Search

Let $L$ be the distinguished Laplacian on the Iwasawa $AN$ group associated with a semisimple Lie group $G$. Assume $F$ is a Borel function on $\mathbb{R}^+$. We give a condition on $F$ such that the kernels of the functions $F(L)$ are uniformly bounded. This condition involves the decay of $F$ only and not its derivatives. By a known correspondence, this implies pointwise estimates for a wide range of functions of the Laplace-Beltrami operator on symmetric spaces. In particular, when $G$ is of real rank one and $F(x)={\rm e}^{it\sqrt x}\psi(\sqrt x)$, our bounds are sharp.

The coherent spin dynamics of holes are investigated for CsPbBr$_3$ and CsPb(Cl,Br)$_3$ perovskite nanocrystals in a glass matrix using the time-resolved Faraday rotation/ellipticity techniques. In an external magnetic field, pronounced Larmor spin precession of the hole spins is detected across a wide temperature range from 5 to 300 K. The hole Land\'e $g$-factor varies in the range of $0.8-1.5$, in which it increases with increasing high energy shift of the exciton due to enhanced confinement in small nanocrystals. The hole spin dephasing time decreases from 1 ns to 50 ps in this temperature range. Nuclear spin fluctuations have a pronounced impact on the hole spin dynamics. The hyperfine interaction of the holes with nuclear spins modifies their spin polarization decay and induces their spin precession in zero external magnetic field. The results can be well described by the model developed in Ref. 41, from which the hyperfine interaction energy of a hole spin with the nuclear spin fluctuation in range of $2-5$ $\mu$eV is evaluated.

This study presents a comprehensive theoretical and empirical analysis of Patricia tries, the fundamental data structure underlying Ethereum's state management system. We develop a probabilistic model characterizing the distribution of path lengths in Patricia tries containing random Ethereum addresses and validate this model through extensive computational experiments. Our findings reveal the logarithmic scaling of average path lengths with respect to the number of addresses, confirming a crucial property for Ethereum's scalability. The study demonstrates high precision in predicting average path lengths, with discrepancies between theoretical and experimental results not exceeding 0.01 across tested scales from 100 to 100,000 addresses. We identify and verify the right-skewed nature of path length distributions, providing insights into worst-case scenarios and informing optimization strategies. Statistical analysis, including chi-square goodness-of-fit tests, strongly supports the model's accuracy. The research offers structural insights into node concentration at specific trie levels, suggesting avenues for optimizing storage and retrieval mechanisms. These findings contribute to a deeper understanding of Ethereum's fundamental data structures and provide a solid foundation for future optimizations. The study concludes by outlining potential directions for future research, including investigations into extreme-scale behavior, dynamic trie performance, and the applicability of the model to non-uniform address distributions and other blockchain systems., Comment: 22 pages

The coherent spin dynamics of electrons and holes in CsPbI3 perovskite nanocrystals in a glass matrix are studied by the time-resolved Faraday ellipticity technique in magnetic fields up to 430 mT across a temperature range from 6 K up to 120 K. The Land\'e g-factors and spin dephasing times are evaluated from the observed Larmor precession of electron and hole spins. The nanocrystal size in the three studied samples varies from about 8 to 16 nm, resulting in exciton transition varying from 1.69 to 1.78 eV at the temperature of 6 K, allowing us to study the corresponding energy dependence of the g-factors. The electron g-factor decreases with increasing confinement energy in the NCs as result of NC size reduction, and also with increasing temperature. The hole g-factor shows the opposite trend. A model analysis shows that the variation of g-factors with NC size arises from the transition energy dependence of the g-factors, which becomes strongly renormalized by temperature.

Detecting planet signatures in protoplanetary disks is fundamental to understanding how and where planets form. In this work, we report dust and gas observational hints of planet formation in the disk around 2MASS-J16120668-301027, as part of the ALMA Large Program "AGE-PRO: ALMA survey of Gas Evolution in Protoplanetary disks". The disk was imaged with the Atacama Large Millimeter/submillimeter Array (ALMA) at Band 6 (1.3 mm) in dust continuum emission and four molecular lines: $^{12}$CO(J=2-1), $^{13}$CO(J=2-1), C$^{18}$O(J=2-1), and H$_2$CO(J=3$_{(3,0)}$-2$_{(2,0)}$). Resolved observations of the dust continuum emission (angular resolution of $\sim 150$ mas, 20 au) show a ring-like structure with a peak at $0.57 ^{\prime \prime}$ (75 au), a deep gap with a minimum at 0.24$^{\prime \prime}$ (31 au), an inner disk, a bridge connecting the inner disk and the outer ring, along with a spiral arm structure, and a tentative detection (to $3\sigma$) of a compact emission at the center of the disk gap, with an estimated dust mass of $\sim 2.7-12.9$ Lunar masses. We also detected a kinematic kink (not coincident with any dust substructure) through several $^{12}$CO channel maps (angular resolution $\sim$ 200 mas, 30 au), located at a radius of $\sim 0.875^{\prime \prime}$ (115.6 au). After modeling the $^{12}$CO velocity rotation around the protostar, we identified a tentative rotating-like structure at the kink location with a geometry similar to that of the disk. We discuss potential explanations for the dust and gas substructures observed in the disk, and their potential connection to signatures of planet formation., Comment: 24 pages, 15 figures

We consider the remote state restoring and perfect transfer of the zero-order coherence matrix (PTZ) in a spin system governed by the XXZ-Hamiltonian conserving the excitation number. The restoring tool is represented by several nonzero Larmor frequencies in the Hamiltonian. To simplify the analysis we use two approximating models including either step-wise or pulse-type time-dependence of the Larmor frequencies. Restoring in spin chains with up to 20 nodes is studied. Studying PTZ, we consider the zigzag and rectangular configurations and optimize the transfer of the 0-order coherence matrix using geometrical parameters of the communication line as well as the special unitary transformation of the extended receiver. Overall observation is that XXZ-chains require longer time for state transfer than XX-chains, which is confirmed by the analytical study of the evolution under the nearest-neighbor approximation. We demonstrate the exponential increase of the state-transfer time with the spin chain length., Comment: 22 pages, 13 figures. arXiv admin note: text overlap with arXiv:2401.09569

Zero-knowledge proofs (ZKPs) have emerged as a promising solution to address the scalability challenges in modern blockchain systems. This study proposes a methodology for generating and verifying ZKPs to ensure the computational integrity of cryptographic hashing, specifically focusing on the SHA-256 algorithm. By leveraging the Plonky2 framework, which implements the PLONK protocol with FRI commitment scheme, we demonstrate the efficiency and scalability of our approach for both random data and real data blocks from the NEAR blockchain. The experimental results show consistent performance across different data sizes and types, with the time required for proof generation and verification remaining within acceptable limits. The generated circuits and proofs maintain manageable sizes, even for real-world data blocks with a large number of transactions. The proposed methodology contributes to the development of secure and trustworthy blockchain systems, where the integrity of computations can be verified without revealing the underlying data. Further research is needed to assess the applicability of the approach to other cryptographic primitives and to evaluate its performance in more complex real-world scenarios.

In this paper we present a general framework to construct integrable $\mathbb{Z}_2^2$-graded extensions of classical, two-dimensional Toda and conformal affine Toda theories. The scheme is applied to define the extended Liouville and Sinh-Gordon models; they are based on $\mathbb{Z}_2^2$-graded color Lie algebras and their fields satisfy a parabosonic statististics. The mathematical tools here introduced are the $\mathbb{Z}_2^2$-graded covariant extensions of the Lax pair formalism and of the Polyakov's soldering procedure. The $\mathbb{Z}_2^2$-graded Sinh-Gordon model is derived from an affine $\mathbb{Z}_2^2$-graded color Lie algebra, mimicking a procedure originally introduced by Babelon-Bonora to derive the ordinary Sinh-Gordon model. The color Lie algebras under considerations are: the $6$-generator $\mathbb{Z}_2^2$-graded $sl_2$, the $\mathbb{Z}_2^2$-graded affine ${\widehat{sl_2}}$ algebra with two central extensions, the $\mathbb{Z}_2^2$-graded Virasoro algebra obtained from a Hamiltonian reduction., Comment: 25 pages

Zero-knowledge proofs have emerged as a powerful tool for enhancing privacy and security in blockchain applications. However, the efficiency and scalability of proof systems remain a significant challenge, particularly in the context of Merkle tree inclusion proofs. Traditional proof aggregation techniques based on AND logic suffer from high verification complexity and data communication overhead, limiting their practicality for large-scale applications. In this paper, we propose a novel proof aggregation approach based on OR logic, which enables the generation of compact and universally verifiable proofs for Merkle tree inclusion. By aggregating proofs using OR logic, we achieve a proof size that is independent of the number of leaves in the tree, and verification can be performed using any single valid leaf hash. This represents a significant improvement over AND aggregation, which requires the verifier to process all leaf hashes. We formally define the OR aggregation logic, describe the process of generating universal proofs, and provide a comparative analysis demonstrating the advantages of our approach in terms of proof size, verification data, and universality. Furthermore, we discuss the potential of combining OR and AND aggregation logics to create complex acceptance functions, enabling the development of expressive and efficient proof systems for various blockchain applications. The proposed techniques have the potential to significantly enhance the scalability, efficiency, and flexibility of zero-knowledge proof systems, paving the way for more practical and adaptive solutions in the blockchain ecosystem.

We consider a system of differential equations and obtain its solutions with exponential asymptotics and analyticity with respect to the spectral parameter. Solutions of such type have importance in studying spectral properties of differential operators. Here, we consider the system of first-order differential equations on a half-line with summable coefficients, containing a nonlinear dependence on the spectral parameter. We obtain fundamental systems of solutions with analyticity in certain sectors, in which it is possible to apply the method of successive approximations. We also construct non-fundamental systems of solutions with analyticity in a large sector, including two previously considered neighboring sectors. The obtained results admit applications in studying inverse spectral problems for the higher-order differential operators with distribution coefficients., Comment: This is an extended version of the paper accepted for publication in Lobachevskii Journal of Mathematics

This paper analyzes sustainable regional economic development and land use employing a case study of Russia. The economics of land management in Russia which is shaped by both historical legacies and contemporary policies represents an interesting conundrum. Following the dissolution of the Soviet Union, Russia embarked on a thorny and complex path towards the economic reforms and transformation characterized, among all, by the privatization and decentralization of land ownership. This transition was aimed at improving agricultural productivity and fostering sustainable regional economic development but also led to new challenges such as uneven distribution of land resources, unclear property rights, and underinvestment in rural infrastructure. However, managing all of that effectively poses significant challenges and opportunities. With the help of the comprehensive bibliographic network analysis, this study sheds some light on the current state of sustainable regional economic development and land use management in Russia. Its results and outcomes might be helpful for the researchers and stakeholders alike in devising effective strategies aimed at maximizing resources for sustainable land use, particularly within their respective regional economies., Comment: 11 pages, 4 figures, 2 tables

Addressing the critical challenge of ensuring data integrity in decentralized systems, this paper delves into the underexplored area of data falsification probabilities within Merkle Trees, which are pivotal in blockchain and Internet of Things (IoT) technologies. Despite their widespread use, a comprehensive understanding of the probabilistic aspects of data security in these structures remains a gap in current research. Our study aims to bridge this gap by developing a theoretical framework to calculate the probability of data falsification, taking into account various scenarios based on the length of the Merkle path and hash length. The research progresses from the derivation of an exact formula for falsification probability to an approximation suitable for cases with significantly large hash lengths. Empirical experiments validate the theoretical models, exploring simulations with diverse hash lengths and Merkle path lengths. The findings reveal a decrease in falsification probability with increasing hash length and an inverse relationship with longer Merkle paths. A numerical analysis quantifies the discrepancy between exact and approximate probabilities, underscoring the conditions for the effective application of the approximation. This work offers crucial insights into optimizing Merkle Tree structures for bolstering security in blockchain and IoT systems, achieving a balance between computational efficiency and data integrity., Comment: 7 pages

The Spin Physics Detector collaboration proposes to install a universal detector in the second interaction point of the NICA collider under construction (JINR, Dubna) to study the spin structure of the proton and deuteron and other spin-related phenomena using a unique possibility to operate with polarized proton and deuteron beams at a collision energy up to 27 GeV and a luminosity up to $10^{32}$ cm$^{-2}$ s$^{-1}$. As the main goal, the experiment aims to provide access to the gluon TMD PDFs in the proton and deuteron, as well as the gluon transversity distribution and tensor PDFs in the deuteron, via the measurement of specific single and double spin asymmetries using different complementary probes such as charmonia, open charm, and prompt photon production processes. Other polarized and unpolarized physics is possible, especially at the first stage of NICA operation with reduced luminosity and collision energy of the proton and ion beams. This document is dedicated exclusively to technical issues of the SPD setup construction.

Electronic Health Record (EHR) datasets from Intensive Care Units (ICU) contain a diverse set of data modalities. While prior works have successfully leveraged multiple modalities in supervised settings, we apply advanced self-supervised multi-modal contrastive learning techniques to ICU data, specifically focusing on clinical notes and time-series for clinically relevant online prediction tasks. We introduce a loss function Multi-Modal Neighborhood Contrastive Loss (MM-NCL), a soft neighborhood function, and showcase the excellent linear probe and zero-shot performance of our approach., Comment: Accepted as a Workshop Paper at TS4H@ICLR2024

Advances in Deep Learning have made possible reliable landmark tracking of human bodies and faces that can be used for a variety of tasks. We test a recent Computer Vision solution, MediaPipe Holistic (MPH), to find out if its tracking of the facial features is reliable enough for a linguistic analysis of data from sign languages, and compare it to an older solution (OpenFace, OF). We use an existing data set of sentences in Kazakh-Russian Sign Language and a newly created small data set of videos with head tilts and eyebrow movements. We find that MPH does not perform well enough for linguistic analysis of eyebrow movement - but in a different way from OF, which is also performing poorly without correction. We reiterate a previous proposal to train additional correction models to overcome these limitations.

In the rapidly evolving landscape of blockchain technology, ensuring the integrity and security of data is paramount. This study delves into the security aspects of Merkle Trees, a fundamental component in blockchain architectures, such as Ethereum. We critically examine the susceptibility of Merkle Trees to hash collisions, a potential vulnerability that poses significant risks to data security within blockchain systems. Despite their widespread application, the collision resistance of Merkle Trees and their robustness against preimage attacks have not been thoroughly investigated, leading to a notable gap in the comprehensive understanding of blockchain security mechanisms. Our research endeavors to bridge this gap through a meticulous blend of theoretical analysis and empirical validation. We scrutinize the probability of root collisions in Merkle Trees, considering various factors such as hash length and path length within the tree. Our findings reveal a direct correlation between the increase in path length and the heightened probability of root collisions, thereby underscoring potential security vulnerabilities. Conversely, we observe that an increase in hash length significantly reduces the likelihood of collisions, highlighting its critical role in fortifying security. The insights garnered from our research offer valuable guidance for blockchain developers and researchers, aiming to bolster the security and operational efficacy of blockchain-based systems., Comment: 4 figures

Studies of Cathode Strip Chamber longevity, comparing Ar+CO2 gas mixtures with fractions of 5%, 2%, and 0% CF4, were performed using several small cathode strip prototype chambers. In each trial, a localized source of radiation was used to irradiate up to an accumulated charge of about 300 mC/cm. Additionally, longevity of a uniformly irradiated prototype operating with 2% CF4 was studied at the CERN Gamma Irradiation Facility GIF++. Post-hoc analysis of the chamber electrodes using spectroscopy techniques was also done.

Blockchain technology has emerged as a revolutionary tool in ensuring data integrity and security in digital transactions. However, the current approaches to data verification in blockchain systems, particularly in Ethereum, face challenges in terms of efficiency and computational overhead. The traditional use of Merkle Trees and cryptographic hash functions, while effective, leads to significant resource consumption, especially for large datasets. This highlights a gap in existing research: the need for more efficient methods of data verification in blockchain networks. Our study addresses this gap by proposing an innovative aggregation scheme for Zero-Knowledge Proofs within the structure of Merkle Trees. We develop a system that significantly reduces the size of the proof and the computational resources needed for its generation and verification. Our approach represents a paradigm shift in blockchain data verification, balancing security with efficiency. We conducted extensive experimental evaluations using real Ethereum block data to validate the effectiveness of our proposed scheme. The results demonstrate a drastic reduction in proof size and computational requirements compared to traditional methods, making the verification process more efficient and economically viable. Our contribution fills a critical research void, offering a scalable and secure solution for blockchain data verification. The implications of our work are far-reaching, enhancing the overall performance and adaptability of blockchain technology in various applications, from financial transactions to supply chain management., Comment: 18 pages, 7 figures

We analytically investigate the one-excitation spin dynamics in a homogeneous closed spin-1/2 chain via diagonalization of the one-excitation block of the XX-Hamiltonian, which allows to derive the analytical expressions for probability amplitudes describing state transfers between any two spins of a chain. We analytically investigate the $M$-neighbor approximation ($M\ge 1$) of spin dynamics with arbitrary initial state and analyze its accuracy using special integral characteristics defined in terms of the above probability amplitudes. We find $M$ providing the required accuracy of evolution approximation for chains of different lengths.

The growing volume of online content prompts the need for adopting algorithmic systems of information curation. These systems range from web search engines to recommender systems and are integral for helping users stay informed about important societal developments. However, unlike journalistic editing the algorithmic information curation systems (AICSs) are known to be subject to different forms of malperformance which make them vulnerable to possible manipulation. The risk of manipulation is particularly prominent in the case when AICSs have to deal with information about false claims that underpin propaganda campaigns of authoritarian regimes. Using as a case study of the Russian disinformation campaign concerning the US biolabs in Ukraine, we investigate how one of the most commonly used forms of AICSs - i.e. web search engines - curate misinformation-related content. For this aim, we conduct virtual agent-based algorithm audits of Google, Bing, and Yandex search outputs in June 2022. Our findings highlight the troubling performance of search engines. Even though some search engines, like Google, were less likely to return misinformation results, across all languages and locations, the three search engines still mentioned or promoted a considerable share of false content (33% on Google; 44% on Bing, and 70% on Yandex). We also find significant disparities in misinformation exposure based on the language of search, with all search engines presenting a higher number of false stories in Russian. Location matters as well with users from Germany being more likely to be exposed to search results promoting false information. These observations stress the possibility of AICSs being vulnerable to manipulation, in particular in the case of the unfolding propaganda campaigns, and underline the importance of monitoring performance of these systems to prevent it., Comment: 19 pages, 5 figures

A novel time-domain technique for supercapacitor characterization is developed, modeled numerically, and experimentally tested on a number of commercial supercapacitors. The method involves momentarily shorting a supercapacitor for a brief duration, denoted as $\tau$, and measuring first $\int Idt$ and second $\int I^2dt$ moments of current along with the potential before and after shorting. The effective $C(\tau)$ and $R(\tau)$ are then obtained from charge preservation and energy dissipation invariants. A linear behavior in $[R(\tau),C(\tau)]$ parametric plot is observed by several orders of $\tau$. This gives a $C/R$ characteristic slope: how much $\Delta C$ we can ``gain'' if we are ready to ``lose'' $\Delta R$ in internal resistance. The $C/R$ characteristic slope characterizes possible energy and power properties of the device in terms of materials and technology used, this is a measure of supercapacitor perfection. The technique has been proven with experimental measurements and then validated through computer modeling, analytic analysis, and impedance spectroscopy on a number of circuit types: transmission line, binary tree, etc., a new n-tree element (nTE) is introduced. The approach offers an alternative to low-frequency impedance spectroscopy and methods outlined in the IEC 62391 standard. It provides valuable insights into the performance and characteristics of supercapacitors., Comment: The technique from arXiv:1908.02559 was extended to obtain R({\tau}). A generalization from [Re Z({\omega}),Im Z({\omega})] to [R({\tau}),C({\tau})] is the main concept of Time Domain Spectroscopy