Classical Manski bounds identify average treatment effects under minimal assumptions but, in finite samples, assume that latent conditional expectations are bounded by the sample's own extrema or that the population extrema are known a priori -- often untrue in firm-level data with heavy tails. We develop a finite-sample, concentration-driven band (concATE) that replaces that assumption with a Dvoretzky--Kiefer--Wolfowitz tail bound, combines it with delta-method variance, and allocates size via Bonferroni. The band extends to a group-sequential design that controls the family-wise error when the first ``significant'' diversity threshold is data-chosen. Applied to 945 listed firms (2015 Q2--2022 Q1), concATE shows that senior-level gender diversity raises Tobin's Q once representation exceeds approximately 30\% in growth sectors and approximately 65\% in cyclical sectors.

Grace Lordan Kaveh Salehzadeh Nobari

Let $M$ be a closed, oriented and smooth manifold of dimension $d$. Let $\L M$ be the space of smooth loops in $M$. Chas and Sullivan introduced loop product, a product of degree $-d$ on the homology of $LM$. In this paper we show how for three manifolds the ``nontriviality'' of the loop product relates to the ``hyperbolicity'' of the underlying manifold. This is an application of the existing powerful tool and results in three dimensional topology such as the prime decomposition, torus decomposition, Seifert theorem, torus theorem.

Hossein Abbaspour

A Hamilton-Jacobi formulation of the Lyapunov spectrum and KS entropy is developed. It is numerically efficient and reveals a close relation between the KS invariant and the classical action. This formulation is extended to the quantum domain using the Madelung-Bohm orbits associated with the Schroedinger equation. The resulting quantum KS invariant for a given orbit equals the mean decay rate of the probability density along the orbit, while its ensemble average measures the mean growth rate of configuration-space information for the quantum system.

M. Hossein Partovi

We characterize the optimal correlative capacity of entangled, separable, and classically correlated states. Introducing the notions of the infimum and supremum within majorization theory, we construct the least disordered separable state compatible with a set of marginals. The maximum separable correlation information supportable by the marginals of a multi-qubit pure state is shown to be an LOCC monotone. The least disordered composite of a pair of qubits is found for the above classes, with classically correlated states defined as diagonal in the product of marginal bases.

M. Hossein Partovi

Entanglement detection criteria are developed within the framework of the majorization formulation of uncertainty. The primary results are two theorems asserting linear and nonlinear separability criteria based on majorization relations, the violation of which would imply entanglement. Corollaries to these theorems yield infinite sets of scalar entanglement detection criteria based on quasi-entropic measures of disorder. Examples are analyzed to probe the efficacy of the derived criteria in detecting the entanglement of bipartite Werner states. Characteristics of the majorization relation as a comparator of disorder uniquely suited to information-theoretical applications are emphasized throughout.

M. Hossein Partovi

We show that the efficient frontier for a portfolio in which short positions precisely offset the long ones is composed of a pair of straight lines through the origin of the risk-return plane. This unique but important case has been overlooked because the original formulation of the mean-variance model by Markowitz as well as all its subsequent elaborations have implicitly excluded it by using portfolio weights rather than actual amounts allocated to individual assets. We also elucidate the properties of portfolios where short positions dominate the long ones, a case which has similarly been obscured by the adoption of portfolio weights.

M. Hossein Partovi

We classify all primes appearing in the denominators of the Hauptmodul $J$ and modular forms for non-arithmetic triangle groups with a cusp. These primes have a congruence condition in terms of the order of the generators of the group. As a corollary we show that for the Hecke group of type $(2,m,\infty)$, the prime $p$ does not appear in the denominator of $J$ if and only if $p\equiv \pm 1\pmod m$.

Hossein Movasati Khosro M. Shokri

We introduce the notion of weakly mutually uncorrelated (WMU) sequences, motivated by applications in DNA-based storage systems and synchronization protocols. WMU sequences are characterized by the property that no sufficiently long suffix of one sequence is the prefix of the same or another sequence. In addition, WMU sequences used in DNA-based storage systems are required to have balanced compositions of symbols and to be at large mutual Hamming distance from each other. We present a number of constructions for balanced, error-correcting WMU codes using Dyck paths, Knuth's balancing principle, prefix synchronized and cyclic codes.

S. M. Hossein Tabatabaei Yazdi Han Mao Kiah Olgica Milenkovic

Let $\Phi$ and $\Psi$ be frames for $\cal H$ and let $M_{m,\Phi,\Psi}$ be a frame multiplier with the symbol $m$. In this paper, we restrict our investigation to show that the operator properties of $M_{m,\Phi,\Psi}$ are stable under the perturbations of $\Phi$, $\Psi$ and $m$. Also, special attention is devoted to the study of invertible frame multipliers. These results are not only of interest in their own right, but also they pave the way for obtaining some new results for Gabor multipliers which have been studied mostly by Hans Georg Feichtinger and his coauthors in recent years.

Hossein Javanshiri

In this article, the basic principle of target detection based on Gaussian state quantum illumination (QI) has introduced. The performance of such system has compared with its classical counterpart, which employs the most classical state of light, i.e., coherent state, to illuminate the target region. By deriving the maximum range equation, we have demonstrated that the quantum illumination based target detection system is especially advantageous at low transmission powers, which make these systems suitable for short range applications like biomedical imaging or covert detection schemes.

Hossein Allahverdi M. H. Qamat M. Nowshadi