Related papers: Symbolic analytic spread: upper bounds and applica…
The incomplete nonextensive statistics in the canonical and microcanonical ensembles is explored in the general case and in a particular case for the ideal gas. By exact analytical results for the ideal gas it is shown that taking the…
Given a nontrivial homogeneous ideal $I\subseteq k[x_1,x_2,\ldots,x_d]$, a problem of great recent interest has been the comparison of the $r$th ordinary power of $I$ and the $m$th symbolic power $I^{(m)}$. This comparison has been…
We refine upper bounds on the permanent saturation time of metric graphs using interval exchange transformations (IETs). Earlier results gave bounds under incommensurable edge lengths, we improve and generalize them by using the ergodic and…
Influence diagrams provide a compact graphical representation of decision problems. Several algorithms for the quick computation of their associated expected utilities are available in the literature. However, often they rely on a full…
A statistical approach based on the interval analysis (IA) is proposed for the analysis of the effects, on the radiation patterns radiated by phased arrays, of random errors and tolerances in the amplitudes and phases of the array-elements…
Let $S = K[x_1,..., x_n]$ be a polynomial ring over a field $K$. Let $I(G) \subseteq S$ denote the edge ideal of a graph $G$. We show that the $\ell$th symbolic power $I(G)^{(\ell)}$ is a Cohen-Macaulay ideal (i.e., $S/I(G)^{(\ell)}$ is…
This paper introduces "Semantic Scaling," a novel method for ideal point estimation from text. I leverage large language models to classify documents based on their expressed stances and extract survey-like data. I then use item response…
The arithmetic rank of an ideal in a polynomial ring over an algebraically closed field is the smallest number of equations needed to define its vanishing locus set-theoretically. We determine the arithmetic rank of the generic $m$-residual…
Implicit stochastic models, where the data-generation distribution is intractable but sampling is possible, are ubiquitous in the natural sciences. The models typically have free parameters that need to be inferred from data collected in…
This paper develops a unified methodology for probabilistic analysis and optimal control design for jump diffusion processes defined by polynomials. For such systems, the evolution of the moments of the state can be described via a system…
We obtain non-asymptotic Gaussian concentration bounds for the difference between the invariant measure $\nu$ of an ergodic Brownian diffusion process and the empirical distribution of an approximating scheme with decreasing time step along…
Let $G$ be a dense graph with good expansion properties and not too close to being bipartite. Let $\boldsymbol d$ be a graphical degree sequence. Under very weak conditions, we find the number of subgraphs of $G$ with degree sequence…
This paper deals with sensors which compute and report linguistic assessments of their values.Such sensors, called symbolic sensors are a natural extension of smart ones when working with control systems which use artificial intelligence…
In this paper, we compute the regularity and Hilbert series of symbolic powers of the cover ideal of a graph $G$ when $G$ is either a crown graph or a complete multipartite graph. We also compute the multiplicity of symbolic powers of cover…
The present work is concerned with characterizing some algebraic invariants of edge ideals of hypergraphs. To this aim, firstly, we introduce some kinds of combinatorial invariants similar to matching numbers for hypergraphs. Then we…
Inferring a diffusion equation from discretely-observed measurements is a statistical challenge of significant importance in a variety of fields, from single-molecule tracking in biophysical systems to modeling financial instruments.…
We present lightweight and generic symbolic methods to improve the precison of numerical static analyses based on Abstract Interpretation. The main idea is to simplify numerical expressions before they are fed to abstract transfer…
We prove that a classical theorem of McAdam about the analytic spread of an ideal in a Noetherian local ring is true for divisorial filtrations on an excellent local ring $R$ which is either of equicharacteristic zero or of dimension $\le…
In science, we are interested not only in forecasting but also in understanding how predictions are made, specifically what the interpretable underlying model looks like. Data-driven machine learning technology can significantly streamline…
Recent work of Ein-Lazarsfeld-Smith and Hochster-Huneke raised the problem of which symbolic powers of an ideal are contained in a given ordinary power of the ideal. Bocci-Harbourne developed methods to address this problem, which involve…