Algoritma golden section bootstrap dalam regersi non parametrik

ABSTRAK Bentuk taksiran kurva regresi nonparametrik ditentukan oleh parameter penghalus h yang lebih dikenal dengan nama bandwidth. Untuk mengetahui taksiran kurva regresi, dengan hubungan regresinya adalah Yi = m(X ) -1- - i = 1, 2, n digunakan metode bootstrap yaitu suatu resampling dari sekumpulan data pengamatan dengan pengembalian dengan massa peluangnya adalah lin untuk setiap titik data. Salah sate metode ini adalah Golden Section Bootstrap. Di sini digunakan penaksir Nadaraya-Watson yang diharapkan akan menghasilkan taksiran kurva regresi nonparametrik yang lebih halus dibanding taksiran kurva regresi dari data aslinya

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Dr. James H. Oliver, Jr., featured in Discover Magazine On-lin

COSM News

Dr. James H. Oliver, Jr., featured in Discover Magazine On-lin

Minimum Degrees of Minimal Ramsey Graphs for Almost-Cliques

For graphs $F$ and $H$, we say $F$ is Ramsey for $H$ if every $2$-coloring of the edges of $F$ contains a monochromatic copy of $H$. The graph $F$ is Ramsey $H$-minimal if $F$ is Ramsey for $H$ and there is no proper subgraph $F'$ of $F$ so that $F'$ is Ramsey for $H$. Burr, Erdos, and Lovasz defined $s(H)$ to be the minimum degree of $F$ over all Ramsey $H$-minimal graphs $F$. Define $H_{t,d}$ to be a graph on $t+1$ vertices consisting of a complete graph on $t$ vertices and one additional vertex of degree $d$. We show that $s(H_{t,d})=d^2$ for all values $1<d\le t$; it was previously known that $s(H_{t,1})=t-1$, so it is surprising that $s(H_{t,2})=4$ is much smaller. We also make some further progress on some sparser graphs. Fox and Lin observed that $s(H)\ge 2\delta(H)-1$ for all graphs $H$, where $\delta(H)$ is the minimum degree of $H$; Szabo, Zumstein, and Zurcher investigated which graphs have this property and conjectured that all bipartite graphs $H$ without isolated vertices satisfy $s(H)=2\delta(H)-1$. Fox, Grinshpun, Liebenau, Person, and Szabo further conjectured that all triangle-free graphs without isolated vertices satisfy this property. We show that $d$-regular $3$-connected triangle-free graphs $H$, with one extra technical constraint, satisfy $s(H) = 2\delta(H)-1$; the extra constraint is that $H$ has a vertex $v$ so that if one removes $v$ and its neighborhood from $H$, the remainder is connected.Comment: 10 pages; 3 figure

New Congruences Modulo 2, 4, and 8 for the Number of Tagged Parts Over the Partitions with Designated Summands

Recently, Lin introduced two new partition functions PD$_t(n)$ and PDO$_t(n)$, which count the total number of tagged parts over all partitions of $n$ with designated summands and the total number of tagged parts over all partitions of $n$ with designated summands in which all parts are odd. Lin also proved some congruences modulo 3 and 9 for PD$_t(n)$ and PDO$_t(n)$, and conjectured some congruences modulo 8. Very recently, Adansie, Chern, and Xia found two new infinite families of congruences modulo 9 for PD$_t(n)$. In this paper, we prove the congruences modulo 8 conjectured by Lin and also find many new congruences and infinite families of congruences modulo some small powers of 2.Comment: 19 page

Concerto Competition Final Round

Competition Coordinator Dr. Robert Rust Jury Cynthia Phelps, viola (Principal, New York Philharmonic) Leonard Hindell, bassoon (Former member, Metropolitan Opera Orchestra & New York Philharmonic) Robert Ward, piano (Director, Concerto Fest Austria) Piano Accompanists Dr. John Tu (Concerto Competition Accompanying Resident) Mr. Tao Lin (Collaborative Piano Faculty) Dr. Yang Shen (Collaborative Piano Faculty) Canvassers Roberta Burns Jack Kracke Finalists Hsin-Hui Liu, piano - Ravel, Piano Concerto in G major (Tu) Giorgi Chkhikvadze, piano - Prokofiev, Piano Concerto No. 2 in G minor, op. 16 (Tu) Dotan Nitzberg, piano - Liszt, Totentanz (Tu) Aneliya Novikova, piano - Rachmaninoff, Piano Concerto No. 3, op. 30 (Tu) Jesse Yukimura, viola - Martinu, Rhapsody Concerto, H, 337 (Lin) LUNCH BREAK Yaroslava Poletaeva, violin - Saint-Saens, Havanaise (Lin) Marina Lenau, violin - Tchaikovsky, Violin Concerto in D Major, op. 35 (Lin) Robert Harrover, trombone - David, Concertino for Trombone in E-flat Major, op. 4 (Tu) John Hong, clarinet - Mozart, Clarinet Concerto in A Major, K. 622 (Tu) Fabiola Porras, clarinet - Nielsen, Clarinet Concerto (Tu