Related papers: On open and closed convex codes
Constant dimension codes, with a prescribed minimum distance, have found recently an application in network coding. All the codewords in such a code are subspaces of $\F_q^n$ with a given dimension. A computer search for large constant…
An embedding of a code is a mapping that preserves distances between codewords. We prove that any code with code distance $\rho$ and length $d$ can be embedded into an MDS code with the same code distance and length but under a larger…
Constrained Optimization solution algorithms are restricted to point based solutions. In practice, single or multiple objectives must be satisfied, wherein both the objective function and constraints can be non-convex resulting in multiple…
We describe coordinate systems adapted for the space between two surfaces, such as those delineating the highly folded cortex in mammalian brains. These systems are estimated in order to satisfy geometric priors, including streamline…
In the intricate architecture of the mammalian central nervous system, neurons form populations. Axonal bundles communicate between these clusters using spike trains. However, these neuron populations' precise encoding and operations have…
The surface code is a two-dimensional topological code with code parameters that scale optimally with the number of physical qubits, under the constraint of two-dimensional locality. In three spatial dimensions an analogous simple yet…
Current deep-learning models for object recognition are known to be heavily biased toward texture. In contrast, human visual systems are known to be biased toward shape and structure. What could be the design principles in human visual…
Neural Networks (NNs) can provide major empirical performance improvements for robotic systems, but they also introduce challenges in formally analyzing those systems' safety properties. In particular, this work focuses on estimating the…
Scalar variables, e.g., the orientation of a shape in an image, are commonly predicted using a single output neuron in a neural network. In contrast, the mammalian cortex represents variables with a population of neurons. In this population…
A superimposed code is a collection of binary vectors (codewords) with the property that no vector is contained in the Boolean sum of any $k$ others, enabling unique identification of codewords within any group of $k$. Superimposed codes…
It has been shown that the activations invoked by an image within the top layers of a large convolutional neural network provide a high-level descriptor of the visual content of the image. In this paper, we investigate the use of such…
Basic algebraic and combinatorial properties of finite vector spaces in which individual vectors are allowed to have multiplicities larger than $ 1 $ are derived. An application in coding theory is illustrated by showing that multispace…
A pressing scientific challenge is to understand how brains work. Of particular interest is the neocortex,the part of the brain that is especially large in humans, capable of handling a wide variety of tasks including visual, auditory,…
Neurons in the visual cortex are correlated in their variability. The presence of correlation impacts cortical processing because noise cannot be averaged out over many neurons. In an effort to understand the functional purpose of…
Understanding what individual neurons encode is a core question in neuroscience. In primary visual cortex (V1), mathematical models (e.g., Gabor functions) capture neural selectivity, but no comparable framework exists for higher areas. We…
Conflict-avoiding codes are used in the multiple-access collision channel without feedback. The number of codewords in a conflict-avoiding code is the number of potential users that can be supported in the system. In this paper, a new upper…
In applications that use knowledge representation (KR) techniques, in particular those that combine data-driven and logic methods, the domain of objects is not an abstract unstructured domain, but it exhibits a dedicated, deep structure of…
Conditional text generation often requires lexical constraints, i.e., which words should or shouldn't be included in the output text. While the dominant recipe for conditional text generation has been large-scale pretrained language models…
A neural code on $ n $ neurons is a collection of subsets of the set $ [n]=\{1,2,\dots,n\} $. Curto et al. \cite{curto2013neural} associated a ring $\mathcal{R}_{\mathcal{C}}$ (neural ring) to a neural code $\mathcal{C}$. A special class of…
Subsystem codes protect quantum information by encoding it in a tensor factor of a subspace of the physical state space. Subsystem codes generalize all major quantum error protection schemes, and therefore are especially versatile. This…