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Justia › US Law › Case Law › Federal Courts › District Courts › District of Columbia › District of Columbia › 1973 › City of Petersburg, Virginia v. United States
City of Petersburg, Virginia v. United States, 354 F. Supp. 1021 (D.D.C. 1973)
US District Court for the District of Columbia - 354 F. Supp. 1021 (D.D.C. 1973)
354 F. Supp. 1021 (1972)
CITY OF PETERSBURG, VIRGINIA, municipal building, Petersburg, Virginia, Plaintiff,
UNITED STATES of America, and Richard G. Kleindienst, Attorney General of the United States, individually and in his official capacity, United States Department of Justice, Washington, D. C. 20530, Defendants, and Charles P. Royall et al., Defendant-Intervenors.
Civ. A. No. 509-72.
United States District Court, District of Columbia.
Judgment Affirmed March 5, 1973.
Mozart G. Ratner, Washington, D. C., John S. Davenport, III, Richmond, Va., for plaintiff.
*1022 Peter Mear, Atty., Department of Justice, Washington, D. C., for defendants.
W. H. C. Venable, Richmond, Va., for intervenors William Diamond et al.
Armand Derfner, Washington, D. C., for intervenors Royall et al.
Before MacKINNON, Circuit Judge, and GASCH and BRYANT, District Judges.
Judgment Affirmed March 5, 1973. See 93 S. Ct. 1441.
PER CURIAM:
The City of Petersburg, like all political subdivisions of the Commonwealth of Virginia, is required to clear changes in its voting procedures in accordance with Section 5 of the Voting Rights Act of 1965 as amended, 79 Stat. 439; 42 U.S.C. § 1973c.[1] The Supreme Court has held that annexations and the changes resulting therefrom may be within the scope of that Section where they have a potential for diluting the votes of black citizens. Perkins v. Matthews, 400 U.S. 379, 91 S. Ct. 431, 27 L. Ed. 2d 476 (1971). Accordingly, the City seeks Section 5 clearance for an annexation which added a net of approximately 7,000 white persons to the City, increasing the white population by nearly half and eliminating a black population majority.
On December 21, 1971, the City submitted its annexation to the Attorney General for approval pursuant to the 60-day provision of Section 5. On February 22, 1972, the Attorney General, acting through the Assistant Attorney General, Civil Rights Division, objected to the annexation in a letter to the attorneys for the City of Petersburg which stated that in view of the facts relating to Petersburg, particularly the use of at-large elections for City Councilmen, it was concluded that the reduction in the proportional voting strength of blacks by the addition of a large number of white residents, diluting the votes of black citizens, amounts to a discriminatory effect on voting under the Voting Rights Act.[2]
*1023 In this suit, filed on March 17, 1972, the City, as plaintiff, prays for this court's declaratory judgment that the change in its election procedures resulting from the annexation to the City of parts of two adjacent counties while retaining the at-large method of electing City Councilmen, "does not have the purpose and will not have the effect of denying or abridging the right to vote on account of race or color."[3]
On motion of the plaintiff City, the court on April 5, 1972, enjoined plaintiff and the Election Board of the City of *1024 Petersburg from conducting any election under Sections 2-1 and 2-3 of Chapter 259 of the Acts of Assembly of Virginia 1961, as amended, until further order of the court. Subsequently the court entered orders allowing Charles P. Royall, et al., and William Diamond, et al., leave to intervene. Trial was had on July 20 and 21, 1972. The evidence consists of several stipulations, various exhibits and testimony of witnesses presented both live and by deposition, and out of it most of the facts emerge practically undisputed.
Petersburg is an independent city in Virginia covering an eight-square-mile area, whose 1970 population was 36,103. In 1971 the City completed steps which it had begun five years earlier to annex 14 square miles of land from adjacent Prince George and Dinwiddie Counties[4] containing 7,323 persons, thus increasing the total population of the new city (as annexed) to 43,426. Before the annexation there were 19,701 (55%) black people, and 16,402 (45%) white people living in the City. Nearly all of the newly acquired group of persons are white and the new city limits include a population of 19,947 (46%) blacks and 23,447 (54%) whites. This amounts to an almost complete reversal percentage-wise in racial makeup.
Although the number of registered voters by race in the old City is not known, calculations based on 1970 census figures indicate that at that time blacks represented about 51% of the registered voters. The same calculations indicate that the annexed area will augment the number of white voters by about 4,800.
The annexation, whose effective date was midnight, December 31, 1971, had been generally supported by the citizens of Petersburg, black and white alike, since the mid-1960's, as a necessary measure to allow the City of expand its tax base and its potential for growth and development. The contours of the annexation were designed to bring in the territory which it was economically feasible to serve, and whose population shared a community of interest with the old City. Joseph H. Owens and Hermanze Fauntleroy, both black, were members of the City Council when it unanimously adopted the annexation ordinance in 1966. In fact, Owens originally introduced the ordinance. Fauntleroy, currently the only black Councilman, testified at the trial that he had no objection to the annexation as such, and regarded it as a feasible step for the City's development.
A map of the city and the surrounding areas is annexed.[5] From this exhibit and the testimony at trial we conclude that the annexation as carried out was fairly intended to accomplish a legitimate governmental purpose. The city limits were expanded into those areas which were most reasonably available and which were the most desirable for accomplishing the legitimate purposes of annexation. The annexation did not include other areas which would have required leaping over the Appomattox River and those lands devoted to Fort Lee (a U. S. Army camp), a state hospital and the adjoining city of Colonial Heights. Because of these barriers annexation beyond those areas was substantially less desirable and even if it had been extended into those areas along with the existing annexation, the racial balance would not have been altered materially over the present result. We thus find nothing in the annexation which indicated that it had a racial purpose.
*1025 Petersburg is governed by a City Council of five members.[6] Each member is elected to a four-year term; elections are at staggered intervals of two years, so that three members are elected in each presidential election year and two members are elected in each off year. In each off-year election the Council chooses one of its own members as mayor and also appoints the city manager. All Council members are chosen in at-large elections which are non-partisan, without political party identification, and the candidate must receive a majority of the votes cast to win. Run-off elections are not infrequent.[7]
As elsewhere in Virginia, there has been a long history of racial segregation and discrimination in the City of Petersburg. By various methods in the past blacks have been restricted in their ability to wield effective political influence in relation to their actual numerical strength by limitations on their voting and political participation which resulted from the operation of laws, customs, and official and individual behavior. Until recently, rigid patterns of segregation by law affected nearly every facet of life.
Although state-imposed segregation has been abated, its long continuance in the past caused a dramatic polarization of the races in Petersburg with respect to voting and this result has not been obliterated. An informal white political structure[8] has wielded a controlling influence in city politics and runs only white candidates.[9] Blacks have not been included in activities such as the slating of "tickets" of candidates for Council elections by community-wide groups or organizations and community-wide efforts in support of issues and programs. In recent years a black political structure has also arisen, and they likewise have run only black candidates. They have not sought to compose "slates" with white candidates.
The simple transformation of a potential black voting majority into a clear minority has no effect on relative racial voting strengths unless votes are cast along racial lines. Analysis of past election results clearly indicates that almost total bloc voting by race has been the well established pattern in Petersburg. In recent Council elections, in which both black and white candidates have participated, the vote in precincts which are racially identifiable as being almost completely black or white has been overwhelmingly along racial lines. This is clear from the following charts *1026 which reflect the results of the last four councilmanic elections.[10]
From this positive showing of racial bloc-voting in the wards which are identifiable as being almost totally black or white it may be inferred that the same type of voting occurs throughout the City of Petersburg in elections affecting local issues. There is no evidence which warrants a contrary conclusion.
It is noted, however, that Councilman Owens, a black, was elected in 1964, at a time when a majority of the registered voting strength of the city was white. In 1966, another black, Councilman Fauntleroy, was elected when the majority voting strength of the city was still white. In 1968, when there was a possibility that by re-electing Mr. Owens and electing another black candidate, the black members would control the council, there was an unusually large turnout of white voters in the white wards,[11] as a result of which Mr. Owens was defeated and the second black candidate also lost. From all the evidence, however, the conclusion is obvious that race has been a dominant factor in Petersburg elections where black candidates opposed white candidates.
The City Council of Petersburg, which has always had a majority of white members, has been generally unresponsive to some of the expressed needs and desires of the black community and has on some occasions rejected or failed to adopt programs, employment policies and appointments recommended by blacks. Without doubt, the same could be said of some programs, policies, and *1027 appointments recommended by some groups of white voters, but the small percentage of black city employees may indicate that black complaints in this respect have merit.[12]
Following annexation, the black member of the City Council, on his own behalf and for the black community, presented and supported a proposal to have members of the City Council elected from single-member districts, as opposed to election at-large. This proposal was made in an effort to reduce the dilutive effect the at-large election would have on black political strength.
We recognize that the election from single-member districts of a number of governmental representatives to a body composed of several members, rather than being elected at-large from the governmental unit, has the effect of making the representatives from the single districts more responsive to the special interests and characteristics of the individual district. Conversely, the election of all such representatives from the governmental unit at-large (as from an entire city) generally causes the representatives to be more responsive to, and characteristic of, the interests of the entire city. Representatives from single districts generally are more responsive to the special interests of their districts, and at-large representatives generally serve the entire community more effectively.
Plaintiff's answer to the proposal to switch to single-member districts is that the advantages of the at-large system when combined with the city manager form of government are so overwhelming that it should not be modified in any way, and that they outweigh any discriminatory effect or disadvantage which might result to the voting strength of blacks in Petersburg. We agree that an at-large system of electing city councilmen has many advantages over the ward system, and that the former method is better calculated to represent majority interests in a city, but the ward system also has some advantages in that it brings the councilman closer to his constituents. Also, to accede to plaintiff's contention in cases such as this would, as a practical matter, exempt all at-large city elections from the provisions of the Voting Rights Act. We do not find that Congress so intended.
In order to obtain the declaratory judgment sought, plaintiff must meet the burden placed upon it by the Voting Rights Act of proving by the preponderance of the evidence that its change in election procedures "does not have the effect of denying or abridging the right to vote on account of race or color."[13]
This is a heavy burden for a community in a state with Virginia's history of past racial discrimination. It requires the plaintiff to prove both that the changed election procedures
(1) Do not have the purpose of denying or abridging the right to vote on account of race or color, and that they
(2) Do not have the effect of denying or abridging the right to vote on account of race or color.
As we have stated, we do not find any evidence here that the changed procedure (the annexation) was for the purpose of denying blacks the right to vote on account of race or color. However, notwithstanding the absence of such evidence as to motivation or purpose, in order for plaintiff to prevail in this action it must prove the changes would not have the effect of discriminatorily *1028 depriving Negroes of the franchise on account of race or color.
It is clear that Congress has placed this burden upon the plaintiff. Congressman McCulloch, the ranking minority member of the House Judiciary Committee, in discussing the burden of proof in Section 5 actions when the 1970 amendments to Section 5 were under consideration, remarked on the floor of the House:
"The burden of proof under Section 5 is rightfully placed upon the jurisdiction to show that the new voting law or procedure is not discriminatory. As in tort law, when circumstances give rise to an inference that there has been misconduct, the party that has access to the facts is called upon to rebut the inference and show that its conduct was proper." (115 Cong. Rec. 38486, December 11, 1969, emphasis added).
In the Senate, similar remarks were made by Senator Fong:
"There are crucial features of strength contained in Section 5 that I wish to underscore. The first is that the burden of proof is placed upon the jurisdiction to show that the new voting law or procedure does not have the purpose or effect of discriminating. Those who know the law or procedure best and what motivated its passage must come forward and explain it." (116 Cong.Rec. 6154, March 5, 1970, emphasis added).
"This section, in effect, freezes election procedures in the covered areas [Virginia included] unless the changes can be shown to be nondiscriminatory."[14] Opponents of the legislation properly characterized the burden of proof placed on affected governmental units in the covered areas as raising a "presumption of illegality" with regard to changed election procedures;[15] and in South Carolina v. Katzenbach, 383 U.S. 301, 335, 86 S. Ct. 803, 822, 15 L. Ed. 2d 769 (1966), the Supreme Court recognized that the statute placed "the burden of proof on the areas seeking relief" and there was "nothing inappropriate" in this. Gaston County v. United States, 395 U.S. 285, 293, 89 S. Ct. 1720, 23 L. Ed. 2d 309 (1969), is to the same effect.
Plaintiff has not met this burden.
The annexation of parts of Dinwiddie and Prince George Counties to the City of Petersburg dilutes the weight, strength and power of the votes of the black voters in the City, with a concomitant effect upon their political influence which is a part of the bundle of individual rights embodied in the franchise as recognized and guaranteed by the Constitution. Perkins v. Matthews, 400 U.S. 379, 388, 91 S. Ct. 431, 27 L. Ed. 2d 476 (1971);[16] Allen v. State Board of *1029 Elections, 393 U.S. 544, 569, 189 S. Ct. 817, 22 L. Ed. 2d 1 (1969); Burns v. Richardson, 384 U.S. 73, 88, 86 S. Ct. 1286, 16 L. Ed. 2d 376 (1966);[17] Reynolds v. Sims, 377 U.S. 533, 555, 84 S. Ct. 1362, 12 L. Ed. 2d 506 (1964).[18] The dilution here has occurred as a result of the annexation in the context of at-large elections and bloc-voting by race, and under these circumstances it abridges the right to vote on account of color by impairing the ability of blacks to elect candidates of their choice and to have their ideas on political matters afforded the recognition to which they are entitled on their merits and by virtue of their individual citizenship and their numerical strength in the community.
The Diamond intervenors, who limited their participation in the case to the submission of a post-trial memorandum and oral argument, raise an additional issue on the basis of evidence submitted by the other parties. They contend that the annexation per se, even with a shift to a ward voting system for councilmanic elections, cannot properly be approved by this Court in a declaratory judgment proceeding under the Voting Rights Act.
First, they argue that this Court's power under the Act is limited in this case to either approving or disapproving the annexation without taking into account the context in which it occurs or any feasible means by which the plaintiffs could annex the areas in question without violating the Act. Second, these intervenors contend that even if this Court does have the power to approve the annexation subject to a change from an at-large to a ward voting system for councilmanic elections, it should not approve this annexation on any conditions for the reason that the election of each of the six "constitutional officers"[19] is necessarily at-large, and would be unaffected by any shift to a ward system for the councilmanic elections. The Court cannot agree with either contention.
In the first place, the Diamond intervenors overlook the fact that by requiring plaintiff to shift to a ward voting system for its councilmanic elections, the Court is not, as these intervenors argue, bringing "into play" its "broad equity power." Rather, it is simply declaring that the Petersburg annexation in the context of an at-large voting system would amount to an expansion of an at-large voting system, and that the expansion, on the evidence in this case, is a change in a "practice or procedure with respect to voting" which will have the effect prohibited by the Act. The basis for this conclusion has already been set forth in this opinion.
*1030 The second contention requires somewhat fuller discussion. In particular, it requires consideration of the purpose of Congress in enacting Section 5 of the Voting Rights Act. Congress deliberately used broad language so as to bring under federal scrutiny the many different means by which jurisdictions in the areas covered by the Act might seek to evade the requirements of the Fifteenth Amendment.[20] The breadth of this coverage has been clearly delineated by the Supreme Court in Perkins v. Matthews, 400 U.S. 379, 91 S. Ct. 431, 27 L. Ed. 2d 476 (1971), and Allen v. State Board of Elections, 393 U.S. 544, 89 S. Ct. 817, 22 L. Ed. 2d 1 (1969). Similarly, Congress used general, although clear, language in describing the kinds of changes in voting practices or procedures which were forbidden under the Act. They are those which have the purpose or effect of "denying or abridging the right to vote on account of race or color." 79 Stat. 439, 42 U.S.C. § 1973c. It is left for a three-judge court to determine whether a given change constitutes the kind of denial or abridgment which Congress had in mind. The plaintiff, as already noted, carries the burden of proving that its proposed change does not fall within this category.
If the view of the Diamond intervenors concerning what constitutes a denial or abridgment in annexation cases were to prevail, no court could ever approve any annexation in areas covered by the Voting Rights Act if there were a history of racial bloc-voting in local elections for any office and if the racial balance were to shift in even the smallest degree as a result of the annexation.[21] It would not matter that the annexation was essential for the continued economic health of a municipality or that it was favored by citizens of all races; because if the demographic makeup of the surrounding areas were such that any annexation would produce a shift of majority strength from one race to another, a court would be required to disapprove it without even considering any other evidence, and the municipality would be effectively locked into its original boundaries. This Court cannot agree that this was the intent of Congress when it enacted the Voting Rights Act.
In support of their position the Diamond intervenors cite Gomillion v. Lightfoot, 364 U.S. 339, 81 S. Ct. 125, 5 L. Ed. 2d 110 (1960). Certainly they are correct in looking to Supreme Court decisions in Fifteenth Amendment cases to cast light upon the nature of the discrimination which the Voting Rights Act is designed to eliminate.[22] However, this reliance on Gomillion is misplaced, for the facts in the instant case are very different from the naked racial gerrymander with which Gomillion dealt.[23] Plaintiff's compelling evidence demonstrating the necessity for this annexation stands in sharp contrast to its plausible but clearly disputable arguments in favor of retaining an at-large voting *1031 system for the councilmanic elections and thereby creating the clear possibility of totally excluding black citizens from participation in the city government.
The Court concludes then, that this annexation, insofar as it is a mere boundary change and not an expansion of an at-large system, is not the kind of discriminatory change which Congress sought to prevent; but it also concludes, in accordance with the Attorney General's findings, that this annexation can be approved only on the condition that modifications calculated to neutralize to the extent possible any adverse effect upon the political participation of black voters are adopted, i. e., that the plaintiff shift from an at-large to a ward system of electing its city councilmen.
In coming to this conclusion with respect to the argument of the intervenors as to the constitutional officers, we take note of several factors:
First, the statute places the responsibility of the initial decision in the Attorney General and he has objected to the voting changes only insofar as they apply to the at-large election of councilmen. His interpretation of this section of the statute, as applied to the facts of this case, is entitled to deference.[24] Also, a substantial number of black citizens approve of the annexation with the change to the ward system.
Second, the voters added to the City of Petersburg by the annexation never previously voted for any city officers. Hence their inclusion in the voting population of the city was a substantial departure from past practices. However, we conclude from the governmental organization of the State of Virginia that these annexed voters did previously vote for "constitutional officers" in their previous district.[25] So in this respect, the annexation was more in the nature of a reapportionment and no evidence was introduced that the change in apportionment created an unfair situation.
Third, to change to the ward system of electing councilmen will most certainly result in a present increase in black representation on the City Council that has every prospect of being permanent. Thus, the force of black voting strength will be increased over the results they have been able presently to achieve even with a majority of the voters. We recognize that it is arguable that black citizens might be able to obtain even greater representation in old Petersburg if the annexation were prohibited, but the smaller city would not be as viable a political unit and the percentage figures which represent the relative voting strengths of the two races after the annexation are not so disparate that, given the proven defection from absolute bloc voting that exists here, the resulting representation and government would not be fairly representative of both races. Under the annexation, the relative voting strengths of the two races are close to being equal and control of the City Council could go either way and might shift from election to election, depending on the interests of the voters in any given election, the qualifications of the candidates, and the apportionment of the Council districts.
None of these factors are dispositive in themselves, but taken together we believe they support our conclusion, which affirms the decision of the Attorney General.
Accordingly, the declaratory judgment sought by plaintiff is denied. Counsel will submit an appropriate order. We retain jurisdiction of the case to consider any matters which may arise in the future under our decision. *1032
[1] 42 U.S.C. § 1973c (1970) provides:
Whenever a State or political subdivision with respect to which the prohibitions set forth in section 1973b(a) of this title based upon determinations made under the first sentence of section 1973b(b) of this title are in effect shall enact or seek to administer any voting qualification or prerequisite to voting, or standard, practice, or procedure with respect to voting different from that in force or effect on November 1, 1964, or whenever a State or political subdivision with respect to which the prohibitions set forth in section 1973b(a) of this title based upon determinations made under the second sentence of section 1973b(b) of this title are in effect shall enact or seek to administer any voting qualification or prerequisite to voting, or standard, practice, or procedure with respect to voting different from that in force or effect on November 1, 1968, such State or subdivision may institute an action in the United States District Court for the District of Columbia for a declaratory judgment that such qualification, prerequisite, standard, practice, or procedure does not have the purpose and will not have the effect of denying or abridging the right to vote on account of race or color, and unless and until the court enters such judgment no person shall be denied the right to vote for failure to comply with such qualification, prerequisite, standard, practice, or procedure: Provided, That such qualification, prerequisite, standard, practice, or procedure may be enforced without such proceeding if the qualification, prerequisite, standard, practice, or procedure has been submitted by the chief legal officer or other appropriate official of such State or subdivision to the Attorney General and the Attorney General has not interposed an objection within sixty days after such submission, except that neither the Attorney General's failure to object nor a declaratory judgment entered under this section shall bar a subsequent action to enjoin enforcement of such qualification, prerequisite, standard, practice, or procedure. Any action under this section shall be heard and determined by a court of three judges in accordance with the provisions of section 2284 of Title 28 and any appeal shall lie to the Supreme Court.
[2] Letter of February 22, 1972:
Dear Mr. Davenport:
This is in reference to your submission under Section 5 of the Voting Rights Act of 1965 of the 1971 annexation to the City of Petersburg, Virginia . . . .
In examining an annexation under Section 5 of the Voting Rights Act, it is incumbent on the Attorney General to determine whether the annexationeither in purpose or effectresults in racial discrimination in voting. In making this evaluation we apply the legal principles which the Courts have developed in the same or analogous situation. Moreover, it is also significant that Section 5 only prohibits implementation of changes affecting voting and provides that such changes may not be enforced without receiving prior approval by the Attorney General or by the District Court for the District of Columbia. Our proper concern then is not with the validity of the annexation but with the changes in voting which proceed from it.
In the case of Petersburg, we can summarize our consideration as follows: The pre-annexation population of Petersburg was made up of 56 percent black citizens and 44 percent white citizens. The city's seven-member governing body was elected at large on a plurality basis. As part of its deliberations the council considered and voted down a proposal that the election of its members be revised so that each would be elected by and would represent a separate district. The annexation was generally supported by both black and white groups, with the exception that some black groups contended that the city should be subdivided into districts to prevent post annexation dilution of the black vote.
The city was expanded by 14 square miles and some 7,000 persons, nearly all of whom were of the white race. The present population is 47 percent black and 53 percent white. The number of councilmen was expanded from five to seven, all of whom are to be elected at at large.
Unquestionably, the above facts indicate that the proportional voting strength of blacks has been reduced. The issue is whether this reduction amounts to a discriminatory effect on voting within the meaning of the Voting Rights Act. We conclude that it does. The reason lies not in the fact of annexationCongress certainly did not intend for all southern cities to be prevented from annexing any territory. Rather, in re-adopting the at large election system in the context of a significant change of populationfrom black to white majorityand simultaneously rejecting a proposed ward system, the potential for an adverse and discriminatory voting effect has been written into the Petersburg election law. While the reasons the city advances for using an at large system are credible and would normally present no special problem, in the particular context of Petersburg we are unable to conclude that the at large feature will not have a discriminatory effect on voting rights. Therefore, under the Voting Rights Act we must register objection to its implementation. See Holt v. City of Richmond [334 F. Supp. 228] (E.D.Va., Civil Action No. 151-71-R).
I wish to stress that this ruling relates only to the voting changes occassioned by the annexation. This objection to the implementation of such changes does not affect the validity of the annexation itself. As the Court in the Holt case ruled, one way to meet this problem would be to hold separate at large elections for a proportional number of councilmen in the pre-annexation of annexed areas. Another would be to adopt a fairly drawn system of single member wards. The Attorney General will consider withdrawal of this objection if these or other modifications calculated to insure against a racial effect on voting are adopted.
Of course, as provided by Section 5, you have an alternative of instituting an action in the United States District Court for the District of Columbia for declaratory judgment that the changes do not have the purpose and will not have the effect of denying or abridging the right to vote on account of race or color.
Sincerely, /s/ David L. Norman DAVID L. NORMAN Assistant Attorney General Civil Rights Division
[3] See note 1, supra.
[4] In Virginia, the area embraced within the limits of a city does not include any land within the limits of a county.
[5] See attached copy of Plaintiff's Exhibit 1-D.
[6] In 1972 the Virginia legislature approved an increase in the size of the Council from five to seven members. This was accomplished by passage of a special act, which is the way such matters are handled in Virginia.
[7] In a run-off election where more than one official is to be elected, a plurality of the vote is sufficient for election.
[8] There was no evidence that this was a formal organization or other than the usual type of informal group of like-minded citizens who generally come together, as elsewhere in the United States, when political elections are in the offing. Testimony showed, however, that the current Democratic Central Committee was composed of 19 white members and 13 black members. The City Council election is nonpartisan.
[9] In the city election of 1970, when two Councilmen were to be elected, persons active in the white political structure did inquire of Councilman Fauntleroy as to whether he would be interested in running on a slate with a white candidate. This inquiry included a question as to whether he would be the only black candidate. This discussion was inconclusive and nothing further developed
[10] Returns of the 1971 House of Delegates election do not indicate otherwise. The black candidate in that election was duly nominated, but her name did not appear on the official printed ballot, and she ran unsuccessfully as a write-in candidate. Under these circumstances, while the results might have some tendency to indicate bloc-voting, the evidence does not support such a conclusion because the result may have been caused by the absence of her name on the printed ballot, by her name not being well known uniformly throughout the city, or by the nature or extent of her campaign.
Total Votes                % of Votes              Total Votes             % of Votes              Total
Ward           Cast for Black             Cast for Black          Cast for White          Cast for White            Votes
No.   Candidate(s)   Candidates   Candidates   Candidates   Cast
CHART 1, 1964 CITY COUNCIL GENERAL ELECTION
3* (black)           339                       82.3%                       73                    17.7%                    412
6    "               356                       81%                         85                    19%                      441
7 (white)            110                        2.7%                    3,949                    97.3%                  4,059
8    "                14                        3.2%                      713                    96.8%                    727
3 (black)            811                       93.8%                       53                     6.2%                    864
6    "               883                       92.8%                       69                     7.2%                    952
7 (white)             70                        1.9%                    3,663                    98.1%                  3,733
3 (black)            725                       96.9%                       56                     3.1%                  1,781
6    "               951                       96.7%                       67                     3.3%                  2,018
8    "                16                         .7%                    2,179                    99.3%                  2,195
* Population of Wards 3 and 6, by race, is 42 whites and 10,547 Negroes. Ward 7 has 7,373 whites
and 20 Negroes. Ward 8 has 1,796 whites and 2 Negroes.
[11] And, presumably, elsewhere in the city.
[12] General testimony at trial on black employment in the city government revealed the following: 1 out of 70 in the Fire Department; 1 or 2 out of 150-200 clerical positions in City Hall; several in Welfare and very few (1 or 2) in any position of responsibility (Tr. 314-316). There was also expressed a dissatisfaction with black representation on the School Board (Tr. 306-310).
[13] See note 1, supra. The constitutionality of this burden was upheld in South Carolina v. Katzenbach, 383 U.S. 301, 331-332, 86 S. Ct. 803, 15 L. Ed. 2d 769 (1966).
[14] Joint Views of 10 Members of the [Senate] Judiciary Committee Relating to Extension of the Voting Rights Act of 1965, printed at 116 Cong.Rec. 5519, March 2, 1970.
[15] H.R.Rep.No.91-397, 91st Cong., 1st Sess. 14 (1969) (separate view of Rep. Poff, R.Va.). "A Federal law which raises a presumption of illegality against a law newly enacted by a State legislature and suspends its operation until the State comes to the Attorney General or a Federal court and proves its legality offends State sovereignty." (Emphasis added.)
[16] "Changing boundary lines by annexations which enlarge the city's number of eligible voters also constitutes the change of a `standard, practice, or procedure with respect to voting.' Clearly, revision of boundary lines has an effect on voting in two ways: (1) by including certain voters within the city and leaving others outside, it determines who may vote in the municipal election and who may not; (2) it dilutes the weight of the votes of the voters to whom the franchise was limited before annexation, and `the right of suffrage can be denied by a debasement or dilution of the weight of a citizen's vote just as effectively as by wholly prohibiting the free exercise of the franchise' . . . ." 400 U.S. at 388, 91 S. Ct. at 437.
[17] "Where the requirements of Reynolds v. Sims are met, apportionment schemes including multi-membered districts will constitute an invidious discrimination only if it can be shown that `designedly or otherwise, a multi-member constituency apportionment scheme, under the circumstances of a particular case, would operate to . . . cancel out the voting strength of racial or political elements of the voting population.'" 384 U.S. at 88, 86 S. Ct. at 1294.
[18] "And the right of suffrage can be denied by a debasement or dilution of the weight of a citizen's vote just as effectively as by wholly prohibiting the free exercise of the franchise." 377 U.S. at 555, 184 S. Ct. at 1378. In South v. Peters, 339 U.S. 276, 279, 70 S. Ct. 641, 94 L. Ed. 834 (1950), Justice Douglas, in dissent, stated:
"The right to vote . . . includes the right to have the vote counted at full value without dilution or discount. That federally protected right suffers substantial diminution . . . [where a] favored group has full voting strength . . . [and] [t]he groups not in favor have their votes discounted."
[19] These officers are those whose election is provided for in the Virginia Constitution. They are: Commonwealth's Attorney, the City Treasurer, the Commissioner of Revenue, the Sheriff, the High Constable, and the Clerk of Courts.
[20] See, e. g., the remarks of Senator Hart, 111 Cong.Rec. 8303, and of Senator Tydings, 111 Cong.Rec. 10725-27 concerning the problem of changes made by Southern states and municipalities in an effort to circumvent the vindication of the Fifteenth Amendment rights of their black citizens.
[21] It should be noted that a literal reading of the Act, coupled with a mechanistic approach to determining whether the franchise has been denied or abridged would require a court to disapprove an annexation which shifted the population ratio from a white to a black majority.
[22] The Act was enacted pursuant to Congressional power to enforce the guarantees of the Fifteenth Amendment. South Carolina v. Katzenbach, 383 U.S. 301, 308, 86 S. Ct. 803, 15 L. Ed. 2d 769 (1966).
[23] The Gomillion court observed that the redrawing of boundaries was, if petitioners' allegations were true, "solely concerned with segregating white and colored voters by fencing Negro citizens out of town so as to deprive them of their preexisting municipal vote." 364 U.S. 339, 341, 81 S. Ct. 125, 5 L. Ed. 2d 110 (1960).
[24] Perkins v. Matthews, 400 U.S. 379, 390-391, 91 S. Ct. 431, 27 L. Ed. 2d 476 (1971).
[25] Const. of Va. (1902) §§ 110, 118, 119, 120; Code of Va. (1950) § 24-156; cf. Const. of Va. (1971), Art. VII, Sched. §§ 2, 3.


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Get Email Updates | Low Bandwidth |
Murray, Cantwell Announce New Center of Excellence Funding
Research hub authorized in new FAA bill would propel research and development of aviation biofuels and other alternative aviation fuels
(Washington, D.C.) – Today, U.S. Senators Patty Murray (D-WA), Chair of the Senate Transportation, Housing, and Urban Development (THUD) Appropriations Subcommittee, and Maria Cantwell (D-WA), chair of the Aviation Subcommittee of the Senate Commerce Committee, announced the inclusion of funding in the Fiscal Year 2013 Senate THUD Appropriations Bill to establish a new Center of Excellence in Alternative Jet-Fuel Research in Civil Aircraft. Cantwell wrote language in the recently passed Federal Aviation Administration Reauthorization bill that authorizes the creation of the Center of Excellence. In February, Cantwell toured a Tri-Cities biofuel lab and called on the FAA to move forward on creating the new aviation biofuel research hub.
The THUD language included by Murray directs the FAA to establish the new Center of Excellence by identifying an educational and research institution after a competitive process.
"This investment in biofuel production research is an excellent opportunity for Washington state," said Sen. Murray. "I was proud to include the funding in the THUD Appropriations Bill and believe this Center will not only help ensure Washington state remains a national leader in renewable energy research and development, but will create jobs and economic growth, foster energy independence, and promote critical environmental sustainability."
"Washington state is uniquely positioned to lead the aviation biofuel industry," Cantwell said. "We have the entire biofuel supply chain in Washington state, from the growers, research institutions and businesses that grow, develop, refine, and use aviation biofuel. We fought hard to get this new biofuel research center authorized in the recently enacted FAA reauthorization because green jet fuel means jobs. This new center of excellence will jumpstart the research and development of 21st century fuel to power airplanes and drive innovation."
With its agricultural land to grow biomass and cutting-edge labs to research and develop new ways to create biofuels, the Pacific Northwest is poised to play an important role in future biofuels research efforts.
Washington state is home to leaders in the research, development and use of aviation biofuels. Notable successes include:
In July 2010, Boeing, Alaska Airlines, the operators of the region's three largest airports – Port of Seattle, Port of Portland and Spokane International Airport, and Washington State University launched Sustainable Aviation Fuels Northwest. The coalition is the nation's first regional stakeholder effort to explore the opportunities of aviation biofuels.
In September 2011, a research team led by WSU received $40 million USDA grant to convert closed timber mills into bioenergy development centers. The UW also received a $40 million USDA grant to research the use of sustainably grown woody energy crops to produce bio-gasoline and renewable aviation fuel.
Imperium Renewables of Grays Harbor, Washington and Pacific Northwest National Laboratory (PNNL) are collaborating on a catalytic process being developed at the lab that converts biomass-based alcohols into renewable drop-in jet fuels.
In November 2011, Alaska Air conducted 75 commercial flights over a two-week period in which each plane used a 20 percent mixture of aviation biofuel.
Permalink: https://www.murray.senate.gov/public/index.cfm/2012/4/murray-cantwell-announce-new-center-of-excellence-funding

redpajama_set_name: RedPajamaCommonCrawl


text:
Police: Drunk Groton driver had illegal fireworks; Ithaca driver had heroin
by Jeff Stein October 14, 2014 October 14, 2014
Ithaca, N.Y. — State police announced two separate arrests of intoxicated drivers on Tuesday.
The sheriff's office had announced two others on Monday.
1 — DWI, fireworks
On Sunday, troopers arrested a Groton man for Driving While Intoxicated — his Blood Alcohol Content was .15%, nearly twice the legal limit, they said.
Anthony J. Beeman, 30, was also found to have illegal fireworks, according to state police. He was arrested after police responded to a speeding call.
Beeman will appear in court on Oct. 20.
2 — DWI, drugs
Also on Saturday, state police in Homer arrested an Ithaca man for Driving While Ability Impaired by Drugs.
Eric J. Tenorio, 41, also faces the charge of seventh-degree possession of a controlled substance. Tenorio is accused of having a small amount of heroin.
Police responded to the Interstate 81 exit 12 ramp to find a three-vehicle accident. Tenorio was accused of causing the accident by following too closely and arrested.
Tenorio will appear in court Oct. 27.
3 — Town of Ithaca arrest
On Saturday at 1:38 a.m., police stopped a 2008 Subaru traveling south in the northbound lane on East Shore Drive in the Town of Ithaca.
Jeannette E. Luther, 29, of Spencer, was arrested
Luther was charged with two counts of Driving While Intoxicated and Failure to Remain in a Designated Lane.
"Luther was released and is to appear in the Town of Ithaca Court on November 5, 2014 at 4:00 PM," police say.
4 — Newfield DWI
On Friday at 12:58 a.m., deputies saw a 2006 Nissan fail to remain in the correct lane on Town Line Road in Newfield.
Philip R. Hasley, 22, of Newfield was arrested and charged with three counts of driving while intoxicated and moving from a designated lane unsafely.
He will reappear in court on Oct. 30.
Follow The Ithaca Voice on Facebook | Twitter
Tagged: city, news
Jeff Stein is the founder and former editor of the Ithaca Voice.	More by Jeff Stein


This site was created in January 2016 by Skipp Topp and friends, and made possible thanks to our sponsors and many generous donors who were gracious enough to contribute money through a crowdfunding campaign to help us to obtain copies of the Steven Avery trial transcripts and case file documents from Manitowoc County, Wisconsin. Like many others, we became aware of and interested in the Steven Avery case after seeing the very popular Netflix series Making a Murderer, and we wanted to know more about what really happened in the trial.
State of Wisconsin v. Avery, Steven A.
All of these trial records were paid for through our crowdfunding campaign, with the exception of a handful of documents/photos that were either obtained and posted online by others or sent to us for publication on this site. As of May 2016 we have nearly 250 exhibit photos and 450 documents from the investigation and trial, totaling over 15,000 pages!


text:
Q: Data from database into an array <?php defined('WROOT') OR die('No direct script access.');

var_dump($channels_cat);

return array(
'category' => array(
      19 => array(
        'name' => 'Cars',
        'class' => 'channel17',
        'slug' => 'cars'
    ),
       4 => array(
        'name' => 'Food',
        'class' => 'channel2',
        'slug' => 'Food'
    ),

    19 => array(
        'name' => 'Fruit',
        'class' => 'channel7',
        'slug' => 'fruit'
    ),
)
);

$channels['category']= db()->read('SELECT * FROM category ORDER BY priority ASC')->fetchAll();
foreach ($channels['category'] as $value):
$channels_cat[$value->category] =  $value->title;
endforeach;
var_dump($channels_cat);

Well, I have this array created by me. I want to create another identical but using data from the database. In the database is 19, 4, 15 (IDs) and cars, fruit and food (category title) . I tried several times, but I failed.

A: How are you accessing the database?

mysql_query("SELECT * FROM `some_database` WHERE id = '19' AND id = '4' AND id = '15'");

redpajama_set_name: RedPajamaStackExchange


, choices the very best collections along with greatest quality just for you, and now this photographs is actually considered one of images collections in this finest graphics gallery about Best Of Image Of Medical Receptionist Resume Examples. I really hope you might as it.
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Name now and the restoration process will probably be underway by the time you dangle up the cellphone. be sure that your pet is inspected when you arrive at your vacation spot airport and obtain a document confirming the inspection. Come work with our workers and dogs on enhancing adoptability. We are going to show you methods to help our canine overcome their issues to assist them get adopted! Must attend a common orientation previous to participating. Class meets periodically and dates are posted on our Facebook page - or you can contact volunteer@ for info on when the next class might be held.
A pop-up informs you of your new pet within the steady. If you already have a pet of that type, a pop-up informs you of this, and the egg and potion should not used. Every egg and hatching potion mixture can solely be used twice (apart from Era 1 pets should you use the Key to the Kennels ). The first time provides you the pet that may be fed and raised to a mount The second time gives you a pet which cannot be fed. You'll be able to solely have one pet and one mount of every type. A 2013 study printed in Physiology and Habits discovered that cats who did not like the sensation but allowed their house owners to stroke them anyway had been more pressured-out than those who averted contact.
Our shelter dogs go through a systematic habits evaluation during which they're screened for friendliness to people, pleasure levels, concern, aggression, and how effectively they know cues. I don't know why you probably did that. As an alternative, get me outdoors as quickly as doable and praise me whenever I pee open air. One thing is stressing me out. It might be a brand new particular person, a brand new pet, or even a new piece of furniture in the home that seems to be encroaching on my territory. When temperatures plunge below zero, owners of enormous animals and livestock producers need to give additional consideration to their animals. Prevention is the important thing to coping with hypothermia, frostbite and other chilly weather accidents in livestock.
Once I was youthful I used to be homeless with my two canine and cats. We we're residing in tents and out of doors in all the elements. The entire time I made certain that my infants had been fed, watered, and taken care of earlier than myself. When my canine acquired Lyme disease during that time I assumed she wasn't going to pull by way of and it broke my coronary heart. She made an enormous turn round thankfully but I actually gave up cash for myself to eat for them to and never as soon as thought twice about myself over my companions. Now years later three of them have crossed the rainbow bridge and the one pup that I nearly lost while homeless remains to be thriving and the happiest chunky lab/Shepard you may ever meet who is the sweetest to my kids and reminds me by means of it all she stuck it out with me. Providing help is essentially the most coronary heart warming thing I can see after being in that place at one time. Thanks women for what you are doing it really means lots to these in that place in life.


Paint booth filters are designed specifically for paint booth operations, are widely used in automotive, railway, machinery, metal and wood producing industries.
As a manufacturer, Clean choose the best raw materials and offer the utmost quality paint booth filters to our customers at competitive prices.
providing a perfect spraying environment and are the key to quality paint jobs and healthy workshops, Paint booth filters are more and more population in industrial spray applications.
Our paint booth filters are including but not limit below.


My soaps are homemade by me with the finest ingredients. I only use natural & organic ingedients and any botannicals used are grown in my organic pesticide free garden.
Ingredients: Pure Olive Oil, Distilled Water, Mica, Essential Oil, Coconut Oil, White Kaolin Clay, Rice Bran Oil, Jojoba Oil, Titanium Dioxide.


Thanks, debralinker, for including my chocolate mint plant in her treasury!
Congrats! I love chocolate mint and I am catching a whiff in my mind.
How could I NOT include you? Your FABULOUS!
Thanks for posting about the treasury! Go MMG BNR!


text:
Q: Joomla 2.5 -adding extra fields to article TUTORIAL: http://docs.joomla.org/Adding_custom_fields_to_the_article_component
When following this tutorial, and actually uploading the included ZIP file as a plugin and enabling it, I am not able to get the extra fields to show up like in the tutorial anywhere!
I am using 2.5.19. Any ideas?
Thanks in advance.

A: Forgot to install patches 28770 and 28771
http://joomlacode.org/gf/project/joomla/tracker/?action=TrackerItemEdit&tracker_id=8103&tracker_item_id=28771


All pupils from P4-7 are on one of our Pupil-led committees. Pupils choose at the start of each year which Committee they would like to serve on. Pupils from P1 -3 classes have representatives in both the Pupil Council and Eco-Committee.
Teaching staff facilitate the committee meetings which are held on a weekly basis.


Facebook's controversial software app for kids, Messenger Kids, is introducing a new feature that will allow the kids to find their friends on the app easily. The parents will finally have to approve of whether the friendship is acceptable on the app but the app has relaxed its stance somewhat.
The parents will have to switch on this feature as this will be off by default. Once the feature is enabled, the app will generate a four-word phrase that is distinct and unique for each kid. So, if a kid wants to add a friend in his contact list he or she will have to reveal this phrase to the friend they want to add. This phrase will then be entered in the friends' app. Both the parents will then be alerted about the development and both parents will have to accept the request to finish the process. The kids can then start chatting.
This does make it easier to find friends even if their parents are not friends themselves on the social networking app. This was the issue before. Though there is some relaxation in terms of finding friends, the parents are still very much in control.


text:
Avengers: Endgame best and worst -- our global review
The CNET global crew reacts to the final chapter in the Marvel Cinematic Universe. Sheer perfection or a waste of time? Spoilers ahead!
April 27, 2019 12:32 p.m. PT
Everybody's talking about Avengers: Endgame. And here at CNET, we're no exception. Our global team is bursting with opinions -- was Endgame a perfect final chapter to the Marvel Cinematic Universe, or a plot-hole-riddled waste of time?
If you haven't seen it, check out our spoiler-free review. And if you have, read on for a range of thoughts...
Core characters
Comic book events are often messy, convoluted affairs, and it would've been so easy for Avengers: Endgame to fall into that trap. Luckily, the Russo brothers focused on the characters we've come to love over the last 11 years. Their emotional journeys anchor this wild adventure. Each of the core Avengers gets at least one fist-pumping standout moment, and I even got choked up a few times. I was confident this movie would at least reach the dizzying heights of Infinity War, but somehow it managed to exceed that superhero masterpiece.
-- Sean Keane (London)
An offer you can't refuse
I expected Endgame would be The Godfather II to Infinity War's The Godfather, on par in quality if not better. I was very wrong. Endgame is like watching The Godfather and Godfather II combined, leaving Infinity War looking like Godfather Part III. It's so rare when a three-hour film has nothing worth trimming, but this film is as tight as Thanos' rear end after hearing the Ant-Man "theory." Endgame will leave you laughing, crying and cheering more than you've ever done in any MCU film.
-- Rebecca Fleenor (San Francisco)
No time to pee
I've never seen so many people get up to pee in one film -- and I couldn't believe they were sacrificing even a second, because Endgame is incredible. I knew it was three hours long going in, but I didn't notice the time go by at all. I just sat and watched something that was both classic Marvel and its own fresh thing. It gets superweird. Weirder than a raccoon sending emails. It mixes time travel film with heist film -- I can't get enough of both of those genres. It proves Nebula is the best character of all (just saying). And it has real stakes. The peeing people in my screening redeemed themselves with the many whoops and cheers that made this a perfect filmgoing experience.
-- Jennifer Bisset (Sydney)
There are some problems...
OK. It's great. Obviously. Emotional, funny, epic, all those good things. Five stars, eight thumbs up.
There's so much wrong with Endgame that I can't get out of my head. Primarily, time travel removes all jeopardy from all future stories. Something goes wrong tomorrow, hop back in the time machine, grab the stones again, solve it and return them. Which leaves the MCU kind of broken.
While we're on the subject, how do you return a Soul Stone? Do you chuck it over the edge and Black Widow comes back to life? Or do you just get store credit?
Also that means Cap bumped into the Red Skull again -- and we didn't see it!
My main gripe about time travel though is that the filmmakers go to great lengths to explain their logic and how it all works, and then just ignore the rules when it suits them. Seriously, @ me if you want to see my corkboard covered in red string, because Ol' Cappy at the end breaks every rule previously established.
-- Drew Stearne (London)
Now playing: Watch this: Avengers: Endgame is a thrilling sequel to every MCU...
Yes, Endgame cheats. As soon as you introduce time travel in the mix you know all bets are off. But who cares: This is a glorious final chapter to what has been an extraordinary cinematic journey. Endgame's filmic qualities as a standalone piece of cinema are secondary to the opportunity to say goodbye to the MCU's beloved characters, but the intimate character-focused story makes it enormously compelling. I laughed, I cried, and that's nothing compared with how the superfans next to me lost their minds. So what if it cheats -- Endgame is the end of a beautiful friendship.
-- Richard Trenholm (London)
Hulk Banner kills the entire concept of the character. Yes, there's comic book precedent for it, but fusing the two sides of the character removes the core premise that makes him work. The mock "Hulk smash" was very funny, but by giving us "the best of both worlds" we've ended up with the true characteristics of neither.
In fact, Hulk is dead. Bruce Banner killed him and is wearing his body like a viper green party suit. I'm supposed to shed tears over the death of Black Widow or Iron Man, but the Incredible Hulk was slaughtered off screen and we just laugh at the selfies. The puny humans finally defeated the Hulk. Boo, I say. BOOOOO!
First off, Infinity War and Endgame are two very different movies. Though the first felt like a roller coaster full of action, the new Avengers flick feels more like a chess match that turns into a rumble in the jungle -- yes, there are fights, but not as many as in other Marvel movies. Or it's a class reunion full of long-held emotions, where not everyone is where you'd expect them to be. The party is headlined by Captain America and Iron Man, with strong support from Hulk, Thor, Black Widow, Nebula, Rocket, Ant-Man, War Machine and Ronin. And as with many large soirées, you might end up feeling happy you went but not sure of who you actually saw or what exactly happened... but at least you enjoyed the fireworks at the end. You can read my review in Spanish here.
-- Gabriel Sama (San Francisco)
Oh, ALSO, the film continually throws away long-established lore in search of a gag or crowd-pleasing moment. I can just about get Cap being able to wield Thor's hammer, but is he now also the God of Thunder shooting lightning? Because last time I checked, those powers didn't come with the tool. Awesome? Abso-damn-lutely! Still bugs me though.
Bear witness
It's difficult for me to put into words how perfectly realized Avengers: Endgame is. There was no other way to complete an 11-year narrative that's snowballed into a cinematic feat I feel downright privileged to have witnessed. There were amazingly awesome comic book moments in this film that were so powerful to witness I couldn't help but exclaim! However, the heartfelt character moments show the medium at its best. Its absolute best. These scenes are the reason you care about the last hour of this movie. I can't wait to watch it again.
-- Eric Franklin (San Francisco)
I've seen some negative opinions about the representation of Thor, the fact that his grief and depression have been channeled into drinking and weight gain and that his loss of confidence and drive make light of mental health issues. I'm not sure the MCU is the best place to explore that fittingly, and Marvel bailing on Tony Stark's mental health and addiction issues pretty sharpish showed they weren't going to delve into that angle. What it did do, though, is make me feel better about my own dadbod, so there's that.
Avengers: Endgame is the ultimate form of fan service. But after 11 years and 22 films, it's the kind of fan service that seems organic and earned. After deftly balancing the screen time of so many characters in Infinity War -- including a fleshed-out villain in Thanos -- Endgame smartly pares back the focus to the core Avengers crew, giving them a fitting swan song.
Endgame is here
Spoiler-free review: Love letter to fans tops Infinity War
Spoiler-packed review: MCU clincher so close to perfect
No postcredits scene, but there's a tiny audio stinger
The biggest spoiler-filled WTF questions
It's three hours long: The best times to pee
Captain America will always be my favorite Avenger
You might be disappointed that some of the newer characters don't get much screen time beyond glorified cameos, but there will be plenty of time for the spotlight to go around in Phase 4. Endgame doesn't always make sense -- inevitable given the plot tricks and twists employed here -- but it has plenty of heart, hits a lot of emotional chords and is just downright funny. The Russo brothers crafted a fitting end to this first era of Marvel films, offering a satisfying conclusion while also laying the groundwork for future films.
-- Roger Cheng (New York)
Show Us Yours: Marvel fandom pictures from our readers
One LAST thing...
OK, everything that's so good about Endgame more than makes up for anything that's overwritten, under-written or just plain stupid. I laughed, it somehow started raining on the faces of many a grown person in the theatre and there were more than a few cheers.
Now, if Spider-Man: Far from Home could address how 3 billion people just reappearing doesn't throw the planet into utter chaos, I might be able to sleep at night...
The perfect final chapter
I watched Avengers: Endgame at the end of an insane 59-hour marathon featuring all 22 Marvel movies, and no amount of fatigue could diminish the power of this film. It made the entire experience worthwhile. I woke up the next morning still trying to absorb everything that had happened. I feel a mixture of happiness and heartache when I think about it. It was also so satisfying.
Now playing: Watch this: How I survived the Marvel Studios 22 Movie Marathon
Watching this movie was actually the perfect way to wrap up a marathon during which I was introduced to (many, many) characters and plotlines. It brought everything together so well, and provided much-needed resolution following the ending of Avengers: Infinity War, which had left me thoroughly heartbroken. After Endgame I could sleep soundly, albeit after the thrills and emotions kept me awake for quite a bit.
I'm going to be taking this one in for a while, as one should with any masterpiece.
-- Abrar Al-Heeti (San Francisco)
2019 movies to geek out over
Discuss: Avengers: Endgame best and worst -- our global review


text:
Team Breakdown
Team Melo struggled to find consistency during their second season on the circuit, but they'll be back with a junior-laden group that should contend for a Peach Jam bid. Justin Lewis was a bright spot on last year's squad, and he'll be back to lead a talented group coached by Sam Brand, also the head coach for Baltimore Polytechnic (MD) high school. Team Melo features five players that play for Brand during the high school season, so team chemistry should be advanced for the Baltimore-based EYBL club.
Junior forward Isaiah Todd departed from Melo in a last-second roster shakeup, but Brand's rotation still features top elite recruits in Lewis and Che Evans Jr., who will now own the star duties. Both Evans and Lewis are longtime members of Team Melo, and their production will likely determine how much success they attain this season.
Lewis (247 No. 102) is fortunate to have the experience to pull from last season, a season that saw him average 7.5 points, 6.3 rebounds, and 2.0 assists after being called up from 16U. Lewis is a physical player down low but he's more than capable of seeing up his own offense from the perimeter. Lewis figures to be a consistent threat for a double-double, and if can improve his shooting percentages from a year ago, Lewis will inevitably a contender for All-EYBL status.
Evans Jr (247 No. 86) is a slasher with good handles, and his athleticism allows him to effectively score around the basket. He can score from all three levels and does a good job of creating contact when he attacks the basket. Evans is transferring to Neumann-Goretti (PA) high school in Philadelphia for his senior season, and his recruitment is down to Boise State, Florida, Ohio State, TCU, & Texas Tech. He became a one-thousand point scorer in February, and he'll be the main scoring threat in the backcourt.
Team Melo junior Che Evans Jr (247 2020 No. 86)
Six guards join Evans in the backcourt. Considering he has terrific size, he will undoubtedly see time at the small forward position. The same can probably be said for Poly (MD) junior guard Brandon Murray. A tough and aggressive guard, the 6-foot-5 Murray was a difference-maker this high school season. Murray finished with a team-high 17 points on 7-for-10 shooting, nine rebounds, and four assists to help lead Poly to their third-straight Maryland 3A State Championship. He is assuredly a Division 1 player and has a chance to turn himself into a high-major prospect before the EYBL is over. He shared a backcourt with Rahim Ali Jr, a 6-foot guard capable of filling it up from the perimeter. These two should have great team chemistry entering the season, and Ali has a chance to turn himself into a Division I recruit.
Sophomore Ryan Conway (247 No. 98) is a tough scoring guard who loves to play fast. Conway played with Evans this past season before Evans decided to transfer, and they both enjoyed standout seasons helping Dulaney (MD) rack up a 21-4 record. Conway is the only underclassmen on the team, and he's obviously given the coaching staff a good reason to play him up in age. The 6-foot-1 Conway plays with confidence and should be an integral part of the backcourt alongside Evans and Murray.
The backcourt is rounded out by Jimma Gatwech (6-foot-4), Jalen Willis (6-foot-4), and Teon Rushing (5-foot-9). Gatwech is an absolutely incredible athlete and he does his best work in transition and on defense. Gatwech makes a strong argument for best dunker in the EYBL, and he will undoubtedly throw down some jaw-dropping dunks on the break. He's a high-level defender, operates with a good motor, and plays within himself. Willis is capable of defending small forwards and shooting guards, and his overall versatility should allow him to be a great glue-guy for Melo. Rushing is the smallest member of the rotation but he should bring a nice spark off the bench. He plays hard and plays great on-ball defense, two characteristics Brand will be relying on in his reserve player.
Jimma Gatwech with the RIDICULOUS in-game dunk at @BojanglesBash @HuntingtonPrep @JTheballer5 pic.twitter.com/UtBa8OPyCb
— Prep Circuit
Lewis will rarely leave the floor, while Evans and Murray will likely need to slide out-of-position more often than not. The only other forward on the roster is junior Ian Wallace. The 6-foot-7 looks the part of a top-100 recruit, offering up a physical, college-ready body in the frontcourt. Wallace has made massive strides in his game over the past year or so, and he's ready to show the country that he's a Division I recruit. He's an improving defender and his skill-set is coming along offensively. If he can consistently knock down the three, he will be a major asset in the pick-and-roll.
Team Melo junior Justin Lewis (247 No. 102)
Melo features three 4-star recruits in their rotation, but they will need to find a solution for their lack of size. Brand's group will play fast and loose, and with their athleticism and length, they have plenty of potential on defense. Losing Todd wasn't in the plans, but Lewis and Evans have more than enough talent to keep Melo competitive in Division B. They will need Murray or Conway to develop into a reliable third scorer, and the rest of the rotation needs to stay locked in on defense.
Team Melo (MD)
Session Awards
Nike EYBL Most Valuable Player: Cade Cunningham
All-EYBL: First Team
All-EYBL: Second Team
All-EYBL: Third Team
All-EYBL: Honorable Mention
Nike EYBL Offensive Player of the Year: Cam Thomas
Nike EYBL Defensive Player of the Year: Ryan Kalkbrenner
All-EYBL: Underclass Team
Nike EYBL Underclassman of the Year: Paolo Banchero
All-EYBL: Breakout Team
Nike EYBL Breakout Player of the Year: Colby Jones
Nike EYBL Performance of the Year: DJ Steward
EYBL News
147 Nike EYBL alumni currently on NBA rosters
Hunter Dickinson breaks down his final four schools - Duke, Florida State, Notre Dame & Michigan
By Pat Lawless 10/14/2019, 12:45pm EDT
Hunter Dickinson is looking at four schools
'The Academy' High School & College Official Rosters
EJ Bates' Son Is a Basketball Prodigy. Coaching Him Is More Relatable Than You'd Think
By Alec Kinsky, SportsEngine 08/06/2019, 3:15pm EDT
VIDEO: 2019 'One Peachy Moment'
By Jon Lopez, Nike 07/17/2019, 2:45pm EDT
Tag(s): News 17U NIKE EYBL Divisions Division B Team Melo (MD) Welcome To The Circuit Team Previews Division B Previews


Bupa Internationaal is 1 van 's werelds grootste health care verzekeraars, in Engeland gevestigd.
Worldwide Medical Insurance is the core of this plan, and gives you the reassurance of covering any essential hospital treatment you may need, whether in an emergency or a planned visit.All surgery, cancer treatment and advanced imaging, whether received whilst staying in hospital or visiting as a day patient, are also covered.
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How many festivals or events have you attended where you'd wish they'd provided recycling?What about when you go to a restaurant or fast-food takeaway and you're given your food in plastic containers, styro-foam (polystyrene) cups? Or maybe you get frustrated with plastic straws at your local bar? This is exactly why Tara Dodson, founder of Full Circle Resource Management set up her business out of frustration.


The months of speculation finally came to an end on Wednesday evening when Enda Kenny announced his decision to step down as leader of Fine Gael — the party he has led for just short of 15 years. Mr Kenny will be stepping down as Taoiseach, once a new Fine Gael party leader is elected by the party and a new Taoiseach is elected by the Dáil.
Since the results of the 2016 General Election it was a matter of when, rather than if, his term as leader of the country would come to an end. After the many months of speculation as to when he would announce his departure, it came at a meeting of the Fine Gael parlimentary party that lasted just seven minutes. At the meeting he said: "Last year I indicated that I would not lead the Fine Gael Party into the next General Election. I have decided to implement that decision today. Therefore I will retire as Leader of Fine Gael effective from midnight tonight.
"I want to assure people that throughout this internal process, I will continue to carry out my duties and responsibilities as Taoiseach in full," Mr Kenny added. "I intend to provide a brief but appropriate period for my successor to engage with groups and members supportive of Government, and with other parties in the Dáil regarding provision of Government for the future."
While national politics will be consumed with the question of who will replace him in the highest position in the country, on a local level, for the Fine Gael party faithful in Mayo, the attention will be even more firmly focused on who will replace him as a candidate in the next general election (assuming, of course, he does not decide to run again ) for the party in the county town. In his parting statement he said: "I thank all my loyal constituents and supporters in Mayo for their unstinting loyalty since 1975, and for their support for my family previously in providing unbroken service to the county in Dáil Éireann since 1954."
It could be construed like he is laying the groundwork for a third generation of Kenny to run for national office for Fine Gael, with his daughter Aoibhinn potentially in the frame to follow her father, and her grandfather, Henry Kenny, into the family business. Others who may be interested in running for the Dáil if a spot opens up for the party could include Castlebar based Senator Paddy Burke, who has been serving in the upper house since 1993 after being elected on the Agricultural Panel.
Mr Kenny was first elected to the Dáil in 1975, succeeding his late father. He has retained his seat in the 12 elections since then in Mayo West and later the Mayo constituency. Before becoming Taoiseach he was minister of state for youth affairs under Garret Fitzgearld in the 1980s, and then minister for tourisim and trade under then-taoiseach John Bruton as part of the mid-nineties rainbow government of Fine Gael, Labour, and Democratic Left.
He first contest for the position as leader of Fine Gael in 2001, but lost out to Michael Noonan. However after a hammering in the general election the following year, Noonan stepped aside and Kenny once again ran for party leader, this time winning the race. He led his party into the 2007 General Election, where they gained an additional 20 seats on the 2002 results. That followed better than expected results in the 2004 local and European elections.
His biggest electoral success, of course, came in the 2011 General Election where, at 59, he was elected as Taoiseach after his party along with the Labour party secured a massive majority, forming a coalition government with Fine Gael winning 76 seats, an increase of 45 from the number they held when Kenny took over as leader of the party. The 2016 General Election saw Fine Gael suffer a big drop in support, winning only 50 seats, but Mr Kenny remained on as Taoiseach of a minority government thanks to the support of independents and a supply and confidence motion with Fianna Fáil.


text:
\section{Introduction}
\label{intro}
In 1988, Pearl devised belief propagation algorithm to solve marginalization and other inference problems. Belief propagation algorithm is a message-passing algorithm using graphs display known as graphical models to solve the problems \cite{Pearl1}.On the other side, Gallager, in 1963, devised a decoding algorithm similar to the belief propagation algorithm to decode his well-known and valuable low-density-parity-check code. One of the significant points of graphical models' capability and generalization is that they appear in variant field of science dealing with mathematics including code theories \cite{Gallager2,McEliece3},physics \cite{MacKay4,Yedidia5}, statistics, and artificial intelligence \cite{Pearl1,Kschischang7}. This diversity, unfortunately, has caused these models and related algorithms lack a single and standard notation. Numerous generalizations, from initial message-passing algorithm to highly complicated approaches, have been made about belief propagation algorithm.Generalization of graphical models and related algorithms on quantum mechanics has been recently noticed by researchers of this field. Poulin et al. worked on this field in 2008. Afterwards, its application was investigated in quantum statistical mechanics \cite{Poulin9,Hasting10,Bilgin11}, and quantum codes \cite{Pawel12}and there were acceptable results. One of the main reasons for this generalization is the quantum mechanics nature as a probabilistic theory being originally identical to graphical models. Despite the basic similarity, the differences between quantum mechanics and classic probability theory have complicated the generalization. Therefore, it can be highly challenging to structure an applicable and unique framework to which we can apply both quantum mechanics and graphical models simultaneously.

At the beginning of this paper, theoretical foundation of classic and quantum Markov network were explained in graph language and their relation with quantum and statistical physics was expanded as well. We have already tried to have an overall review on previous researches, so we hope this paper is an opening to familiarizing with graphical models and it may have interesting ideas about quantum.\\
\section{Pairwise Markov Random Field (MRF)}
\label{sec:1}
Pairwise Markov random field was used as an inference model in computer vision early last decade \cite{Hovington13}. It may seem indisputable to some computer science researchers to solve problems like objects recognition or other preliminary computer vision problems. What we are looking for in graphical models is to give some data and get the answer. In computer vision, for instance, we give a series of two-dimensional pixels and expect to receive optimal image. This is challenging by itself.
\\To solve computer vision, MRF has applied a highly interesting theoretical model \cite{William14}. What we are generally looking for in these problems is to guess the input in terms of output. To elucidate more, suppose that we have a $100\times100$ black and white output image sent to us through a channel. Some of these pixels are maybe flipped or their colors are changed (black to white and white to black) while transferring. We intend to reconstruct the original image (as it was before transferring through the channel).
Generally, we aim to infer input data \ensuremath{x_i} out of output data \ensuremath{y_i} (each pixel variable). Index \ensuremath{i} may indicate pixel's place or a small collection of pixels. Another assumption is that, there is a statistical relation between \ensuremath{x_i} and \ensuremath{y_i} for each \ensuremath{i} called compatibility function \ensuremath{\Phi_i(x_i,y_i)}.  Function \ensuremath{\Phi_i(x_i,y_i)} is usually called as an evidence of \ensuremath{x_i}. Eventually, to well infer \ensuremath{x_i} we have to consider a structure for it. Neglecting such a structure will lead incomplete computer vision problems. To understand the general shape of this structure, consider the \ensuremath{i}th variable in a two-dimensional square network. Variable \ensuremath{x_i} should be compatible with the nearest variable \ensuremath{x_j} which is shown by compatibility function \ensuremath{\Psi_{ij}(x_i,y_j)} where \ensuremath{\Psi_{ij}} only connects neighboring points; the total probability function is as follows:
\begin{equation}
p(\{x\},\{y\})=\frac{1}{z}\prod_{ij}\Psi_{ij}(x_i,y_j)\prod_{i}\Phi_i(x_i,y_i)
\end{equation}
\\Where Z is a normalization constant and the product on (i, j) consist all neighboring points in the square network. The above graphical model is shown in \cite{Geman15}. Filled circles indicate observed values \ensuremath{y_i} while unfilled circles show hidden values \ensuremath{x_i}. Since compatibility functions only depend on one pair of nodes or variables \ensuremath{i} and \ensuremath{j}, MRF was called pairwise.\\
\begin{figure}
\includegraphics[width=0.6\textwidth]{fig1}
\caption{two-dimensional square pairwise MRF network}
\label{fig:1}
\end{figure}

\section{MRF based on graphs}
\label{sec:2}
Graphical models having different applications serve in numerous areas including Bayesian networks(artificial intelligence), factor graph(image reconstruction), Tanner graph(code theory), and Markov networks(statistical physics). Besides naming, these models bear numerous common attributes which are based on graphs. Graphical models are completely convertible to each others. In this section, hence, emphasizing MRF, we try to mathematically expand graphical models in the form of graph theories which has a significant role in graphical models generalization on quantum counterpart.
Each graphical model is shown by $G= (V, E)$, where V and E are collections of vertices and edges, respectively,and a graph vertex \ensuremath{x\in V} is given to each random variable x. In fact, each graphical model denotes a distribution as \ensuremath{P(V)=P(x_1,x_2,...)}and the edge $e= (u, v)$, $e\in E$ shows the dependence between random variables $u$ and $v$ in probability distribution $P$.\\\\
\textbf{Conditional independence:} Take $A$, $B$, and $C$ as three random variable sets wit distribution $P (A, B, C)$. $A$ and $C$ are independent given $B$ if conditional mutual information \ensuremath{I(A:C \mid B )=0}:
\begin{equation}
I(A:C \mid B)=H(A,B)+H(C,B)-H(A,B,C)-H(B)
\end{equation}\\
Where $H$ is Shannon entropy. And for each arbitrary distribution, $p(x)$ is defined as \cite{Nielsen16}:
\begin{equation}
H(P(x))=-\sum_{x}p(x)\ln p(x)
\end{equation}\\
\textbf{Markov Random Field (MRF):} Graph $G= (V, E)$ and distribution $P(V)$ are given. Pair $(G,P(V))$ creates the MRF If \ensuremath{I(U:V-U-n(U)\mid n(U)=0}) for each $U \subset V$ where $n(U)$ is the neighboring sets of $U$. In other words, $U$ is protected by neighboring points \cite{Jonathan17}(fig 2 \cite{Lauritzen18}).
\begin{figure}
\includegraphics[width=0.6\textwidth]{fig2}
\caption{Markov Random Field (MRF)}
\label{fig:2}
\end{figure}\\
\textbf{Clique:}is a set of graph nodes which are all connected together. The set of all cliques of graph G is shown by C(G). Cliques are shown in Figure 3.\\
\begin{figure}
\includegraphics[width=0.6\textwidth]{fig3}
\caption{illustration of cliques which belong to MRF}
\label{fig:3}
\end{figure}\\
\textbf{Hammersley Clifford theorem \cite{Matt19}:}Pair $(G, P(V))$ creates a positive MRF $(P>0)$ if and only if the distribution function can be written in following form:
\begin{equation}
P(V)=\frac{1}{Z}\prod_{c \in C(G)}W(c)
\end{equation}
$W(c)$ is the local probability distribution function on cliques and $Z$ is the normalization constant. See \cite{Hammersley20} to familiarize more with graphical models.\\
\textbf{Example}: Pairwise MRF: When the maximum number of available nodes in cliques is 2, then MRF distribution can be written as:
\begin{equation}
P(V)=\frac{1}{Z}\prod_{x \in V}W(x)\prod_{(x,y)\in E}\mu(x,y)
\end{equation}
Looking more precisely at above definitions, we can infer a highly-rich relation between them. Conditional independence which gives a highly innovative idea of belief propagation algorithm, plays a basic role in MRF definition. To make a background, we pose a discussion here.\\
\begin{figure}
\includegraphics[width=0.6\textwidth]{fig4}
\caption{MRF with three set of nodes: $A, B$ and $C$}
\label{fig:4}
\end{figure}
Suppose that the sets A and C in figure 4 \cite{D.Poulin21} are independent given B. If we want to determine the probability of B being in a certain state, we should consider its interaction with other nodes of graph. We also know that if we determine B, the relation between A and C is totally disconnected. So we can separately investigate the interaction of "B and A", and "B and C" which is of significant help in decreasing calculation complexities. It can be said:\\\\
\textbf{The probability of B in a certain state= $P(B \mid C) \times P(B \mid A)$}\\\\
The above explanations show the importance of conditional independence in defining MRF. However, we know that calculating conditional mutual information for all complicated arbitrary nodes in large graphs is time consuming and practically impossible. Hammersley-Clifford theorem is a shortcut to avoid such calculations. By a graph's shape or its corresponding distribution, this theorem shows that whether or not it is MRF. So, by connecting Hammersley-Clifford theorem and conditional independence property in defining MRF, we can access conditions in which calculation complexity is highly reduced.
\section{Quantum Markov Network}
Now we want to generalize classical concepts of graphical models on quantum. Before doing so, it is worth noting that this generalization is used in quantum mechanics and statistical physics, and interested readers can see \cite{Leifer8}. Each graphical model is classically shown by graph $G= (V, E)$ where $V$ shows nodes and $E$ shows lines called edges. Variables \ensuremath{x_i}, here, are quantum systems e.g. spin and local functions operate in Hilbert space. General distribution function is density matrix,\ensuremath{\rho} , which is as below for a pairwise MRF:
\begin{equation}
\rho=\prod_{x \in V}v_{x}\prod_{(x,y)\in E}\mu_xy
\end{equation}
\\In above equation, $v_{x}$ and $\mu_xy$ are positive operators in Hilbert space $H_{x}$ and $H_{x}\otimes H_{y}$ respectively. $\rho$ operates in Hilbert space $H=\otimes_{x \in V}H_x$ and the edge $e=(x,y)$ shows the dependency between variables $x$ and $y$ in $\rho v$. We work with Gibbs distribution in statistical physics  which is $\rho \equiv \frac{1}{Z} \exp(- \beta H)$, where $H$ and $\beta$ are Hamiltonian and inverse of temperature, respectively.\\
\textbf{Conditional independence:}If we take $A$, $B$, and $C$ as three quantum systems with joint distribution $\rho(A, B, C)$, then $A$ and $C$ are independent given B if conditional mutual information $I(A:C\mid B)$ =0.
\begin{equation}
I(A:C\mid B)=S(A,B)+S(C,B)-S(A,B,C)-S(B)
\end{equation}\\
$S$ is Von-Neumann entropy and for each arbitrary density matrix is defined as:
\begin{equation}
S(\rho)=-tr(\rho\ln(\rho))
\end{equation}\\
\textbf{Quantum Markov Network\cite{Leifer8,Brown22}:}Graph $G=(V, E)$ and density matrix $\rho$ are given. Pair $(G,\rho (V))$ creates MRF if $I(A:C\mid B)=0$ for each arbitrary $A$, $B$, and $C$, where $A$, $B$, and $C$ are separate subsets of $V$ so that $B$ protects $A$ against $C$. On the other hand, $B$ is the collection of neighboring points of $A$ and $C=V-A-B$ (figure 5 \cite{D.Poulin21}).
\begin{figure}
\includegraphics[width=0.6\textwidth]{fig5}
\caption{$A,B$ and $C$ for an arbitrary MRF}
\label{fig:5}
\end{figure}
\\So far, only classical concepts explained before, have been generalized. However, in quantum systems, we encounter non-commutativity of operators. So, we should be a bit cautious in generalization of MRF to quantum, because in quantum counterpart, it is not easy to understand conditional independency through graph shape or corresponding distribution. We will come to this challenge later. to elucidate the topic, we take a look at an example from statistical physics in which the system is classic and H is defined as:
\begin{subequations}
\begin{equation}
H(x_{1},x_{2},x_{3},...)=h(x_{1},x_{2})+h(x_{2},x_{3})+...
\end{equation}
\begin{equation}
Z=\sum_{x_1,x_2,...} e^{-H(x_1,x_2,...)}       \text{Partition Function}
\end{equation}
\begin{equation}
=\sum_{x_2,x_3,...}\underbrace{ \lgroup \sum_{x_1}e^{-h(x_{1},x_{2})} \rgroup}_{Z_{1,2}(x_2)}
\end{equation}
\begin{equation}
=\sum_{x_3,x_4,...}\underbrace{ \lgroup \sum_{x_2}Z_{1,2}(x_2)e^{-h(x_{2},x_{3})} \rgroup}_{Z_{2,3}(x_3)}
\end{equation}
\begin{equation}
=\sum_{x_N}Z_{N-1,N}(x_N)e^{-h(x_{N-1},x_{N})}
\end{equation}
\end{subequations}
Now we are ready to generalize these equations to their quantum counterpart:
\begin{subequations}
\begin{equation}
H(x_{A},x_{B},x_{C},...)=h(x_{A},x_{B})+h(x_{B},x_{C})+...
\end{equation}
\begin{equation}
h_{BC}=I_{A}\otimes h_{BC}\otimes I_{D}\otimes ... \textrm{Two-body hermitian operator}
\end{equation}
\begin{equation}
Z=Tr(e^{-H(x_{A},x_{B},x_{C},...)})
\end{equation}
\begin{equation}
\neq Tr_{BC...}\{ Tr_{A}(e^{-h(x_{A},x_{B})})e^{-h(x_{x_{B},x_{C}})...}\}
\end{equation}
\end{subequations}\\
equality does not happens because Hamiltonian terms dose not commute.\\\\
\textbf{Quantum Hammersley Clifford Theorem:\cite{Leifer8,Brown22}}
Now the question arises is that if we can generalize Hammersley Clifford theorem to quantum Or more precisely, if this theorem can absolutely identify whether a quantum statistical system with Gibbs distribution is MRF or not? In reply we can say that there is a quantum counterpart for Hammersley Clifford theorem. The only difference is that, in quantum, we encounter the above limitations, And this theorem in quantum state is only true in one direction.\\\\
\textbf{Theorem 1}\cite{Leifer8}: Let $G =(V,E)$ be a graph and $\rho$ be a density matrix for the particles located at the vertices of G. If the pair ($\rho$,G) is a positive quantum Markov network, then the state $\rho$ can be expressed as $\rho=e^H$ where $H= \sum_{Q\in C} h_Q$ is the sum of Hermitian operators $h_{Q}$ on the particles located in cliques Q.\\
For the reverse direction, we have can consider the below theorem.\\\\
\textbf{Theorem 2}\cite{Brown22}: Let $G=(E,V )$ be a graph and $H= \sum_{Q\in C} h_Q$ , $[h_{Q},h_{Q'}]=0$ be a local commuting Hamiltonian on that graph. Then ($\rho$,G) is a positive quantum Markov network for $\rho=\frac{1}{z}e^H$ ,where $Z$ is a normalization constant.\\\\
\textbf{The reverse happens when all $h_{Q}$s commutate together.}\\\\
\textbf{Example:} It is the right time for us to investigate these claims in just simple examples. Our example is a system with five spins on which applied local magnetic fields. The following Hamiltonian describe this system, while $S^{i}$ are Pauli matrixes (see figure 6).
\begin{subequations}
\begin{equation}
h_{12}=(S^{x}\otimes S^{x})\otimes I\otimes I\otimes I+h_{1}(S^{z}\otimes I \otimes I\otimes I\otimes I)
\end{equation}
\begin{equation}
h_{23}=I\otimes(S^{x}\otimes S^{x})\otimes I\otimes I+\frac{1}{2}h_{2}(I\otimes I\otimes S^{z}\otimes I\otimes I)
\end{equation}
\begin{equation}
h_{34}=I\otimes I\otimes(S^{x}\otimes S^{x})\otimes I+\frac{1}{2}h_{2}(I\otimes I \otimes S^{z}\otimes I\otimes I)
\end{equation}
\begin{equation}
h_{45}=I\otimes I\otimes I\otimes (S^{x}\otimes S^{x})+h_{3}(I\otimes I\otimes I\otimes I\otimes S^{z})
\end{equation}
\begin{equation}
H=h_{12}+h_{23}+h_{34}+h_{45}
\end{equation}
\end{subequations}
Where h's describe local magnetic fields. What we anticipate is that conditional $I$ over different parts of relevant graph must be nonzero, because there are some non-commutative terms in Hamiltonian. For a sample, we can see figure 7 which illustrate the $I(A:C\mid B)$, where $A$, $C$ and $B$ comprise spins $(1 \& 2)$, $(4 \& 5)$ and $3$ respectively. Putting $h_{1},h_{2},h_{3}=2$, in the figure 7 as we can see $I(A:C\mid B)$ is nonzero except for $\beta=0$, because $h_{ij}$'s for $i,j=1,…,5$ are not commuting.
Now what happens if we put $h_{2}=0$? AS a result of this manipulation we have all $h_{ij}$'s commuting. Consequently, as we can see in figure 8 for $I(A:C\mid B)$ described above is zero for all $\beta$. These examples make an intuitive sense for the Quantum Hammersley-Clifford theorem.
\begin{figure}
\includegraphics[width=0.6\textwidth]{fig6}
\caption{a system with five spins}
\label{fig:6}
\end{figure}
\begin{figure}
\includegraphics[width=0.6\textwidth]{fig7}
\caption{$I(A:C\mid B)$ for a five-particle system, where $A, B$ and $C$ comprise spins $(1 \& 2), (4 \& 5)$ and 3 respectively and  $h_{1},h_{2},h_{3}=2$}
\label{fig:7}
\end{figure}\\
\begin{figure}
\includegraphics[width=0.6\textwidth]{fig8}
\caption{$I(A:C\mid B)$ for a five-particle system, where $A$, $B$ and $C$ comprise spins $(1 \& 2)$, $(4 \& 5)$ and $3$ respectively, with $h_{1}$ ,$h_{3}=2$ and $h_{2}=0$}
\label{fig:8}
\end{figure}\\
\section{Conclusion}
The authors merely aimed at posing primary ideas and questions. In this paper, it is primarily guessed that commutativity equals being Markov in quantum case. This guess can be highly valuable for if we can identify quantum Markov network, then we can use conditional independence and so inference problems in quantum mechanics will be much easier. Now, we are in a state to use message-passing algorithm in graphical models for inference problems in quantum mechanics. This proposition by itself can form into a new research. On the other side, graphical models based on quantum physics form a problem which can attract enthusiasts.
In the following, there are some recommendations for those who are interested in. One of them is more investigation on quantum graphical models and generalization of MRF to quantum. More precisely, when can we say strongly that a quantum distribution and its related graph is a quantum MRF? On the other side, can we answer this question decisively? Or only under certain conditions we are able to say whether or not a quantum distribution is MRF.

redpajama_set_name: RedPajamaArXiv


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Amy Witting was born in Sydney in 1918. She attended Sydney University, then taught French and English in state schools. Beginning late in life she published six novels, including The Visit, I for Isobel, Isobel on the Way to the Corner Shop and Maria's War; two collections of short stories; two books of verse, Travel Diary and Beauty is the Straw; and her Collected Poems. She had numerous... I'd never heard of Amy Witting, the Australian poet and novelist, who has died aged 83. As far as I was concerned, she was my French teacher, Mrs Levick.
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In 1989, the Australian author Amy Witting published I for Isobel, a coming-of-age novel broken into five short story-like sections that each focus on a key moment in the life of the title character as she grows up in 1950s-1960s Australia.