Properties and algorithms of the (n, k)-arrangement graphs

The (n, k)-arrangement interconnection topology was first introduced in 1992. The (n, k )-arrangement graph is a class of generalized star graphs. Compared with the well known n-star, the (n, k )-arrangement graph is more flexible in degree and diameter. However, there are few algorithms designed for the (n, k)-arrangement graph up to present. In this thesis, we will focus on finding graph theoretical properties of the (n, k)- arrangement graph and developing parallel algorithms that run on this network. The topological properties of the arrangement graph are first studied. They include the cyclic properties. We then study the problems of communication: broadcasting and routing. Embedding problems are also studied later on. These are very useful to develop efficient algorithms on this network. We then study the (n, k )-arrangement network from the algorithmic point of view. Specifically, we will investigate both fundamental and application algorithms such as prefix sums computation, sorting, merging and basic geometry computation: finding convex hull on the (n, k )-arrangement graph. A literature review of the state-of-the-art in relation to the (n, k)-arrangement network is also provided, as well as some open problems in this area.

Properties and algorithms of the hyper-star graph and its related graphs

The hyper-star interconnection network was proposed in 2002 to overcome the drawbacks of the hypercube and its variations concerning the network cost, which is defined by the product of the degree and the diameter. Some properties of the graph such as connectivity, symmetry properties, embedding properties have been studied by other researchers, routing and broadcasting algorithms have also been designed. This thesis studies the hyper-star graph from both the topological and algorithmic point of view. For the topological properties, we try to establish relationships between hyper-star graphs with other known graphs. We also give a formal equation for the surface area of the graph. Another topological property we are interested in is the Hamiltonicity problem of this graph. For the algorithms, we design an all-port broadcasting algorithm and a single-port neighbourhood broadcasting algorithm for the regular form of the hyper-star graphs. These algorithms are both optimal time-wise. Furthermore, we prove that the folded hyper-star, a variation of the hyper-star, to be maixmally fault-tolerant.

Medical sketches of the campaigns of 1812, 13, 14

Full Title: Medical sketches of the campaigns of 1812, 13, 14 : to which are added, surgical cases, observations on military hospitals, and flying hospitals attached to a moving army : also, an appendix comprising a dissertation on dysentery which obtained the Boylstonian prize medal for the year 1806 and observations on the winter epidemic of 1815-16, denominated peripneumonia notha, as it appeared at Sharon and Rochester, state of Massachusetts

Charles Larned letter, April 3, 1813.

Charles Larned (1791-1834) was a lawyer and American military officer who served during the War of 1812. He was the son of Simon Larned (1753-1817), who served as a captain in the Revolutionary War and was a member of the United States Congress from Massachusetts from 1804-1805. Charles studied law in the office of Henry Clay in Kentucky, and was dining with a group of prominent citizens when word was received that General William Henry Harrison could soon be overpowered by General Henry Proctor. Colonel Owen, a member of the group, organized a regiment to reinforce Harrison’s troops. Larned became a member and subsequently survived the River Raisin Massacre and was later present at the Battle of the Thames. He was also part of a group of men who learned of General William Hull’s plan to surrender Detroit to the British and planned to overtake him should this occur. However, the plan failed, Hull did surrender and the men became prisoners of the British. After the war, Larned became a lawyer, and served as Attorney General of Michigan Territory during the Black Hawk War. During the cholera epidemic of 1834, he worked tirelessly to assist others, but was stricken with the disease and died. Letter Transcription: Pittsfield, April 8, 1813 I think that by this time my dear Charles you will allow I have some reason to give you a gentle reprimand for breach of duty—but I will not censure you upon suspicion maybe you have substantial reasons—at any rate one cannot very graciously reproach the other for negligence I for one am healthy as ham & that we have so seldom exchanged letters during your absence & on my honor promise to be a better girl in future—but the truth is my Dear Charles I am secretary for the Family—Mama you know never writes & James but seldom & they are all dispersed in different directions, consequently I have many calls upon my time—this to be sure is a pleasant duty & I urge it only as a slight palliation for my remissness if you should consider it as such—now I have finished my preface—I will try to be more interesting & doubtless I succeed. Our dear Father we hope & trust is now in Green Bush, where he will probably remain a month perhaps & from thence he expects to go to Sacket’s harbor—at which place you know our troops are fast collecting-- We shall hope to see him either here or there before he goes. Brother George I believe is [still] at Plattsburgh but expects soon to be removed to some other military part perhaps with Papa (I hope so at least). We have just got letters from Brothers Sylvester & Joseph at Middlebury—they are in good health. Mama has for some weeks been afflicted with an inflammation in her eyes but seems now to be convalescing. Sister Martha has been somewhat unwell for a few weeks but is now tolerably recovered. James & myself are both in our usual good health & at this time seated by the same stand, one reading, the other writing. Thus my Dear Charles have I given you an abstract history of our Family—but here indeed is a wonderful omission; not a word about Miss Harriet Hunt, who in truth ought to have been noted first but the last she’s not the least in my memory. She is much grown since you saw her, but does not speak as fluently as we could wish—a few word she can say. Probably before this you have been informed of the great loss your friend Sherrill has sustained in the death of his mother—also of the revolution that has taken place in Hackbridge as it respects the religion & morality of the place that more than one hundred on the plain have become religious converts & c—indeed I am at a loss what to say that will afford your pleasure—a narrative at this time must be gloomy indeed. The distressing situation of our country at this time would make almost any recital melancholy. The prevailing epidemic has swept off many of your acquaintance no doubt. Mrs. Dewey of Williamstown, the sister of Mrs. Danforth, has left a Husband, Children & many Friends sincerely to lament her loss—some few have died in our village, but we have escaped astonishingly –it has raged in every town about us--If we are unwilling to acknowledge a God in his mercies. I fear she shall be compelled to do it in the awfulness of his judgments.--------I am much [pleased] with our new neighbors the Parsons Wife & a Miss Woodward her cousin is a fine girl, I think, Mrs. Allen has not a handsome face but something in her manner that interests one her person I think the handsomest I ever saw & the Parson seems well pleased with his selection—Mrs. Ripley is with them this winter & will probably remain thro the summer—Her husband at [Sackett’s Harbor] little or no alteration is apparent since her marriage—she seems as gay & fond of company as ever.-------Mrs. [McKnight] it is expected will commence housekeeping in about three weeks in the house formerly occupied by Mr…. [Report] says that Mr. Goodman & Clarissa Weller are soon to be married & many other things that I must omit to mention for Mama wants a… PS reserved--now my Dear Charles remember you are considerably… & I am confident you have as much leisure as I have –… be ceremonious but write whenever I find time not & I beg… the same – I tell James I shall not send his love for he must write himself. I shall anxiously expect you to write & do not disappoint your affectionate, sister--H One word my Dear Charles from your affectionate Mother who longs to see Her Dear son Charles—but being deprived of that rich blessing at present—begs Him so to conduct that she may hope for it ere long—do you search the Scriptures and keep the Sabbath holy unto the Lord—and all the sacred Commandments of God—it is my ardent desire…He would protect, support and provide for your soul and body and believe me your affectionate friend and Mother. R Larned.

Properties and Algorithms of the KCube Graphs

The KCube interconnection topology was rst introduced in 2010. The KCube graph is a compound graph of a Kautz digraph and hypercubes. Compared with the at- tractive Kautz digraph and well known hypercube graph, the KCube graph could accommodate as many nodes as possible for a given indegree (and outdegree) and the diameter of interconnection networks. However, there are few algorithms designed for the KCube graph. In this thesis, we will concentrate on nding graph theoretical properties of the KCube graph and designing parallel algorithms that run on this network. We will explore several topological properties, such as bipartiteness, Hamiltonianicity, and symmetry property. These properties for the KCube graph are very useful to develop efficient algorithms on this network. We will then study the KCube network from the algorithmic point of view, and will give an improved routing algorithm. In addition, we will present two optimal broadcasting algorithms. They are fundamental algorithms to many applications. A literature review of the state of the art network designs in relation to the KCube network as well as some open problems in this field will also be given.

Charles Larned letter - April 3, 1813

Letter Transcription: Pittsfield, April 8, 1813 I think that by this time my dear Charles you will allow I have some reason to give you a gentle reprimand for breach of duty—but I will not censure you upon suspicion maybe you have substantial reasons—at any rate one cannot very graciously reproach the other for negligence I for one am healthy as ham & that we have so seldom exchanged letters during your absence & on my honor promise to be a better girl in future—but the truth is my Dear Charles I am secretary for the Family—Mama you know never writes & James but seldom & they are all dispersed in different directions, consequently I have many calls upon my time—this to be sure is a pleasant duty & I urge it only as a slight palliation for my remissness if you should consider it as such—now I have finished my preface—I will try to be more interesting & doubtless I succeed. Our dear Father we hope & trust is now in Green Bush, where he will probably remain a month perhaps & from thence he expects to go to Sacket’s harbor—at which place you know our troops are fast collecting-- We shall hope to see him either here or there before he goes. Brother George I believe is [still] at Plattsburgh but expects soon to be removed to some other military part perhaps with Papa (I hope so at least). We have just got letters from Brothers Sylvester & Joseph at Middlebury—they are in good health. Mama has for some weeks been afflicted with an inflammation in her eyes but seems now to be convalescing. Sister Martha has been somewhat unwell for a few weeks but is now tolerably recovered. James & myself are both in our usual good health & at this time seated by the same stand, one reading, the other writing. Thus my Dear Charles have I given you an abstract history of our Family—but here indeed is a wonderful omission; not a word about Miss Harriet Hunt, who in truth ought to have been noted first but the last she’s not the least in my memory. She is much grown since you saw her, but does not speak as fluently as we could wish—a few word she can say. Probably before this you have been informed of the great loss your friend Sherrill has sustained in the death of his mother—also of the revolution that has taken place in Hackbridge as it respects the religion & morality of the place that more than one hundred on the plain have become religious converts & c—indeed I am at a loss what to say that will afford your pleasure—a narrative at this time must be gloomy indeed. The distressing situation of our country at this time would make almost any recital melancholy. The prevailing epidemic has swept off many of your acquaintance no doubt. Mrs. Dewey of Williamstown, the sister of Mrs. Danforth, has left a Husband, Children & many Friends sincerely to lament her loss—some few have died in our village, but we have escaped astonishingly –it has raged in every town about us--If we are unwilling to acknowledge a God in his mercies. I fear she shall be compelled to do it in the awfulness of his judgments.--------I am much [pleased] with our new neighbors the Parsons Wife & a Miss Woodward her cousin is a fine girl, I think, Mrs. Allen has not a handsome face but something in her manner that interests one her person I think the handsomest I ever saw & the Parson seems well pleased with his selection—Mrs. Ripley is with them this winter & will probably remain thro the summer—Her husband at [Sackett’s Harbor] little or no alteration is apparent since her marriage—she seems as gay & fond of company as ever.-------Mrs. [McKnight] it is expected will commence housekeeping in about three weeks in the house formerly occupied by Mr…. [Report] says that Mr. Goodman & Clarissa Weller are soon to be married & many other things that I must omit to mention for Mama wants a… PS reserved--now my Dear Charles remember you are considerably… & I am confident you have as much leisure as I have –… be ceremonious but write whenever I find time not & I beg… the same – I tell James I shall not send his love for he must write himself. I shall anxiously expect you to write & do not disappoint your affectionate, sister--H One word my Dear Charles from your affectionate Mother who longs to see Her Dear son Charles—but being deprived of that rich blessing at present— begs Him so to conduct that she may hope for it ere long—do you search the Scriptures and keep the Sabbath holy unto the Lord—and all the sacred Commandments of God—it is my ardent desire…He would protect, support and provide for your soul and body and believe me your affectionate friend and Mother. R Larned.

Order to create a General Board of Health in the Town of Niagara, June 25, 1832

In the early nineteenth century, a widespread outbreak of cholera occurred in continental Europe, eventually spreading to the British Isles. The disease subsequently spread to Canada as impoverished British immigrants seeking a better life arrived in the country. To help curb the spread of the disease, local Boards of Health were created.

Order to create a General Board of Health in the Town of Niagara, June 25, 1832.

In the early nineteenth century, a widespread outbreak of cholera occurred in continental Europe, eventually spreading to the British Isles. The disease subsequently spread to Canada as impoverished British immigrants seeking a better life arrived in the country. To help curb the spread of the disease, local Boards of Health were created.

Properties and Algorithms of the KCube Interconnection Networks

The KCube interconnection network was first introduced in 2010 in order to exploit the good characteristics of two well-known interconnection networks, the hypercube and the Kautz graph. KCube links up multiple processors in a communication network with high density for a fixed degree. Since the KCube network is newly proposed, much study is required to demonstrate its potential properties and algorithms that can be designed to solve parallel computation problems. In this thesis we introduce a new methodology to construct the KCube graph. Also, with regard to this new approach, we will prove its Hamiltonicity in the general KC(m; k). Moreover, we will find its connectivity followed by an optimal broadcasting scheme in which a source node containing a message is to communicate it with all other processors. In addition to KCube networks, we have studied a version of the routing problem in the traditional hypercube, investigating this problem: whether there exists a shortest path in a Qn between two nodes 0n and 1n, when the network is experiencing failed components. We first conditionally discuss this problem when there is a constraint on the number of faulty nodes, and subsequently introduce an algorithm to tackle the problem without restrictions on the number of nodes.