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1. On Explicit Constructions of Extremely Depth Robust Graphs

   https://doi.org/10.4230/LIPIcs.STACS.2022.14  

   Blocki, Jeremiah; Cinkoske, Mike; Lee, Seunghoon; Son, Jin Young (January 2022, Leibniz international proceedings in informatics)

   Berenbrink, Petra and (Ed.)

   A directed acyclic graph G = (V,E) is said to be (e,d)-depth robust if for every subset S ⊆ V of |S| ≤ e nodes the graph G-S still contains a directed path of length d. If the graph is (e,d)-depth-robust for any e,d such that e+d ≤ (1-ε)|V| then the graph is said to be ε-extreme depth-robust. In the field of cryptography, (extremely) depth-robust graphs with low indegree have found numerous applications including the design of side-channel resistant Memory-Hard Functions, Proofs of Space and Replication and in the design of Computationally Relaxed Locally Correctable Codes. In these applications, it is desirable to ensure the graphs are locally navigable, i.e., there is an efficient algorithm GetParents running in time polylog|V| which takes as input a node v ∈ V and returns the set of v’s parents. We give the first explicit construction of locally navigable ε-extreme depth-robust graphs with indegree O(log |V|). Previous constructions of ε-extreme depth-robust graphs either had indegree ω̃(log² |V|) or were not explicit. 

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2. Approximating Cumulative Pebbling Cost Is Unique Games Hard

   https://doi.org/10.4230/LIPIcs.ITCS.2020.13  

   Blocki, J; Lee, S; Zhou, S. (January 2020, Leibniz international proceedings in informatics)

   null (Ed.)

   The cumulative pebbling complexity of a directed acyclic graph G is defined as cc(G) = min_P ∑_i |P_i|, where the minimum is taken over all legal (parallel) black pebblings of G and |P_i| denotes the number of pebbles on the graph during round i. Intuitively, cc(G) captures the amortized Space-Time complexity of pebbling m copies of G in parallel. The cumulative pebbling complexity of a graph G is of particular interest in the field of cryptography as cc(G) is tightly related to the amortized Area-Time complexity of the Data-Independent Memory-Hard Function (iMHF) f_{G,H} [Joël Alwen and Vladimir Serbinenko, 2015] defined using a constant indegree directed acyclic graph (DAG) G and a random oracle H(⋅). A secure iMHF should have amortized Space-Time complexity as high as possible, e.g., to deter brute-force password attacker who wants to find x such that f_{G,H}(x) = h. Thus, to analyze the (in)security of a candidate iMHF f_{G,H}, it is crucial to estimate the value cc(G) but currently, upper and lower bounds for leading iMHF candidates differ by several orders of magnitude. Blocki and Zhou recently showed that it is NP-Hard to compute cc(G), but their techniques do not even rule out an efficient (1+ε)-approximation algorithm for any constant ε>0. We show that for any constant c > 0, it is Unique Games hard to approximate cc(G) to within a factor of c. Along the way, we show the hardness of approximation of the DAG Vertex Deletion problem on DAGs of constant indegree. Namely, we show that for any k,ε >0 and given a DAG G with N nodes and constant indegree, it is Unique Games hard to distinguish between the case that G is (e_1, d_1)-reducible with e_1=N^{1/(1+2 ε)}/k and d_1=k N^{2 ε/(1+2 ε)}, and the case that G is (e_2, d_2)-depth-robust with e_2 = (1-ε)k e_1 and d_2= 0.9 N^{(1+ε)/(1+2 ε)}, which may be of independent interest. Our result generalizes a result of Svensson who proved an analogous result for DAGs with indegree 𝒪(N). 

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3. Individual differences and long-term consequences of tDCS augmented cognitive training

   Katz, B.; Au, J.; Buschkuehl, M.; Abagis, T.; Zabel, C.; Jaeggi, S.; Jonides, J. (October 2017, Journal of cognitive neuroscience)

   A gr e at d e al of i nt er e st s urr o u n d s t h e u s e of tr a n s cr a ni al dir e ct c urr e nt sti m ul ati o n (t D C S) t o a u g m e nt c o g niti v e tr ai ni n g. H o w e v er, eff e ct s ar e i n c o n si st e nt a cr o s s st u di e s, a n d m et aa n al yti c e vi d e n c e i s mi x e d, e s p e ci all y f o r h e alt h y, y o u n g a d ult s. O n e m aj or s o ur c e of t hi s i n c o n si st e n c y i s i n di vi d u al diff er e n c e s a m o n g t h e p arti ci p a nt s, b ut t h e s e diff er e n c e s ar e r ar el y e x a mi n e d i n t h e c o nt e xt of c o m bi n e d tr ai ni n g/ sti m ul ati o n st u di e s. I n a d diti o n, it i s u n cl e ar h o w l o n g t h e eff e ct s of sti m ul ati o n l a st, e v e n i n s u c c e s sf ul i nt er v e nti o n s. S o m e st u di e s m a k e u s e of f oll o w- u p a s s e s s m e nt s, b ut v er y f e w h a v e m e a s ur e d p erf or m a n c e m or e t h a n a f e w m o nt hs aft er a n i nt er v e nti o n. H er e, w e utili z e d d at a fr o m a pr e vi o u s st u d y of t D C S a n d c o g niti v e tr ai ni n g [ A u, J., K at z, B., B u s c h k u e hl, M., B u n arj o, K., S e n g er, T., Z a b el, C., et al. E n h a n ci n g w or ki n g m e m or y tr ai ni n g wit h tr a n scr a ni al dir e ct c urr e nt sti m ul ati o n. J o u r n al of C o g niti v e N e u r os ci e n c e, 2 8, 1 4 1 9 – 1 4 3 2, 2 0 1 6] i n w hi c h p arti ci p a nts tr ai n e d o n a w or ki n g m e m or y t as k o v er 7 d a y s w hil e r e c ei vi n g a cti v e or s h a m t D C S. A n e w, l o n g er-t er m f oll o w- u p t o a ss es s l at er p erf or m a n c e w a s c o n d u ct e d, a n d a d diti o n al p arti ci p a nt s w er e a d d e d s o t h at t h e s h a m c o n diti o n w a s b ett er p o w er e d. W e a s s e s s e d b a s eli n e c o g niti v e a bilit y, g e n d er, tr ai ni n g sit e, a n d m oti v ati o n l e v el a n d f o u n d si g nifi c a nt i nt er a cti o ns b et w e e n b ot h b as eli n e a bilit y a n d m oti v ati o n wit h c o n diti o n ( a cti v e or s h a m) i n m o d els pr e di cti n g tr ai ni n g g ai n. I n a d diti o n, t h e i m pr o v e m e nt s i n t h e a cti v e c o nditi o n v er s u s s h a m c o n diti o n a p p e ar t o b e st a bl e e v e n a s l o n g a s a y e ar aft er t h e ori gi n al i nt er v e nti o n. ■ 

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4. 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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5. Subdivided Claws and the Clique-Stable Set Separation Property

   https://doi.org/10.1007/978-3-030-62497-2  

   Chudnovsky, Maria and (February 2021, MATRIX book series)

   null (Ed.)

   Let C be a class of graphs closed under taking induced subgraphs. We say that C has the clique-stable set separation property if there exists c ∈ N such that for every graph G ∈ C there is a collection P of partitions (X, Y ) of the vertex set of G with |P| ≤ |V (G)| c and with the following property: if K is a clique of G, and S is a stable set of G, and K ∩ S = ∅, then there is (X, Y ) ∈ P with K ⊆ X and S ⊆ Y . In 1991 M. Yannakakis conjectured that the class of all graphs has the clique-stable set separation property, but this conjecture was disproved by M. G¨o¨os in 2014. Therefore it is now of interest to understand for which classes of graphs such a constant c exists. In this paper we define two infinite families S, K of graphs and show that for every S ∈ S and K ∈ K, the class of graphs with no induced subgraph isomorphic to S or K has the clique-stable set separation property. 

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