Related papers: A self-consistent criterion for the range of valid…
We consider the linear complementarity problem with uncertain data modeled by intervals, representing the range of possible values. Many properties of the linear complementarity problem (such as solvability, uniqueness, convexity, finite…
Linear Response theory aims to predict how added forcing alters the statistical properties of an unforced system. These kinds of questions have been studied predominantly for autonomous dynamical systems, yet many systems in the physical,…
One of my recent papers transforms an NP-Complete problem into the question of whether or not a feasible real solution exists to some Linear Program. The unique feature of this Linear Program is that though there is no explicit bound on the…
Dynamic control via optimized, piecewise-constant pulses is a common paradigm for open-loop control to implement quantum gates. While numerous methods exist for the synthesis of such controls, there are many open questions regarding the…
In this paper we present a method to generate independent samples for a general random variable, either continuous or discrete. The algorithm is an extension of the acceptance-rejection method, and it is particularly useful for kinetic…
In this paper, we present a theoretical analysis of the model reduction algorithm for linear switched systems. This algorithm is a reminiscence of the balanced truncation method for linear parameter varying systems. Specifically in this…
This paper proposes a feedback linearizing law for single-track dynamic models, allowing the design of a trajectory tracking controller exploiting linear control theory. The main characteristics of this algorithm are its simplicity, its…
We introduce a necessary and sufficient criterion for determining the existence and the values of ratio limits of complex sequences generated by arbitrary linear recurrences.
A popular approach for improving the correctness of output from large language models (LLMs) is Self-Consistency - poll the LLM multiple times and output the most frequent solution. Existing Self-Consistency techniques always generate a…
Hamiltonian Truncation Effective Theory is a framework that aims to improve the results of Hamiltonian truncation in a systematic, order-by-order fashion using Effective Field Theory methodology. The result is a truncated effective…
The long-term average response of observables of chaotic systems to dynamical perturbations can often be predicted using linear response theory, but not all chaotic systems possess a linear response. Macroscopic observables of complex…
This paper considers the problem of variable-length intrinsic randomness. We propose the average variational distance as the performance criterion from the viewpoint of a dual relationship with the problem formulation of variable-length…
The intractability of any problem and the randomness of its solutions have an obvious intuitive connection. However, the challenge till now has been that there is no practical way to firmly establish if the solution to a problem is actually…
Precisely controlling the length of generated text is a common requirement in real-world applications. However, despite significant advancements in following human instructions, Large Language Models (LLMs) still struggle with this task. In…
We consider a Lurie system obtained via a connection of a linear time-invariant system and a nonlinear feedback function. Such systems often have more than a single equilibrium and are thus not contractive with respect to any norm. We…
It is regrettable that the quantum length of an object is rarely if ever discussed, because it provides an ideal pedagogical paradigm for understanding how a physicist uses classical intuition to define quantum properties and how such…
A linear parameter must be consumed exactly once in the body of its function. When declaring resources such as file handles and manually managed memory as linear arguments, a linear type system can verify that these resources are used…
Conformal symmetry is broken in physical QCD; nevertheless, one can use conformal symmetry as a template, systematically correcting for its nonzero $\beta$ function as well as higher-twist effects. For example, commensurate scale relations…
Self-consistency has emerged as a powerful method for improving the accuracy of short answers generated by large language models. As previously defined, it only concerns the accuracy of a final answer parsed from generated text. In this…
We study the law of the iterated logarithm (LIL) for the maximum likelihood estimation of the parameters (as a convex optimization problem) in the generalized linear models with independent or weakly dependent ($\rho$-mixing, $m$-dependent)…