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Neural networks are reported to be vulnerable under minor and imperceptible attacks. The underlying mechanism and quantitative measure of the vulnerability still remains to be revealed. In this study, we explore the intrinsic trade-off between accuracy and robustness in neural networks, framed through the lens of the "uncertainty principle". By examining the fundamental limitations imposed by this principle, we reveal how neural networks inherently balance precision in feature extraction with susceptibility to adversarial perturbations. Our analysis highlights that as neural networks achieve higher accuracy, their vulnerability to adversarial attacks increases, a phenomenon rooted in the uncertainty relation. By using the mathematics from quantum mechanics, we offer a theoretical foundation and analytical method for understanding the vulnerabilities of deep learning models. [ABSTRACT FROM AUTHOR]

Dense communities of bacteria, also known as biofilms, are ubiquitous in all of our everyday life. They are not only always surrounding us, but are also active inside our bodies, for example in the oral cavity. While some biofilms are beneficial or even necessary for human life, others can be harmful. Therefore, it is highly important to gain an in-depth understanding of biofilms which can be achieved by in vitro or in vivo experiments. Since these experiments are often time-consuming or expensive, in silico models have proven themselves to be a viable tool in assisting the description and analysis of these complicated processes. Current biofilm growth simulations are using mainly two approaches for describing the underlying models. The volumetric approach splits the deformation tensor into a growth and an elastic part. In this approach, the mass never changes, unless some additional constraints are enforced. The density-based approach, on the other hand, uses an evolution equation to update the growing tissue by adding mass. Here, the density stays constant, and no pressure is exerted. The in silico model presented in this work combines the two approaches. Thus, it is possible to capture stresses inside of the biofilm while adding mass. Since this approach is directly derived from Hamilton's principle, it fulfills the first and second law of thermodynamics automatically, which other models need to be checked for separately. In this work, we show the derivation of the model as well as some selected numerical experiments. The numerical experiments show a good phenomenological agreement with what is to be expected from a growing biofilm. The numerical behavior is stable, and we are thus capable of solving complicated boundary value problems. In addition, the model is very reactive to different input parameters, thereby different behavior of various biofilms can be captured without modifying the model. [ABSTRACT FROM AUTHOR]

The connection between the equivalence principle and Noether's theorem was discussed in Capozziello and Ferrara (Int J Geom Methods Mod Phys 21:2440014, 2024). However, it is known that the Noether symmetry condition is independent of the equations of motions as follows from Hamilton's principle. In this paper, we critically examine the analysis presented in the aforementioned work, highlighting its flaws, and provide a detailed demonstration that there is no connection between Noether's theorem and the equivalence principle. Furthermore, we offer various insights on symmetry analysis to prevent the perpetuation of inaccuracies regarding Noether's work. [ABSTRACT FROM AUTHOR]

The proposed generalized electric spring (G-ES) topology effectively reduces the redundancy caused by the parallel structure of multiple electric springs in a microgrid system. A modeling method for the G-ES is urgently needed to accurately determine the G-ES parameters and to evaluate its transient operation characteristics. The correspondence between Hamilton's principle in mechanics and electricity is introduced, and the feasibility of Hamilton's principle under the smart load topology is verified. The modeling method of the G-ES under Hamilton's principle is discussed, followed by the application of repetitive control strategies on the G-ES. The filter parameters are designed using the normalization method and a simplified parameter design using repetitive controllers was applied. This article introduces the impedance analysis method into the generalized electric spring to analyze its stability under weak network conditions. This work also derives the stability judgment criteria for generalized electric springs. Finally, the feasibility of modeling the G-ES based on the Hamilton's principle was verified using MATLAB and a DSP hardware system. In addition, the consistency between the G-ES and a single intelligent load was verified under the Hamilton's modeling principle. The G-ES stability and dynamic performance under this modeling method meet industry requirements. [ABSTRACT FROM AUTHOR]

In this work, numerous rogue wave solution strategy (MRWSS) agreeing to the Hirota bilinear hypothesis is utilized. The said strategy to build different soliton wave solutions for the generalized Hirota-Satsuma-Ito (GHSI) condition is considered. These numerous soliton wave solutions incorporate first-order, second-order, third-order, and fourth-order waves solutions and so on, which are all depending on the starting theory of chosen capacities. For the lump solution with one most extreme or least esteem, the properties of the Hessian lattice are examined. Besides, the arrangements are contained the lump-two kink arrangements, cross-kink wave arrangements, periodic wave arrangements, and periodic-kink wave arrangements. The various classes of arrangements are gotten. We make utilize of the direct superposition procedure to find out N-soliton wave arrangements to the said condition. The appropriateness and viability of the obtained arrangements is detailed through the reenactment comes about within the shape of 3-D, density, and 2-D charts. The gotten comes about in this work are anticipated to open modern viewpoints for the traveling wave theory. [ABSTRACT FROM AUTHOR]

In this work, we consider a resonant bar detector of gravitational waves in the generalized uncertainty principle (GUP) framework with linear and quadratic momentum uncertainties. The phonon modes in these detectors vibrate due to the interaction with the incoming gravitational wave. In this uncertainty principle framework, we calculate the resonant frequencies and transition rates induced by the incoming gravitational waves on these detectors. We observe that the energy eigenstates and the eigenvalues get modified by the GUP parameters. We also observe non-vanishing transition probabilities between two adjacent energy levels due to the existence of the linear order momentum correction in the generalized uncertainty relation which was not present in the quadratic GUP analysis (Class Quantum Gravity 37:195006, 2020). We finally obtain bounds on the dimensionless GUP parameters using the form of the transition rates obtained during this analysis. [ABSTRACT FROM AUTHOR]

Context: In this study, a small set of 1,3-dipolar cycloaddition reactions that proceed at the same exothermicity is presented. Our main objective was to extend the application of the reaction force constant concept to gain an understanding of the reactivity principles. Inspired by a recent article where we show that the Bell-Evans-Polanyi principle is fulfilled under the condition of an equal degree of (a)synchronicity, here, we demonstrate that the reaction force constant is also a suitable descriptor to quantify the principle of non-perfect synchronization proposed by Bernasconi as a way to understand deviations from the Bell-Evans-Polanyi principle. Methods: Reaction profiles V (ξ) , F (ξ) , and κ (ξ) were performed at the B3LYP/6-31G(d,p) level of theory. The stabilizing interactions were characterized using the energy decomposition analysis combined with the natural orbitals for chemical valence, EDA-NOCV, method. The present work was done using Gaussian 09 and Multiwfn programs. [ABSTRACT FROM AUTHOR]

The use of adhesives in the marine sector is rather limited at the time being, but their use in specific areas of the ship would be an advantage due, among other things, to their low weight and low stress concentration along the bonding joint. The aim of this work is to predict the long-term behaviour of the material, as this is a critical factor when using adhesive as a bonding method in ships, since its durability must be guaranteed throughout a previously defined life cycle. This can be predicted by applying the time–temperature superposition principle (TTS), which involves carrying out a test at different temperatures for each specimen, considerably reducing the test time. Two types of experiments have been carried out according with operation modes in dynamic mechanical analysis (DMA): a dynamic frequency sweep and a stationary creep test under constant stress, to check the behaviour of the adhesive under both dynamic and sustained loading. The master curve for the frequency study will be constructed in such a way as to cover the whole range of relevant vibrations that can occur on the vessel, while that for the creep test the curve obtained covers a range of 25 years, which is usually used as the minimum service life in shipbuilding. For both, a temperature range from room temperature to the maximum operating temperature of the material established by the manufacturer shall be studied. [ABSTRACT FROM AUTHOR]

The effect of the noise induced by gravitons in the case of a freely falling particle from the viewpoint of an external observer has been recently calculated in Phys. Rev. D 107, 066024 (2023). There the authors have calculated the quantum gravity modified Newton's law of free fall where the spacetime has been considered to be weakly curved. In our work, we extend this work by calculating the variance in the velocity and eventually the momentum of the freely falling massive particle. From this simple calculation, we observe that the product of the standard deviation in the position with that of the standard deviation in momentum picks up a higher order correction which is proportional to the square of the standard deviation in momentum. We also find out that in the Planck limit (both Planck length and Planck mass), this uncertainty product gives the well-known form of the generalized uncertainty principle. We then calculate a similar uncertainty product when the graviton is in a squeezed state, and eventually, we get back the same uncertainty product. Finally, we extend our analysis for the gravitons being in a thermal state and obtain a temperature-dependent uncertainty product. If one replaces this temperature with the Planck temperature and the mass of the particle by the Planck mass, the usual uncertainty product appears once again. We also obtain an upper bound of the uncertainty product thereby giving a range of the product of the variances in position and momentum. [ABSTRACT FROM AUTHOR]

The equivalence principle, being one of the building blocks of general relativity, seems to be crucial for analysis of quantum effects in gravity. In this paper we consider the relation between the equivalence principle and the consistency of quantum information processing in gravitational field. We propose an analysis with a looped evolution consisting of steps both in the gravitational field and in the accelerated reference frame. We show that without the equivalence principle the looped quantum evolution cannot be unitary and looses its consistency. For this reasoning the equivalence principle is formulated in terms of the gauge transformations and is analyzed for particles acquiring an appropriate phase associated with the action over the looped path. In consequence, to keep consistency of quantum operations in gravitational field, it is required to keep a quantum variant of the equivalence principle. This proves importance of the quantized version of this fundamental gravitational principle for quantum information processing. [ABSTRACT FROM AUTHOR]

The article "If the Difference Principle Won't Make a Real Difference in Algorithmic Fairness, What Will?: Response to 'Rawlsian Algorithmic Fairness and a Missing Aggregation Property of the Difference Principle'" examines the challenges of applying John Rawls' difference principle to algorithmic fairness. The authors argue that implementing the principle at a local level is not enough to ensure fairness at a societal level. They provide examples and simulations to support their argument and suggest that addressing inequality through measures like taxing billionaires or implementing universal basic income may be more effective. The article also raises questions about the practicality of Rawlsian principles and proposes alternative policies that focus on broader patterns of distributional justice. It explores different perspectives on justice and responsibility, emphasizing the need for collective action to bring about meaningful change. The author critiques the limitations of Rawlsian political philosophy and calls for a more comprehensive approach to algorithmic fairness. [Extracted from the article]

The electronic, optical, and thermoelectric properties of the pure and (S, Se, and Te)-doped into the oxygen site of LaAlO3 and KNbO3 compounds have been investigated using the Locale Density Approximation with modified Becke and Johnson, based on the density functional theory. These doped structures represent p-type semiconductors with a direct band gap, since the concentration of chalcogens impurities increases to 16.66% for LaAlO3 and up to 12.5% for KNbO3, respectively. Furthermore, the optical properties for the doped systems are favorable in the visible region, especially for KNbO3 doped with 8.33 and 12.5% of Te making KNbO3Te more favorable for photovoltaic application compared to LaAlO3Te. Moreover, the thermoelectric properties indicate that the electrical conductivity increases with increasing temperature. However, it decreases after doping compounds with varying S/Se/Te concentrations compared to pure ones, indicating an increase in the collision between atomic vibration and the movements of electrons. All examined compounds exhibit an increase of the thermal conductivity as temperature increase. [ABSTRACT FROM AUTHOR]

In this paper, the averaging principle for stochastic Caputo fractional differential equations with the nonlinear terms satisfying the non-Lipschitz condition is considered. The work in the article is roughly divided into three parts. Firstly, we establish a generalized Gronwall inequality with singular integral kernel which is a key part in our analysis. Secondly, we discuss the existence and uniqueness of solution. And finally, the averaging principle is considered. [ABSTRACT FROM AUTHOR]

Abstract Microfinance is an alternative banking service available to low-income individuals or organizations for whom no institutional financial services are available. A widely accepted approach to assisting disadvantaged and excluded communities, especially in remote rural areas, is microcredit. The purpose of microfinance is to promote financial equality and inclusion by acting as a substitute for traditional lending methods for the marginalized. In India, Self-Help Groups (SHGs)—Bank Linkage Program that led microfinance—gained maximum popularity. The National Bank for Agriculture and Rural Development architected this model. In this model, Grameen Banks are associated with SHGs. The model is familiar as the SHG-Bank Linkage Program (SBLP). A microfinance program’s theoretical foundation is the “Rawls’ Difference Principle” embedded in the “Theory of Justice.” The microcredit program, through the Self-Help Group-Bank Linkage Program (SBLP), gained maximum popularity in India. These SBLPs are registered with the “Deendayal Antyodaya Yojana—National Rural Livelihoods Mission (DAY-NRLM)” under the scheme Aajeevika. In harmony with “Rawls’ Difference Principle,” the ultimate goal of Aajeevika is social cohesion for all. The current study aims to assess the effectiveness of the SBLP-driven microfinance program in promoting financial inclusion. Furthermore, unlike earlier studies, the present study also considers whether or not involvement in SBLP increases social cohesion, which is a crucial component of the Difference Principle. The empirical research is conducted using novel data collected through a field survey of 335 participants and 490 non-participants from Nagaon, Morigaon, and Hojai districts of Central Assam. The “Propensity Score Matching” method facilitates the impact analysis of SBLP. The participation decision in the SBLP is positively influenced by the level of education. Empirical results also indicate that Hindus and low-caste women are interested in participating in SBLP. Contrarily, distance from the bank and operational land holdings are negatively influencing the participation decision. The empirical findings support higher financial inclusion through SBLP involvement but do not support greater social cohesion. Based on the empirical results, we suggest that more SBLPs be enrolled with DAY-NRLP under “Aajeevika.” Simultaneously, social cohesion may be achieved only by guaranteeing participation for every deserving individual, irrespective of religion, caste, and class.

Making a history of the principle of inertia, as of any other principle or concept, is a complex but still possible operation. In this work it has been chosen to make a back story which seemed the most natural way for a reconstruction. On the way back, it has been decided to stop at the 6th century CE with the contribution of Ioannes Philoponus. The principle he stated, although very different from the modern one, is certainly associated with it. Going back in time it is still possible and of course one could proceed to the origins of the homo sapiens who perhaps posed the problem of why a club thrown with his hand could go so far from him. But the similarities that one can find with the modern principle are very vague, too perhaps. Without going so far one could see an embryonic idea of the principle of inertia in the atomistic theory of Democritus in the 5th century BCE. The motion of atoms whirling with no apparent reason can suggest the idea that a body can also move with no reason. But the transition from the atom, a metaphysical being, to the body, an empirical being, is far from immediate. [ABSTRACT FROM AUTHOR]

Milgrom’s Modified Newtonian Dynamics (MOND) correction to Newtonian gravity is shown to be equivalent to a more fundamental transformation between a non-inertial local reference frame and the fixed background of the observable universe, complying with Mach’s principle. Both Newton’s gravitational constant and Milgrom’s MOND acceleration parameter or scale constant are substituted for the speed of light and two varying and measurable cosmological parameters under the justification of Schrödinger’s and Sciama’s interpretation of Mach’s principle: causally connected mass and size of the universe. This Machian interpretation, free from fundamental constants and parameters with the exception of the speed of light as the speed of gravity, is based on relative field intensities of the small and large scale of the universe. The Machian MOND approximation is a necessary feature of a phenomenological theory of modified inertia which incorporates Mach’s principle in agreement with galaxy rotation curves. [ABSTRACT FROM AUTHOR]

It has long been known that in the context of axiomatic second-order logic (SOL), Hume's Principle (HP) is mutually interpretable with "the universe is Dedekind infinite" (DI). In this paper, we offer a more fine-grained analysis of the logical strength of HP, measured by deductive implications rather than interpretability. Our main result is that HP is not deductively conservative over SOL + DI. That is, SOL + HP proves additional theorems in the language of pure second-order logic that are not provable from SOL + DI alone. Arguably, then, HP is not just a pure axiom of infinity, but rather it carries additional logical content. On the other hand, we show that HP is Π 1 1 conservative over SOL + DI, and that HP is conservative over SOL + DI + "the universe is well ordered" (WO). Next, we show that SOL + HP does not prove any of the simplest and most natural versions of the axiom of choice, including WO and weaker principles. Lastly, we discuss other axioms of infinity. We show that HP does not prove the Splitting or Pairing principles (axioms of infinity stronger than DI). [ABSTRACT FROM AUTHOR]

Unifying quantum theory and gravity remains a fundamental challenge in physics. While most existing literature focuses on the ultraviolet modifications of quantum theory due to gravity, this work shows that generic infrared modifications arise when we describe quantum theory in curved spacetime. We explicitly demonstrate that the modifications to the position-momentum algebra are proportional to curvature invariants (such as the Ricci scalar and Kretschmann scalar). Our results, derived through a rigorous application of Dirac's quantization procedure, demonstrate that infrared effects in quantum systems can be axiomatically derived. We study particle dynamics in an arbitrary curved spacetime by embedding them in a higher-dimensional flat geometry. Our approach, which involves embedding particle dynamics in a higher-dimensional flat geometry and utilizing Dirac's quantization procedure, allows us to capture the dynamics of a particle in 4-dimensional curved spacetime through a modified position-momentum algebra. When applied to various spacetimes, this method reveals that the corrections due to the spacetime curvature are universal. We further compare our results with those derived using extended uncertainty principles. Finally, we discuss the implications of our work for black holes and entanglement. [ABSTRACT FROM AUTHOR]

An estimate of the convergence rate is obtained in the Riemann localization principle for trigonometric series. [ABSTRACT FROM AUTHOR]

An attempt is made to give an accurate mathematical interpretation of the energy–time uncertainty relation. [ABSTRACT FROM AUTHOR]

The principle of total evidence says that one should conditionalize one's degrees of belief on one's total evidence. In the first part, I propose a justification of this principle in terms of its epistemic optimality. The justification is based on a proof of I. J. Good and embedded into a new account of epistemology based on optimality-justifications. In the second part, I discuss an apparent conflict between the principle of total evidence and the political demands of anti-discrimination. These demands require, for example, that information about the sex of the applicant for a job should not be included in the relevant evidence. I argue that if one assesses the applicant's qualification in terms of those properties that are directly causally relevant for the job performance, then properties that are merely indirectly relevant, such as sex, race, or age, are screened off, i.e., become irrelevant. So, the apparent conflict disappears. [ABSTRACT FROM AUTHOR]

Background: The effectiveness of clinical ethics counselling in medicine in terms of satisfaction of the participants, support of ethical decision-making, perceived impact on clinical care, moral competence and quality of communication is now empirically well validated. In psychiatry, more and more institutions have structures for clinical ethics consultation as well; however, there is still a lack of evaluative accompanying research on the benefits and differential indications of the various forms and models of clinical ethics counselling in psychiatry. Aim of the work: The article presents the principles and the step by step application of the principle-oriented clinical ethics consultation according to the Basel model 2.0. Material and methods: The article is based on material and procedures developed at the Clinical Ethics Unit of the University Hospital Basel and the University Psychiatric Clinics Basel for the principle-oriented clinical ethics consultation according to the Basel model 2.0. Results and discussion: Principle-oriented clinical ethics consultation according to the Basel model 2.0 is suitable for dealing with moral issues and conflicts in psychiatric practice and for their ethical reflection; however, further evaluative accompanying research is needed on the benefits and differential indications of this and other models of clinical ethics support in psychiatry. [ABSTRACT FROM AUTHOR]

In this study, first-order necessary optimality conditions, in the form of a weak maximum principle, are derived for discrete optimal control problems with mixed equality and inequality constraints. Such conditions are achieved by using the Dubovitskii–Milyutin formalism approach. Nondegenerate conditions are obtained under the constant rank of the subspace component (CRSC) constraint qualification, which is an important generalization of both the Mangasarian–Fromovitz and constant rank constraint qualifications. Beyond its theoretical significance, CRSC has practical importance because it is closely related to the formulation of optimization algorithms. In addition, an instance of a discrete optimal control problem is presented in which CRSC holds while other stronger regularity conditions do not. [ABSTRACT FROM AUTHOR]

First principle calculations of the elastic constants of perovskite-type hydride NaBeH3 material have been accomplished using the density functional theory (DFT) within the local density approximation (LDA) and the pseudopotential plane-wave method. The elastic constants were compared fairly well with those previously calculated. We have also calculated the dependence of the elastic constants on hydrostatic pressure from 0 up to 96.55 GPa. We have found that the elastic constants follow a quadratic law with respect to the pressure. In this study, the bulk modulus, shear modulus, Young's modulus, Poisson's ratio, acoustic wave speed and Debye temperature of cubic NaBeH3 material are also determined as a function of pressure. Both the acoustic wave speed and the Debye temperature of NaBeH3 material change monotonously and non-linearly with increasing the pressure from 0 up to 96.55 GPa. [ABSTRACT FROM AUTHOR]

In this article, we have investigated the electronic structure of Co2Si monolayer by first-principle calculations, and the phonon spectrum calculation results do not show any imaginary frequencies, indicating its stable existence. The calculation of electronic structure shows that there are two nodal loops centered on gamma in the Kz=0 plane, and these two nodal loops still exist considering the coupling of spin and orbitals. The calculation results of free energy indicate that Co2Si monolayer is very suitable as a catalyst for hydrogen evolution reactions. Its Gibbs free energy for adsorbing hydrogen atom is as low as -0.067 eV, which is superior to many other catalytic materials and comparable to Pt. In addition, when electron or hole doping is carried out, its Gibbs free energy for hydrogen absorption changes accordingly. These results indicate that Co2Si monolayer has the potential to become a high-performance and inexpensive catalyst for hydrogen evolution reactions. [ABSTRACT FROM AUTHOR]

The aim of this study is to present an alternative way to deduce the equations of motion of general (i. e. also nonlinear) nonholonomic constrained systems starting from the d'Alembert principle and proceeding by an algebraic procedure. The two classical approaches in nonholonomic mechanics – C ˇ etaev method and vakonomic method – are treated on equal terms, avoiding integrations or other steps outside algebraic operations. In the second part of the work, we compare our results with the standard forms of the equations of motion associated with the two method and we discuss the role of the transpositional relation and of the commutation rule within the question of equivalence and compatibility of the C ˇ etaev and vakonomic methods for general nonholonomic systems. [ABSTRACT FROM AUTHOR]

We prove the almost sure invariance principle (ASIP) with close to optimal error rates for nonuniformly hyperbolic maps. We do not assume exponential contraction along stable leaves, therefore our result covers in particular slowly mixing invertible dynamical systems as Bunimovich flowers, billiards with flat points as in Chernov and Zhang (Stoch Dyn 5:535–553, 2005a, Nonlinearity 18:1527–1553, 2005b) and Wojtkowski' (Commun Math Phys 126:507–533, 1990) system of two falling balls.For these examples, the ASIP is a new result, not covered by prior works for various reasons, notably because in absence of exponential contraction along stable leaves, it is challenging to employ the so-called Sinai's trick (Sinai in Russ Math Surv 27:21–70, 1972; Bowen, Lecture Notes in Math vol. 470 (1975)) of reducing a nonuniformly hyperbolic system to a nonuniformly expanding one. Our strategy follows our previous papers on the ASIP for nonuniformly expanding maps, where we build a semiconjugacy to a specific renewal Markov shift and adapt the argument of Berkes et al. (Ann Probab 42:794–817, 2014). The main difference is that now the Markov shift is two-sided, the observables depend on the full trajectory, both the future and the past. [ABSTRACT FROM AUTHOR]

The generalized uncertainty relation is expected to be an essential element in a theory of quantum gravity. In this work, we examine its effect on the Hawking radiation of a Schwarzschild black hole formed from collapse by incorporating a minimal uncertainty length scale into the radial coordinate of the background. This is implemented in both the ingoing Vaidya coordinates and a family of freely falling coordinates. We find that, regardless of the choice of the coordinate system, Hawking radiation is turned off at around the scrambling time. Interestingly, this phenomenon occurs while the Hawking temperature remains largely unmodified. [ABSTRACT FROM AUTHOR]

A new law of energies summation – principle of superposition of energy states (PSES) – is proposed, and possibilities of its application in the theory of fundamental interactions are considered. [ABSTRACT FROM AUTHOR]

This article assesses Landauer's principle from information theory in the context of area quantization of the Schwarzschild black hole. Within a quantum-mechanical perspective where Hawking evaporation can be interpreted in terms of transitions between the discrete states of the area (or mass) spectrum, we justify that Landauer's principle holds consistently in the saturated form when the number of microstates of the black hole goes as 2 n , where n is a large positive integer labeling the levels of the area/mass spectrum in the semiclassical regime. This is equivalent to the area spacing Δ A = α l P 2 (in natural units), where α = 4 ln 2 for which the entropy spacing between consecutive levels in Boltzmann units coincides exactly with one bit of information. We also comment on the situation for other values of α prevalent in the literature. [ABSTRACT FROM AUTHOR]

Environmental emergencies are increasingly the subject of debate. As defined in this article, these emergencies start on a State's territory but can have consequences beyond its borders. The interconnectedness of the environment and the growing concern about environmental threats lead to the question of whether third States might have a legal interest in some of these environmental emergencies. It triggers a debate similar to past debates on human rights violations, resulting in the Responsibility to Protect. This article investigates the circumstances under which States can lawfully intervene without using force in another State in response to environmental emergencies. By analysing the principle of non-intervention and the effect of international environmental law on the scope of the domaine réservé, the article discusses whether certain environmental interventions can be justified under the current legal framework of the principle of non-intervention. The emphasis lies on the no-harm principle and the concept of the common concern of humankind as a means to address environmental emergencies with direct transboundary impacts or those threatening the environment at a global level. The article concludes that the no-harm principle and the concept of the common concern of humankind can potentially reduce the scope of the domaine réservé. Consequently, States' actions in response to an environmental emergency can be lawful under the principle of non-intervention. This lawful environmental intervention has the potential to develop from an activist idea into a legal tool. [ABSTRACT FROM AUTHOR]

Purpose: To compare the risk of immune-associated pneumonitis between PD-1 and PD-L1 inhibitors, the meta-analysis was designed. Method: The difference in risk of immune-associated pneumonitis between PD-1 and PD-L1 inhibitors was assessed by two different meta-analysis methods, the Mirror-pairing and the PRISMA guidelines. Results: A total of eighty-eight reports were used for meta-analysis, while thirty-two studies were used for the Mirror-pairing. Both PD-1 and PD-L1 inhibitors (used alone or combined with chemotherapy) increased the risk of developing immune-related pneumonitis (P < 0.00001; P < 0.00001). Based on indirect analyses results (subgroup analyses), the risk of PD-L1-induced pneumonitis was weaker than that of PD-1 inhibitors when the control group was chemotherapy (OR = 3.33 vs. 5.43) or placebo (OR = 2.53 vs. 3.19), while no obvious significant differences were found (P = 0.17; P = 0.53). For the Mirror-pairing-based meta-analysis, the risk of PD-1-induced pneumonitis was significantly higher than that of PD-L1 inhibitors (OR = 1.46, 95%CI [1.08, 1.98], I2 = 0%, Z = 2.47 (P = 0.01)). However, this difference was not significant, when they were combined with chemotherapy (OR = 1.05, 95%CI [0.68, 1.60], I2 = 38%, Z = 0.21 (P = 0.84)). Conclusion: Both PD-1 and PD-L1 inhibitors increased the risk of immune-related pneumonitis, while the risk of PD-1-induced pneumonitis was significantly higher than that of PD-L1 inhibitors. [ABSTRACT FROM AUTHOR]

Perceptual grouping, a fundamental mechanism in our visual system, significantly influences our interpretation of and interaction with the surrounding world. This study explores the impact of the proximity principle from the perspective of the Two Visual Systems (TVS) model. The TVS model argues that the visual system comprises two distinct streams: the ventral stream, which forms the neural basis for "vision-for-perception," and the dorsal stream, which underlies "vision-for-action." We designed a perceptual grouping task using dot lattices as well as a line-orientation discrimination task. Data were collected using vocal and mouse methods for the vision-for-perception mode, and joystick and pen-paper methods for the vision-for-action mode. Each method, except for vocal, included separate blocks for right and left hands. The proximity data were fitted using exponential and power models. Linear mixed-effects models were used for the statistical analyses. The results revealed similar line-orientation discrimination accuracy across all conditions. The exponential model emerged as the best fit, demonstrating adherence to the Pure Distance Law in both perceptual modes. Sensitivity to the proximity principle was higher in the vision-for-action mode compared to the vision-for-perception. In terms of orientation biases, a strong preference for vertical orientation was observed in the vision-for-perception mode, whereas a noticeable preference toward either of the oblique orientations was detected in the vision-for-action mode. Analysis of free-drawn lines demonstrated an affordance bias in the vision-for-action mode. This suggests a remarkable tendency to perceive organizations within specific orientations that offer more affordances due to the interaction between the body postures and tools. [ABSTRACT FROM AUTHOR]

We show that the formulations of non-relativistic quantum mechanics can be derived from an extended least action principle. The principle can be considered as an extension of the least action principle from classical mechanics by factoring in two assumptions. First, the Planck constant defines the minimal amount of action a physical system needs to exhibit during its dynamics in order to be observable. Second, there is constant vacuum fluctuation along a classical trajectory. A novel method is introduced to define the information metrics to measure additional observability due to vacuum fluctuations, which is then converted to an additional action through the first assumption. Applying the variational principle to minimize the total actions allows us to recover the basic quantum formulations including the uncertainty relation and the Schrödinger equation in the position representation. In the momentum representation, the same method can be applied to obtain the Schrödinger equation for a free particle while further investigation is still needed for a particle with an external potential. Furthermore, the principle brings in new results on two fronts. At the conceptual level, we find that the information metrics for vacuum fluctuations are responsible for the origin of the Bohm quantum potential. Even though the Bohm potential for a bipartite system is inseparable, the underlying vacuum fluctuations are local. Thus, inseparability of the Bohm potential does not justify a non-local causal relation between the two subsystems. At the mathematical level, quantifying the information metrics for vacuum fluctuations using more general definitions of relative entropy results in a generalized Schrödinger equation that depends on the order of relative entropy. The extended least action principle is a new mathematical tool. It can be applied to derive other quantum formalisms such as quantum scalar field theory. [ABSTRACT FROM AUTHOR]

The authors give a stochastic maximum principle for square-integrable optimal control of linear stochastic systems. The control domain is not necessarily convex and the cost functional can have a quadratic growth. In particular, they give a stochastic maximum principle for the linear quadratic optimal control problem. [ABSTRACT FROM AUTHOR]

This paper proposed the additional fractional gradient descent identification algorithm based on the multi-innovation principle for autoregressive exogenous models. This algorithm incorporates an additional fractional order gradient to the integer order gradient. The two gradients are synchronously used to identify model parameters, thereby accelerating the convergence of the algorithm. Furthermore, to address the limitation of conventional gradient descent algorithms, which only use the information of the current moment to estimate the parameters of the next moment, resulting in low information utilisation, the multi-innovation principle is applied. Specifically, the integer-order gradient and additional fractional-order gradient are expanded into multi-innovation forms, and the parameters of the next moment are simultaneously estimated using multi-innovation matrices, thereby further enhancing the parameter estimation speed and identification accuracy. The convergence of the algorithm is demonstrated, and its effectiveness is verified through simulations and experiments involving the identification of a 3-DOF gyroscope system. [ABSTRACT FROM AUTHOR]

Due to high energy density, clean combustion products and abundant resources, natural gas hydrates (NGHs) have been regarded as an important clean energy source with the potential for large-scale development and utilization. However, pilot tests in NGHs show that their production rates are far below commercial needs. Multilateral well technology may lead to a solution to this problem because it can dramatically expand the drainage area of production wells. This paper presents the practical rate transient analysis for multilateral horizontal wells in NGHs. In developing solution to the diffusivity equation of multilateral horizontal wells in NGHs, the superposition principle and reciprocity are applied. We wrote the governing equation in cylindrical coordinates to describe the NGH flow process. We used the moving boundaries and dissociation coefficients to model the solid-to-gas transition process in hydrates. To obtain solutions for flow in hydrate reservoirs, we used Laplace transforms and the Stehfest numerical inversion method. Superposition principle and Gaussian elimination are applied to obtain the desired solution for multilateral horizontal wells. We validated our proposed model with a commercial numerical simulator. By performing sensitivity analyses, effects on production behavior of the number of branches, dissociation coefficient, radius of the region with dissociated hydrate, and dispersion ratio are determined. A synthetic case study is conducted to show the typical production behaviors. [ABSTRACT FROM AUTHOR]

This paper presents a quantum image encryption algorithm based on a novel 3D chaotic system and the quantum Rubik's cube principle. Initially, we propose a new 3D chaotic system for generating chaotic key sequences and chaotic images. Subsequently, we introduce the quantum Rubik's cube principle, which serves as a fundamental component of our encryption scheme. The scheme consists of two stages: In the first stage, chaotic key sequences control the operation of the quantum Rubik's cube principle, enabling pixel permutation in the encrypted image. In the second stage, the scrambled image undergoes bitwise XOR with the chaotic image, facilitating pixel diffusion through quantum bitwise XOR operations. By leveraging the chaotic system's sensitivity to initial values and its large key space, our proposed scheme effectively resists statistical attacks and noise interference. The time complexity of our scheme is exponential reduced compared to its classical counterpart. We also conduct experiments on both the IBM Qiskit platform and a classical computer and analyze the results. [ABSTRACT FROM AUTHOR]

The main objective of this paper is to demonstrate the uniform large deviation principle (UDLP) for the solutions of two-dimensional stochastic Navier–Stokes equations (SNSE) in the vorticity form when perturbed by two distinct types of noises. We first consider an infinite-dimensional additive noise that is white in time and colored in space and then consider a finite-dimensional Wiener process with linear growth coefficient. In order to obtain the ULDP for 2D SNSE in the vorticity form, where the noise is white in time and colored in space, we utilize the existence and uniqueness result from B. Ferrario et. al., Stochastic Process. Appl.,129 (2019), 1568–1604, and the uniform contraction principle. For the finite-dimensional multiplicative Wiener noise, we first prove the existence of a unique local mild solution to the vorticity equation using a truncation and fixed point arguments. We then establish the global existence of the truncated system by deriving a uniform energy estimate for the local mild solution. By applying stopping time arguments and a version of Skorokhod’s representation theorem, we conclude the global existence and uniqueness of a solution to our model. We employ the weak convergence approach to establish the ULDP for the law of the solutions in two distinct topologies. We prove ULDP in the C ([ 0 , T ] ; L p (T 2)) topology, for p > 2 , taking into account the uniformity of the initial conditions contained in bounded subsets of L p (T 2) . Finally, in C ([ 0 , T ] × T 2) topology, the uniformity of initial conditions lying in bounded subsets of C (T 2) is considered. [ABSTRACT FROM AUTHOR]

In this paper, we generalize the Avalanche Principle in [Ann. of. Math. (2), 2001, 154(1): 155–203]. [ABSTRACT FROM AUTHOR]

The superposition principle delivers a probabilistic representation of a solution of the Fokker–Planck–Kolmogorov equation in terms of a solution of the martingale problem with operator . We generalize the superposition principle to the case of equations on a domain, examine the transformation of the measure and the operator under a change of variables, and obtain new conditions for the validity of the superposition principle under the assumption of the existence of a Lyapunov function for the unbounded part of the drift coefficient. [ABSTRACT FROM AUTHOR]

Abstract This research investigates how the avoidance of initial gemination in Maltese is motivated by conformity to the Obligatory Contour Principle (OCP) and the Strict Layer Hypothesis (SLH) in light of Optimality Theory (OT) as a framework. The data of this study were collected and analyzed qualitatively. The data in this study were harvested from existing literature reviews peculiar to the Phonology of Maltese. Furthermore, the same data were verified by consulting several native speakers of Maltese when necessary. This study concludes that initial gemination in Semitic verbs of pattern V (t-C1iC2C2eC3) derives from the assimilation of the [+coronal] feature of prefixes to the initial consonant of the following stem to conform to the OCP. Vowel prosthesis helps to affiliate an initial semi-syllable, as the peripheral member of this type of gemination, to the syllable node in order to comply with the SLH. Vowel prosthesis serves to ensure conformity to the OCP and to geminate integrity by the underlying initial geminates in non-Semitic verbs (from English and Italian) of CC-stems, which obey the SLH since their members belong to the same morpheme, unlike derivational forms. This research demonstrates the insightfulness of Optimality Theory (OT) as a framework to account for these phenomena in Maltese. The results of this study lead to future research pertinent to the analysis of both segmental and suprasegmental structures in Maltese in light of OT and their relationship to other languages such as Arabic, English, and Italian.

The matrix-valued Allen-Cahn (MAC) equation was first introduced as a model problem of finding the stationary points of an energy for orthogonal matrix-valued functions and has attracted much attention in recent years. It is well known that the MAC equation satisfies the maximum bound principle (MBP) with respect to either the matrix 2-norm or the Frobenius norm, which plays a key role in understanding the physical meaning and the wellposedness of the model. To preserve this property, we extend the explicit integrating factor Runge-Kutta (IFRK) method to the MAC equation. Moreover, we construct a new three-stage third-order and a new four-stage fourth-order IFRK schemes based on the classical Runge-Kutta schemes. Under a reasonable time-step constraint, we prove the MBP preservation of the IFRK method with respect to the matrix 2-norm, based on which, we further establish their optimal error estimates in the matrix 2-norm. Although numerical results indicate that the IFRK method preserves the MBP with respect to the Frobenius norm, a detailed analysis shows that it is hard to prove this preservation by using the same approach for the case of 2-norm. Several numerical experiments are carried out to test the convergence of the IFRK schemes and to verify the MBP preservation with respect to the matrix 2-norm and the Frobenius norm, respectively. Energy stability is also observed, which clearly indicates the orthogonality of the stationary solution of the MAC equation. In addition, we simulate the coarsening dynamics to verify the motion law of the interface for different initial conditions. [ABSTRACT FROM AUTHOR]

An initial-boundary value problem for the multi-term time-fractional wave equation on a bounded domain is considered. For the largest and smallest orders of the involved Caputo fractional time-derivatives, α and α m , it is assumed 1 < α < 2 and α - α m ≤ 1 . Subordination principle with respect to the corresponding single-term time-fractional wave equation of order α is deduced. Injectivity of the integral transform, defined by the subordination relation, is established. The subordination identity is used to prove uniqueness for a coefficient inverse problem for the multi-term equation, based on an analogous property for the related single-term one. In addition, the subordination relation is applied for deriving a regularity estimate. [ABSTRACT FROM AUTHOR]

In this paper we investigate optimal control problems perturbed by random events. We assume that the control has to be decided prior to observing the outcome of the perturbed state equations. We investigate the use of probability functions in the objective function or constraints to define optimal or feasible controls. We provide an extension of differentiability results for probability functions in infinite dimensions usable in this context. These results are subsequently combined with the optimal control setting to derive a novel Pontryagin’s optimality principle. [ABSTRACT FROM AUTHOR]

Does the assumption of a weak form of computational functionalism, according to which the right form of neural computation is sufficient for consciousness, entail that a digital computational simulation of such neural computations is conscious? Or must this computational simulation be implemented in the right way, in order to replicate consciousness? From the perspective of Karl Friston's free energy principle, self-organising systems (such as living organisms) share a set of properties that could be realised in artificial systems, but are not instantiated by computers with a classical (von Neumann) architecture. I argue that at least one of these properties, viz. a certain kind of causal flow, can be used to draw a distinction between systems that merely simulate, and those that actually replicate consciousness. [ABSTRACT FROM AUTHOR]