These notes are a considerably revised and expanded version of expository lectures given at the Fields Institute Workshop on "Nonlinear Dispersive Partial Differential Equations and Inverse Scattering" in August 2017. We give a complete and self-cont...
We study a set of truncated matrices, given by Smith~\cite{Smith2005}, in connection to an identification criterion for the ground state in our proposed quantum adiabatic algorithm for Hilbert's tenth problem. We identify the origin of the trouble...
possible, practicable, feasible mean capable of being realized. possible implies that a thing may certainly exist or occur given the proper conditions.
Given a finite set of arbitrarily distributed points in affine space with arbitrary multiplicity structures, we present an algorithm to compute the reduced Groebner basis of the vanishing ideal under the lexicographic ordering. Our method discloses t...
The Gemini theorem asserts that, given certain reasonable assumptions, no physical system can be certainly aware of its own existence. The theorem can be proved algorithmically, but the proof of this theorem is somewhat obscure, and there exists very...
In this paper, we extend the notions of $λ$-cent-dian and generalized-center from Facility Location Theory to the more intricate domain of Network Design. Our focus is on the task of designing a sub-network within a given underlying network while ad...
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In the window mean-payoff objective, given an infinite path, instead of considering a long run average, we consider the minimum payoff that can be ensured at every position of the path over a finite window that slides over the entire path. Chatterjee...
Quantum Computing promises accelerated simulation of certain classes of problems, in particular in plasma physics. Given the nascent interest in applying quantum computing techniques to study plasma systems, a compendium of the relevant literature wo...
Modern machine learning techniques, including deep learning, are rapidly being applied, adapted, and developed for high energy physics. Given the fast pace of this research, we have created a living review with the goal of providing a nearly comprehe...
Given the current interest in quantum information tasks with higher-dimensional systems, we present three possible extensions of the bit-flip channel to qutrit systems based on different interpretations of the channel. We compared our results with th...
Note: All of the snarky comments that amount of "cause the GOP sucks" are fun and all, and hey, I mostly agree, but I'm trying to see what the actual like given reason by the GOP is. [Live updates: G...
These notes are a written version of lectures given in the 2024 Les Houches Summer School on {\it Large deviations and applications}. They are are based on a series of works published over the last 25 years on steady properties of non-equilibrium sys...
##UPDATE: The Megathreads are now locked, and we are returning to regular order here in r/NFL. For three days we have given you all the opportunity to freely talk about the events of the past week. W...
The U.S. has given Ukraine and Russia a June deadline to reach a peace deal, according to President Volodymyr Zelenskyy.
The wonderful teams at Kepler Interactive and Sandfall have given us some region free codes for their incredible game 'Clair Obscur Expedition 33'. At the Golden Joystick Awards 2025, which were dete...
Recently, it was discovered that the `quantum partial information' needed to merge one party's state with another party's state is given by the conditional entropy, which can be negative [Horodecki, Oppenheim, and Winter, Nature 436, 673 (2005)]. H...
Given a split classical group of symplectic type and a split general linear group over a local field $F$, we use Langlands-Shahidi method to construct their Rankin-Selberg local $γ$-factors and prove the corresponding analytic stability for generic...
The U.S. has given Ukraine and Russia a June deadline to reach a peace deal, according to President Volodymyr Zelenskyy.
In this paper, the closed-form analytic solutions of two new Faraday's standing solitary waves due to the parametric resonance of liquid in a vessel vibrating vertically with a constant frequency are given for the first time. Using a model based on t...