arXiv subjects

Eitan Bachmat

Publications and source records attributed to Eitan Bachmat.

10 recordsLinked to original sources

arXiv2026

Minkowski-Space Modeling of Hyperbolic Lenses

The extreme anisotropy of hyperbolic materials enables extreme wave confinement, but it is also associated with an inherent misalignment between phase and energy flow, which complicates device modeling and design. Here we introduce a Minkowski-space approach to describe hyperbolic wave propagation, showing that this complexity is geometric rather than physical. By embedding anisotropy into an effective Lorentzian metric, we establish a rational design framework for hyperbolic interfaces and lenses, and analytically derive their transfer function and resolution limits, enabling ultra-large numerical apertures and deep sub-diffraction focusing. We validate our theory with the design and full-wave modeling of a planar van der Waals polaritonic lens operating in the mid-infrared frequency range.

physics.optics↗

arXiv2026

Fairness in Limited Resources Settings

In recent years many important societal decisions are made by machine-learning algorithms, and many such important decisions have strict capacity limits, allowing resources to be allocated only to the highest utility individuals. For example, allocating physician appointments to the patients most likely to have some medical condition, or choosing which children will attend a special program. When performing such decisions, we consider both the prediction aspect of the decision and the resource allocation aspect. In this work we focus on the fairness of the decisions in such settings. The fairness aspect here is critical as the resources are limited, and allocating the resources to one individual leaves less resources for others. When the decision involves prediction together with the resource allocation, there is a risk that information gaps between different populations will lead to a very unbalanced allocation of resources. We address settings by adapting definitions from resource allocation schemes, identifying connections between the algorithmic fairness definitions and resource allocation ones, and examining the trade-offs between fairness and utility. We analyze the price of enforcing the different fairness definitions compared to a strictly utility-based optimization of the predictor, and show that it can be unbounded. We introduce an adaptation of proportional fairness and show that it has a bounded price of fairness, indicating greater robustness, and propose a variant of equal opportunity that also has a bounded price of fairness.

cs.CY↗

arXiv2026

Whom to Query for What: Adaptive Group Elicitation via Multi-Turn LLM Interactions

Eliciting information to reduce uncertainty about latent group-level properties from surveys and other collective assessments requires allocating limited questioning effort under real costs and missing data. Although large language models enable adaptive, multi-turn interactions in natural language, most existing elicitation methods optimize what to ask with a fixed respondent pool, and do not adapt respondent selection or leverage population structure when responses are partial or incomplete. To address this gap, we study adaptive group elicitation, a multi-round setting where an agent adaptively selects both questions and respondents under explicit query and participation budgets. We propose a theoretically grounded framework that combines (i) an LLM-based expected information gain objective for scoring candidate questions with (ii) heterogeneous graph neural network propagation that aggregates observed responses and participant attributes to impute missing responses and guide per-round respondent selection. This closed-loop procedure queries a small, informative subset of individuals while inferring population-level responses via structured similarity. Across three real-world opinion datasets, our method consistently improves population-level response prediction under constrained budgets, including a >12% relative gain on CES at a 10% respondent budget.

cs.LG↗

arXiv2023

Lenses in Minkowski space optimize queues by hiding bottleneck units

We mathematically construct focal lenses for positive-mass particles in Minkowski space. Particles emanating from a point source, refocus with synchronized proper time regardless of initial direction and velocity. Minkowski space offers a useful representation of the passenger queue formed during airplane boarding. The blocking relations between passengers coincide with the past-future relation in spacetime, and the boarding time is determined by the longest blocking chain. All blocking chains can be kept equally long if slow passengers are placed according to a lens in Minkowski space. The two media of the lens correspond to a grouping of fast and slow passengers, and the lens specifies the optimal placement of fast and slow passengers in the queue at the gate. Not only the boarding time, but also its variance is minimized.

physics.soc-ph↗

arXiv2020

Lorentzian geometry and variability reduction in airplane boarding: Slow passengers first outperforms random boarding

Airlines use different boarding policies to organize the queue of passengers waiting to enter the airplane. We analyze three policies in the many-passenger limit by a geometric representation of the queue position and row designation of each passenger and apply a Lorentzian metric to calculate the total boarding time. The boarding time is governed by the time each passenger needs to clear the aisle, and the added time is determined by the aisle-clearing time distribution through an effective aisle-clearing time parameter. The non-organized queues under the common random boarding policy are characterized by large effective aisle-clearing time. We show that, subject to a mathematical assumption which we have verified by extensive numerical computations in all realistic cases, the average total boarding time is always reduced when slow passengers are separated from faster passengers and the slow group is allowed to enter the airplane first. This is a universal result that holds for any combination of the three main governing parameters: the ratio between effective aisle-clearing times of the fast and the slow group, the fraction of slow passenger, and the congestion of passengers in the aisle. Separation into groups based on aisle-clearing time allows for more synchronized seating, but the result is non-trivial, as the similar fast-first policy -- where the two groups enter the airplane in reverse order -- is inferior to random boarding for a range of parameter settings. The asymptotic results conform well with discrete-event simulations with realistic number of passengers, and both the slow-first and the fast-first policies have the ability to perform unboundedly better than random boarding. Parameters based on empirical data, with hand luggage as criteria for separating passengers into the slow group, give a 13\% reduction in total boarding time for slow first compared to random boarding.

physics.soc-ph↗

arXiv2019

Lorentzian geometry based analysis of airplane boarding policies highlights slow passengers first as better

We study airplane boarding in the limit of large number of passengers using geometric optics in a Lorentzian metric. The airplane boarding problem is naturally embedded in a 1+1 dimensional space-time with a flat Lorentzian metric. The duration of the boarding process can be calculated based on a representation of the one-dimensional queue of passengers attempting to reach their seats, into a two-dimensional space-time diagram. The ability of a passenger to delay other passengers depends on their queue positions and row designations. This is equivalent to the causal relationship between two events in space-time, whereas two passengers are time-like separated if one is blocking the other, and space-like if both can be seated simultaneously. Geodesics in this geometry can be utilized to compute the asymptotic boarding time, since space-time geometry is the many-particle (passengers) limit of airplane boarding. Our approach naturally leads to a novel definition of an effective refractive index. The introduction of an effective refractive index enables, for the first time, an analytical calculation of the average boarding time for groups of passengers with different aisle-clearing time distribution. In the past, airline companies attempted to shorten the boarding times by trying boarding policies that either allow slow or fast passengers to board first. Our analytical calculations, backed by discrete-event simulations, support the counter-intuitive result that the total boarding time is shorter with the slow passengers boarding before the fast passengers. This is a universal result, valid for any combination of the parameters that characterize the problem --- percentage of slow passengers, ratio between aisle-clearing times between the fast and the slow groups, and the density of passengers along the aisle. We find an improvement of up to 28% compared with the Fast-First boarding policy.

physics.soc-ph↗

arXiv2007

Discrete spacetime and its applications

We survey some results about the asymptotic behavior of discrete spacetime models, which appeared in diverse settings in the physics and math literature. We then discuss some recent applications, including scheduling in disk drives and analysis of airplane boarding strategies.

gr-qc↗

arXiv2006

Analysis of disk scheduling, increasing subsequences and space-time geometry

We consider the problem of estimating the average tour length of the asymmetric TSP arising from the disk scheduling problem with a linear seek function and a probability distribution on the location of I/O requests. The optimal disk scheduling algorithm of Andrews, Bender and Zhang is interpreted as a simple peeling process on points in a 2 dimensional space-time w.r.t the causal structure. The patience sorting algorithm for finding the longest increasing subsequence in a permutation can be given a similar interpretation. Using this interpretation we show that the optimal tour length is the length of the maximal curve with respect to a Lorentzian metric on the surface of the disk drive. This length can be computed explicitly in some interesting cases. When the probability distribution is assumed uniform we provide finer asymptotics for the tour length. The interpretation also provides a better understanding of patience sorting and allows us to extend a result of Aldous and Diaconis on pile sizes

math.OC↗

arXiv2005

Analysis of airplane boarding via space-time geometry and random matrix theory

We show that airplane boarding can be asymptotically modeled by 2-dimensional Lorentzian geometry. Boarding time is given by the maximal proper time among curves in the model. Discrepancies between the model and simulation results are closely related to random matrix theory. We then show how such models can be used to explain why some commonly practiced airline boarding policies are ineffective and even detrimental.

physics.soc-ph↗

arXiv2004

The information entropy of quantum mechanical states

It is well known that a Shannon based definition of information entropy leads in the classical case to the Boltzmann entropy. It is tempting to regard the Von Neumann entropy as the corresponding quantum mechanical definition. But the latter is problematic from quantum information point of view. Consequently we introduce a new definition of entropy that reflects the inherent uncertainty of quantum mechanical states. We derive for it an explicit expression, and discuss some of its general properties. We distinguish between the minimum uncertainty entropy of pure states, and the excess statistical entropy of mixtures.

quant-ph↗