Locally-iterative Distributed (Δ + 1)-coloring and Applications

We consider graph coloring and related problems in the distributed message-passing model. Locally-iterative algorithms are especially important in this setting. These are algorithms in which each vertex decides about its next color only as a function of the current colors in its 1-hop-neighborhood . In STOC’93 Szegedy and Vishwanathan showed that any locally-iterative Δ + 1-coloring algorithm requires Ω (Δ log Δ + log * n ) rounds, unless there exists “a very special type of coloring that can be very efficiently reduced” [ 44 ]. No such special coloring has been found since then. This led researchers to believe that Szegedy-Vishwanathan barrier is an inherent limitation for locally-iterative algorithms and to explore other approaches to the coloring problem [ 2 , 3 , 19 , 32 ]. The latter gave rise to faster algorithms, but their heavy machinery that is of non-locally-iterative nature made them far less suitable to various settings. In this article, we obtain the aforementioned special type of coloring. Specifically, we devise a locally-iterative Δ + 1-coloring algorithm with running time O (Δ + log * n ), i.e., below Szegedy-Vishwanathan barrier. This demonstrates that this barrier is not an inherent limitation for locally-iterative algorithms. As a result, we also achieve significant improvements for dynamic, self-stabilizing, and bandwidth-restricted settings. This includes the following results: We obtain self-stabilizing distributed algorithms for Δ + 1-vertex-coloring, (2Δ - 1)-edge-coloring, maximal independent set, and maximal matching with O (Δ + log * n ) time. This significantly improves previously known results that have O(n) or larger running times [ 23 ]. We devise a (2Δ - 1)-edge-coloring algorithm in the CONGEST model with O (Δ + log * n ) time and O (Δ)-edge-coloring in the Bit-Round model with O (Δ + log n ) time. The factors of log * n and log n are unavoidable in the CONGEST and Bit-Round models, respectively. Previously known algorithms had superlinear dependency on Δ for (2Δ - 1)-edge-coloring in these models. We obtain an arbdefective coloring algorithm with running time O (√ Δ + log * n ). Such a coloring is not necessarily proper, but has certain helpful properties. We employ it to compute a proper (1 + ε)Δ-coloring within O (√ Δ + log * n ) time and Δ + 1-coloring within O (√ Δ log Δ log * Δ + log * n ) time. This improves the recent state-of-the-art bounds of Barenboim from PODC’15 [ 2 ] and Fraigniaud et al. from FOCS’16 [ 19 ] by polylogarithmic factors. Our algorithms are applicable to the SET-LOCAL model [ 25 ] (also known as the weak LOCAL model). In this model a relatively strong lower bound of Ω (Δ 1/3 ) is known for Δ + 1-coloring. However, most of the coloring algorithms do not work in this model. (In Reference [ 25 ] only Linial’s O (Δ 2 )-time algorithm and Kuhn-Wattenhofer O (Δ log Δ)-time algorithms are shown to work in it.) We obtain the first linear-in-Δ Δ + 1-coloring algorithms that work also in this model.

Engineering a PAM-flexible SpdCas9 variant as a universal gene repressor

The RNA-guided CRISPR-associated Cas9 proteins have been widely applied in programmable genome recombination, base editing or gene regulation in both prokaryotes and eukaryotes. SpCas9 from Streptococcus pyogenes is the most extensively engineered Cas9 with robust and manifold functionalities. However, one inherent limitation of SpCas9 is its stringent 5′-NGG-3′ PAM requirement that significantly restricts its DNA target range. Here, to repurpose SpCas9 as a universal gene repressor, we generate and screen variants of the deactivated SpCas9 (SpdCas9) with relaxed 5′-CAT-3′ PAM compatibility that can bind to the start codon ATG of almost any gene. Stepwise structure-guided mutations of the PAM-interacting residues and auxiliary PAM-proximal residues of the SpdNG (5′-NG-3′ PAM) create a PAM-flexible variant SpdNG-LWQT that preferentially accommodates 5′-NRN-3′ PAMs. SpdNG-LWQT is demonstrated to be effective in gene repression with the advantage of customizable sgRNA design in both Escherichia coli and Saccharomyces cerevisiae. This work validates the feasibility of purposeful PAM expansion of Cas9 towards signature PAMs and establishes a universal SpdCas9-based gene repressor.

Seamlessly Unifying Attributes and Items: Conversational Recommendation for Cold-start Users

Static recommendation methods like collaborative filtering suffer from the inherent limitation of performing real-time personalization for cold-start users. Online recommendation, e.g., multi-armed bandit approach, addresses this limitation by interactively exploring user preference online and pursuing the exploration-exploitation (EE) trade-off. However, existing bandit-based methods model recommendation actions homogeneously. Specifically, they only consider the items as the arms, being incapable of handling the item attributes , which naturally provide interpretable information of user’s current demands and can effectively filter out undesired items. In this work, we consider the conversational recommendation for cold-start users, where a system can both ask the attributes from and recommend items to a user interactively. This important scenario was studied in a recent work [54]. However, it employs a hand-crafted function to decide when to ask attributes or make recommendations. Such separate modeling of attributes and items makes the effectiveness of the system highly rely on the choice of the hand-crafted function, thus introducing fragility to the system. To address this limitation, we seamlessly unify attributes and items in the same arm space and achieve their EE trade-offs automatically using the framework of Thompson Sampling. Our Conversational Thompson Sampling (ConTS) model holistically solves all questions in conversational recommendation by choosing the arm with the maximal reward to play. Extensive experiments on three benchmark datasets show that ConTS outperforms the state-of-the-art methods Conversational UCB (ConUCB) [54] and Estimation—Action—Reflection model [27] in both metrics of success rate and average number of conversation turns.

Law’s Elasticity An Inquiry into the Relation of Law and Power in Finance

Law is a powerful commitment device. By entering into a binding contract, a contracting party can invoke the coercive law enforcement powers of states to compel another party to perform. Many, if not most, contracts are carried out without ever invoking these coercive powers; they operate in the shadow of the law. Less attention has been paid to the flip side of law’s shadow: the possibility of relaxing or suspending the full force of the law, or making law elastic. While this may seem anathema to the “rule of law”, it is not an infrequent occurrence, especially in times of crisis. The elasticity of law should be distinguished from the incompleteness of law, that is, the inherent limitation lawmakers face in trying to anticipate all future contingencies. In this paper I will offer two tales of the American Insurance Group (AIG) to illustrate the elasticity of contracts as well as of law.

Development and Experimental Validation for Quantifying the Moisture Carryover in a Moisture Separator Using an Air/Water Test Facility

The moisture carryover (MCO) of the primary separator in a steam generator is the most important design parameter to ensure high efficiency in a steam generator. There is an inherent limitation to experimentally evaluate the MCO under the prototype conditions. In this study, the air/water test facility was constructed based on the similarity law, and a new isokinetic system was developed to quantify the MCO. Several experiments were performed for the mass quality ranging from 0.315 to 0.382. The accuracy and versatility of the experimental method was verified experimentally using a full and half scale of separators. The test results were compared with the prototype results. It was proved to be a reliable experimental method for evaluating the MCO of the moisture separator.

Tracking single particles for hours via continuous DNA-mediated fluorophore exchange

Monitoring biomolecules in single-particle tracking experiments is typically achieved by employing fixed organic dyes or fluorescent fusion proteins linked to a target of interest. However, photobleaching typically limits observation times to merely a few seconds, restricting downstream statistical analysis and observation of rare biological events. Here, we overcome this inherent limitation via continuous fluorophore exchange using DNA-PAINT, where fluorescently-labeled oligonucleotides reversibly bind to a single-stranded DNA handle attached to the target molecule. Such versatile and facile labeling allows uninterrupted monitoring of single molecules for extended durations. We demonstrate the power of our approach by observing DNA origami on membranes for tens of minutes, providing perspectives for investigating cellular processes on physiologically relevant timescales.

Use of a Collar-Mounted Triaxial Accelerometer to Predict Speed and Gait in Dogs

Accelerometry has been used to measure treatment efficacy in dogs with osteoarthritis, although interpretation is difficult. Simplification of the output into speed or gait categories could simplify interpretation. We aimed to determine whether collar-mounted accelerometry could estimate the speed and categorise dogs’ gait on a treadmill. Eight Huntaway dogs were fitted with a triaxial accelerometer and then recorded using high-speed video on a treadmill at a slow and fast walk, trot, and canter. The accelerometer data (delta-G) was aligned with the video data and records of the treadmill speed and gait. Mixed linear and logistic regression models that included delta-G and a term accounting for the dogs’ skeletal sizes were used to predict speed and gait, respectively, from the accelerometer signal. Gait could be categorised (pseudo-R2 = 0.87) into binary categories of walking and faster (trot or canter), but not into the separate faster gaits. The estimation of speed above 3 m/s was inaccurate, though it is not clear whether that inaccuracy was due to the sampling frequency of the particular device, or whether that is an inherent limitation of collar-mounted accelerometers in dogs. Thus, collar-mounted accelerometry can reliably categorise dogs’ gaits into two categories, but finer gait descriptions or speed estimates require individual dog modelling and validation. Nonetheless, this accelerometry method could improve the use of accelerometry to detect treatment effects in osteoarthritis by allowing the selection of periods of activity that are most affected by treatment.

Joint desirability foundations of social choice and opinion pooling

We develop joint foundations for the fields of social choice and opinion pooling using coherent sets of desirable gambles, a general uncertainty model that allows to encompass both complete and incomplete preferences. This leads on the one hand to a new perspective of traditional results of social choice (in particular Arrow’s theorem as well as sufficient conditions for the existence of an oligarchy and democracy) and on the other hand to using the same framework to analyse opinion pooling. In particular, we argue that weak Pareto (unanimity) should be given the status of a rationality requirement and use this to discuss the aggregation of experts’ opinions based on probability and (state-independent) utility, showing some inherent limitation of this framework, with implications for statistics. The connection between our results and earlier work in the literature is also discussed.

Sub 3-Hour Marathon Runners for Five Consecutive Decades Demonstrate a Reduced Age-Related Decline in Performance

Estimation of the age-related decline in athletic performance by analyzing age-group world record performances presents an inherent limitation because the records generally belong to different individuals. Longitudinal studies describing the changes in performance with advancing age for the same individuals with a consistent training regimen are more appropriate to determine age-related changes in performance. The aim of this longitudinal study was to examine the age-related decline in running performance of sub 3-h marathoners for five consecutive calendar decades. The best marathon performances for each decade from the 1970s to the 2010s were analyzed for 40 sub 3-h runners (39 males and 1 female). The cohort mean personal best performance was 2 h 23 min ± 9 min at an age of 28.6 ± 4.7 years. The mean difference in age between the first and the last sub 3-h marathon races was 32.9 ± 1.6 years. The time difference in marathon performance between the personal best and the worst performance during the 5th decade was 26 ± 9 min, corresponding to a mean increase of 1 min 4 s per year, i.e., a decrease in running speed of 0.67 ± 0.29% per year. These results suggest that with consistent training and racing regimens, it is possible to limit the age-related decline in marathon performance to less than 7% per decade at least until 60 years of age. Further studies are required to verify if such a low rate of age-related decline in endurance performance could be maintained after 60 years of age.

Numerical Study of the Thermodynamic Uncertainty Relation for the KPZ-Equation

A general framework for the field-theoretic thermodynamic uncertainty relation was recently proposed and illustrated with the $$(1+1)$$ ( 1 + 1 ) dimensional Kardar–Parisi–Zhang equation. In the present paper, the analytical results obtained there in the weak coupling limit are tested via a direct numerical simulation of the KPZ equation with good agreement. The accuracy of the numerical results varies with the respective choice of discretization of the KPZ non-linearity. Whereas the numerical simulations strongly support the analytical predictions, an inherent limitation to the accuracy of the approximation to the total entropy production is found. In an analytical treatment of a generalized discretization of the KPZ non-linearity, the origin of this limitation is explained and shown to be an intrinsic property of the employed discretization scheme.