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We prove that if the smallest modulus of a covering system with distinct moduli is $5$, then the largest modulus is at least 108. We also prove that if the smallest modulus of a covering system with distinct moduli is $5$, then the least common multiple of the moduli is at least 1440. Finally, we prove that if the smallest modulus of a covering system with distinct moduli is 6, then the least common multiple of the moduli is at least $5040$. The constants $108$, $1440$ and $5040$ are best possible. This resolves a conjecture of Krukenberg, a problem of Dalton and Trifonov, and a generalization thereof.
Cross-chain bridges are essential decentralized applications (DApps) to facilitate interoperability between different blockchain networks. Unlike regular DApps, the functionality of cross-chain bridges relies on the collaboration of information both on and off the chain, which exposes them to a wider risk of attacks. According to our statistics, attacks on cross-chain bridges have resulted in losses of nearly 4.3 billion dollars since 2021. Therefore, it is particularly necessary to understand and detect attacks on cross-chain bridges. In this paper, we collect the largest number of cross-chain bridge attack incidents to date, including 49 attacks that occurred between June 2021 and September 2024. Our analysis reveal that attacks against cross-chain business logic cause significantly more damage than those that do not. These cross-chain attacks exhibit different patterns compared to normal transactions in terms of call structure, which effectively indicates potential attack behaviors. Given the significant losses in these cases and the scarcity of related research, this paper aims to detect attacks against cross-chain business logic, and propose the BridgeGuard tool. Specifically,
Debugging transactions and understanding their execution are of immense importance for developing OLAP applications, to trace causes of errors in production systems, and to audit the operations of a database. However, debugging transactions is hard for several reasons: 1) after the execution of a transaction, its input is no longer available for debugging, 2) internal states of a transaction are typically not accessible, and 3) the execution of a transaction may be affected by concurrently running transactions. We present a debugger for transactions that enables non-invasive, post-mortem debugging of transactions with provenance tracking and supports what-if scenarios (changes to transaction code or data). Using reenactment, a declarative replay technique we have developed, a transaction is replayed over the state of the DB seen by its original execution including all its interactions with concurrently executed transactions from the history. Importantly, our approach uses the temporal database and audit logging capabilities available in many DBMS and does not require any modifications to the underlying database system nor transactional workload.
In addition to the regular Schwabe cycles of approximately 11 y, "prolonged solar activity minima" have been identified through the direct observation of sunspots and aurorae, as well as proxy data of cosmogenic isotopes. Some of these minima have been regarded as grand solar minima, which are arguably associated with the special state of the solar dynamo and have attracted significant scientific interest. In this paper, we review how these prolonged solar activity minima have been identified. In particular, we focus on the Dalton Minimum, which is named after John Dalton. We review Dalton's scientific achievements, particularly in geophysics. Special emphasis is placed on his lifelong observations of auroral displays over approximately five decades in Great Britain. Dalton's observations for the auroral frequency allowed him to notice the scarcity of auroral displays in the early 19th century. We analyze temporal variations in the annual frequency of such displays from a modern perspective. The contemporary geomagnetic positions of Dalton's observational site make his dataset extremely valuable because his site is located in the sub-auroral zone and is relatively sensitive to mino
The database of Prof. Rogers (1887), which includes wheat prices in England in the Middle Ages, was used to search for a possible influence of solar activity on the wheat market. We present a conceptual model of possible modes for sensitivity of wheat prices to weather conditions, caused by solar cycle variations, and compare expected price fluctuations with price variations recorded in medieval England. We compared statistical properties of the intervals between wheat price bursts during years 1249-1703 with statistical properties of the intervals between minimums of solar cycles during years 1700-2000. We show that statistical properties of these two samples are similar, both for characteristics of the distributions and for histograms of the distributions. We analyze a direct link between wheat prices and solar activity in the 17th Century, for which wheat prices and solar activity data (derived from 10Be isotope) are available. We show that for all 10 time moments of the solar activity minimums the observed prices were higher than prices for the correspondent time moments of maximal solar activity (100% sign correlation, on a significance level < 0.2%). We consider these resu
Read-only caches are widely used in cloud infrastructures to reduce access latency and load on backend databases. Operators view coherent caches as impractical at genuinely large scale and many client-facing caches are updated in an asynchronous manner with best-effort pipelines. Existing solutions that support cache consistency are inapplicable to this scenario since they require a round trip to the database on every cache transaction. Existing incoherent cache technologies are oblivious to transactional data access, even if the backend database supports transactions. We propose T-Cache, a novel caching policy for read-only transactions in which inconsistency is tolerable (won't cause safety violations) but undesirable (has a cost). T-Cache improves cache consistency despite asynchronous and unreliable communication between the cache and the database. We define cache-serializability, a variant of serializability that is suitable for incoherent caches, and prove that with unbounded resources T-Cache implements this new specification. With limited resources, T-Cache allows the system manager to choose a trade-off between performance and consistency. Our evaluation shows that T-Cache
As we are heading towards the next solar cycle, presumably with a relatively small amplitude, it is of significant interest to reconstruct and describe the past grand minima on the basis of actual observations of the time. The Dalton Minimum is often considered one of the grand minima captured in the coverage of telescopic observations. Nevertheless, the reconstructions of the sunspot group number vary significantly, and the existing butterfly diagrams have a large data gap during the period. This is partially because most long-term observations have remained unexplored in historical archives. Therefore, to improve our understanding on the Dalton Minimum, we have located two series of Thaddäus Derfflinger's observational records (a summary manuscript and logbooks) as well as his Brander's 5.5-feet azimuthal-quadrant preserved in the Kremsmünster Observatory. We have revised the existing Derfflinger's sunspot group number with Waldmeier classification and eliminated all the existing 'spotless days' to remove contaminations from solar meridian observations. We have reconstructed the butterfly diagram on the basis of his observations and illustrated sunspot distributions in both solar
Ethereum is a permissionless blockchain ecosystem that supports execution of smart contracts, the key enablers of decentralized finance (DeFi) and non-fungible tokens (NFT). However, the expressiveness of Ethereum smart contracts is a double-edged sword: while it enables blockchain programmability, it also introduces security vulnerabilities, i.e., the exploitable discrepancies between expected and actual behaviors of the contract code. To address these discrepancies and increase the vulnerability coverage, we propose a new smart contract security testing approach called transaction encapsulation. The core idea lies in the local execution of transactions on a fully-synchronized yet isolated Ethereum node, which creates a preview of outcomes of transaction sequences on the current state of blockchain. This approach poses a critical technical challenge -- the well-known time-of-check/time-of-use (TOCTOU) problem, i.e., the assurance that the final transactions will exhibit the same execution paths as the encapsulated test transactions. In this work, we determine the exact conditions for guaranteed execution path replicability of the tested transactions, and implement a transaction te
In addition to regular Schwabe cycles (~ 11 years), solar activity also shows longer periods of enhanced or reduced activity. Of these, reconstructions of the Dalton Minimum provide controversial sunspot group numbers and limited sunspot positions, partially due to limited source record accessibility. We analysed Stephan Prantner's sunspot observations from 1804--1844, the values of which had only been known through estimates despite their notable chronological coverage during the Dalton Minimum. We identified his original manuscript in Stiftsarchiv Wilten, near Innsbruck, Austria. We reviewed his biography (1782--1873) and located his observational sites at Wilten and Waidring, which housed the principal telescopes for his early and late observations: a 3.5-inch astronomical telescope and a Reichenbach 4-feet achromatic erecting telescope, respectively. We identified 215 days of datable sunspot observations, which are twice as much data as his estimated data in the existing database (= 115 days). Prantner counted up to 7--9 sunspot groups per day and measured sunspot positions, which show their distributions in both solar hemispheres. These results strikingly emphasise the differe
To minimize network latency and remain online during server failures and network partitions, many modern distributed data storage systems eschew transactional functionality, which provides strong semantic guarantees for groups of multiple operations over multiple data items. In this work, we consider the problem of providing Highly Available Transactions (HATs): transactional guarantees that do not suffer unavailability during system partitions or incur high network latency. We introduce a taxonomy of highly available systems and analyze existing ACID isolation and distributed data consistency guarantees to identify which can and cannot be achieved in HAT systems. This unifies the literature on weak transactional isolation, replica consistency, and highly available systems. We analytically and experimentally quantify the availability and performance benefits of HATs--often two to three orders of magnitude over wide-area networks--and discuss their necessary semantic compromises.
We present and analyse the sunspot observations performed by Franz I. C. Hallaschka in 1814 and 1816. These solar observations were carried out during the so-called Dalton minimum, around the maximum phase of the Solar Cycle 6. These records are very valuable because they allow us to complete observational gaps in the collection of sunspot group numbers, improving its coverage for this epoch. We have analysed and compared the observations made by Hallaschka with the records made by other contemporary observers. Unfortunately, the analysis of the sunspot areas and positions showed that they are too inaccurate for scientific use. But, we conclude that sunspot counts made by Hallaschka are similar to those made by other astronomers of that time. The observations by Hallaschka confirm a low level of the solar activity during the Dalton minimum.
This paper builds and extends on the authors' previous work related to the algorithmic tool, Cylindrical Algebraic Decomposition (CAD), and one of its core applications, Real Quantifier Elimination (QE). These topics are at the heart of symbolic computation and were first implemented in computer algebra systems decades ago, but have recently received renewed interest as part of the ongoing development of SMT solvers for non-linear real arithmetic. First, we consider the use of iterated univariate resultants in traditional CAD, and how this leads to inefficiencies, especially in the case of an input with multiple equational constraints. We reproduce the workshop paper [Davenport and England, 2023], adding important clarifications to our suggestions first made there to make use of multivariate resultants in the projection phase of CAD. We then consider an alternative approach to this problem first documented in [McCallum and Brown, 2009] which redefines the actual object under construction, albeit only in the case of two equational constraints. We correct an unhelpful typo and provide a proof missing from that paper. We finish by revising the topic of how to deal with SMT or Real QE
Over the past decades automated debugging has seen major achievements. However, as debugging is by necessity attached to particular programming paradigms, the results are scattered. To alleviate this problem, the Automated and Algorithmic Debugging workshop (AADEBUG for short) was organised in 1993 in Link"oping (Sweden). As this workshop proved to be successful, subsequent workshops have been organised in 1995 (Saint-Malo, France), 1997 (again in Link"oping, Sweden) and 2000 (Munich, Germany). In 2003, the workshop is organised in Ghent, Belgium, the proceedings of which you are reading right now.
Ethereum is one of the most popular platforms for the development of blockchain-powered applications. These applications are known as Dapps. When engineering Dapps, developers need to translate requests captured in the front-end of their application into one or more smart contract transactions. Developers need to pay for these transactions and, the more they pay (i.e., the higher the gas price), the faster the transaction is likely to be processed. Therefore developers need to optimize the balance between cost (transaction fees) and user experience (transaction processing times). Online services have been developed to provide transaction issuers (e.g., Dapp developers) with an estimate of how long transactions will take to be processed given a certain gas price. These estimation services are crucial in the Ethereum domain and several popular wallets such as Metamask rely on them. However, their accuracy has not been empirically investigated so far. In this paper, we quantify the transaction processing times in Ethereum, investigate the relationship between processing times and gas prices, and determine the accuracy of state-of-the-practice estimation services. We find that transact
Cosmology's standard model posits an infinite flat universe forever expanding under the pressure of dark energy. First-year data from the Wilkinson Microwave Anisotropy Probe (WMAP) confirm this model to spectacular precision on all but the largest scales (Bennett {\it et al.}, 2003 ; Spergel {\it et al.}, 2003). Temperature correlations across the microwave sky match expectations on scales narrower than $60^{\circ}$, yet vanish on scales wider than $60^{\circ}$. Researchers are now seeking an explanation of the missing wide-angle correlations (Contaldi {\it et al.}, 2003 ; Cline {\it et al.}, 2003). One natural approach questions the underlying geometry of space, namely its curvature (Efstathiou, 2003) and its topology (Tegmark {\it et al.}, 2003). In an infinite flat space, waves from the big bang would fill the universe on all length scales. The observed lack of temperature correlations on scales beyond $60^{\circ}$ means the broadest waves are missing, perhaps because space itself is not big enough to support them. Here we present a simple geometrical model of a finite, positively curved space -- the Poincaré dodecahedral space -- which accounts for WMAP's observations with no
I review the current status of combing weak gravitational lensing with depth information from redshifts as a direct probe of dark matter and dark energy in the Universe. In particular I highlight: (1) The first maximum likelihood measurement of the cosmic shear power spectrum, with the COMBO17 dataset (Brown et al 2003); (2) A new method for mapping the 3-D dark matter distribution from weak shear, and its first application to the COMBO17 dataset (Taylor et al 2003); (3) A new method for measuring the Dark Energy of the Universe using purely the geometry of gravitational lensing, based on cross-correlation tomography (Jain & Taylor 2003). I show that this method can constrain the equation of state of the universe and its evolution to a few percent accuracy.
There has been an increasing number of applications of machine learning to the field of Computer Algebra in recent years, including to the prominent sub-field of Symbolic Integration. However, machine learning models require an abundance of data for them to be successful and there exist few benchmarks on the scale required. While methods to generate new data already exist, they are flawed in several ways which may lead to bias in machine learning models trained upon them. In this paper, we describe how to use the Risch Algorithm for symbolic integration to create a dataset of elementary integrable expressions. Further, we show that data generated this way alleviates some of the flaws found in earlier methods.
This paper presents Pot, a system that leverages the concept of preordered transactions to achieve deterministic multithreaded execution of programs that use Transactional Memory. Preordered transactions eliminate the root cause of nondeterminism in transactional execution: they provide the illusion of executing in a deterministic serial order, unlike traditional transactions which appear to execute in a nondeterministic order that can change from execution to execution. Pot uses a new concurrency control protocol that exploits the serialization order to distinguish between fast and speculative transaction execution modes in order to mitigate the overhead of imposing a deterministic order. We build two Pot prototypes: one using STM and another using off-the-shelf HTM. To the best of our knowledge, Pot enables deterministic execution of programs using off-the-shelf HTM for the first time. An experimental evaluation shows that Pot achieves deterministic execution of TM programs with low overhead, sometimes even outperforming nondeterministic executions, and clearly outperforming the state of the art.
It is well known that the variable ordering can be critical to the efficiency or even tractability of the cylindrical algebraic decomposition (CAD) algorithm. We propose new heuristics inspired by complexity analysis of CAD to choose the variable ordering. These heuristics are evaluated against existing heuristics with experiments on the SMT-LIB benchmarks using both existing performance metrics and a new metric we propose for the problem at hand. The best of these new heuristics chooses orderings that lead to timings on average 17% slower than the virtual-best: an improvement compared to the prior state-of-the-art which achieved timings 25% slower.
We use the Pareto Joint Inversion, together with the Particle Swarm Optimization, to invert the Love and quasi-Rayleigh surface-wave speeds, obtained from dispersion curves, in order to infer the elasticity parameters, mass densities and layer thickness of the model for which these curves are generated. For both waves, we use the dispersion relations derived by Dalton et al. (2017). Numerical results are presented for three angular frequencies, 15 Hz, 60 Hz and 100 Hz, and for two, five and seven modes, respectively. Comparisons of the model parameters with the values inverted with error-free input indicate an accurate process. If, however, we introduce a 5% error to the input, the results become significantly less accurate, which indicates that the inverse operation, even though stable, is error-sensitive. Correlations between the inverted elasticity parameters indicate that the layer parameters are more sensitive to input errors than the halfspace parameters. In agreement with Dalton et al. (2017), the fundamental mode is mainly sensitive to the layer parameters whereas higher modes are sensitive to both the layer and halfspace properties; for the second mode, the results are mor