The original SCR theory proposed that inflation has two distinct expressions: circulation inflation, measured by rising transaction prices, and reservation inflation, measured by the rising real weight of monetary symbols, debt contracts, reserve claims, and other nominal stores of value relative to physical goods. A companion Japan paper tested one side of this theory by showing that, after money entered a reserve-dominant phase, monetary-base expansion no longer translated strongly into consumer-price inflation. This paper tests the other side of SCR: whether reservation inflation can arise when monetary issuance is constrained and circulation inflation is absent. The classical gold-standard deflation of 1873-1896 provides a clean historical setting. Using long-run British retail price data and the Minneapolis Fed historical U.S. CPI series, I show that the price level declined in both economies. Between 1873 and 1896, Britain's price index fell from 18.0 to 14.7, while the U.S. historical CPI fell from 36.0 to 25.0. Yet this deflation mechanically increased the real value of fixed nominal claims. A fixed-claim reservation index rose by 22.4% in Britain and 44.0% in the United St
We give here new O-C diagrams of the two classical Cepheids RY Cas and V Lac, established on a large basis of times of maximum of light, which covers more than a century. These two Cepheids present a variation of their period for which it is possible to calculate an annual rate. This rate equals +1.86 s/yr for RY Cas and -0.81 s/yr for V Lac. Based on these two new O-C diagrams neither of them seems to show any association to a binary system.
After mathematicians and physicists had learned that the structure of physical space was not necessarily Euclidean, it became conceivable that the global topological structure of space was non-trivial. In the context of the late 19th century debates on physical space this speculation gave rise to the problem of classifying spaces of constant curvature from a topological point of view. William Kingdon Clifford, Felix Klein and Wilhelm Killing, the latter of whom devoted a substantial amount of work to the topic in the early 1890s, clearly perceived this problem as relevant for both mathematics and natural philosophy (i.e., physics or cosmology). To some extent, a cosmological interest may even be found among those authors who restated the space form problem in more modern terms in the early 20th century, such as Heinz Hopf.
Validation of robotic systems critically depends on the operating conditions under which they are assessed. Scenario selection and variation are often manual, experience-driven, and difficult to scale, which harms reproducibility and weakens validation conclusions. We propose a scenario-based methodology that models scenarios compositionally and formalizes how these dimensions are varied, instantiated, executed, and interpreted. Building on this, we introduce RoboVAST, a framework that realizes declarative campaign specifications, plugin-based scenario generation, and scalable containerized execution with integrated result analysis. We demonstrate the approach with a navigation dataset comprising 5480 scenario configurations and over 100000 execution runs across five indoor maps with varied paths, sensor noise, software parameters, and obstacle settings, totaling more than 1800 hours of simulated operation and 1873 km traveled. Twenty repetitions per configuration allow us to distinguish systematic failures from stochastic anomalies.
In 1873, James C. Maxwell conjectured that the electric field generated by $n$ point charges in generic position has at most $(n-1)^2$ isolated zeroes. The first (non-optimal) upper bound was only obtained in 2007 by Gabrielov, Novikov and Shapiro, who also posed two additional interesting conjectures. In this article, we give the best upper bound known to date on the number of zeroes of the electric field, and construct a counterexample to a conjecture of Gabrielov, Novikov and Shapiro that the number of equilibria cannot exceed those of the distance function defined by the unit point charges. Finally, we note that it is quite possible that Maxwell's quadratic upper bound is not tight, so it is prudent to find smaller bounds. Hence, we also explore examples and construct configurations of charges achieving the highest ratios of the number of electric field zeroes by point charges found to this day.
Multimodal-attributed graphs (MAGs) are a fundamental data structure for multimodal graph learning (MGL), enabling both graph-centric and modality-centric tasks. However, our empirical analysis reveals inherent topology quality limitations in real-world MAGs, including noisy interactions, missing connections, and task-agnostic relational structures. A single graph derived from generic relationships is therefore unlikely to be universally optimal for diverse downstream tasks. To address this challenge, we propose Task-aware Modality and Topology co-Evolution (TMTE), a novel MGL framework that jointly and iteratively optimizes graph topology and multimodal representations toward the target task. TMTE is motivated by the bidirectional coupling between modality and topology: multimodal attributes induce relational structures, while graph topology shapes modality representations. Concretely, TMTE casts topology evolution as multi-perspective metric learning over modality embeddings with an anchor-based approximation, and formulates modality evolution as smoothness-regularized fusion with cross-modal alignment, yielding a closed-loop task-aware co-evolution process. Extensive experiments
We study two uncoupled oscillators, one horizontal and one vertical, moving in a rectilinear polygon (with only vertical and horizontal sides) and undergoing elastic reflections at its boundary. The main purpose of the article is to analyze the occurrence of resonance in such systems, depending on the shape of the analytic potentials that determine the oscillators. We define resonant energy levels; roughly speaking, these are levels for which the resonance phenomenon occurs for a large set of values of the parameter. We focus on unimodal analytic potentials whose unique minimum is at zero. The most important result of the work describes the size of the set of resonance levels in the form of the following trichotomy: it is either empty, a singleton, or large, namely non-empty and open. In the latter case, we show that an abundance of resonant orbits occurs only when the potentials are of a special type; we denote this family by $\mathcal{SP}$. This result can be regarded as a distant analogue of the classical Bertrand's theorem (1873), which characterizes centrally symmetric potentials in the presence of an abundance of periodic orbits.
Antonie (Anton) Pannekoek (1873-1960) is remembered as one of the initiators of the field of stellar atmospheres. A second part of his research concerned Galactic astronomy. He was convinced that the sidereal system was built up of clouds of stars in a smooth, low-density stratum. In addition there were dark clouds together with streaks with little or no extinction in between. Pannekoek looked at bright star clouds and estimated their distance from their contribution to star counts. He found values of tens of kpc, which would mean their distribution was similar in extent to that of Shapleys globular cluster system. Later he had to reduce his distance by a factor over two, and later still retract the method. He developed a rigorous method of estimating distances of dark clouds from modeling star counts off and on the cloud, preceding Wolf's quick and dirty method. He should have received more credit for this. He started isophotal maps of the northern and southern Milky Way, first from visual observations, later from photographic surface photometry using out-of-focus exposures. I compare Pannekoeks maps with detailed photographic surface photometry of the south by the group in Bochum
Today's thermodynamics is largely based on the combined law for equilibrium systems and statistical mechanics derived by Gibbs in 1873 and 1901, respectively, while irreversible thermodynamics for nonequilibrium systems resides essentially on the Onsager Theorem as a separate branch of thermodynamics developed in 1930s. Between them, quantum mechanics was invented and was quantitatively solved in terms of density functional theory (DFT) in 1960s. These three scientific domains operate based on different principles and are very much separated from each other. In analogy to the parable of the blind men and the elephant articulated by Perdew, they individually represent different portions of a complex system and thus are incomplete by themselves alone, resulting in the lack of quantitative agreement between their predictions and experimental observations. Over the last two decades, the author's group has developed a multiscale entropy approach (recently termed as zentropy theory) that integrates DFT-based quantum mechanics and Gibbs statistical mechanics and is capable of accurately predicting entropy and free energy of complex systems. Furthermore, in combination with the combined la
First discovered by Ernest Abbe in 1873, the resolution limit of a far-field microscope is considered determined by the numerical aperture and wavelength of light, approximately $λ$/2NA. With the advent of modern fluorescence microscopy and nanoscopy methods over the last century, it is recognized that Abbe's resolution definition alone could not solely characterize the resolving power of the microscope system. To determine the practical resolution of a fluorescence microscope, photon noise remains one essential factor yet to be incorporated in a statistics-based theoretical framework. Techniques such as confocal allow trading photon noise in gaining its resolution limit, which may increase or worsen the resolvability towards fluorescently tagged targets. Proposed as a theoretical measure of fluorescence microscopes' resolving power with finite photons, we quantify the resolvability of periodic structures in fluorescence microscopy systems considering both the diffraction limit and photon statistics. Using the Cramer-Rao Lower Bound of a parametric target, the resulting precision lower bound establishes a practical measure of the theoretical resolving power for various modern fluor
We investigate the single production of vector-like quarks at the High Luminosity LHC (HL-LHC). With the assumed (enhanced) couplings to third generation quarks of the standard model, vector-like quarks $B/X$ are produced in association with a bottom ($b$) or top ($t$) quark, which correspond to $Bbq$ and $Btq/Xtq$ production modes, including an additional soft forward jet from the spectator quark ($q$). This study focuses on high-mass vector-like quarks $B/X$ decaying into a top quark and a $W$ boson, resulting in the final state jets emerging from hadronically decaying top quark ($t\to Wb$) and $W$ boson ($W\to q\bar{q}'$). The events with $W$ boson and $t$ quark have been analysed using tagging techniques for large-radius jets. The scan ranges of the mass ($1000<m_{B/X}<3000$ GeV) for the relative width $Γ_{B/X}/m_{B/X}=0.1$ and $Γ_{B/X}/m_{B/X}=0.01$ of vector-like $B/X$ quarks have been investigated. From the results of the analysis, the masses of vector like quarks $B$($X$) up to $2491$ ($2364$) GeV and $2018$ ($1873$) GeV can be excluded corresponding to these relative width cases at $95\%$ CL depending on the type and branching scenarios at integrated luminosity proje
We continue our study of integral points on moduli schemes by combining the method of Faltings (Arakelov, Parsin, Szpiro) with modularity results and Masser-Wüstholz isogeny estimates. In this work we explicitly bound the height and the number of integral points on coarse Hilbert moduli schemes outside the branch locus. In the first part we define and study coarse Hilbert moduli schemes with their heights and branch loci. In the second part we establish the effective Shafarevich conjecture for abelian varieties $A$ over a number field $K$ such that $A_{\bar{K}}$ has CM or $A_{\bar{K}}$ is of GL2-type and isogenous to all its $G_\mathbb Q$-conjugates. In the third part we continue our explicit study of the Parsin construction given by the forgetful morphism of Hilbert moduli schemes. We now work out our strategy for arbitrary number fields $K$ and we explicitly bound the number of polarizations and module structures on abelian varieties over $K$ with real multiplications. In the last part we illustrate our results by applying them to two classical surfaces first studied by Clebsch (1871) and Klein (1873): We explicitly bound the Weil height and the number of their integral points.
Motivated by some conjectures originating in the Physics literature, we use Foscolo's construction of Ricci-flat Kahler metrics on K3 surfaces to locate, with high precision, several closed geodesics and compute their index (their length is also approximately known). Interestingly, the construction of these geodesics is related to an open problem in electrostatics posed by Maxwell in 1873. Our construction is also of interest to modern Physicists working on (supersymmetric) non-linear sigma models with target space such a K3 surface.
The discovery of the backpropagation algorithm ranks among one of the most important moments in the history of machine learning, and has made possible the training of large-scale neural networks through its ability to compute gradients at roughly the same computational cost as model evaluation. Despite its importance, a similar backpropagation-like scaling for gradient evaluation of parameterised quantum circuits has remained elusive. Currently, the most popular method requires sampling from a number of circuits that scales with the number of circuit parameters, making training of large-scale quantum circuits prohibitively expensive in practice. Here we address this problem by introducing a class of structured circuits that are not known to be classically simulable and admit gradient estimation with significantly fewer circuits. In the simplest case -- for which the parameters feed into commuting quantum gates -- these circuits allow for fast estimation of the gradient, higher order partial derivatives and the Fisher information matrix. Moreover, specific families of parameterised circuits exist for which the scaling of gradient estimation is in line with classical backpropagation,
The standard non-invasive imaging technique used to assess the severity and extent of Coronary Artery Disease (CAD) is Coronary Computed Tomography Angiography (CCTA). However, manual grading of each patient's CCTA according to the CAD-Reporting and Data System (CAD-RADS) scoring is time-consuming and operator-dependent, especially in borderline cases. This work proposes a fully automated, and visually explainable, deep learning pipeline to be used as a decision support system for the CAD screening procedure. The pipeline performs two classification tasks: firstly, identifying patients who require further clinical investigations and secondly, classifying patients into subgroups based on the degree of stenosis, according to commonly used CAD-RADS thresholds. The pipeline pre-processes multiplanar projections of the coronary arteries, extracted from the original CCTAs, and classifies them using a fine-tuned Multi-Axis Vision Transformer architecture. With the aim of emulating the current clinical practice, the model is trained to assign a per-patient score by stacking the bi-dimensional longitudinal cross-sections of the three main coronary arteries along channel dimension. Furthermo
An example of a time-invariant time-delay system that is uniformly globally attractive and exponentially stable, hence forward complete, but whose reachability sets from bounded initial conditions are not bounded over compact time intervals is provided. This gives a negative answer to two current conjectures by showing that (i) forward completeness is not equivalent to robust forward completeness (i.e. boundedness of reachability sets) and (ii) global asymptotic stability is not equivalent to uniform global asymptotic stability. In addition, a novel characterization of robust forward completeness for systems having a finite number of discrete delays is provided. This characterization relates robust forward completeness of the time-delay system with the forward completeness of an associated nondelayed finite-dimensional system.
While extending a famous problem asked and solved by Bertrand in 1873, Darboux found in 1877 a family of abstract surfaces of revolution, each endowed with a force function, with the striking property that all the orbits are periodic on open sets of the phase space. We give a description of this family which explains why they have this property: they are the Darboux inverses of the Kepler problem on constant curvature surfaces. What we call the Darboux inverse was briefly introduced by Darboux in 1889 as an alternative approach to the conformal maps that Goursat had just described.
Proton-conducting oxides are potential materials for electrochemical devices such as fuel cells, hydrogen pumps, hydrogen sensors, and the tritium purification and recovery system in nuclear fusion reactors. The hydrogen concentration in oxide materials is important, but its precise measurement is difficult. In this study, thermal desorption spectroscopy (TDS) was used to investigate hydrogen dissolution and release behavior in proton-conducting oxides, yttrium (Y), and cobalt (Co) doped barium-zirconates in the temperature range of 673-1273 K using deuterium (D2) and heavy water (D2O). Specimens were prepared with conventional powder metallurgy: the powder of three zirconates, BaZr0.9Y0.1O3-a (BZY), BaZr0.955Y0.03Co0.015O3-a (BZYC), and CaZr0.9In0.1O2.95 (CZI) was pressed into discs and fired in the air at 1873 K for 20 h. The densities of the sintered BZY, BZYC, and CZI specimens were 98 percent, 99.7 percent, and 99.5 percent of the theoretical densities respectively. XRD, SEM, and EDX were performed for the structural and morphological analysis of the sintered samples. From TDS measurement, a similar trend of temperature-dependent hydrogen solubility was obtained for all sample
We present the second catalog of high-energy gamma-ray sources detected by the Large Area Telescope (LAT), the primary science instrument on the Fermi Gamma-ray Space Telescope (Fermi), derived from data taken during the first 24 months of the science phase of the mission, which began on 2008 August 4. Source detection is based on the average flux over the 24-month period. The Second Fermi-LAT catalog (2FGL) includes source location regions, defined in terms of elliptical fits to the 95% confidence regions and spectral fits in terms of power-law, exponentially cutoff power-law, or log-normal forms. Also included are flux measurements in 5 energy bands and light curves on monthly intervals for each source. Twelve sources in the catalog are modeled as spatially extended. We provide a detailed comparison of the results from this catalog with those from the first Fermi-LAT catalog (1FGL). Although the diffuse Galactic and isotropic models used in the 2FGL analysis are improved compared to the 1FGL catalog, we attach caution flags to 162 of the sources to indicate possible confusion with residual imperfections in the diffuse model. The 2FGL catalog contains 1873 sources detected and cha
As rewards of reading two great papers of Hermite from 1873, we trace the historical origin of the integral Niven used in his well-known proof of the irrationality of $π$, uncover a rarely acknowledged simple proof by Hermite of the irrationality of $π^2$, give a new proof of the irrationality of $r\tan r$ for nonzero rational $r^2$, and generalize it to a proof of the irrationality of certain ratios of Bessel functions.