arXiv subjects
Publications and source records attributed to Jeffrey Uhlmann.
Extends previous work on block-partitioned mixed generalized inverses from two subsets of system variables with distinct consistency requirements to three subsets. Does not include any notable theoretical contributions.
In this paper we introduce the notion of explicit worst-case bounded adaptive algorithms for applications with fixed process-completion requirements. Such applications demand that a process be guaranteed to complete within an established time interval while adaptively reducing computational overhead during that interval, e.g., so as to reduce total energy usage. Our principal contribution is the access-adaptive priority search tree (AAPST), which can provide efficient distribution-sensitive performance comparable to the splay tree, but do so within strict - and O(logn) optimal - worst-case per-query bounds. More specifically, while the splay tree is conjectured to offer optimal adaptive amortized query complexity, it may require O(n) for individual queries, whereas the AAPST offers competitive distribution-sensitive performance with strict O(logn) time complexity. This makes the AAPST more suitable for certain interactive (e.g., online and real-time) applications such as space system modules with reliability constraints involving rigid process-completion time intervals with secondary energy-minimization incentives.
In this paper we provide a latent-variable formulation and solution to the recommender system (RS) problem in terms of a fundamental property that any reasonable solution should be expected to satisfy. Specifically, we examine a novel tensor completion method to efficiently and accurately learn parameters of a model for the unobservable personal preferences that underly user ratings. By regularizing the tensor decomposition with a single latent invariant, we achieve three properties for a reliable recommender system: (1) uniqueness of the tensor completion result with minimal assumptions, (2) unit consistency that is independent of arbitrary preferences of users, and (3) a consensus ordering guarantee that provides consistent ranking between observed and unobserved rating scores. Our algorithm leads to a simple and elegant recommendation framework that has linear computational complexity and with no hyperparameter tuning. We provide empirical results demonstrating that the approach significantly outperforms current state-of-the-art methods.
A recently-derived alternative method for computing the relative gain array (RGA) for singular and/or non-square systems has been proposed that provably guarantees unit invariance. This property is not offered by the conventional method that uses the Moore-Penrose (MP) pseudoinverse. In this paper we note that the absence of the scale-invariance property by the conventional MP-RGA does not necessarily imply a practical disadvantage in real-world applications. In other words, while it is true that performance of a controller should not depend on the choice of units on its input and output variables, this does not {\em necessarily} imply that the resulting MP-RGA measures of component interaction lead to different controller-design input-output pairings. In this paper we consider the application of the MP-RGA to a realistic system (a Sakai fractional distillation system) to assess whether or not the choice of unit, which in this case relates to temperature, affects the choice of input-output pairings determined by the resulting RGA matrix. Our results show that it does, thus confirming that unit-sensitivity of the MP-RGA undermines its rigorous use for MIMO controller design.
This paper presents the Cascaded Metric Tree (CMT) for efficient satisfaction of metric search queries over a dataset of N objects. It provides extra information that permits query algorithms to exploit all distance calculations performed along each path in the tree for pruning purposes. In addition to improving standard metric range (ball) query algorithms, we present a new algorithm for exploiting the CMT cascaded information to achieve near-optimal performance for k-nearest neighbor (kNN) queries. We demonstrate the performance advantage of CMT over classical metric search structures on synthetic datasets of up to 10 million objects and on the 564K Swiss-Prot protein sequence dataset containing over $200$ million amino acids. As a supplement to the paper, we provide reference implementations of the empirically-examined algorithms to encourage improvements and further applications of CMT to practical scientific and engineering problems
In this paper we examine methods for taking game-related information provided in one sensory modality and transforming it to another sensor modality in order to more effectively accommodate sensory-constrained players. We then consider methods for the adaptation and design of games for which gameplay interactions are constrained to a subset of sensory modalities in ways that preserve a common level of novelty-of-experience for players with different sensory capabilities. It is hoped that improved shared experiences can promote interactions among a more diverse spectrum of players.
In this paper we examine the potential of computer-assisted proof methods to be applied much more broadly than commonly recognized. More specifically, we contend that there are vast opportunities to derive useful mathematical results and properties that are extremely narrow in scope, and of practical relevance only to highly-specialized engineering applications, that are presently overlooked because they have characteristics atypical of those that are conventionally pursued in the areas of pure and applied mathematics. As a concrete example, we demonstrate use of automated methods for certifying polynomial nonnegativity as a part of a dimension-pinning strategy to prove that the inverse of the relative gain array (RGA) of a d-dimensional positive-definite matrix is doubly-stochastic for $d\leq 4$.
We propose and discuss the summarization of superpixel-type image tiles/patches using mean and covariance information. We refer to the resulting objects as covapixels.
In this paper we generalize the canonical positive scaling of rows and columns of a matrix to the scaling of selected-rank subtensors of an arbitrary tensor. We expect our results and framework will prove useful for sparse-tensor completion required for generalizations of the recommender system problem beyond a matrix of user-product ratings to multidimensional arrays involving coordinates based both on user attributes (e.g., age, gender, geographical location, etc.) and product/item attributes (e.g., price, size, weight, etc.).
In this paper we propose and develop a relatively simple and efficient approach for estimating unknown elements of a user-rating matrix in the context of a recommender system (RS). The critical theoretical property of the method is its consistency with respect to arbitrary units implicitly adopted by different users to construct their quantitative ratings of products. It is argued that this property is needed for robust performance accuracy across a broad spectrum of RS application domains.
In this paper we provide a case study of the use of relatively sophisticated mathematics and algorithms to redefine and adapt a simple traditional game/puzzle to exploit the computational power of smart devices. The focus here is not so much on the end product as it is on the process and considerations underpinning its development. Ancillary results of the venture include generalizations of the circular-shift operator and examination of its computational complexity.
In this paper we propose and examine gap statistics for assessing uniform distribution hypotheses. We provide examples relevant to data integrity testing for which max-gap statistics provide greater sensitivity than chi-square ($χ^2$), thus allowing the new test to be used in place of or as a complement to $χ^2$ testing for purposes of distinguishing a larger class of deviations from uniformity. We establish that the proposed max-gap test has the same sequential and parallel computational complexity as $χ^2$ and thus is applicable for Big Data analytics and integrity verification.
In this paper we derive a representation of an arbitrary real matrix M as the difference of a real matrix A and the transpose of its inverse. This expression may prove useful for progressing beyond known results for which the appearance of transpose-inverse terms prove to be obstacles, particularly in control theory and related applications such as computational simulation and analysis of matrix representations of articulated figures.
In this paper we identify a significant deficiency in the literature on the application of the Relative Gain Array (RGA) formalism in the case of singular matrices. Specifically, we show that the conventional use of the Moore-Penrose pseudoinverse is inappropriate because it fails to preserve critical properties that can be assumed in the nonsingular case. We then discuss how such properties can be rigorously preserved using an alternative generalized matrix inverse.
In this paper we provide an intuitive-level discussion of the challenges and opportunities offered by quantum-based methods for supporting secure communications, e.g., over a network. The goal is to distill down to the most fundamental issues and concepts in order to provide a clear foundation for assessing the potential value of quantum-based technologies relative to classical alternatives. It is hoped that this form of exposition can provide greater clarity of perspective than is typically offered by mathematically-focused treatments of the topic. It is also hoped that this clarity extends to more general applications of quantum information science such as quantum computing and quantum sensing.
It is well-understood that the robustness of mechanical and robotic control systems depends critically on minimizing sensitivity to arbitrary application-specific details whenever possible. For example, if a system is defined and performs well in one particular Euclidean coordinate frame then it should be expected to perform identically if that coordinate frame is arbitrarily rotated or scaled. Similarly, the performance of the system should not be affected if its key parameters are all consistently defined in metric units or in imperial units. In this paper we show that a recently introduced generalized matrix inverse permits performance consistency to be rigorously guaranteed in control systems that require solutions to underdetermined and/or overdetermined systems of equations.
There has recently been renewed recognition of the need to understand the consistency properties that must be preserved when a generalized matrix inverse is required. The most widely known generalized inverse, the Moore-Penrose pseudoinverse, provides consistency with respect to orthonormal transformations (e.g., rotations of a coordinate frame), and a recently derived inverse provides consistency with respect to diagonal transformations (e.g., a change of units on state variables). Another well-known and theoretically important generalized inverse is the Drazin inverse, which preserves consistency with respect to similarity transformations. In this paper we note a limitation of the Drazin inverse is that it does not generally preserve the rank of the linear system of interest. We then introduce an alternative generalized inverse that both preserves rank and provides consistency with respect to similarity transformations. Lastly we provide an example and discuss experiments which suggest the need for algorithms with improved numerical stability.
The purpose of this paper is to introduce a set of four test images containing features and structures that can facilitate effective examination and comparison of image processing algorithms. More specifically, the images are designed to more explicitly expose the characteristic properties of algorithms for image compression, virtual resolution adjustment, and enhancement. This set was developed at the Naval Research Laboratory (NRL) in the late 1990s as a more rigorous alternative to Lena and other images that have come into common use for purely ad hoc reasons with little or no rigorous consideration of their suitability. The increasing number of test images appearing in the literature not only makes it more difficult to compare results from different papers, it also introduces the potential for cherry-picking to influence results. The key contribution of this paper is the proposal to establish {\em some} canonical set to ensure that published results can be analyzed and compared in a rigorous way from one paper to another, and consideration of the four NRL images is proposed for this purpose.