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We formalize symmetry breaking as a set-covering problem. For the case of breaking symmetries on graphs, a permutation covers a graph if applying it to the graph yields a smaller graph in a given order. Canonical graphs are those that cannot be made smaller by any permutation. A complete symmetry break is then a set of permutations that covers all non-canonical graphs. A complete symmetry break with a minimal number of permutations can be obtained by solving an optimal set-covering problem. The challenge is in the sizes of the corresponding set-covering problems and in how these can be tamed. The set-covering perspective on symmetry breaking opens up a range of new opportunities deriving from decades of studies on both precise and approximate techniques for this problem. Application of our approach leads to optimal LexLeader symmetry breaks for graphs of order $n\leq 10$ as well as to partial symmetry breaks which improve on the state-of-the-art.
We propose a novel framework to analyze symmetry breaking in dynamical systems through the lens of entropy and information transfer. Information transfer quantifies the directional exchange of entropy between observables, allowing us to anticipate the onset of symmetry breaking. For local symmetry breakings, namely, local Spontaneous Symmetry Breaking (SSB) and Dynamical Symmetry Breaking (DSB), we show that as a system loses symmetry, its trajectories exhibit a pronounced slowdown accompanied by an increase in Shannon entropy. This establishes a direct link between symmetry loss, dynamical slowing down, and entropy growth. We also extend the analysis to global symmetry breaking and characterize its associated entropy change. Finally, we demonstrate the efficacy of the proposed framework using representative examples, showing that information theoretic quantities can serve as reliable precursors and diagnostics of symmetry breaking transitions.
Disc warping, and possibly disc breaking, has been observed in protoplanetary discs around both single and multiple stars. Large warps can break the disc, producing multiple observational signatures. In this work, we use comparisons of disc timescales to derive updated formulae for disc breaking, with better predictions as to when and where a disc is expected to break and how many breaks could occur. Disc breaking is more likely for discs with small inner cavities, cooler temperatures, and steeper power-law profiles, such that thin, polar-aligning discs are more likely to break. We test our analytic formulae using 3D grid-based simulations of protoplanetary discs warped by the gravitational torque of an inner binary. We reproduce the expected warp behaviors in different viscosity regimes and observe disc breaking at locations in agreement with our derived equations. As our simulations only show disc breaking when disc viscosity is low, we also consider a viscous criterion for disc breaking, where rapid alignment to the precession vector can prevent a break by reducing the maximum misalignment between neighboring rings. We apply these results to the GW Orionis circumtriple disc, and
Symmetry breaking for graphs and other combinatorial objects is notoriously hard. On the one hand, complete symmetry breaks are exponential in size. On the other hand, current, state-of-the-art, partial symmetry breaks are often considered too weak to be of practical use. Recently, the concept of graph patterns has been introduced and provides a concise representation for (large) sets of non-canonical graphs, i.e.\ graphs that are not lex-leaders and can be excluded from search. In particular, four (specific) graph patterns apply to identify about 3/4 of the set of all non-canonical graphs. Taking this approach further we discover that graph patterns that derive from permutations that are involutions play an important role in the construction of symmetry breaks for graphs. We take advantage of this to guide the construction of partial and complete symmetry breaking constraints based on graph patterns. The resulting constraints are small in size and strong in the number of symmetries they break.
Contextuality and measurement incompatibility are two fundamental aspects of nonclassicality, and their manifestations in observed quantum correlations are often deeply interconnected. Recently, measurement incompatibility has been studied in connection with nonlocality, particularly in terms of their robustness under various quantum channels. This line of investigation helps establish a connection between the channels that break nonlocality and those that break incompatibility. In this study, we focus on an asymmetric bipartite Bell scenario involving three and four inputs on Alice and Bob sides, respectively, with each of these inputs having dichotomous outcomes. Under the assumption of locality, the observed statistics in this asymmetric scenario obeys the Elegant Bell inequality (EBI). Here, we use a different version of the EBI that relies on the assumption of the preparation noncontextuality. By taking the violation of this noncontextual version of EBI as a witness of preparation contextuality we establish a connection between the channels that break contextuality and the channels that break triple-wise measurement incompatibility. Our results suggest that any channel which b
Main sequence stars transition at mid-F spectral types from slowly rotating (cooler stars) to rapidly rotating (hotter stars), a transition known as the Kraft Break (Kraft 1967) and attributed the disappearance of the outer convective envelope, causing magnetic braking to become ineffective. To define this Break more precisely, we assembled spectroscopic measurements of 405 F stars within 33.33 pc. Once young, evolved and candidate binary stars are removed, the distribution of projected rotational velocities shows the Break to be well-defined and relatively sharp. Nearly all stars redder than G_BP-G_RP = 0.60 mag are slowly rotating (vsini < 20 km/s), while only 4 of 40 stars bluer than G_BP-G_RP = 0.54 mag are slowly rotating, consistent with that expected for a random distribution of inclinations. The Break is centered at an effective temperature of 6550 K and has a width of about 200 K, corresponding to a mass range of 1.32 - 1.41 M_Sun. The Break is ~450 K hotter than the stellar temperature at which hot Jupiters show a change in their obliquity distribution, often attributed to tidal realignment. The Break, as defined above, is nearly but not fully established in the ~650 M
Word Break is a prototypical factorization problem in string processing: Given a word $w$ of length $N$ and a dictionary $\mathcal{D} = \{d_1, d_2, \ldots, d_{K}\}$ of $K$ strings, determine whether we can partition $w$ into words from $\mathcal{D}$. We propose the first algorithm that solves the Word Break problem over the SLP-compressed input text $w$. Specifically, we show that, given the string $w$ represented using an SLP of size $g$, we can solve the Word Break problem in $\mathcal{O}(g \cdot m^ω + M)$ time, where $m = \max_{i=1}^{K} |d_i|$, $M = \sum_{i=1}^{K} |d_i|$, and $ω\geq 2$ is the matrix multiplication exponent. We obtain our algorithm as a simple corollary of a more general result: We show that in $\mathcal{O}(g \cdot m^ω + M)$ time, we can index the input text $w$ so that solving the Word Break problem for any of its substrings takes $\mathcal{O}(m^2 \log N)$ time (independent of the substring length). Our second contribution is a lower bound: We prove that, unless the Combinatorial $k$-Clique Conjecture fails, there is no combinatorial algorithm for Word Break on SLP-compressed strings running in $\mathcal{O}(g \cdot m^{2-ε} + M)$ time for any $ε> 0$.
Constructing a suitable schedule for sports competitions is a crucial issue in sports scheduling. The round-robin tournament is a competition adopted in many professional sports. For most round-robin tournaments, it is considered undesirable that a team plays consecutive away or home matches; such an occurrence is called a break. Accordingly, it is preferable to reduce the number of breaks in a tournament. A common approach is first to construct a schedule and then determine a home-away assignment based on the given schedule to minimize the number of breaks (first-schedule-then-break). In this study, we concentrate on the problem that arises in the second stage of the first-schedule-then-break approach, namely, the break minimization problem(BMP). We prove that this problem can be reduced to an odd cycle transversal problem, the well-studied graph problem. These results lead to a new approximation algorithm for the BMP.
We develop a projection-based decomposition to disentangle structural breaks in the factor variance and factor loadings. Our approach yields test statistics that can be compared against standard distributions commonly used in the structural break literature. Because standard methods for estimating factor models in macroeconomics normalize the factor variance, they do not distinguish between breaks of the factor variance and factor loadings. Applying our procedure to U.S. macroeconomic data, we find that the Great Moderation is more naturally accommodated as a break in the factor variance as opposed to a break in the factor loadings, in contrast to extant procedures which do not tell the two apart and thus interpret the Great Moderation as a structural break in the factor loadings. Through our projection-based decomposition, we estimate that the Great Moderation is associated with an over 70\% reduction in the total factor variance, highlighting the relevance of disentangling breaks in the factor structure.
Measurement of a jet geometry transition region is an important instrument of assessing the jet ambient medium properties, plasma bulk motion acceleration, parameters of a black hole and location of a jet launching radius. In this work we explore the possibility of a presence of a core shift break, associated with the geometry and jet physical properties transition. We obtain the relations on the core shift offset jump due to a change in a core shift exponent. The condition of a proper frame magnetic field continuity and the core shift break can be used as an instrument to refine the magnetic field estimates upstream the break. This method is applied to the jet in NGC 315. We speculate that the localised in a flow plasma heating either by reconnection or due to particles acceleration at the shock will also lead to a core shift break, but of a different type, than the one observed in NGC 315. We propose to use the multi-frequency core shift measurements to increase the number of sources with a detected jet shape break and to boost the accuracy of assessing the properties of a jet geometry transition region.
Oxidative DNA single strand breaks arise continuously in cells and defects in their repair have been implicated in neurological disease. While much progress has been made in understanding how chromosomal single strand breaks are repaired little is known about the changes chromatin structure that accompany this process. Here, we show that nascent recombinant histone H3.1 protein accumulates and is deposited into chromatin at sites of DNA strand breakage in quiescent human cells following oxidative stress, and that core components of the single-strand break repair machinery are required for this process. We show that the SSBR sensor and scaffold proteins poly (ADP-ribose) polymerase and XRCC1 facilitate accumulation of chromatin assembly factor-1 (CAF-1) at sites of oxidative DNA strand breakage, which in turn mediates the deposition of Histone H3.1. We also demonstrate that depletion of CAF-1 slows global rates of DNA strand break repair in quiescent cells following oxidative stress, demonstrating that single-strand break repair and histone deposition are tightly coordinated processes. These data describe a novel role for the DNA singlestrand break repair machinery and implicate his
Gamma-ray Burst (GRB) collimation has been inferred with the observations of achromatic steepening in GRB light curves, known as jet breaks. Identifying a jet break from a GRB afterglow lightcurve allows a measurement of the jet opening angle and true energetics of GRBs. In this paper, we reinvestigate this problem using a large sample of GRBs that have an optical jet break which is consistent with being achromatic in the X-ray band. Our sample includes 99 GRBs from February 1997 to March 2015 that have optical and, for Swift GRBs, X-ray lightcurves that are consistent with the jet break interpretation. Out of 99 GRBs we have studied, 55 GRBs are found to have temporal and spectral behaviors both before and after the break consistent with the theoretical predictions of the jet break models, respectively. These include 53 long/soft (Type II) and 2 short/hard (Type I) GRBs. Only 1 GRB is classified as the candidate of a jet break with energy injection. Another 41 and 3 GRBs are classified as the candidates with the lower and upper limits of the jet break time, respectively. The typical beaming correction factor $f_b^{-1} \sim 1000$ for Type II GRBs, suggesting an even higher total GR
This report explores the use of paragraph break probability estimates to help predict the location of sentence breaks in English natural language text. We show that a sentence break predictor based almost solely on paragraph break probability estimates can achieve high accuracy on this task. This sentence break predictor is trained almost entirely on a large amount of naturally occurring text without sentence break annotations, with only a small amount of annotated data needed to tune two hyperparameters. We also show that even better results can be achieved across in-domain and out-of-domain test data, if paragraph break probability signals are combined with a support vector machine classifier trained on a somewhat larger amount of sentence-break-annotated data. Numerous related issues are addressed along the way.
Rail breaks are one of the most common causes of derailments internationally. This is no different for the South African Iron Ore line. Many rail breaks occur as a heavy-haul train passes over a crack, large defect or defective weld. In such cases, it is usually too late for the train to slow down in time to prevent a de-railment. Knowing the risk of a rail break occurring associated with a train passing over a section of rail allows for better implementation of maintenance initiatives and mitigating measures. In this paper the Ore Line's specific challenges are discussed and the currently available data that can be used to create a rail break risk prediction model is reviewed. The development of a basic rail break risk prediction model for the Ore Line is then presented. Finally the insight gained from the model is demonstrated by means of discussing various scenarios of various rail break risk. In future work, we are planning on extending this basic model to allow input from live monitoring systems such as the ultrasonic broken rail detection system.
This study proposes a point estimator of the break location for a one-time structural break in linear regression models. If the break magnitude is small, the least-squares estimator of the break date has two modes at the ends of the finite sample period, regardless of the true break location. To solve this problem, I suggest an alternative estimator based on a modification of the least-squares objective function. The modified objective function incorporates estimation uncertainty that varies across potential break dates. The new break point estimator is consistent and has a unimodal finite sample distribution under small break magnitudes. A limit distribution is provided under an in-fill asymptotic framework. Monte Carlo simulation results suggest that the new estimator outperforms the least-squares estimator. I apply the method to estimate the break date in U.S. real GDP growth and U.S. and UK stock return prediction models.
We investigate the behaviour of a finite chain of Brownian particles, interacting through a pairwise potential $U$, with one end of the chain fixed and the other end pulled away, in the limit of slow pulling speed and small Brownian noise. We study the instant when and the place where the chain "breaks", that is, the distance between two neighbouring particles becomes larger than a certain threshold. We assume $U$ to be attractive and strictly convex up to the break distance, and three times continuously differentiable. We consider the regime, where both the pulling and the noise significantly influence the distribution of the break time and break position. It turns out that in this regime there is a universality of both the break time distribution and the break position distribution, in the sense that the limiting quantities do not depend on the details of $U$, but only on its curvature at the break distance.
The conventional derivation of the gamma-ray burst afterglow jet break time uses only the blast wave fluid Lorentz factor and therefore leads to an achromatic break. We show that in general gamma-ray burst afterglow jet breaks are chromatic across the self-absorption break. Depending on circumstances, the radio jet break may be postponed significantly. Using high-accuracy adaptive mesh fluid simulations in one dimension, coupled to a detailed synchrotron radiation code, we demonstrate that this is true even for the standard fireball model and hard-edged jets. We confirm these effects with a simulation in two dimensions. The frequency dependence of the jet break is a result of the angle dependence of the emission, the changing optical depth in the self-absorbed regime and the shape of the synchrotron spectrum in general. In the optically thin case the conventional analysis systematically overestimates the jet break time, leading to inferred opening angles that are underestimated by a factor 1.32 and explosion energies that are underestimated by a factor 1.73, for explosions in a homogeneous environment.
In the set of 236 GRB afterglows observed by Swift between January 2005 and March 2007, we identify 30 X-ray light-curves whose power-law fall-off exhibit a steepening ("break") at 0.1-10 day after trigger, to a decay steeper than t^{-1.5}. For most of these afterglows, the X-ray spectral slope and the decay indices before and after the break can be accommodated by the standard jet model although a different origin of the breaks cannot be ruled out. In addition, there are 27 other afterglows whose X-ray light-curves may also exhibit a late break to a steep decay, but the evidence is not that compelling. The X-ray emissions of 38 afterglows decay slower than t^{-1.5} until after 3 day, half of them exhibiting such a slow decay until after 10 day. Therefore, the fraction of well-monitored Swift afterglows with potential jet-breaks is around 60 percent, whether we count only the strongest cases for each type or all of them. This fraction is comparable to the 75 percent of pre-Swift afterglows whose optical light-curves displayed similar breaks at ~1 day. The properties of the prompt emission of Swift afterglows with light-curve breaks show the same correlations (peak energy of GRB spe
Typical security contests focus on breaking or mitigating the impact of buggy systems. We present the Build-it Break-it Fix-it BIBIFI contest which aims to assess the ability to securely build software not just break it. In BIBIFI teams build specified software with the goal of maximizing correctness performance and security. The latter is tested when teams attempt to break other teams submissions. Winners are chosen from among the best builders and the best breakers. BIBIFI was designed to be open-ended - teams can use any language tool process etc. that they like. As such contest outcomes shed light on factors that correlate with successfully building secure software and breaking insecure software. During we ran three contests involving a total of teams and two different programming problems. Quantitative analysis from these contests found that the most efficient build-it submissions used CC but submissions coded in a statically-typed language were less likely to have a security flaw build-it teams with diverse programming-language knowledge also produced more secure code. Shorter programs correlated with better scores. Break-it teams that were also build-it teams were significan
A minimal SO(10) model with {\bf 126} Higgs field breaking B-L symmetry has been shown recently to predict large solar and atmospheric mixings in agreement with observations if it is assumed that the neutrino mass follows from the triplet dominated type II seesaw formula. No additional symmetries need to be assumed for this purpose. We discuss the conditions on the way SO(10) symmetry breaks down to MSSM and the Higgs multiplets in the model, required for the triplet dominated type II seesaw formula to hold. We find that (i) SO(10) must break to a nonminimal SU(5) before breaking to the standard model; (ii) $B-L$ symmetry must break at the time of SO(10) breaking and (iii) constraints of unification seem to require that the minimal model must have a {\bf 54} dimensional Higgs field together with a {\bf 210} and {\bf 126} to break the GUT symmetry.