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# Probability of overlap between independent samples of different sizes

Today, I was trying to use probabilities to make an 'everyday' (and not very important) decision... but I found that I'd forgotten how to approach this sort of problem (if I am correct in believing that I ever knew how to deal with a problem like this).

Here is the form of the problem I was trying to solve:

There are Q objects in a container, each with its own unique color. Agent1 takes a sample G of M unique objects out of the container, and then puts those M objects back into the container.

If Agent2 takes a sample V of L unique objects out of the container, then...

1. What is the probability that the larger of the sets G and V will contain the smaller of these sets?

2. What is the probability that the sets G and V will have an overlap of T elements?

To give you a rough idea of what I was trying to figure out, I was thinking: "Hmm... There are 10,000 'things' to choose from, and I assume (for simplicity!) that each one has an equal chance of being chosen. I've picked 900 'things'. My friend picked 1500 things... and he picked 890 things in common with me. How likely is it that my friend peeked at my 'picking' history, and copied me?"

• Question 2 is a simpler version of stats.stackexchange.com/questions/52004/…, which concerns three samples. If you take any one of those three to be all the contents of the container you will obtain the answer. Question 1 is a special case of question 2.
– whuber
Mar 19 '13 at 22:51

This is kind of similar to capture-recapture (or mark-and-recapture) sampling, but instead of assuming random selection and trying to estimate the population size (you know it already), you want to see if the recapture is consistent with resampling 'at random'. Your problem turns out to be easier.

So imagine you have an urn full of white balls. When you sample yours, you magically turn them black before putting them back. So now the urn has (otherwise identical) black and white balls.

Your friend draws his sample, and your interest is "does he get 'too many' black balls?". If he's sampling at random, the number of black balls in his sample follows a hypergeometric distribution.

You can assess the probability of getting as many as he got, or more (i.e. a sample at least as unusual as his) by finding the upper tail probability from the hypergeometric. In large samples like yours, you could use a normal approximation (I'd be inclined to use a continuity correction).

To formally test whether it could have happened by chance, you'd compare that upper tail probability with your favorite significance level.

This tells you the probability of a result at least as weird as he got if he wasn't copying you. To compute the actual probability you ask about:

"Hmm... There are 10,000 'things' to choose from, and I assume (for simplicity!) that each one has an equal chance of being chosen. I've picked 900 'things'. My friend picked 1500 things... and he picked 890 things in common with me. How likely is it that my friend peeked at my 'picking' history, and copied me?"

- which flips the conditioning around - would require taking a Bayesian approach. Which means you need a prior probability that he copied you.

Using the numbers in your question, to look at the upper tail probabilities mentioned before, the numbers you give already start to look a little bit suspicious at 152 items in common:

> phyper(152,900,10000-900,1500,lower.tail=FALSE)
[1] 0.04497392

quite suspicious at by 160:

> phyper(160,900,10000-900,1500,lower.tail=FALSE)
[1] 0.007129847

And you can certainly rule out random selection producing results like that well before it gets as high as 890.

That doesn't automatically imply that your friend copied you - perhaps there's some other source of nonrandomness. It just says 'this didn't just happen by chance'.

The give the numbers in a particular instance, the probability that 'the larger includes the smaller' is just an extreme-tail hypergeometric probability. This will generally be very small, unless there are hardly any items in the smaller sample.


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# Multidimensional Binary Vector Assignment problem: standard, structural and above guarantee parameterizations

DMTCS Vol. 19 Nb. 4

## Journal - Discrete Mathematics and Theoretical Computer Science (2017)

Authors: Marin Bougeret and Guillerme Duvillié and Rodolphe Giroudeau and Rémi Watrigant

In this article we focus on the parameterized complexity of the Multidimensional Binary Vector Assignment problem (called $\textbf{bMVA}$). An input of this problem is defined by $m$ disjoint sets $V^1, V^2, \dots, V^m$, each composed of $n$ binary vectors of size $p$. An output is a set of $n$ disjoint $m$-tuples of vectors, where each $m$-tuple is obtained by picking one vector from each set $V^i$. To each $m$-tuple we associate a $p$ dimensional vector by applying the bit-wise AND operation on the $m$ vectors of the tuple. The objective is to minimize the total number of zeros in these $n$ vectors. mBVA can be seen as a variant of multidimensional matching where hyperedges are implicitly locally encoded via labels attached to vertices, but was originally introduced in the context of integrated circuit manufacturing.

We provide for this problem FPT algorithms and negative results ($ETH$-based results, $W$[2]-hardness and a kernel lower bound) according to several parameters: the standard parameter $k$ i.e. the total number of zeros), as well as two parameters above some guaranteed values.

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# Posters

• PULSARS and NEUTRON STARS
• 1.01
• Katie Auchettl
• ### X-ray analysis of the proper motion and PWN for PSR J1741-2054

We report on the X-ray analysis of PSR J1741-2054 carried out as a part of the Chandra XVP program (6 ACIS-S observations, totalling ~300 ks over 5 months). By registering this new epoch of observations using X-ray point sources in the field of view to an archival observation taken 3.2 years earlier, we are able to measure the proper motion of the pulsar with > 3 sigma significance. We also investigate the spatial and spectral properties of the pulsar, its compact nebula and extended tail. We find that the compact nebula can be well described with an absorbed power-law with photon index of Gamma=1.6+/-0.2, while the tail shows no evidence of variation in the spectral index with the distance from the pulsar. We have also investigated the X-ray spectrum of the neutron star.

• 1.02
• Werner Becker
• ### A Search for X-ray Counterparts of Radio Pulsars

Cross-correlating the radio timing positions of all known radio pulsars with archival X-ray observations, we identified new X-ray counterparts of radio pulsars. In most cases the archival data are too sparse to support a detailed spectral and timing analysis. About one-third of the new detections are millisecond-pulsars. The others belong to the group of Vela-like and middle-aged pulsars. Furthermore, we deduced upper limits of the X-ray flux for more than 200 other radio pulsars. This large sample enables us to study the X-ray efficiency of those sources and to put further constrains on models which describe the thermal evolution of neutron stars.

• 1.03
• Celia Sanchez-Fernandez
• ### INTEGRAL observations of GRO J1744-28 during the 2014 outburst

We present here preliminary results of the analysis of INTEGRAL observations of GRO J1744-28, the bursting pulsar, during the 2014 outburst.

Poster

• 1.04
• Frederick Seward
• ### Where are the Low-mass Neutron Stars?

Neutron stars are predicted to be stable over the mass range ≈0.1 to ≈3 M⊙. At 1.4 M⊙, 98% of the mass is in a core with supernuclear density and 1-2 % forms a thin crust and atmosphere. As mass decreases, the fraction of mass in the crust increases until at 0.1 M⊙, all material is at nuclear density or below and the star is all crust. Observationally, the masses of ≈ 60 neutron stars have been measured and all fall between 1 M⊙ and 2 M⊙. It is of interest to search for low-mass neutron stars, those with M < 0.5 M⊙. These should have different characteristics and might be found in high-mass binaries, as high-velocity objects, and perhaps as Magnetars.

Poster

• SUPERNOVAE and SUPERNOVAE REMNANTS
• 2.01
• Glenn Allen
• ### The Expansion Rate and Age of the Supernova Remnant G266.2-1.2 (Vela Jr.)

We analyzed the Chandra ACIS data for the supernova remnant G266.2-1.2. The data for a portion of the northwestern rim indicate that it is expanding at the rate of 0.42 +/- 0.10 arcsec/yr (half the rate reported by Katsuda, Tsunemi & Mori (2008) for an analysis of XMM data). A hydrodynamic analysis was performed using broad ranges of initial kinetic energies, ejecta masses, ejecta mass density distributions, ambient densities, and evolutionary states. The results were constrained by the Chandra expansion rate (assuming it is representative of the remnant as a whole), an inferred lower limit on the forward shock speed, an upper limit on the inferred thermal X-ray emission, and energy considerations. The results suggest that G266.2-1.2 is most likely between 2.4 and 5.1 kyr old.

Poster

• 2.02
• Kazimierz Borkowski
• ### Asymmetric High-Velocity Ejecta in the Youngest Galactic SNR G1.9+0.3

Chandra has revealed highly asymmetric supernova ejecta in G1.9+0.3. Iron dominates thermal emission in the radio-bright northern rim, while only intermediate-mass elements are found along the SE-NW axis. The measured X-ray expansion rates decrease radially by about 60% along this axis from 0.84% yr^(-1) to 0.52% yr^(-1). This corresponds to undecelerated ages of 120 - 190 yr, confirming the young age of G1.9+0.3, and implying that the blast wave is much more decelerated than the reverse shock. Only the outermost ejecta with very high (>18,000 km s^(-1)) free-expansion velocities have been shocked so far. We discuss G1.9+0.3 in the framework of recent asymmetric 3D delayed-detonation Type Ia explosions from Seitenzahl et al. (2013). Their N3 model provides the best match.

Poster

• 2.03
• Paul Plucinsky
• ### XMM and Chandra Spectroscopy of the Brightest Supernova Remnants in M33

We present a spectral analysis of the X-ray brightest Supernova Remnants (SNRs) in the nearby, spiral galaxy M33 from our deep XMM-Newton survey that complements our previous survey with Chandra (ChASeM33) by covering the entire galaxy. We have simultaneously fit the XMM and Chandra spectra (when available) to better constrain the fitted parameters. We do not find any young (t<1,000 yr) SNRs that could be analogs of Cas A or the Crab, but we find several older SNRs that show evidence of enhanced abundances. These bright X-ray SNRs appear to occur in regions with a higher than average ISM density, assuming they are in the Sedov phase. We include the first detailed spectral analysis of the third most luminous X-ray SNR in M33, which was outside the ChASeM33 survey area.

• 2.04
• Tea Temim
• ### Deep Chandra Observations of the Composite Supernova Remnant G327.1-1.1

G327.1-1.1 is a composite SNR containing a symmetric radio shell and a PWN that has likely been disrupted by the reverse shock. Previous X-ray studies reveled a complex morphology; a compact core embedded in bow-shock-like structure, prong-like features extending into large arcs, and thermal emission from the SNR shell. We present deep, 350 ks Chandra observations of G327.1-1.1 that provide new information about the properties of the system, such as the spatial variations in the spectral index across the observed PWN structures, and the thermal temperature across the SNR shell. We also present preliminary HD simulations of an asymmetric PWN/SNR interaction in a system with a moving pulsar, expanding into a non-uniform ISM density, which offer new insight into the nature of the remnant.

• 2.05
• Martin Weisskopf
• ### Monitoring of the Crab Nebula with Chandra, HST, and Keck

Subsequent to the detections AGILE and Fermi/LAT of the gamma-ray flares from the Crab Nebula in the fall of 2010, this team has been monitoring the X-Ray emission from the Crab on a regular basis. Initially X-Ray observations took place once per month when viewing constraints allowed. More recently observations with Chandra and HST have taken place four times per year. There have been notable exceptions, e.g. in April of 2011 and March 2013 when we initiated a set of Chandra Target of opportunity observations in conjunction with bright gamma-ray flares. Often Keck observations were obtained. The aim of this program to characterize, in depth, the X-ray, optical, and infrared variations that take place in the nebula, and, by so doing, determine the regions which contribute to the harder X-ray variations and, if possible, determine the precise location within the Nebula of the origin of the gamma-ray flares. As part of this project members of the team have applied Singular Value Decomposition techniques to sequences of images in order to more accurately characterize features and their behavior. The current status of the project will be discussed highlighting studies of the inner knot and possible correlations with the gamma-ray flares.

• STARS, PLANETARY NEBULAE and STAR CLUSTERS
• 3.01
• Thomas Ayres
• ### The Ups and Downs of Alpha Centauri

Nearby Alpha Centauri is destined for a pivotal chapter in human history, as first stop of future starfarers from Earth: 3x closer than the next nearest star; three very different objects to visit -- Alpha Cen A (G2V), B (K1V), and C (M6V); and B hosts an Earth-mass companion, albeit in a hot, lifeless orbit. For its part, Chandra has been keeping intent watch on the high-energy starspot cycles of AB, with semi-annual pointings over the past decade. Only HRC-I can separate AB as they plunge toward a close approach of 4'' in 2016; and LETGS has countered that an abrupt 50x drop in XMM count rate of sun-like A in early 2005, ominously reported as the "darkening of the solar twin," simply is a soft sensitivity issue, not an unprecedented, inexplicable case of corona interrupta.

Poster

• 3.02
• Patrick Broos
• ### A First Look at "The Tarantula -- Revealed by X-rays" (T-ReX)

30 Doradus is the most important star-forming complex in the Local Group, offering a microscope on starburst astrophysics. At its heart is R136, the most massive resolved stellar cluster, containing the most massive stars known. Across 30~Dor's 250-pc extent, stellar winds and supernovae have carved its ISM into an amazing display of arcs, pillars, and bubbles. Chandra is observing 30~Dor this year for the 2-Ms AO15 XVP "T-ReX". This deep observation will finally exploit Chandra's fine spatial resolution to study ISM interfaces on 1--10 pc scales, the full complement of massive stars, and the brightest pre-main sequence stars that trace 25~Myrs of star formation in this incomparable nearby starburst. Here we give preliminary results from the first 900~ks of Chandra observations.

Poster

• 3.03
• Nancy Remage Evans
• ### Cepheid Companions and Clusters: X-ray Certified

X-ray flux provides a decisive diagnostic to separate old low-mass field stars from young low mass stars which were formed at the same time as massive stars (Cepheids). We have used this to investigate two aspects of these 6 Msun stars which have implications for star formation: resolved companions and larger stellar groups (clusters and association remnants). We have observed 11 Cepheids with Chandra and XMM which have possible resolved companions. X-ray active low mass stars were ONLY found within 6300 AU of the Cepheid, establishing an outer limit for gravitationally bound companions. For clusters, we have identified low mass members of a new cluster containing S Mus, as well as possible cluster remnants around several other Cepheids.

• 3.04
• Jeremy Drake
• ### Probing Coronal Supersaturation in Pre-Cataclysmic Binaries

Evolution of pre-cataclysmic and cataclysmic binaries is thought to be dominated by orbital angular momentum loss through coronally-driven winds of the late-type secondary star. However, coronal activity of stars at the extremes of rotation found in cataclysmic variables (CVs) remains essentially unexplored: existing studies reach to rotation periods of 0.3-0.2 days - significantly longer than the periods of CVs. The aim of this study is to explore the X-ray supersaturation regime close to 0.1 day periods using short Chandra snapshot observations for a small sample of the fastest rotating stars outside of accreting systems. We will present the results and discuss their relevance for understanding the timescales of CV evolution and the possible road to Type 1a supernovae.

• 3.05
• Marcus Freeman
• ### Exploring Diffuse X-ray Emission from Planetary Nebulae

The Chandra Planetary Nebula Survey (ChanPlaNS) has established that diffuse X-ray emission, generated by energetic, nebula-shaping wind shocks, emanates from ~1/4 of planetary nebulae (PNe). Such X-ray emission sources are found only in the youngest, most compact nebulae with the highest nebular densities, implying active PN "sculpting" lifetimes of \<~5000 years. The diffuse X-ray detection rate is 100% for the (five) ChanPlaNS sample PNe with Wolf-Rayet ([WR]) type central stars. We present preliminary results from 3D structural reconstructions of PNe that are designed to investigate the apparent systematic differences between the diffuse X-ray emission morphologies of PNe with [WR] vs. non-[WR] central stars, as well as the possibility of enhanced, intranebular X-ray absorption.

• 3.06
• Vinay Kashyap
• ### 15 Years of Chandra Observations of Capella

The Chandra Galactic Bulge Survey (GBS) is a shallow survey with a flux limit of 1e-14 erg/cm2/s (0.5-10.0 keV) that covers a pair of 6 sq. deg. areas centred 1.5 deg. above and below the Galactic Center. The extinction and crowding in these regions are such that optical/infrared counterparts to the 1640 X-ray sources found with Chandra are accessible to detailed follow-up. The GBS is designed to set constraints on four important areas in astrophysics: stellar-mass black hole formation, the neutron star equation of state, the nature of the progenitors of type Ia supernovae and the common envelope evolution. Here I present the survey properties and goals, our multiwavelength methods to identify and clasify the counterparts to the X-ray sources and the first scientific results.

• 3.07
• Alejandro Nunez
• ### Stellar Coronal Activity & Rotation at 500 Myr: Chandra Observation of M37.

A quantitative description of the stellar age-rotation-magnetic activity relation (ARAR) is a work in progress. Empirical calibrations of it rely on observations of co-eval populations of stars in open clusters. ROSAT observations were used to characterize coronal X-ray emission, a tracer of a star's magnetic activity, in the ~500-Myr-old Hyades and Praesepe clusters. These data differ a lot, casting doubt on the universality of the age-activity relation. We present our results from a Chandra observation of the 500-Myr-old M37 cluster. We observed it for 450 ksec using the ACIS-I chips and detected 250 cluster members. We use our data and public M37 rotation periods catalogs to decouple the age-rotation and rotation-activity relations, and to determine the universality of the 500-Myr ARAR.

Poster

• 3.08
• Jose M. Torrejon
• ### Exploring the innermost wind region of the massive star QV Nor.

QV Nor is the B0I donor of the HMXB 4U1538-52. The neutron star orbits its massive companion in less than 4 days probing, along its eccentric orbit, the innermost (r < 1.4R*) wind regions of the stellar wind. In this work we will present the first high resolution X-ray spectrum of QV Nor, using Chandra HETG. We will present and analysis of the emission lines arising in its photoionized wind as well as the fluorescence Fe K alpha line probing the dense and cold matter. The implications for the wind structure in early type stars will be discussed.

• 3.09
• Smriti Vats
• ### X-ray Source Populations in Old Open Clusters - Collinder 261

We are carrying out an X-ray survey of old open clusters (OCs) with the Chandra X-ray Observatory. Single old stars emit very faint X-rays, making X-rays produced by mass transfer in CVs, or by rapid rotation of the stars in tidally-locked, detached binaries detectable, without contamination from single stars. By comparing properties of interacting binaries in different environments, we aim to study binary evolution, and how dynamical encounters with other cluster members affect it. Collinder (Cr) 261 is an old OC(~7Gyr), with one of the richest populations inferred, of close binary populations and blue stragglers of all OCs. We will present the first results, detailing the X-ray population of Cr 261, in conjugation with other OCs, and in comparison with populations in globular clusters.

• 3.10
• Leisa Townsley
• ### The Birth of the Hot Interstellar Medium

Diffuse X-ray Emission in Massive Star-Forming Regions Chandra is providing remarkable new views of massive star-forming regions, revealing the effects of massive star feedback on natal molecular filaments and clouds. We will explore the extensive Chandra data on such regions, highlighting processes that characterize the life of a massive stellar cluster, from ultracompact HII regions to superbubbles so large that they shape our views of galaxies. These complexes are suffused by parsec-scale diffuse X-ray emission outlined (and sometimes confined) by colder structures seen in long-wavelength images; these are the long-sought signatures of multi-million-degree plasmas created by fast O-star winds. They show us the birth of the hot interstellar medium.

Poster

• GALAXIES and POPULATIONS
• 4.01
• Vallia Antoniou
• ### Understanding young X-ray binaries in the Small Magellanic Cloud

We present results from a Chandra Visionary Project to study the X-ray source populations in the Small Magellanic Cloud (SMC) down to unprecedented luminosity limit of 5x10^(32) erg/s in fields with young (<100 Myr) stellar populations of different ages. We detect 50-100 sources per field and measure their X-ray photometric and spectroscopic parameters. Light curve analysis is used to identify accreting pulsars and flaring objects. Based on source multi-wavelength properties, we identify high-mass X-ray binaries (XRBs) and study their connection with star-forming regions. These data provide the deepest X-ray luminosity functions for XRBs in a low metallicity (0.2Z\sun) star-forming galaxy and allow us to measure the formation efficiency of young XRBs and its evolution with time.

Poster

• 4.02
• Frederick Baganoff
• ### NuSTAR Insights into Energetic Phenomena in the Galactic Center

The Nuclear Spectroscopic Telescope Array (NuSTAR) has performed extensive observations of our Galactic Center. NuSTAR's unique ability to produce high-energy X-ray spectra with fast timing resolution and sub-arcminute angular resolution, combined with higher angular resolution observations made with Chandra and XMM-Newton in low-energy X-rays plus VLA observations in the radio waveband, have yielded important insights into a variety of energetic phenomena in this region. Here we describe what has been learned about Sgr A* flares, the candidate pulsar wind nebula CXOGC J174545.5-285829, aka "the Cannonball", and the nonthermal filament Sgr A-E (G359.89-0.08).

• 4.03
• Jimmy Irwin
• ### Giant Brief X-ray Flares in Extragalactic Globular Clusters

We present the discovery of luminous (7e39 - 5e40 ergs/s), very brief (1-10 minute) X-ray flares in two extragalactic globular clusters discovered with Chandra. While brief in duration, these outbursts represent the most energetic events ever recorded in globular clusters, temporarily increasing the luminosity of the source by a factor of 100-200. Such powerful rapid variability is rivaled only by gamma-ray bursts and outbursts from soft gamma repeaters, yet these sources show little resemblance to these two classes of objects. Instead, the outbursts resemble Type 1 bursts seen in Galactic neutron stars, but scaled up in luminosity by two orders of magnitude. We discuss the origin of these sources, and their possible connection to black holes within globular clusters.

• 4.04
• Roy Kilgard
• ### Characterizing the X-ray Point Source Population of M51

The galaxy M51 is perhaps the best example of a major interacting galaxy in the nearby universe. We present our efforts to date to characterize the discrete X-ray source population of M51 using new data from a Chandra Very Large Project (PI Kuntz). When combined with archival data, we reach a total exposure of 865 ksec, representing the deepest exposure in high-resolution X-ray of the full disk of any spiral galaxy. Here we highlight our catalog and processing efforts and present initial results.

• 4.05
• Dong-Woo Kim
• ### Chandra Galaxy Atlas

The hot ISM in early type galaxies (ETGs) plays a crucial role in understanding their formation and evolution. Structural features of the hot ISM identified by Chandra (including jets, cavities, cold fronts, filaments and tails) point to key evolutionary mechanisms, e.g., AGN feedback, merging history, accretion/stripping and star formation and its quenching. In our new project, the Chandra Galaxy Atlas, we will systematically analyze the archival Chandra data of 137 ETGs to study the hot ISM. Taking full advantage of the Chandra capabilities, we will derive uniform data products of spatially resolved datasets with additional spectral information. We will make these products publicly available and use them for our focused science goals.

Poster

• 4.06
• K.D. Kuntz
• ### Diffuse Emission in Normal Spiral Galaxies

Diffuse X-ray emission in the disks of late-type spiral galaxies is not well understood. Correlations exist between the X-ray surface brightness (X) the FUV surface brightness (U), the X-ray hardness (H) and the galactocentric radius (R). We have used deep Chandra observations of three nearby face-on galaxies, M101, M83, and M51 to understand the relations among the observed correlations. In particular, we find that at a given galactocentric radius X=A U^0.5, and the normalization, A, decreases with radius, more strongly in galaxies with short disk scale-lengths than in those with long scale-lengths. H seems to show more variation with R than with the local density, probably due to the long cooling time. Both of these correlations appear to be mediated by the mid-plane density.

• 4.07
• Zhiyuan Li
• ### X-ray emissivity from old stellar populations: a Local Group census

We study the unresolved X-ray emission from three Local Group dwarf elliptical galaxies (NGC147, NGC185 and NGC205), which is thought to originate from a collection of weak X-ray sources primarily consisting of cataclysmic variables and coronally active binaries. The derived 0.5-2 keV X-ray emissivities (per unit stellar mass) of these dwarfs are comparable to that in the Solar neighborhood, but are significantly higher than the average cumulative emissivity of X-ray sources in four Galactic globular clusters, indicating a reduced binary fraction in the latter. Our results are also important for studies of the apparently diffuse X-ray emission in nearby normal galaxies.

Poster

• 4.08
• Liliana Rivera
• ### The faint cataclysmic variable population of the globular cluster 47 Tuc

The cores of globular clusters (GCs) are perfect places to study dynamical interactions between stars because of the high stellar densities (up to 10E6 stars/pc3). In this work we use new near-ultraviolet images of the massive GC 47 Tuc obtained with the Hubble Space Telescope (HST), Chandra X-ray data and optical HST data to study the compact binaries in 47 Tuc, especially the population of faint cataclysmic variableS (CVs). These data allow us to obtain one of the deepest measurements of the globular-cluster CV luminosity function, which we compare with the measured CV luminosity function in the field and with those of other GCs. Our aim is to explore the effects of dynamical interactions on the formation and evolution of compact binary populations, in particular on that of CVs.

Poster

• 4.09
• Dacheng Lin
• ### Properties of X-ray Binaries in NGC 3115 from Chandra XVP Observation

We present our study of low-mass X-ray binaries (LMXBs) in NGC 3115 using the Ms Chandra XVP observations. By systematically comparing their spectral dependence on luminosity with those of Galactic X-ray binaries, we show that most bright sources in NGC 3115 are neutron star LMXBs in the soft state, except ten that are probably black hole LMXBs due to very soft spectra. We construct the X-ray luminosity function (XLF) down to the limit of ~10^36 erg/s, and show significant flattening of the overall XLF from dN/dL \propto L^2.2 above 6X10^37 erg/s to dN/dL \propto L^1.0 below it. The XLF of globular cluster LMXBs is flatter than the field XLF, indicating their different origins. We also observed spatial variation of field XLFs. We discuss the physical implications of all these results.

Poster

• COSMOLOGY, AGN, QUASARS and JETS
• 5.01
• August Chen
• ### Chandra's 14 Years with the M87 Jet

We have reanalyzed 83 observations of M87 taken by Chandra from 2000 July to 2014 March. Preliminary results from light curves for each knot in 3 energy bands include: (a) The spectrum of HST-1 is harder during the rise of the giant flare of 2005 than during the decay. (b) There is a 2 year segment during which the decay rates in the 3 energy bands are consistent with synchrotron losses from a magnetic field of 1 to 10 mG. (c) Knot D is increasing slowly. (d) Knot A is slowly fading. (e) Knot M, the "Maverick" is not part of the jet; rather it is an obstacle that deflects the jet (both radio and optical). It has a harder spectrum than other knots and it has no detectable optical or radio emission. This work was supported by NASA grants GO2-13133X, GO3-14106X, and GO4-15095X.

• 5.02
• Chien-Ting Chen
• ### AGN accretion, obscuration and star formation in luminous galaxies

I will present studies of connections between star formation (SF) and supermassive black hole (SMBH) accretion in galaxies, using large galaxy and AGN samples from the wide-field Boötes survey. We find a linear relationship between galactic SF rate and the average SMBH accretion rate, consistent with a strong physical connection between these processes despite the fact that SMBH and galaxy growth rates in individual AGN host galaxies are not directly correlated due to the short variability timescale of AGN relative to SF. I will also present evidence for a link between nuclear obscuration and host galaxy SF in powerful quasars. These results support a scenario in which galaxy and SMBH grow from a common gas reservoir that can obscure the central SMBH during the luminous quasar phase.

Poster

• 5.03
• ### Using gravitational lensing to study the X-ray spectrum of distant QSO

The unique imaging capabilities of Chandra have been successfully used to perform microlensing studies of distant QSOs. The main aim was to infer the dimensions of their X-ray emitting regions. Using data from the Chandra archive, we built-up an XMM-Newton program devoted to using the magnification due to gravitational lenses to characterize in detail the broad band spectra and variability of distant AGN. Here we present preliminary results of the XMM-Newton observation of QSO B1422+231 at z=3.62.

• 5.04
• Andy Goulding
• ### Evolution of galaxies and their black holes to z less than 1.4

Many models require a close link between the growth of BHs and their host galaxies through feedback processes. These active galactic nuclei (AGN) are capable of releasing enormous quantities of energy over their lifetimes, often comparable to the binding energy of their hosts. We have performed a set of statistical population analyses that combines Chandra's exquisite angular resolution with available multi-wavelength data across over 100 deg^2 of the sky, to build the most complete view of AGN and their host galaxies throughout the last 9 Gyrs. We show that galaxy evolution proceeds similarly with or without the inclusion of an AGN, but through X-ray stacking, we also find that many AGN still remain hidden even in the most nearby galaxies, lying below typical AGN detection thresholds.

• 5.05
• Christina Graefe
• ### Chandra's X-ray guide to Centaurus A

Centaurus A is the closest radio-loud active galactic nucleus (AGN). At a distance of 3.8 Mpc the angular resolution of 0.5 arcsec of Chandra/ACIS translates into ~10 pc. This gives us the unique opportunity to disentangle the X-ray emission from different components. We analyzed archival data (2000-2013) and study timing and spectral properties of the core region and the diffuse gas in Cen A. Using the soft X-ray emission lines, we study the nature of this diffuse material. The core region of Cen A emits time- and spectrally-variable hard X-rays. We report that a circumnuclear "halo" (up to 0.5 kpc away from the core) also emits an Fe K-alpha line, and we investigate the nature of this emission.

Poster

• 5.06
• Paul Green
• ### Testing Eddington Analogies with Observations of Supermassive Black Holes

Similarities between the observational accretion signatures of X-ray Binary (XRB) systems and active galactic nuclei (AGN) are still ardently sought. XRB spectral states show an inflected correlation between X-ray spectral hardness and Eddington ratio. Large AGN samples may also serve to catch supermassive black hole accretion in different states. We discuss and lambaste recent such tests, including our own using the Chandra Source Catalog and SDSS, of such analogies. Significant strides can and must be made, and we delineate related plans and hopes using SDSS spectroscopy and wide-area X-ray imaging.

Poster

• 5.07
• Stephanie LaMassa
• ### Highlights of the Stripe 82 X-ray Survey

We are undertaking a large area X-ray survey overlapping SDSS Stripe 82, a region rich with multi-wavelength coverage and high optical spectroscopic completeness. The current X-ray coverage in Stripe 82 is 16.5 deg^2, from archival Chandra and archival and proprietary XMM-Newton data. In the coming year, another 20 deg^2 will be added to our survey with XMM-Newton, as well as ~2 deg^2 from Chandra GTO observations. "Stripe 82X" finds more rare, high luminosity AGN than some models predict should exist. I will highlight the contribution of Chandra data in discovering high luminosity AGN and optically dull, infrared bright sources, revealing the often over-looked, though important, population of growing supermassive black holes.

Poster

• 5.08
• Lauranne Lanz
• ### Jet Feedback on the Interstellar Medium of the Radio Galaxy 3C293

We present a 70 ks Chandra observation of the radio galaxy 3C293. This galaxy contains 3.7 x 10^9 solar masses of 100 K molecular hydrogen in an extended 10 kpc scale region, heated by jet-driven shocks. With Chandra, we observe emission from the jets both within and outside the host galaxy to study the effect of jet feedback on the ISM. We model the spectra of the nucleus, the inner jets, and the X-ray features along the 100-kpc radio jets. The nucleus and inner jets show evidence of 10^7 K shock-heated gas. The jets' kinetic power is more than sufficient to heat the X-ray emitting gas, which serves as a reservoir of thermal and turbulent energy to maintain the molecular hydrogen emission over 10^7 years. We examine the connection between the X-ray and molecular hydrogen emissions.

Poster

• 5.09
• Dacheng Lin
• ### Multiwavelength Follow-up Observation of a Tidal Disruption Event

The source 2XMMi J184725.1-631724 was serendipitously detected in two XMM-Newton observations in 2006-2007. It is a tidal disruption event (TDE) candidate because of its ultrasoft X-ray spectra (kT ~ 0.07-0.09 keV), high peak luminosity (~10^44 erg/s), possible transient nature, coincidence with an inactive galaxy, Here we report the multiwavelength follow-up observations of the event. Especially, our 2013 Chandra observation indicates that the 0.2-10 keV flux of our source has decreased by a factor of more than 500 from the peak, confirming its transient nature. Our XMM-Newton and Swift observations also detectd a UV source, which seems blue and is fainter in 2013 than near the peak, thus most likely associated with the event. Such UV emission was seldom detected in X-ray detected TDEs.

Poster

• 5.10
• Eileen Meyer
• ### The surprising nature of quasar jets as revealed by Fermi

The physical origin of the X-ray emission in powerful quasar jets has been a long-standing mystery. Though these jets start out on the sub-pc scale as highly relativistic flows, we do not have any direct measurement of their speeds on the kpc scale, where the vast distances from the core necessitate in situ particle acceleration. If the jets remain highly relativistic, then the X-rays could be due to inverse-Compton off the CMB. However, the IC/CMB explanation also predicts a high level of gamma-ray emission, which has been ruled out in several cases, including the famous source 3C 273 (Meyer & Georganopoulos 2014), suggesting the X-rays are synchrotron in origin. I will discuss the surprising implications of these findings for the energetics and radiative output of powerful quasars.

Poster

• 5.11
• Kendrah Murphy
• ### A Chandra-HETG View of MCG +8-11-11

We present a spectral analysis of the 118 ks High Energy Transmission Gratings (HETG) observation of the X-ray bright Seyfert 1.5 galaxy MCG +8-11-11, in conjunction with 100 ks of archival Suzaku data. Fe K-alpha line emission is clearly detected and is likely resolved by the HETG. The data are consistent with reprocessing by a distant, neutral torus that is marginally Compton thick and out of the line-of-sight. We do not find compelling evidence of a relativistically-broadened Fe-K emission line and, contrary to previous results, warm absorption is not required by the data. The HETG data are consistent with the presence of a soft excess, a feature that may be missed by considering Suzaku data alone.

• 5.12
• Alessandro Paggi
• ### Early-type galaxies in the Chandra COSMOS Survey: Stacking Analysis

We present a stacking analysis of Chandra data for the complete sample of Early Type Galaxies (ETGs) in C-COSMOS to explore the relation between the X-ray luminosity of the hot gas halos and the stellar luminosity in these sources for 0<z<1.5. In the local universe this relation suggests the presence of virialized halos for nearby ETGs, while a recent analysis of X-ray detected ETGs in C-COSMOS showed that more luminous ETGs tend to diverge from the local relation, with enhanced X-ray emission likely due to hidden AGN or evolution of hot halos. The results of our analysis reveal enhanced X-ray luminosities also for a population of less luminous ETGs, with increased HR suggesting contribution to X-ray emission by AGN with M_BH~10^{7\div 8}M_{\astrosun} and \dot{m}\sim{10}^{-4}.

Poster

• 5.13
• Kevin Schawinski
• ### Exploring black hole seed formation and early growth at high and low redshift

The 4 Msec (soon 7 Msec) Chandra Deep Field South is the deepest X-ray image of the sky and one of the extraordinary legacies of the first 15 years of Chandra. The CDFS tracks the growth of supermassive black holes and can potentially shed light on the formation of seed black holes and their first growth episodes. Recent efforts to locate these first growth spurts in the deepest Chandra surveys are yielding increasingly strong constraints on seed formation models that start to challenge theory. Most surprising is the lack of any evidence for black hole accretion in z>5 galaxies. At the same time, observations of intermediate redshift galaxies with Chandra may hold clues to how and when normal mass black holes - like that at the center of the Milky Way - formed and grew up.

• 5.14
• Aneta Siemiginowska
• ### High Redshift X-ray Jets detections with Chandra

We present the results from morphological studies of X-ray jets observed in the two highest redshift quasars with Chandra X-ray Observatory. We apply a novel computational technique to work with low counts Poisson images and separate jet emission from a strong quasar core. The X-ray angular resolution matches the resolution of the radio maps allowing for direct studies of the location of X-ray and radio jet emission. We attempt to constrain the parameters of the jet emission process and estimate a jet power for these jets.

Poster

• 5.15
• Aneta Siemiginowska
• ### Signatures of jet impact on the ISM in radio galaxy 4C+29.30

We present results of a deep Chandra observation of a low-z radio galaxy with signs of the complex interactions between the radio plasma and ISM. The Chandra image shows regions of enhanced X-ray emission correlated with radio structures along the jet axis. The larger scale X-ray diffuse emission outside the radio source correlates with the morphology of known optical line-emitting regions. We measure the temperature of the ISM and identify regions heated by weak shocks with the Mach number of 1.6. The X-ray emitting gas is most likely heated by the radio source expanding within this galaxy. The multi-band data supply a complex view of the source, signaling feedback processes closely associated with the central active nucleus.

Poster

• 5.16
• Hyewon Suh
• ### Eddington ratio distribution of X-ray selected broad-line AGNs at 1.0<z<2.2

We investigate the Eddington ratio distribution of X-ray selected broad-line AGNs in the redshift range 1.0<z<2.2, where the number density of AGNs peaks. Combining the optical and Subaru/FMOS near-infrared spectroscopy, we estimate black hole masses for broad-line AGNs in the CDFS, ECDFS, and the XMM-LH surveys. AGNs with similar black hole masses show a broad range of AGN bolometric luminosities, indicating that the accretion efficiency of black holes is widely distributed. We propose that the observed downsizing trend can be interpreted as massive black holes with low accretion rates, which are relatively fainter than less massive black holes with efficient accretion.

Poster

• 5.17
• Junfeng Wang
• ### Disentangling AGN-Host Galaxy Interactions with Chandra

The circum-nuclear region in active galaxies is often complex with presence of high excitation gas, collimated radio outflow, and star forming regions, besides the active central supermassive black hole. In Chandra studies of a number of archetypal Seyfert galaxies to investigate AGN-host galaxy interaction, we were able to evaluate the mass outflow rate and shock heating by radio jet. For galaxies in the throes of a violent merging event such as NGC6240, we were able to resolve 70MK hot gas surrounding the double nuclei and discovered a large scale soft X-ray halo. The unique resolving power of Chandra also enables more discovery of such dual AGN systems and signs of past AGN outburst activities.

• CLUSTERS of GALAXIES
• 6.01
• ### The spectacular merger event in A3411: Shock fronts and radio relics

The study of galaxy cluster merger events is of major astrophysical interest as they have a profound and long-lasting impact on the thermodynamic evolution of the ICM. Observed as part of our large Chandra XVP program on the Planck ESZ sample, we discovered that the cluster A3411 is undergoing a spectacular merger event. Radio observations also reveal the presence of large-scale diffuse emission, suggesting the presence of shocks and turbulence in the ICM. Most interestingly, in the Chandra observations we indeed find evidence of a brightness discontinuity, roughly at the location of the radio emission. This suggests that a shock could be responsible for the acceleration of particles to relativistic energies and makes A3411 an ideal laboratory to study this poorly understood process.

Poster

• 6.02
• Laurence David
• ### The Double Merging Cluster Abell 1758

A1758 comprises two X-ray luminous clusters (A1758N and A1758S) which are probably gravitationally bound. A deep Chandra observation shows that both A1758N and A1758S are undergoing major mergers. The merger in A1758N is at an advanced stage with heavily stripped cores and shock heated gas at large radii. In contrast, the merger in A1758S is at an early stage with shocked gas confined to the region between the merging cores. X-ray emission is also detected between A1758N and A1758S. The combined mass of A1758N and A1758S is comparable to the Coma cluster, which is one of the most massive clusters in the near by universe. Thus, our deep Chandra observation of A1758 is a window into the formation of the most massive systems presently residing in the local universe.

• 6.03
• Eric Miller
• ### Exploring the Outskirts of Galaxy Clusters

Recent studies have traced the hot ICM to the virial radius in a number of galaxy clusters. These results have begun to clarify the thermodynamic conditions at the edge of clusters, constraining models of cluster growth and evolution. We are embarked on a program to observe a sample of relaxed clusters with Suzaku, fully imaging each cluster to beyond R200, and leveraging complementary data from XMM-Newton and Chandra. We see indications of low-entropy substructures and azimuthal variations in temperature and surface brightness. I will present the latest results from this project, explore the possible sources of systematic error, and discuss the remarkable "universality" of thermodynamic profiles to the outer limits of galaxy clusters.

Poster

• 6.04
• Paul Nulsen
• ### Energy Flows in Cygnus A, the Prototype of Powerful Radio Sources

Based on the Chandra data for Cygnus A, I will discuss findings concerning its jets, inflation of its radio lobes and their interactions with its cluster atmosphere. While the inner parts of its cocoon shocks emit mainly thermal X-rays, in the more remote parts the emission is primarily nonthermal. Its inner X-ray cavities support models that produce strong backflows from the radio/X-ray hotspots. X-ray jets revealed by Chandra are best explained by synchrotron emission models that require large powers to be flowing through the jets. This implies that the primary energy flow in Cygnus A is via the X-ray jets rather than its radio jets. Estimates will be presented for key jet parameters based on matching the X-ray jets to the hotspots.

• 6.05
• Rachel Paterno-Mahler
• ### Merger Signatures in the Galaxy Cluster Abell 98

X-ray data from Abell 98 show a galaxy cluster with a bright north subcluster (A98N), a disturbed south subcluster (A98S), and a faint far south subcluster (A98SS). Surface brightness and temperature asymmetries in A98N show a region consistent with shock-heating created by an early stage merger of A98N and A98S. A98S has an asymmetric temperature structure due to a separate ongoing merger, also seen in optical data. It also has a wide-angle tail radio source from an AGN. A lobe is evacuating a cavity, suggesting AGN feedback. The subclusters project along a line, suggesting a large-scale filament. A surface brightness profile of emission between A98N and A98S is consistent with overlap between extended gas haloes. A98N and A98S are bound with 67% probability; A98S and A98SS are not bound.

• 6.06
• Alessandro Baldi
• ### The ACCEPT2 database of galaxy clusters: early results on global properties and morphology

The public ACCEPT database of cluster properties (Cavagnolo et al. 2008, 2009) included radial profiles of temperature, density,entropy, and cooling time. With the new ACCEPT2 project we are currently doubling the number of clusters in ACCEPT and expanding the current suite of properties to include uniformly measured profiles of mass along with signatures of dynamical relaxation (centroid shift, power ratios, surface brightness ! concentration, temperature ratios) and global quantities such as core-excised temperatures, X- ray luminosities, and metallicities. This project has the potential of yielding key results on the physics of galaxy clusters and cosmology and represent a benchmark for years to come, here we are highlighting the first early results ! obtained on the evolution of metal abundance content, the evolution of X-ray scaling relations, and the relation between cool cores and dynamical relaxation.

Poster

• BINARIES
• 7.01
• David Goldfinger
• ### Observation of SS 433 with Chandra and the VLBA

We present results from a 2 day observation of SS 433 in the X-ray using Chandra. SS 433 is an X-ray binary with strong, Doppler shifted emission lines from a highly collimated jet. Past observations at radio frequencies have shown that the jets form from discrete clumps, whereas X-ray observations have shown that the Doppler shift of jets changes smoothly through time. In order to address this relationship, this observation was made concurrently with radio observations made with the VLBA. The simultaneous data sets allow for evaluating several scenarios that aim to explain how the continuously evolving jet direction and speed is related to the formation of discrete features.

• 7.02
• Margarita Karovska
• ### Where is the X-ray emission coming from in RT Cru Symbiotic System?

RT Cru is a member of a new sub-class of symbiotic interacting binaries with copious hard X-ray emission. It consists of a high-mass WD (>1.3 Ms) accreting from the wind of an M giant, and it is an important system to study in order to constrain precursor conditions for asymmetric PN and SN Ia. The Chandra HRC-I observation (Dec 2012), and an overlapping Swift observation, detected intermittent soft X-ray flaring, and we find evidence for a significant soft component in the spectrum. The flaring could be a consequence of clumped absorption columns moving in and out of the line of sight, or the variations could be due to changes at the accretion boundary layer. Further observations are needed to determine the origin of the soft emission and its relation to the hard emission.

Poster

• 7.03
• Silas Laycock
• ### A Decade in the Life of the Massive Black-Hole Binary IC10 X-1

Chandra thanks to its angular resolution, sensitivity and endurance has been able to monitor individual X-ray binaries in the starburst galaxy IC 10. The WR+BH binary known as IC10 X-1 is regarded as one of the most massive stellar black holes; a class of objects representing the pinnacle of the stellar mass function. BH binaries occupy key roles in seeding SMBHs, producing long GRBs at birth, and gravitational waves at death. We report our use of Chandra to refine the orbital ephemeris of X1 and match-up the radial velocity curve of the optical spectral lines with the X-ray eclipse. The resulting phase offset has fascinating implications for our understanding of the interactions between the WR star, its wind, and the radiation field of the BH.

Poster

• 7.04
• Gerardo Luna
• ### Testing the cooling flow model in magnetic cataclysmic variables

We use the best available X-ray data from an intermediate polar to study the cooling-flow model often applied to model their X-ray spectra. After deriving the EMD from different models, we calculate line fluxes and H-like to He-like line ratios and compare them with a 496 ks Chandra/HETG observation of the intermediate polar EX~Hya. We find that the H/He ratios are not well reproduced by simple isobaric cooling flow models. We discuss and discard mechanisms such as photoionization, resonant scattering, and Compton cooling. Thermal conduction transfers energy from the region above 10$^{7.0}$, where the H-like lines are mostly formed, to the cooler region where the He-like ions of the lower-Z elements are formed, so it at least partly resolves the problem.

• 7.05
• Joey Neilsen
• ### Chandra Takes on Heavy Jets and Massive Winds in 4U 1630-47

Recently, Díaz Trigo et al. reported the discovery of relativistic baryons in a jet in XMM/ATCA observations of the 2012 outburst of the black hole 4U 1630-47. We present a search for a similarly massive jet earlier in the same outburst using high-resolution X-ray spectra from the Chandra HETGS. Despite a detection of radio emission with ATCA, we find no evidence of a heavy jet in the X-ray spectrum, with tight upper limits on the relativistic emission lines seen by Díaz Trigo eight months later. Instead, we find deep absorption lines from a massive, highly ionized disk wind, whose properties can be probed with detailed photoionization models. We explore several scenarios to explain the two modes of massive outflow in this remarkable black hole system.

Poster

• 7.06
• Michael Nowak
• ### Chandra-HETGS Observations of LMC X-1

The High Mass X-ray Binary, Black Hole Candidate (BHC) system LMC X-1 is among those that has been claimed to exhibit evidence for near maximal spin. However, compared to other systems, LMC X-1 is rather unusual in that it never shows evidence for ever reaching a "stable" minimum effective area. Here we discuss a series of Chandra-High Energy Transmission Gratings observations that cover a number of different orbital phases. We find spectroscopic evidence for emission from the high mass companion's wind. Additionally, we explore whether there is orbital phase-dependent absorption by this wind, as has been previously suggested. Finally, we use Comptonization models to describe the continuum spectrum, and discuss those aspects of the fits that are driving the suggestion for maximal spin.

Poster

• 7.07
• Doosoo Yoon
• ### The Interaction of Microquasar Jets with a Stellar wind in HMXBs.

Jets powered by high-mass X-ray binaries must traverse the powerful wind of the companion star. We present the first global 3D simulations of jet-wind interaction in high-mass X-ray binaries. We show that the jet can be re-collimated where the internal jet pressure is equal to the wind ram pressure, and beyond the re-collimation, the jet thickness follows from pressure equilibrium between the jet and bow-shock. From this analytic jet model, we analyze the effects of jet-wind interaction, bending the jet to an asymptotic angle f. Through both numerical and analytic approach, we formularize the angle f as a function of jet and wind parameters, which can be used to constrain the jet power. We apply the formula to the case of Cyg X-1 and Cyg X-3, and estimate the minimum jet power.

• 7.08
• Angelo Varlotta
• ### Soft X-ray Excesses and X-ray Line Variability in Cygnus X-3

Cygnus X-3 is an X-ray binary (XRB) containing a stellar-mass compact object, likely a black hole, and a Wolf-Rayet star, which produces collimated, relativistic jets, placing it in the sub-class of XRBs known as microquasars. During a Chandra and Swift/XRT monitoring program, a soft X-ray excess (below 1 keV) was observed at certain states and phases of activity. This soft excess seems similar to the soft emission seen in Seyfert galaxies. The presence of these features would argue for a greater support of the black-hole nature of the compact object and serve to highlight the similarities of microquasars and AGN. We show the results of our studies of these soft excesses, as well as the changes of the X-ray Fe line region (6.4-7.0 keV) in function of the state activity and orbital phase.

Poster

• 7.09
• Victoria Grinberg
• ### Variability of the focussed wind in Cyg X-1 / HDE 226868 system

Binary systems with a compact object are a unique chance to investigate the strong, clumpy, line-driven winds of early type supergiants by using the compact object's X-rays as a probe of the wind structure. Here, we analyze the two-component wind of HDE 226868, the O9.7Iab giant companion of the black hole Cyg X-1. Using Chandra-HETG we separate signatures of the hot gas phase from that due to additional absorption by the clumps and, using 5 hard state observations, study orbital variations and thus the spatial structure of the wind. Using ~4.8 Msec of RXTE data we probe the orbital variability of the wind on 2 ksec time scales throughout different accretion regimes of the black hole. We review our results in the light of current focused wind models and models for winds of O/B type stars.

Poster

• SOFTWARE and INSTRUMENTS
• 8.01
• Tom Aldcroft
• ### Behind the curtain: a look at the thermal models used for Chandra planning

The Chandra Science and Flight Operations Teams face a continual challenge in scheduling peer-reviewed and TOO observations while maintaining a safe thermal environment for all spacecraft components. Due to degradation of the silverized insulation that protects Chandra from the extremes of space, overall spacecraft temperatures have been increasing steadily since launch. The heating of different components depends on pitch angle, so staying within thermal limits is a delicate balancing act. A key part of the observation planning process is predicting on-board temperatures using the Xija thermal modeling framework which allows time-series modeling using pluggable components written in Python. In this poster we describe Xija and how it is used to make your Chandra observations happen.

Poster

• 8.02
• Lia Corrales
• ### Atomic Data Unleashed: Interactive and scriptable interfaces to atomic databases

X-rays are uniquely suited for studying interstellar metals, significant fraction of which are locked up in dust. I will focus primarily on the phenomenon of X-ray scattering by dust, which produces a diffuse arcminute scale halo around bright point sources that lie behind a sufficient dust column. The scattering cross-section is most sensitive to large grains, for which the size distribution cannot be constrained with UV, optical, and infrared studies. Chandra has a compact PSF and unsurpassed spatial resolution, making it uniquely suited for studying dust scattering halos. I will demonstrate how a Bayesian analysis of a scattering halo profile can be used to measure the upper limit to the grain size distribution and provide insights to the spatial distribution of diffuse ISM dust.

Poster

• 8.03
• Javier Garcia
• ### Benchmarks of Accurate Atomic Data with Chandra Grating Spectra

Chandra High Energy Transmission Grating (HETG) spectra of most sources reveal ISM lines and edges of dozens of atomic species at extraordinary precision. Our analyses of X-ray binaries have yielded the first detection of the K-alpha, K-beta, and K-gamma resonances in several ionic species. In particular, our studies of the O I absorption lines have brought to light an outstanding discrepancy between observation, theory and laboratory data: In a novel use of Chandra data, we have identified these lines, benchmarked their wavelengths and thereby improved model reliability. Additionally, using the superb Chandra data we have calibrated our cross sections for the Ne K-, Fe L-, and O K-edge regions and produced a much-improved X-ray absorption model of the ISM.

• 8.04
• Kenny Glotfelty
• ### Simplifying Chandra aperture photometry with srcflux

This poster will highlight some of the features of the srcflux script in CIAO. This script combines many threads and tools together to compute photometric properties for sources: counts, rates, various fluxes, and confidence intervals or upper limits. Beginning and casual X-ray astronomers greatly benefit from the simple interface: just specify the event file and a celestial location, while power-users and X-ray astronomy experts can take advantage of the all the parameters to automatically produce catalogs for entire fields. Current limitations and future enhancements of the script will also be presented.

Poster

• 8.05
• Paul Gorenstein
• ### High Resolution X-Ray Astronomy in the Far Future

Perhaps the best resolution that grazing incidence optics can achieve is 100 marcsec. Further improvement may be obtainable with a technology based on diffractive-refractive transmitting optics. The telescope would be light weight and inexpensive. However, the focal length is ~1000 km so mission operations are challenging. The optics and detector are aboard separate S/C. Aligning the two S/C and changing targets require propulsion engines. A low thrust engine, ~50 microN can neutralize gravity gradients to maintain the telescope-detector alignment. A higher thrust engine, ~50 miliN is needed to change targets within a time of 100,000 seconds. The large focal plane scale limits the field of view in practice to less than an arc second.

• 8.06
• Catherine Grant
• ### Fifteen years of the Advanced CCD Imaging Spectrometer

As the Advanced CCD Imaging Spectrometer (ACIS) on the Chandra X-ray Observatory enters its fifteenth year of operation on orbit, it continues to perform well and produce spectacular scientific results. The response of ACIS has evolved over the lifetime of the observatory due to radiation damage, molecular contamination and aging of the spacecraft in general. Here we present highlights from the instrument team's monitoring program and our expectations for the future of ACIS. While the radioactive decay of the ACIS calibration source has decreased its utility, it continues to provide valuable data on the health of the instrument. Performance changes on ACIS continue to be manageable, and do not indicate any limitations on ACIS lifetime.

Poster

• 8.07
• Li Ji
• ### X-ray Line Diagnostics and Non-equilibrium Ionization Applications

Based on newly updated AtomDB v3.0, we will present our theoretical investigations of X-ray line Diagnostics and a couple of applications for some typical non-equilibrium ionization(NEI) plasmas in massive star binaries, stellar cluster winds and supernova remnants.

Poster

• 8.08
• Young-Dae Jung
• ### Thomson scattering process in astrophysical turbulent plasmas

The effects of turbulence on the Thomson scattering process are investigated in turbulent plasmas by the scattering of electromagnetic waves. The Thomson scattering cross section in turbulent plasmas is obtained by the fluctuation-dissipation theorem and plasma dielectric function as a function of the diffusion coefficient, wave number, and Debye length. It is demonstrated that the turbulence effect suppresses the Thomson scattering cross section. It is also shown that the turbulence effect on the Thomson scattering process decreases with increasing thermal energy. The dependence of the wave number on the total Thomson scattering cross section including the turbulent structure factor is also discussed.

• 8.09
• Omar Laurino
• ### Sherpa - On the Move to Open, Collaborative Development

Sherpa is the CIAO modeling and fitting application. Sherpa evolved from an X-ray specific analysis package to a general-purpose fitting engine with advanced capabilities. Building and installing Sherpa as a standalone Python package was problematic, but starting from version 4.7 Sherpa does not depend on CIAO and can be built or installed as a standalone package. This is the first step towards migrating the Sherpa codebase to GitHub, so that a wider community can be engaged in its development. Sherpa will be available in binary form using the Conda package manager, as well as a source distribution. Advanced configurations for custom setups are supported. This new version of Sherpa can thus be easily used along with other python tools like ipython notebooks and astropy.

Poster

• 8.10
• Jonathan McDowell
• ### 15 Years of CIAO

The first release of the Chandra data analysis system CIAO in the summer of 1999 enabled initial Chandra guest observer science. We continue to extend and improve the CIAO package, supporting both advanced use by experienced X-ray astronomers and simple analysis by novice users. Ongoing recent usability improvements include high level scripts to automate common, repetitive tasks and simplify the data reduction process, and improved support for merging observations that have been split due to thermal constraints. We present these improvements, discuss new documentation threads and present statistics on CIAO downloads and helpdesk usage.

• 8.11
• Randall Smith
• ### Arcus: The next generation of high-resolution X-ray grating spectra

The next generation of high-resolution X-ray grating spectra Abstract: We present the design and scientific motivation for Arcus, an X-ray grating spectrometer mission to be deployed on the International Space Station. This mission will observe structure formation at and beyond the edges of clusters and galaxies, feedback from supermassive black holes, the structure of the interstellar medium and the formation and evolution of stars. Key mission requirements will be R>2500 and >600 cm^2 of effective area at the crucial O VII and O VIII lines, with the full bandpass going from 8-52 Angstroms, with an overall minimum resolution of 1300 and effective area >150 cm^2. We will use the silicon pore optics proposed for ESAís Athena mission, paired with off-plane gratings being developed at the University of Iowa and combined with MIT/Lincoln Labs CCDs.

• 8.13


text:
# Left-aligned PlotLabel?

Is it possible to have the text generated by PlotLabel (or any other function) aligned to the left side of the plot instead of in the center?

 Labeled[Plot[Sinc[x], {x, 0, 9}], Style["plot label", "Section"], {{Top, Left}}]

Also

Panel[Plot[Sinc[x], {x, 0, 9}], Style["plot label", "Section"], {{Top, Left}},
Appearance -> "Frameless"]

• This is exactly what I was looking for. – Matthew Apr 16 '13 at 19:01
• How can I change the color? – Dinesh Shankar Mar 20 '19 at 12:54
• @Dinesh, you use Style["plot label", "Section", Blue] instead of Style["plot label", "Section"] – kglr Mar 20 '19 at 15:41

You can specify your PlotLabel to be a construct that takes a TextAlignment or Alignment option, such as Pane. For example:

Plot[Sin[x], {x, 0, 5},
PlotLabel -> Framed@Pane["This is the title", Alignment -> Left,
ImageSize -> 270], ImageSize -> 300]

The Framed isn't necessary; I just included it so you could see what was going on.

The main trick is that you need to specify the size of both the total graphic and the Pane, so that the text will align to the left edge of the graphic or the axis, as shown here.

If you don't do it this way, the Pane will indeed be left-aligned text, but it will "shrink" to fit the text and still be aligned center, like this:

Plot[Sin[x], {x, 0, 5},
PlotLabel -> Framed@Pane["This is the title", Alignment -> Left]]

As an alternative, you can bend AxesLabel to fit, by working out how wide the label will be in pixels, and then adding that amount of spacing to its left in a Row construct to make the argument to AxesLabel. This is similar in spirit to Mr.Wizard's answer but has the advantage of automation of the spacing.

With[{space =
Plot[Sinc[x], {x, 0, 10}, AxesLabel -> Row[{Spacer[space], Sinc[x]}] ]]

Obviously if you have styled the label for the plot label in some other way, you will need to adjust the argument to Rasterize accordingly.

• Nice. For some reason I didn't think Pane worked. +1! – Mr.Wizard Apr 7 '13 at 5:06

You can use Epilog to insert the plot label wherever you wish within the PlotRange.

Edit: There is a drawback to this approach. Because the title will be within the graph region, there is a possibility that the title will be appear over part of the graph of the function.

Plot[Sinc[x], {x, 0, 9},
Epilog -> Text[Style["This is where my plot label goes", {Blue, 16}],
Offset[{30, -10}, Scaled[{0, 1}]], {-1, 0}]]

In the example, the text, the title is offset 30 printer's points (30/72 in) to the right and 10 printers points (10/72 in) under the upper left corner (Scaled[{0,1}]) of the Graphic. It is left-justified, {-1,0}.

Not directly that I am aware of. You could of course fake it with spacing:

Plot[Sinc[x], {x, 0, 9}, PlotLabel -> Row@{"Text", Spacer[300]}]

Simpler may be use Column but it is not part of the Graphics object itself:

Column@{"Text", Plot[Sinc[x], {x, 0, 9}]}

• I need the label to be part of the Graphics object. The spacing option isn't very dynamic. I guess there's no "easy" way to do it. – Matthew Apr 7 '13 at 0:10
• @Matthew Fortunately there is, and I was merely ignorant. See Verbeia's answer. :-) – Mr.Wizard Apr 7 '13 at 5:07

Here is a refinement of @DavidC's approach.

We can use PlotRangeClipping->False and then stick the label outside of the plot range and still have it show up. In order to do this we need to know the ImagePadding of the plot, and the height of the plot label. Here is the plot:

plot = Plot[Sinc[x], {x, 0, 9}]

We can find out the image padding using my GraphicsInformation function. Install with:

PacletInstall[
"GraphicsInformation",
"Site" -> "http://raw.githubusercontent.com/carlwoll/GraphicsInformation/master"
];

<<GraphicsInformation

GraphicsInformation returns a list of rules:

pad = "ImagePadding" /. GraphicsInformation[plot]

{{16.1531, 1.5}, {1.5, 0.5}}

To get the size of the label, we can use Rasterize:

label = Style["Plot label", "Section"];

Rasterize[label, "BoundingBox"]

{105, 33, 27}

The second element of the list is the height in points. Now, we are ready to add the label to the plot:

Show[
plot,
Graphics @ Text[label, Offset[{-16, 10}, Scaled[{0, 1}]], {-1, -1}],
PlotRangeClipping->False,
`


text:
# Sparse Estimation with Structured Dictionaries

David P. Wipf

In the vast majority of recent work on sparse estimation algorithms, performance has been evaluated using ideal or quasi-ideal dictionaries (e.g., random Gaussian or Fourier) characterized by unit $\ell_2$ norm, incoherent columns or features. But in reality, these types of dictionaries represent only a subset of the dictionaries that are actually used in practice (largely restricted to idealized compressive sensing applications)... (read more)

PDF Abstract

No code implementations yet. Submit your code now


text:
# Lorentz group representation

I'm a bit confused about Lorentz group representations. I see that Lorentz group is non compact and therefore there is no faithful irreducibile unitary finite dimensional representation. In fact I can see that rotation group generators are antihermitian, while boost generators are hermitian and because of this the representation is not unitary. The same thing is in Dirac representation.

When I introduce Poincaré group, I see that translation operator acts upon $C_{\infty}$ functions, so I also need generators for boosts and rotations that may give a infinite representation of lorentz group; I therefore use generic angular momentum operator.

My question is, why don't I have infinite dimensional representation also for spinors? Is it because spinorial representation of Lorentz group act on spin degrees of freedom only?

Moreover, in "An Introduction to Quantum Field Theory" by Peskin and Schroeder at page 41 it says: "In fact the Lorentz group, being non compact, has no faithful, finite-dimensional representations that are unitary. But that does not matter to us, since $\psi$ is not a wavefunction; it is a classical field." What does this mean?! I'm confused!

Dirac-Spinors in relativistic theory are finite-dimensional representations of the Lorentz-group with peculiarity of being non-unitary.

$\psi^\alpha = \Lambda^\alpha_\beta \psi^\beta$

with finite-dimensional $\Lambda \approx 1+\frac{1}{2}\omega_{\mu \nu}M^{\mu\nu}$ where $M^{\mu\nu}$ is a matrix belonging to the generators of the Lorentz group and $\omega_{\mu \nu}$ an antisymmetric matrix containing the 3-dim. angle $\bf{\alpha}$ parameter and the 3-dim.velocity $\bf{v}/c$ parameter.

In non-relativistic theory you need the modulus of the wavefunction $|\psi'|^2= (U\psi)^{\dagger} U\psi = \psi^{\dagger}\psi= |\psi|^2$ being invariant, indeed that can only be achieved with unitary representations, for instance with those of the $SO(3)$-group. However, the corresponding modulus $|\psi|^2=\psi^+ \psi= \bar{\psi}\gamma^0\psi$ in the relativistic theory actually transforms like a 0-component of a 4-vector, so it is not invariant under Lorentz-transformations. So non-unitarity of the Lorentz-transformations is not a problem.

However, if you consider the Poincare'-group, one obtains also infinite-dimensional representations with spinors which transform like this:

$\psi'^{\alpha}(x')= U(\Lambda)\psi^\alpha(x) U(\Lambda^{-1})=D(\Lambda^{-1})^\alpha_\beta\psi^\beta(\Lambda x)$

And they are infinite-dimensional and unitary.

For relativistic Weyl-spinors it is rather similar, the formal expressions in this answer are the same apart from the detail that the size of the matrices and their matrix elements then used has to be adapted. Above all a tentative expression like $|\psi|^2\sim \psi^{\dagger \dot{A}}\psi_A$ (if such an expression made any sense I am not sure of) formed by Weyl-spinors neither does not need to be invariant, therefore unitarity of the finite Lorentz transformation representation is not required.

For more details the literature has to be consulted. A choice in this respect is for instance the book of Srednicki.


text:
# The area of a circle inscribed in an equilateral triangle is 154 square centimeters. What is the perimeter of the triangle? Use pi=22/7 and square root of 3= 1.73.

Jan 6, 2016

Perimeter $= 36.33$ cm.

#### Explanation:

This is Geometry, so lets look at at a picture of what we are dealing with:

${A}_{\text{circle") = pi*r^2color(white)("XXX")rarrcolor(white)("XXX}} r = \sqrt{\frac{A}{\pi}}$

We are told
color(white)("XXX")A=152 "cm"^2
and to use
$\textcolor{w h i t e}{\text{XXX}} \pi = \frac{22}{7}$

$\Rightarrow r = 7$ (after some minor arithmetic)

If $s$ is the length of one side of the equilateral triangle and $t$ is half of $s$

$\textcolor{w h i t e}{\text{XXX}} t = r \cdot \cos \left({60}^{\circ}\right)$

$\textcolor{w h i t e}{\text{XXXx}} = 7 \cdot \frac{\sqrt{3}}{2}$

and
$\textcolor{w h i t e}{\text{XXX}} s = 2 t = 7 \cdot \sqrt{3}$

$\textcolor{w h i t e}{\text{XXXx}} = 12.11$ (since we are told to use $\sqrt{3} = 1.73$)

Perimeter $= 3 s$

$\textcolor{w h i t e}{\text{XXXXXX}} = 3 \times 12.11 = 36.33$


text:
The MNIST dataset is a large set of 28-pixel square grayscale images of handwritten digits. The task of assigning each image to one of ten classes (digits zero through nine) can be considered a simple computer vision task. It has been used historically to evaluate machine learning algorithms. The Julia program below uses stochastic mini-batch gradient descent to fit a logistic linear model to the training set of 55,000 images. It then evaluates the model on a test set of 10,000 images and prints the accuracy of the classification. It runs in a few minutes.

Remember to run Pkg.add("TensorFlow") before running it.

The program includes functions from https://github.com/malmaud/TensorFlow.jl to download and decompress the dataset from an internet source.

include(Pkg.dir("TensorFlow", "examples", "mnist_loader.jl"))

The model has $28 \times 28 = 784$ input values and 10 output values:

exampleInput = TensorFlow.placeholder(Float64, shape=[nothing, 784])
exampleOutput = TensorFlow.placeholder(Float64, shape=[nothing, 10])

The dataset is provided to us as input vectors without $x_0 = 1$ elements for $\theta_0$. Therefore, we separate the $\vec{\theta_0}$ from the remaining $\vec{\theta}$:

thetas = TensorFlow.Variable(TensorFlow.ones((784, 10)))
theta0 = TensorFlow.Variable(TensorFlow.ones((1, 10)))

The model function is slightly different from the logistic function used previously. softmax() divides the logistic result for each class by the sum of the results over all classes, producing a probability distribution across the possible outputs. The modified cost function reflects this variation.

modelOutput = TensorFlow.nn.softmax(
TensorFlow.matmul(exampleInput, thetas) + theta0
)
cost = TensorFlow.reduce_mean(
-TensorFlow.reduce_sum(
TensorFlow.multiply(exampleOutput, TensorFlow.log(modelOutput)),
axis=2
)
)

In SGD, the overall cost can be expected to fluctuate from iteration to iteration. The size of the gradients will fluctuate also. Therefore, we don’t bother printing the starting cost of the model, and we iterate a fixed number of times rather than continuing until the gradients get close to zero:

for i = 1:16000
run(sess, [updateThetas, updateTheta0], getFeeds())
if (0 == i % 100) print(".") end
end

Finally, we extend the graph to measure the accuracy of the model. This is done by comparing the arg_max() of the model output—returning the digit with the highest probability—with the arg_max() of the example output vector—the digit corresponding to the position with a 1. equal() will return True if the two are equal. cast() will convert True values to 1.0 and False values to 0.0.

accuracy = TensorFlow.reduce_mean(
TensorFlow.cast(
TensorFlow.equal(TensorFlow.arg_max(modelOutput, 2), TensorFlow.arg_max(exampleOutput, 2)),
TensorFlow.Float32
)
)

The program below should run in a few minutes and produce a model able to correctly classify over 91% of the test images. This is not a bad result, but next, we’ll look at more complex models that do even better.


text:
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# How many 5 letter combinations can be made from the letters

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics
Author Message
TAGS:

### Hide Tags

Senior Manager
Joined: 21 Oct 2013
Posts: 435
How many 5 letter combinations can be made from the letters [#permalink]

### Show Tags

18 Jul 2014, 11:53
1
2
00:00

Difficulty:

25% (medium)

Question Stats:

71% (01:18) correct 29% (01:41) wrong based on 222 sessions

### HideShow timer Statistics

How many 5 letter combinations can be made from the letters of the word VERMONT if the first letter has to be a vowel and the last letter has to be a consonant, and each letter can be used only once?

A. 21
B. 42
C. 120
D. 600
E. 720
Math Expert
Joined: 02 Sep 2009
Posts: 46141
Re: How many 5 letter combinations can be made from the letters [#permalink]

### Show Tags

18 Jul 2014, 11:58
1
5
goodyear2013 wrote:
How many 5 letter combinations can be made from the letters of the word VERMONT if the first letter has to be a vowel and the last letter has to be a consonant, and each letter can be used only once?

A. 21
B. 42
C. 120
D. 600
E. 720

{vowel}{X}{X}{X}{consonant}

VERMONT consists of 2 vowels and 5 consonants:

The number of way to choose a vowel for the first letter = $$C^1_2=2$$.
The number of way to choose a consonant for the last letter= $$C^1_5=5$$.

The number of ways to choose middle three letters out of 5 remaining letters = $$C^3_5=10$$.
The number of arrangements of these three letters = 3! = 6.

Total = 2*5*10*6 = 600.

_________________
Current Student
Joined: 25 Jun 2014
Posts: 42
GMAT 1: 690 Q48 V37
WE: Operations (Computer Software)
Re: How many 5 letter combinations can be made from the letters [#permalink]

### Show Tags

25 Feb 2016, 02:04
1
1
Vowel: E O

Consonants: V R M N T

First letter can be filled in 2 Ways ( As the question states that "first letter has to be a vowel")
Fifth letter can be filled in 5 Ways ( As the question states that "the last letter has to be a consonant")

Now since each letter can be used only once, and 2 letters out of 7 letters are already used in First and Fifth letter

Second letter can be filled in 5 Ways
Third letter can be filled in 4 Ways
Fourth letter can be filled in 3 Ways

So, Total number of ways = 2 Ways x 5 Ways x 4 ways x 3 ways x 5 ways = 600

_________________

Intern
Joined: 25 Feb 2016
Posts: 2
Re: How many 5 letter combinations can be made from the letters [#permalink]

### Show Tags

25 Feb 2016, 04:06
i normally tend to do it using fill in the blanks

- - - - - the first place has condition which can be either O or E and the last place by V.R.M,N,T as for the 2nd 3rd and 4th we have the remaning ones

so its like first place =2
Last place 5
second place 5
third place 4 and 4th place 3

so number of combinations = 2*5*4*3*5 = 600

so 600 ways
Manager
Joined: 18 Jun 2017
Posts: 60
Re: How many 5 letter combinations can be made from the letters [#permalink]

### Show Tags

04 Aug 2017, 05:20
VERMONT has 2 vowels and 5 consonants.
Hence first letter can be chosen in 2 ways.
Hence last letter can be chosen in 5 ways.
Remaining 3 can be selected in 5*4*3 ways.
So total ways the letters can be arranged in that sequence
2*5*4*3*5=600 ways.
Option D.
Re: How many 5 letter combinations can be made from the letters   [#permalink] 04 Aug 2017, 05:20
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# How many 5 letter combinations can be made from the letters

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text:
A projectile is shot from the ground at a velocity of 12 m/s and at an angle of (7pi)/12. How long will it take for the projectile to land?

Jun 3, 2017

$2.4$ $\text{s}$

Explanation:

We're asked to find the time when the projectile lands when it is launched with a known initial velocity. We need to find the time $t$ when the height $\Delta y$ is $0$.

We can use the equation

$\Delta y = {v}_{0 y} t - \frac{1}{2} g {t}^{2}$

to find this. Our known quantities are

• $\Delta y$ must be $0$, because we're trying to find the time when this occurs.

• to find the initial $y$-velocity ${v}_{0 y}$, we can use the equation ${v}_{0 y} = {v}_{y} \sin \alpha$, so ${v}_{0 y} = 12 \text{m"/"s"sin((7pi)/12) = 11.6"m"/"s}$

• $g$, the acceleration due to gravity near Earth's surface, is 9.8"m"/("s"^2)

If we make $\Delta y$ zero, we can rearrange the equation to solve for $t$:

$0 = {v}_{0 y} t - \frac{1}{2} g {t}^{2}$

$t = \frac{2 {v}_{0 y}}{g}$

Therefore,

t = (2(11.6cancel("m")/"s"))/(9.8cancel("m")/(cancel("s"^2))) = color(red)(2.4 color(red)("s"

The projectile will land after $2.4$ seconds.


text:
### Lei Mao

Machine Learning, Artificial Intelligence, Computer Science.

# Simple Proof to the Container With Most Water Problem

### Introduction

One of my friends asked me a question on a popular LeetCode problem Container With Most Water Problem. He told me that the solution algorithm is easy to implement and he sort of has an intuition to the solution. However, he was not able to prove the correctness of the algorithm, neither did he understand the complicated explanation or proof in the discussion section. So he asked me if I could give a (simple) proof which he could understand easily.

After looking at the problem, I was able to come up with the solution algorithm using the two pointers based on my gut feelings, which is almost the same to the solution on the official LeetCode website. However, it took me hours on brain-twisting proofs before I finally came up with a simple proof.

In this blog post, I am going to introduce the problem, and the two-pointer algorithm solution to the problem first for completeness. Then I will give a simple proof for algorithm correctness.

### Problem

#### Description

Given $n$ non-negative integers $a_1, a_2, \cdots, a_n$, where each represents a point at coordinate $(i, a_i)$. $n$ vertical lines are drawn such that the two endpoints of line $i$ is at $(i, a_i)$ and $(i, 0)$. Find two lines, which together with $x$-axis forms a container, such that the container contains the most water.

Note: You may not slant the container and $n$ is at least 2.

#### Example

Input: [1,8,6,2,5,4,8,3,7]
Output: 49

### Solutions

#### Brute Force Solution

The brute force solution is simple. It took $O(n^2)$ runtime and $O(1)$ space since the combination of container walls is $O(n^2)$. I am not going to show the solution here.

#### Two Pointer Approach

The volume of the container is computed as $S(i,j)=(j-i)\min(a_i, a_j)$. We put the left pointer at the first wall and put the right pointer at the last wall respectively. In each step, if the left wall is shorter than the right wall, we move the left pointer right by one, and similarly, if the right wall is shorter than the left wall, we move the right pointer left by one, until the left wall meets the right wall. In each step, we also compute the volume of the container, keep the maximum volume and optionally the corresponding container wall indices.

The gut feeling is that we are decreasing the value of $(j-i)$ after each step, using the above method would find larger $\min(a_i, a_j)$, and therefore a possible candidate for maximum volume. It would only need to compute the area at most $n-1$ times (you could do some simple wall height comparisons to avoid area computation sometimes if you want to further optimize the algorithm), while the brute force combination needs to compute the area $\frac{n(n-1)}{2}$ times. Therefore, the asymptotic runtime complexity is $O(n)$ and the space complexity is also $O(1)$.

I have attached my simple implementation using C++ to the above algorithm.

class Solution {
public:
int maxArea(vector<int>& height) {
int i = 0;
int j = height.size() - 1;
int maxVol = -1;
int vol;
while (i < j)
{
if (height[i] < height[j])
{
vol = (j - i) * height[i];
if (vol > maxVol)
{
maxVol = vol;
}
i ++;
}
else
{
vol = (j - i) * height[j];
if (vol > maxVol)
{
maxVol = vol;
}
j --;
}
}
return maxVol;
}
};

While it passed all the tests on the LeetCode grading system, how do we know this algorithm always give the correct result? We only computed the area $n-1$ times and found the maximum of them. How do we know the rest of the combinations, which have not been computed in the above algorithm, do not have the area larger than this particular maximum?

### Proof

#### Proof by Elimination

We have an array of $a_1, a_2, \cdots, a_n$, without loss of generality, we assume $a_1 \leq a_n$, then $\min(a_1, a_n) = a_1$.

In the first iteration, we put the left pointer at $1$, and the right pointer at index $n$.

This means that the area of container $S(1,2), S(1,3), \cdots, S(1,n) \leq S(1,n)$. This is because $\min(a_1, a_2), \min(a_1, a_3), \cdots, \min(a_1, a_n) \leq \min(a_1, a_n)$. Note that $\min(a_1, a_j) \leq a_1$ for $1 < j \leq n$, and $\min(a_1, a_n) = a_1$.

In the first iteration, we eliminated $n-2$ candidates, $(1,j)$ for $1 < j < n$, for maximum container volume.

In the second iteration, the left pointer is at $2$, and the right pointer is at index $n$. Without further loss of generality, we assume $a_2 > a_n$, then $\min(a_2, a_n) = a_n$.

This means that the area of container $S(2,n), S(3,n), \cdots, S(n-1,n) \leq S(2,n)$. This is because $\min(a_2, a_n), \min(a_3, a_n), \cdots, \min(a_{n-1}, a_n) \leq \min(a_2, a_n)$. Note that $\min(a_i, a_n) \leq a_n$ for $2 \leq i < n-1$ and $\min(a_2, a_n) = a_n$.

In the second iteration, we eliminated $n-3$ candidates, $(i,n)$ for $1 < i < n-1$, for maximum container volume.

We iterate until the left wall and the right wall meet. This final iteration eliminates zero candidates.

The total number of iterations is $n-1$.

Taken together, we have eliminated $(n-2) + (n-3) + \cdots + 1 + 0 = \frac{(n-1)(n-2)}{2}$ combinations and measured the area of $n-1$ containers. Note that $\frac{(n-1)(n-2)}{2} + (n-1)$ is exactly $\frac{n(n-1)}{2}$. There is no overlap between the eliminated candidates in each iteration because the eliminated candidates in each iteration would always have a unique index. In our case, in the first iteration, the unique index is 1 on the left, and it would not show up in the later eliminated candidates. In the second iteration, the unique index is $n$ on the right, and so on.

The whole proof is very simple, and it does not actually care which side of container wall is higher or lower. Other proofs, which might be correct, are very likely to be brain-twisting.

### Final Remarks

I personally never thought highly of those coding questions. Because some problems are actually very hard or tricky to solve and prove theoretically. Taking this problem as an example, you might be able to come up with a solution based on your gut feelings in a 45-minute coding interview. However, you did not actually know whether the algorithm you were using is correct or not, even if your implementation has passed all the test examples.

This reminded me of a mathematics examination I attended in high school many years ago. There was a multiple-choice question on the test paper. “If you cut a cube of side length $a$ with a knife to get a hexagon plain. What is the largest area of the plain possible?” It gave me several options to choose from. I was stumped by the question, which was at the beginning of the test paper. Later because of this, I did not perform very well in that particular examination.

After the exam, I discussed it with my classmates. They all thought cutting in the middle of the sides and getting a regular hexagon gives you the largest area. When I asked them why, holy shit nobody knew. When the teacher discussed the test paper in the class, she skipped this question because she thought the answer was too easy and straightforward, and nobody except me lost the points in that particular problem. However, when I asked, she did not know the proof either.

I was frustrated. Later I spent several hours to write a formal proof for this and showed the proof to the teacher. The regular hexagon does give you the largest area in that particular problem. But only I knew why that was the case in the entire class, and I was the only person in the class who did not get the points for that particular problem in the test paper which everybody else considered it easy.

### Conclusions

A right attitude toward the problem is more important than getting a correct solution to it.


text:
# Finding critical points of f(x,y)

Find the critical point of $$f(x,y) = 3x^3 + 3y^3 + x^3y^3$$

To do this, I know that I need to set $$f_y = 0, f_x = 0$$

So $$f_x= 9x^2 + 3x^2y^3$$ $$f_y = 9y^2 + 3y^2x^3$$

Then you solve for x, but substituting these two equations into each other.

But somehow I ended up with $$x = y$$ and thats not very helpful.

Is there something I did wrong or misunderstood?

-
 You could solve $f_{x} = 0$ so that you get $3x^2(3 + y^3) = 0$ then substitute that in your $f_{y}$ equation. That will give you the common roots of $f_{x}$ and $f_{y}$. – acyrl Sep 30 '12 at 19:26 If you did indeed end up with $x=y$ as a necessary condition for being a critical point, use that observation in one of the two derivatives you found to solve for, say, $x$, then go back and find $y$. – bwsullivan Sep 30 '12 at 19:41

Well, $f_x=0$ is $3x^2(3-y^3)=0$, so either $x=0$ or $y^3=3$ (among reals it's $\sqrt[3]3$). And, at the same time $f_y=0$ must also hold, that is ($y=0$ or $x=\sqrt[3]3$).
It gives you the $(0,0)$ and $(\sqrt[3]3,\sqrt[3]3)$ solutions.
 It's $3+y^3$, not $3-y^3$. – Hans Lundmark Sep 30 '12 at 20:16


text:
# learn

## February 8, 2022

ToriOS Internship Program – version 1.0

• We need people who enjoy #programming and want to do it for fun, to create really nice small things that can be used easily by almost anyone.
• All levels of programming are fine.
• People need to have #motivation to do this because they want to, themselves. They need motivation to learn more because they are growing.
• They must have the ability to #fail and #learn from it.
• As long as those exist, #skills will come. Anything anyone already has to begin with is fine.
• Rust, serde, FLTK, DBus, X11/etc, XDG, lexer, TUI, Linux, Every Window Manager there is, Rust coreutils/chroot/squashfs?/etc for building, TOML/JSON/INI/etc, HIG/UI/UX accessibility, Bash scripting.

Goals:

1- Oxidize the C++ programs used in ToriOS, and improve them. 2- Oxidize the scripted builds. 3- Oxidize the scripts used in ToriOS, and use serde for configuration, support multiple formats in and out. 4- Build separate libraries for separate tasks. Many small libraries that can be reused are better than one big one for everything. 5- Bring these components together and create a desktop environment using any window manager. 6- Replace GNU with Rust equivalents to make Oxidized Linux as the base of the operating system. 7- Configure multiple window managers using the same graphical tool, allowing for the conversion of one window manager format to another, seamlessly. 8- build menus for window managers with an oxidized menu generator. 9- Oxidize FLTK applications menu program. 10- Make portrait and landscape layouts for the desktop. Using dbus to load things when needed.

Longer term wish list goals:

1- Rust + FLTK to create a modern panel/tray system. 2- Handle the virtual desktops, use ~/Desktop.d/... for handling multiple desktops with multiple icon layouts. Just a desktop manager, not a file manager. 3- Build our design of a very modular onscreen keyboard. 4- Make all GUI apps display a TUI when no $DISPLAY exists. 5- Volume manager to trigger whatever events are configured. 6- Pre-built Phone images to flash as well as ISOs to download. 7- replace any GTK specific programs with Rust + FLTK versions. 8- use a native Rust GUI toolkit when one is mature enough. Note: The word [#Oxidize] is used to mean converting an older program to use Rust, instead of whatever programming language it was originally written in. IF AND ONLY IF YOU MEET ALL THE REQUIREMENTS, please apply by sending an email to: [ ali AT torios DOT top ] • Subject Line must contain [ToriOS Internship ver 1.0] • Introduce yourself – mention your REAL name. • Country – wherever you currently live. • Written consent that have read + agree on each and everything mentioned in this post. • Please explain WHY you think I should let you in? • NO begging please. Begging means reject. • DO NOT send any Resume/CV because that means reject. ## May 29, 2020 Free Code Camp – Visual Design 7 Now fully completed Applied Visual Design module with FreeCodeCamp so have now reached 100% of the way through the module On onto Applied Accessibility next Happy to provide help and support via decentralised social media. I can be contacted on Mastodon here. You can get a free account on the http://qoto.org instance by following this link. Licenced under Attribution 4.0 International (CC BY 4.0) ## May 27, 2020 Free Code Camp – Visual Design 6 Completed more of the Applied visual design module with FreeCodeCamp so now reached 73% of the way through the module More tomorrow. Happy to provide help and support via decentralised social media. I can be contacted on Mastodon here. You can get a free account on the http://qoto.org instance by following this link. Licenced under Attribution 4.0 International (CC BY 4.0) ## May 26, 2020 Free Code Camp – Visual Design 5 Completed 10% more of the Applied visual design module with FreeCodeCamp so now reached 60% of the way through the module Happy to provide help and support via decentralised social media. I can be contacted on Mastodon here. You can get a free account on the http://qoto.org instance by following this link. Licenced under Attribution 4.0 International (CC BY 4.0) ## May 23, 2020 Free Code Camp – Visual Design 4 Completed some more of the visual design module in FreeCodeCamp so now reached 50% of the way through the module So lots of progress made on this, and more useful skills being developed. Happy to provide help and support via decentralised social media. I can be contacted on Mastodon here. You can get a free account on the http://qoto.org instance by following this link. Licenced under Attribution 4.0 International (CC BY 4.0) ## May 19, 2020 Free Code Camp – Visual Design 3 Completed some more of the visual design module in FreeCodeCamp so now reached 37% of the way through the module Lots of useful design tips in this section of the course, so great for making small adjustments to css, which can really help to improve the visual look of page(s). Happy to provide help and support via decentralised social media. I can be contacted on Mastodon here. You can get a free account on the http://qoto.org instance by following this link. Licenced under Attribution 4.0 International (CC BY 4.0) ## May 16, 2020 Free Code Camp – Visual Design 2 Completed some more of the visual design module in FreeCodeCamp so am sharing my progress here. So far this is proving really useful, and the website is really easy to follow. ## May 14, 2020 Free Code Camp – Visual Design 1 Finally got round to undertaking the first part of Applied visual Design on FreeCodeCamp so am sharing my progress here. So far so good. ## April 11, 2020 LaTeX and Chemistry LaTeX is very useful for typesetting Chemistry. A few examples are below Normally we would the chemical formula for Methane as$CH_4$How do we achieve this in LaTeX? We to use maths mode. $CH_4$ So the underscore gives us the required Subscript 4. The$ tells latex to use maths mode.

If we want to include both the Atomic number and Mass of an element. For example Hydrogen.

$H^1_1$

$H^6_12$

Or Carbon (illustrating how to type 2 numbers)

$C^6_{12}$

$C^6_{12}$

Puts one number above the other. So in the case the ^ gives us our superscript.

If we wanted to write Sodium as an ion we would put

$Na^{1+}$ Note that the 1+ has been put inside curly braces {1+}

$Na^{1+}$

So far this is pretty straightforward

You can also type chemical equations, which is a little more involved:

$H_2O(l) \hspace{0.5cm} \xrightarrow[\text{}]{\text{heat}}\hspace{0.5cm} = \hspace{0.5cm} H_2O (g)$

The first \text{} would put any text under the arrow, while clearly the second puts the text on top.

As per instructions you need to tell LaTeX to use the package mathtools

\usepackage{mathtools}

I have also added some horizontal spacing so the equation is not squashed together.

however writefreely does not seem to render this fully. You can view this equation in Overleaf here

Licenced under Attribution 4.0 International (CC BY 4.0)

## Learn LaTeX

Learn LaTeX is a new website that aims to give users enough information to get started.

It looks very good so far and hopefully will help build up skills in this area. It won't cover everything but doesn't need to. Hopefully some of my posts will also complement this website.

It is great to see so many fresh resources out there. With the upcoming release of TeX Live 2020 the timing for this could not have been better.

# Resources

Licenced under Attribution 4.0 International (CC BY 4.0)


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# Revision history [back]

I don't think this is possible now, but it's an interesting idea. I wonder how hard it would be to implement.


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# Revision history [back]

### Why you needed to use sudo’ when executing Wireshark? (what would happen if you did not use sudo’).

Why you needed to use sudo’ when executing Wireshark? (what would happen if you did not usesudo’).

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### Why you needed to use sudo’ when executing Wireshark? (what would happen if you did not use sudo’).

Why you needed to use sudo’ sudo when executing Wireshark? (what would happen if you did not useuse sudosudo’). ).