Convergence time to equilibrium distributions of autonomous and periodic non-autonomous graphs

We present some estimates of the time of convergence to the equilibrium distribution in autonomous and periodic non-autonomous graphs, with ergodic stochastic adjacency matrices, using the eigenvalues of these matrices. On this way we generalize previous results from several authors, that only considered reversible matrices.

A pointwise constrained version of the Liapunov convexity theorem for vectorial linear first-order control systems

We generalize the Liapunov convexity theorem's version for vectorial control systems driven by linear ODEs of first-order p = 1 , in any dimension d ∈ N , by including a pointwise state-constraint. More precisely, given a x ‾ ( ⋅ ) ∈ W p , 1 ( [ a , b ] , R d ) solving the convexified p-th order differential inclusion L p x ‾ ( t ) ∈ co { u 0 ( t ) , u 1 ( t ) , … , u m ( t ) } a.e., consider the general problem consisting in finding bang-bang solutions (i.e. L p x ˆ ( t ) ∈ { u 0 ( t ) , u 1 ( t ) , … , u m ( t ) } a.e.) under the same boundary-data, x ˆ ( k ) ( a ) = x ‾ ( k ) ( a ) & x ˆ ( k ) ( b ) = x ‾ ( k ) ( b ) ( k = 0 , 1 , … , p − 1 ); but restricted, moreover, by a pointwise state constraint of the type 〈 x ˆ ( t ) , ω 〉 ≤ 〈 x ‾ ( t ) , ω 〉 ∀ t ∈ [ a , b ] (e.g. ω = ( 1 , 0 , … , 0 ) yielding x ˆ 1 ( t ) ≤ x ‾ 1 ( t ) ). Previous results in the scalar d = 1 case were the pioneering Amar & Cellina paper (dealing with L p x ( ⋅ ) = x ′ ( ⋅ ) ), followed by Cerf & Mariconda results, who solved the general case of linear differential operators L p of order p ≥ 2 with C 0 ( [ a , b ] ) -coefficients. This paper is dedicated to: focus on the missing case p = 1 , i.e. using L p x ( ⋅ ) = x ′ ( ⋅ ) + A ( ⋅ ) x ( ⋅ ) ; generalize the dimension of x ( ⋅ ) , from the scalar case d = 1 to the vectorial d ∈ N case; weaken the coefficients, from continuous to integrable, so that A ( ⋅ ) now becomes a d × d -integrable matrix; and allow the directional vector ω to become a moving AC function ω ( ⋅ ) . Previous vectorial results had constant ω, no matrix (i.e. A ( ⋅ ) ≡ 0 ) and considered: constant control-vertices (Amar & Mariconda) and, more recently, integrable control-vertices (ourselves).

Representing image captions as concept graphs using semantic information

Conceptual interpretation of languages has gathered peak interest in the world of artificial intelligence. The challenge in modeling various complications involved in a language is the main motivation behind our work. Our main focus in this work is to develop conceptual graphical representation for image captions. We have used discourse representation structure to gain semantic information which is further modeled into a graphical structure. The effectiveness of the model is evaluated by a caption based image retrieval system. The image retrieval is performed by computing subgraph based similarity measures. Best retrievals were given an average rating of . ± . out of 4 by a group of 25 human judges. The experiments were performed on a subset of the SBU Captioned Photo Dataset. This purpose of this work is to establish the cognitive sensibility of the approach to caption representations

Representing image captions as concept graphs using semantic information

Conceptual interpretation of languages has gathered peak interest in the world of artificial intelligence. The challenge in modeling various complications involved in a language is the main motivation behind our work. Our main focus in this work is to develop conceptual graphical representation for image captions. We have used discourse representation structure to gain semantic information which is further modeled into a graphical structure. The effectiveness of the model is evaluated by a caption based image retrieval system. The image retrieval is performed by computing subgraph based similarity measures. Best retrievals were given an average rating of . ± . out of 4 by a group of 25 human judges. The experiments were performed on a subset of the SBU Captioned Photo Dataset. This purpose of this work is to establish the cognitive sensibility of the approach to caption representations.