Related papers: Magnificent Four
In probability theory, the partition function is a factor used to reduce any probability function to a density function with total probability of one. Among other statistical models used to represent joint distribution, Markov random fields…
Let $X$ be a compact complex Calabi-Yau 4-fold. Under certain assumptions, we define Donaldson-Thomas type deformation invariants ($DT_{4}$ invariants) by studying moduli spaces of solutions to the Donaldson-Thomas equations on $X$. We also…
We review and elaborate on certain aspects of the connections between instanton counting in maximally supersymmetric gauge theories and the computation of enumerative invariants of smooth varieties. We study in detail three instances of…
We describe the modern formalism, ideas and applications of the instanton calculus for gauge theories with, and without, supersymmetry. Particular emphasis is put on developing a formalism that can deal with any number of instantons. This…
The exactly solvable four-vertex model with the fixed boundary conditions in the presence of inhomogeneous linearly growing external field is considered. The partition function of the model is calculated and represented in the determinantal…
We define Donaldson-Thomas invariants of Calabi-Yau orbifolds and we develop a topological vertex formalism for computing them. The basic combinatorial object is the orbifold vertex, a generating function for the number of 3D partitions…
We show that a partition function of topological twisted N=4 Yang-Mills theory is given by Seiberg-Witten invariants on a Riemannian four manifolds under the condition that the sum of Euler number and signature of the four manifolds vanish.…
Motivated by an increasing demand for models that can effectively describe features of complex multivariate time series, e.g. from sensor data in biomechanics, motion analysis, and sports science, we introduce a novel state-space modeling…
We consider Donaldson-Witten theory on four-manifolds of the form $X=Y \times {\bf S}^1$ where $Y$ is a compact three-manifold. We show that there are interesting relations between the four-dimensional Donaldson invariants of $X$ and…
The partition function is an essential quantity in statistical mechanics, and its accurate computation is a key component of any statistical analysis of quantum system and phenomenon. However, for interacting many-body quantum systems, its…
Probabilistic graphical models are a key tool in machine learning applications. Computing the partition function, i.e., normalizing constant, is a fundamental task of statistical inference but it is generally computationally intractable,…
We perform an exact computation of the gauged linear sigma model associated to a D1-D5 brane system on a resolved A_1 singularity. This is accomplished via supersymmetric localization on the blown-up two-sphere. We show that in the…
Supersymmetric D-branes supported on the complex two-dimensional base $S$ of the local Calabi-Yau threefold $K_S$ are described by semi-stable coherent sheaves on $S$. Under suitable conditions, the BPS indices counting these objects (known…
Let $\sigma$ be a stability condition on the bounded derived category $D^b({\mathop{\rm Coh}\nolimits} W)$ of a Calabi-Yau threefold $W$ and $\mathcal{M}$ a moduli stack parametrizing $\sigma$-semistable objects of fixed topological type.…
We analyze instantons in the very strongly coupled large-$N$ limit ($N\to\infty$ with $g^2$ fixed) of large-$N$ gauge theories, where the effect of the instantons remains finite. By using the exact partition function of four-dimensional…
The construction of good effective models is an essential part of understanding and simulating complex systems in many areas of science. It is a particular challenge for correlated many body quantum systems displaying emergent physics. We…
We introduce and study tetrahedron instantons, which can be realized in string theory by D$1$-branes probing a configuration of intersecting D$7$-branes in flat spacetime with a proper constant $B$-field. Physically they capture instantons…
Suppose some random resource (energy, mass or space) $\chi \geq 0$ is to be shared at random between (possibly infinitely many) species (atoms or fragments). Assume ${\Bbb E}\chi =\theta <\infty $ and suppose the amount of the individual…
A popular approach for testing if two univariate random variables are statistically independent consists of partitioning the sample space into bins, and evaluating a test statistic on the binned data. The partition size matters, and the…
We study the distribution of the Schmidt coefficients of the reduced density matrix of a quantum system in a pure state. By applying general methods of statistical mechanics, we introduce a fictitious temperature and a partition function…