相关论文: Quadratization of Symmetric Pseudo-Boolean Functio…

The local minima of a quadratic functional depending on binary variables are discussed. An arbitrary connection matrix can be presented in the form of quasi-Hebbian expansion where each pattern is supplied with its own individual weight.…

Let $\Delta_x f(x,y)=f(x+1,y)-f(x,y)$ and $\Delta_y f(x,y)=f(x,y+1)-f(x,y)$ be the difference operators with respect to $x$ and $y$. A rational function $f(x,y)$ is called summable if there exist rational functions $g(x,y)$ and $h(x,y)$…

Generalisations of the bent property of a boolean function are presented, by proposing spectral analysis with respect to a well-chosen set of local unitary transforms. Quadratic boolean functions are related to simple graphs and it is shown…

Optimization of convex functions subject to eigenvalue constraints is intriguing because of peculiar analytical properties of eigenvalues, and is of practical interest because of wide range of applications in fields such as structural…

Calibration is a widely used method in survey sampling to adjust weights so that estimated totals of some chosen calibration variables match known population totals or totals obtained from other sources. When a large number of auxiliary…

This paper considers the problem of approximating a Boolean function $f$ using another Boolean function from a specified class. Two classes of approximating functions are considered: $k$-juntas, and linear Boolean functions. The $n$ input…

We consider quadratic optimization in variables $(x,y)$ where $0\le x\le y$, and $y\in\{0,1\}^n$. Such binary $y$ are commonly refered to as "indicator" or "switching" variables and occur commonly in applications. One approach to such…

Mapping functions on bits to Hamiltonians acting on qubits has many applications in quantum computing. In particular, Hamiltonians representing Boolean functions are required for applications of quantum annealing or the quantum approximate…

A unary constraint (on the Boolean domain) is a function from {0,1} to the set of real numbers. A free use of auxiliary unary constraints given besides input instances has proven to be useful in establishing a complete classification of the…

One matrix structure in the area of monotone Boolean functions is defined here. Some of its combinatorial, algebraic and algorithmic properties are derived. On the base of these properties, three algorithms are built. First of them…

The approximate degree of a Boolean function $f(x_{1},x_{2},\ldots,x_{n})$ is the minimum degree of a real polynomial that approximates $f$ pointwise within $1/3$. Upper bounds on approximate degree have a variety of applications in…

We study the computational power of polynomial threshold functions, that is, threshold functions of real polynomials over the boolean cube. We provide two new results bounding the computational power of this model. Our first result shows…

We design a sublinear-time approximation algorithm for quadratic function minimization problems with a better error bound than the previous algorithm by Hayashi and Yoshida (NIPS'16). Our approximation algorithm can be modified to handle…

We consider the problem of jointly minimizing forms of two Boolean functions $f, g \colon \{0,1\}^J \to \{0,1\}$ such that $f + g \leq 1$ and so as to separate disjoint sets $A \cup B \subseteq \{0,1\}^J$ such that $f(A) = \{1\}$ and $g(B)…

This paper studies the $H^0$ norm and $H^1$ seminorm of quadratic functions. The (semi)norms are expressed explicitly in terms of the coefficients of the quadratic function under consideration when the underlying domain is an $l_p$-ball (1…

Quadratic Unconstrained Binary Optimization models are useful for solving a diverse range of optimization problems. Constraints can be added by incorporating quadratic penalty terms into the objective, often with the introduction of slack…

For any pair $(X,Z)$ of correlated random variables we can think of $Z$ as a randomized function of $X$. Provided that $Z$ is short, one can make this function computationally efficient by allowing it to be only approximately correct. In…

General methods of solving equations deal with solving N equations in N variables and the solutions are usually a set of discrete values. However, for problems with a softly broken symmetry these methods often first find a point which would…

The {\em Total Influence} ({\em Average Sensitivity) of a discrete function is one of its fundamental measures. We study the problem of approximating the total influence of a monotone Boolean function \ifnum\plusminus=1 $f: \{\pm1\}^n…

The ${\mathcal D}$-pseudo-boson formalism is illustrated with two examples. The first one involves deformed complex Hermite polynomials built using finite-dimensional irreducible representations of the group ${\rm GL}(2,{\mathbb C})$ of…