J. E. Pascoe
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View article: The geometry of inconvenience and perverse equilibria in trade networks
The geometry of inconvenience and perverse equilibria in trade networks Open
The structure bilateral trading costs is one of the key features of international trade. Drawing upon the freeness-of-trade matrix, which allows the modeling of N-state trade costs, we develop a ``geometry of inconvenience'' to better unde…
View article: Indices of quadratic programs over reproducing kernel Hilbert spaces for fun and profit
Indices of quadratic programs over reproducing kernel Hilbert spaces for fun and profit Open
We give an abstract perspective on quadratic programming with an eye toward long portfolio theory geared toward explaining sparsity via maximum principles. Specifically, in optimal allocation problems, we see that support of an optimal dis…
View article: Stable polynomials and admissible numerators in product domains
Stable polynomials and admissible numerators in product domains Open
Given a polynomial with no zeros in the polydisk, or equivalently the poly‐upper half‐plane, we study the problem of determining the ideal of polynomials with the property that the rational function is bounded near a boundary zero of . We …
View article: Strategic Considerations for Selecting Artificial Intelligence Solutions for Institutional Integration: A Single-Center Experience
Strategic Considerations for Selecting Artificial Intelligence Solutions for Institutional Integration: A Single-Center Experience Open
Artificial intelligence (AI) promises to revolutionize health care. Early identification of disease, appropriate test selection, and automation of repetitive tasks are expected to optimize cost-effective care delivery. However, pragmatic s…
View article: Stable polynomials and admissible numerators in product domains
Stable polynomials and admissible numerators in product domains Open
Given a polynomial $p$ with no zeros in the polydisk, or equivalently the poly-upper half-plane, we study the problem of determining the ideal of polynomials $q$ with the property that the rational function $q/p$ is bounded near a boundary…
View article: Matrix convex verbatim enumeration functions are graphical
Matrix convex verbatim enumeration functions are graphical Open
We give a relation between verbatim generating functions of what we call Pythagorean languages and matrix convexity. Namely, several multivariate matrix convex functions occurring in the existing matrix analysis literature arise naturally …
View article: Invariant structure preserving functions and an Oka-Weil Kaplansky density type theorem
Invariant structure preserving functions and an Oka-Weil Kaplansky density type theorem Open
We develop the theory of invariant structure preserving and free functions on a general structured topological space. We show that an invariant structure preserving function is pointwise approximiable by the appropriate analog of polynomia…
View article: The royal road to automatic noncommutative real analyticity, monotonicity, and convexity
The royal road to automatic noncommutative real analyticity, monotonicity, and convexity Open
It was shown classically that matrix monotone and matrix convex functions must be real analytic by Löwner and Kraus respectively. Recently, various analogues have been found in several noncommuting variables. We develop a general framework…
View article: Analytic Continuation of Concrete Realizations and the McCarthy Champagne Conjecture
Analytic Continuation of Concrete Realizations and the McCarthy Champagne Conjecture Open
In this paper, we give formulas that allow one to move between transfer function type realizations of multi-variate Schur, Herglotz, and Pick functions, without adding additional singularities except perhaps poles coming from the conformal…
View article: Geometric Dilations and Operator Annuli
Geometric Dilations and Operator Annuli Open
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View article: Monotonicity of the principal pivot transform
Monotonicity of the principal pivot transform Open
We prove that the principal pivot transform (also known as the partial inverse, sweep operator, or exchange operator in various contexts) maps matrices with positive imaginary part to matrices with positive imaginary part. We show that the…
View article: Noncommutative partially convex rational functions
Noncommutative partially convex rational functions Open
Motivated by classical notions of bilinear matrix inequalities (BMIs) and partial convexity, this article investigates partial convexity for noncommutative functions. It is shown that noncommutative rational functions that are partially co…
View article: Local theory of stable polynomials and bounded rational functions of several variables
Local theory of stable polynomials and bounded rational functions of several variables Open
We provide detailed local descriptions of stable polynomials in terms of their homogeneous decompositions, Puiseux expansions, and transfer function realizations. We use this theory to first prove that bounded rational functions on the pol…
View article: Averaged mixed Julia-Fatou type theory with applications to spectral foliation
Averaged mixed Julia-Fatou type theory with applications to spectral foliation Open
Classically, theorems of Fatou and Julia describe the boundary regularity of functions in one complex variable. The former says that a complex analytic function on the disk has non-tangential boundary values almost everywhere, and the latt…
View article: Monotonicity of the principal pivot transform
Monotonicity of the principal pivot transform Open
We prove that the principal pivot transform (also known as the partial inverse, sweep operator, or exchange operator in various contexts) maps matrices with positive imaginary part to matrices with positive imaginary part. We show that the…
View article: Zero-free regions near a line
Zero-free regions near a line Open
We analyze metrics for how close an entire function of genus one is to being real rooted. These metrics arise from truncated Hankel matrix positivity-type conditions built from power series coefficients at each real point. Specifically, if…
View article: Macroscale behavior of random lower triangular matrices
Macroscale behavior of random lower triangular matrices Open
We analyze the macroscale behavior of random lower (and therefore upper) triangular matrices with entries drawn iid from a distribution with nonzero mean and finite variance. We show that such a matrix behaves like a probabilistic version …
View article: Free noncommutative principal divisors and commutativity of the tracial fundamental group
Free noncommutative principal divisors and commutativity of the tracial fundamental group Open
We define the principal divisor of a free noncommuatative function. We use these divisors to compare the determinantal singularity sets of free noncommutative functions. We show that the divisor of a noncommutative rational function is the…
View article: Trace minmax functions and the radical Laguerre-Pólya class
Trace minmax functions and the radical Laguerre-Pólya class Open
We classify functions $f:(a,b)\rightarrow \mathbb{R}$ which satisfy the inequality $$\operatorname{tr} f(A)+f(C)\geq \operatorname{tr} f(B)+f(D)$$ when $A\leq B\leq C$ are self-adjoint matrices, $D= A+C-B$, the so-called trace minmax funct…
View article: Noncommutative free universal monodromy, pluriharmonic conjugates, and plurisubharmonicity
Noncommutative free universal monodromy, pluriharmonic conjugates, and plurisubharmonicity Open
We show that the monodromy theorem holds on arbitrary connected free sets for noncommutative free analytic functions. Applications are numerous-- pluriharmonic free functions have globally defined pluriharmonic conjugates, locally invertib…
View article: Automatic real analyticity and a regal proof of a commutative multivariate Löwner theorem
Automatic real analyticity and a regal proof of a commutative multivariate Löwner theorem Open
We adapt the "royal road" method used to simplify automatic analyticity theorems in noncommutative function theory to several complex variables. We show that certain families of functions must be real analytic if they have certain nice pro…
View article: An entire free holomorphic function which is unbounded on the row ball
An entire free holomorphic function which is unbounded on the row ball Open
We give an entire free holomorphic function $f$ which is unbounded on the row ball. That is, we give a holomorphic free noncommutative function which is continuous in the free topology developed by Agler and McCarthy but is unbounded on th…
View article: Noncommutative Schur-type products and their Schoenberg theorem
Noncommutative Schur-type products and their Schoenberg theorem Open
Schoenberg showed that a function $f:(-1,1)\rightarrow \mathbb{R}$ such that $C=[c_{ij}]_{i,j}$ positive semi-definite implies that $f(C)=[f(c_{ij})]_{i,j}$ is also positive semi-definite must be analytic and have Taylor series coefficient…
View article: Singularities of rational inner functions in higher dimensions
Singularities of rational inner functions in higher dimensions Open
We study the boundary behavior of rational inner functions (RIFs) in dimensions three and higher from both analytic and geometric viewpoints. On the analytic side, we use the critical integrability of the derivative of a rational inner fun…
View article: The outer spectral radius and dynamics of completely positive maps
The outer spectral radius and dynamics of completely positive maps Open
We examine a special case of an approximation of the joint spectral radius given by Blondel and Nesterov, which we call the outer spectral radius. The outer spectral radius is given by the square root of the ordinary spectral radius of the…
View article: Committee spaces and the random column-row property
Committee spaces and the random column-row property Open
A committee space is a Hilbert space of power series, perhaps in several or noncommuting variables, such that $\|z^α\|\|z^β\| \geq \|z^{α+β}\|.$ Such a space satisfies the true column-row property when ever the map transposing a column mul…