Internal Representation Sample Clauses

Internal Representation. The most notable feature of saucy is its use of ordered partition pairs (OPPs), which are indexed pairs of partitions that keep track of which nodes can be validly mapped to other nodes. The search occurs by choosing an element of a ”top” partition and force it to map to a node in the ”bottom.” JAUNTY also represents intermediate permutations using using an Ordered Partitions Pair. Σ Σ Σ Σ An ordered partition π = [W1] [W2] . . . [Wm] of V is an ordered list of non- empty subsets that form a partition of V . The subsets Wi are called the cells of the partition. An Ordered partition is unit if it consists of exactly one cell, and discrete if every elements of v is in a distinct cell. An ordered partition pair Π can be denoted Π = πT = T1|T2| . . . |Tm B1|B2| . . . |Bk with πT and πB referring to the top and bottom, respectively. An OPP is isomor- phic if the top and bottom have the same number of cells, and |Ti| = |Bi| for all integers i, 1 ≤ i ≤ m, otherwise it is non-isomorphic. An OPP is discrete (resp. unit) if its top and bottom partitions are discrete (resp. unit). If an OPP is isomorphic, we can think of it as encoding a set of potential permu- tations, in particular those that send each element of Ti to some unique element of Bi for all integers i, 1 ≤ i ≤ m. Hence, a unit OPP represents Sym(V ) while a discrete OPP represents a single permutation. Non-isomorphic OPPs represent the empty set, because it is not possible to find a permutation in such an OPP. Σ Σ For a more in-depth survey of how OPPs are used, see Katebi et. al.[32]. A search tree is created by taking a single top element eT of some cell Ti, and then for each element eB of corresponding cell Bi, create a new branch with the new OPP being created by removing eT and eB and from their cells and placing them in new corresponding unit cells. So for example, if Π = 0, 1, 2 , then if Σ Σ eT = 0 and eb = 1, our resulting OPP is Π = 0|1, 2 , and the permutations 1|0, 2 it represents is {(0, 1), (0, 1, 2)}. The meaning of this is “element 0 is mapped to element 1.” This step is performed recursively until it results in a unit OPP. The only change between this and what JAUNTY does is that when we map literal x to literal y we also map ¬x to ¬y at the same time.
Sample 1
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Related to Internal Representation

  • General Representations Borrower represents and warrants to Lender as of the Closing Date that, except to the extent (if any) disclosed on Schedule III with reference to a specific subsection of this Section 3.1:

  • Additional Representation Section 3 is amended by the addition at the end thereof of the following additional representations (provided that the representation in Section 3(h) will be made by Party A only):

  • Financial Representations Included with the Pubco SEC Documents are true, correct, and complete copies of audited balance sheets for Pubco dated as of November 30, 2006 and unaudited balance sheets for Pubco dated as of August 31, 2007 (the “Pubco Accounting Date”), together with related statements of income, cash flows, and changes in shareholder’s equity for the fiscal year and interim period then ended (collectively, the “Pubco Financial Statements”). The Pubco Financial Statements: (a) are in accordance with the books and records of Pubco; (b) present fairly the financial condition of Pubco as of the respective dates indicated and the results of operations for such periods; and (c) have been prepared in accordance with GAAP. Pubco has not received any advice or notification from its independent certified public accountants that Pubco has used any improper accounting practice that would have the effect of not reflecting or incorrectly reflecting in the Pubco Financial Statements or the books and records of Pubco, any properties, assets, Liabilities, revenues, or expenses. The books, records, and accounts of Pubco accurately and fairly reflect, in reasonable detail, the assets, and Liabilities of Pubco. Pubco has not engaged in any transaction, maintained any bank account, or used any funds of Pubco, except for transactions, bank accounts, and funds which have been and are reflected in the normally maintained books and records of Pubco.

  • Additional Representations Section 3 is hereby amended by adding the following additional subsections:

  • Mutual Representations Each party hereby represents and warrants to the other party as follows:

  • 10b-5 Representation At the time of effectiveness of the Registration Statement (or at the time of any post-effective amendment to the Registration Statement) and at all times subsequent thereto up to the Closing Date and the Option Closing Date, if any, the Registration Statement, the Statutory Prospectus and the Prospectus do and will contain all material statements that are required to be stated therein in accordance with the Act and the Regulations, and did or will, in all material respects, conform to the requirements of the Act and the Regulations. The Registration Statement, as of the Effective Date and at the Applicable Time, did not, and the amendments and supplements thereto, as of their respective dates, will not contain any untrue statement of a material fact or omit to state any material fact required to be stated therein or necessary to make the statements therein not misleading. The Prospectus, as of its date and the Closing Date or the Option Closing Date, as the case may be, did not, and the amendments and supplements thereto, as of their respective dates, will not, include any untrue statement of a material fact or omit to state a material fact necessary in order to make the statements therein, in the light of the circumstances under which they were made, not misleading. The Statutory Prospectus, as of the Applicable Time (or such subsequent Applicable Time pursuant to Section 2.1.1), did not include any untrue statement of a material fact or omit to state a material fact necessary in order to make the statements therein, in the light of the circumstances under which they were made, not misleading. When any Preliminary Prospectus or the Statutory Prospectus was first filed with the Commission (whether filed as part of the Registration Statement for the registration of the Public Securities or any amendment thereto or pursuant to Rule 424(a) of the Regulations) and when any amendment thereof or supplement thereto was first filed with the Commission, such Preliminary Prospectus or the Statutory Prospectus and any amendments thereof and supplements thereto complied or will have been corrected in the Statutory Prospectus and the Prospectus to comply in all material respects with the applicable provisions of the Act and the Regulations and did not and will not contain an untrue statement of a material fact or omit to state any material fact necessary in order to make the statements therein, in the light of the circumstances under which they were made, not misleading. The representation and warranty made in this Section 2.2.1 does not apply to statements made or statements omitted in reliance upon and in conformity with written information furnished to the Company with respect to the Underwriters by the Underwriters expressly for use in the Registration Statement, the Statutory Prospectus or the Prospectus or any amendment thereof or supplement thereto. The parties acknowledge and agree that such information provided by or on behalf of the Underwriters consists solely of the following: the names of the Underwriters, the information with respect to stabilization transactions contained in the section entitled “Underwriting - Stabilization” and the identity of counsel to the Underwriters contained in the section entitled “Legal Matters” (such information, collectively, the “Underwriters’ Information”).

  • Basic Representations Section 3(a) of the Agreement is hereby amended by the deletion of “and” at the end of Section 3(a)(iv); the substitution of a semicolon for the period at the end of Section 3(a)(v) and the addition of Sections 3(a)(vi), as follows:

  • ERISA Representation (a) Each Lender (x) represents and warrants, as of the date such Person became a Lender party hereto to, and (y) covenants, from the date such Person became a Lender party hereto to the date such Person ceases being a Lender party hereto, for the benefit of, the Administrative Agent, each Arranger and their respective Affiliates, that at least one of the following is and will be true: (i) such Lender is not using “plan assets” (within the meaning of Section 3(42) of ERISA or otherwise) of one or more Benefit Plans in connection with the Loans, (ii) the transaction exemption set forth in one or more PTEs, such as PTE 84-14 (a class exemption for certain transactions determined by independent qualified professional asset managers), PTE 95-60 (a class exemption for certain transactions involving insurance company general accounts), PTE 90-1 (a class exemption for certain transactions involving insurance company pooled separate accounts), PTE 91-38 (a class exemption for certain transactions involving bank collective investment funds) or PTE 96-23 (a class exemption for certain transactions determined by in-house asset managers), is applicable with respect to such Lender’s entrance into, participation in, administration of and performance of the Loans and the Agreement, (iii) (A) such Lender is an investment fund managed by a “Qualified Professional Asset Manager” (within the meaning of Part VI of PTE 84-14), (B) such Qualified Professional Asset Manager made the investment decision on behalf of such Lender to enter into, participate in, administer and perform the Loans and the Agreement, (C) the entrance into, participation in, administration of and performance of the Loans and the Agreement satisfies the requirements of sub-sections (b) through (g) of Part I of PTE 84-14 and (D) to the best knowledge of such Lender, the requirements of subsection (a) of Part I of PTE 84-14 are satisfied with respect to such Lender’s entrance into, participation in, administration of and performance of the Loans and the Agreement, or (iv) such other representation, warranty and covenant as may be agreed in writing between the Administrative Agent, in its sole discretion, and such Lender. (b) In addition, unless either (1) sub-clause (i) in the immediately preceding clause (a) is true with respect to a Lender or (2) a Lender has provided another representation, warranty and covenant in accordance with sub-clause (iv) in the immediately preceding clause (a), such Lender further (x) represents and warrants, as of the date such Person became a Lender party hereto, to, and (y) covenants, from the date such Person became a Lender party hereto to the date such Person ceases being a Lender party hereto, for the benefit of, the Administrative Agent, each Arranger and their respective Affiliates, that none of the Administrative Agent, any Arranger or any of their respective Affiliates is a fiduciary with respect to the assets of such Lender involved in the Loans and this Agreement (including in connection with the reservation or exercise of any rights by the Administrative Agent under this Agreement, any Loan Document or any documents related hereto or thereto).

  • Legal Representation of the Parties This Agreement was negotiated by the parties with the benefit of legal representation, and any rule of construction or interpretation otherwise requiring this Agreement to be construed or interpreted against any party shall not apply to any construction or interpretation hereof.

  • ERISA Representations Each Note Owner that is subject to Title I of ERISA, Section 4975 of the Code or Similar Law, by accepting an interest or participation in a Note, is deemed to represent that its purchase, holding and disposition of that interest or participation is not and will not result in a non-exempt prohibited transaction under Title I of ERISA or Section 4975 of the Code due to the applicability of a statutory or administrative exemption from the prohibited transaction rules (or, if the Note Owner is subject to Similar Law, the purchase, holding and disposition is not and will not result in a non-exempt violation of that Similar Law).

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