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A Mobile Game to Explore the Use of Location Awareness on Collaboration

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On the boundedness of n-folds with κ(X) = n - 1

Stefano Filipazzi

In this note, we study certain sufficient conditions for a set of minimal klt pairs ( X, triangle) with kappa ( X, triangle) = dim( X ) - 1 to be bounded. ...

European Mathematical Soc-Ems2024

A lower bound on opaque sets

János Pach

It is proved that the total length of any set of countably many rectifiable curves whose union meets all straight lines that intersect the unit square U is at least 2.00002. This is the first improvement on the lower bound of 2 known since 1964. A similar ...

ELSEVIER SCIENCE BV2019

New Moduli For Banach Spaces

Grigory Ivanov

Modifying the moduli of supporting convexity and supporting smoothness, we introduce new moduli for Banach spaces which occur, for example, as lengths of catheti of right-angled triangles (defined via so-called quasiorthogonality). These triangles have two ...

Tusi Mathematical Research Group2017

On Simplices in Diameter Graphs in R-4

Andrei Kupavskii

A graph G is a diameter graph in R-d if its vertex set is a finite subset in R-d of diameter 1 and edges join pairs of vertices a unit distance apart. It is shown that if a diameter graph G in R-4 contains the complete subgraph K on five vertices, then any ...

Maik Nauka/Interperiodica/Springer2017

Stability Results For The Volume Of Random Simplices

Gergely Ambrus

It is known that for a convex body K in R-d of volume one, the expected volume of random simplices in K is minimized if K is an ellipsoid, and for d = 2, maximized if K is a triangle. Here we provide corresponding stability estimates. ...

Johns Hopkins Univ Press2014

Hiding in the Mobile Crowd: Location Privacy through Collaboration

Jean-Pierre Hubaux, Panagiotis Papadimitratos, Reza Shokri, Georgios Theodorakopoulos, Ehsan Kazemi

Location-aware smartphones support various location-based services (LBSs): users query the LBS server and learn on the fly about their surroundings. However, such queries give away private information, enabling the LBS to track users. We address this probl ...

IEEE Transactions on Dependable and Secure Computing (TDSC), vol. 11, no. 3, pp. 266-2792014

Hiding in the Mobile Crowd: Location Privacy through Collaboration

Jean-Pierre Hubaux, Panagiotis Papadimitratos, Reza Shokri, Georgios Theodorakopoulos, Ehsan Kazemi

Ieee Computer Soc2014

Exponentiality of the exchange algorithm for finding another room-partitioning

Laura Sanità

Let T be a triangulated surface given by the list of vertex-triples of its triangles, called rooms. A room-partitioning for T is a subset R of the rooms such that each vertex of T is in exactly one room in R. Given a room-partitioning R for T, the exchange ...

Elsevier Science Bv2014

Diameter Graphs in R-4

Andrei Kupavskii

A diameter graph in is a graph whose set of vertices is a finite subset of and whose set of edges is formed by pairs of vertices that are at diameter apart. This paper is devoted to the study of different extremal properties of diameter graphs in and on a ...

Springer2014

Upper bounds for the perimeter of plane convex bodies

Filip Moric

We show that the maximum total perimeter of k plane convex bodies with disjoint interiors lying inside a given convex body C is equal to , in the case when C is a square or an arbitrary triangle. A weaker bound is obtained for general plane convex bodies. ...

Springer2014