Sistem pintar pengecaman bentuk agregat berasaskan rangkaian neural

Penghasilan sesebuah konkrit bergantung kepada kandungan agregat (batu baur) yang terkandung di dalam konkrit tersebut. Bentuk agregat-agregat yang terdapat di dalam konkrit dikatakan mempengaruhi kualiti konkrit yang akan dihasilkan. Agregat yang mempunyai bentuk yang dikatakan elok (well-shaped) akan menghasilkan konkrit yang bermutu tinggi dengan mengurangkan kadar air kepada simen di dalam konkrit. Sebaliknya, bentuk agregat-agregat yang buruk (poor-shaped) selalunya menyebabkan penghasilan sesebuah konkrit itu memerlukan kadar air kepada simen yang tinggi. Kebiasaannya, kualiti sesebuah konkrit ditentukan dengan mengira kadar peratusan kandungan agregat yang elok kepada agregat yang buruk yang terkandung di dalam konkrit. Masalah penentuan secara manual ini ialah lambat, terlalu subjektif dan memerlukan tenaga buruh yang ramai, sekaligus menyebabkan tidak efektif dan mahal. Dalam usaha untuk mengurangkan masalah ini, penyelidikan yang dilakukan telah memfokuskan kepada pembangunan sistem pengecaman pintar bentuk agregat berasaskan rangkaian neural. Sistem yang dibangunkan menggunakan teknik pemprosesan imej digital dan rangkaian neural untuk mengkelaskan bentuk-bentuk agregat yang diperolehi kepada dua kategori, "elok" dan "buruk". Sistem ini merangkumi dua bahagian utama iaitu pengekstrakan ciri-ciri imej dan pengecaman. Dalam bahagian pengekstrakan ciri-ciri imej, ciri-ciri yang dipertimbangkan ialah momen Zernike, momen Hu, saiz dan ukurlilit. Pengekstrakan ciri-ciri momen Zernike dan momen Hu dikira berdasarkan kepada saiz dan ukurlilit objek. Disebabkan momen Hu peringkat tinggi lebih sensitif kepada hingar, maka hanya momen Hu peringkat pertama dan kedua sahaja digunakan. Bagi ciri momen Zernike pula, nilai momen yang digunakan ialah jumlah penambahan nilai momen Zernike dari tertib 0 hingga tertib 4 kerana ia memberikan keputusan perkelompokan yang lebih baik. Dalam bahagian pengecaman, rangkaian neural yang dibangunkan ialah rangkaian hibrid berbilang lapisan perceptron (HMLP). Rangkaian tersebut telah dilatih menggunakan algoritma ralat ramalan berulang terubahsui (MRPE) dan memberikan prestasi pengecaman sebanyak 85.53%. Ini membuktikan sistem pengecaman bentuk agregat secara automatik yang dibangunkan berjaya mengkelaskan bentuk-bentuk agregat kepada dua kategori iaitu "elok" dan "buruk". Sebagai langkah awal untuk menghasilkan sistem pengecaman bentuk agregat mudah alih, sistem pengecaman menggunakan mikro pengawal juga telah dihasilkan dan dibuktikan keberkesanan dan kebolehpercayaannya. Sistem pengecaman yang berasaskan mikro pengawal ini telah menghasilkan peratus pengecaman yang sama nilainya dengan peratus pengecaman yang diperolehi menggunakan komputer peribadi

Progress on the adjacent vertex distinguishing edge colouring conjecture

A proper edge colouring of a graph is adjacent vertex distinguishing if no two adjacent vertices see the same set of colours. Using a clever application of the Local Lemma, Hatami (2005) proved that every graph with maximum degree $\Delta$ and no isolated edge has an adjacent vertex distinguishing edge colouring with $\Delta + 300$ colours, provided $\Delta$ is large enough. We show that this bound can be reduced to $\Delta + 19$. This is motivated by the conjecture of Zhang, Liu, and Wang (2002) that $\Delta + 2$ colours are enough for $\Delta \geq 3$.Comment: v2: Revised following referees' comment

Planar posets have dimension at most linear in their height

We prove that every planar poset $P$ of height $h$ has dimension at most $192h + 96$. This improves on previous exponential bounds and is best possible up to a constant factor. We complement this result with a construction of planar posets of height $h$ and dimension at least $(4/3)h-2$.Comment: v2: Minor change

Information-theoretic lower bounds for quantum sorting

We analyze the quantum query complexity of sorting under partial information. In this problem, we are given a partially ordered set $P$ and are asked to identify a linear extension of $P$ using pairwise comparisons. For the standard sorting problem, in which $P$ is empty, it is known that the quantum query complexity is not asymptotically smaller than the classical information-theoretic lower bound. We prove that this holds for a wide class of partially ordered sets, thereby improving on a result from Yao (STOC'04)

Weighted graphs defining facets: a connection between stable set and linear ordering polytopes

A graph is alpha-critical if its stability number increases whenever an edge is removed from its edge set. The class of alpha-critical graphs has several nice structural properties, most of them related to their defect which is the number of vertices minus two times the stability number. In particular, a remarkable result of Lov\'asz (1978) is the finite basis theorem for alpha-critical graphs of a fixed defect. The class of alpha-critical graphs is also of interest for at least two topics of polyhedral studies. First, Chv\'atal (1975) shows that each alpha-critical graph induces a rank inequality which is facet-defining for its stable set polytope. Investigating a weighted generalization, Lipt\'ak and Lov\'asz (2000, 2001) introduce critical facet-graphs (which again produce facet-defining inequalities for their stable set polytopes) and they establish a finite basis theorem. Second, Koppen (1995) describes a construction that delivers from any alpha-critical graph a facet-defining inequality for the linear ordering polytope. Doignon, Fiorini and Joret (2006) handle the weighted case and thus define facet-defining graphs. Here we investigate relationships between the two weighted generalizations of alpha-critical graphs. We show that facet-defining graphs (for the linear ordering polytope) are obtainable from 1-critical facet-graphs (linked with stable set polytopes). We then use this connection to derive various results on facet-defining graphs, the most prominent one being derived from Lipt\'ak and Lov\'asz's finite basis theorem for critical facet-graphs. At the end of the paper we offer an alternative proof of Lov\'asz's finite basis theorem for alpha-critical graphs

Disproof of the List Hadwiger Conjecture

The List Hadwiger Conjecture asserts that every $K_t$-minor-free graph is $t$-choosable. We disprove this conjecture by constructing a $K_{3t+2}$-minor-free graph that is not $4t$-choosable for every integer $t\geq 1$

Smaller Extended Formulations for the Spanning Tree Polytope of Bounded-genus Graphs

We give an $O(g^{1/2} n^{3/2} + g^{3/2} n^{1/2})$-size extended formulation for the spanning tree polytope of an $n$-vertex graph embedded on a surface of genus $g$, improving on the known $O(n^2 + g n)$-size extended formulations following from Wong and Martin.Comment: v3: fixed some typo

Pathwidth and nonrepetitive list coloring

A vertex coloring of a graph is nonrepetitive if there is no path in the graph whose first half receives the same sequence of colors as the second half. While every tree can be nonrepetitively colored with a bounded number of colors (4 colors is enough), Fiorenzi, Ochem, Ossona de Mendez, and Zhu recently showed that this does not extend to the list version of the problem, that is, for every $\ell \geq 1$ there is a tree that is not nonrepetitively $\ell$-choosable. In this paper we prove the following positive result, which complements the result of Fiorenzi et al.: There exists a function $f$ such that every tree of pathwidth $k$ is nonrepetitively $f(k)$-choosable. We also show that such a property is specific to trees by constructing a family of pathwidth-2 graphs that are not nonrepetitively $\ell$-choosable for any fixed $\ell$.Comment: v2: Minor changes made following helpful comments by the referee