相关论文: Inverse Determinant Sums and Connections Between F…

This work considers normalized inverse determinant sums as a tool for analyzing the performance of division algebra based space-time codes for multiple antenna wireless systems. A general union bound based code design criterion is obtained…

This paper considers shifted inverse determinant sums arising from the union bound of the pairwise error probability for space-time codes in multiple-antenna fading channels. Previous work by Vehkalahti et al. focused on the approximation…

Inverse determinant sums appear naturally as a tool for analyzing performance of space-time codes in Rayleigh fading channels. This work will analyze the growth of inverse determinant sums of a family of quasi-orthogonal codes and will show…

Since the invention of space-time coding numerous algebraic methods have been applied in code design. In particular algebraic number theory and central simple algebras have been on the forefront of the research. In this paper we are turning…

This work aims at providing new bounds for the diversity multiplexing gain trade-off of a general class of division algebra based lattice codes. In the low multiplexing gain regime, some bounds were previously obtained from the high…

Consider multiple sums $S_n$ on the $d$-dimensional integer grid,which are generated by i.i.d.\ random variables with a positive expectation. We prove the strong law of large numbers, the law of the iterated logarithm and the distributional…

In this paper we study the dynamics and ergodic theory of certain economic models which are implicitly defined. We consider 1-dimensional and 2-dimensional overlapping generations models, a cash-in-advance model, heterogeneous markets and a…

We derive a priori bounds on the size of the structure constants of the free Lie algebra over a set of indeterminates, relative to its Hall bases. We investigate their asymptotic growth, especially as a function of the length of the…

Computation of polynomial relative invariants is a classical tool in algebra. Relative differential invariants are central for the equivalence problem of geometric structures. We address the fundamental problem of finite generation of their…

We study the learnability of sums of independent integer random variables given a bound on the size of the union of their supports. For $\mathcal{A} \subset \mathbf{Z}_{+}$, a sum of independent random variables with collective support…

Decision-making problems are commonly formulated as optimization problems, which are then solved to make optimal decisions. In this work, we consider the inverse problem where we use prior decision data to uncover the underlying…

While machine-learning models are flourishing and transforming many aspects of everyday life, the inability of humans to understand complex models poses difficulties for these models to be fully trusted and embraced. Thus, interpretability…

Data augmentation is one of the most widely used techniques to improve generalization in modern machine learning, often justified by its ability to promote invariance to label-irrelevant transformations. However, its theoretical role…

In distributed optimization and distributed numerical linear algebra, we often encounter an inversion bias: if we want to compute a quantity that depends on the inverse of a sum of distributed matrices, then the sum of the inverses does not…

The paper is devoted to the development of the theory of inverse problems for evolution equations with terms rapidly oscillating in time. A new approach to setting such problems is developed for the case in which additional constraints are…

This article presents a modern deterministic framework for the study of leading significant digit distributions in numerical data. Rather than relying on traditional probabilistic or mixture-based explanations, we demonstrate that the…

We integrate information-theoretic concepts into the design and analysis of optimistic algorithms and Thompson sampling. By making a connection between information-theoretic quantities and confidence bounds, we obtain results that relate…

The aim of this paper is threefold: a) Finding new direct and inverse results in the additive number theory concerning Minkowski sums of dilates. b) Finding a connection between the above results and some direct and inverse problems in the…

Performance of reliable communication over a coherent slow fading channel at high SNR is succinctly captured as a fundamental tradeoff between diversity and multiplexing gains. We study the problem of designing codes that optimally tradeoff…

Bounding volumes are an established concept in computer graphics and vision tasks but have seen little change since their early inception. In this work, we study the use of neural networks as bounding volumes. Our key observation is that…