

On the probability that a random subgraph contains a circuit

Let $μ> 2$ and $ε> 0$. We show that, if $G$ is a sufficiently large simple graph of average degree at least $μ$, and $H$ is a random spanning subgraph of $G$ formed by including each edge independently with probability $p \ge \tfrac{1}{μ-1} + ε$, then $H$ contains a cycle with probability at least $1 - ε$.

math.CO↗
arXiv2014

The densest matroids in minor-closed classes with exponential growth rate

The $\mathit{growth\ rate\ function}$ for a nonempty minor-closed class of matroids $\mathcal{M}$ is the function $h_{\mathcal{M}}(n)$ whose value at an integer $n \ge 0$ is defined to be the maximum number of elements in a simple matroid in $\mathcal{M}$ of rank at most $n$. Geelen, Kabell, Kung and Whittle showed that, whenever $h_{\mathcal{M}}(2)$ is finite, the function $h_{\mathcal{M}}$ grows linearly, quadratically or exponentially in $n$ (with base equal to a prime power $q$), up to a constant factor. We prove that in the exponential case, there are nonnegative integers $k$ and $d \le \tfrac{q^{2k}-1}{q-1}$ such that $h_{\mathcal{M}}(n) = \frac{q^{n+k}-1}{q-1} - qd$ for all sufficiently large $n$, and we characterise which matroids attain the growth rate function for large $n$. We also show that if $\mathcal{M}$ is specified in a certain `natural' way (by intersections of classes of matroids representable over different finite fields and/or by excluding a finite set of minors), then the constants $k$ and $d$, as well as the point that `sufficiently large' begins to apply to $n$, can be determined by a finite computation.

math.CO↗
arXiv2014

Survey of Period Variations of Superhumps in SU UMa-Type Dwarf Novae. VI: The Sixth Year (2013-2014)

Continuing the project described by Kato et al. (2009, PASJ, 61, S395, arXiv:0905.1757), we collected times of superhump maxima for 56 SU UMa-type dwarf novae mainly observed during the 2013-2014 season and characterized these objects. We detected negative superhumps in VW Hyi and indicated that the low number of normal outbursts in some supercycle can be interpreted as a result of the disk tilt. This finding, combined with the Kepler observation of V1504 Cyg and V344 Lyr, suggests that the disk tilt is responsible for modulating the outburst pattern in SU UMa-type dwarf novae. We also studied the deeply eclipsing WZ Sge-type dwarf nova MASTER OT J005740.99+443101.5 and found evidence of a sharp eclipse during the phase of early superhumps. The profile can be reproduced by a combination of the eclipse of the axisymmetric disk and the uneclipsed light source of early superhumps. This finding confirms the lack of evince of a greatly enhanced hot spot during the early stage of WZ Sge-type outburst. We detected growing (stage A) superhumps in MN Dra and give a suggestion that some of SU UMa-type dwarf novae situated near the critical condition of tidal instability may show long-lasting stage A superhumps. The large negative period derivatives reported in such systems can be understood a result of the combination of stage A and B superhumps. The WZ Sge-type dwarf novae AL Com and ASASSN-13ck showed a long-lasting (plateau-type) rebrightening. In the early phase of the rebrightening, both objects showed a precursor-like outburst, suggesting that the long-lasting rebrightening is triggered by a precursor outburst.

astro-ph.SR↗
arXiv2014

On the existence of asymptotically good linear codes in minor-closed classes

Let $\mathcal{C} = (C_1, C_2, \ldots)$ be a sequence of codes such that each $C_i$ is a linear $[n_i,k_i,d_i]$-code over some fixed finite field $\mathbb{F}$, where $n_i$ is the length of the codewords, $k_i$ is the dimension, and $d_i$ is the minimum distance. We say that $\mathcal{C}$ is asymptotically good if, for some $\varepsilon > 0$ and for all $i$, $n_i \geq i$, $k_i/n_i \geq \varepsilon$, and $d_i/n_i \geq \varepsilon$. Sequences of asymptotically good codes exist. We prove that if $\mathcal{C}$ is a class of GF$(p^n)$-linear codes (where $p$ is prime and $n \geq 1$), closed under puncturing and shortening, and if $\mathcal{C}$ contains an asymptotically good sequence, then $\mathcal{C}$ must contain all GF$(p)$-linear codes. Our proof relies on a powerful new result from matroid structure theory.

math.CO↗