arXiv subjects

Lukas Graf

Publications and source records attributed to Lukas Graf.

At least 19 recordsLinked to original sources

arXiv2026

Tolls for Dynamic Equilibrium Flows

We consider dynamic network flows and study the following question: Which dynamic edge flows can be implemented as tolled dynamic equilibrium flows? We study this question for the heterogeneous-user model, where the flow particles are partitioned into populations characterized by their own source,destination-pairs and a cost function associating with any walk and departure time some costs. As our two main results, we first provide a duality-based characterization of implementability of dynamic edge flows for the multi-source, multi-destination case. Secondly, we derive both, a combinatorial and duality-based characterization of implementability of dynamic edge flows for the multi-source, single-destination case. Both results are derived under a fairly general network loading model. For the proof, we make several technical contributions: We formulate a novel infinite dimensional optimization problem, where the goal is to minimize the aggregated costs of the particles with respect to the fixed network loading induced by the given edge flow. This requires the recently introduced concept of autonomous network loadings for which we show several new structural insights. In particular, we give an alternative (tighter) characterization of the existence of autonomous network loadings for our setting by deriving a generalization of a result of M.A. Zarecki\u{\i} on the Lusin $N^{-1}$ property of absolutely continuous monotone functions which may also be of independent interest. These insights allow us to prove the stated characterizations under the assumption of strong duality. Finally, for the case of a single-destination, we are able to provide a non-trivial proof that this assumption is always fulfilled for finitely supported edge flows with costs representing weighted travel times.

cs.GT↗

arXiv2025

Are System Optimal Dynamic Flows Implementable by Tolls?

A seminal result of [Fleischer et al. and Karakostas and Kolliopulos, both FOCS 2004] states that system optimal multi-commodity static network flows are always implementable as tolled Wardrop equilibrium flows even if users have heterogeneous value-of-time sensitivities. Their proof uses LP-duality to characterize the general implementability of network flows by tolls. For the much more complex setting of $\textit{dynamic flows}$, [Graf et al., SODA 2025] identified necessary and sufficient conditions for a dynamic $s$-$d$ flow to be implementable as a tolled dynamic equilibrium. They used the machinery of (infinite-dimensional) strong duality to obtain their characterizations. Their work, however, does not answer the question of whether system optimal dynamic network flows are implementable by tolls. We consider this question for a general dynamic flow model involving multiple commodities with individual source-destination pairs, fixed inflow rates and heterogeneous valuations of travel time and money spent. We present both a positive and a, perhaps surprising, negative result: For the negative result, we provide a network with multiple source and destination pairs in which under the Vickrey queuing model no system optimal flow is implementable -- even if all users value travel times and spent money the same. Our counter-example even shows that the ratio of the achievable equilibrium travel times by using tolls and of the system optimal travel times can be unbounded. For the single-source, single-destination case, we show that if the traversal time functions are suitably well-behaved (as is the case, for example, in the Vickrey queuing model), any system optimal flow is implementable.

cs.GT↗

arXiv2024

Stochastic Prediction Equilibrium for Dynamic Traffic Assignment

Stochastic effects significantly influence the dynamics of traffic flows. Many dynamic traffic assignment (DTA) models attempt to capture these effects by prescribing a specific ratio that determines how flow splits across different routes based on the routes' costs. Other models take a game-theoretic perspective and describe the equilibria resulting from the individual traffic participants' decisions instead of prescribing flow splits, however they usually neglect stochastic effects. In this paper, we propose a new unifying framework for DTA that incorporates the interplay between the routing decisions of each single traffic participant, the potentially stochastic nature of predicting the future state of the network, and the physical flow dynamics. Our framework consists of an edge loading operator modeling the physical flow propagation and a routing operator modeling the routing behavior of traffic participants. The routing operator is assumed to be set-valued and, thus, capable to model complex (deterministic) equilibrium conditions as well as stochastic equilibrium conditions assuming that measurements for predicting traffic are noisy. As our main results, we derive several quite general equilibrium existence and uniqueness results which not only subsume known results from the literature but also lead to new results. Specifically, for the new stochastic prediction equilibrium, we show existence and uniqueness under natural assumptions on the probability distribution over the predictions.

math.OC↗

arXiv2024

A Decomposition Theorem for Dynamic Flows

The famous flow decomposition theorem of Gallai (1985) states that any static edge $s$,$d$-flow in a directed graph can be decomposed into a nonnegative linear combination of incidence vectors of paths and cycles. In this paper, we study the decomposition problem for the setting of dynamic edge $s$,$d$-flows assuming a quite general dynamic flow propagation model. We prove the following decomposition theorem: For any integrable dynamic edge $s$,$d$-flow, there exists a decomposition into a nonnegative linear combination of $s$,$d$-walk inflows and cycles of zero transit time. We show that a variant of the classical algorithmic approach of iteratively subtracting walk inflows from the current dynamic edge flow converges to a dynamic circulation and that every such circulation can be induced by inflows into cycles of zero transit time. The algorithm terminates in finite time, if there is a lower bound on the minimum edge travel times and the flow is finitely supported. We further characterize those dynamic edge flows which can be decomposed purely into nonnegative linear combinations of $s$,$d$-walk inflows. The proofs rely on the new concept of autonomous network loadings which allows us to describe how particles of a different walk flow would hypothetically propagate throughout the network under the fixed travel times induced by the given edge flow. We show several technical properties of this type of network loading and, as a byproduct, we also derive some general results on dynamic flows which could be of interest outside the context of this paper as well.

cs.DS↗

arXiv2023

An Implantable Piezofilm Middle Ear Microphone: Performance in Human Cadaveric Temporal Bones

Purpose: One of the major reasons that totally implantable cochlear microphones are not readily available is the lack of good implantable microphones. An implantable microphone has the potential to provide a range of benefits over external microphones for cochlear implant users including the filtering ability of the outer ear, cosmetics, and usability in all situations. This paper presents results from experiments in human cadaveric ears of a piezofilm microphone concept under development as a possible component of a future implantable microphone system for use with cochlear implants. This microphone is referred to here as a drum microphone (DrumMic) that senses the robust and predictable motion of the umbo, the tip of the malleus. Methods: The performance was measured of five DrumMics inserted in four different human cadaveric temporal bones. Sensitivity, linearity, bandwidth, and equivalent input noise were measured during these experiments using a sound stimulus and measurement setup. Results: The sensitivity of the DrumMics was found to be tightly clustered across different microphones and ears despite differences in umbo and middle ear anatomy. The DrumMics were shown to behave linearly across a large dynamic range (46 dB SPL to 100 dB SPL) across a wide bandwidth (100 Hz to 8 kHz). The equivalent input noise (0.1-10 kHz) of the DrumMic and amplifier referenced to the ear canal was measured to be 54 dB SPL and estimated to be 46 dB SPL after accounting for the pressure gain of the outer ear. Conclusion: The results demonstrate that the DrumMic behaves robustly across ears and fabrication. The equivalent input noise performance was shown to approach that of commercial hearing aid microphones. To advance this demonstration of the DrumMic concept to a future prototype implantable in humans, work on encapsulation, biocompatibility, connectorization will be required.

eess.AS↗

arXiv2023

The UmboMic: A PVDF Cantilever Microphone

Objective: We present the "UmboMic," a prototype piezoelectric cantilever microphone designed for future use with totally-implantable cochlear implants. Methods: The UmboMic sensor is made from polyvinylidene difluoride (PVDF) because of its low Young's modulus and biocompatibility. The sensor is designed to fit in the middle ear and measure the motion of the underside of the eardrum at the umbo. To maximize its performance, we developed a low noise charge amplifier in tandem with the UmboMic sensor. This paper presents the performance of the UmboMic sensor and amplifier in fresh cadaveric human temporal bones. Results: When tested in human temporal bones, the UmboMic apparatus achieves an equivalent input noise of 32.3 dB SPL over the frequency range 100 Hz to 7 kHz, good linearity, and a flat frequency response to within 10 dB from about 100 Hz to 6 kHz. Conclusion: These results demonstrate the feasibility of a PVDF-based microphone when paired with a low-noise amplifier. The reported UmboMic apparatus is comparable in performance to a conventional hearing aid microphone. Significance: The proof-of-concept UmboMic apparatus is a promising step towards creating a totally-implantable cochlear implant. A completely internal system would enhance the quality of life of cochlear implant users.

eess.AS↗

arXiv2022

Side-Constrained Dynamic Traffic Equilibria

We study dynamic traffic assignment with side-constraints. We first give a counter-example to a key result from the literature regarding the existence of dynamic equilibria for volume-constrained traffic models in the classical edge-delay model. Our counter-example shows that the feasible flow space need not be convex and it further reveals that classical infinite dimensional variational inequalities are not suited for the definition of side-constrained dynamic equilibria. We propose a new framework for side-constrained dynamic equilibria based on the concept of feasible $\gamma$-deviations of flow particles in space and time. Under natural assumptions, we characterize the resulting equilibria by means of quasi-variational and variational inequalities, respectively. Finally, we establish first existence results for side-constrained dynamic equilibria for the non-convex setting of volume-constraints.

math.OC↗

arXiv2022

Dynamic Traffic Assignment for Electric Vehicles

We initiate the study of dynamic traffic assignment for electrical vehicles addressing the specific challenges such as range limitations and the possibility of battery recharge at predefined charging locations. We pose the dynamic equilibrium problem within the deterministic queueing model of Vickrey and as our main result, we establish the existence of an energy-feasible dynamic equilibrium. There are three key modeling-ingredients for obtaining this existence result: * We introduce a walk-based definition of dynamic traffic flows which allows for cyclic routing behavior as a result of recharging events en route. * We use abstract convex feasibility sets in an appropriate function space to model the energy-feasibility of used walks. * We introduce the concept of capacitated dynamic equilibrium walk-flows which generalize the former unrestricted dynamic equilibrium path-flows. Viewed in this framework, we show the existence of an energy-feasible dynamic equilibrium by applying an infinite dimensional variational inequality, which in turn requires a careful analysis of continuity properties of the network loading as a result of injecting flow into walks. We complement our theoretical results by a computational study in which we design a fixed-point algorithm computing energy-feasible dynamic equilibria. We apply the algorithm to standard real-world instances from the traffic assignment community illustrating the complex interplay of resulting travel times, energy consumption and prices paid at equilibrium.

cs.GT↗

arXiv2022

A Finite Time Combinatorial Algorithm for Instantaneous Dynamic Equilibrium Flows

Instantaneous dynamic equilibrium (IDE) is a standard game-theoretic concept in dynamic traffic assignment in which individual flow particles myopically select en route currently shortest paths towards their destination. We analyze IDE within the Vickrey bottleneck model, where current travel times along a path consist of the physical travel times plus the sum of waiting times in all the queues along a path. Although IDE have been studied for decades, several fundamental questions regarding equilibrium computation and complexity are not well understood. In particular, all existence results and computational methods are based on fixed-point theorems and numerical discretization schemes and no exact finite time algorithm for equilibrium computation is known to date. As our main result we show that a natural extension algorithm needs only finitely many phases to converge leading to the first finite time combinatorial algorithm computing an IDE. We complement this result by several hardness results showing that computing IDE with natural properties is NP-hard.

cs.GT↗

arXiv2021

Machine-Learned Prediction Equilibrium for Dynamic Traffic Assignment

We study a dynamic traffic assignment model, where agents base their instantaneous routing decisions on real-time delay predictions. We formulate a mathematically concise model and define dynamic prediction equilibrium (DPE) in which no agent can at any point during their journey improve their predicted travel time by switching to a different route. We demonstrate the versatility of our framework by showing that it subsumes the well-known full information and instantaneous information models, in addition to admitting further realistic predictors as special cases. We then proceed to derive properties of the predictors that ensure a dynamic prediction equilibrium exists. Additionally, we define $\varepsilon$-approximate DPE wherein no agent can improve their predicted travel time by more than $\varepsilon$ and provide further conditions of the predictors under which such an approximate equilibrium can be computed. Finally, we complement our theoretical analysis by an experimental study, in which we systematically compare the induced average travel times of different predictors, including two machine-learning based models trained on data gained from previously computed approximate equilibrium flows, both on synthetic and real world road networks.

cs.GT↗

arXiv2021

2, 12, 117, 1959, 45171, 1170086, ...: A Hilbert series for the QCD chiral Lagrangian

We apply Hilbert series techniques to the enumeration of operators in the mesonic QCD chiral Lagrangian. Existing Hilbert series technologies for non-linear realizations are extended to incorporate the external fields. The action of charge conjugation is addressed by folding the $\frak{su}(n)$ Dynkin diagrams, which we detail in an appendix that can be read separately as it has potential broader applications. New results include the enumeration of anomalous operators appearing in the chiral Lagrangian at order $p^8$, as well as enumeration of $CP$-even, $CP$-odd, $C$-odd, and $P$-odd terms beginning from order $p^6$. The method is extendable to very high orders, and we present results up to order $p^{16}$. (The title sequence is the number of independent $C$-even $P$-even operators in the mesonic QCD chiral Lagrangian with three light flavors of quarks, at chiral dimensions $p^2$, $p^4$, $p^6$, ...)

hep-ph↗

arXiv2020

Analysis of Light Neutrino Exchange and Short-Range Mechanisms in $0νββ$ Decay

Neutrinoless double beta decay ($0νββ$) is a crucial test for lepton number violation. Observation of this process would have fundamental implications for neutrino physics, theories beyond the Standard Model and cosmology. Focussing on so called short-range operators of $0νββ$ and their potential interplay with the standard light Majorana neutrino exchange, we present the first complete calculation of the relevant nuclear matrix elements, performed within the interacting boson model (IBM-2). Furthermore, we calculate the relevant phase space factors using exact Dirac electron wavefunctions, taking into account the finite nuclear size and screening by the electron cloud. The obtained numerical results are presented together with up-to-date limits on the standard mass mechanism and effective $0νββ$ short-range operators in the IBM-2 framework. Finally, we interpret the limits in the particle physics scenarios incorporating heavy sterile neutrinos, Left-Right symmetry and R-parity violating supersymmetry.

hep-ph↗

arXiv2020

Flavoured Neutrinoless Double Beta Decay

We discuss a mechanism of neutrinoless double beta decay, where neutrinos of different flavours come into play. This is realized by effective flavour-violating scalar interactions. As one consequence, we find that within the normal mass ordering the neutrino effective mass may no longer vanish due to contributions from other flavours. We evaluate the necessary nuclear matrix elements, consider the interference between the standard diagram and the new scalar one, and analyze a UV-complete model that realizes the scalar interaction. Tests of the complete model are possible at colliders and future neutrino experiments. Our scenario represents an alternative mechanism for neutrinoless double beta decay, where nevertheless lepton number violation resides only in Majorana mass terms of light neutrinos.

hep-ph↗

arXiv2020

Searching for New Physics in Two-Neutrino Double Beta Decay

Motivated by non-zero neutrino masses and the possibility of New Physics discovery, a number of experiments search for neutrinoless double beta decay. While hunting for this hypothetical nuclear process, a significant amount of two-neutrino double beta decay data has become available. Although these events are regarded and studied mostly as the background of neutrinoless double beta decay, they can be also used to probe physics beyond the Standard Model. In this paper we show how the presence of right-handed leptonic currents would affect the energy distribution and angular correlation of the outgoing electrons in two-neutrino double beta decay. Consequently, we estimate constraints imposed by currently available data on the existence of right-handed neutrino interactions without having to assume their nature. In this way our results complement the bounds coming from the non-observation of neutrinoless double beta decay as they limit also the exotic interactions of Dirac neutrinos. We perform a detailed calculation of two-neutrino double beta decay under the presence of exotic (axial-)vector currents and we demonstrate that current experimental searches can be competitive to existing limits.

hep-ph↗

arXiv2020

The Price of Anarchy for Instantaneous Dynamic Equilibria

We consider flows over time within the deterministic queueing model and study the solution concept of instantaneous dynamic equilibrium (IDE) in which flow particles select at every decision point a currently shortest path. The length of such a path is measured by the physical travel time plus the time spent in queues. Although IDE have been studied since the eighties, the efficiency of the solution concept is not well understood. We study the price of anarchy for this model and show an upper bound of order $\mathcal{O}(U\cdot \tau)$ for single-sink instances, where $U$ denotes the total inflow volume and $\tau$ the sum of edge travel times. We complement this upper bound with a family of quite complex instances proving a lower bound of order $\Omega(U\cdot\log\tau)$.

cs.GT↗

arXiv2020

Disorder-induced coupling of Weyl nodes in WTe$_2$

The finite coupling between Weyl nodes due to residual disorder is investigated by magnetotransport studies in WTe$_2$. The anisotropic scattering of quasiparticles is evidenced from classical and quantum transport measurements. A new theoretical approach using a real band structure is developed to calculate the dependence of the scattering anisotropy with the correlation length of the disorder. A comparison between theory and experiments reveals for the first time a short correlation length in WTe$_2$ ($ξ$~nm). This result implies a significant coupling between Weyl nodes and other bands, so that inter-node scattering strongly reduces topologically non-trivial properties, such as the chiral anomaly.

cond-mat.mes-hall↗

arXiv2020

Neutrino Self-Interactions and Double Beta Decay

Neutrino Self-Interactions ($ν$SI) beyond the Standard Model are an attractive possibility to soften cosmological constraints on neutrino properties and also to explain the tension in late and early time measurements of the Hubble expansion rate. The required strength of $ν$SI to explain the $4σ$ Hubble tension is in terms of a point-like effective four-fermion coupling that can be as high as $10^9\, G_F$, where $G_F$ is the Fermi constant. In this work, we show that such strong $ν$SI can cause significant effects in two-neutrino double beta decay, leading to an observable enhancement of decay rates and to spectrum distortions. We analyze self-interactions via an effective operator as well as when mediated by a light scalar. Data from observed two-neutrino double beta decay is used to constrain $ν$SI, which rules out the regime around $10^9\, G_F$.

hep-ph↗

arXiv2020

Dynamic Flows with Adaptive Route Choice

We study dynamic network flows and introduce a notion of instantaneous dynamic equilibrium (IDE) requiring that for any positive inflow into an edge, this edge must lie on a currently shortest path towards the respective sink. We measure current shortest path length by current waiting times in queues plus physical travel times. As our main results, we show: 1. existence and constructive computation of IDE flows for single-source single-sink networks assuming constant network inflow rates, 2. finite termination of IDE flows for multi-source single-sink networks assuming bounded and finitely lasting inflow rates, 3. the existence of IDE flows for multi-source multi-sink instances assuming general measurable network inflow rates, 4. the existence of a complex single-source multi-sink instance in which any IDE flow is caught in cycles and flow remains forever in the network.

cs.GT↗