Additional Assumptions Research Articles

Breast density quantification in dual-energy mammography using virtual anthropomorphic phantoms.

Breast density is a significant risk factor for breast cancer and can impact the sensitivity of screening mammography. Area-based breast density measurements may not provide an accurate representation of the tissue distribution, therefore volumetric breast density (VBD) measurements are preferred. Dual-energy mammography enables volumetric measurements without additional assumptions about breast shape. In this work we evaluated the performance of a dual-energy decomposition technique for determining VBD by applying it to virtual anthropomorphic phantoms. The dual-energy decomposition formalism was used to quantify VBD on simulated dual-energy images of anthropomorphic virtual phantoms with known tissue distributions. We simulated 150 phantoms with volumes ranging from 50 to 709mL and VBD ranging from 15% to 60%. Using these results, we validated a correction for the presence of skin and assessed the method's intrinsic bias and variability. As a proof of concept, the method was applied to 14 sets of clinical dual-energy images, and the resulting breast densities were compared to magnetic resonance imaging (MRI) measurements. Virtual phantom VBD measurements exhibited a strong correlation (Pearson's ) with nominal values. The proposed skin correction eliminated the variability due to breast size and reduced the bias in VBD to a constant value of -2%. Disagreement between clinical VBD measurements using MRI and dual-energy mammography was under 10%, and the difference in the distributions was statistically non-significant. VBD measurements in both modalities had a moderate correlation (Spearman's =0.68). Our results in virtual phantoms indicate that the material decomposition method can produce accurate VBD measurements if the presence of a third material (skin) is considered. The results from our proof of concept showed agreement between MRI and dual-energy mammography VBD. Assessment of VBD using dual-energy images could provide complementary information in dual-energy mammography and tomosynthesis examinations.

A novel application of data-consistent inversion to overcome spurious inference in genome-wide association studies.

The genome-wide association studies (GWAS) typically use linear or logistic regression models to identify associations between phenotypes (traits) and genotypes (genetic variants) of interest. However, the use of regression with the additive assumption has potential limitations. First, the normality assumption of residuals is the one that is rarely seen in practice, and deviation from normality increases the Type-I error rate. Second, building a model based on such an assumption ignores genetic structures, like, dominant, recessive, and protective-risk cases. Ignoring genetic variants may result in spurious conclusions about the associations between a variant and a trait. We propose an assumption-free model built upon data-consistent inversion (DCI), which is a recently developed measure-theoretic framework utilized for uncertainty quantification. This proposed DCI-derived model builds a nonparametric distribution on model inputs that propagates to the distribution of observed data without the required normality assumption of residuals in the regression model. This characteristic enables the proposed DCI-derived model to cover all genetic variants without emphasizing on additivity of the classic-GWAS model. Simulations and a replication GWAS with data from the COPDGene demonstrate the ability of this model to control the Type-I error rate at least as well as the classic-GWAS (additive linear model) approach while having similar or greater power to discover variants in different genetic modes of transmission.

Reliability-based design optimization for a vertical-type breakwater with multiple limit-state equations under Korean marine environments varying from sea to sea

In this study, as part of basic research aimed at enhancing the accuracy of load and resistance coefficients to ensure their suitability for practical design and promoting the application of underutilized reliability-based design in Korea, the author conducts optimal design based on the reliability analysis of a vertical-type breakwater in the seas off of Haeundae, Yeosu, Mokpo, Gunsan, and Incheon—representative ports in Korea. In doing so, the author utilized the double-loop approach, which simultaneously addresses a reliability problem nested within an optimization process, employing the Polak–He optimization algorithm. To mitigate the substantial numerical effort required by the double-loop approach based on the Polak–He optimization algorithm, which necessitates the gradients of both cost and constraint functions, the subset simulation method was employed. In this process, the author deliberately refrained from using design waves of a specific return period and linear probabilistic models such as the Gaussian distribution, especially concerning wave and lift forces, often viewed as barriers to the widespread application of reliability-based design in Korea. Instead, the author focused on characterizing the uncertainties associated with the wave force, lift force, and overturning moment—variables that significantly impact the integrity of vertical-type breakwaters—by developing probabilistic models for these random variables directly from long-term in situ wave data. These models capture the varied characteristics of the Korean marine environment from sea to sea. In this way, the need for additional assumptions concerning the interrelationship between significant wave and maximum wave heights, along with the wave period, can be eliminated. Following Occam's razor principle, which suggests that explanations constructed with the smallest possible set of assumptions are superior, the reliability-based design optimization of a vertical-type breakwater presented in this study demonstrates promise in terms of simplicity and practicality. The limit state of the vertical-type breakwater was defined to encompass sliding, overturning, and collapse failures, and the strong interrelations between the wave force, lift force, and overturning moment were described using the Nataf joint distribution. As anticipated, simulation results show that solely considering sliding failure, as in the current reliability-based design platform in Korea, leads to an underestimated failure probability. Furthermore, ensuring a consistent failure probability for vertical-type breakwaters using design waves with a specific return period, as in past studies, is not feasible. In contrast, this study demonstrated that breakwaters optimally designed to meet the reliability index requirement of β = 3.5–4 consistently maintain a target failure probability in all sea areas.

Computationally Secure Semi‐Quantum All‐Or‐Nothing Oblivious Transfer from Dihedral Coset States

AbstractThe quest for perfect quantum oblivious transfer (QOT) with information‐theoretic security remains a challenge, necessitating the exploration of computationally secure QOT as a viable alternative. Unlike the unconditionally secure quantum key distribution (QKD), the computationally secure QOT relies on specific quantum‐safe computational hardness assumptions, such as the post‐quantum hardness of learning with errors (LWE) problem and quantum‐hard one‐way functions. This raises an intriguing question: Are there additional efficient quantum hardness assumptions that are suitable for QOT? In this work, leveraging the dihedral coset state derived from the dihedral coset problem (DCP), a basic variant of OT, known as the all‐or‐nothing OT, is studied in the semi‐quantum setting. Specifically, the DCP originates from the dihedral hidden subgroup problem (DHSP), conjectured to be challenging for any quantum polynomial‐time algorithms. First, a computationally secure quantum protocol is presented for all‐or‐nothing OT, which is then simplified into a semi‐quantum OT protocol with minimal quantumness, where the interaction needs merely classical communication. To efficiently instantiate the dihedral coset state, a powerful cryptographic tool called the LWE‐based noisy trapdoor claw‐free functions (NTCFs) is used. The construction requires only a three‐message interaction and ensures perfect statistical privacy for the receiver and computational privacy for the sender.

First-time Sensitive Homeomorphisms

AbstractWe introduce first-time sensitivity for a homeomorphism of a compact metric space, that is a condition on the first increasing times of open balls of the space. Continuum-wise expansive homeomorphisms, the shift map on the Hilbert cube, and also some partially hyperbolic diffeomorphisms satisfy this condition. We prove the existence of local unstable continua satisfying similar properties with the local unstable continua of continuum-wise expansive homeomorphisms, but assuming first-time sensitivity. As a consequence we prove that first-time sensitivity (with some additional technical assumptions) implies positive topological entropy.

Two innovative equivalent statements of the third law of thermodynamics

Abstract It is found from textbooks and literature that there are three different statements for the third law of thermodynamics, i.e., the Nernst theorem, the unattainability statement of absolute zero temperature, and the heat capacity statement. It is pointed out that such three statements correspond to three thermodynamic parameters, which are, respectively, the entropy, temperature, and heat capacity, and can be obtained by extrapolating the experimental results of different parameters at ultra-low temperatures to absolute zero. It is expounded that because there is no need for additional assumptions in the derivation of the Nernst equation, the Nernst theorem should be renamed as the Nernst statement. Moreover, it is proved that both the Nernst statement and the heat capacity statement are mutually deducible and equivalent, while the unattainability of absolute zero temperature is only a corollary of the Nernst statement or the heat capacity statement so that it is unsuitably referred to as one statement of the third law of thermodynamics. The conclusion is that the Nernst statement and the heat capacity statement are two equivalent statements of the third law of thermodynamics.

SL(n) contravariant function-valued valuations on polytopes

We present a complete classification of SL(n) contravariant, C(Rn∖{o})-valued valuations on polytopes, without any additional assumptions. It extends the previous results of the second author Li (2020) [10] which have a good connection with the Lp and Orlicz Brunn-Minkowski theory. Additionally, our results deduce a complete classification of SL(n) contravariant symmetric-tensor-valued valuations on polytopes.

Adaptive suboptimal control of some discrete-time plants with nonstochastic bounded disturbances

This paper deals with the adaptive suboptimal control of linear, discrete-time, time-invariant, minimum phase, scalar plants in the presence of nonstochastic bounded unmeasurable disturbances whose upper and lower bounds, which may be asymmetric, are assumed to be unknown a priori. Additional assumption is that an order of the difference equation describing the plant is known a priori. The distinguishing feature of the problem stated in this paper is that neither bounds on the unmeasured disturbances, nor bounds on an allowable region to which the unknown plant parameters belong are assumed to be known a priori. To solve this problem, adaptation procedures for the point and membership set estimation are utilized. The standard recursive procedure with adjustable dead zone is employed in order to derive the point estimates of unknown plant parameters together with the point estimate of time-invariant disturbance component. The size of this dead zone depends on the previous point estimate of the bounds on the time-varying disturbance component and also on a fixed suboptimality index chosen by the designer. The estimates generated by the point estimation procedure are directly exploited to derive the adaptive control law. The main idea advanced in this paper is that, instead of unknown a priori membership set of these parameters, their peculiar hypothetical a posteriori membership sets are designed via the use of the measured system’s signals together with the current point estimate of bounds on the time-varying disturbance component. Contrary to the usual membership set estimation approach, this set is updated if only it is discovered that the unknown parameter vector does not belong in reality to this set. To this end, a remarkable property of the point estimation procedure is utilized. Such an approach makes it possible to reconstruct this set and to update the previous estimate of the bounds on the time-varying disturbance component. The finite convergence of the adaptation procedures and also the ultimate boundedness of system’s signals are established. To demonstrate an efficiency of the adaptive controller and support the theoretical study, simulation results are presented.

Why is the Cobb-Douglas production function so popular?

It is well known that, in continuous time, the Cobb-Douglas function can be derived from the underlying, data governing, accounting identity under some reasonable assumptions (factor shares are constant, and the weighted growth of the labour input price and the capital input price is constant). In this article these results are generalized in three ways: (1) the accounting identity contains a (pure) profit term; (2) continuous time is replaced by discrete time periods; (3) additional assumptions appear to be superfluous. The article also discusses extensions: from two to multiple inputs, from value added to gross output, and from a single production unit to an ensemble of those units.

On the coupling of Hamilton's principle and thermodynamic extremal principles

Extremal principles can generally be divided into two rather distinct classes. There are, on the one hand side, formulations based on the Lagrangian or Hamiltonian mechanics, respectively, dealing with time dependent problems, but essentially resting on conservation of energy and thus being not applicable to dissipative systems in a consistent way. On the other hand, there are formulations based essentially on maximizing the dissipation, working efficiently for the description of dissipative systems, but being not suitable for including inertia effects. Many attempts can be found in the literature to overcome this split into incompatible principles. However, essentially all of them possess an unnatural appearance. In this work, we suggest a solution to this dilemma resting on an additional assumption based on the thermodynamic driving forces involved. Applications to a simple dissipative structure and a material with varying mass demonstrate the capability of the proposed approach.

Cosmic-ray boosted dark matter confronted by constraints on new light mediators

The detectability of light dark matter in direct detection experiments is limited by the small kinetic energy of the recoiling targets. Thus, scenarios where dark matter is boosted to relativistic velocities provide a useful tactic to constrain sub-GeV dark matter particles. Of the possible dark matter boosting mechanisms, cosmic-ray upscattering is an appealing paradigm as it does not require any additional assumptions beyond dark matter coupling to nucleons or electrons. However, detectable signals are obtained only with relatively large cross sections which, in turn, can only be realized with large couplings, light mediators or composite dark matter. In this work we consider a general set of light mediators that couple dark matter to hadrons. Using data from Borexino, XENON1T, LZ and Super-K, we show that existing constraints on such mediators preclude appreciable cosmic-ray dark matter upscattering. This finding highlights the limited applicability of cosmic-ray upscattering constraints and suggests they only be used in model-dependent studies. Published by the American Physical Society 2024

Infinite horizon LQG Graphon Mean Field Games: Explicit Nash values and local minima

In this study, we generalize the analysis of infinite horizon linear quadratic Gaussian (LQG) Mean Field Games within the framework of Graphon Mean Field Games (GMFG) introduced in Caines and Huang (2018) over finite horizons. Graphon Mean Field Games (GMFGs) are non-uniform generalizations of Mean Field Games where the non-uniformity of agents is characterized by the nodes on which they are located in a network. Under mild assumptions on the structure of the network and parameters of the game, we obtain for almost every node, an explicit analytical expression for the Nash values (i.e. the cost at equilibrium). With additional assumptions, we provide sufficient conditions for nodes to have locally minimal Nash values. We illustrate the results for the uniform attachment network.

Free groups generated by two unipotent maps

Abstract Let A and B be two unipotent elements of SU ⁢ ( 2 , 1 ) {\mathrm{SU}(2,1)} with distinct fixed points. In [S. B. Kalane and J. R. Parker, Free groups generated by two parabolic maps, Math. Z. 303 2023, 1, Paper No. 9], the authors gave several conditions that guarantee the subgroup 〈 A , B 〉 {\langle A,B\rangle} is discrete and free by using Klein’s combination theorem. We will improve their conditions by using a variant of Klein’s combination theorem. With the same arguments and the additional assumption that AB is unipotent, we also extend Parker and Will’s condition that guarantees the subgroup 〈 A , B 〉 {\langle A,B\rangle} is discrete and free in [J. R. Parker and P. Will, A complex hyperbolic Riley slice, Geom. Topol. 21 2017, 6, 3391–3451].

Identification of causal diffusion effects using placebo outcomes under structural stationarity

Abstract Social and biomedical scientists have long been interested in the process through which ideas and behaviours diffuse. In this article, we study an urgent social problem, the spatial diffusion of hate crimes against refugees in Germany, which has admitted more than 1 million asylum seekers since the 2015 refugee crisis. Despite its importance, identification of causal diffusion effects, also known as peer and contagion effects, remains challenging because the commonly used assumption of no omitted confounders is often untenable due to contextual confounding and homophily bias. To address this long-standing problem, we examine causal identification using placebo outcomes under a new assumption of structural stationarity, which formalizes the underlying diffusion process with a class of nonparametric structural equation models with recursive structure. We show under structural stationarity that a lagged dependent variable is a general, valid placebo outcome for detecting a wide range of biases, including the 2 types mentioned above. We then propose a difference-in-differences style estimator that can directly correct biases under an additional causal assumption. Analysing fine-grained geo-coded hate crime data from Germany, we show when and how the proposed methods can detect and correct unmeasured confounding in spatial causal diffusion analysis.

A Bayesian Spatial Model to Correct Under-Reporting in Urban Crowdsourcing

Decision-makers often observe the occurrence of events through a reporting process. City governments, for example, rely on resident reports to find and then resolve urban infrastructural problems such as fallen street trees, flooded basements, or rat infestations. Without additional assumptions, there is no way to distinguish events that occur but are not reported from events that truly did not occur--a fundamental problem in settings with positive-unlabeled data. Because disparities in reporting rates correlate with resident demographics, addressing incidents only on the basis of reports leads to systematic neglect in neighborhoods that are less likely to report events. We show how to overcome this challenge by leveraging the fact that events are spatially correlated. Our framework uses a Bayesian spatial latent variable model to infer event occurrence probabilities and applies it to storm-induced flooding reports in New York City, further pooling results across multiple storms. We show that a model accounting for under-reporting and spatial correlation predicts future reports more accurately than other models, and further induces a more equitable set of inspections: its allocations better reflect the population and provide equitable service to non-white, less traditionally educated, and lower-income residents. This finding reflects heterogeneous reporting behavior learned by the model: reporting rates are higher in Census tracts with higher populations, proportions of white residents, and proportions of owner-occupied households. Our work lays the groundwork for more equitable proactive government services, even with disparate reporting behavior.

UFDA: Universal Federated Domain Adaptation with Practical Assumptions

Conventional Federated Domain Adaptation (FDA) approaches usually demand an abundance of assumptions, which makes them significantly less feasible for real-world situations and introduces security hazards. This paper relaxes the assumptions from previous FDAs and studies a more practical scenario named Universal Federated Domain Adaptation (UFDA). It only requires the black-box model and the label set information of each source domain, while the label sets of different source domains could be inconsistent, and the target-domain label set is totally blind. Towards a more effective solution for our newly proposed UFDA scenario, we propose a corresponding methodology called Hot-Learning with Contrastive Label Disambiguation (HCLD). It particularly tackles UFDA's domain shifts and category gaps problems by using one-hot outputs from the black-box models of various source domains. Moreover, to better distinguish the shared and unknown classes, we further present a cluster-level strategy named Mutual-Voting Decision (MVD) to extract robust consensus knowledge across peer classes from both source and target domains. Extensive experiments on three benchmark datasets demonstrate that our method achieves comparable performance for our UFDA scenario with much fewer assumptions, compared to previous methodologies with comprehensive additional assumptions.

Layer Collaboration in the Forward-Forward Algorithm

Backpropagation, which uses the chain rule, is the de-facto standard algorithm for optimizing neural networks nowadays. Recently, Hinton (2022) proposed the forward-forward algorithm, a promising alternative that optimizes neural nets layer-by-layer, without propagating gradients throughout the network. Although such an approach has several advantages over back-propagation and shows promising results, the fact that each layer is being trained independently limits the optimization process. Specifically, it prevents the network's layers from collaborating to learn complex and rich features. In this work, we study layer collaboration in the forward-forward algorithm. We show that the current version of the forward-forward algorithm is suboptimal when considering information flow in the network, resulting in a lack of collaboration between layers of the network. We propose an improved version that supports layer collaboration to better utilize the network structure, while not requiring any additional assumptions or computations. We empirically demonstrate the efficacy of the proposed version when considering both information flow and objective metrics. Additionally, we provide a theoretical motivation for the proposed method, inspired by functional entropy theory.

Lorentzian Calderón problem near the Minkowski geometry

We study a Lorentzian version of the well-known Calderón problem that is concerned with determination of lower order coefficients in a wave equation on a smooth Lorentzian manifold, given the associated Dirichlet-to-Neumann map on its timelike boundary. In the earlier work of the authors it was shown that zeroth order coefficients can be uniquely determined under a two-sided spacetime curvature bound and the additional assumption that there are no conjugate points along null or spacelike geodesics. In this paper we show that uniqueness for the zeroth order coefficient holds for manifolds satisfying a weaker curvature bound and for spacetime perturbations of such manifolds. This relies on a new enhanced optimal unique continuation principle for the wave equation in the exterior regions of double null cones. In particular, we solve the Lorentzian Calderón problem near the Minkowski geometry.

Solutions with pure radiation and gyratons in 3D massive gravity theories

We find exact solutions of topologically massive gravity (TMG) and new massive gravity (NMG) in 2 + 1 dimensions (3D) with an arbitrary cosmological constant, pure radiation, and gyratons, i.e. with possibly non-zero T uu and T ux in canonical coordinates. Since any ‘reasonable’ geometry in 3D (i.e. admitting a null geodesic congruence) is either expanding Robinson–Trautman ( Θ≠0 ) or Kundt ( Θ=0 ), we focus on these two classes. Assuming expansions Θ=1/r (‘GR-like’ Robinson–Trautman) or Θ=0 (general Kundt), we systematically integrate the field equations of TMG and NMG and identify new classes of exact solutions. The case of NMG contains an additional assumption of g ux being quadratic in r, which is automatically enforced in TMG as well as in 3D GR. In each case, we reduce the field equations as much as possible and identify new classes of solutions. We also discuss various special subclasses and study some explicit solutions.

Constraining the giant radio galaxy population with machine learning and Bayesian inference

Large-scale sky surveys at low frequencies, such as the LOFAR Two-metre Sky Survey (LoTSS), allow for the detection and characterisation of unprecedented numbers of giant radio galaxies (GRGs, or `giants', of at least $l_ p,GRG Mpc $ long). This, in turn, enables us to study giants in a cosmological context. A tantalising prospect of such studies is a measurement of the contribution of giants to cosmic magnetogenesis. However, this measurement requires en masse radio--optical association for well-resolved radio galaxies and a statistical framework to infer GRG population properties. By automating the creation of radio--optical catalogues, we aim to significantly expand the census of known giants. With the resulting sample and a forward model that takes into account selection effects, we aim to constrain their intrinsic length distribution, number density, and lobe volume-filling fraction (VFF) in the Cosmic Web. We combined five existing codes into a single machine learning (ML)--driven pipeline that automates radio source component association and optical host identification for well-resolved radio sources. We created a radio--optical catalogue for the entire LoTSS Data Release 2 (DR2) footprint and subsequently selected all sources that qualify as possible giants. We combined the list of ML pipeline GRG candidates with an existing list of LoTSS DR2 crowd-sourced GRG candidates and visually confirmed or rejected all members of the merged sample. To infer intrinsic GRG properties from GRG observations, we developed further a population-based forward model and constrained its parameters using Bayesian inference. Roughly half of all GRG candidates that our ML pipeline identifies indeed turn out to be giants upon visual inspection, whereas the success rate is 1 in 11 for the previous best giant-finding ML technique in the literature. We confirm $5,647$ previously unknown giants from the crowd-sourced LoTSS DR2 catalogue and $2,597$ previously unknown giants from the ML pipeline. Our confirmations and discoveries bring the total number of known giants to at least $11,585$. Our intrinsic GRG population forward model provides a good fit to the data. The posterior indicates that the projected lengths of giants are consistent with a curved power law probability density function whose initial tail index $ p,GRG changes by $ 0.3$ over the interval up to $l_ p Mpc $. We predict a comoving GRG number density $n_ GRG Mpc $, close to a recent estimate of the number density of luminous non-giant radio galaxies. With the projected length distribution, number density, and additional assumptions, we derive a present-day GRG lobe VFF $ V GRG-CW (z=0) = 1.4 $ in clusters and filaments of the Cosmic Web. We present a state-of-the-art ML-accelerated pipeline for finding giants, whose complex morphologies, arcminute extents, and radio-emitting surroundings pose challenges. Our data analysis suggests that giants are more common than previously thought. More work is needed to make GRG lobe VFF estimates reliable, but tentative results imply that it is possible that magnetic fields once contained in giants pervade a significant ($ gtrsim 10<!PCT!>$) fraction of today's Cosmic Web.