Related papers: Improving Modular Bootstrap Bounds with Integralit…
We consider integer programming problems in standard form $\max \{c^Tx : Ax = b, \, x\geq 0, \, x \in Z^n\}$ where $A \in Z^{m \times n}$, $b \in Z^m$ and $c \in Z^n$. We show that such an integer program can be solved in time $(m…
Modularity is appealing for solving many problems in optimization. It brings the benefits of manufacturability and reconfigurability to structural optimization, and enables a trade-off between the computational performance of a Periodic…
Our recent study (Lin and Ohtsuka, 2024) proposed a new penalty method for solving mathematical programming with complementarity constraints (MPCC). This method first reformulates MPCC as a parameterized nonlinear programming called gap…
We establish a precise relation between the modular bootstrap, used to constrain the spectrum of 2D CFTs, and the sphere packing problem in Euclidean geometry. The modular bootstrap bound for chiral algebra $U(1)^c$ maps exactly to the…
Recently, a novel bootstrap method for numerical calculations in matrix models and quantum mechanical systems is proposed. We apply the method to certain quantum mechanical systems derived from some well-known local toric Calabi-Yau…
Binary embedding is the problem of mapping points from a high-dimensional space to a Hamming cube in lower dimension while preserving pairwise distances. An efficient way to accomplish this is to make use of fast embedding techniques…
Using variational density matrix optimization with two- and three-index conditions we study the one-dimensional Hubbard model with periodic boundary conditions at various filling factors. Special attention is directed to the full…
Based on the results of a recent reexamination of the quantization of systems with first-class and second-class constraints from the point of view of coherent-state phase-space path integration, we give additional examples of the…
We present the first linear lower bound for the number of bits required to be accessed in the worst case to increment an integer in an arbitrary space- optimal binary representation. The best previously known lower bound was logarithmic. It…
In this paper, we Fourier transform the Wightman function concerning energy and angular momentum on the $S^{D-1}$ spatial slice in radial quantization in $D=2,3$ dimensions. In each case, we use the conformal Ward Identities to solve…
A covering code is a set of codewords with the property that the union of balls, suitably defined, around these codewords covers an entire space. Generally, the goal is to find the covering code with the minimum size codebook. While most…
We present exact mixed-integer linear programming formulations for verifying the performance of first-order methods for parametric quadratic optimization. We formulate the verification problem as a mixed-integer linear program where the…
We study settings where gradient penalties are used alongside risk minimization with the goal of obtaining predictors satisfying different notions of monotonicity. Specifically, we present two sets of contributions. In the first part of the…
We study two fundamental optimization problems: (1) scaling a symmetric positive definite matrix by a positive diagonal matrix so that the resulting matrix has row and column sums equal to 1; and (2) minimizing a quadratic function subject…
Neural networks offer a computationally efficient approximation of model predictive control, but they lack guarantees on the resulting controlled system's properties. Formal certification of neural networks is crucial for ensuring safety,…
A popular approach in combinatorial optimization is to model problems as integer linear programs. Ideally, the relaxed linear program would have only integer solutions, which happens for instance when the constraint matrix is totally…
A matching in a graph is induced if no two of its edges are joined by an edge, and finding a large induced matching is a very hard problem. Lin et al. (Approximating weighted induced matchings, Discrete Applied Mathematics 243 (2018)…
We present necessary and sufficient optimality conditions for finite time optimal control problems for a class of hybrid systems described by linear complementarity models. Although these optimal control problems are difficult in general…
We suggest a way to implement conformal bootstrap program for the case of the ${\cal N}=1$ SCFT in three dimensions using the previous analysis of the Ising model in \cite{CB}. We find approximate values for the conformal dimensions of…
We consider generalizations of parity polytopes whose variables, in addition to a parity constraint, satisfy certain ordering constraints. More precisely, the variable domain is partitioned into $k$ contiguous groups, and within each group,…