Abstract:
I argue that opposite arrows of time, while being logically possible, cannot realistically be assumed to exist during one and the same epoch of our universe.

Abstract:
I argue that opposite arrows of time, while being logically possible, cannot realistically be assumed to exist during one and the same epoch of this universe.

Abstract:
A model in which two weakly coupled systems maintain opposite running thermodynamic arrows of time is exhibited. Each experiences its own retarded electromagnetic interaction and can be seen by the other. The possibility of opposite-arrow systems at stellar distances is explored and a relation to dark matter suggested.

Abstract:
We present a quantum model for the motion of N point particles, implying nonlocal (i.e., superluminal) influences of external fields on the trajectories, that is nonetheless fully relativistic. In contrast to other models that have been proposed, this one involves no additional space-time structure as would be provided by a (possibly dynamical) foliation of space-time. This is achieved through the interplay of opposite microcausal and macrocausal (i.e., thermodynamic) arrows of time.

Abstract:
We prove the compatibility at places dividing l of the local and global Langlands correspondences for the l-adic Galois representations associated to regular algebraic essentially (conjugate) self-dual cuspidal automorphic representations of GL_n over an imaginary CM or totally real field. We prove this compatibility up to semisimplification in all cases, and up to Frobenius semisimplification in the case of Shin-regular weight.

Abstract:
This paper makes an account of the design and investigations done for the still image watermarking technique used in the 2nd edition of the BOWS challenge. This technique is named ￠ € broken arrows ￠ € for some reasons given later on, and abbreviated ￠ € BA. ￠ € This zero-bit algorithm is an implementation of a recent theoretical result by Merhav and Sabbag (2008) with precautions taken with respect to robustness, security, and imperceptibility. A new robustness criterion, based on the nearest border point of a cone, is proposed. The security constraint is taken into account by increasing the diversity of the watermark, sculpturing and randomizing the shape of the detection regions. The imperceptibility and robustness are also provided by adopting proportional embedding in the wavelet domain. The algorithm has been benchmarked using a database of 2000 images. For a probability of false alarm below 3 ￠ …10 ￠ ’6 and a PSNR of 43 ￠ € ‰dB, the overall robustness regarding various classical image processing seems a promising and strong basis for the challenge.

Abstract:
Antiparticles may be interpreted as ordinary particles travelling backwards in time and the two descriptions are considered equivalent, at least in special relativity and relativistic quantum mechanics. It is suggested that, vice versa, the discovery of antimatter should be the confirmation that our world is "endowed" with two opposite time-arrows and such a description could be more useful and convenient from the point of view of the understanding of the world itself, at least for a simple reason: whenever phenomena are observed from a "reference frame" from which the world appears more symmetric, it is easier to understand the physical laws which regulate it. If, in the future, it is possible to discover how a macroscopic system of antimatter behaves, it will be also possible to confirm (or not) the "reality" of the two arrows of time.

Abstract:
The familiar textbook quantum mechanics of laboratory measurements incorporates a quantum mechanical arrow of time --- the direction in time in which state vector reduction operates. This arrow is usually assumed to coincide with the direction of the thermodynamic arrow of the quasiclassical realm of everyday experience. But in the more general context of cosmology we seek an explanation of all observed arrows, and the relations between them, in terms of the conditions that specify our particular universe. This paper investigates quantum mechanical and thermodynamic arrows in a time-neutral formulation of quantum mechanics for a number of model cosmologies in fixed background spacetimes. We find that a general universe may not have well defined arrows of either kind. When arrows are emergent they need not point in the same direction over the whole of spacetime. Rather they may be local, pointing in different directions in different spacetime regions. Local arrows can therefore be consistent with global time symmetry.

Abstract:
We define the compatibility JSJ tree of a group G over a class of subgroups. It exists whenever G is finitely presented and leads to a canonical tree (not a deformation space) which is invariant under automorphisms. Under acylindricity hypotheses, we prove that the (usual) JSJ deformation space and the compatibility JSJ tree exist, and we describe their flexible subgroups. We apply these results to finitely generated CSA groups, \Gamma-limit groups (allowing torsion), and relatively hyperbolic groups.

Abstract:
We report outside protrusion of resorbable Biofix arrows after repair of a medial meniscus tear in a 10-year-old boy. One arrow protruded spontaneously. At surgery the other partially resorbed arrow was found subcutaneously. The tear of the medial meniscus had healed.