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Ali Kanso

Publications and source records attributed to Ali Kanso.

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A global mobile network coverage raster product at 1km resolution, 1999--2030

Where a mobile signal is available shapes who can work, learn, bank, seek health care and respond to crises in the digital age, yet no globally consistent, sub-national record of mobile network coverage exists. We present such a record: annual 1km maps of the probability of 2G, 3G and 4G coverage for 214 countries and territories for the years 1999 to 2030. The maps are produced by three independent models: a calibrated machine-learning model, a techno-economic simulator of network build-out, and a spatial deep-learning model. The three estimates are then combined, per country and technology and in proportion to their measured accuracy, into a single best estimate with per-pixel 90% uncertainty bands; all four layers are released as part of the dataset. Because mobile roll-out closely follows a country's socio-economic conditions (population distribution, electrification, physical infrastructure), the models are grounded in existing geospatial data and tuned on 2,409 quality-screened operator-reported coverage maps, which are available up to 2020. For 2021--2024 the maps are predicted from recent geospatial data alone; for 2025--2030 they are extrapolated from demographic and infrastructure projections. On countries held out during training, the machine-learning model attains AUC 0.89--0.92. Baseline comparisons and the combined product's external validation are reported in Technical Validation. The dataset supports mapping the global digital divide, linking connectivity to household-survey outcomes, and humanitarian and infrastructure planning.

cs.CY

Reinforcement learning for graph theory, II. Small Ramsey numbers

We describe here how the recent Wagner's approach for applying reinforcement learning to construct examples in graph theory can be used in the search for critical graphs for small Ramsey numbers. We illustrate this application by providing lower bounds for the small Ramsey numbers $R(K_{2,5}, K_{3,5})$, $R(B_3, B_6)$ and $R(B_4, B_5)$ and by improving the lower known bound for $R(W_5, W_7)$.

math.CO

Reinforcement learning for graph theory, I. Reimplementation of Wagner's approach

We reimplement here the recent approach of Adam Zsolt Wagner [arXiv:2104.14516], which applies reinforcement learning to construct (counter)examples in graph theory, in order to make it more readable, more stable and much faster. The presented concepts are illustrated by constructing counterexamples for a number of published conjectured bounds for the Laplacian spectral radius of graphs.

math.CO

On the Second-Order Wiener Ratios of Iterated Line Graphs

The Wiener index W(G) of a graph G is the sum of distances between all unordered pairs of its vertices. Dobrynin and Mel'nikov [in: Distance in Molecular Graphs - Theory, 2012, p. 85-121] propose the study of estimates for extremal values of the ratio R_k(G) = W(L^k(G))/W(G) where L^k(G) denotes the k-th iterated line graph of G. Hri\v{n}\'akov\'a, Knor and \v{S}krekovski [Art Discrete Appl. Math. 1 (2018) #P1.09] prove that for each k>2, the path P_n has the smallest value of the ratio R_k among all trees of large order n, and they conjecture that the same holds for the case k=2. We give a counterexample of every order n>21 to this conjecture.

math.CO

On Hosoya's dormants and sprouts

In a recent series of papers, Hosoya drew the attention to a particular aspect of constructing cospectral graphs by using coalescences: that cospectral graphs can be constructed by attaching multiple copies of a rooted graph in different ways to subsets of vertices of an underlying graph. Our principal focus is to address the expectations and questions raised in Hosoya's papers with regards to this construction. We give an explicit formula for the characteristic polynomial of such multiple coalescences, from which we obtain a necessary and sufficient condition for their cospectrality. We enumerate such cospectral multiple coalescences for a few families of underlying graphs, and show the infinitude of cospectral multiple coalescences having paths as underlying graphs, which were deemed rare by Hosoya.

math.CO