arXiv subjects

Hayato Hirai

Publications and source records attributed to Hayato Hirai.

9 recordsLinked to original sources

arXiv2025

Adaptive Inference through Bayesian and Inverse Bayesian Inference with Symmetry-Bias in Nonstationary Environments

This study proposes the novel Bayesian and inverse Bayesian (BIB) inference framework that incorporates symmetry bias into the Bayesian updating process to perform both conventional and inverse Bayesian updates concurrently. Conventional Bayesian inference is constrained by a fundamental trade-off between adaptability to abrupt environmental changes and accuracy during stable periods. The BIB framework addresses this limitation by dynamically modulating the learning rate via inverse Bayesian updates, thereby enhancing adaptive flexibility. The BIB model was evaluated in a sequential estimation task involving observations drawn from a Gaussian distribution with a stochastically time-varying mean, where it exhibited spontaneous bursts in the learning rate during environmental transitions, transiently entering high-sensitivity states that facilitated rapid adaptation. This burst-relaxation dynamic serves as a mechanism for balancing adaptability and accuracy. Furthermore, avalanche analysis, detrended fluctuation analysis, and power spectral analysis revealed that the BIB system likely operates near a critical state-a property not observed in standard Bayesian inference. This suggests that the BIB model uniquely achieves a coexistence of computational efficiency and critical dynamics, resolving the adaptability-accuracy trade-off while maintaining scale-free behavior. These findings offer a new computational perspective on scale-free dynamics in natural systems and provide valuable insights for the design of adaptive inference systems in nonstationary environments.

stat.ME↗

arXiv2025

A Simple Walk Model for Reproducing Power Laws in Human mobility

Identifying statistical patterns characterizing human trajectories is crucial for public health, traffic engineering, city planning, and epidemic modeling. Recent developments in global positioning systems and mobile phone networks have enabled the collection of substantial information on human movement. Analyses of these data have revealed various power laws in the temporal and spatial statistical patterns of human mobility. For example, jump size and waiting time distributions follow power laws. Zipf's law was also established for the frequency of visits to each location and rank. Relationship $S(t)\sim t^μ$ exists between time t and the number of sites visited up to that time t. Recently, a universal law of visitation for human mobility was established. Specifically, the number of people per unit area $ρ(r,f)$, who reside at distance r from a particular location and visit that location f times in a given period, is inversely proportional to the square of rf, i.e., $ρ(r,f) \propto (rf)^{-2}$ holds. The exploration and preferential return (EPR) model and its improved versions have been proposed to reproduce the above scaling laws. However, some rules that follow the power law are preinstalled in the EPR model. We propose a simple walking model to generate movements toward and away from a target via a single mechanism by relaxing the concept of approaching a target. Our model can reproduce the abovementioned power laws and some of the rules used in the EPR model are generated. These results provide a new perspective on why or how the scaling laws observed in human mobility behavior arise.

physics.soc-ph↗

arXiv2024

Walk model that continuously generates Brownian walks to Lévy walks depending on destination attractiveness

The Lévy walk, a type of random walk characterized by linear step lengths that follow a power-law distribution, is observed in the migratory behaviors of various organisms, ranging from bacteria to humans. Notably, Lévy walks with power exponents close to two, also known as Cauchy walks, are frequently observed, though their underlying causes remain elusive. This study proposes a walk model in which agents move toward a destination in multi-dimensional space and their movement strategy is parameterized by the extent to which they pursue the shortest path to the destination. This parameter is taken to represent the attractiveness of the destination to the agents. Our findings reveal that if the destination is very attractive, agents intensively search the area around it using Brownian walks, whereas if the destination is unattractive, they explore a distant region away from the point using Lévy walks with power exponents less than two. In the case where agents are unable to determine whether the destination is attractive or unattractive, Cauchy walks emerge. The Cauchy walker searches the region with a probability inversely proportional to the distance from the destination. This suggests that it preferentially searches the area close to the destination, while concurrently having the potential to extend the search area much further. Our model, which can change the search method and search area depending on the attractiveness of the destination, has the potential to be utilized for exploring the parameter space of optimization problems.

cs.MA↗

arXiv2023

Dress code for infrared safe scattering in QED

We study the $S$-matrix and inclusive cross-section for general dressed states in quantum electrodynamics. We obtain an infrared factorization formula of the $S$-matrix elements for general dressed states. It enables us to study what dressed states lead to infrared-safe $S$-matrix elements. The condition for dressed states can be interpreted as the memory effect which is nothing but the conservation law of the asymptotic symmetry. We derive the generalized soft photon theorem for general dressed states. We also compute inclusive cross-section using general dressed states. It is necessary to use appropriate initial and final dressed states to evaluate interference effects, which cannot be computed correctly by using Fock states due to the infrared divergence.

hep-th↗

arXiv2020

IR finite S-matrix by gauge invariant dressed states

Dressed states were proposed to define the infrared (IR) finite $S$-matrix in QED or gravity. We show that the original Kulish-Faddeev dressed states are not enough to cure the IR divergences. To illustrate this problem, we consider QED with background currents (Wilson lines). This theory is exactly solvable but shares the same IR problems as the full QED. We show that naive asymptotic states lead to IR divergences in the $S$-matrix and are also inconsistent with the asymptotic symmetry, even if we add the original Kulish-Faddeev dressing operators. We then propose new dressed states which are consistent with the asymptotic symmetry. We show that the $S$-matrix for the dressed states is IR finite. We finally conclude that appropriate dressed asymptotic states define the IR finite $S$-matrix in the full QED.

hep-th↗

arXiv2020

Shrinking of Operators in Quantum Error Correction and AdS/CFT

We first show that a class of operators acting on a given bipartite pure state on $\mathcal{H}_{A}\otimes\mathcal{H}_{B}$ can shrink its supports on $\mathcal{H}_{A}\otimes\mathcal{H}_{B}$ to only $\mathcal{H}_{A}$ or $\mathcal{H}_{B}$ while keeping its mappings. Using this result, we show how to systematically construct the decoders of the quantum error-correcting codes against erasure errors. The implications of the results for the operator dictionary in the AdS/CFT correspondence are also discussed. The "subalgebra code with complementary recovery" introduced in the recent work of Harlow is a quantum error-correcting code that shares many common features with the AdS/CFT correspondence. We consider it under the restriction of the bulk (logical) Hilbert space to a subspace that generally has no tensor factorization into subsystems. In this code, the central operators of the reconstructed algebra on the boundary subregion can emerge as a consequence of the restriction of the bulk Hilbert space. Finally, we show a theorem in this code which implies the validity of not only the entanglement wedge reconstruction but also its converse statement with the central operators.

hep-th↗

arXiv2019

Dressed states from gauge invariance

The dressed state formalism enables us to define the infrared finite $S$-matrix for QED. In the formalism, asymptotic charged states are dressed by clouds of photons. The dressed asymptotic states are originally obtained by solving the dynamics of the asymptotic Hamiltonian in the far past or future region. However, there was an argument that the obtained dressed states are not gauge invariant. We resolve the problem by imposing a correct gauge invariant condition. We show that the dressed states can be obtained just by requiring the gauge invariance of asymptotic states. In other words, Gauss's law naturally leads to proper asymptotic states for the infrared finite $S$-matrix. We also discuss the relation between the dressed state formalism and the asymptotic symmetry for QED.

hep-th↗

arXiv2018

Towards Entanglement of Purification for Conformal Field Theories

We argue that the entanglement of purification for two dimensional holographic CFT can be obtained from conformal blocks with internal twist operators. First, we explain our formula from the view point of tensor network model of holography. Then, we apply it to bipartite mixed states dual to subregion of AdS${}_3$ and the static BTZ blackhole geometries. The formula in CFT agrees with the entanglement wedge cross section in the bulk, which has been recently conjectured to be equivalent to the entanglement of purification.

hep-th↗

arXiv2018

Conservation Laws from Asymptotic Symmetry and Subleading Charges in QED

We present several results on memory effects, asymptotic symmetry and soft theorems in massive QED. We first clarify in what sense the memory effects are interpreted as the charge conservation of the large gauge transformations, and derive the leading and subleading memory effects in classical electromagnetism. We also show that the sub-subleading charges are not conserved without including contributions from the spacelike infinity. Next, we study QED in the BRST formalism and show that parts of large gauge transformations are physical symmetries by justifying that they are not gauge redundancies. Finally, we obtain the expression of charges associated with the subleading soft photon theorem in massive scalar QED.

hep-th↗