Related papers: The Lost Melody Phenomenon
A mathematical concept is identified and analyzed that is implicit in the 2012 paper Turing Incomputable Computation, presented at the Alan Turing Centenary Conference (Turing-100, Manchester). The concept, called dynamic level sets, is…
We provide algorithmically verifiable necessary and sufficient conditions for fundamental system theoretic properties of discrete time linear systems subject to data losses. More precisely, the systems in our modeling framework are subject…
We introduce two notions of effective reducibility for set-theoretical statements, based on computability with Ordinal Turing Machines (OTMs), one of which resembles Turing reducibility while the other is modelled after Weihrauch…
Fixed point iterations are known to generate chaos, for some values in their parameter range. It is an established fact that Turing Machines are fixed point iterations. However, as these Machines operate in integer space, the standard…
Metastability is a spurious mode of operation in digital signals, where an electrical signal fails to settle into a stable state within a specified time, leading to uncertainty and potentially failing downstream hardware. A system that…
In this article we consider questions related to the behavior of the moments $M_{m}\left( \left\{ z_{j}\right\} \right) $ when the indices are restricted to specific subsequences of integers, such as the even or odd moments. If $n\geq2$ we…
Nonnegative matrix factorization (NMF) has been shown to be identifiable under the separability assumption, under which all the columns(or rows) of the input data matrix belong to the convex cone generated by only a few of these columns(or…
A simple model of an irreversible process is introduced. The equation of iterations in the model includes a noise generation term. We study the properties of the system when the noise generation term is a stochastic process (e.g. a random…
We prove structural results for measure preserving systems, called Furstenberg systems, naturally associated with bounded multiplicative functions. We show that for all pretentious multiplicative functions these systems always have rational…
We discuss probabilistic neural networks with a fixed internal representation as models for machine understanding. Here understanding is intended as mapping data to an already existing representation which encodes an {\em a priori}…
The association of information with entropy has been argued on plausibility arguments involving the operation of imaginary engines and beings, and it is not a universal theorem. In this paper, a theorem by Charles Bennett on reversible…
This paper investigates some issues arising in categorical models of reversible logic and computation. Our claim is that the structural (coherence) isomorphisms of these categorical models, although generally overlooked, have decidedly…
We study the question of whether the "termination with probability 1" property of a randomized algorithm is preserved when one replaces the atomic registers that the algorithm uses with linearizable (implementations of) registers. We show…
Quantum monotone metric was introduced by Petz,and it was proved that quantum monotone metrics on the set of quantum states with trace one were characterized by operator monotone functions. Later, these were extended to monotone metrics on…
Our main models of computation (the Turing Machine and the RAM) make fundamental assumptions about which primitive operations are realizable. The consensus is that these include logical operations like conjunction, disjunction and negation,…
We show that in the setting of fair-coin measure on the power set of the natural numbers, each sufficiently random set has an infinite subset that computes no random set. That is, there is an almost sure event $\mathcal A$ such that if…
We consider the verification of distributed systems composed of an arbitrary number of asynchronous processes. Processes are identical finite-state machines that communicate by reading from and writing to a shared memory. Beyond the…
The discrete data encoded in the power moments of a positive measure, fast decaying at infinity on euclidean space, is incomplete for recovery, leading to the concept of moment indeterminateness. On the other hand, classical integral…
Each step that results in a bit of information being ``forgotten'' by a computing device has an intrinsic energy cost. Although any Turing machine can be rewritten to be thermodynamically reversible without changing the recognized language,…
We present a hybrid neural network and rule-based system that generates pop music. Music produced by pure rule-based systems often sounds mechanical. Music produced by machine learning sounds better, but still lacks hierarchical temporal…