1,721,065 research outputs found
Lie Groups, Differential Equations, and Geometry. Advances and Surveys
No full textThis book collects a series of contributions addressing the various contexts in which the theory of Lie groups is applied. A preliminary chapter serves the reader both as a basic reference source and as an ongoing thread that runs through the subsequent chapters. From representation theory and Gerstenhaber algebras to control theory, from differential equations to Finsler geometry and Lepage manifolds, the book introduces young researchers in Mathematics to a wealth of different topics, encouraging a multidisciplinary approach to research. As such, it is suitable for students in doctoral courses, and will also benefit researchers who want to expand their field of interest
Binary Hamming codes and Boolean designs
Full text linkIn this paper we consider a finite-dimensional vector space P over the Galois field GF(2), and the family Bk (respectively, B∗k) of all the k-sets of elements of P (respectively, of P∗=P∖{0}) summing up to zero. We compute the parameters of the 3-design (P,Bk) for any (necessarily even) k, and of the 2-design (P∗,B∗k) for any k. Also, we find a new proof for the weight distribution of the binary Hamming code. Moreover, we find the automorphism groups of the above designs by characterizing the permutations of P, respectively of P∗, that induce permutations of Bk, respectively of B∗k. In particular, this allows one to relax the definitions of the permutation automorphism groups of the binary Hamming code and of the extended binary Hamming code as the groups of permutations that preserve just the codewords of a given Hamming weight
Mumford representation and Riemann Roch space of a divisor on a hyperelliptic curve
Full text linkFor an (imaginary) hyperelliptic curve of genus , with a
Weierstrass point , taken as the point at infinity, we determine a
basis of the Riemann-Roch space , where
is of degree zero, directly from the Mumford representation of
. This provides in turn a generating matrix of a Goppa code.Comment: 8 page
Permutations of zero-sumsets in a finite vector space
Full text linkIn this paper, we consider a finite-dimensional vector space P over the Galois field GF(p), with p being an odd prime, and the family Bxk of all k-sets of elements of P summing up to a given element x. The main result of the paper is the characterization, for x=0, of the permutations of P inducing permutations of B0k as the invertible linear mappings of the vector space P if p does not divide k, and as the invertible affinities of the affine space P if p divides k. The same question is answered also in the case where the elements of the k-sets are required to be all nonzero, and, in fact, the two cases prove to be intrinsically inseparable
Enhancing Robot Assistive Behaviour by Mentalising User Intent and Beliefs with Reinforcement Learning
No full textAdaptation to user preferences and the ability to infer and interpret human beliefs and intents, known as the Theory of Mind (ToM), are two critical aspects of effective human-robot collaboration. Despite their importance, very few studies have investigated the impact of adaptive robots with ToM capabilities. This work presents an exploratory comparative study to investigate how social robots simulating ToM capabilities affect user performance and perception. We design a two-tier architecture. The Q-learning agent on the first layer learns the robot’s higher-level behaviour. On the second layer, a heuristic-based ToM infers the user’s intended strategy and is responsible for implementing the robot’s assistance, as well as providing the motivation behind its choice. We conducted a user study in a real-world setting, involving 56 participants who interacted with either an adaptive robot simulating ToM capabilities, or with a robot lacking such capabilities. Our results suggest that participants in the ToM condition performed better, accepted the robot’s assistance more often, and perceived its ability to adapt, predict and detect their intentions to a greater extent. Our preliminary findings could inform future research and pave the way for the design of robot architectures for adaptive behaviour with ToM capabilities, where the choice of action is decoupled from its implementation
Additivity of affine designs
No full textWe show that any affine block design D = (P, B) is a subset of a suitable commutative group G_D, with the property that a k-subset of P is a block of D if and only if its k elements sum up to zero. As a consequence, the group of automorphisms of any affine design D is the group of automorphisms of G_D that leave P invariant. Whenever k is a prime p, G_D is an elementary abelian p-group
Steiner Loops of Affine Type
Full text linkSteiner loops of affine type are associated to arbitrary Steiner triple systems. They behave to elementary abelian 3-groups as arbitrary Steiner Triple Systems behave to affine geometries over GF(3). We investigate algebraic and geometric properties of these loops often in connection to configurations. Steiner loops of affine type, as extensions of normal subloops by factor loops, are studied. We prove that the multiplication group of every Steiner loop of affine type with n elements is contained in the alternating group An and we give conditions for those loops having An as their multiplication groups (and hence for the loops being simple)
It Is the Way You Lie: Effects of Social Robot Deceptions on Trust in an Assistive Robot
Full text linkPersuasion is defined as the process of changing people's attitudes and behaviours and social assistive robots are used to favour such changes through a variety of mechanisms. While human-robot deception is considered to present philosophical and psychological issues, it still may have positive consequences. In particular, prosocial deception can be beneficial and have positive influences, such as increasing trust. This work presents an exploration of robot deception and its effects on people's changes in behaviour and trust in a social assistive robot. In particular, we explore the effects of different types of deception states (superficial, external, and hidden states) on people's compliance with a social robot during an assistive game scenario. We collected the responses of 63 participants to evaluate their perception of trust in the robot, and their perception of the robot's deceiving behaviours. Our results showed that the deceiving behaviours of the robot affected people's trust and that superficial state deception has higher negative effects on people's perception of the robot and trust in it compared to the other two deceptive states
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