Recently, several authors have criticized time-symmetrized quantum theory originated by the work of Aharonov et al. (1964). The core of this criticism was the proof, which appeared in various forms, showing that counterfactual interpretation of time-symmetrized quantum theory cannot be reconciled with the standard quantum theory. I argue here that the apparent contradiction appears due to inapp...

Stanley's symmetrized chromatic polynomial is a generalization of the ordinary to graph invariant with values in ring polynomials infinitely many variables. The specialization one. To each orientable embedded single vertex, simple associated, which called intersection graph. As result, we can define for any vertex. Our goal extend graphs arbitrary number vertices, and not necessarily orientable...

A brief review of the time-symmetrized quantum formalism originated by Aharonov, Bergmann and Lebowitz is presented. Symmetry of various measurements under the time reversal is analyzed. Timesymmetrized counterfactuals are introduced. It is argued that the time-symmetrized formalism demonstrates novel profound features of quantum theory and that recent criticism of the formalism is un-

We define a class of multivariate Laurent polynomials closely related to Chebyshev polynomials and prove the simple but somewhat surprising (in view of the fact that the signs of the coefficients of the Chebyshev polynomials themselves alternate) result that their coefficients are non-negative. As a corollary we find that Tn(c cos θ) and Un(c cos θ) are positive definite functions. We further s...

One of the main open questions in liaison theory is whether every homogeneous Cohen-Macaulay ideal in a polynomial ring is glicci, i.e. if it is in the G-liaison class of a complete intersection. We give an affirmative answer to this question for StanleyReisner ideals defined by simplicial complexes that are weakly vertex-decomposable. This class of complexes includes matroid, shifted and Goren...

We study the use of GAI-decomposable utility functions for representing ordinal rankings on combinatorial sets of objects. Considering only the relative order of objects leaves a lot of freedom for choosing a particular utility function, which allows one to get more compact representations. We focus on the problem of learning such representations, and give a polynomial PAC-learner for the case ...

A new method of model registration is proposed using graphical templates. A graph of landmarks is chosen in the template image. All possible candidates for these landmarks are found in the data image using local operators. A dynamic programming algorithm on decomposable subgraphs of the template graph nds the optimal match to a subset of the candidate points in polynomial time. This combination...