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Finite (or Discrete) Fourier Transforms (FFT) are essential tools in engineering disciplines based on signal transmission, which is the case in most of them. FFT are related with circulant matrices, which can be viewed as group matrices of…
This paper considers a secure multigroup multicast multiple-input single-output (MISO) communication system aided by an intelligent reflecting surface (IRS). Specifically, we aim to minimize the transmit power at the Alice via jointly…
We generalize to the super context, the known fact that if an affine algebraic group $G$ over a commutative ring $k$ acts freely (in an appropriate sense) on an affine scheme $X$ over $k$, then the dur sheaf $X\tilde{\tilde{/}}G$ of…
This paper derives nonlinear feedback control synthesis for general control affine systems using second-order actions---the second-order needle variations of optimal control---as the basis for choosing each control response to the current…
We show that the affine quantum group $U_q(\hat{sl_2})$ is isomorphic to a bicrossproduct central extension $C Z{}_\chi\cross U_q(Lsl_2)$ of the quantum loop group $U_q(Lsl_2)$ by a quantum cocycle $\chi$, which we construct. We prove the…
Post-training processes are essential phases in grounding pre-trained language models to real-world tasks, with learning from demonstrations or preference signals playing a crucial role in this adaptation. We present a unified theoretical…
A variety of idealized models of communication systems exist, and all may have something in common. Starting with Shannons communication model and ending with the OSI model, this paper presents progressively more advanced forms of modeling…
The use of channel output feedback to improve the reliability of fading channels has received scant attention in the literature. In most work on feedback for fading channels, only channel state information (CSI) feedback has been exploited…
This paper studies secure layered video transmission in a multiuser multiple-input single-output (MISO) beamforming downlink communication system. The power allocation algorithm design is formulated as a non-convex optimization problem for…
An affine semigroup is a finitely generated subsemigroup of $(\mathbb Z_{\ge 0}^d, +)$, and a numerical semigroup is an affine semigroup with $d = 1$. A growing body of recent work examines shifted families of numerical semigroups, that is,…
This paper proposes an optimization with penalty-based feedback design framework for safe stabilization of control affine systems. Our starting point is the availability of a control Lyapunov function (CLF) and a control barrier function…
We consider the problem of boundary feedback control of single-input-single-output (SISO) one-dimensional linear hyperbolic systems when sensing and actuation are anti-located. The main issue of the output feedback stabilization is that it…
This paper derives nonlinear feedback control synthesis for general control affine systems using second-order actions---the needle variations of optimal control---as the basis for choosing each control response to the current state. A…
We characterize affine semigroups having one Betti element and we compute some relevant non-unique factorization invariants for these semigroups. As an example, we particularize our description to numerical semigroups.
A site-specific Type-II codebook design is proposed for downlink massive multiple-input multiple-output (MIMO) limited-feedback beamforming. The key idea is to embed a learned site-specific propagation prior into the Type-II channel state…
This letter proposes a fluid reconfigurable intelligent surface (FRIS) paradigm, extending the conventional reconfigurable intelligent surface (RIS) technology to incorporate position reconfigurability of the elements. In our model, a…
This paper studies the boundary feedback stabilization of a class of diagonal infinite-dimensional boundary control systems. In the studied setting, the boundary control input is subject to a constant delay while the open loop system might…
The takeoff point of this paper is to generalize the existing stock trading results for a class of affine feedback controller to include consideration of a stop-loss order. Using the geometric Brownian motion as the underlying stock price…
An upper bound on the feedback capacity of unifilar finite-state channels (FSCs) is derived. A new technique, called the $Q$-contexts, is based on a construction of a directed graph that is used to quantize recursively the receiver's output…
We study convergence and stability properties of control-affine systems. Our considerations are motivated by the problem of stabilizing a control-affine system by means of output feedback for states in which the output function attains an…