Recognising that child protection assessment is a complex, ongoing and dynamic process that is most effective when undertaken in partnership with families and their identified networks, PFS utilises a comprehensive collaborative assessment and planning framework adapted from the Signs of Safety assessment and planning protocol and the Massachusetts safety mapping framework. This process involves having all the key stakeholders who are involved with a child work together in gathering and analysing relevant information into key child protection domains, helping to move the assessment process from something that happens "to" families to something that happens "with" families.
The CAP framework offers a common language to help gather and analyse case information, increasing clarity about what has gone on in the past that is concerning, what has happened or is happening in the present to keep the child safe, and what needs to occur going forward to move toward enduring safety for the child. It also makes use of scaling questions to help children, families and workers be clear about their own judgement and what steps are needed to move the case forward.
 See Turnell and Edwards (1999), Turnell & Parker (2009), and Chin, Decter, Madsen and Vogel (2010).
Developed in New Zealand by Nicki Weld and Maggie Greening, the 'Three Houses' is a simple yet powerful tool designed to help child protection workers include the voices of children, young people and families in all aspects of the child protection process. Within PFS, a simplified version of the 'Three Houses' tool is used to help workers understand children's and young people's views about what is happening in their lives and to help children and young people participate in the assessment and planning process.
Gaining parents'/caregivers' and family members' views can be a difficult task for child protection professionals, particularly when family members may be angry or scared, may have little trust in professionals and may feel anxious about the possible consequences of speaking openly. Developed in Australia by Sonja Parker, the 'Future House' is a visual tool that is designed to help child protection professionals elicit parents' and family members' ideas and visions about what actions are needed to build safety for the children. Eliciting the parents'/caregivers' safety goals is a necessary first step in working with families to develop a joint vision (between caregivers, children, their safety network and child protection professionals) of enduring safety for the children.
The 'Safety House' is a practical, visual tool, developed by Sonja Parker in Western Australia, that is designed to include children in the safety planning process and specifically to elicit their views on what would need to happen within their family to ensure that they are safe. Through this process, children are able to offer very detailed ideas from their perspective about what actions would need to occur to help them feel safer in their homes and which adults are best able to support that.
Children in out-of-home care or involved with the child protection system frequently have little or no understanding as to how or why they are in care or even why child protection professionals are involved with their family. Developed in the UK by Susie Essex, John Gumbleton and Colin Luger (as part of the Resolutions Approach to working with 'denied' child abuse), the 'Words and Pictures' method provides a developmentally appropriate process and explanation to help children understand what has happened in their family that has led to the current situation. In a words and pictures process, family members and professionals work together to co-construct a storyboard to describe the sometimes difficult information about what has happened in a family's life and what the family is now trying to do to respond. Within the "Partnering for Safety" approach, this storyboarding process is also used as part of safety planning to help children, family members, their identified network and other professionals understand what has happened that led to child protection involvement with the family.
A critical component of the "Partnering for Safety" approach is the identification, development and involvement of a safety and support network for the children; a concept that was developed within the Resolutions Approach. This network is made up of family, friends and professionals who care about the children and family and who are willing to work with the family and with child protection professionals to develop, implement and monitor an ongoing safety plan.
The 'Circles of Safety and Support' tool, inspired by the concentric circles used by Susie Essex in the 'Words & Pictures' method and the circles concept from the protective behaviours approach, was designed by Sonja Parker from Western Australia to help family members identify people for the family's safety and support network. This tool also helps child protection professionals to have conversations with family members about why a safety and support network is necessary, about the role of the safety and support network and the process of assessing who would be the most appropriate people to participate in this network.
The "Family Roadmap" process is a dynamic, participatory and collaborative child protection assessment and planning process that has been designed to elicit the views and ideas of family members (and their safety network) in preparation for the family's participation in the development of comprehensive safety plans. This collaborative assessment process creates a platform of shared understanding that is necessary for professionals and families to then be able to work together to develop effective safety plans for children.
The "Family Roadmap" is created on a wall, a large table or on the floor: what's important is that everyone can see everything that is being recorded in the 'roadmap' so that they have the greatest possible opportunity to participate in the process. This high level of participation is the other key characteristic of the "Family Roadmap" process, as family members are actively involved in writing and creating the 'roadmap'.
Creating a 'family roadmap' in Japan.
Safety planning is a complex process that involves all the significant people in a child's life working together to develop a detailed safety plan. This family safety plan is one that will describe the day-to-day arrangements that a family and their safety network have agreed to put into place to ensure that the child will be safe in the future in relation to the identified dangers or worries. This process also involves monitoring and reviewing the safety plan over time, so that everyone is satisfied that the plan is working and will continue to work even once child protection withdraws.
Developing these kinds of safety plans usually involves multiple meetings - first with the parents/caregivers, then with the children (if they are old enough) and the safety network. I developed this safety planning tool to help provide direction and focus for these family safety meetings and for the creation of these detailed safety plans.
Appreciative Inquiry (AI) is an approach to organizational change developed by David Cooperrider at Case Western University in the US that draws on a core belief very closely related to Solution-Focused practice: That what we pay the most attention to has the best chance of growing. Appreciative Inquiry is a core component of the "Partnering for Safety' approach* and is used within the case mapping process, in supervision, case consultation and as part of coaching and mentoring to elicit and amplify examples of good practice.
AI involves taking time within our teams and organizations to notice and then ask questions about the skills, knowledge and high-point moments of people's work. It is a counter-practice to the fear, blame, and defensiveness that can characterize child protection work. As a process, it can help solidify new ways of working within an organization and assist individuals in recognizing their own skills and solutions to difficult problems.
* Our use of AI has been significantly influenced by the work of Andrew Turnell in utilizing AI within the child protection context.
The approach to implementation utilised within the "Partnering for Safety" approach is one that moves quickly from "stand and deliver" trainings to in-office practice, coaching and mentorship. Research on transference of learning in child protection shows that even multiple trainings done by dynamic and exciting trainers will not result in sustained behavior change over time. While the foundational practices of the Partnering for Safety approach are best introduced in a training, most of the skill development that needs to take place for successful uptake of these practices requires ongoing workplace coaching, identifying groups of people most likely to be able to spread the practice ('early adopters'), and applying the practice within multiple settings such as case consultation and supervision. Each of these strategies is discussed briefly below.
'Early adopters' are members of the workforce who are likely to be the most excited about receiving training and coaching. They are staff within the organization often held in some esteem by their peers, and potentially could be people who could become trainers, coaches or leaders themselves in the future. This approach to implementation strongly suggests that these 'early adopters' be identified and provided extra support throughout the implementation process. As "pioneers" in a way, they become the initial staff members who go deep into the practice and then are responsible for "coming back", being visible in the organization, telling stories about their work and diffusing the practice throughout the organization. Ultimately, it is these 'early adopters' who often become the biggest champions of the practice and have the biggest influence on their peers.
The Partnering for Safety assessment and planning framework can be used as an organising framework for case consultation and supervision in order to support ongoing learning and skill development. This enhanced case consultation process is a facilitated process, lead by a supervisor, experienced practitioner or coach who uses the framework to help workers think critically about the family and their work with them. This process helps workers to develop and refine their assessment and casework skills while more fully embedding the approach into their ongoing work.
Similarly, the framework can be used in a group supervision context, helping workers and units to develop a culture of transparency, openness and shared learning within the group. In particularly complex cases, this group supervision process can also create a sense of shared ownership for the work.


text:
Brakpoort Pass (R328 / TR 33-2)
This 4,27 km long tarred pass is a northern extension of the fabulous Robinson Pass and sweeps through the Brakpoort about 18 km south-west of Oudtshoorn. The road descends 144 vertical metres, producing an average gradient of 1:30 with the steepest section presenting at 1:14. There is one dangerous corner of 90 degrees where some negative cross-flow has seen several vehicles departing the road for the much rougher ground of the ravine on the right. On the sharpest part of this corner, solid concrete crash barriers have been created and judging by the many metal scrapes and paint marks on the concrete, it has already served its purpose in saving lives.
Gouritz River Pass (N2)
This is a long pass on the N2 at 13,3 km which connects Albertinia in the west with Mossel Bay in the east. The western side is fairly straight with few bends and more gentle gradients, but the eastern side is much steeper and includes a set of double S-bends. The road straddles the Gouritz River - one of the major rivers in the area via a high bridge which spans the gorge adjacent to two old steel latticed bridges, which until 2005 were used as a bungee jumping and bridge swing site for the adrenaline junkies.
Robinson Pass (R328 / TR33-2)
The Robinson Pass on the R328 route, is a modern classic of the Southern Cape with beautiful sweeping curves and superb views around every corner. It's administrative number is TR 33-2. It connects the coastal port of Mossel Bay with Oudtshoorn. The pass has been rebuilt several times over the past 140 years and offers not only fabulous scenery, but many pages of history around every bend. The pass is subject to heavy rain and frequent mountain mists, which reduces visibility and makes the pass dangerous. It has claimed many lives over the years including a bus full of international tourists. A memorial stone in their memory stands on the left hand side of the road about halfway up the pass.
Hagelkraal Pass - near Herbertsdale
This smallish pass forms part of a great gravel drive along some farm roads under the towering backdrop of the Outeniqua mountains not far from the R328 and the Robinson Pass. It traverses two deep valleys and offers tranquil pastoral scenery in this dairy farming region with its steep hills and many rivers. As a bonus it provides a lovely drive through the countryside, with access to the Robinson Pass and several other passes in the area, including Cloetes Pass, Du Plessis Pass, Attakwaskloof Pass and Jan Muller Pass.
Du Plessis Pass (R327)
This easy, tarred pass lies on the R327 between Mossel Bay and Herbertsdale, and finds its end amongst green fields on the banks of the Gouritz River. The pass dates back as far as 1850. It's above the national average at 8,5 km and descends a substantial 253m producing an average gradient of 1:34 via 13 bends, corners and curves.
The main geographical feature of this pass, is its proximity to the Gouritz River which has a huge drainage area of 45,715 sq.km. The Gourits River flows from the confluence of the Gamka River and Olifants River and is joined by the Groot River, before flowing through the Langeberg Mountains and coastal plain. It eventually drains into the sea through the Gourits Estuary near Gouritsmond. At the point where the pass kisses the banks of the river, is one of the few places where the river can be accessed in tranquil mood over a wide floodplain.
Attaquaskloof (Old ox-wagon route)
This is one of the great historical gravel passes which winds its way through the Outeniqua Mountains north of Mossel Bay. It has subsequently been replaced by a significantly more convenient, tarred pass (Robinson Pass). Attaquaskloof Pass is now frequented mostly by die-hard 4x4 enthusiasts and a few local farmers.
However, the 22,3 km of gravel road is definitely worth each and every meter of its history-rich length! A permit is required to drive this route and there are locked gates. Keys are obtained on issue of your permit at the start point, which is the Bonniedale farm. Note - this route can only be driven in one direction (west to east).
30th May, 2017 - News just in from Bonniedale farm: "The Attaquaskloof is part of the old Ox-Wagon Route from Heidelberg to de Vlugd. There is a section of it (20km) that goes through the Attaquaskloof to the R328. Unfortunately Cape Nature has now closed their section of the road. You can still do part of the Trail on Bonniedale. (As well as other 4x4 Trails on Bonniedale), but you are not able to go all the way through. You can however use the alternate route (public road), from Bonniedale to the R328, and meet up again with the Ox-Wagon Route from there again."

redpajama_set_name: RedPajamaCommonCrawl


To register for a booth at the Southeastern HME Convention, sponsored by ADMEA, you must be an Associate Member at the Silver, Gold or Platinum level.
Bronze level members may register for a booth by paying an additional $600, which will also elevate your membership level to Silver.
To reserve your booth(s), complete this form. If you have already paid dues at the Silver level or above, no additional payment is due, unless you wish to purchase additional booths at $400 each. Otherwise, you will owe $600, which you may pay on line via credit card. An invoice is available on request.
Non-members and current members who have not renewed should join or renew first, then complete this form.


The ring has a distance to the tube of 0.197 inch (5mm) at the top and 0.591 inch (15mm) below. The inside diameter of the tube can be selected from the following choices: 1.141 inch (29mm), 1.378 inch (35mm), 1.496 inch (38mm) or 1.732 inch (44mm). You can choose the overall length between 2.366 inch (60mm) and 5.118 inch (130mm). The following ring sizes are available: 1.496 inch (38mm), 1.574 inch (40mm), 1.653 inch (42mm), 1.771 inch (45mm), 1.85 inch (47mm), 1.968 inch (50mm). Special sizes are possible.
Steelheart 2 was added to our catalog on Tuesday 30 December, 2008.


If not tracked and managed properly, basic assets tax can appear as a ample abruptness at tax-filing time. In fact, abounding taxpayers don't apprehend they accept a basic accretion until they get their 1099 anatomy in January and see a basic accretion distribution. Here's what you charge to know.
Capital assets are accustomed back you advertise a basic asset for added than your base in that asset. Basic assets are about article of bulk like your home, a car and added investments. Base is about the aboriginal bulk of the asset actuality sold. The aberration amid the sales bulk of the asset and your base is the bulk of the taxable basic gain.
The IRS taxes concise basic assets for assets endemic beneath than one year as accustomed assets up to 37 percent, but taxes abiding basic assets at a best 23.8 percent (20 percent additional a abeyant 3.8 percent net advance tax).
Hold investments for added than one year. Abiding assets (assets awash added than a year afterwards acquisition) are burdened at the lower basic assets rate. If you are able to authority assets for added than a year, you will save tax dollars by alienated the accretion actuality classified as accustomed income.
Sell ample assets in low-income years. If you apprehend lower assets this year, it ability be a acceptable time to advertise some of your basic accretion investments. Since the basic assets tax brackets chase the bordering assets tax brackets, if you are in a lower assets tax bracket in a accustomed year you may pay a lower basic assets tax. You can booty advantage of this with both abiding and concise gains.
Harvest ample losses in advantageous years. If you accept a advantageous year you can save taxes by affairs investments that accept absent money. Basic losses advice abate your basic assets with the tax accountability affected on the net amount. Be acquainted of IRS applique rules that crave you to net abiding losses with abiding assets and concise losses with concise gains. If one after-effects in a net accident and the added a net gain, they are again netted adjoin anniversary other. If the final bulk after-effects in a net loss, the best you can abstract adjoin accustomed assets in one year is $3,000. The balance losses charge again be agitated advanced to approaching tax years.
Gift your investments to your kids. You are accustomed to allowance up to $15,000 per year to anniversary of your kids ($30,000 per affiliated couple). If you allowance accepted investments to a adolescent beneath 19 and they again advertise that investment, anniversary adolescent can accept favorable tax ysis on up to $2,100 from their taxes. Be accurate if you go over the anniversary exemption. Higher levels of unearned assets for children, including basic gains, is now accountable to acreage and assurance tax rates.
Consider altruistic property. If you accord accepted acreage to a able alms you can abstract the donation as an itemized deduction. Even better, if the acreage is endemic by you for added than one year, you can abstract the accepted bazaar bulk after actuality accountable to basic accretion tax.
Sale of primary abode exclusion. If you advertise your home, you may authorize to exclude $250,000 of the accretion from basic assets tax ($500,000 if affiliated filing jointly). In adjustment to qualify, you charge to own the home and accept active the home as your primary abode for at atomic two of the antecedent bristles years. The two years do not charge to be simultaneous.
There are abounding factors that appear into comedy back affairs or affairs an asset. Just accomplish abiding the tax implications are advised afore you accomplish the transaction.
As always, should you accept any questions or apropos apropos your bearings amuse feel chargeless to call.
James Angell is a Willits based Certified Public Accountant. His appointment is amid at 461 S. Main St. and he can be accomplished at 459-4205.


HARRISBURG – Rep. Mike Reese (R-Westmoreland/Somerset) today issued the following statement after legislation containing tax increases totaling $3.8 billion over two years was soundly defeated on the House floor with a bipartisan, 73 to 127 vote.
"The residents of the 59th Legislative District cannot afford to send more of their hard earned dollars to Harrisburg. While the governor campaigned on establishing a natural gas severance tax for his increased spending, the reality was that 90 percent of his $3.8 billion dollars in new taxes over two years was on the backs of the hardworking families throughout the Commonwealth.
"Now, the message to Gov. Tom Wolf should be clear; pushing for higher taxes is not supported by the Commonwealth's residents. And to this point, his insistence otherwise has accomplished nothing but to hold the school districts and human services organizations that rely on state funding as hostages.
"The tax increases that were wisely defeated today would have cost the average Pennsylvania taxpayer an additional $263 via the Personal Income Tax (PIT). In addition, there would have been a negative impact on small businesses that also pay the PIT through the individual tax code. This describes nearly 80 percent of the Commonwealth's small businesses, who provide the vast majority of our family sustaining jobs. The governor's proposal, had it not been defeated, would have slowed growth in this important part of our economy and would have placed these jobs at risk. Placing this tax burden on our job creators is unacceptable.
"We have put forward solid ideas on revenue creation through the privatization of liquor sales and establishing proper cost controls in order to contain the unfunded liability of the state's pension program, both of which the governor vetoed. These reforms would improve Pennsylvania's economic climate instead of passing the burden on to overtaxed residents.


text:
Where to find hidden gems in Paris
SEEN: Middletown High School graduation 2022
Middletown's 25th annual 'Cruise Night on Main' returns Wednesday
Middletown PrideFEST is this weekend. Here's what to know.
SEEN: Xavier High School Prom 2022
Middletown church offering Christmas dinner
Pet of the week: Jasmine
Pet of the week: Elsa
Buttonwood Tree holding holiday improv show Dec. 12
Pet of the week: Cooper
Pets of the week: Petunia and Duke
Guardian readers, The Guardian
d87dbeec-0dd8-4897-9e25-02f649ecd646
WINNING TIP: L'Entrepôt
This venue comprises three small, comfortable cinemas showing a huge number of films each week, from arthouse and world cinema to mainstream and children's. There's an art gallery on the top floor, a restaurant with tables outside in the summer, plus regular live music. Or you can just call by for a coffee or a beer and there'll be a good soundtrack playing.
7 rue Francis de Pressensé, +33 1 45 40 07 05,lentrepot.fr
cmarodgers
Au Lapin Agile
This tiny cabaret/chansonnier on the north side of Montmartre hasn't changed much since the days when unknowns such as Picasso, Utrillo and Matisse used to drink here and pay the bill with their artworks. It may seem expensive – entrance fee of $38.54 ($27.53 for students), including one small drink, but you are paying for the music, the poems and the fun – and you can make one drink last all evening. Helps if you speak French.
22 rue des Saules, +33 1 46 06 85 87,au-lapin-agile.com
Gjill2
Mémorial des martyrs de la déportation
A small, stark and savagely detailed underground memorial, on the southern tip of Îsle de la Cité behind Notre Dame, which goes unnoticed by the thousands of tourists who take selfies of themselves in front of the adjoining cathedral every day. Inaugurated by Charles de Gaulle in 1962, it commemorates 200,000 people who were deported from Vichy France, many to concentration camps from which few returned. It is a place for tears and quiet contemplation; a refuge from the crowds and a reminder of one of the darkest episodes in recent history.
Square de l'Île de France, +33 1 46 33 87 56,cheminsdememoire.gouv.fr
Simon177
Musée Albert Kahn
Albert Kahn was a rich French banker and philanthropist who lost everything in the crash of 1929. But the archives of a project he embarked on in the early years of the 20th century still remain in the Musée Albert Kahn beside his former home. Kahn sent teams of photographers around the world to record changing and vanishing cultures and the museum stages regular exhibitions of this amazing collection of black-and-white, colour and movie film. Kahn also created wonderful gardens around his house in Japanese, French and English styles and these in themselves are worth the journey to the end of Line 10.
10-14 rue du Port, +33 1 55 19 28 00,albert-kahn.hauts-de-seine.net
Le Rubis
Le Rubis is my favourite zinc bar in Paris. Hidden away, round the corner from the Place Vendôme, it is unashamedly untouristy. No English is spoken, the food is simple French home cooking and the wine list is huge and impressive. If you are lucky enough to sit down, then this is the place to soak up real Paris, where office workers are rubbing shoulders with genteel old couples and workmen.
10 rue du Marché Saint-Honoré, +33 1 42 61 03 34, no website
lebingleybelle
Dernier Bar Avant la Fin du Monde
If this truly were the last bar before the end of the world, you'd have no reason to complain. It is a pop culture haven in which you can sip themed cocktails with names like 42, The Dude and Jedi Knight, play table-top games on leather armchairs, limp along on their Paris Zombie Walk and take Avengers shots so strong, you'll worry you'll go blind. Come for the décor. Stay for the atmosphere. Never want to leave.
19 avenue Victoria, +33 1 53 00 98 95,dernierbar.com, open 10am-1am
ElleEmSee
Les Enfants Terribles
Beautiful food, friendly service and reasonable prices. No alcohol served but there's a range of brilliant alcohol-free cocktails. There's even a no-alcohol carte des vins. So, no sniffy waiters who lose interest when they see there's no money to be made from the wine list. Ambiance welcoming, and booking – or at least turning up early – advisable.
197 avenue Daumesnil, +33 1 43 43 24 61,resto-lesenfantsterribles.fr
ChrisTrotter
Les Cascades
Tucked away in leafy Belleville is Les Cascades, an arty cafe that really belongs to its customers and the local community. Feast on delicious salads for €8 or huge sandwiches for $6.88, while debates on topical issues rage, free gigs featuring local talent get people jiving, or up-and-coming art exhibitions reflect the rich creativity and energy of Paris. It's laid back and bohemian so don't be afraid to join in – you'll be welcomed by patrons and owners.
82 rue des Cascades, +33 1 46 36 56 92, no website
This amazing little-known – even to French people – park is in the un-touristy, north-eastern 19th arrondissement. Overlooking Paris, it includes a 30m waterfall, a suspension bridge, a lake, a grotto and a temple. The sloping lawns are great for a picnic while watching the sun go down. It's well-served by bus (the best way to visit Paris) or the metro station bearing the park's name.
1 rue Botzaris,equipement.paris.fr
Masmingou
Meudon Observatoire
On the outskirts of Paris lies the Meudon Observatoire, the plush green gardens of which provide a view of Paris to rival that from the Effiel Tower and the Sacré Coeur. It's on the banks of a lake, in a field of wild flowers, and you can take in a view of the whole city while enjoying bread and cheese from the local bakery and delis. The perfect spot to get away from all the hustle and bustle of the city.
61 avenue de l'Observatoire, +33 1 40 51 22 21,obspm.fr
lkhankin
This article originally appeared on guardian.co.uk


text:
\section{Introduction}\label{sec:intro}

Dark matter halos grow by a sequence of mergers and accretion events in cold dark matter (CDM) cosmology.  Due to the absence of scale in this heirarchical structure formation scenario, dark matter haloes are expected to be merely scaled-up or down versions of each other with the total mass being the scaling parameter \citep{Navarro+97}.  Observation of galaxies at different masses show that this is clearly not the case.  At the high end, clusters have thousands of galaxies, i.e., subhaloes, in line with theoretical predictions \citep{Natarajan+04}.  However, galactic size halos have a few bright satellites, e.g., our Milky Way (MW), in constrast with theoretical models of the MW halo (e.g. \citealt{Diemand+08}), and dwarfs have no bright satellites.  This qualitative difference at the faint end has come to be known as the substructure or ``missing satellites`` problem \citep{Klypin+99,Kravtsov04,Madau08,Kravtsov10}\footnote{To be precise, the ''missing satellites`` problem refers to the lack of observed satellites in the MW halo compared to what is expected theoretically.}.

\citet{Kravtsov10} recently review the possible solutions to the ''missing satellites`` problem.  To summarized, solving the ''missing satellites`` problem demands that a scale be introduced either in structure formation of dark matter haloes or in the physics of galaxy formation to suppress the number of observed systems at small scales.  Namely, the power spectrum of fluctuations must be suppressed at small scales via warm dark matter \citep{Zentner+03,Hooper+07,Primack09} or star formation is suppressed in dwarfs due to reionization \citep{Bullock+00,Okamoto+09,Busha+10,Iliev+10} or feedback from the first stars \citep{Wise+08}.

Recent discoveries of dwarf galaxies in the MW and M31 have
relieve some of this tension (for a review see \citealt{Willman10}). These dwarfs are the most dark matter dominated \citep{Strigari+08} and metal poor systems known \citep{Kirby+08}.  While their unusual properties point to the difficulty of forming stars in these systems, the number density of these dwarfs may alleviate the "missing satellite" problem once completeness corrections are accounted for \citep{Tollerud+08}.

The evidence from the MW observations and theoretical predictions point to the existence of many nearly dark subhaloes hosting few stars.  For instance, \citet{Bullock+10} recently pointed out that these stealth galaxies would be missed in current survey, having surface brightnesses that are too diffuse.
This motivates finding alternative means to constrain this dark subhalo population.

In a recent series of papers \citep[hereafter CB09 and CB10, respectively]{Chakrabarti+09,Chakrabarti+10},
CB09 and CB10 made the assumption that the observed disturbances in the outer atomic hydrogen gas disc of the MW \citep{Levine+06} are due to the tidal interaction with a dark matter dominated dwarf galaxy.  Proceeding under this hypothesis, CB09 and CB10 numerically simulated a suite of encounters with dwarf galaxies interacting with the MW, and developed an approach to infer the mass and current location of satellites from analysis of their tidal imprints on outer gas discs.
The Fourier amplitudes (CB09) and phase (CB10) of the suite of simulations were
compared to the observed amplitudes and phases to
determine the pericenter approach, current position (in radius and azimuth), and mass of the subhalo
that drove the observed disturbances.  In doing so, CB09 and CB10 demonstrated how to characterize a dark subhalo from looking at it's effects on the primary galaxy's extended HI disc.  Following this work, we demonstrated the
validity of this method by performing the analysis with respect to galaxies with $\it{known}$ optical companions \citep[hereafter CBCB]{Chakrabarti+11}.  We showed that the method accurately recovers the mass of the satellite and its position purely from analysis of observed disturbances in the HI disc,
without requiring any knowledge of the optical light from the satellites.

In this paper, we continue this work and develop a simplified test particle approach to studying the generation of these disturbances in extended HI discs by dark matter subhaloes.  Using this approach, we develop scaling relations between the satellite mass and Fourier amplitudes of the resultant surface density of the HI disc.  These relations can be utilized by observers who wish to determine the satellite mass directly from the observed HI map, without having to take recourse to full numerical simulations. Our simplified approach is motivated by the fact that DM subhaloes have a much lower velocity dispersion, i.e., gravitational potential, than the host halo in which they sit.  Thus, we calculate the motions of the gas (or stars) in the epicyclic approximation and show that this approximation matches the results of both test body calculations and full numerical simulations.

This work is complementary to the work of CB09, CB10, and CBCB.  Rather than compare the results of numerical simulations to observations of specific extended HI discs, this work focuses on the physics of the subhalo excitation and exploration of its parameter space.  In the future, we will apply these scaling relationships to a large sample of local spiral galaxies to determine the statistical viablity of the Tidal Analysis method, i.e., the incidence of false positives.  Moreover, we will attempt to constrain the population of dwarf galaxies in the Local Volume.

This paper is organized as follows.  In \S \ref{sec:equations}, we take the equations of motion for a test particle and develop its modal equivalent in the epicyclic approximation.  We then show how the modal viewpoint can be related to the test particle viewpoint.  This modal analysis is shown to reproduce test particle calculations accurately.  In addition, the invariance of the modal energy response (in the absence of dissipation) provides us an unique vantage point to study the response of the disc.  In \S\ref{sec:influence}, we study the modal energy response and the corresponding density response.  We also compute global quantities from these responses as a measure of the global properties of the disturbances raised by the passing DM subhalo in \S\ref{sec:scaling}.  We demonstrate a scaling relation between the disc response and the mass of the satellite where the amplitude of the modes scale like $M_{\rm s}^{1/2}$.  To show that our analysis accurately models the relevant physics, we then compare our results to those computed from large scale simulations in \S\ref{sec:sph}.  The good agreement between the SPH simulations and our results is encouraging.  In addition, the scaling which we derived from our simplified calculation continues to hold.  Finally, we close in \S\ref{sec:conclusions} with a discussion of how these methods can be used to constrain the properties of DM subhaloes in galaxy haloes.

\section{Basic Equations}\label{sec:equations}

We begin with the equations of motion of a test particle in 2-D
($r,\theta$ coordinates):
\begin{eqnarray}
\frac{dr}{dt} &=& v_r \label{eq:1}\\
\frac{d\phi}{dt} &=& \frac{J}{r^2}\\
\frac{\partial v_r}{\partial t} &+&
v_r\frac{\partial v_r}{\partial r} + \frac{J}{r^2}\frac{\partial
  v_r}{\partial \theta} = \frac{J^2}{r^3}-\frac{\partial \Phi}{\partial r}\\
\frac{\partial J}{\partial t} &+&
 v_r\frac{\partial J}{\partial r} + \frac{J}{r^2}\frac{\partial
  J}{\partial \theta} = -\frac {\partial \Phi}{\partial \theta}\label{eq:4},
\end{eqnarray}
where $v_r$ is the radial velocity, $J=\dot{\phi}r^2$ is the angular
momentum, $\phi(t)$ is the $\theta$ position of the particle, and
$\Phi$ is the gravitational potential.  We assume a background
state of circular orbits, i.e., $v_{r,0} = 0$, about
an axissymmetric potential, $\Phi_{0}$.  Expanding equations
(\ref{eq:1}) - (\ref{eq:4}) to linear order, e.g., $r \rightarrow r + \delta
r$, we find
\begin{eqnarray}
\frac{d\delta r}{dt} &=& \delta v_r \label{eq:linear1}\\
\frac{d\delta\phi}{dt} &=& \frac{\delta J}{r^2} - \frac{2 J}{r^2}\frac{\delta
r}{r}\\
\frac{\partial \delta v_r}{\partial t} &+&
\frac{J}{r^2}\frac{\partial
  \delta v_r}{\partial \theta} = \frac{2J\delta J}{r^3} -
\frac{3J^2}{r^3}\frac{\delta r}{r} - \frac{\partial \delta\Phi}{\partial r}\\
\frac{\partial \delta J}{\partial t} &+&
 \delta v_r\frac{\partial J}{\partial r} + \frac{J}{r^2}\frac{\partial
 \delta J}{\partial \theta} = -\frac {\partial \delta \Phi}{\partial
\theta}\label{eq:linear4}.
\end{eqnarray}
We assume that the perturbation to the potential, $
\delta\Phi$, arises from external perturbers ignoring the self-gravity of the particles.
This simplification is safe for typical HI disc parameters.

Assuming solutions of the form $\exp(im(\theta - \Omega(r)t))$, where
$\Omega(r) = \dot\phi(r)$, e.g.
\begin{displaymath}
\delta r \propto \sum_{m=1}^M\delta r_m(r,t)\exp(im(\theta - \Omega(r)t)),
\end{displaymath}
reduces equations (\ref{eq:linear1}) - (\ref{eq:linear4}) to M
separate wave equations, sourced by the Fourier components of the
perturbing potential:
\begin{eqnarray}
\frac{\partial\delta r}{\partial t} &=& \delta v_r \label{eq:modal1}\\
\frac{\partial\delta\phi}{\partial t} &=& \frac{\delta J}{r^2} - \frac{2
J}{r^2}\frac{\delta r}{r}\\
\frac{\partial \delta v_r}{\partial t} &=& \frac{2J\delta J}{r^3} -
\frac{3J^2}{r^3}\frac{\delta r}{r} - \frac{\partial \delta\Phi}{\partial
r}\exp\left(im\Omega(r)t\right)\\
\frac{\partial \delta J}{\partial t} &=& -\delta v_r\frac{\partial J}{\partial
r} - im\delta \Phi\exp\left(im\Omega(r)t\right).\label{eq:modal4}
\end{eqnarray}
Solving these perturbed equations for a finite $M$ (say $M=10$) allows
us to estimate the linear response of a circular ring of of orbiting
particles to external disturbances, i.e., passing DM subhaloes.  Thus,
any individual particle's perturbed orbit, whose guiding center is at
radius $r$, can be found by summing over this response.  Namely, we reconstruct the particle positions from these modes using:
\begin{eqnarray}\label{eq:reconstruction 1}
r_i(t) = r_{i,0} + \delta r_i(t), \\
\phi_i(t) = \phi_{i,0} + \delta \phi_i(t),\label{eq:reconstruction 2}
\end{eqnarray}
where $r_{i,0}$ and $\phi_{i,0}$ are the initial radius and azimult of the particle, $i$, and
\begin{eqnarray}
\delta r_i(t) = \sum_{m=1}^M\delta r_m(r_{i,0},t)\exp(im(\phi_{i,0} - \Omega(r_{i,0})t)),\\
\delta \phi_i(t) = \sum_{m=1}^M\delta \phi_m(r_{i,0},t)\exp(im(\phi_{i,0} - \Omega(r_{i,0})t)),
\end{eqnarray}
This greatly simplifies this orbit into a sum of $M$ simple harmonic oscillators,
whose natural frequency only depends on their radial position.

\begin{figure*}
  \begin{center}
  \subfigure[]{
  \includegraphics[width=0.45\textwidth]{nbody.eps}}
  \subfigure[]{
  \includegraphics[width=0.45\textwidth]{mode.eps}}
  \end{center}
\caption{Comparison between a direct integration (left) and the mode
  calculation (right) of a collisionless particle disc excited by a
  passing DM subhalo.  In this calculation, we use 50000 particles for the test-particle calculation. For the modal calculation, we set $M=64$ for 200 rings.  From this plot it is clear that modal and N-body calculation agree.}
\label{fig:nbody_vs_analytic}
\end{figure*}

To illustrate the power of this formalism, we compare a direct numerical calculation of a collisionless particle disc with that of the modal calculation above and show the results of the direct test particle calculation and our modal reconstruction in Figure
\ref{fig:nbody_vs_analytic}.  Here, the broad features of the response is captured between
the mode calculation and the N-body calculation.  It is evident that the modal calculation captures the details of the perturbation accurately.

Our formalism makes the analogy between the different modes of a radial
ring and a collection of uncoupled simple harmonic oscillators, whose oscillator
frequency just depends on their radius. Hence it is natural to think of the
modal energy,
\begin{eqnarray}\label{eq:energy}
E_m = \frac 1 2 \delta v_{r,m}^2 + \frac 1 2 \kappa^2 \delta r_m'^2,
\end{eqnarray}
where $\kappa = \sqrt{R(\partial\Omega^2/\partial r + 4\Omega^2}$ is the epicyclic frequency and
\begin{equation}
\delta r_m' = \delta r_m - \frac {2 \Omega \delta J_m} {r\kappa^2}
\end{equation}
is the perturbed radial mode $m$ that accounts for the perturbation to the guiding center.
Looking at the oscillators energy has the major advantage that it remains constant in the absence of dissipation or excitation, whereas the density response of a disc varies with time.  This is advantageous in elucidating the physics.  In the next section, we show the benefit of this mode of analysis and relate its properties to the density response.

\section{Disc Response}\label{sec:influence}

For the purposes of this work, we make a series of simplifying assumptions. First, we assume a static potential for both the primary galaxy and the subhalo, i.e., we do not use a "live halo".  Second, we assume a constant density HI disc motivated by observations of the Galactic HI disc \citet{Wong+02} and the extended HI discs of external galaxies \citet{Bigiel+10}.  There also exists an exponential gas disc, but we ignore this for the sake of simplicity.\footnote{CB09, CB10, and CBCB use an exponential gas disc with an added flat HI disc.}  These assumptions allow us to develop a simplified approach to the modeling of disturbances in extended HI discs.  We demonstrate the accuracy of the results of the simplified approach to that of a full simulation later in \S\ref{sec:sph}.

\subsection{Modal Energy Response}\label{sec:modal energy response}

\begin{figure*}
\begin{center}
\subfigure[]{
\includegraphics[width=.27\textwidth]{Em100_20kpc/0.eps}}
\subfigure[]{
\includegraphics[width=.27\textwidth]{Em100_20kpc/1.eps}}
\subfigure[]{
\includegraphics[width=.27\textwidth]{Em100_20kpc/2.eps}}
\subfigure[]{
\includegraphics[width=.27\textwidth]{Em100_20kpc/3.eps}}
\subfigure[]{
\includegraphics[width=.27\textwidth]{Em100_20kpc/4.eps}}
\subfigure[]{
\includegraphics[width=.27\textwidth]{Em100_20kpc/5.eps}}
\end{center}
\caption{Modal energies of the disc in response to the disturbances by a coplanar 1:100 perturber with an $r_{\rm peri} = 20$ kpc.  In the upper left hand corner of each plot is the radial distance of the perturber.  Initially when the perturber is far away (a), only the other disc responds to the perturber.  However, as the perturber gets closer, more and more of the disc is perturbed.  In (c), the perturber is at $\ensuremath{r_{\rm peri}}$ and we note a kink in the $m=0$ modal energy at $r=\ensuremath{r_{\rm peri}}$.  This kink on the modal energy shows up in the subsequent plots (d), (e), and (f) in the other modes as well.  This kink is the result on an increase modal energy response at $\ensuremath{r_{\rm peri}}$ and serves as an indicator of $\ensuremath{r_{\rm peri}}$ of perturbing subhaloes.  We also note the advantage of studying the modal energy as modal energy is fixed after the interaction with the perturber in the absence of dissipation.}
\label{f:Em100_20kpc}
\end{figure*}

As we mentioned earlier in \S\ref{sec:equations}, the modal equations reduce to a number of simple harmonic oscillators.  A passing perturber excites these simple harmonic oscillators, each to a different amplitude and phase. In the absence of dissipation, the modal amplitude or energy remains constant.  We illustrate this point in Figure \ref{f:Em100_20kpc} where we show six snapshots of
the orbit of a coplanar subhalo with $r_{\rm peri} = 20$ kpc.  Initially, the energy is  zero, but rises dramatically after the disc suffers an encounter, before asymptoting to a constant.  This property of the modal energy response makes them illuminating for studying the response of the disc.  We should point out that while the energy is already substantial when the perturber is at pericenter, the {\it density} response of the disc does not happen until much later.  This is because, the energy imparted by the perturber at pericenter serves mainly to increase the perturbed velocity.  However, this perturbed velocity only translates into perturbed density after $\sim$ dynamical time.

How does the modal (energy) profile depend on the orbital parameter?  To answer this question, let us first fix the mass and the orbit to be that of a parabolic ($E=0$) coplanar orbit so that the modal profile only depends on the pericenter distance of the perturber. In Figure \ref{f:Em100}, we plot modal energies as a function of radius for a 1:100 encounter for $r_{\rm peri} = 10$ kpc (left plot) and $20$ kpc (right plot).  Note the dramatic increase in modal energy for the oscillator at $r=r_{\rm peri}$.  Indeed this increase in modal energy is seen for 1:10 and 1:1000 coplanar encounters as shown in Figure \ref{f:Em1000}.
We also note that the amplitude of the modal profile depends only on the mass and is only weakly dependent on $\ensuremath{r_{\rm peri}}$ at least at large distances.

\begin{figure*}
\begin{center}
\subfigure[]{
\includegraphics[width=.45\textwidth]{Em100_20kpc/5.eps}}
\subfigure[]{
\includegraphics[width=.45\textwidth]{Em100_30kpc/5.eps}}
\end{center}
\caption{Modal energies of the disc for a 1:100 perturber with $\ensuremath{r_{\rm peri}} = 20$ kpc (a) and $30$ kpc (b).  In both case the perturber sits at roughly $r_p\approx 80$ kpc after its interaction.  As the modal energy is fixed at this point in the absence of dissipation, we can look in detail at the structure of the interaction.  Note that in both cases, a kink on the modal energy appears at $r=\ensuremath{r_{\rm peri}}$.  This strengthens the point made in Figure \ref{f:Em100_20kpc} that these kinks serves as a good proxy for $\ensuremath{r_{\rm peri}}$.}
\label{f:Em100}
\end{figure*}

\begin{figure*}
\begin{center}
\subfigure[]{
\includegraphics[width=.45\textwidth]{Em1000_20kpc/5.eps}}
\subfigure[]{
\includegraphics[width=.45\textwidth]{Em1000_30kpc/5.eps}}
\end{center}
\caption{Same as Figure \ref{f:Em100} but for a 1:1000 perturber with $\ensuremath{r_{\rm peri}} = 20$ kpc (a) and $30$ kpc (b).}
\label{f:Em1000}
\end{figure*}

We now fix $r_{\rm peri} = 20$ kpc to study the effects of inclination in Figure \ref{f:Em100_inclination}. In the coplanar case studied above, all the modes showed a similar feature at $\ensuremath{r_{\rm peri}}$.  Here, we instead see that only the $m=0$ mode consistently shows this same feature as the  coplanar case. Specifically, for all inclinations, ranging from $+\pi/2$ (prograde coplanar) to $0$ vertical to $-\pi/2$ (retrograde coplanar), the $m=0$ modal energy increases dramatically as $r > r_{\rm peri}$.

The effect of inclination on the $m\neq 0$ modal energies is more complicated.
For the coplanar prograde interaction, we also see a large increase in the modal
energy at $r=\ensuremath{r_{\rm peri}}$ for all $m\neq 0$ modes.  However, this is now true for the
other interactions.  For instance, the retrograde coplanar interaction
($-\pi/2$) shows a large amplitude for the $m=1$ mode inside of $\ensuremath{r_{\rm peri}}$ and it
decreases outward.  Nevertheless, it is clear the modal energies does show a
sudden change at $\ensuremath{r_{\rm peri}}$.

In these examples above, we have studied the effect of varying the inclination for purely prograde encounter, i.e., the case where the disc crossing radius is equal to the pericenter distance.  Though we do not present them here, we have also studied the case of fixing $\ensuremath{r_{\rm peri}}$ and the inclination and varying the angle at which the perturber crosses the disc, i.e., $\phi \ne 0$ for the disc crossing point on the y-axis.  In these examples, the modal energies also show a change at $\ensuremath{r_{\rm peri}}$, which suggest that looking for changes in the modal energy in the disc is a good way to deduce $\ensuremath{r_{\rm peri}}$.  We briefly comment on this in the next subsection, but reserve a more extensive discussion on the operational details to future work.

\begin{figure*}
\begin{center}
\subfigure[]{
\includegraphics[width=.23\textwidth]{Em100_inc/90deg.eps}}
\subfigure[]{
\includegraphics[width=.23\textwidth]{Em100_inc/60deg.eps}}
\subfigure[]{
\includegraphics[width=.23\textwidth]{Em100_inc/30deg.eps}}
\subfigure[]{
\includegraphics[width=.23\textwidth]{Em100_inc/0deg.eps}}
\subfigure[]{
\includegraphics[width=.23\textwidth]{Em100_inc/m30deg.eps}}
\subfigure[]{
\includegraphics[width=.23\textwidth]{Em100_inc/m60deg.eps}}
\subfigure[]{
\includegraphics[width=.23\textwidth]{Em100_inc/m90deg.eps}}
\end{center}
\caption{Modal energy profiles of a 1:100 perturber with $r_{\rm peri} = 20$ kpc for different
inclinations: $i = 90$ (a), 60 (b), 30 (c), 0 (d), -30 (e), -60 (f), -90 (g) degrees.  The kink in the modal energy profile in the coplanar case (a) and Figure \ref{f:Em100_20kpc} is only persistent for the $m=0$ mode for all inclinations. However, the modal energy profile near $r = \ensuremath{r_{\rm peri}}$ shows features in all cases like peaks, e.g., $m=1$ case for -30 (e), -60 (f), and -90 (g) degrees. }
\label{f:Em100_inclination}
\end{figure*}

\subsection{Density Response}

The modal energies provide a good proxy for the response of the disc, but our analysis of modal energies here is new.
We now link this modal energy response to the density response, which is the observed manifestation of these perturbations. To calculate the density response from the modal energies, we reconstruct the position of the particles using equations (\ref{eq:reconstruction 1}) - (\ref{eq:reconstruction 2}).  From this, we obtain the density of particles as a function of $r$, $\phi$, and $t$, from which the Fourier amplitudes can be calculated.

Our analysis of modal energies show that they are localized to certain regions of the disc.  This suggests that the density perturbations also follow a similar pattern.  We show this in Figure \ref{f:dens100_20kpc} where we show density perturbation from modal theory for the same six snapshots of the orbit of a coplanar subhalo with $r_{\rm peri} = 20$ kpc as in Figure \ref{f:Em100_20kpc}.  Note that we have only not included the $m=0$ mode here in constrast to the modal energy comparison.  While, we can define such an axisymmetric perturbation based on the initial (unperturbed) configuration, such a construction would not be well defined if we compare this to observations or simulations (see \S\ref{sec:sph}).  As we anticipate such a comparison, we have ignored the perturbed $m=0$ mode in the density response.  In addition, we have normalized the $m=1-4$ modes relative to the {\it complete} $m=0$ mode, which is dominated by the unperturbed component to further facilitate comparisons to observations and simulations.

We also show the same six snapshots using a full test-particle calculation in Figure \ref{f:dens100_20kpc_nbody}.  Note the similarity of Figure \ref{f:dens100_20kpc} and \ref{f:dens100_20kpc_nbody}, which increases our confidence in our method of solution.  Comparing Figure \ref{f:Em100_20kpc} and \ref{f:dens100_20kpc} side by side, it is clear that the modal energies are already significant as the perturber crossed $\ensuremath{r_{\rm peri}}$, while the density perturbations occur later.  As discussed above, this is because the modal energies is initially concentrated in the perturbed velocities and the densities response only arises after $\sim$ dynamical time.

The abrupt increase in the modal energies at $r=\ensuremath{r_{\rm peri}}$, which was previously identified by looking at modal energies, is also seen in the density response.  The density response like the modal energies remains small in the regions $r\lesssim \ensuremath{r_{\rm peri}}$, but increase rapidly for $r\gtrsim \ensuremath{r_{\rm peri}}$.  What is also interesting is that the identification of $\ensuremath{r_{\rm peri}}$ from the density response in Figure \ref{f:dens100_20kpc} and \ref{f:dens100_20kpc_nbody} seems to be clearer than the modal energy response plotted in Figure \ref{f:Em100_20kpc}.  In addition, the density response appears to be much more localized than the modal energy response (Fig. \ref{f:Em100_20kpc}). Namely, it is strong between \ensuremath{r_{\rm peri}}\ and $\ensuremath{r_{\rm peri}} + 10$ kpc, whereas the modal energy response is strong all the way out to the end of the disc.

To help illiustrate the effect of this density response, we define a synthetic measure of the power of these modes as:
\begin{equation}\label{eq:atot}
a_{\rm tot}(r) =  \sqrt{\sum_{m=0}^{4} \frac {|a_m(r)|^2} 5},
\end{equation}
and plot this in Figures \ref{f:dens100_20kpc} and \ref{f:dens100_20kpc_nbody}.

We now use this synthetic measure (eq.[\ref{eq:atot}]) to show that this localized response around $\ensuremath{r_{\rm peri}}$ continues to hold as we vary the orbit with different inclinations and different angles.   In Figure \ref{f:dens100_inclination}, we show the effects of different inclination on the Fourier power of the resulting density structure, while holding angle fixed.  Comparing Figure \ref{f:dens100_inclination} with \ref{f:Em100_inclination}, we find that again that the rapid increase in the $m=0$ power is a good discriminant for $\ensuremath{r_{\rm peri}}$.  The $m\neq 0$ modes also show good discriminating power though not as the $m=0$ mode.  However, what is really encouraging is that, while the $m=1$ mode varies signficantly with inclination in Figure \ref{f:Em100_inclination}, its effect on the density response is much milder.  From looking at these plots, it is clear that the $m=0$ modes has the most discriminating power, but $a_{\rm tot}$ appears to be adequate for determining \ensuremath{r_{\rm peri}}.

\begin{figure*}
\begin{center}
\subfigure[]{
\includegraphics[width=.27\textwidth]{dens100_20kpc/0.eps}}
\subfigure[]{
\includegraphics[width=.27\textwidth]{dens100_20kpc/1.eps}}
\subfigure[]{
\includegraphics[width=.27\textwidth]{dens100_20kpc/2.eps}}
\subfigure[]{
\includegraphics[width=.27\textwidth]{dens100_20kpc/3.eps}}
\subfigure[]{
\includegraphics[width=.27\textwidth]{dens100_20kpc/4.eps}}
\subfigure[]{
\includegraphics[width=.27\textwidth]{dens100_20kpc/5.eps}}
\end{center}
\caption{Fourier amplitudes of the density response of a disc suffering a 1:100 perturber encounter with $r_{\rm peri} = 20$ kpc. The perturber has a coplanar orbit ($i = 90$).  This corresponds to the modal energy calculation of Figure \ref{f:Em100_20kpc}, where we showed that the encounter generates a kink in the modal energy at $r=\ensuremath{r_{\rm peri}}$.  Here we see that the result of this modal energy kink is reflected in the density response of the disc in (d), (e), and (f).  Namely, the density response is peaked at $r\approx \ensuremath{r_{\rm peri}}$.  The response of $m=1-4$ is compared to the
$m=0$ mode.  For the $m=0$ line shown, we have only included the perturbation and compared it to the initial uniform background. }
\label{f:dens100_20kpc}
\end{figure*}

\begin{figure*}
\begin{center}
\subfigure[]{
\includegraphics[width=.27\textwidth]{dens100_20kpc_nbody/0.eps}}
\subfigure[]{
\includegraphics[width=.27\textwidth]{dens100_20kpc_nbody/1.eps}}
\subfigure[]{
\includegraphics[width=.27\textwidth]{dens100_20kpc_nbody/2.eps}}
\subfigure[]{
\includegraphics[width=.27\textwidth]{dens100_20kpc_nbody/3.eps}}
\subfigure[]{
\includegraphics[width=.27\textwidth]{dens100_20kpc_nbody/4.eps}}
\subfigure[]{
\includegraphics[width=.27\textwidth]{dens100_20kpc_nbody/5.eps}}
\end{center}
\caption{Same as Figure \ref{f:dens100_20kpc} but using the test particle
calculation.}
\label{f:dens100_20kpc_nbody}
\end{figure*}

\begin{figure*}
\begin{center}
\subfigure[]{
\includegraphics[width=.23\textwidth]{dens100_inc/90deg.eps}}
\subfigure[]{
\includegraphics[width=.23\textwidth]{dens100_inc/60deg.eps}}
\subfigure[]{
\includegraphics[width=.23\textwidth]{dens100_inc/30deg.eps}}
\subfigure[]{
\includegraphics[width=.23\textwidth]{dens100_inc/0deg.eps}}
\subfigure[]{
\includegraphics[width=.23\textwidth]{dens100_inc/m30deg.eps}}
\subfigure[]{
\includegraphics[width=.23\textwidth]{dens100_inc/m60deg.eps}}
\subfigure[]{
\includegraphics[width=.23\textwidth]{dens100_inc/m90deg.eps}}
\end{center}
\caption{ Snapshots of 1:100 perturber $r_{\rm peri} = 20$ kpc for different
inclinations. For each inclination, we have taken the same snapshot, which
corresponds to (f) of Figure \ref{f:dens100_20kpc}. The density response peaks around $r = r_{\rm peri}$ in each of these
snapshots, in line with the expectations from our energy analysis.}
\label{f:dens100_inclination}
\end{figure*}

\section{Scaling Relations: Inferring Satellite Mass from Fourier Amplitudes}\label{sec:scaling}

Our discussion in \S~\ref{sec:influence} shows while the overall dynamical response of the disc depends on the orbital parameters, i.e., $\ensuremath{r_{\rm peri}}$, inclination and angle, the density response of the disc is generally localized around $\ensuremath{r_{\rm peri}}$ and \ensuremath{r_{\rm peri}}\ + 10 kpc.  This localized response, especially for the $m=0$ mode allows us to constrain \ensuremath{r_{\rm peri}}\ of the orbit.  We now discuss the effect of the subhalo's mass on the disc response with an aim toward developing scaling relations between the response and the perturber's mass.

We begin by defining an appropriate global measure of the response of the disc in the much the same spirit as our earlier definition of $a_{\rm tot}$ (eq.[\ref{eq:atot}]).  As we have seen already that the disc response is localized, we define the effective amplitude of the disc as
\begin{equation} \label{eq:effective amplitude}
a_{\rm m, eff} = (\Delta r)^{-1}\int_{\ensuremath{r_{\rm peri}}}^{\ensuremath{r_{\rm peri}}+\Delta r} |a_m(r)| dr,
\end{equation}
where $\Delta r = 10$ kpc, motivated by the results of the previous section.  We then define the total effective amplitude as
\begin{equation}
a_{\rm t, eff} = \sqrt{\frac 1 4 \sum_{m=1}^4 |a_{\rm m,eff}}|^2.
 \end{equation}
A major advantage of defining such global quantities is that like the modal energies, their overall amplitudes settles into a relatively constant range after the initial excitation, in the absence of dissipation.  We show this in Figure \ref{f:atot}, for DM perturbers with mass ratios of 1:10, 1:100, and 1:1000.  Note that $a_{\rm t,eff}$ settles into a constant range that depends on the mass ratio $\approx 1$ Gyr after their interaction,  which is roughly one rotation period of the outer disc.

\begin{figure}
  \includegraphics[width=0.45\textwidth]{atot.eps}
  \caption{Plot of the synthetic Fourier amplitude of the density response as a function of time.  Note that after the initial interaction, the amplitude stay relatively constant in the absence of gaseous dissipation.  Whereas this is expected for the modal energies, it is surprising that this is preserved in the density response as well.  It points out that the synthetic amplitude is a good proxy for measuring the global properties of the response in a robust manner.}
\label{f:atot}
\end{figure}

Motivated by this result, we average $a_{\rm t,eff}$ after $\sim$ one rotation period for different inclinations and angles in Figure \ref{f:atot_inc}.  The error bars define the variation in $a_{\rm t,eff}$ for different angles.  The bands represent the variation of $a_{\rm t,eff}$ for each mass ratio as we vary the inclination angle from 90 to -90.  The variation in the inclinations is  $\approx 2$.  However, the average amplitude over which $a_{\rm t,eff}$ varies depends strongly
on the mass ratio of the satellite.  We show this mass ratio dependence more clearly in Figure \ref{f:atot_mass} where we collate the results of Figure \ref{f:atot_inc} and plot the overall disc response as a function of $m_{\rm s}$.  The error bars represent the variation over inclination and angle (same as the banded structures in Fig \ref{f:atot_inc}). In addition we plot the following fitting formula (dotted line)
\begin{equation}\label{eq:fit}
 a_{\rm t,eff} = 0.5 \sqrt{\frac {m_s} M}.
\end{equation}
Equation (\ref{eq:fit}) provides a reasonable fit to the numerical results as shown by the dashed line in Figure \ref{f:atot_mass}.  It suggests that the energy of the modes, $E \propto a^2 \propto M_{\rm s}$.  This is different from the expectations of the impulse approximation which instead suggest that the $E \propto M_{\rm s}^2$ \citep{White00}.  The fact our results differ from the impulse approximation means that the impulse approximation is not a good approximation for the interaction of subhaloes with extended HI discs, a point already discussed by CB09, CB10, and CBCB.

\begin{figure}
  \includegraphics[width=0.5\textwidth]{atot_inc.eps}
  \caption{Late time amplitude as a function of the inclination for 1:10 (top set of points), 1:100 (middle set of points), and 1:1000 (bottom set of points).  The error bar represent the 1-$\sigma$ spread in the synthetic amplitude as the angle is varied and the banded regions represents the 1-$\sigma$ spread in the range of synthetic amplitude as inclination is varied.}
\label{f:atot_inc}
\end{figure}

\begin{figure}
  \includegraphics[width=0.5\textwidth]{atot_mass.eps}
  \caption{The central and the ranges of $a_{\rm t,eff}$ as a function of mass ratio, varying from 1:1000 (left point) to 1:10 (right points).  The x's show the results from the full SPH simulations described in \S \ref{sec:sph}. The dotted line shows a relation that scales like $m_s^{1/2}$.  }
\label{f:atot_mass}
\end{figure}

\section{Comparison to SPH Simulations}\label{sec:sph}

To confirm our analysis, we compare our results from the modal analysis above to full-scale numerical galactic simulations.  We use the smooth particle hydrodynamic code, Gadget-2 \citep{Springel05} using the methodology presented in CB09.    GADGET-2 uses an N-body method to follow the evolution of the collionsionless components, and SPH to follow the gaseous component.  The simulations of disc galaxies tidally interacting with dark matter mini-halos reported here (unless otherwise noted) have gravitational softening lengths of $100~\rm pc$ for the gas and stars,
and $200~\rm pc$ for the halo.  The number of gas, stellar, and halo particles in the primary galaxy are $4 \times 10^{5}$, $4 \times 10^{5}$ and $1.2 \times 10^{6}$ respectively for our fiducial case. We refer the interested reader to CB09 for additional details on the simulation methodology.

We focus here on a few representative cases that span a reasonable range in parameter space. We list in Table 1 the parameters for the simulations that we use for this comparison. They vary in mass ratio between 1:10 and 1:300 and have coplanar and polar inclinations.

As an example, Figure \ref{f:SPH-1:100} shows the density response for a few time snapshots of the interaction for the 1:100 coplanar example.  The general response of the disc in the full simulation is visually similar our modal calculations of Figure \ref{fig:nbody_vs_analytic} especially that of $t = 0.650$ Gyrs.  This is somewhat unsurprising as the dominant physics in both calculation is the gravity of the primary halo and the subhalo.  However, it does highlight that much of the physics that has been ignored in the simplified calculation, i.e., a live dark matter halo, tidal stripping of the subhalo, gas dissipation, star formation, and self-gravity,
does lead to some difference in the appearance of the disturbances in the HI disc.
A main physical effect that has not been taken into account in these calculations is gas dissipation.  Neglecting this effect allows for simplicity of calculation as the modal energy (and the Fourier amplitudes once generated) are constant in the absence of dissipation.  In the presence of gas dissipation, the Fourier amplitudes decrease as a function of time as disturbances in the gas disc damp out on the order of a dynamical time.  We do not model this effect here, which would be needed to identify the current location of a satellite from observed disturbances in the HI disc as done earlier in the SPH calculations by CBCB.

\begin{figure*}
  \includegraphics[width=0.9\textwidth]{100R33Snap26.ps}
  \caption{{The time evolution of the gaseous density images of a Milky Way like galaxy interacting with a 1:100 dark sub-halo with a pericentric approach distance of 33 kpc. The units of time, marked in the figure, are in Gyr.  The box extends from -60 kpc to 60 kpc. }}
\label{f:SPH-1:100}
\end{figure*}

Motivated by the visual agreement of the SPH and modal calculation, we focus on comparing $a_{\rm t,eff}$ for the SPH simulation and the modal calculation.  Here the agreement is striking.  In the final column of Table 1, we list the $a_{\rm t,eff}$ for the various SPH simulations that we have performed.  We also $a_{\rm t,eff}$ for the SPH simulations as x's in Figure \ref{f:atot_inc} and \ref{f:atot_mass}.  The SPH simulation and the modal calculation show striking agreement especially for the 1:100 case.  We have also computed the 1:300 case and it too shows excellent agreement between the modal calculation and the SPH calculation.  The 1:10 case show some mild disagreement between the SPH simulation and the simplified modal calculation.  This is not unexpected as linear theory should start to break down for
sufficiently massive satellites (mass ratios $\gtrsim$ 1:10).  The overlaid points from the SPH simulation in Figure \ref{f:atot_mass} gives additional support to the $a_{\rm t,eff} \propto m_s^{1/2}$ scaling that we initially found from the modal calculation.

\begin{table}
\label{table:sim}
 \centering
 \begin{minipage}{90mm}
  \caption{Parameters of SPH simulations and $a_{\rm e,tot}$}
  \begin{tabular}{rrrrrrrr}
  \hline
   mass ratio &  $\ensuremath{r_{\rm peri}}$ [kpc] & orientation & $a_{\rm e,tot}$\\
  \hline
      1:10    &   30  & coplanar & 0.22\\
                   &         & polar       & 0.11\\
      1:100   &   32  & coplanar & 0.061\\
                   &          & polar        &   0.055 \\
      1:300   &   34  & coplanar & 0.039\\
                   &          & polar        &  0.036    \\
\hline
\end{tabular}
\end{minipage}
\end{table}

\section{Conclusion and Discussion}\label{sec:conclusions}

Subhalo interactions with the HI discs of galaxies should leave measurable effects on the gas long after the subhalo has passed by as demonstrated by CB09, CB10, and CBCB.  In this paper, we look carefully at the dynamics of these interactions in the context of a simplified epicyclic approximation.

$\bullet$ By performing a modal analysis on the equations of motion, we show that we can reproduce the orbital dynamics
and distribution of particles of a test-particle calculation for identical conditions.  While this may not seem surprising given the mass range of the perturbers that we are interested in ($\lesssim 0.1$), we show that performing such an analysis, we can understand crucial aspects of the nature of such interations.  In particular, we show that the modal energy shows sharp variations at $\sim r_{\rm peri}$.

$\bullet$
By developing a sense of what to look for from the modal analysis, we then showed that such variations also show up in the Fourier modes of the $\it{perturbed~density}$.  Namely, we find sudden increases in the Fourier modes of the density response at $\sim r_{\rm peri}$.  Such sharp variations at large radii are a distinct signature of tidal interaction and would argue against a secular origin.

$\bullet$ We also showed that this simplified analysis agrees with test particle calculations as well as more extensive SPH simulations.  This demonstrates that the physics ignored in the simplified approach (a live dark matter halo, tidal stripping of the subhalo, gas dissipation effects, self gravity and star formation, and dynamical friction) do not significantly alter the
production of the
disturbances in the HI discs.

$\bullet$ One of our main results here that can be readily employed by observers is that the effective Fourier amplitdues of the resultant surface density scales as the square root of the mass of the satellite, i.e., $a_{\rm t,eff} \propto m_{\rm s}^{1/2}$.  This suggests that the energy of the modes is $\propto m_{\rm s}$.  This scaling relation can be used to analyze observed HI maps and detemine the mass of the perturbing satellite without having to take recourse to full numerical simulation.

In future work, we will apply these scaling relations to analyze results from cosmological simulations to determine how the dark sub-halos will impact the disc.  To do this, we will generalize our method to incorporate multiple perturbers.
The effect of multiple perturbers is not yet known, but it may be the case that multiple perturbers do not significantly alter our results.  Namely, if the timescale between encounters is significantly longer than a dynamical time, the disturbances in the gas disc from the first encounter will be damped out.   This $\it{short-term~memory}$ of the gaseous component allows us to more cleanly disentangle the effect of the last perturber from the ones that impacted the disc previously.  Simulations predict impacts with $\sim 1:100$ mass ratio perturbers occur only once every $\sim \rm Gyr$ \citep{Kazantzidis+08}, which bodes well for this possibility.

\section*{Acknowledgments}
We thank Leo Blitz and Eric Gawiser for helpful discussions.  P.C. is supported by the Canadian Institute for Theoretical Astrophysics.

\bibliographystyle{mn2e}

redpajama_set_name: RedPajamaArXiv


What if you could burst your own filter bubble by seeking out fake news? There's an app for that!
During the Hackathon we created an app called Quicknews. The program provides a swift view of current news articles from other websites. Users can swipe through article summaries and choose to read the ones they deem interesting. By swiping either left or right, users can indicate which news they prefer and thus personalize their feed. This filter is transparent and can always be adjusted by the consumer.
Nowadays it's important for people to be able to review whether the information they read is trustworthy. Therefore, we have integrated a trust meter at the top of every article based on the reputability of the news source. Users can also report an article as "fake" if the story doesn't appear realistic to them after having read the entire article. If a significant number of readers reports the article as fake, it will be marked as such and the publisher of the article will be notified.
We integrated a quiz function that lets users guess whether an article is true or fake. Users can challenge their friends to do the same. We're hoping that this fun feature will push readers to new topics and get out of their bubble.
We challenged ourselves to empower news consumers without creating echo chambers. Surely there must be a way to offer casual news readers the news they're interested in, without the result being that they end up reading only information they already agree with? We thought it through: there is a solution!
Quicknews provides readers with an easy way to breeze through the news and allows them to look at stories critically by taking quizzes on their veracity, thus challenging the views they hold!
Our coding crew developed the App in React Native, allowing for both an Android and iOS version of the app. The mockup articles were created in Adobe Illustrator.


It's also important to remember that the average person can't easily afford $8,000 out of pocket for a medical procedure. The option for Paul to travel to Canada to buy "world-renowned" treatment isn't practical for many of the people he represents in Congress.
That's also a part of the discussion, even if his press secretary wants others to believe there is nothing to this story.
The other part of their argument was that going to a government managed system would eliminate any rights we have to seek specific, personalized or non-approved procedures.
Clearly that's all a lie.
I still want to know what a thurday is.
He longs for the days of his childhood pet hound, Onthur.
Slaves didn't have a choice in the matter, as they were the equivlent of livestock, and would be forced to consume enough food to perform their required tasks.
Paul isn't paying, he is using the government to force his neighbor to pay.
He also used a practice outside of the country that has greatly benefited from universal health care, the very thing that he rails against. That is the very definition of hypocrisy.
Good for them. Has literally zero to do with whether or not he acted in a hypocritical fashion. Which he did.
The assault was over a longstanding disagreement, not politically motivated.
His democrat neighbor owes him the money. His neighbor is the one that initiated the force, so he is owed. He has to use the government to recoup the money from his violent demoncrat neighbor because that is the law.
It's not hypocritical at all. Healthcare would be better and cheaper in a free market. It's not hypocritical to use a doctor that is overpriced due to socialism.
Healthcare would be better and cheaper in a free market. It's not hypocritical to use a doctor that is overpriced due to socialism.
yes.... that's a common complaint up here. Doctors are overpriced because socialism.
Make sure not to pay for a service that you want. That would be hypocritical to your socialist share the wealth views.
I'll start by mentioning once again this will be yet another conversation you are trying to start with me while having abandoned our past ones. Climate Change and our discussion on China being the most recent examples.
And while based on past interactions I have serious doubts on the sincerity of this point, I'll go ahead and bite anyways because this incidentally is a good way to illustrate the underlying reasoning for what I said.
So lets start with a simple thought experiment by comparing two types of surgeries so maybe you catch on as well, your example, Lasik, and lets just pick stopping internal bleeding after a car crash.
What are some notable differences in the decision-making process for these two services?
The obvious one is duress. It's hard to make informed decisions under duress. Another obvious differing factor is level of knowledge, you or I are not doctors, and even if we were we would not have the tools to make an informed decision about what needs to be done to repair our bodies after a car wreck. A third differing factor is agency. If I am being escorted from the scene of an accident I am not in a place to make a value judgement about price, doctor rating, or hospital preference, in fact, that option isn't even an option if you are escorted in an ambulance.
Long story longer, the presumption in economics when it comes to decision-making is that they will follow the rational decision-making model. I.E. decisions are made with symmetrical information(both the buyer and seller are relatively equally informed and knowledgeable about the product/service they are selling/buying), the person is of sound, stable mind(not being coerced, in a panic etc.), and that the good or service and the buyer will have the time and capacity to follow an ordered, rational,decision-making process that works through and analyzes the pro's and con's of alternatives against one another. There is also the presumption that the goods and services you are deciding on are relatively elastic and non-critical.
All of those things are things that are often not capable of being fully satisfied in a lot of healthcare. Which leads to market failures. Is that shortness of breath a temporary issue or a sign of something much deeper? Is this particular pill the only thing that can keep you alive? Are there even any other qualified specialty doctors within 100 miles? I am concussed and bleeding in the back of an ambulance, what to do?
But this isn't one size fits all, there are plenty of places in the healthcare space where normal market forces can reasonably operate. Which is pretty much in areas of elective and cosmetic products and services. But these distinctions are often things I find libertarians and people like yourself look over and you just can't if you want to make an informed decision or opinion about healthcare economics. Because it is a bad assumption borne out by the results that the market for a life changing drug or decisions made under duress and/or poor information is going to end up operating efficiently and effectively like a normal market for something like Lasik or tennis shoes. Which is why no system has managed to work without a lot of subsidization, regulation, and intervention.
Markets almost always require a rational-decision making process to function properly and much of the healthcare space lacks that. Lasik and other cosmetic surgeries are the exception to that.
I suppose I could possibly see some rationality in your theory if all healthcare decisions that's aren't cosmetic were made under extreme duress, but they're not.
And some are under duress for cosmetic surgeries too. So yeh I disagree.
Never share anything with anyone ever. That would make the frogs turn gay.
Wow. You really have no understanding at all of what is happening here, do you?
Try again Onthurday, this is exactly what I was prefacing about you NEVER engaging in these threads with respect or hoensty.
It is not simply duress that leads to these identifiable failures in many parts of this market space. Duress is but one issue that perverts the normal mechanisms that high functioning markets are hinged on. And none of that even got to the issues on the supply side that perverts the situation. Where you have issues of monopoly control of inelastic products and inadequate competitors and pricing mechanisms along with perverse market incentives in places like the employer market and amongst insurers.
You really have trouble articulating your arguments.
Why do you think healthcare has become so expensive since the 1960s.
It wasn't always this way, what changed then.
Lol. Like for example, when people deliver babies back then, you call some lady who's done it b4 and hope it goes well. Today, you do a bunch of screening, counseling to avoid stuff that can harm your babies, etc, to ensure the best possible outcome.
You're really asking about medical advancement?
is there something less than none?


text:
namespace tcmalloc {
namespace tcmalloc_internal {

// CentralFreeList implementation that uses a real central freelist to allocate
// objects. It implements additional methods used by benchmarks and tests.
//
// This is useful for benchmarking in cases where, for instance, we can test the
// efficiency of TCMalloc's frontend as it has to access real central freelist
// upon a miss.
class RealCentralFreeListForTesting : public CentralFreeList {
 public:
  void AllocateBatch(void** batch, int n);
  void FreeBatch(absl::Span<void*> batch);
};

class FakeCentralFreeListBase {
 public:
  FakeCentralFreeListBase() {}
  FakeCentralFreeListBase(const FakeCentralFreeListBase&) = delete;
  FakeCentralFreeListBase& operator=(const FakeCentralFreeListBase&) = delete;

  static constexpr void Init(size_t) {}
};

// CentralFreeList implementation that backs onto the system's malloc.
//
// Useful for unit tests and fuzz tests where identifying leaks and correctness
// is important.
class FakeCentralFreeList : public FakeCentralFreeListBase {
 public:
  void InsertRange(absl::Span<void*> batch);
  int RemoveRange(void** batch, int N);

  void AllocateBatch(void** batch, int n);
  void FreeBatch(absl::Span<void*> batch);
};

// CentralFreeList implementation that does minimal work but no correctness
// checking.
//
// Useful for benchmarks where you want to avoid unrelated expensive operations.
class MinimalFakeCentralFreeList : public FakeCentralFreeListBase {
 public:
  void InsertRange(absl::Span<void*> batch);
  int RemoveRange(void** batch, int N);

  void AllocateBatch(void** batch, int n);
  void FreeBatch(absl::Span<void*> batch);

 private:
  absl::base_internal::SpinLock lock_;
};

// CentralFreeList implementation that allows intercepting specific calls.  By
// default backs onto the system's malloc.
//
// Useful for intrusive unit tests that want to verify internal behavior.
class RawMockCentralFreeList : public FakeCentralFreeList {
 public:
  RawMockCentralFreeList() : FakeCentralFreeList() {
    ON_CALL(*this, InsertRange).WillByDefault([this](absl::Span<void*> batch) {
      return static_cast<FakeCentralFreeList*>(this)->InsertRange(batch);
    });
    ON_CALL(*this, RemoveRange).WillByDefault([this](void** batch, int n) {
      return static_cast<FakeCentralFreeList*>(this)->RemoveRange(batch, n);
    });
  }

  MOCK_METHOD(void, InsertRange, (absl::Span<void*> batch));
  MOCK_METHOD(int, RemoveRange, (void** batch, int N));
};

using MockCentralFreeList = testing::NiceMock<RawMockCentralFreeList>;

}  // namespace tcmalloc_internal
}  // namespace tcmalloc

#endif  // TCMALLOC_MOCK_CENTRAL_FREELIST_H_

redpajama_set_name: RedPajamaGithub


Are you interested in the UniCarriers EPM or EPH? Take a look at the brochure to find out more.
UniCarriers is very pleased to announce that it has been nominated for two awards in the prestigious International Forklift Truck of the Year (IFOY) competition. Our high-lifting EPH 125 order picker is nominated in the Warehouse Truck of the Year category, while the innovative Driver Presence Sensor (DPS) feature is nominated in the Special of the Year category. The nominated trucks and features will be examined rigourously during test days in March 2017, and the best in each category will be decided by a jury of 25 respected trade journalists, from 16 countries. The winners will be revealed at Munich's Transport Logistic trade fair in May - we're hoping to see you there!
Order picking is an intensive process, which can put strain on the truck operator. With their ergonomic designs, the EPM and EPH make picking easier for operators, leading to higher productivity in the warehouse. High visibility around the truck, especially through the ProVision mast, enhances safety and means the operator doesn't have to strain themselves to get a good view. The trucks' essential controls can be moved up and down, and backwards and forwards, so each operator can be comfortable, and a low step in height makes it easier when the operator is frequently entering and exiting the truck. A floor sensor which covers the whole cabin floor, rather than a 'dead man' foot switch, gives the operator free movement around the cabin during operation.