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1. Constraining the Clustering Transition for Colorings of Sparse Random Graphs

   Anastos, Michael; Frieze, Alan; Pegden, Wesley (March 2018, The Electronic journal of combinatorics)

   Let Ωq denote the set of proper [q]-colorings of the random graph Gn,m,m=dn/2 and let Hq be the graph with vertex set Ωq and an edge {σ,τ} where σ,τ are mappings [n]→[q] iff h(σ,τ)=1. Here h(σ,τ) is the Hamming distance |{v∈[n]:σ(v)≠τ(v)}|. We show that w.h.p. Hq contains a single giant component containing almost all colorings in Ωq if d is sufficiently large and q≥cdlogd for a constant c>3/2. 

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2. Energy Harvesting Performance of a Flapping Foil with Leading Edge Motion

   Prier, M. (April 2019, Dissertation)

   F or c e d at a f or a fl a p pi n g f oil e n er g y h ar v e st er wit h a cti v e l e a di n g e d g e m oti o n o p er ati n g i n t h e l o w r e d u c e d fr e q u e n c y r a n g e i s c oll e ct e d t o d et er mi n e h o w l e a di n g e d g e m oti o n aff e ct s e n er g y h ar v e sti n g p erf or m a n c e. T h e f oil pi v ot s a b o ut t h e mi dc h or d a n d o p er at e s i n t h e l o w r e d u c e d fr e q u e n c y r a n g e of 𝑓𝑓 𝑓𝑓 / 𝑈𝑈 ∞ = 0. 0 6 , 0. 0 8, a n d 0. 1 0 wit h 𝑅𝑅 𝑅𝑅 = 2 0 ,0 0 0 − 3 0 ,0 0 0 , wit h a pit c hi n g a m plit u d e of 𝜃𝜃 0 = 7 0 ∘ , a n d a h e a vi n g a m plit u d e of ℎ 0 = 0. 5 𝑓𝑓 . It i s f o u n d t h at l e a di n g e d g e m oti o n s t h at r e d u c e t h e eff e cti v e a n gl e of att a c k e arl y t h e str o k e w or k t o b ot h i n cr e a s e t h e lift f or c e s a s w ell a s s hift t h e p e a k lift f or c e l at er i n t h e fl a p pi n g str o k e. L e a di n g e d g e m oti o n s i n w hi c h t h e eff e cti v e a n gl e of att a c k i s i n cr e a s e d e arl y i n t h e str o k e s h o w d e cr e a s e d p erf or m a n c e. I n a d diti o n a di s cr et e v ort e x m o d el wit h v ort e x s h e d di n g at t h e l e a di n g e d g e i s i m pl e m e nt f or t h e m oti o n s st u di e d; it i s f o u n d t h at t h e m e c h a ni s m f or s h e d di n g at t h e l e a di n g e d g e i s n ot a d e q u at e f or t hi s p ar a m et er r a n g e a n d t h e m o d el c o n si st e ntl y o v er pr e di ct s t h e a er o d y n a mi c f or c e s. 

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3. Tight Bounds on the Number of Closest Pairs in Vertical Slabs

   https://doi.org/10.4230/LIPIcs.WADS.2025.8  

   Biniaz, Ahmad; Bose, Prosenjit; Chung, Chaeyoon; De_Carufel, Jean-Lou; Iacono, John; Maheshwari, Anil; Odak, Saeed; Smid, Michiel; Tóth, Csaba D (January 2025, Schloss Dagstuhl – Leibniz-Zentrum für Informatik)

   Morin, Pat; Oh, Eunjin (Ed.)

   Let S be a set of n points in ℝ^d, where d ≥ 2 is a constant, and let H₁,H₂,…,H_{m+1} be a sequence of vertical hyperplanes that are sorted by their first coordinates, such that exactly n/m points of S are between any two successive hyperplanes. Let |A(S,m)| be the number of different closest pairs in the {(m+1) choose 2} vertical slabs that are bounded by H_i and H_j, over all 1 ≤ i < j ≤ m+1. We prove tight bounds for the largest possible value of |A(S,m)|, over all point sets of size n, and for all values of 1 ≤ m ≤ n. As a result of these bounds, we obtain, for any constant ε > 0, a data structure of size O(n), such that for any vertical query slab Q, the closest pair in the set Q ∩ S can be reported in O(n^{1/2+ε}) time. Prior to this work, no linear space data structure with sublinear query time was known. 

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4. On Single-Distance Graphs on the Rational Points in Euclidean Spaces

   https://doi.org/10.4153/S0008439520000181  

   Bau, Sheng; Johnson, Peter; Noble, Matt (March 2021, Canadian Mathematical Bulletin)

   null (Ed.)

   Abstract For positive integers n and d > 0, let $$G(\mathbb {Q}^n,\; d)$$ denote the graph whose vertices are the set of rational points $$\mathbb {Q}^n$$ , with $$u,v \in \mathbb {Q}^n$$ being adjacent if and only if the Euclidean distance between u and v is equal to d . Such a graph is deemed “non-trivial” if d is actually realized as a distance between points of $$\mathbb {Q}^n$$ . In this paper, we show that a space $$\mathbb {Q}^n$$ has the property that all pairs of non-trivial distance graphs $$G(\mathbb {Q}^n,\; d_1)$$ and $$G(\mathbb {Q}^n,\; d_2)$$ are isomorphic if and only if n is equal to 1, 2, or a multiple of 4. Along the way, we make a number of observations concerning the clique number of $$G(\mathbb {Q}^n,\; d)$$ . 

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5. Toward Personalizing Students' Education with Crowdsourced Tutoring

   https://doi.org/10.1145/3430895.3460130  

   Prihar, Ethan; Patikorn, Thanaporn; Botelho, Anthony; Sales, Adam; Heffernan, Neil (June 2021, Lerning @ Scale 2021)

   null (Ed.)

   A s m or e e d u c at or s i nt e gr at e t h eir c urri c ul a wit h o nli n e l e ar ni n g, it i s e a si er t o cr o w d s o ur c e c o nt e nt fr o m t h e m. Cr o w ds o ur c e d t ut ori n g h a s b e e n pr o v e n t o r eli a bl y i n cr e a s e st u d e nt s’ n e xt pr o bl e m c orr e ct n e s s. I n t hi s w or k, w e c o n fir m e d t h e fi n di n g s of a pr e vi o u s st u d y i n t hi s ar e a, wit h str o n g er c o n fi d e n c e m ar gi n s t h a n pr e vi o u sl y, a n d r e v e al e d t h at o nl y a p orti o n of cr o w d s o ur c e d c o nt e nt cr e at or s h a d a r eli a bl e b e n e fit t o st ud e nt s. F urt h er m or e, t hi s w or k pr o vi d e s a m et h o d t o r a n k c o nt e nt cr e at or s r el ati v e t o e a c h ot h er, w hi c h w a s u s e d t o d et er mi n e w hi c h c o nt e nt cr e at or s w er e m o st eff e cti v e o v er all, a n d w hi c h c o nt e nt cr e at or s w er e m o st eff e cti v e f or s p e ci fi c gr o u p s of st u d e nt s. W h e n e x pl ori n g d at a fr o m Te a c h er A SSI S T, a f e at ur e wit hi n t h e A S SI S T m e nt s l e ar ni n g pl atf or m t h at cr o w d s o ur c e s t ut ori n g fr o m t e a c h er s, w e f o u n d t h at w hil e o v erall t hi s pr o gr a m pr o vi d e s a b e n e fit t o st u d e nt s, s o m e t e a c h er s cr e at e d m or e eff e cti v e c o nt e nt t h a n ot h er s. D e s pit e t hi s fi n di n g, w e di d n ot fi n d e vi d e n c e t h at t h e eff e cti v e n e s s of c o nt e nt r eli a bl y v ari e d b y st u d e nt k n o wl e d g e-l e v el, s u g g e sti n g t h at t h e c o nt e nt i s u nli k el y s uit a bl e f or p er s o n ali zi n g i n str u cti o n b a s e d o n st u d e nt k n o wl e d g e al o n e. T h e s e fi n di n g s ar e pr o mi si n g f or t h e f ut ur e of cr o w d s o ur c e d t ut ori n g a s t h e y h el p pr o vi d e a f o u n d ati o n f or a s s e s si n g t h e q u alit y of cr o w d s o ur c e d c o nt e nt a n d i n v e sti g ati n g c o nt e nt f or o p p ort u niti e s t o p er s o n ali z e st u d e nt s’ e d u c ati o n. 

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