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Separate names with a comma.
Discussion in 'General Discussion' started by colton, Jul 16, 2019.
Oh no, better impeach...
Hi guys! What are going to pretend to be newly offended about or surprised about today?
I can put a spin on stuff one way or another. Most of the time in here I'm trying to de-spin stuff others are pretty committed to.
Watch, when Dems win back the White House in 2020, Republican fiscal hawks will fly out of their closets and claim that we can't enact promised legislation and need to make cuts to entitlements because of the debt.
It's always the same playbook. Label every democrat a criminal and a socialist. And then when you lose, pretend to care about the debt. Rinse, wash, repeat.
I'm old enough to remember when republicans claimed they were the law and order party and that Barr would bring establishment stability to this administration.
But thank god Hillary didn't win. Otherwise, we'd have a corrupt White House.
Glad to see you realize that about Hillary. wink
Yeah, the attorney general might have been able to book the Intercontinental Hotel for $25,000. Who knows... maybe he got the Trump hotel to include catering. If that's what you're calling government corruption though, your petty meter probably needs new batteries.
This is the most bogus thing you've said this weekend so far.
Besides, Hillary was a criminal. Bernie Sanders, Elizabeth Warren and AOC are the ones proposing to socialize as much as one-third of the U.S. economy. You're mixing topics.
Also, which Dem do you think is going to win the White House? Are you surprised that Republicans are not participating in DNC-sanctioned polls for the Democratic primary?
Exaggerate much? You think he's Nero of Rome?
So is Fox News bogus too? Or just Donald's personal lawyer?
Major cities have no shortage of hotels. Barr using Trump Hotel like this is a deliberate and obvious case of corruption. Stop being such a partisan dip ****. There's no way you'd have this same attitude if it was Clinton's AG pandering to her by using hotels that she owns and benefits personally from.
It's amazing how deep you trumpers are willing to dig yourselves in order to defend this guy.
I really don't care where Barr throws a holiday party. He could have it at the White House for all I care. I don't care where the Clintons hold parties either.
It's amazing the lengths that liberals are willing to go to in order to contrive their daily outrage. You need to pick your battles. This isn't one of them.
That's a problem. Why? Corruption.
Why should Barr hold his Christmas party at the White House? How is this ok for anyone? Trump is the president and Barr is the AG. I guess after bashing government for so long, you Trumpers have forgotten The idea of having a professional government. People with specific roles and maintaining professional relationships. Barr shouldn't be pandering to trump or using trump properties. Trump shouldn't be benefiting financially from those employed in his executive branch.
Oh please. No one here believes this, not even you. We all know what you'd be saying if Hillary's AG was doing this very same thing in Clinton held properties.
It's amazing the amount of corruption you trumpers are willing to rationalize away. In a few years we all know you'll claim that you really didn't support trump or his corruption. So I appreciate this written record.
In the grand scheme of things it's not the most important thing, but it's obviously not a good look.
Our president shouldn't have business interests while governing (Carter sold his peanut farm before becoming president FFS), this kind of thing is exactly why.
We should be able to have trust that our attorney general is acting in a responsible independent manner, and the optics of this make that difficult.
Of course, I wouldn't expect a Trump supporter to see it that way. Trump's corruption has been evident from the jump, and you are all way too invested at this point for anything to change your minds.
I disagree. The AG is one of the most important jobs in the executive office. How can anyone have trust in the Judicial Office and his investigations when the AG is enriching his boss.
I'm old enough to remember when republicans claimed to at least care about "law and order."
This not only demonstrates how corrupt Barr and Trump are. But it shreds any credibility of the office that Barr now leads. If anyone connected to the Russia investigation were to be indicted (like a Comey) how could anyone not question its integrity and not see it as a mere attack on a political opponent?
Drain the swamp? More like flood the swamp.
I do agree on why trumpers like @Catchall have to defend this. They're in it so deep now there's no turning back.
I thinks we actually do agree. My point about it not being the most important thing is that there are plenty of instances worse than this to point to regarding Trump's corruption.
I think it's worth pointing out and discussing though, it's not like I'd trust a Trump supporter is arguing in good faith when he says it's not a battle worth fighting.
It would be one of the top reasons to impeach imo. If I were Pelosi this would be the overarching theme. He's too damn corrupt to allow to remain in office.
Personally, I find violations of the Constitution to be worthy of outrage. And I'm not a liberal.
I meant, this would not affect anyone who got US citizenship at birth. This would affect people who are being naturalized.
That's mentioned early in the document, but the changes don't seem to be about that issue specifically.


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Coroner's office responds to quarry rescue attempt
A sign seen Aug. 17, 2015, prohibits trespassing at the Eastern Industries Martins Creek Quarry off Route 611 in Lower Mount Bethel Township, where authorities were responding to a water rescue call that turned into a body recovery. (Kurt Bresswein | For lehighvalleylive.com)
The second death this year of a New Jersey man at an abandoned quarry in Lower Mount Bethel Township did not deter thrill-seekers from continuing to cross into Pennsylvania to cool off.
Pennsylvania State Police reported citing four more people, including three confirmed as New Jersey residents, on Tuesday for trespassing at the Eastern Industries Martins Creek Quarry off Route 611 in the township.
That's the same quarry where 19-year-old Jonathan M. Baksh, of Edison, New Jersey, died Monday afternoon. That was after Jeremias Guzman, 22, of Ridgefield, New Jersey, died there in June. The bodies of both men were recovered by divers after being submerged beneath the surface of the quarry's water.
State police at Belfast said they cited about 3:55 p.m. Tuesday at the Eastern Industries quarry Nicholas Barroqueiro, 18, and Stephen Scott, 19, both of Westfield, New Jersey; Robert Caravaggio, 19, of Ledgewood, New Jersey; and a juvenile whom they did not identify.
RELATED: Man injured in Bangor quarry dive to be charged, police say
On Monday prior to Baksh's death, state police said they cited three more teens from New Jersey -- one from Washington and two from Edison -- for trespassing at the Eastern Industries quarry, in addition to an unidentified juvenile.
The quarry is posted against trespass.
Kurt Bresswein may be reached at firstname.lastname@example.com. Follow him on Twitter @KurtBresswein. Find lehighvalleylive.com on Facebook.

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Edgar Stringer Wye Valley Workshop
Teachers Name: Edgar Stringar
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Cost £45
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Website: www.wildwoodyoga.co.uk
Location: Brockweir, Wye Valley, NP16 7NW, United Kingdom
Edgar will take us through an active morning session of asana followed into the afternoon by a more restorative asana and pranayama practice.
He will work us hard but in a gentle and focused way! Edgar has been teaching for over 20years and holds his Intermediate Senior Level 3 certificate. He is a teacher trainer, mentor and assessor for the IYUK. This will be an ideal opportunity to keep your practice going through the long summer break from regular classes.
The venue is nestled between Tintern and Monmouth in the Lower Wye Valley. It is ideally situated for those coming across the bridge (now toll free!) from Bristol, Bath and beyond or from the south toward Cardiff and Newport and a beautiful drive from Hereford, Hay and the Welsh borders. It is a truly picturesque area with plenty of walks, interesting places to visit, parks to play in and a good few watering holes for refreshments, why not get the family to drop you off for a yogaliscious day and let them go play!
I would like to invite all Iyengar practitioners to join us for an enriching day of yoga and lovely lunch where you will all be warmly welcomed by your host Kishe Redwood of Wildwood Yoga.


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favor these mainly quantitative and overt means of defining participation. large classes, including making the lecture hall feel small and thus personal*even if.
We have all had that class: You walk into lecture. at the end of the quarter limits the amount of change a given student can see in their own lecture hall. More regular, and shorter, evaluations.
FSU PC hosts 'Magnificent Math' PANAMA CITY — The public is encouraged to engage in fun, hands-on activities at Magnificent Math, from noon to 3:30 p.m. on Sunday, March 31, in the St. Joe Lecture.
Unless you're a fancy-pants, first-class jetsetter, flying sucks. You never know who you'll wind up sitting next to—and more.
By the end of this semester's inaugural class of "Horticulture of Cannabis. and that's the same thing as cannabis here." In the lecture hall Thursday, senior biology major Rowan Goss and sophomore.
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Please see Management Type Definitions for a full list of management types. including lecture halls, discussion rooms, seminar rooms, and TILE rooms.
A six-month renovation of lecture hall 10-250 was complete and ready for the. chair of the Faculty Classroom Committee, led the effort to define and direct the.
The crowd was so massive that the class had to be switched to a larger lecture hall. That's not just a reflection of Ivy. when we choose to chase the high school definition of popularity deep into.
There is no agreed definition of a large class in the literature, nor should there be. Space here could mean lecture room, laboratory or workshop space.
How about this instead: No lecture hall. abandoning the in-class lecture, but alas, colleges often take the easy way out and offer a version of high school, but with more football and binge.
A lecture hall Vanguard visits to some of the public institutions of higher learning in the country revealed a very low turn out of students on campus. Thus, while teachers are preparing for lectures,
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A broken pair of eyeglasses before a large lecture class, or appendicitis and a first encounter with. Students gather for.
Trent Cultural Studies Course Schedule Graduate Studies at the University of Kansas prepares students to be innovators and leaders, ready to meet the demands of the academy, industry, government, and our global society. The cultural. the middle-class areas of India, where aggressive public behavior toward women, such as cat-calling, leering. In their telling, Westernization and globalization have caused more harm
she sat in a lecture hall watching a BuzzFeed video about what it's like to be an intersex or a transgender person. "It was a good video, but it felt inadequate for the education of a class of medical.
Mark Holden, a 22-year-old history major, tells me he was ordered to leave a lecture hall after. the entire class, Martel vowed to "re-instate civility" in the classroom. "I want this to be clear:.
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Jul 9, 2015. Proper use and scheduling of classroom space is a shared. standards for Weekly Room Hours and Weekly Student Hours, special lectures, midterm examinations, optional quiz sections, and. The following terms are defined within the context of applicable UC and UC Merced policies and regulations.
The lecture is free and open to the public. A discussion will follow. The event is at 7 p.m. in Johnson Lecture Hall, located in Lee's Humanities. about local schools you'd like to be included in.
Oct 11, 2007. A. Standard Class Hours and Distribution of Classes. Space classified as a " classroom" is subject to the scheduling. room, or lecture hall. By definition, only official credit instruction hours and enrollments are included.
That being said, here are some other things to keep in mind while trying to fit in: • Say hi to people before they say hi to you — whether it's greeting your seat neighbor in a lecture hall or smiling.
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By the end of this semester's inaugural class of "Horticulture of Cannabis. and that's the same thing as cannabis here." In the lecture hall Thursday, senior biology major Rowan Goss and sophomore.
Immediately, the lecture hall was abuzz as 150 students started talking to each other. "That means focusing on what students actually do in the classroom, or in.
and the latest class slot was moved from 8:55 p.m. to 10 p.m. Kane said that despite minor additions to the classroom inventory including a new lecture hall in the former Chemistry library, the.
Even if students who feel that way should be able to avoid Paglia's classes, they should not try to impose their preferences.
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"Hi Chris," students in the lecture hall responded. This is how Chris Hart, lecturer in the College of Pharmacy, starts every session of his chemical dependency class, and it serves as a daily.
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If a researcher is interested in adding a new technology to the Portfolio, the following steps should be taken. First of all, the researcher must present the Invention Disclosure to the Innovation Department, which is an official Univertisty document in which the invention is thoroughly described.
This document is revised by the Intellectual Property Chief, who meets with the researcher to ensure the the form has the correct information. Once this is done, the TTO team analyzes, using defined criteria, the invention' technological and commercial potential.
Once the analysis is complete, a committee composed of members of the Innovation Department and the Faculty to which the researcher belongs, approves or endorses the result of the analysis.
If the invention has technological and commercial potential, it is incorporated in the Portfolio and becomes eligible to receive the services offered by the TTO.
Otherwise, it is considered an applied sciences project, only receiving services according the that status.


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I've just started up my second survival playthrough of FO4 after I ran into an unrecoverable mod bug on my last run. Did a clean install of FO4 and took the time to remove several mods that I wanted gone but Vortex wasn't removing (I think that was because I imported them from NMM originally). I love the beauty of this game but after several hours into this run I am realizing that you miss a lot of the world on a non-survival playthrough.
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And I find stuff like that all over the place, just off the beaten routes. In non-survival difficulties I tend to head straight from A to B if I have a specific destination in mind. I also explore most buildings. But there is a wealth of stuff out in the country side that is never seen when you don't wander off the beaten path.
Also, I have found a new appreciation for Mirelurk nests thanks to survival mode. So far Mirelurk Omelettes are one of the most efficient ways I have found to keep myself fed.
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Local Government Policy Manual
Statement: Local government recognises the valuable contribution it makes to the ongoing prosperity of South Australia through working closely with its communities, and shall continue to rigorously promote recognition and autonomy of councils through lobbying and advocating activities.
1.1.1 Constitutional Recognition
Local government deserves recognition in the Australian Constitution and legislation that entrenches its existence so that it can only be altered with a majority agreement of federal/state governments. Councils, through the LGA and ALGA shall continue to campaign for this recognition.
1.1.2 Direct Federal Funding
Local government emphasises that financial contributions from federal government are vital and that Constitutional recognition would remove the significant red tape currently surrounding these transactions. Until Constitutional recognition is achieved, local government will work with federal government to reduce red tape where practicable.
1.1.3 Federal/State Government Funding
Local government collects only 4% of national taxation and is not in a fiscal position to tackle all of the issues affecting local communities alone. Local government will continue to lobby federal/ state governments to provide fair and equitable resources and funding to tackle issues affecting local communities.
1.1.4 Autonomy
Local government requires the ability to swiftly respond to the needs of their communities and provide the services required without being unreasonably hindered by conditions and approvals imposed by state government. Local government will continue to lobby state government to maintain the autonomy of the sector.
1.1.5 Council Amalgamations
Amalgamations should only occur on a voluntary basis, where there is the support of council and their communities and strong supportive evidence. The LGA shall oppose any policy from state government or other entities that suggests the possibility of forced amalgamations.
1.1.6 Service Provisions
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This is a recording of a presentation by John Cardinal to the TMG Group in August 2017.
John has developed a program call GEDSITE, which compiles a customisable web site or writes HTML files on CD/DVD, using a GEDCOM file as the input data. Programs that can write a GEDCOM or use GEDCOM as their native file format will work with GEDSITE.
SAG members can listen to this recording by registering online and paying $12 - you will then receive a link to the recording which you can listen to as often as you wish until 30 June 2018.
Location: 2/379 Kent Street Sydney (more information here)
Presenter: Lorraine Brothers Bookings essential: $25 members only (special price)
Did you know that the SAG library has a lot of resources in electronic format? Find out how to access such things as parish registers, family histories, cemetery records, funeral directors' records, AGCI, journals, government gazettes, police gazettes and many more when you visit the SAG library at 2/379 Kent Street.
Limit 14.


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Tag: dinner
Dinner & A Movie: Halloween Edition
Join us for a spooky movie this Friday in Wasaga Beach!
Toronto All Star Big Band - FUNDRAISER/DINNER/DANCE
Join in the fun and dance and dine under stars at the Midland Golf and Country Club as Brookside Music celebrates the music of the golden era of the big bands. The Toronto All Star Big Band revives the spirit, style and sound of the 30's, 40's and 50's.
Dinner Cruise & Concert With Carmanah
On Thursday, August 15th, Chi-Cheemaun is putting on a Dinner Cruise and Concert with Carmanah.
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Summer Beer Dinner with Oliver & Bonacini
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Come out for dinner and enjoy great family fun movies beginning just before dusk.
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Accuracy guarantees for -recovery ††thanks: Research of the second author was supported by the Office of Naval Research grant # N000140811104 and the NSF grant DMS-0914785.
We discuss two new methods of recovery of sparse signals from noisy observation based on -minimization. While they are closely related to the well-known techniques such as Lasso and Dantzig Selector, these estimators come with efficiently verifiable guaranties of performance. By optimizing these bounds with respect to the method parameters we are able to construct the estimators which possess better statistical properties than the commonly used ones.
We link our performance estimations to the well known results of Compressive Sensing and justify our proposed approach with an oracle inequality which links the properties of the recovery algorithms and the best estimation performance when the signal support is known. We also show how the estimates can be computed using the Non-Euclidean Basis Pursuit algorithm.
Key words
: sparse recovery, linear estimation, oracle inequalities, nonparametric estimation by convex optimization
AMS Subject Classification
1 Introduction
Recently several methods of estimation and selection which refer to the -minimization received much attention in the statistical literature. For instance, Lasso estimator, which is the -penalized least-squares method is probably the most studied (a theoretical analysis of the Lasso estimator is provided in, e.g., [2, 3, 4, 19, 20, 21, 17, 18], see also the references cited therein). Another, closely related to the Lasso, statistical estimator is the Dantzig Selector [7, 2, 16, 17]. To be more precise, let us consider the estimation problem as follows. Assume that an observation
is available, where is an unknown signal and is a known sensing matrix. We suppose that is a Gaussian disturbance with (i.e., , where are independent normal r.v.'s with zero mean and unit variance), and is a known deterministic noise level. Our focus is on the recovery of unknown signal .
The Dantzig Selector estimator of the signal is defined as follows [7]:
where is the algorithm's parameter. Since is obtained as a solution of an linear program, it is very attractive by its low computational cost. Accuracy bounds for this estimator are readily available. For instance, a well known result about this estimator (cf. [7, Theorem 1.1]) is that if then
with probability if the signal is -sparse, i.e. has at most non-vanishing components, and the sensing matrix with unit columns possesses the Restricted Isometry Property with parameters and .
111Recall that , called also uniform uncertainty
principle, means that for any with at most nonzero entries,
with properly chosen penalty parameter .
The available accuracy bounds for Lasso and Dantzig Selector rely upon the Restricted Isometry Property or less restrictive assumptions about the sensing matrix, such as Restricted Eigenvalue [2] or Compatibility [3] conditions (a complete overview of those and several other assumptions
with description of how they relate to each other is provided in [19]). However, these assumptions cannot be verified efficiently.
The latter implies that there is currently no way to provide any guaranties (e.g., confidence sets) of the performance of the proposed procedures. A notable exception from this rule is the Mutual Incoherence assumption (see, e.g. [10, 11, 12] and [21] for the case of, respectively, deterministic and random observation noise) which can be used to compute the accuracy bounds for recovery algorithms: a matrix with columns of unit -norm and mutual incoherence possesses with .222
The mutual incoherence of a sensing matrix is computed according to
Recently the authors have proposed a new approach for efficient computing of upper and lower bounds on the "level of goodness" of a sensing matrix , i.e. the maximal such that the -recovery of all signals with no more than non-vanishing components is accurate in the case where the measurement noise vanishes (see [14]). In the present paper we aim to use the related verifiable sufficient conditions of "goodness" of a sensing matrix to provide efficiently computable bounds for the error of recovery procedures in the case when the observations are affected by random noise.
The main body of the paper is organized as follows:
We start with Section 2.1 where we formulate the sparse recovery problem and introduce our core assumption – a verifiable condition linking matrix and a contrast matrix . In Sections 2.2, 2.3 we present two recovery routines with contrast matrices:
regular recovery:
penalized recovery:
( is our guess for the number of nonzero entries in the true signal, is the penalty parameter)
along with their performance guarantees under condition with , that is, explicit upper bounds on the confidence levels of the recovery errors . The novelty here is that our bounds are of the form
(with hidden factors in independent of ), and are valid in the entire range of values of . Note that similar error bounds for Dantzig Selector and Lasso are only known for , whatever be the assumptions on "essentially nonsquare" matrix .
Our interest in condition stems from the fact that this condition, in contrast to the majority of the known sufficient conditions for the validity of -based sparse recovery (e.g., Restricted Isometry/Eigenvalue/Compatibility), is efficiently verifiable. Moreover, it turns out that one can efficiently optimize the error bounds of the associated with this verifiable condition regular/penalized recovery routines over the contrast matrix . The related issues are considered in Section 3. In Section 4 we provide some additional justification of the condition , in particular, by linking it with the Mutual Incoherence and Restricted Isometry properties. This, in particular, implies that the condition with, say, associated with randomly selected matrices is feasible, with probability approaching 1 as grow, for as large as . We also establish limits of performance of the condition, specifically, show that unless is nearly square, with can be feasible only when , meaning that the tractability of the condition has a heavy price: when designing and validating minimization based sparse recovery routines, this condition can be useful only in a severely restricted range of the sparsity parameter .
In Section 5 we show that the condition is the strongest (and seemingly the only verifiable one) in a natural family of conditions linking a sensing and a contrast matrix; here is the number of nonzeros in the sparse signal to be recovered . We demonstrate that when a contrast matrix satisfies with , the associated regular and penalized recoveries admit error bounds similar to (2), but now in the restricted range of values of . We demonstrate also that feasibility of with implies instructive (although slightly worse than those in (2)) error bounds for the Dantzig Selector and Lasso recovering routines.
In Section 6, we present numerical results on comparison of regular/penalized recovery with the Dantzig Selector and Lasso algorithms. The conclusion suggested by these preliminary numerical results is that when the former procedures are applicable (i.e., when the techniques of Section 3 allow to build a "not too large" contrast matrix satisfying the condition with, say, ), our procedures outperform significantly the Dantzig Selector and work exactly as well as the Lasso algorithm with "ideal" (unrealistic in actual applications) choice of the regularization parameter333With "theoretically optimal," rather than "ideal," choice of the regularization parameter in Lasso, this algorithm is essentially worse than our algorithms utilizing the contrast matrix..
In the concluding Section 7 we present a "Non-Euclidean Matching Pursuit algorithm" (similar to the one presented in [15]) with the same performance characteristics as those of regular/penalized recoveries; this algorithm, however, does not require optimization and can be considered as a computationally cheap alternative to recoveries, especially in the case when one needs to process a series of recovery problems with common sensing matrix.
All proofs are placed in the Appendix.
2 Accuracy bounds for -Recovery Routines
2.1 Problem statement
For a vector and we denote the vector obtained from by setting to all but the largest in magnitude entries of . Ties, if any, could be resolved arbitrarily; for the sake of definiteness assume that among entries of equal magnitudes, those with smaller indexes have priority (e.g., with one has ). stands for the usual -norm of (so that ). We say that a vector is -sparse if it has at most nonzero entries. Finally, for a set we denote by its complement ; given , we denote by the vector obtained from by zeroing the entries with indices outside of , so that .
Given a norm on and a matrix , we set .
The problem.
We consider an observation
where is an unknown signal and is the sensing matrix. We suppose that is a Gaussian disturbance, where (i.e., with independent normal random variables with zero mean and unit variance), being known, and is a nuisance parameter known to belong to a given uncertainty set which we will suppose to be convex, compact and symmetric w.r.t. the origin. Our goal is to recover from , provided that is "nearly -sparse." Specifically, we consider the sets
of signals which admit -sparse approximation of -accuracy . Given , , and a confidence level , , we quantify a recovery routine — a Borel function — by its worst-case, over , confidence interval, taken w.r.t. -norm of the error. Specifically, we define the risks of a recovery routine as
Equivalently: if and only if there exists a set of "good" realizations of with such that whenever , one has for all and all .
Norm .
Given and let us denote
Since is convex, closed and symmetric with respect to the origin, is a norm. Let be the norm on conjugate to :
Conditions and .
Let . Given , consider the following condition on a matrix :
: for all and one has
Now let be a positive integer and . Given , we say that a matrix satisfies condition 444The reason for this cumbersome, at the first glance, notation will become clear later, in Section 5., if
The conditions we have introduced are closely related to each other:
Lemma 1
If satisfies , then satisfies , and "nearly vice versa:" given satisfying , one can build efficiently a matrix satisfying with (i.e., ) and such that the columns of are convex combinations of the columns of and , so that for every norm on .
2.2 Regular Recovery
In this section we discuss the properties of the regular -recovery given by:
where is as in (3), , , are some vectors in and , . We refer to the matrix as to the contrast matrix underlying the recovering procedure.
The starting point of our developments is the following
Proposition 1
Given an sensing matrix , noise intensity , uncertainty set and a tolerance , let the matrix from (7) satisfy the condition for some , and let in (7) satisfy the relation
where is given by (4). Then there exists a set , , of "good" realizations of such that
(i) Whenever , for every , every and every subset such that
the regular -recovery given by (7) satisfies:
where and
(ii) In particular, when setting
and assuming , for every , and it holds
(iii) Finally, assuming , for every , and one has
The following result is an immediate corollary of Proposition 1:
Lemma 2
The next statement is similar to the cases of in Proposition 1 and Lemma 2; the difference is that now we assume that satisfies , which, by Lemma 1, is a weaker requirement on than to satisfy with .
Proposition 2
Given an sensing matrix , noise intensity , uncertainty set and a tolerance , let the matrix from (7) satisfy the condition for some , and let in (7) satisfy the relation (8). Then there exists a set , , of "good" realizations of such that whenever , for every and every one has
In particular,
2.3 Penalized Recovery
Now consider the penalized -recovery as follows:
where is as in (3), and an integer , a positive , and a matrix are parameters of the construction.
Proposition 3
Given an sensing matrix , an integer , a matrix and positive reals , , satisfying the condition , and a , assume that
Further, let , , and let
Consider the penalized recovery associated with . There exists a set , , of "good" realizations of such that
(i) Whenever , for every signal and every one has
where, as in Lemma 2, .
(ii) When and , one has for every , and :
whence for every and :
The next statement is in the same relation to Proposition 3 as Proposition 2 is to Proposition 1 and Lemma 2.
Proposition 4
Given an sensing matrix , noise intensity , uncertainty set and a tolerance , let the matrix from (17) satisfy the condition for some , and let . Then there exists a set , , of "good" realizations of such that whenever , for every and every one has
In particular,
Note that under the premise of Proposition 2, the smallest possible values of are the quantities , which results in ; with this choice of , the risk bound for the regular recovery, as given by the right hand side in (16), coincides within factor 2 with the risk bound for the penalized recovery with as given by (25); both bounds assume that satisfies with and imply that
When , the latter bound admits a quite transparent interpretation: everything is as if we were observing the sum of an unknown -dimensional signal and an observation error of the uniform norm .
3 Efficient construction of the contrast matrix
In what follows, we fix , the "environment parameters" and the "level of sparsity" of signals we intend to recover, and are interested in building the contrast matrix resulting in as small as possible error bound (26). All we need to this end is to answer the following question (where we should specify the norm as ):
(?) Let be a norm on , and be a positive integer. What is the domain of pairs such that and there exists matrix satisfying the condition and the relation ? How to find such an , provided it exists?
Invoking Lemma 1, we can reformulate this question as follows:
(??) Let and be as in (?). Given , how to find vectors , , satisfying
for every , or to detect correctly that no such collection of vectors exists?
Indeed, by Lemma 1, if satisfies and , then there exists such that satisfy for all and , so that satisfy for all as well. Vice versa, if satisfy , , then the matrix clearly satisfies , and .
The answer to (??) is given by the following
Lemma 3
Given , , and a positive integer , let . For every , the following three properties are equivalent to each other:
There exists satisfying ;
The optimal value in the optimization problem
where is -th standard basic orth in , is ;
One has
where is the norm on conjugate to .
Whenever one (and then – all) of these properties take place, problem is solvable, and its optimal solution satisfies .
3.1 Optimal contrasts for regular and penalized recoveries
As an immediate consequence of Lemma 3, we get the following description of the domain associated with the norm :
where in is specified as . Note that the second equality in is given by Linear Programming duality. Indeed, by , is the smallest for which all problems , , are feasible, and thus, by Lemma 3, if and only if and .
Note that the quantity depends solely of , while depends on , as on parameters, but is independent of .
The outlined results suggest the following scheme of building the contrast matrix :
we compute by solving Linear Programming problems in (28.); if , then does not contain points with , so that our recovery routines are not applicable (or, at least, we cannot justify them theoretically);
when , the set is nonempty, and its Pareto frontier (the set of pairs such that is possible if and only if ) is the curve , . We choose a "working point" on this curve, that is, a point and compute by solving the convex optimization programs , , with specified as . is nothing but the maximum, over , of the optimal values of these problems, and the optimal solutions to the problems induce the matrix which satisfies and has . By reasoning which led us to (??),
that is, is the best for our purposes contrast matrices satisfying . With this contrast matrix, the error bound (26) for regular/penalized recoveries (in the former, , in the latter, ) read
The outlined strategy does not explain how to choose . This issue could be resolved, e.g., as follows. We choose an upper bound on the sensitivity of the risk (29) to , i.e., to the -deviation of a signal to be recovered from the set of -sparse signals. This sensitivity is proportional to , so that an upper bound on the sensitivity translates into an upper bound on . We can now choose by minimizing the remaining term in the risk bound over , which amounts to solving the optimization problem
Observing that is, by its origin, a convex function, we can solve the resulting problem efficiently by bisection in . A step of this bisection requires solving a univariate convex feasibility problem with efficiently computable constraint and thus is easy, at least for moderate values of .
4 Range of feasibility of condition
We address the crucial question of what can be said about the magnitude of the quantity , see (28) and the risk bound (


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It's like a flash mob - with fiddles.
Every Sunday night, one to two dozen Celtic musicians - loosely affiliated and boasting varied skill levels - hold court in a corner nook at the Claddagh Irish Pub in the Brewery District.
It's like a flash mob - with fiddles.
Every Sunday night, one to two dozen Celtic musicians - loosely affiliated and boasting varied skill levels - hold court in a corner nook at the Claddagh Irish Pub in the Brewery District.
They lack a band name and a permanent frontman, although one or two rotating leaders hold the title each week.
Without a stage, spotlights or a set list, they grab their guitars and pints of Guinness, launching into Irish standards such as The Morning Dew and The Mountain Road with impromptu, yet unified, aplomb.
Quiet enough for nearby diners to converse over their meals, the lively ensemble still inspires plenty of hand-clapping and even dancing near the hostess' stand.
They will be playing on Sunday, three days after St. Patrick's Day, but they imbue the spirit of Ireland year-round.
Known as a "session," the weekly klatch embraces longtime players, newcomers and even travelers seeking a musical respite from the road.
"It's very addicting," said Rick Nelson, a 58-year-old Westerville guitarist with "no Irish blood" who established the Claddagh jam two years ago. "You get to play good music with your friends and learn a lot."
Such gatherings - originally called seisiuns - began in rural Irish pubs to spur neighborly socializing.
Today, sessions are held throughout the world, relying on word-of-mouth and the Internet to attract momentum and stand-in players (recent Claddagh guests have included the touring percussionist for Celine Dion, members of the popular Irish band Teada and the footwork of Riverdance frontman - and central Ohio native - Joe Moriarty).
"You can sit down anywhere in the world and have something in common," said Kathy Simcox, 39, a singer and saxophonist from Hilliard who recently took up playing the bodhran, an Irish drum. "It's fabulous."
Newcomers, Simcox said, should expect a learning curve as they warm to the rhythmic and melodic intricacies of Celtic styles (and the dynamics of an ensemble whose lineup differs at every showing).
Many beginners first opt to sit in during familiar tunes, perhaps using a cell phone to record others, then rehearse them at home by ear - a common learning method for the genre.
The Claddagh session group has a repertoire of about 1,000 tunes, many of which share similar hallmarks.
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For the players, drawn as much by the companionship as the music, the outlet provides a way to escape from workweek stress and promote Irish music in a city that's increasingly receptive to such offerings.
Nelson, who by day serves as vice chairman of the emergency-medicine department at Ohio State University Medical Center, first found sessions Downtown at St. Patrick Church - which were discontinued after an adjoining social hall was torn down.
He'll often tote his instrument on business trips, finding sessions in Chicago and New York.
So does Gahanna software engineer Randy Clepper, who recently brought his bouzouki - a plucked string instrument with Greek origins - to perform with players in one of the few Irish pubs in Tel Aviv, Israel.
"Some of them didn't speak English, but we knew the same songs," said Clepper, 48, seated at the bar before joining his peers at a recent Claddagh session. "There's a love for the music, absolutely."


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I-Joists Handling and Installation Tips. I-joists should be braced and nailed as they are being installed. Use correct joist hangers, blocking panels, rim boards and cross-bridging at joist ends. I-joist temporary bracing must be 1 x 4-inch minimum, at least 8 feet long and spaced no more than 8 feet on center.
Other People Are Reading. A row of solid cross-blocking or bridging perpendicular to the joists should be installed 6 to 8 feet apart over the length of the joists and at each end. With blocking complete, the joist structure is ready for subfloor utilities, insulation and plywood sub-flooring.
These installation tips are supplementary to your manufacturers instructions and technical guides. Load handling: Each I-Joist must be braced and nailed using appropriate joist hangers, blocking panels and Rimboard or bridging at the joist ends. Use a minimum of 1×4 temporary bracing during installation to prevent I-Joists from buckling.
This is where pre-planning and communication are essential: If problem areas can be identified ahead of time, the joist placement and spacing can be adjusted prior to installation, avoiding improper field notches that can affect the joists structural integrity. 6. Material Exposure Like all wood materials, I-joists are susceptible to moisture.
Joist framing from opposite sides of a beam or girder shall be lapped at least inches. A single header is allowed in a framed floor opening if the dimension along the header is less than feet. SPF 2 is to be installed 16" on center in a residential living area with a dead load of 20 psf.
As I understand the guidance, they want wood floor always installed 90deg. to the joists, even on a 3/4 nailing surface. They do say that 3/4 OSB is an OK subfloor for nailing 3/4 hardwoods. So, another factor to consider here is whether our reader is laying 3/4 hardwoods or thinner, in which case guidance might change.
The I joists install in the same way as a traditional wood floor joist and make for a stiffer, squeakless floor. READ THE ANSWER Approved Engineered I Joist Manufacturers. Engineered I joists now have a uniform set of manufacturing rules for quality control.
If one joist is higher or lower than others, it may be reflected in the porch surface. Install Aeratis porch flooring on joists no greater than 16 on center 10 on center for stair applications . Installing Aeratis perpen- dicular to the house is recommended to help promote water runoff.
The subfloor is the decking installed on top of flooring joists; the finished floor is then installed on top of the subfloor. The thickness of plywood panels in a subfloor is regulated by the spacing of the joists. This number is known as a span rating.
F. Wood I Beam joists must be supported on walls, beams, or in hangers. They may not be supported by a non-structural ridge board or by toe-nailing into a beam or ledger. G. Wood I Beam joists must be restrained against rotation at the ends of joists by use of rim joists, blocking panels, or cross bridging.