Artificial reinforcement learning (RL) is a widely used technique in artificial intelligence that provides a general method for training agents to perform a wide variety of behaviours. RL as used in computer science has striking parallels to reward and punishment learning in animal and human brains. I argue that present-day artificial RL agents have a very small but nonzero degree of ethical im...

The (noiseless) fixed-length source coding theorem states that, except for outcomes in a set of vanishing probability, a source can be encoded at its entropy but not more efficiently. It is well known that the Asymptotic Equipartition Property (AEP) is a sufficient condition for a source to be encodable at its entropy. This paper shows that the AEP is necessary for the source coding theorem to ...

We study the problem of estimating the coefficients in linear ordinary differential equations (ODE’s) with a diverging number of variables when the solutions are observed with noise. The solution trajectories are first smoothed with local polynomial regression and the coefficients are estimated with nonconcave penalty proposed by [4]. Under some regularity and sparsity conditions, we show the p...

We examine two types of similarity network­ s each based on a distinct notion of rele­ vance. For both types of similarity network­ s we present an efficient inference algorith­ m that works under the assumption that ev­ ery event has a nonzero probability of oc­ currence. Another inference algorithm is de­ veloped for type 1 similarity networks that works under no restriction, albeit less effi...

for an n-by-n complex matrix a in a block form with the (possibly) nonzero blocks only on the diagonal above the main one, we consider two other matrices whose nonzero entries are along the diagonal above the main one and consist of the norms or minimum moduli of the diagonal blocks of a. in this paper, we obtain two inequalities relating the numeical radii of these matrices and also determine ...

We derive the transformation for the optimal universal quantum anti-cloner which produces two anti-parallel outputs for a single input state. The fidelity is shown to be 2/3 which is same as the measurement fidelity. We consider a probabilistic quantum anti-cloner and show quantum states can be anti-cloned exactly with nonzero probability and its efficiency is higher than the efficiency of dist...

Several years ago Linial and Meshulam [8] introduced a model calledXd(n, p) of random n-vertex d-dimensional simplicial complexes. The following question suggests itself very naturally: What is the threshold probability p = p(n) at which the d-dimensional homology of such a random d-complex is, almost surely, nonzero? Here we derive an upper bound on this threshold. Computer experiments that we...

We show that, given finitely many line-segment mirrors in the plane, that do not touch, and an arbitrary point source of light, if all angles made by lines parallel to mirrors are rational multiples of π, then all but countably many emitted light beams escape. This result is shown to imply that, for a given point source of light, a randomly chosen configuration of finitely many nontouching line...

Unquenched lattice SU(2) is studied at nonzero chemical potential in the strong coupling limit. The topic of diquark condensation is addressed analyzing the probability distribution function of the diquark condensate. We present results at zero external source without using any potentially dangerous extrapolation procedure. We find strong evidences for a (high density) second order phase transi...

Behavioral conditions such as compound invariance for risky choice and constant decreasing relative impatience for intertemporal choice have surprising implications for the underlying decision model. They imply a multiplicative separability of outcomes and either probability or time. Hence the underlying model must be prospect theory or discounted utility on the domain of prospects with one non...