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Generalized Shifted Inverse Iterations on Grassmann Manifolds 1
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1 Proceedings of the Sixteenth International Symposium on Mathematical Networks and Systems (MTNS 2004), Leuven, Belgium Generalized Shifted Inverse Iterations on Grassmann Manifolds 1 J. Jordan α, P.-A. Absil β and R. Sepulchre γ α Department of Mathematics, University of Würzburg, Würzburg, Germany. β School of Computational Science and Information Technology, Florida State University, Tallahassee FL , USA. γ Department of Electrical Engineering and Computer Science, Institut Monteore, B28 Université de Liège, B-4000 Liège, Belgium. Abstract: We discuss a family of feedback maps for the generalized Inverse Iterations on the Grassmann manifold. The xed points of the resulting algorithms correspond to the eigenspaces of a given matrix. A sucient condition for local convergence is given. 1 Introduction In many applications it is necessary to nd a p-dimensional eigenspace of a given matrix A. There exist several dierent strategies to design algorithms for eigenspace computation, see for example the approaches in [7, 8, 10]. A classical and very successful algorithm for the case p = 1 and A = A T is the Rayleigh quotient iteration (RQI). Its dynamics can be described on the projective space, see for example [4, 9, 11]. A block version of the RQI method for 1 p < n was proposed in [3]. The iteration was shown to induce an iteration on the Grassmann manifold (i.e. the set of p-dimensional subspaces of R n ) and was therefore called Grassmann- RQI. Assuming A = A T, the Grassmann-RQI is locally cubic convergent to a p-dimensional invariant subspace of A. 1 This paper presents research partially supported by the Belgian Program on Interuniversity Poles of Attraction, initiated by the Belgian State, Prime Minister's Oce for Science, Technology and Culture. This work was completed while the rst author was a guest at the University of Liege under a grant from the Control Training Site (CTS). The second author's work was supported by the National Science Foundation of the USA under Grant ACI and by the School of Computational Science and Information Technology of Florida State University.
2 2 The Grassmann-RQI can be interpreted as a shifted Inverse Iteration on the Grassmann manifold with a certain feedback control. In this paper we want to generalize this idea by using dierent feedback strategies instead of the Rayleigh quotient. We introduce a set of feedback laws which ensure that the corresponding algorithm is well-posed on the Grassmann manifold. Similar to the Grassmann-RQI eigenspaces are corresponding to the xed points of the algorithm. Furthermore we prove local convergence for a certain set of algorithms. The paper is organized as follows. In Section 2 we generalize the Grassmann- RQI. Therefore we introduce a set of feedback maps. In Section 3 we discussed the algebraic structure of the feedback maps. Section 4 deals with the singularities of the algorithm. The correspondence between xed points and eigenspaces is discussed in Section 5. We give sucient criteria for local convergence in Section 6. Finally, we give some concluding remarks in Section 7. 2 The generalized shifted Inverse Iteration The Grassmann Rayleigh Quotient Iteration described in [1, 3] is a subspace iteration on the Grassmann manifold Grass(p, n). It can can be interpreted as a discrete-time system with a certain feedback control. In this section we introduce a family of feedback controls which generalizes this idea. Note that we do not assume symmetry of the matrix A in this section. We use the following notation. With ST(p, n) we denote the set of real full rank n by p matrices. Note that ST(p, n) is open in R n p and has therefore, in a canonical way, a smooth manifold structure (called the noncompact Stiefel manifold). Let π be the canonical projection π : ST(p, n) Grass(p, n) that maps Y ST(p, n) to its column space. For any X, Y ST(p, n) exists M GL p (R) such that X = Y M if and only if π(x) = π(y ). Given an initial iterate Y 0 Grass(p, n), the Grassmann-RQI [3] computes a sequence of subspaces Y t = Φ R (Y t 1 ), t = 1,..., t final, where Φ R is dened as follows. Algorithm 2.1 (Grassmann-RQI mapping Φ R ) Given Y Grass(p, n), 1) Choose Y π 1 (Y), i.e. a matrix Y ST(p, n) with π(y ) = Y. 2) Solve the Sylvester equation AY + Y + R(Y ) = Y (1) with the Rayleigh quotient map R : Y (Y T Y ) 1 Y T AY. 3) Dene Φ R (Y) := Y + := π(y + ). The map Φ R is well dened under the following assumptions: (i) the Sylvester equation (1) admits one and only one solution, (ii) this solution has full rank and (iii) Y + is independent of the choice of Y π 1 (Y). One can show that assumptions (i) and (ii) holds for an open and dense subset of matrices Y ST(p, n).
3 3 Moreover, if (i) and (ii) are fullled then (iii) is fulllled as well. This is due to the following homogeneity property of R X ST(p, n), M GL p (R) : R(XM) = M 1 R(X)M. (2) We call a map F : ST(p, n) GL p (R) with Property (2) a feedback map and denote the set of all feedback maps with F. For any F F we dene the iteration mapping Φ F as follows. Algorithm 2.2 (Grassmann shifted Inverse Iteration mapping Φ F ) Given Y Grass(p, n), 1) Choose Y π 1 (Y). 2) Solve the Sylvester equation 3) Dene Φ F (Y) := Y + := π(y + ). AY + Y + F (Y ) = Y (3) We denote the corresponding iterative algorithm Y k = Φ F (Y k 1 ), the Generalized Shifted Inverse Iteration. Note that Property (2) ensures that the new iterate Y + does not depend on the choice of Y in algorithm step 1. It is possible to choose a time varying F F. This leads to a discrete-time control system Y 0 Grass(p, n), Y t+1 = Φ(F t, Y t ), F t F. (4) In this paper we consider algorithms of type (2.2) with xed F F. But the dynamic properties of (4) will be the aim of future work. 3 The algebra of feedback maps We have dened the Generalized Shifted Inverse Iteration for any feedback map F F. Obviously F is not empty, since the Rayleigh quotient map belongs to F. In this section we give some more examples and show that F has a rich algebraic structure. Theorem 3.1 With multiplication F G : X F (X)G(X), addition F + G : X F (X) + G(X), scalar multiplication λf : X λf (X), zero element X 0 R p p and one element X I R p p, F is a real algebra. Using Theorem (3.1) is not dicult to construct examples of feedback maps. In particular every algebraic combination of the following examples is an element of F. Examples 3.2 1) F 0. This choice of F leads to the (unshifted) Inverse Iteration on Grass(p, n).
4 4 2) The Rayleigh quotient map R : X (X T X) 1 X T AX is an element of F. Note that F := R gives Algorithm ) For W R n p the map F W : X (W T X) 1 W T AX dened for all X with W T X GL p (R) is in F. 4) Let F be a feedback map and f : ST(p, n) R be a map with f(xm) = f(x) for all X ST(p, n) and all M GL p (R). Then the map ff : X f(x)f (X) is an element of F. 5) Let B : ST(p, n) R n n be a map with B(XM) = B(X) for all X ST(p, n) and all M GL p (R). Then the map F B : X (X T X) 1 X T B(X)X is also element of F. One can construct an innite set of linear independent maps F α F. Therefore F has innite dimension as a vector space. 4 Singularities of Φ F In general, there may exist subspaces Y Grass(p, n) for which Φ F (Y) is not a well-dened element of Grass(p, n). This happens if and only if either Equation (3) fails to have an unique solution, or the unique solution fails to have full rank. Remarkably, under convenient conditions on F, Φ F is well dened on a generic subset of Grass(p, n). With M F we denote the set of all matrices Y ST(p, n) such that Equation (3) has a unique solution and this solution has full rank. If X ST(p, n) and Y ST(p, n) represent the same element of Grass(p, n) (i.e. π(x) = π(y )) then X M F if and only if Y M F. Therefore, the question if Φ F is well dened or not, does not depend on the choice of the representation Y of Y Grass(p, n). A reasonable assumption for F is to be a rational functions of the entries y ij of Y ST(p, n) as in the case of the generalized Rayleigh quotient map. Our results also hold for a wider class of feedback maps. We call a continuous map F : A B quasi open if for every S A with nonempty interior F (S) has nonempty interior in B. Theorem 4.1 Let F : R n p R p p rational or quasi open and continuous on ST(p, n). a) The set of matrices Y for which Equation (3) has a unique solution is open and dense, unless F λ p I for any eigenvalue λ p of A. b) π(m F ) is either open and dense in Grass(p, n), or empty. Note that the case π(m F ) = is rather exceptional and easy to verify. particular this is the case if F λ p I for any eigenvalue λ p of A. In 5 Correspondence between xed points and eigenspaces If the feedback law F is an element of F, then the xed points of Algorithm 2.2 are related to the eigenspaces of A. Let V be a xed point of the map
5 5 Φ F : Y Y +, then there exits M GL p (R) such that AY M Y MF (Y ) = Y. (5) Using Property (2) we get AY = Y P with P = (M 1 + F (Y M 1 )) R p p. Thus, Aπ(Y ) π(y ). Theorem 5.1 If Y Grass(p, n) is a xed point of Φ F then Y is an eigenspace of A. Conversely, if Y is an eigenspace of A, then Y is a xed point of Φ F provided that Y π(m F ). Observe that the unshifted algorithm (i.e. the choice F O) reduces to the Inverse Iteration. In this case the set of xed points and the set of eigenspaces of A coincide. In the shifted algorithm no new xed point is created but some eigenspaces may become singularities. This is for instance the case of the Grassmann-RQI. Its very nature makes every eigenspace a singularity of the algorithm, thereby accelerating the rate of convergence. Nevertheless, the Grassmann-RQI mapping Φ R has a continuous extension such that xed points of the extended map coincide with the eigenspaces. 6 Local convergence In the following we want to state a sucient condition on F which guarantees local convergence of Algorithm 2.2 for symmetric matrices A. To measure distances on Grass(p, n) we use d(x, Y) := Π X Π Y 2 where Π X denotes the orthogonal projection on X. Note that the topology induced on Grass(p, n) by the distance d(x, Y) is identical to the one induced by the canonical projection π : ST(p, n) Grass(p, n) (see [6]). Because the following theorem is stated in local coordinates we need some terminology and properties of the geometry on Grass(p, n). Let X Grass(p, n) be a xed element. We choose an orthogonal X π 1 (X ) and X R (n p) p such that Q := (X X ) O n (R). Furthermore, we use the notation ( ) Q T A11 A AQ = 12. (6) A 21 A 22 X is called spectral (with respect to A) if A 11 R p p and A 22 R (n p) (n p) have no eigenvalues in common. For Y Grass(p, n) which is not orthogonal to X (i.e. X T Y GL p (R) for Y π 1 (Y)), pick Ỹ π 1 (Y) and dene σ X (Y) = Ỹ (X T Ỹ ) 1. One easily veries that σ X (Y) is independent of the choice Ỹ π 1 (Y). Thus, the map K X : Grass(p, n) R (n p) p, Y X T σ X(Y) is well dened. Note that K X denes a coordinate chart for Grass(p, n). The distance of a point Y Grass(p, n) which is not orthogonal to X can be approximated in terms of the local coordinate K X (Y) by d(x, Y) = K X (Y) 2 + O( K X (Y) 3 2). (7)
6 6 For a deeper introduction to the geometry on Grass(p, n) see [1, 3, 2, 10]. The following theorem gives a sucient condition for local convergence of Algorithm 2.2. Theorem 6.1 Let A be a symmetric n by n matrix and X be a p-dimensional spectral eigenspace of A. Let X π 1 (X ) be orthogonal and θ > 0 a constant. Let F F be continuous with property F (σ X Y) X T AX 2 = O( K X (Y) θ 2), (8) for all Y in a neighborhood of X. The Grassmann shifted Inverse Iteration mapping Φ F admits a continuous extension on a neighborhood of X. The point X is an attractive xed point of the extended mapping, and the rate of convergence is θ + 1. In particular Theorem 6.1 gives locally cubic convergence for the Rayleigh quotient R(Y ) = (Y T Y ) 1 Y T AY. This result was already proved in [1]. It is possible to construct other maps F which fulll the conditions of the theorem. Nevertheless Condition (8) is certainly a very hard restriction on the choice of F. If one wants to apply Theorem 6.1 to prove cubic convergence close to a certain eigenspace X, F has to behave locally like the Rayleigh quotient map. On the other hand, since we have a freedom in the choice of F F, Algorithm 2.2 may open new possibilities to improve the global behavior of the iteration. 7 Conclusion and future work Given a matrix A R n n we have constructed a family of iterations dened on suciently large subsets of Grass(p, n). The xed points of the algorithms correspond to the p-dimensional eigenspaces of A. Therefore these algorithms may be used for eigenspace calculations. Furthermore, we state a condition for local convergence to the xed points. The Grassmann-RQI can be seen as a particular case with a constant control. In the case p = 1 (i.e. Grass(p, n) = RP n 1 ) the Grassmann-RQI reduces to the well-known Rayleigh quotient iteration which is an ideal shift-strategy in a certain sense and has some useful global properties ([4, 11]). In our future work we want to study control systems of type (4). In particular we want toinvestigate if the generalized Rayleigh quotient map R is (locally) an ideal choice compared with other possible shifts. Furthermore we want to construct feedback strategies which improve the global behavior. References [1] P.-A. Absil, Invariant Subspace Computation: A Geometric Approach, PhD Thesis, Liege (2003). [2] P.-A. Absil and R. Mahony and R. Sepulchre, Riemannian geometry of Grassmann manifolds with a view on algorithmic computation, Acta Appl. Math. 80, No 2, (2004), pp
7 REFERENCES 7 [3] P.-A. Absil, R. Mahony, R. Sepulchre and P. Van Dooren, A Grassmann-Rayleigh Quotient Iteration for Computing Invariant Subspaces, SIAM Review, 44, No 1, (2002), pp [4] S. Batterson and J. Smillie, The dynamics of Rayleigh quotient iteration, SIAM J. Numer. Anal., 26 (1989), pp [5] S. Batterson and J. Smillie, Rayleigh quotient iteration for nonsymmetric matrices, Math. Comp., 55, No 191,(1990), pp [6] J. Ferrer, M.I. García, and F. Puerta, Dierential families of subspaces, Linear Algebra Appl., 199(1994), pp [7] U. Helmke, J. Moore, Optimization and Dynamical Systems, Springer- Verlag, New York, (1994). [8] K. Hüper, A calculus approach to matrix eigenvalue algorithms, Habilitationsschrift, Würzburg (2002). [9] I. C. F. Ipsen, Computing an eigenvector with inverse iteration, SIAM Rev. 39 (1997), pp [10] G.W. Stewart, Error and perturbation bounds for subspace associated with certain eigenvalue problems, Siam Review, 15, No 4, (1973), pp [11] B. N. Parlett, The Rayleigh Quotient Iteration and Some Generalizations for Nonnormal Matrices, Mathematics of Computation, 28, No 127, (1974), pp [12] P. Van Dooren, R. Sepulchre, 'Shift policies in QR like algorithms and feedback control of self-similar ows', Open Problems in Mathematical Systems and Control Theory (V. Blondel, E. Sontag, M. Vidyasagar and J.C. Willems; Eds.), Springer, London (1999), pp
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text:
Slides and Waterslide Rentals
Rent Inflatables slides in ottawa CALL NOW! 613-695-JUMP(5867)
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Rent Industrial Slides and Waterslides. Prices do not include delivery and installation. Please Add all the items you want to rent or purchase to the Online Shopping Cart, complete your details and hit submit.We will follow up with your request within 24 Hours to help you complete your request. We will also ask you for more details if you your quote is for Rentals. Shipping and Delivery Rate will be also provided.

subset: commoncrawl


text:
Postville Board of Education Meeting
Regular Scheduled Meeting at 6:30 P.M.
Fine Arts Lobby
August 13, 2018
President Smith called the regular meeting of the Postville Board of Education to order at 6:30 P.M. on Monday, August 13, 2018, with the following members present: Jeff Cox, Tony Gericke, JoAnn Jacobs, and Staci Malcom.
President Smith welcomed the visitors.
Erica Nosbisch and Dr. Reimer, representing NICC, presented information on the NICC Bond Election.
Motion by Gericke, second by Jacobs, to approve the agenda with the addition of one open enrollment. Carried unanimously.
Motion by Malcom, second by Gericke, to approve the consent agenda with the addition of one hire. Carried unanimously.
- Approve the July 16, 2018 Regular Meeting Minutes.
- Approve the monthly invoices (reviewed by Jamie Smith) and financial reports.
- Approve the hire of Keisha Kerr/Nurse; Shelly Tafollo/Custodian.
- Approve the resignations of Marcy Kraus/Softball Coach; Abdiwahab Ali/Somali Liaison; Lorri Pladsen/Elementary Associate.
- Approve District Appointments: Title I Coordinator/Jenny Schutte, Equity Coordinator/Brendan Knudtson, Title IX Coordinator/Brendan Knudtson, 504 Coordinator/Jenny Schutte, Special Education Co-Directors/Jenny Schutte and Brendan Knudtson, Bully/Harassment Investigators/Jenny Schutte and Brendan Knudtson, Affirmative Action Coordinator/Ryan Zurbriggen, Level I Investigators/Jenny Schutte, Ryan Zurbriggen, and Brendan Knudtson, Level I Alternate Investigator/Tim Dugger, Level II Investigator/Postville Police Department, Homeless Liaison/Denise Mauss, Teacher Quality Committee Administrator/Tim Dugger, School Improvement Advisory Chairperson/Ryan Zurbriggen, ELL Coordinators/Jenny Schutte and Brendan Knudtson, and Food and Fitness Administrator/Ryan Zurbriggen.
Superintendent Dugger shared information on the in-service schedule with new staff.
Principal Knudtson updated on the school scrimmage.
Principal Schutte shared information on harassment complaint data.
Motion by Cox, second by Jacobs, to approve seven open enrollments into district requests. Carried unanimously.
Motion by Gericke, second by Cox, to approve the K-6, 7-12, and Alternative School Parent/Student Handbooks. Carried unanimously.
Motion by Cox, second by Jacobs, to approve the contract between Postville CSD and Postville Child Care Services for the four-year-old program. Carried unanimously.
Motion by Gericke, second by Cox, to approve a Resolution to Consider Continued Participation in the Instructional Support Program and to schedule a Public Hearing. Carried unanimously.
Motion by Gericke, second by Malcom, to approve the first reading of the following board policies. Carried unanimously.
- 105 Assistance Animals. This new policy to clarifies the use of service animals, assistive animals, therapy animals and emotional support animals.
- 3 Animals in the Classroom. This policy was updated to be consistent with Board Policy 105 which allows service, assistive, therapy, and emotional support animals.
- 1 Purchasing – Bidding. The amended policy adds language that requires compliance with federal and state laws for the selection and suspension of federal and state contractors.
- 1R1 Suspension and Debarment of Vendors and Contractors Procedure. The new regulation adds a procedural framework for evaluating and screening contractors who have been suspended or debarred from continuing to transact with the District.
- 1 School Nutrition Program. The amended policy adds language that requires compliance with federal and state laws for the selection and suspension of federal and state contractors.
Motion by Cox, second by Malcom, to approve the Communications Tower lease with Julie Szabo for the Digital Repeater System at $650 per year. Carried unanimously.
Motion by Jacobs, second by Gericke, to approve a change order for the roofing project in the amount of $7,446. Carried unanimously.
Items for the September Board Meeting are:
- Public hearing for the instruction support program
- Resolution to consider participation in the instruction support program
The September Board Meeting for the Postville Board of Education will be held on September 10, 2018, at 6:30 P.M, at the Postville Fine Arts Center Lobby.
Motion by Cox, second by Jacobs, to adjourn the meeting at 7:09 PM. Carried unanimously.
____________________________ ___________________________________
Jamie Smith, President Melissa Fettkether, Secretary


text:
Sarah Smith Horrell , 73, of Erwin passed away Thursday, April 5 , 2018.
The service for Mrs. Horrell will be held on Sunday April 8, 2018 at 3:00 pm at Sansom Community Church in Dunn, NC. Visitation with the family will precede the service at 2:00 pm. The service will be officiated by Rev. Turner Matthews and Rev. Jerome Pope. Interment will follow the service at Erwin Memorial Garden.
Sarah was born February 8, 1945 in Dunn, NC. Her parents were Welton Smith and Vida Mae Smith. She worked as a Child Support Enforcement Officer until retirement in .
Sarah enjoyed many hobbies such as cooking, sewing and working in the yard. She enjoyed going to the beach and particularly camping. But Sarah's greatest love by far was her children and her grandchildren. Sarah was kind and loving to everyone she came in contact with and she was loved by all who knew her.
Sarah is survived by her son, Arthur Weeks of Willow Springs, NC, her daughter Beverly Oakley and husband David of Emerald Isle, NC, her daughter Elaine Ellis and husband Condary of Dunn, NC, her step-son, Gary Horrell and wife, Winnie of Erwin, her step-daughter, Sheila Beasley and husband Ricky of Coats, her sister Belinda Sessoms and husband, Glendell "Bunky" of Erwin, NC, 8 grandchildren and 5 great-grandchildren. She was preceded in death by her husband, C.J. Horrell, her mother, Vida Mae Smith and her father, Welton Smith.
Services have been entrusted to West & Dunn Funeral Home in Erwin.


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Separate names with a comma.
Discussion in 'Projects' started by Hunter
, Sep 5, 2016.
gif forever
I feel useful C:
Sorry for the wait everyone!
We've been on a small hiatus (haha.) and would like to announce that we are almost finished with the collab! All we have left is the transition into the finisher and lastly, the finisher!
Keep on your toes, because we're about to GIF it up.
-eyes on my profile picture-
Sounds very interesting! But I never really made any gif animations. ):
Good luck with this collab though!
Hi guys! So, as you guys probably have noticed, the last update on this thread was back in September 2nd, 2017. It is November 7th, 2018. Unfortunately, and I'm sad to say that, since then, there hasn't been as much progress to the collab as we'd like. AznMagix has stepped down from the finisher due to being too busy, and as of today, Hunter and I are going to pick up from it. I have just finished compiling everything in addition to adding sound effects to every part, which means the only thing left is the finisher, and the finisher alone. Again, I apologize for the wait, and the necropost too, but I thought it'd be nice to keep everyone updated on what's going on here. I have no plans on just shoving the finisher in, but I'll still try my very best to put out something worthwhile. Thank you for your time. c:


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T. Hasegawa USA reports 365 Days without a Lost Time Accident and Counting
Mar 19, 2019, 08:07 ET
CERRITOS, Calif., March 19, 2019 /PRNewswire/ -- T. Hasegawa USA, Inc. announced today that it recently marked 365 days without a lost time accident at its Corona, CA facility which marks 4 years total without a lost time accident. The achievement was celebrated throughout the company on March 11th with a luncheon and custom t-shirts for employees.
"We strive for a safe work environment and promote commitment to working safely at all times," said Tom Damiano, CEO. "We are grateful to everyone on our team for helping us reach this milestone and achieving 4 years is a great success."
Chris Grayson, Vice President of Operations, stated "Our safety team members and supervisors create a climate of safety and are devoted to operating by the best safety practices. We will not compromise safety for any reason! Our continuous improvement philosophy, along with our manufacturing processes, assures the customer of continuous improvement in the areas of productivity, product performance, customer satisfaction and cost."
T. Hasegawa has now achieved 365 days without a time lost accident at both of its manufacturing facilities in California. Ernesto Dominguez, Safety Manager, reveals "Safety is not just a word in our facilities it is part of our corporate culture. An action plan is built that addresses any potential issue and our team rallies to solve any issue so we can continue to be considered leaders in maintaining a safe and healthy workplace."
T. Hasegawa has the distinctive ability to create exceptional taste in food and beverages which not only deliver superior flavor in line with market demands but creates value. Our palette of unique flavors are a direct reflection of our creativity and strong understanding of the market.
About T. Hasegawa USA, Inc.
Being a global top-10 flavor and fragrance company, T. Hasegawa continues to pioneer the flavor industry with a customer experience that is optimized to rapidly respond with technical expertise. We deliver superior products that meet all your requirements no matter how complex the demand. Recognizing that the food industry needs flexibility, we proactively listen to our customers' needs in an effort to develop better ways of delivering formulations that have excellent taste and aroma to fit form and function.
Doug Resh
Director Commercial Marketing
SOURCE T. Hasegawa USA, Inc.


text: Survival of Patients With Vancomycin-Resistant Enterococcus faecium Bacteremia Treated With Conventional or High Doses of Daptomycin or Linezolid Is Associated With the Rate of Bacterial Clearance*Chuang, Yu-Chung, MD, PhD1,2; Lin, Hsin-Yi, PhD3; Chen, Pao-Yu, MD2; Lin, Chi-Ying, MD4; Chen, Yee-Chun, MD, PhD2; Wang, Jann-Tay, MD, PhD2; Chang, Shan-Chwen, MD, PhD2Critical Care Medicine: October 2018 - Volume 46 - Issue 10 - p 1634–1642 doi: 10.1097/CCM.0000000000003264 Clinical Investigations Buy SDC Abstract Author InformationAuthors Article MetricsMetrics Objectives: Vancomycin-resistant enterococci are important pathogens for healthcare-associated infections. Although linezolid is bacteriostatic and daptomycin is rapidly bactericidal against vancomycin-resistant enterococci in vitro, it is not clear whether they differ in their effect on bacterial clearance in patients with vancomycin-resistant enterococci bloodstream infections. Design: Prospective observational study. Setting: Two university hospitals and research laboratory. Patients: Patients with vancomycin-resistant enterococci bloodstream infection proven by blood cultures were prospectively enrolled from January 2010 to July 2015. Interventions: Sequential blood samples were collected. Real-time quantitative polymerase chain reaction was used to monitor bacterial loads. Measurements and Main Results: One hundred eight patients with vancomycin-resistant enterococci bloodstream infection were enrolled. Quantitative polymerase chain reaction assays were performed on 465 blood isolates. We found this method to be closely correlated with colony-forming units and more sensitive than culture. Sixty-three patients (58.3%) received "conventional dose" daptomycin (6–9 mg/kg), 15 (13.9%) received high-dose daptomycin (≥ 9 mg/kg), and 30 (27.8%) were treated with linezolid (600 mg every 12 hr) as sole agents. The initial mean bacterial load was 1.03 log10 copies/mL and unrelated to survival. Survivors had a more rapid early bacterial clearance than nonsurvivors (Δ log10 copies/mL/d; –0.16 vs 0.31; p = 0.02). Multivariable logistic regression showed that a slower early bacterial clearance independently predicted increased mortality (odds ratio, 3.21; 95% CI, 1.03–10.02; p = 0.045). Conventional dose daptomycin was associated with a significantly slower rate of bacterial clearance than high-dose daptomycin (Δ log10 copies/mL/d; –0.04 vs –0.41; p < 0.001) and linezolid (–0.04 vs –0.56; p = 0.043). Conclusions: We found that survivors of vancomycin-resistant enterococci bloodstream infection had a significantly more rapid early bacterial clearance by quantitative polymerase chain reaction than nonsurvivors. High-dose daptomycin and linezolid were associated with more rapid bacterial clearance than conventional dose daptomycin. These results support recommendations that conventional dose daptomycin not be used for the treatment of patients with vancomycin-resistant enterococci bloodstream infection. 1Graduate Institute of Clinical Medicine, College of Medicine, National Taiwan University, Taipei, Taiwan. 2Department of Internal Medicine, National Taiwan University Hospital, Taipei, Taiwan. 3Department of Economics, National Chengchi University, Taipei, Taiwan. 4Department of Internal Medicine, National Taiwan University Hospital Yun-Lin Branch, Yun-Lin, Taiwan. *See also p. 1700. Drs. Wang and Chang contributed equally to this article. Supplemental digital content is available for this article. Direct URL citations appear in the printed text and are provided in the HTML and PDF versions of this article on the journal's website (http://journals.lww.com/ccmjournal). Supported partially by the Ministry of Science and Technology, Taiwan (104-2314-B-002-103-MY3, 104-2314-B-002-109-MY3, and 104-2410-H-004-009), the Ministry of Health and Welfare, Taiwan (MOHW107-TDU-B-211-113002), and National Taiwan University Hospital (NTUH.107-M3978). Drs. Chuang, H.-Y. Lin, C.-Y. Lin, Y.-C. Chen, Wang, and Chang's institutions received funding from the Ministry of Science and Technology, Taiwan. Dr. P.-Y. Chen has disclosed that he does not have any potential conflicts of interest. For information regarding this article, E-mail: email@example.com Copyright © by 2018 by the Society of Critical Care Medicine and Wolters Kluwer Health, Inc. All Rights Reserved.


text:
Trees are beautiful and add life to our natural surroundings and are pleasure to our eyes. Tress plays the integral for supplying oxygen to the living thing. This section we are going to see the advantages of trees maintenance.
To help shape the young trees maintenance have to be thoroughly taken. With proper pruning and early care, the trees can grow with strong structure that will retain its harness for more years. Regular trees maintenance such as pruning, trimming and sharping can give your trees best shot at long lasting success. By eradicating unnecessary branches off shoots or trunk division promote a sounder trunk.
Proper maintenance of trees gives them a good air flow. Proper pruning allows for space in between the tree's branches and leaves. Proper pruning of trees also allow light passing thus creating more space for air flow. For a tree to be able to stand the strong wind pruning should be done frequently. The freedom of movement in the trees top helps them to be more suited to supporting their natural purposes and more flexible .
The advantage of the trees maintenance of trees is to prevent safely hazards. Removing of the weak and dead branches from the trees by pruning may help prevent accident. In the places where the wind is strong this weak and dead trees should removed before thy fall down on your homes causing accidents. In order to avoid wounding the trees the proper pruning should be done when removing the dead and weak branches.
Another benefit if trees maintenance is to avoid desertification. Mulching is another way to prevent trees from drying up thus avoiding desertification . Watering of young trees can help prevent them from drying thus eliminating desertification.
Trees gives as medicines and so we should maintain them have continuous supply of medicine to the people. Be sure to click the link to know more!
Soil erosion and strong wind can be eradicated by proper maintenance of trees. Planting more trees and maintain the trees may be the best way to prevent soil erosion in country. Planting of trees and maintaining them well may help you avoid accidents caused but strong wind.
maintenance of the trees is important because the world animals continue getting food and shelter. Due to many animals depending on trees on food and shelter there is an urge for you to maintain the trees . Trees also give as water, the forest ate the sources of river. In order to attract rain we have to plant and maintain the trees. The trees are the source of beauty in a country and so we are urged to plant and maintain them. Make sure to click here for info!


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- Single Family
- 5 Beds
- 6 Baths
- 7,517 SqFt
The Belles at Empire Pass
Ski-In-Ski-Out Deer Valley®
The Belles is a ski-in-ski-out community of 17 rustic-contemporary residences with magnificent views and superior amenities. Direct access to Deer Valley® and within steps of Talisker Tower Club, providing dining, fitness center, swimming, golf, limo service and social club.
Ski Access:
- Adjacent to Silver Strike Lift
- Ski Access to Blue Bell, Banner & Silver Buck Trails
- Ski Access to Northside Express & Silver Strike Express Chairlifts
* More Information about finishes further down on this page.
The Belles at Empire Pass
Mountain Craftsmanship With a Sampling of Finishes:
- Native Stone
- Cedar Shake Roof With Copper Trim
- Heated Driveways and Decks. Lower deck includes hot tub. Deck surfaces include stamped concrete and designer exterior tiles.
- Wood flooring in red oak or cherry wood with 4", 5&6" widths with beveled edges in a stained satin finish.
- Cabinetry in alder or cherry wood raised panel fronts and self-closing drawers
- Bathrooms include limestone or travertine flooring as well as exquisitely tiled showers and bathroom surrounds
- Wood ceilings in all vaulted ceiling areas.
- Great Room includes an alder entertainment center with native stone fireplace
- Plumbing includes a circulatory hot water system, water softener and one humidifier per floor.
- Radiant heat throughout including garage, decks, and driveway.
- Air conditioning throughout
Gourmet Kitchen and Appliances
- SubZero 48" side by side refrigerator
- Wolf 48" gas range with 2 electric ovens
- Two Asko dishwashers with custom cabinet panels
- Kitchen Aid compactor
- Wolf microwave in stainless steel
- Wolf 30" single oven in stainless steel
- Wine storage
- Wet bar refrigerator, ice maker, wine cooler
- Whirlpool duet washer and dryer
Developer : Pat Prothro, Bellecorp
Architect : Mark Walker, Otto/Walker Architects
Builder : Anderson Construction


text:
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Mrs C from Yorkshire was helping her mother to the car when she tripped and fell due to a defective paving slab, She advise that as she put her foot on a slab and it sunk exposing the raised edge of an adjoining slab. The slab had been reported to Yorkshire Housing over a period of about 12 months by numerous residents but to no avail.
What we did
We wasted no time in initiating proceedings and Mrs C was successfully awarded £6,333.34 in compensation for the injuries she sustained due to the accident.
If you have suffered an accident that wasn't your fault, then The Personal Injury Practice's team of No Win No Fee Solicitors are here to help you. Find out for FREE today if you can Claim call 0800 783 9577 or alternately fill out our quick form for your FREEadvice today. Claim!


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It may look like a blonde ale, but it drinks closer to a roasty stout. What is it? It's Trying to Decide Blonde Stout! This innovative beer starts with a light base, adding flaked oats and barley to give added body and richness. A few small hop additions balance out the malt profile. However, it is the cocoa nibs and coffee added after primary fermentation that gives this beer dark, roasted notes that make it drink like a stout. Your mind and taste buds might be confused as you sip down a light beer that tastes like a stout! An interesting new development in beer, the blonde stout, also known as a white stout or ivory stout, is a fun new beer to try brewing, and we are proud to bring you this kit to try it yourself!
Complete instructions are included with the beer kit. Our instructions include target gravity levels, hop addition times, suggested and required equipment lists, and all the important brewing steps! If you need any help, you can just call us!
All of our extract kits come with malt extract, hops, specialty grains (pre-crushed), grain bag, instructions, and yield 5 gallons of delicious homebrew. Yeast is not included but we've provided a selection of recommended yeast (liquid and dry) that you can add to your order in the drop downs above. Clarifying agents (i.e. Irish moss) and priming sugar can be purchased separately.


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At one point, most home interiors were painted with oil-based paint. But, this type of paint is becoming outdated. Many people are choosing to use latex/ acrylic based paint instead.
What if you want to paint over your oil-based paint with water-based acrylic? How do you prevent chipping and peeling? Will it look as good?
Want to learn more? Keep reading to learn how to transition from oil to acrylic based paint.
Oil-Based Versus Water-Based Paint
There are options when it comes to what type of paint to choose for your home interior. You can choose oil-based paint or water-based paint.
Oil-Based Paint
Oil-based paint will dry slowly and level nicely. Oil based paints are typically used for interior trim. But, oil-based paint is more likely to turn yellow, crack, or fade were there is little light. Especially on the back sides of closets door.
Another thing to consider is the fumes of oil paint. Oil-based paint is considered a household hazardous waste.
It's flammable and has to be disposed of properly. It has extremely high levels of volatile organic compounds (VOCs) like toluene and xylene.
Oil-based paints are also notoriously difficult to clean. If you get paint on a surface, you need to clean it with a toxic chemical such as mineral spirits or denatured alcohol.
Water-Based Paint
Water-based paint – also known as acrylic or latex paint – dries faster and is less likely to turn yellow over time. It also doesn't give off those strong fumes. If you get paint on surfaces, you can easily clean it up with water and soap.
In fact, water-based paint is more environmentally-friendly. It's not considered a hazardous waste. Just make sure you purchase an acrylic enamel if your searching for comparable durability of oil.
Tips for Going from Oil to Acrylic
Ready to update the look of your home? Here's how to go from oil-based to water-based paint.
Prep the Area
Before applying acrylic paint, you want to prep the area. If you try applying water-based paint over an oil paint surface, it won't adhere well.
Use fine-grit sandpaper to remove the gloss from the surface you're painting. You want to use the sandpaper to remove just the glossy part, not all the old paint.
After you sand the surface lightly, wipe it down and remove any dust.
Use TSP to Clean the Area (optional)
You want to apply the fresh paint on a clean, even surface. To properly clean the area, use a solution one-fourth cup trisodium phosphate (TSP) and a gallon of water.
Make sure you wear safety glasses and gloves when dealing with TSP because it's a hazardous chemical. Use the mixture to clean all the dirt. Then let dry.
Use a Primer
After preparing the area, apply a light coat of bonding primer. Sherwin – Williams have great bonding primers. Bonding primer will help the water-based paint adhere over the old oil paint. Allowing 2 – 3 days for the primer to cure is important. It will help prevent the likely hood of the primer coat chipping or peeling, allowing maximum adhesion.
For maximum adhesion you may want to apply two coats of primer over the surface.
Apply Paint
Since this blog is primarily about transitioning from oil paint to latex, we will not spend a lot of time covering additional prep such as caulking cracks or puttying nail holes.
So, let's jump directly into applying the paint. By now your surface should be de-glossed, clean, and primed.
Apply a minimum of two coats of acrylic paint. You can watch YouTube videos to learn proper painting techniques from the pros. Allow the paint to dry before applying a additional coats.
Tips to Follow for Painting
Here are some extra tips to follow to make sure your paint job looks great.
Use the Proper Tools
Depending on what you're painting, have the proper tools ready. You don't want to start painting and then have to stop and go to the store to buy another paintbrush or roller.
Also, quality matters when it comes to your painting tools. Invest in a good roller and paint brush. A bad paint job will stand out in your home.
Cover Your Stuff
You'll be careful, you tell yourself. Next thing you know, you have paint splatters all over your floor and furniture. Before you start painting, cover your floors and all your furniture with protective plastic or cloth.
Don't Be Cheap with the Paint
When buying paint, you should buy high-quality paint. High-quality paint will last longer and is more resistant to fading. Sherwin – Williams has several great interior products. In terms of trim paint Sherwin – Williams Emerald Urethane enamel is one of the best products Sherwin – Williams has to offer.
Other notable mentions by Sherwin – Williams are: Pro-classic Waterborne Alkyd, Harmony Semi-Gloss and Duration Home seems to have a newly formulated semi – gloss. We have not used or tested that product but are anxious to do so.
Don't use cheap trim paint. You will not be happy if you do. Cheap trim paints tend to hold more dust and loose their natural sheen sooner.
Choose the Right Finish
In addition to choosing a paint color, there are finishes you can choose. Your choice of finish will depend on which rooms you're painting, the finish that you are painting over and the style or overall feel of the home.
Final Tips for Applying Sherwin Williams Paints
Now that you know how to apply Sherwin Williams paint types over oil-based paint, you can decide whether you want to go the DIY route or hire a professional.
If you think you won't have the time or skills to complete the job, you can consider hiring a professional. Professional painters will do all the hard work for you.
If you're ready to transform your home, contact us for a free quote.


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- Material:80% Polyester + 20% Cotton.
- Size:For Perfect Fit,Please carefully read the SIZE CHART to select the size you need, if you can't decide your size, please email us your measurements:height,bust,waist,shoulder or hip, then we could check which size fit you well.
- polyester,cotton
- This Velvet Padded Hoodie Coat is made of premium fabrics,soft and comfortable;Fashion camouflage stitching design and luminous pattern on the back of the hoody that will glow light in the darkness, keep you warmth and vogue during those Cold Winter Months.
- Perfect gift for Anime Lovers! Ideal for Casual, Sports, Home, Hang-out, Travel, School, Street Wear, Couple Wear, Party Wear, Daily Life and other Outdoor Activities.
- Garment Care:Machine Wash/ Hand Wash Recommended.
Product description
All of our product is brand new and high quality, You can rest assured quality guaranteed absolutely. If you want other styles we have more pattern options, Please check in our Store.
If you are not satisfy with something, please don't leave us negative or neutral feedback right away. Please contact us via email. We promise to provide 100% fine customer service and try best to make every customer get good mood with fine shopping experience here.
Note: 1. Dimensions are measured by hand, may be 1-2 cm deviations. / 2. Color may slightly different due to the color calibration of your monitor.


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Opportunity!! 6bedroom 5 1/2 bath 7422sqft home on 9.11 acres with a full in-law suite!! This is a rare opportunity, property will require some TLC but a tremendous value with a little sweat equity
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Find Cheap Palmer, MA Auto Insurance Online
Most people will start their research on the Internet, searching for individual car insurance providers, helping to get one that will offer them a much lower rate. There search could be prompted by an increase in their car insurance premiums from their existing company as a result of a claim that they filed recently. If this is the case, you can begin to get individual quotes from each of the businesses that you find to see which one can save you the most money. However, this could be a very time-consuming process, so the following cheap automobile insurance tips will help you streamline your search for the best coverage the lowest possible price in Hampden county.
Cheap Palmer Car Insurance Online Tips
The following cheap car insurance online tips are probably ones that you have heard of before, but you may not have used. These strategies are not secret. They have been utilized by people for decades in order to get the best premiums on their auto insurance policies. The Internet has changed many things when it comes to finding cheaper rates for any type of insurance in Palmer, Massachusetts that you may have. It gives you instant access to a multitude of companies that you may not have known about, businesses that can literally save you hundreds of dollars in premiums every month. The goal is to take your time and make sure that you are looking at every possible option. You can actually use multiple tips simultaneously. The goal is to do everything that you can to lower your premiums, especially if they have recently gone up, so that you can have more money to spend on yourself or your family.
Use Online Review Sites
Things You Can Do To Lower Your Premiums
If you don't want to switch to a business that you are not sure of, even though they offer lower premiums, might want to consider doing a few things that can help get your premiums back to normal. For example, you may want to choose a deductible that is much higher, a strategy that will almost instantly lower your premiums without changing your coverage. You could also drop some of the coverage that you have especially if your car is free and clear, and does not require comprehensive coverage or no-fault insurance.
Ways To Automatically Lower Your Premiums
There are actually a few things that can lower your premiums automatically without having to do anything. For example, if you turn 25, you will notice that your premiums will dramatically go down in price. If you are only driving a few thousand miles a year, due to the minimal amount that you are now driving, this can also cause your premiums to go down significantly. Finally, if you are going to school, you may qualify for lower rates simply because you are a student. This is something that you will need to show proof of in order to take advantage of the lower rates.
Combine Your Insurance Policies
Another great way to lower your premiums without having to do anything is to combine the different insurance policies that you have. If you currently have homeowners insurance and medical insurance with an insurance provider, and car insurance with a completely different company, you might want to ask the homeowners and health insurance provider if they offer vehicle insurance rates. By combining everything together you can qualify for a group rate which could lead to a substantial savings. This is a strategy that many people use just to make it easier to pay their bills, but it can also lead to lower premiums each and every month.
These are just a few of the many strategies that you can use when you are looking for cheap car insurance online. Your best bet is to utilize online services that can submit your request for a quote to multiple companies, and use one of the many that send their quote to you. As mentioned earlier, some of these businesses may not advertise heavily so you may not have heard of them before. You can always verify the authenticity of an insurance company by checking the Better Business Bureau, and if they check out, this is a great way to save hundreds or thousands of dollars every year on your auto insurance premiums. Hopefully these affordable vehicle insurance online tips will lead you to the best possible insurance provider that can give you the best coverage at the lowest possible rates in Palmer, MA.
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More Informaiton and Tips About Palmer, MA Car Insurance
Car insurance coverage is anything that everyone is needed by law to have, and the auto insurance businesses know this simple fact and take entire edge. If you happen to be hunting for automobile insurance coverage, you may have to be well prepared to offer with all varieties of cons and hidden troubles. Study on to discover out how.
Becoming a careful driver can actually conserve you money on insurance policies. Certainly, insurers would instead insure good motorists and will offer reduce rates for very good motorists, but did you know that creating an incident can make your insurance charges virtually double? It is abundantly obvious that driving safely is one of the greatest methods to hold your insurance policy rates low!
Another kind of car insurance policies protection in your policy, is healthcare coverage. This coverage normally takes treatment of your injuries and those accidents to other men and women in your car. Some states just make this a optional protection in your insurance policies. If you stay in a no-fault point out, health care payments are changed by private harm security.
There are several distinct kinds of car insurance coverage firms out there. Get prices from all of them to uncover out what is the ideal cost. Several businesses now provide rates on-line, in excess of the telephone, or you can go into any insurance coverage brokers business office and make an appointment to go in excess of your possibilities.
You can help your little one out by adding him/her to your vehicle insurance policies as an authorized person. If your kid is a very good driver, not only will he or she be in a position to help save funds on future policies, but the "authorized" label on the insurance coverage policy will also bode nicely for their credit history score, offering them a fantastic head begin in the credit score department.
When you carefully contemplate these guidelines, you will discover that your navigation and knowing of car insurance policies is now higher. Expertise is the most critical component of your encounter with automobile insurance policy. You have to have it, so it is well worth studying about. Now you have equipment you require for insurance coverage achievement.


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How can i run a jBPM process through job executor. Currently i am running the jBPM processes by executionService.startProcessInstanceByKey("abc"). This method is called in for loop to it is executing the jBPM processes sequentially. Is there any way i can store this process as job and will be later executed by job executor.
I have read to put about async continuations but i think it will be for activities. I want the Entire process should be executed by jBPM job executor.
I am using jbpm 4.3.
Any help would be highly appreciated.
Retrieving data ...


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Adding gifs to your pull requests (PRs) can get them approved faster. Gifs can also help your tickets or issues get accepted. It works as you are showing the code or issue in action. Ryan Kienstra will show you how.
Labs are hands-on coding projects that you build along with Tonya as she explains the code, concepts, and thought processes behind it. You can use the labs to further your code knowledge or to use right in your projects. Each lab ties into the Docx to ensure you have the information you need.
Each lab is designed to further your understanding and mastery of code. You learn more about how to think about its construction, quality, maintainability, programmatic and logical thought, and problem-solving. While you may be building a specific thing, Tonya presents the why of it to make it adaptable far beyond that specific implementation, thereby giving you the means to make it your own, in any context.
Getting Your PRs Merged Faster with Gifs
Git Hooks
Git gives us hooks in order to get our work done and further automate our process. In this hands-on coding lab, you will dive deep into the hooks that are available in git. When is it coming? This lab has been put on hold and will be added to a future workflow roadmap. Prerequisities What you will to need in order to maximize the benefits of this lab. Before you get started in this lab, we recommend the following: Have git globally installed and configured on your machine. Have a GitHub account. Have SSH setup on your machine and GitHub. […]
Alias – Delete Local and Remote Branch
In Git Contributing, you learned how to delete a local branch. The command of -D is fairly straightforward. But what if you want to delete both the local and remote branches. Let's build an alias.
Prep for Complex Aliases
In order to build complex aliases, we want to open up the global .gitconfig file in the text editor that is wired to git. Then we'll add some commenting to provide more context and details for our aliases. If you have not yet wired up your text editor to git, I highly….highly….highly recommend that you do so. Why? The main reason is for writing more detailed commit messages as well as doing rebasing too. Check out this lab for a Mac or Windows to wire yours up.
Git Productive
Let's tame git. Let's create a rich set of commands and shortcuts that make sense and are intuitive. Let's build a set of scripts that are callable by a single command, such as `git uncommit` or `git rollback`, i.e. commands that wrap up repetitive tasks and automate them via a single command. In this hands-on coding lab, you'll build a rich collection of these commands via git aliases and bash scripting to git you more productive.
Alias – Rollback to Last Commit
There are times when you are working on a change and then realize that you've gone in the wrong direction. At that point, you want to rollback your project back to the last commit, i.e. meaning you want to delete all of the changes and return your codebase back to the last commit. There are multiple steps to do this task as you need to delete everything in the staging and working areas. Let's build an alias.
Alias – Commit All Changes from Working and Staging
Recall from Simply Git and Git Contributing how to commit changes. It is a two-step process of adding the changes from working into staging and then running git commit to move from staging into the storage (commit) area. Git gives you a way to combine those steps into one step. Typically, my workflow is: Commit the changes Pop open the editor Add my commit message Clear off the command line console View the status display View the log That's a lot of steps to type over and over again. Let's build a complex alias to give us one command git […]
Alias – Rename Current Branch
Imagine that you are working along on a change and then decide you need to rename the branch. Git gives you an option to move a branch to a new branch. But like most git commands, it's not intuitive or rememberable. Let's build an alias.
Alias – Display Less Verbose Status
You know that you can use git status to view what is currently in the working and staging areas. In this episode, let's make an alias for a less verbose status.