Browsing Universidad Torcuato Di Tella by Author "Pinasco, Damián"
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Farkas’ Lemma in the bilinear setting and evaluation functionals
Zalduendo, Ignacio; Aron, Richard; García, Domingo; Pinasco, Damián (Real Academia de Ciencias Exactas, Físicas y Naturales, 2023)We prove the following Farkas’ Lemma for simultaneously diagonalizable bilinear forms: If A1, . . . , Ak, and B : Rn × Rn → R are bilinear forms, then one—and only one—of the following holds: (i) B = a1A1 +· · ·+ak Ak ... -
On the n−th linear polarization constant of Rn
Pinasco, Damián (Mathematische Nachrichten, 2023)Abstract. We prove that given any set of n unit vectors {vi}n i=1 ⊂ Rn, the inequality sup kxkRn=1 |hx, v1i · · · hx, vni| ≥ n−n/2 holds for n ≤ 14. Moreover, the equality is attained if and only if {vi}n i=1 is an ... -
On the volume ratio of projections of convex bodies
Pinasco, Damián; Galicer, Daniel; Litvak, Alexander E.; Merzbaher, Mariano (Universidad Torcuato Di Tella, 2022)We study the volume ratio between projections of two convex bodies. Given a high-dimensional convex body K we show that there is another convex body L such that the volume ratio between any two projections of fixed rank ... -
Segregation patterns for non-homogeneous locations in Schellings model
Pinasco, Damián; Schiaffino, Pablo; Arcón, Victoria; Caridi, Inés (Universidad Torcuato Di Tella, 2023)We study a variant of the classical spatial proximity Schelling’s segregation model, including a function that breaks the homogeneity over the land. This weighting function represents objective and subjective assessments ...