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We develop combinatorial test generation algorithms for progressively more powerful theorem provers, covering formula languages ranging from the implicational fragment of intuitionistic logic to full intuitionistic propositional logic. Our…
Optical lenses are pervasive in various areas of sciences and technologies. It is well-known that the resolving power of a lens and thus optical systems is limited by the diffraction of light. Recently, various plasmonics and metamaterials…
We demonstrate, in the full vector formulation of electromagnetic fields, that the well-known optical theorem pertinent for the characterization of a scatterer's extinction power and associated cross section can be expressed in a multitude…
Borrowing methods and formulas from Prof. Goodman's classic Introduction to Fourier Optics textbook [1], I have developed a software package [2] that has been used in both industrial research and classroom teaching [3]. This paper briefly…
Precise engineering of materials and surfaces has been at the heart of some of the recent advances in optics and photonics. These advances around the engineering of materials with new functionalities have also opened up exciting avenues for…
Occam's Razor tells us to pick the simplest model that fits our observations. In order to make sense of his process mathematically, we interpret it in the context of posets of functions. Our approach leads to some unusual new combinatorial…
Hyperspaces form a powerful tool in some branches of mathematics: lots of fractal and other geometric objects can be viewed as fixed points of some functions in suitable hyperspaces - as well as interesting classes of formal languages in…
Recommender systems play a fundamental role in web applications in filtering massive information and matching user interests. While many efforts have been devoted to developing more effective models in various scenarios, the exploration on…
Currently it is widely accepted that the language of science is mathematics. This book explores an alternative idea where the future of science is based on the language of algorithms and programs. How such a language can actually be…
Despite the flexibility and popularity of mixture models, their associated parameter spaces are often difficult to represent due to fundamental identification problems. This paper looks at a novel way of representing such a space for…
A description is an entity that can be interpreted as true or false of an object, and using feature structures as descriptions accrues several computational benefits. In this paper, I create an explicit interpretation of a typed feature…
The choice of how to represent an abstract type can have a major impact on the performance of a program, yet mainstream compilers cannot perform optimizations at such a high level. When dealing with optimizations of data type…
Many visual scenes can be described as compositions of latent factors. Effective recognition, reasoning, and editing often require not only forming such compositional representations, but also solving the decomposition problem. One popular…
Iterative refinement -- start with a random guess, then iteratively improve the guess -- is a useful paradigm for representation learning because it offers a way to break symmetries among equally plausible explanations for the data. This…
In the same sense as classical logic is a formal theory of truth, the recently initiated approach called computability logic is a formal theory of computability. It understands (interactive) computational problems as games played by a…
Any representational enterprise must omit variation in order to function. NASA still uses Newtonian mechanics, though Einstein superseded Newton, and the standard picture of scientific progress cannot explain how. A description that omitted…
The cartesian structure possessed by relations, spans, profunctors, and other such morphisms is elegantly expressed by universal properties in double categories. Though cartesian double categories were inspired in part by the older program…
We show that every linear optical component can be completely described as a device that converts one set of orthogonal input modes, one by one, to a matching set of orthogonal output modes. This result holds for any linear optical…
Constructor theory seeks to express all fundamental scientific theories in terms of a dichotomy between possible and impossible physical transformations - those that can be caused to happen and those that cannot. This is a departure from…
Classifiers are important components in many computer vision tasks, serving as the foundational backbone of a wide variety of models employed across diverse applications. However, understanding the decision-making process of classifiers…