The state function of a quantum object is undetermined with respect to its phase. This indeterminacy does not matter if it is global, but what if the components of the state have unknown relative phases? Can useful computations be performed in spite of this local indeterminacy? We consider this question in relation to the problem of the rotation of a qubit and examine its broader implications f...

Let G be a simple graph with vertex set V (G). The common neighborhood graph or congraph of G, denoted by con(G), is a graph with vertex set V (G), in which two vertices are adjacent if and only if they have at least one common neighbor in G. We compute the congraphs of some composite graphs. Using these results, the congraphs of several special graphs are determined.

Abstract. We examine the issue of stability of probability in reasoning about complex systems with uncertainty in structure. Normally, propositions are viewed as probability functions on an abstract random graph where it is implicitly assumed that the nodes of the graph have stable properties. But what if some of the nodes change their characteristics? This is a situation that cannot be covered...

While it is known that every closed orientable 3-manifold M contains an arithmetic link L (since the figure-eight knot complement is both arithmetic and universal), Theorem 2 asserts that L can be chosen so that M \ L is homeomorphic to the complement of a link in S3. Recall that a link L in S3 (resp. in M) is hyperbolic if S3 \L (resp. M \L) is homeomorphic to H3/Γ, where H3 is hyperbolic 3-sp...

Each Emergency Medical Assistance Centre in France (SAMU), includes an emergency call service. It provides an adequate and immediate response to medical problems. The processing of the incoming calls can be seen as a collaborative process involving several stakeholders. The control of such a process is crucial. Indeed, the effectiveness of the response to these incoming calls strongly impacts t...

It is a widely accepted doctrine in epistemology that knowledge has greater value than mere true belief. But although epistemologists regularly pay homage to this doctrine, evidence for it is shaky. Is it based on evidence that ordinary people on the street make evaluative comparisons of knowledge and true belief, and consistently rate the former ahead of the latter? Do they reveal such a prefe...

We know how to integrate a function over a flat region in a plane, but what if the function is defined over a curved surface? To evaluate one of these so-called surface integrals, we rewrite it as a double integral over a region in a coordinate plane beneath the surface (Figure 16.38). Surface integrals are used to compute quantities such as the flow of liquid across a membrane or the upward fo...

We study the so-called Skorokhod reflection problem (SRP) posed for real-valued functions defined on a partially ordered set (poset), when there are two boundaries, considered also to be functions of the poset. The problem is to constrain the function between the boundaries by adding and subtracting nonnegative nondecreasing (NN) functions in the most efficient way. We show existence and unique...

We propose a way of creating product maps with self-organizing maps (SOMs) for purchase decision making. We previously proposed a way of purchase decision support using SOMs and the Analytic Hierarchy Process (AHP). We provided several class boundaries, which divided the input features into several classes before creating self-organizing product maps. Because the number of classes and their bou...