arXiv subjects

Amir Rahnamai Barghi

Publications and source records attributed to Amir Rahnamai Barghi.

6 recordsLinked to original sources

arXiv2026

The Coercive Projection Theorem for Canonical Reciprocal Costs

We develop a finite-data framework for certifying \emph{zero-defect} (neutral) configurations of positive vectors under the canonical separable reciprocal cost. We show that this scalar cost is characterized among non-constant continuous costs by the Recognition Composition Law together with a local quadratic calibration at balance; in particular, reciprocity symmetry and the normalization at the neutral point follow from the composition law. Under a conservation constraint and short-window observations of a rational (finite--state) signal class, we construct a canonical decision procedure that is \emph{locally maximal on the identifiability locus} among all sound procedures: any sound rule that resolves a datum must agree with the canonical output, and cannot resolve strictly more cases. The method is organized as $Φ^\ast=A\circ B\circ P$: the projection/coercivity core is forced by the canonical-cost axioms, while the aggregation/reconstruction step is specified on a non-degenerate identifiability locus (e.g.\ a Hankel invertibility condition).

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arXiv2026

Reciprocal Convex Costs for Ratio Matching: Functional-Equation Characterization and Decision Geometry

We study ratio-induced mismatch costs of the form $c(s,o)=J(ι_S(s)/ι_O(o))$, built from positive scale maps $ι_S:S\to(0,\infty)$ and $ι_O:O\to(0,\infty)$ and a penalty $J:(0,\infty)\to[0,\infty)$. Assuming inversion symmetry, strict convexity, normalization $J(1)=0$, and a multiplicative d'Alembert identity, we show that $f(u):=1+J(e^u)$ satisfies the additive d'Alembert equation and hence $J(x)=\cosh(a\log x)-1=\tfrac12(x^a+x^{-a})-1$ for some $a>0$. We then analyze the associated argmin mapping over feasible scale sets: existence under explicit subspace-closedness hypotheses, geometric-mean decision boundaries for finite dictionaries with stability away from boundaries, exact compositionality for product models, and an optimal sequential mediation principle given by a geometric mean (or its log-space projection when infeasible). The paper is purely mathematical; any semantic interpretation is optional and external to the theorems proved here.

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arXiv2019

On Characters of a Class of P-polynomial table algebras and applications

In this paper, we study the characters of homogeneous monotonic P-polynomial table algebras with finite dimension d>=5. We then apply them to association schemes. To this end, we develop some methods using tridiagonal matrices and Z-transform. Moreover, we calculate the eigenvalues of a special tridiagonal matrix which is found through the first intersection matrix of P-polynomial table algebras.

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arXiv2019

The Application of Tridiagonal Matrices in P-polynomial Table Algebras

In this paper, we study the characters of two classes of P-polynomial table algebras using tridiagonal matrices. To this end, we obtain some results about the eigen-structure of special tridiagonal matrices. We also find a recursive relation for the characteristic polynomial of the first intersection matrix of P-polynomial table algebras by means of LU factorization.

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arXiv2015

On circular-arc graphs with association schemes

In this paper, we give a characterization of the class of all circular-arc graphs whose schemes are association. Moreover, all association schemes which are the scheme of a circular-arc graph are characterized, specially it is proved that they are Schurian.

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arXiv2007

The basis digraphs of p-schemes

It is proved that association schemes with bipartite basis graphs are exactly 2-schemes. This result follows from a characterization of p-schemes for an arbitrary prime p in terms of basis digraphs.

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