arXiv subjects

Elena Tartaglia

Publications and source records attributed to Elena Tartaglia.

14 recordsLinked to original sources

arXiv2023

Bottom-Up Stratified Probabilistic Logic Programming with Fusemate

This paper introduces the Fusemate probabilistic logic programming system. Fusemate's inference engine comprises a grounding component and a variable elimination method for probabilistic inference. Fusemate differs from most other systems by grounding the program in a bottom-up way instead of the common top-down way. While bottom-up grounding is attractive for a number of reasons, e.g., for dynamically creating distributions of varying support sizes, it makes it harder to control the amount of ground clauses generated. We address this problem by interleaving grounding with a query-guided relevance test which prunes rules whose bodies are inconsistent with the query. % This is done We present our method in detail and demonstrate it with examples that involve "time", such as (hidden) Markov models. Our experiments demonstrate competitive or better performance compared to a state-of-the art probabilistic logic programming system, in particular for high branching problems.

cs.LO↗

arXiv2023

Bottom-Up Grounding in the Probabilistic Logic Programming System Fusemate

This paper introduces the Fusemate probabilistic logic programming system. Fusemate's inference engine comprises a grounding component and a variable elimination method for probabilistic inference. Fusemate differs from most other systems by grounding the program in a bottom-up way instead of the common top-down way. While bottom-up grounding is attractive for a number of reasons, e.g., for dynamically creating distributions of varying support sizes, it makes it harder to control the amount of ground clauses generated. We address this problem by interleaving grounding with a query-guided relevance test which prunes rules whose bodies are inconsistent with the query. We present our method in detail and demonstrate it with examples that involve "time", such as (hidden) Markov models. Our experiments demonstrate competitive or better performance compared to a state-of-the art probabilistic logic programming system, in particular for high branching problems.

cs.AI↗

arXiv2023

Applying causal inference to inform early-childhood policy from administrative data

Improving public policy is one of the key roles of governments, and they can do this in an evidence-based way using administrative data. Causal inference for observational data improves on current practice of using descriptive or predictive analyses to inform policy decisions. Causal inference allows analysts to estimate the impact a policy change would have on the population if the encoded assumptions about the data generation process are valid. In this paper, we discuss the importance of causal analysis methods when analysing data to inform policy decisions. We take the education sector as a case study and provide examples of when to use a causal analysis. We use simulation to demonstrate the vital role causal diagrams play in variable selection and how bias can be introduced if extraneous variables are included in the model. Our exploration provides clear evidence for the utility of causal methods and practical examples of how to conduct such analyses. The paper promotes the incorporation of these methods in policy both for improved educational outcomes and scientific understanding.

stat.AP↗

arXiv2022

GLM for partially pooled categorical predictors with a case study in biosecurity

National governments use border information to efficiently manage the biosecurity risk presented by travel and commerce. In the Australian border biosecurity system, data about cargo consignments are collected from records of directions: that is, the records of actions taken by the biosecurity regulator. This data collection is complicated by the way directions for a given entry are recorded. An entry is a collection of import lines where each line is a single type of item or commodity. Analysis is simple when the data are recorded in line mode: the directions are recorded individually for each line. The challenge comes when data are recorded in container mode, because the same direction is recorded against each line in the entry. In other words, if at least one line in an entry has a non-compliant inspection result, then all lines in that entry are recorded as non-compliant. Therefore, container mode data creates a challenge for estimating the probability that certain items are non-compliant, because matching the records of non-compliance to the line information is impossible. We develop a statistical model to use container mode data to help inform biosecurity risk of items. We use asymptotic analysis to estimate the value of container mode data compared to line mode data, do a simulation study to verify that we can accurately estimate parameters in a large dataset, and we apply our methods to a real dataset, for which important information about the risk of non-compliance is recovered using the new model.

stat.AP↗

arXiv2022

Movement Analytics: Current Status, Application to Manufacturing, and Future Prospects from an AI Perspective

Data-driven decision making is becoming an integral part of manufacturing companies. Data is collected and commonly used to improve efficiency and produce high quality items for the customers. IoT-based and other forms of object tracking are an emerging tool for collecting movement data of objects/entities (e.g. human workers, moving vehicles, trolleys etc.) over space and time. Movement data can provide valuable insights like process bottlenecks, resource utilization, effective working time etc. that can be used for decision making and improving efficiency. Turning movement data into valuable information for industrial management and decision making requires analysis methods. We refer to this process as movement analytics. The purpose of this document is to review the current state of work for movement analytics both in manufacturing and more broadly. We survey relevant work from both a theoretical perspective and an application perspective. From the theoretical perspective, we put an emphasis on useful methods from two research areas: machine learning, and logic-based knowledge representation. We also review their combinations in view of movement analytics, and we discuss promising areas for future development and application. Furthermore, we touch on constraint optimization. From an application perspective, we review applications of these methods to movement analytics in a general sense and across various industries. We also describe currently available commercial off-the-shelf products for tracking in manufacturing, and we overview main concepts of digital twins and their applications.

cs.AI↗

arXiv2021

Real-Time Evolution in the Hubbard Model with Infinite Repulsion

We consider the real-time evolution of the Hubbard model in the limit of infinite coupling. In this limit the Hamiltonian of the system is mapped into a number-conserving quadratic form of spinless fermions, i.e. the tight binding model. The relevant local observables, however, do not transform well under this mapping and take very complicated expressions in terms of the spinless fermions. Here we show that for two classes of interesting observables the quench dynamics from product states in the occupation basis can be determined exactly in terms of correlations in the tight-binding model. In particular, we show that the time evolution of any function of the total density of particles is mapped directly into that of the same function of the density of spinless fermions in the tight-binding model. Moreover, we express the two-point functions of the spin-full fermions at any time after the quench in terms of correlations of the tight binding model. This sum is generically very complicated but we show that it leads to simple explicit expressions for the time evolution of the densities of the two separate species and the correlations between a point at the boundary and one in the bulk when evolving from the so called generalised nested Néel states.

cond-mat.stat-mech↗

arXiv2018

Entanglement and diagonal entropies after a quench with no pair structure

A typical working condition in the study of quantum quenches is that the initial state produces a distribution of quasiparticle excitations with an opposite-momentum-pair structure. In this work we investigate the dynamical and stationary properties of the entanglement entropy after a quench from initial states which do not have such structure: instead of pairs of excitations they generate $ν$-plets of correlated excitations with $ν>2$. Our study is carried out focusing on a system of non-interacting fermions on the lattice. We study the time evolution of the entanglement entropy showing that the standard semiclassical formula is not applicable. We propose a suitable generalisation which correctly describes the entanglement entropy evolution and perfectly matches numerical data. We finally consider the relation between the thermodynamic entropy of the stationary state and the diagonal entropy, showing that when there is no pair structure their ratio depends on the details of the initial state and lies generically between $1/2$ and $1$.

cond-mat.stat-mech↗

arXiv2017

On superuniversality in the $q$-state Potts model with quenched disorder

We obtain the exact scale invariant scattering solutions for two-dimensional field theories with replicated permutational symmetry $\mathbb{S}_q$. After sending to zero the number of replicas they correspond to the renormalization group fixed points of the $q$-state Potts model with quenched disorder. We find that all solutions with non-zero disorder possess $q$-independent sectors, pointing to superuniversality (i.e. symmetry independence) of some critical exponents. The solution corresponding to the random bond ferromagnet, for which disorder vanishes as $q\to 2$, allows for superuniversality of the correlation length exponent $ν$ [PRL 118 (2017) 250601]. Of the two solutions which are strongly disordered for all values of $q$, one is completely $q$-independent and accounts for the zero-temperature percolation fixed point of the randomly bond diluted ferromagnet. The other is the main candidate to describe the Nishimori-like fixed point of the Potts model with $\pm J$ disorder, and leaves room for superuniversality of the magnetic exponent $η$, a possibility not yet excluded by available numerical data.

cond-mat.stat-mech↗

arXiv2017

Quantum Quench in the Infinitely Repulsive Hubbard Model: the Stationary State

We use the Quench Action approach to study the non-equilibrium dynamics after a quantum quench in the Hubbard model in the limit of infinite interaction. We identify a variety of low-entangled initial states for which we can directly compute the overlaps with the Hamiltonian's eigenstates. For these initial states, we analytically find the rapidity distributions of the stationary state characterising the expectation values of all local observables. Some of the initial states considered are not reflection symmetric and lead to non-symmetric rapidity distributions. To study such cases, we have to introduce a generalised form for the reduced entropy which measures the entropy restricted to states with non-zero overlap. The initial states considered are of direct experimental realisability and also represent ideal candidates for studying non-equilibrium dynamics in the Hubbard model for finite interactions.

cond-mat.stat-mech↗

arXiv2017

Classifying Potts critical lines

We use scale invariant scattering theory to exactly determine the lines of renormalization group fixed points invariant under the permutational symmetry $S_q$ in two dimensions, and show how one of these scattering solutions describes the ferromagnetic and square lattice antiferromagnetic critical lines of the $q$-state Potts model. Other solutions we determine should correspond to new critical lines. In particular, we obtain that a $S_q$-invariant fixed point can be found up to the maximal value $q=(7+\sqrt{17})/2$. This is larger than the usually assumed maximal value 4 and leaves room for a second order antiferromagnetic transition at $q=5$.

cond-mat.stat-mech↗

arXiv2017

Logarithmic Minimal Models with Robin Boundary Conditions

We consider general logarithmic minimal models ${\cal LM}(p,p')$, with $p,p'$ coprime, on a strip of $N$ columns with the $(r,s)$ Robin boundary conditions introduced by Pearce, Rasmussen and Tipunin. The associated conformal boundary conditions are labelled by the Kac labels $r\in{\Bbb Z}$ and $s\in{\Bbb N}$. The Robin vacuum boundary condition, labelled by $(r,s\!-\!\frac{1}{2})=(0,\mbox{$\textstyle \frac{1}{2}$})$, is given as a linear combination of Neumann and Dirichlet boundary conditions. The general $(r,s)$ Robin boundary conditions are constructed, using fusion, by acting on the Robin vacuum boundary with an $(r,s)$-type seam consisting of an $r$-type seam of width $w$ columns and an $s$-type seam of width $d=s-1$ columns. The $r$-type seam admits an arbitrary boundary field which we fix to the special value $ξ=-\tfracλ{2}$ where $λ=\frac{(p'-p)π}{2p'}$ is the crossing parameter. The $s$-type boundary introduces $d$ defects into the bulk. We consider the associated quantum Hamiltonians and calculate analytically the boundary free energies of the $(r,s)$ Robin boundary conditions. Using finite-size corrections and sequence extrapolation out to system sizes $N+w+d\le 26$, the conformal spectrum of boundary operators is accessible by numerical diagonalization of the Hamiltonians. Fixing the parity of $N$ for $r\ne 0$ and restricting to the ground state sequences $w=\big\lfloor\frac{|r|p'}{p}\big\rfloor$, $r\in{\Bbb Z}$ with the inverse $r=(-1)^{N+w+d}\big\lceil \frac{p w}{p'}\big\rceil$, we find that the conformal weights take the values $Δ^{p,p'}_{r,s-\frac12}$ where $Δ^{p,p'}_{r,s}$ is given by the usual Kac formula. The $(r,s)$ Robin boundary conditions are thus conjugate to scaling operators with half-integer values for the Kac label $s-\mbox{$\textstyle \frac{1}{2}$}$.

hep-th↗

arXiv2017

Fused RSOS Lattice Models as Higher-Level Nonunitary Minimal Cosets

We consider the Forrester-Baxter RSOS lattice models with crossing parameter $λ=(m'\!-\!m)π/m'$ in Regime~III. In the continuum scaling limit, these models are described by the minimal models ${\cal M}(m,m')$. We conjecture that, for $λ<π/n$, the $n\times n$ fused RSOS models with $n\ge 2$ are described by the higher-level coset $(A^{(1)}_1)_k\otimes (A^{(1)}_1)_n/(A^{(1)}_1)_{k+n}$ at fractional level $k=nM/(M'\!-\!M)-2$ with $(M,M')=\big(nm-(n\!-\!1)m',m'\big)$. To support this conjecture, we investigate the one-dimensional sums arising from Baxter's off-critical corner transfer matrices. In unitary cases ($m=m'\!-\!1$) it is known that, up to leading powers of $q$, these coincide with the branching functions $b_{r,s,\ell}^{m'\!-n,m'\!,n}(q)$. For general nonunitary cases ($m<m'\!-\!1$), we identify the ground state one-dimensional RSOS paths and relate them to the quantum numbers $(r,s,\ell)$ in the various sectors. For $n=1,2,3$, we obtain the local energy functions $H(a,b,c)$ in a suitable gauge and verify that the associated one-dimensional sums produce finitized forms that converge, as $N$ becomes large, to the fractional level branching functions $b_{r,s,\ell}^{M,M'\!,n}(q)$. Extending the work of Schilling, we also conjecture finitized bosonic branching functions $b_{r,s,\ell}^{M,M'\!,n;(N)}(q)$ for general $n$ and check that these agree with the one-dimensional sums for $n=1,2,3$ out to system sizes $N=14$. Lastly, the finitized Kac characters $χ_{r,s,\ell}^{P,P'\!,n;(N)}(q)$ of the $n\times n$ fused logarithmic minimal models ${\cal LM}(p,p')$ are obtained by taking the {\em logarithmic limit\/} $m,m'\to\infty$ with $m/m'\to p/p'+$.

hep-th↗

arXiv2014

Kac boundary conditions of the logarithmic minimal models

We develop further the implementation and analysis of Kac boundary conditions in the general logarithmic minimal models ${\cal LM}(p,p')$ with $1\le p<p'$ and $p,p'$ coprime. Working in a strip geometry, we consider the $(r,s)$ boundary conditions, which are organized into infinitely extended Kac tables labeled by $r,s=1,2,3,...$. They are conjugate to Virasoro Kac representations with conformal dimensions $Δ_{r,s}$ given by the usual Kac formula. On a finite strip of width $N$, built from a square lattice, the associated integrable boundary conditions are constructed by acting on the vacuum $(1,1)$ boundary with an $s$-type seam of width $s-1$ columns and an $r$-type seam of width $ρ-1$ columns. The $r$-type seam contains an arbitrary boundary field $ξ$. The usual fusion construction of the $r$-type seam relies on the existence of Wenzl-Jones projectors restricting its application to $r\leρ<p'$. This limitation was recently removed by Pearce, Rasmussen and Villani who further conjectured that the conformal boundary conditions labeled by $r$ are realized, in particular, for $ρ=ρ(r)=\lfloor \frac{rp'}{p}\rfloor$. In this paper, we confirm this conjecture by performing extensive numerics on the commuting double row transfer matrices and their associated quantum Hamiltonian chains. Letting $[x]$ denote the fractional part, we fix the boundary field to the specialized values $ξ=\fracπ{2}$ if $[\fracρ{p'}]=0$ and $ξ=[\frac{ρp}{p'}]\fracπ{2}$ otherwise. For these boundary conditions, we obtain the Kac conformal weights $Δ_{r,s}$ by numerically extrapolating the finite-size corrections to the lowest eigenvalue of the quantum Hamiltonians out to sizes $N\le 32-ρ-s$. Additionally, by solving local inversion relations, we obtain general analytic expressions for the boundary free energies allowing for more accurate estimates of the conformal data.

hep-th↗

arXiv2014

Logarithmic Superconformal Minimal Models

The higher fusion level logarithmic minimal models LM(P,P';n) have recently been constructed as the diagonal GKO cosets (A_1^{(1)})_k oplus (A_1^{(1)})_n / (A_1^{(1)})_{k+n} where n>0 is an integer fusion level and k=nP/(P'-P)-2 is a fractional level. For n=1, these are the logarithmic minimal models LM(P,P'). For n>1, we argue that these critical theories are realized on the lattice by n x n fusion of the n=1 models. For n=2, we call them logarithmic superconformal minimal models LSM(p,p') where P=|2p-p'|, P'=p' and p,p' are coprime, and they share the central charges of the rational superconformal minimal models SM(P,P'). Their mathematical description entails the fused planar Temperley-Lieb algebra which is a spin-1 BMW tangle algebra with loop fugacity beta_2=x^2+1+x^{-2} and twist omega=x^4 where x=e^{i(p'-p)pi/p'}. Examples are superconformal dense polymers LSM(2,3) with c=-5/2, beta_2=0 and superconformal percolation LSM(3,4) with c=0, beta_2=1. We calculate the free energies analytically. By numerically studying finite-size spectra on the strip with appropriate boundary conditions in Neveu-Schwarz and Ramond sectors, we argue that, in the continuum scaling limit, these lattice models are associated with the logarithmic superconformal models LM(P,P';2). For system size N, we propose finitized Kac character formulas whose P,P' dependence only enters in the fractional power of q in a prefactor. These characters involve Motzkin and Riordan polynomials defined in terms of q-trinomial coefficients. Using the Hamiltonian limit, we argue that there exist reducible yet indecomposable representations for which the Virasoro dilatation operator L_0 exhibits rank-2 Jordan blocks confirming that these theories are indeed logarithmic. We relate these results to the N=1 superconformal representation theory.

hep-th↗