Classification Of Points Research Articles

Physics simulation capabilities of LLMs

Large Language Models (LLMs) can solve some undergraduate-level to graduate-level physics textbook problems and are proficient at coding. Combining these two capabilities could one day enable AI systems to simulate and predict the physical world. We present an evaluation of state-of-the-art (SOTA) LLMs on PhD-level to research-level computational physics problems. We condition LLM generation on the use of well-documented and widely-used packages to elicit coding capabilities in the physics and astrophysics domains. We contribute ∼50 original and challenging problems in celestial mechanics (with REBOUND), stellar physics (with MESA), 1D fluid dynamics (with Dedalus) and non-linear dynamics (with SciPy). Since our problems do not admit unique solutions, we evaluate LLM performance on several soft metrics: counts of lines that contain different types of errors (coding, physics, necessity and sufficiency) as well as a more educational’ Pass-Fail metric focused on capturing the salient physical ingredients of the problem at hand. As expected, today's SOTA LLM (GPT4) zero-shot fails most of our problems, although about 40% of the solutions could plausibly get a passing grade. About 70%–90% of the code lines produced are necessary, sufficient and correct (coding & physics). Physics and coding errors are the most common, with some unnecessary or insufficient lines. We observe significant variations across problem class and difficulty. We identify several failure modes of GPT4 in the computational physics domain, such as poor physical units handling, poor code versioning, tendency to hallucinate plausible sub-modules, lack of physical justification for global run parameters (e.g., simulation time, or upper-lower bounds for parametric exploration) and inability to define steady-state or stopping conditions reliably. Our reconnaissance work provides a snapshot of current computational capabilities in classical physics and points to obvious improvement targets if AI systems are ever to reach a basic level of autonomy in physics simulation capabilities.

Retrospective analysis of ideal needle puncture angles and depths for temporomandibular joint arthrocentesis using CBCT data

BackgroundThis study aimed to investigate the range of angles and depths necessary for effective entry into the TMJ using CBCT images, focusing on classical Holmlund Hellsing points and a two-needle approach.MethodsA retrospective cohort of CBCT images from January 2020 to November 2023 was analysed using 3D analysis to determine the variance in the required angles and depths.ResultsThe average age of the 68 participants included in the study was 29.5 ± 11.1, 58.8% of the participants were female and 41.2% were male. The anterior needle measurements showed a relatively low standard deviation(SD) in depth(SD:3.6) with a low variance coefficient(12.5%), whereas the axial and coronal angles exhibited greater variability(SD:9.1 and 7.6, respectively). For the posterior needles, moderate SDs in depth(SD:3.5) and greater variabilities in axial and coronal angles(SD:9.6 and 5.3, respectively) were observed. A weak negative correlation was observed between the axial angle of the posterior needle and age(p: 0.028, Pearson r: -0.29) Anterior needle depth (p:0.037) and posterior needle axial angle(p:0.014) were greater in males than females. The anterior needle depth in patients with temporamandibular disease was greater than in those without(p:0,03).ConclusionThere were significant differences in the angle measurements for both anterior and posterior needles, but lower variance in depth. The depths and angles of the needles did not correlate with age.

On Estimation of Shannon’s Entropy of Maxwell Distribution Based on Progressively First-Failure Censored Data

Shannon’s entropy is a fundamental concept in information theory that quantifies the uncertainty or information in a random variable or data set. This article addresses the estimation of Shannon’s entropy for the Maxwell lifetime model based on progressively first-failure-censored data from both classical and Bayesian points of view. In the classical perspective, the entropy is estimated using maximum likelihood estimation and bootstrap methods. For Bayesian estimation, two approximation techniques, including the Tierney-Kadane (T-K) approximation and the Markov Chain Monte Carlo (MCMC) method, are used to compute the Bayes estimate of Shannon’s entropy under the linear exponential (LINEX) loss function. We also obtained the highest posterior density (HPD) credible interval of Shannon’s entropy using the MCMC technique. A Monte Carlo simulation study is performed to investigate the performance of the estimation procedures and methodologies studied in this manuscript. A numerical example is used to illustrate the methodologies. This paper aims to provide practical values in applied statistics, especially in the areas of reliability and lifetime data analysis.

Bandpass filter induced by imaginary resistance in the low-pass discrete electrical transmission lattice

We examine a discrete low-pass electrical line in presence of imaginary resistance. The linear lattice is analyzed both from direct Kirchhoff law and classical points of view. The direct Kirchhoff law allows obtaining a linear Schrödinger equation which mimics quantum physics. From this point of view, it has been found that the imaginary resistance transforms the non-hermitian Hamiltonian due to the loss of pseudo-hermitian ones. The energy spectrum shifts from the low to the passband. The angular frequency is identical to the energy spectrum of the direct Kirchhoff law. The full integration of the lattice confirms the phase shift of the dispersion relation due to the imaginary resistance with the localization of the wave with a frequency equal to the cutoff frequency of the low pass filter and the propagation of the nonlinear voltage with the same frequency for different values of imaginary resistance.

A Harder–Narasimhan stratification of the -Grassmannian

We establish a Harder–Narasimhan formalism for modifications of $G$-bundles on the Fargues–Fontaine curve. The semi-stable stratum of the associated stratification of the ${B^+_{{\rm dR}}}$-Grassmannian coincides with the variant of the weakly admissible locus defined by Viehmann, and its classical points agree with those of the basic Newton stratum. When restricted to minuscule affine Schubert cells, the stratification corresponds to the Harder–Narasimhan stratification of Dat, Orlik and Rapoport. We also study basic geometric properties of the strata, and the relation to the Hodge–Newton decomposition.

Optimization technique for increasing resolution in computed tomography imaging

Starting from the importance of conforming to biological reality in medicine, in this paper we propose an optimization technique for increasing resolution of computed tomography (CT) images acquired using various existing scanners. Considering a three-dimensional Hounsfield Units (HU) array, together with the corresponding spatial metadata of interest (pixel sizes and slice thickness), the procedure is based on halving each voxel along the directions of the device's Cartesian frame of reference and find those values which are both satisfying the X-Rays attenuation coefficient average requirement and minimizing the HU distance to classical interpolation points. The discussed method was tested by implementing a C# .Net 6, cross-platform library containing two algorithm flavors that could be independently applied: “Z” for doubling the number of slices, and “XY” for doubling the resolution of individual slices. This design allows also chaining (e.g. one could apply the “Z,XY,Z” sequence in order to reduce four times slice thickness). In the context of existing unavoidable limitations, the first results are suggesting the “CT compatible” interpolation technique could provide a reasonable approximation of reality. However, the main advantage comes from satisfying mass conservation, which is of high importance in medical diagnosis and treatment.•The Hounsfield Units scale is defined as a linear transformation of the X-Rays attenuation coefficients. Thus, splitting a computed tomography voxel into two congruent volumes must satisfy the HU average requirement (the initial value must equal the average of the two output HU values).•Existing interpolation methods (linear, spline, etc.) are not compatible with the computed tomography HU average requirement. This could also result in mass estimate anomalies with significant impact in medical diagnosis.•The proposed “CT compatible” interpolation method is based on finding those values which are both satisfying the X-Rays attenuation coefficient average requirement and minimizing the Hounsfield Units distance to classical interpolation points.

Similarities between Ashi acupoints and myofascial trigger points: Exploring the relationship between body surface treatment points.

Although acupuncture points and myofascial trigger points (TPs) are based in different medical fields, the two points share important attributes. We explored the relationship between acupuncture points and TPs based on their characteristics and the results of previous studies. We outlined the relationship between acupuncture points and TPs by examining their similarities and differences. Among the acupuncture point subgroups, TPs mostly corresponded to Ashi points. Based on the common features of TPs and Ashi points, we suggest that TPs are more closely related to Ashi points than to other acupoints. However, TPs also share some features, such as pain indication and location, with classical acupuncture points (CA) and extra acupuncture points (EA), which makes it difficult to elucidate their relationship with other subgroups. Therefore, we suggest to understand the relationship of CAs, EAs, Ashi points, and TPs. In this report, we concluded that concerning muscular pain symptoms Ashi points and TPs are indistinguishable.

Hard X-Ray Emission from the Eastern Jet of SS 433 Powering the W50 “Manatee” Nebula: Evidence for Particle Reacceleration

We present a broadband X-ray study of W50 (the “Manatee” nebula), the complex region powered by the microquasar SS 433, that provides a test bed for several important astrophysical processes. The W50 nebula, a Galactic PeVatron candidate, is classified as a supernova remnant but has an unusual double-lobed morphology likely associated with the jets from SS 433. Using NuSTAR, XMM-Newton, and Chandra observations of the inner eastern lobe of W50, we have detected hard nonthermal X-ray emission up to ∼30 keV, originating from a few-arcminute-sized knotty region (“Head”) located ≲18′ (29 pc for a distance of 5.5 kpc) east of SS 433, and constrained its photon index to 1.58 ± 0.05 (0.5–30 keV band). The index gradually steepens eastward out to the radio “ear” where thermal soft X-ray emission with a temperature kT ∼ 0.2 keV dominates. The hard X-ray knots mark the location of acceleration sites within the jet and require an equipartition magnetic field of the order of ≳12 μG. The unusually hard spectral index from the “Head” region challenges classical particle acceleration processes and points to particle injection and reacceleration in the subrelativistic SS 433 jet, as seen in blazars and pulsar wind nebulae.

The universal p-adic Gross–Zagier formula

Let \(\mathrm {G}\) be the group \( (\mathrm {GL}_{2}\times \mathrm{GU}(1))/\mathrm {GL}_{1}\) over a totally real field F, and let \(\mathscr {X}\) be a Hida family for \(\mathrm {G}\). Revisiting a construction of Howard and Fouquet, we construct an explicit section \(\mathscr {P}\) of a sheaf of Selmer groups over \(\mathscr {X}\). We show, answering a question of Howard, that \(\mathscr {P}\) is a universal Heegner class, in the sense that it interpolates geometrically defined Heegner classes at all the relevant classical points of \(\mathscr {X}\). We also propose a ‘Bertolini–Darmon’ conjecture for the leading term of \(\mathscr {P}\) at classical points. We then prove that the p-adic height of \(\mathscr {P}\) is given by the cyclotomic derivative of a p-adic L-function. This formula over \(\mathscr {X}\) (which is an identity of functionals on some universal ordinary automorphic representations) specialises at classical points to all the Gross–Zagier formulas for \(\mathrm {G}\) that may be expected from representation-theoretic considerations. Combined with a result of Fouquet, the formula implies the p-adic analogue of the Beilinson–Bloch–Kato conjecture in analytic rank one, for the selfdual motives attached to Hilbert modular forms and their twists by CM Hecke characters. It also implies one half of the first example of a non-abelian Iwasawa main conjecture for derivatives, in \(2[F:\mathbf {Q}]\) variables. Other applications include two different generic non-vanishing results for Heegner classes and p-adic heights.

Fock state-enhanced expressivity of quantum machine learning models

The data-embedding process is one of the bottlenecks of quantum machine learning, potentially negating any quantum speedups. In light of this, more effective data-encoding strategies are necessary. We propose a photonic-based bosonic data-encoding scheme that embeds classical data points using fewer encoding layers and circumventing the need for nonlinear optical components by mapping the data points into the high-dimensional Fock space. The expressive power of the circuit can be controlled via the number of input photons. Our work sheds some light on the unique advantages offered by quantum photonics on the expressive power of quantum machine learning models. By leveraging the photon-number dependent expressive power, we propose three different noisy intermediate-scale quantum-compatible binary classification methods with different scaling of required resources suitable for different supervised classification tasks.

Improving effort estimation of software products by augmenting class point approach with regression analysis

Software products are essential parts of many organizations on-going business up to a large extent. The main factors contributing to the successful delivery of a software product are its timely completion within the allocated budget and its quality compliance. Customer goodwill and profitability are very important for a software organization’s continued business. A large proportion of software products are delivered late or go over-budget causing significant inconvenience to the customers. This work proposes an accurate development effort estimation approach for software products. The Class Point (CP) approach with regression analysis method has been used for estimation of the development effort. This work uses a two step estimation approach. In the first step, an enhanced CP approach is used to evaluate the development effort of the system. In the second step, regression analysis models are utilized to refine the estimated effort accuracy. The results derived by applying the proposed two step approach confirmed the validity and the accuracy of this approach. It was observed that the SVR with RBF kernel is providing the best accuracy compared to other approaches.

Out-of-equilibrium dynamics arising from slow round-trip variations of Hamiltonian parameters across quantum and classical critical points

We address the out-of-equilibrium dynamics of many-body systems subject to slow time-dependent round-trip protocols across quantum and classical (thermal) phase transitions. We consider protocols where one relevant parameter w is slowly changed across its critical point wc = 0, linearly in time with a large time scale ts, from wi < 0 to wf > 0 and then back to wi < 0, thus entailing multiple passages through the critical point. Analogously to the one-way Kibble-Zurek protocols across a critical point, round-trip protocols develop dynamic scaling behaviors at both classical and quantum transitions, put forward within renormalization-group frameworks. The scaling scenario is analyzed within some paradigmatic models undergoing quantum and classical transitions belonging to the two-dimensional Ising universality class, such as one-dimensional quantum Ising models and fermionic wires, and two-dimensional classical Ising models (supplemented with a purely relaxational dynamics). While the dynamic scaling frameworks are similar for classical and quantum systems, substantial differences emerge due to the different nature of their dynamics, which is purely relaxational for classical systems (implying thermalization in the large-time limit at fixed model parameters), and unitary in the case of quantum systems. In particular, when the critical point separates two gapped (short-ranged) phases and the extreme value wf > 0 is kept fixed in the large-ts limit of the round-trip protocol, we observe hysteresis-like scenarios in classical systems, while quantum systems do not apparently develop a sufficiently robust scaling limit along the return way, due to the presence of rapidly oscillating relative phases among the relevant quantum states.

P-adic L-functions via local–global interpolation: the case of

AbstractLet F be a totally real field, and let $E/F$ be a CM quadratic extension. We construct a p-adic L-function attached to Hida families for the group $\mathrm {GL}_{2/F}\times \mathrm {Res}_{E/F}\mathrm {GL}_{1}$ . It is characterized by an exact interpolation property for critical Rankin–Selberg L-values, at classical points corresponding to representations $\pi \boxtimes \chi $ with the weights of $\chi $ smaller than the weights of $\pi $ .Our p-adic L-function agrees with previous results of Hida when $E/F$ splits above p or $F=\mathbf {Q}$ , and it is new otherwise. Exploring a method that should bear further fruits, we build it as a ratio of families of global and local Waldspurger zeta integrals, the latter constructed using the local Langlands correspondence in families.In an appendix of possibly independent recreational interest, we give a reality-TV-inspired proof of an identity concerning double factorials.

Optimal global approximation of systems of jump-diffusion SDEs on equidistant mesh

In this paper, we provide a construction of two algorithms for approximation of the system of the jump-diffusion SDEs. Both methods are based on the classical Milstein steps and use equidistant discretization points. We construct implementable algorithm and their derivative-free version. We show that constructed methods are asymptotically optimal in the class of methods that use equidistant discretization of the interval [0,T]. Moreover, we report numerical experiments performed for some test equations, which confirm theoretical properties.

Covariance of error terms related to the Dirichlet eigenvalue problem

We explore the covariance of error terms coming from Weyl's conjecture regarding the number of Dirichlet eigenvalues up to size X. We also consider this problem in short intervals, that is, the error term of the number of eigenvalues in the window [ X , X + S ] $[X, X+S]$ for some S ( X ) $S(X)$ . We look at these error terms for planar domains where the Dirichlet eigenvalues can be explicitly calculated. In these cases, the error term is closely related to the error term from the classical lattice points counting problem of expanding planar domains. We give a formula for the covariance of such error terms, for general planar domains. We also give a formula for the covariance of error terms in short intervals, for sufficiently large intervals. Going back to the Dirichlet eigenvalue problem, we give results regarding the covariance of the error terms in short intervals of “generic” rectangles. We also explore a specific example, namely we compute the covariance between the error terms of an equilateral triangle and various rectangles.

The anatomic, clinical, and physiologic correspondences of myofascial trigger points and classical acupuncture points

The anatomic, clinical, and physiologic correspondences of myofascial trigger points and classical acupuncture points

Characterizing groundwater flow paths in an undeveloped region through synoptic river sampling for environmental tracers

AbstractSynoptic sampling of three rivers for a suite of environmental tracers is shown to be an efficient way to gain an understanding of groundwater flow paths for a previously unstudied large area in Alberta, Canada. For regional‐scale characterization, classical hydrogeological techniques are limited by the location and number of groundwater wells. This study demonstrates that rivers can become an easily accessible location to sample the distribution of groundwater flow paths discharging to surface water. Modelling of groundwater discharge to the rivers and groundwater mean age helps generate knowledge of groundwater circulation for a large area, which is useful for conceptual model development and focusing future characterization efforts. Results indicate that the benchland areas in this region, with higher topographic relief, had hydrogeological conditions that favoured deeper groundwater circulation with a modelled mean age greater than 100 years from recharge to discharge. Lower relief areas, which coincide with a transition in bedrock formations in this region, appeared to have much shorter and shallower groundwater circulation. The approach required a field program completed in 5 days and financial budget approximately equivalent to drilling a single borehole and installing a monitoring well. It is concluded that under the right conditions, where few classical observation points exist and knowledge is limited, synoptic sampling of rivers can be used to develop scientifically defensible conceptual models at a comparable scale to regional planning and resource management.

Experimental evidence of quint points and non-quantum chirality in a minimalist autonomous electronic oscillator

Recent intensive simulations have uncovered remarkable phenomena in stability diagrams of classical oscillators, for instance, quint points, parameter rings, and chiral structures of non-quantum origin. So far, their experimental observation has remained elusive. Here, using a simple electronic circuit, we report the experimental detection of five phases of oscillation spread around a quint point, an exceptional point where five oscillatory modes meet. This finding corroborates predictions of non-quantum chirality in the control parameter space of nonlinear oscillators governed by rate equations.

Проблема происхождения религии в зеркале психологии: от классиков к современникам

Objective. To present the classical points of view on the problem of the origin of religion and give an overview of modern views. Acquaintance with the described approaches will make it possible to better represent the current state of this problem and develop the own position on the basis of the directions developed in domestic psychology. Background. The problem of the origin of religion — the important socio-psychological phenomenon — was not in the focus of attention of domestic psychologists, therefore, with rare exceptions, the approaches to its solution proposed abroad were not highlighted in the scientific literature. In the spring of 2020, the international journal “Archive of Psychology of Religion” prepared a special issue dealing with the stated problem. It was another proof of the interest of foreign scientists in this topic and demonstrated the main approaches that have been formed to date on this issue. Methodology. Descriptive and comparative analysis methods. Conclusions. It is shown that at the present stage the main opposition on the problem of the origin of religion is observed between the supporters of the cognitive direction, who consider the emergence of religion exclusively as a result of the work of cognitive processes, as an accidental by-product of evolution, and supporters of cultural evolutionists, who consider religion a useful adaptation in the process of evolution. The examples of the works of the leading representatives of these areas demonstrate the most characteristic features of these approaches and the main discussion points. In this article we also discussed the work of researches who were trying to build a bridge between these opposing points of view and bring them closer together.

Test Points for Online Monitoring of Quantum Circuits

Noisy Intermediate-Scale Quantum (NISQ) computers consisting of tens of inherently noisy quantum bits (qubits) suffer from reliability problems. Qubits and their gates are susceptible to various types of errors. Due to limited numbers of qubits and high error rates, quantum error correction cannot be applied. Physical constraints of quantum hardware including the error rates are used to guide the design and the layout of quantum circuits. The error rates determine the selection of qubits and their operations. The resulting circuit is executed on the quantum computer. This study explores the risk of unexpected changes in the error rates of NISQ computers post-calibration. We show that unexpected changes in error rates can alter the output state of a quantum circuit. To detect these changes, we propose the insertion of test points into the quantum circuit to enable online monitoring of the physical qubit behavior. We utilize classical, superposition, and uncompute test points. Furthermore, we use a gate error coverage metric to assess the quality of the tests. We verify the effectiveness of the proposed scheme on different IBM quantum computers (IBM Q), in addition to a noisy simulation that shows the scalability of the proposed approach.