Related papers: On system rollback and totalised fields
Relations between two definitions of (total) angular momentum operator, as a generator of rotations and in the Lagrangian formalism, are explored in quantum field theory. Generally, these definitions result in different angular momentum…
This paper generalizes the results obtained in an earlier paper (math.OA/0003087) for finite factors to infinite but still semifinite factors. First we give a characterization of cyclic and separating vectors for infinite semifinite factors…
Several predictive algorithms are described. Highlighted are variants that make predictions by superposing fields associated to the training data instances. They operate seamlessly with categorical, continuous, and mixed data. Predictive…
Causal-consistent reversibility is the reference notion of reversibility for concurrency. We introduce a modular framework for defining causal-consistent reversible extensions of concurrent models and languages. We show how our framework…
The invertibility of integral linear operators is a major problem of both theoretical and practical importance. In this paper we investigate the relation between an operator invertibility and the rank of its integral kernel to develop a…
In this article I propose an approach for defining replicability for prediction rules. Motivated by a recent NAS report, I start from the perspective that replicability is obtaining consistent results across studies suitable to address the…
Aggregation functions are widely used in answer set programming for representing and reasoning on knowledge involving sets of objects collectively. Current implementations simplify the structure of programs in order to optimize the overall…
Recursive queries have been traditionally studied in the framework of datalog, a language that restricts recursion to monotone queries over sets, which is guaranteed to converge in polynomial time in the size of the input. But modern big…
We prove for the first time that, if a linear inverse problem exhibits a group symmetry structure, gradient-based optimizers can be designed to exploit this structure for faster convergence rates. This theoretical finding demonstrates the…
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…
An element $g$ of a group is called reversible if it is conjugate in the group to its inverse. An element is an involution if it is equal to its inverse. This paper is about factoring elements as products of reversibles in the group…
This paper concerns the general problem of classifying the finite deterministic automata that admit a synchronizing (or reset) word. (For our purposes it is irrelevant if the automata has initial or final states.) Our departure point is the…
An operator connection is a binary operation assigned to each pair of positive operators satisfying monotonicity, continuity from above and the transformer inequality. In this paper, we introduce and characterize the concepts of…
Reversible logic synthesis is a crucial component in quantum electronic design automation. While rule-based methodologies have gained prominence in reversible circuit optimization, the completeness of the transformation rule systems is a…
In some cases in two and three bulk dimensions without bulk local degrees of freedom, I look for area operators in a fixed boundary theory. In each case, I define an exact quantum error-correcting code (QECC) and show that it admits a…
An invertible field transformation is such that the old field variables correspond one-to-one to the new variables. As such, one may think that two systems that are related by an invertible transformation are physically equivalent. However,…
Data reconciliation in general, and filesystem synchronization in particular, lacks rigorous theoretical foundation. This paper presents, for the first time, a complete analysis of synchronization for two replicas of a theoretical…
The theory of generalized inverses of matrices and operators is closely connected with projections, i.e., idempotent (bounded) linear transformations. We show that a similar situation occurs in any associative ring $\mathcal{R}$ with a unit…
The powers of generating functions and its properties are analyzed. A new class of functions is introduced, based on the application of compositions of an integer $n$, called composita. The methods for obtaining reciprocal and reverse…
Common meadows are commutative and associative algebraic structures with two operations (addition and multiplication) with additive and multiplicative identities and for which inverses are total. The inverse of zero is an error term…