Related papers: Half-Iterates and Delta Conjectures
Large-scale optimization problems that involve thousands of decision variables have extensively arisen from various industrial areas. As a powerful optimization tool for many real-world applications, evolutionary algorithms (EAs) fail to…
A promising method for calculating free energy differences Delta F is to generate non-equilibrium data via ``fast-growth'' simulations or experiments -- and then use Jarzynski's equality. However, a difficulty with using Jarzynski's…
Alternating automata have been widely used to model and verify systems that handle data from finite domains, such as communication protocols or hardware. The main advantage of the alternating model of computation is that complementation is…
This paper investigates simple bilevel optimization problems where we minimize an upper-level objective over the optimal solution set of a convex lower-level objective. Existing methods for such problems either only guarantee asymptotic…
The difference Delta F between free energies has applications in biology, chemistry, and pharmacology. The value of Delta F can be estimated from experiments or simulations, via fluctuation theorems developed in statistical mechanics.…
We compute $\delta$-derivations of simple Jordan algebras with values in irreducible bimodules. They turn out to be either ordinary derivations ($\delta = 1$), or scalar multiples of the identity map ($\delta = \frac 12$). This can be…
In the context of the shuffle theorem, many classical integer sequences appear with a natural refinement by two statistics $q$ and $t$: for example the Catalan and Schr\"oder numbers. In particular, the bigraded Hilbert series of diagonal…
In a recent paper it has been shown that if Cesaro and Abel limits for a certain discrete time optimal control problem are not equal, then there is a duality gap between a certain infinite-dimensional linear programming problem and its…
A simple classical, deterministic, local situation violating the Bell inequality is described. The detectors used in the experiment are ideal and the observers who decide which pair of measuring devices to choose for a given pair of…
This paper presents some considerations about the Goldbach's conjecture (GC). The work is based on elementary results of the number theory and it provides a constructive method that permits, given an even integer, to find at least a pair of…
We consider various iterative algorithms for solving the linear equation $ax=b$ using a quantum computer operating on the principle of quantum annealing. Assuming that the computer's output is described by the Boltzmann distribution, it is…
Machine Learning (ML) is applicable to scientific problems, i.e. to those which have a well defined answer, only if this answer can be brought to a peculiar form ${\cal G}: X\longrightarrow Z$ with ${\cal G}(\vec x)$ expressed as a…
We extend the Bell inequality known for two qubits to the four-level atom, including an artificial atom realized by the superconducting circuit, and qudit with j=3/2. We formulate the extended inequality as the inequality valid for an…
Simultaneous machine translation attempts to translate a source sentence before it is finished being spoken, with applications to translation of spoken language for live streaming and conversation. Since simultaneous systems trade quality…
Entity linkage (EL) is a critical problem in data cleaning and integration. In the past several decades, EL has typically been done by rule-based systems or traditional machine learning models with hand-curated features, both of which…
The current paper presents a new quantum algorithm for finding multicollisions, often denoted by $\ell$-collisions, where an $\ell$-collision for a function is a set of $\ell$ distinct inputs that are mapped by the function to the same…
Let $\Delta(x)$ denote the error term in the Dirichlet divisor problem, and let $E(T)$ denote the error term in the asymptotic formula for the mean square of $|\zeta(1/2+it)|$. If $E^*(t) := E(t) - 2\pi\Delta^*(t/(2\pi))$ with $\Delta^*(x)…
The document tries to put focus on sequences with certain properties and periods leading to the first value smaller than the starting value in the Collatz problem. With the idea that, if all starting numbers lead ultimately to a smaller…
Widely used methods for analyzing missing data can be biased in small samples. To understand these biases, we evaluate in detail the situation where a small univariate normal sample, with values missing at random, is analyzed using either…
$\ell_1$ optimization is a well known heuristic often employed for solving various forms of sparse linear problems. In this paper we look at its a variant that we refer to as the \emph{partial} $\ell_1$ and discuss its mathematical…