### Top 10 Arxiv Papers Today

##### #1. Signals of a Quantum Universe
###### Daniel Green, Rafael A. Porto
Structure in the Universe is widely believed to have originated from quantum fluctuations during an early epoch of accelerated expansion. Yet, the patterns we observe today do not distinguish between quantum or classical primordial fluctuations; current cosmological data is consistent with either possibility. We argue here that a detection of primordial non-Gaussianity can resolve the present situation, and provide a litmus-test for the quantum origin of cosmic structure. Unlike in quantum mechanics, vacuum fluctuations cannot arise in classical theories and therefore long-range classical correlations must result from (real) particles in the initial state. Similarly to flat-space scattering processes, we show how basic principles require these particles to manifest themselves as poles in the $n$-point functions, in the so-called folded configurations. Following this observation, and assuming fluctuations are (i) correlated over large scales, and (ii) generated by local evolution during an inflationary phase, we demonstrate that:...
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RelativityPaper: Signals of a Quantum Universe. https://t.co/t7KmKjyOzY
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##### #2. Learning to Catch Security Patches
###### Arthur D. Sawadogo, Tegawendé F. Bissyandé, Naouel Moha, Kevin Allix, Jacques Klein, Li Li, Yves Le Traon
Timely patching is paramount to safeguard users and maintainers against dire consequences of malicious attacks. In practice, patching is prioritized following the nature of the code change that is committed in the code repository. When such a change is labeled as being security-relevant, i.e., as fixing a vulnerability, maintainers rapidly spread the change and users are notified about the need to update to a new version of the library or of the application. Unfortunately, oftentimes, some security-relevant changes go unnoticed as they represent silent fixes of vulnerabilities. In this paper, we propose a Co-Training-based approach to catch security patches as part of an automatic monitoring service of code repositories. Leveraging different classes of features, we empirically show that such automation is feasible and can yield a precision of over 90% in identifying security patches, with an unprecedented recall of over 80%. Beyond such a benchmarking with ground truth data which demonstrates an improvement over the...
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##### #3. On $σ$-arithmetic graphs of finite groups
###### Alexander N. Skiba
Let $G$ be a finite group and $\sigma$ a partition of the set of all? primes $\Bbb{P}$, that is, $\sigma =\{\sigma_i \mid i\in I \}$, where $\Bbb{P}=\bigcup_{i\in I} \sigma_i$ and $\sigma_i\cap \sigma_j= \emptyset$ for all $i\ne j$. If $n$ is an integer, we write $\sigma(n)=\{\sigma_i \mid \sigma_{i}\cap \pi (n)\ne \emptyset \}$ and $\sigma (G)=\sigma (|G|)$. We call a graph $\Gamma$ with the set of all vertices $V(\Gamma)=\sigma (G)$ ($G\ne 1$) a $\sigma$-arithmetic graph of $G$, and we associate with $G\ne 1$ the following three directed $\sigma$-arithmetic graphs: (1) the $\sigma$-Hawkes graph $\Gamma_{H\sigma }(G)$ of $G$ is a $\sigma$-arithmetic graph of $G$ in which $(\sigma_i, \sigma_j)\in E(\Gamma_{H\sigma }(G))$ if $\sigma_j\in \sigma (G/F_{\{\sigma_i\}}(G))$; (2) the $\sigma$-Hall graph $\Gamma_{\sigma Hal}(G)$ of $G$ in which $(\sigma_i, \sigma_j)\in E(\Gamma_{\sigma Hal}(G))$ if for some Hall $\sigma_i$-subgroup $H$ of $G$ we have $\sigma_j\in \sigma (N_{G}(H)/HC_{G}(H))$; (3) the $\sigma$-Vasil'ev-Murashko...
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mathGRbot: Alexander N. Skiba : On $σ$-arithmetic graphs of finite groups https://t.co/suaDUaiazE https://t.co/iRLeiuPzyX
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##### #4. A Combinatorial View of the Service Rates of Codes Problem, its Equivalence to Fractional Matching and its Connection with Batch Codes
###### Fatemeh Kazemi, Esmaeil Karimi, Emina Soljanin, Alex Sprintson
We propose a novel technique for constructing a graph representation of a code through which we establish a significant connection between the service rate problem and the well-known fractional matching problem. Using this connection, we show that the service capacity of a coded storage system equals the fractional matching number in the graph representation of the code, and thus is lower bounded and upper bounded by the matching number and the vertex cover number, respectively. This is of great interest because if the graph representation of a code is bipartite, then the derived upper and lower bounds are equal, and we obtain the capacity. Leveraging this result, we characterize the service capacity of the binary simplex code whose graph representation, as we show, is bipartite. Moreover, we show that the service rate problem can be viewed as a generalization of the multiset primitive batch codes problem.
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mathITbot: Fatemeh Kazemi, Esmaeil Karimi, Emina Soljanin, Alex Sprintson : A Combinatorial View of the Service Rates of Codes Problem, its Equivalence to Fractional Matching and its Connection with Batch Codes https://t.co/eauRAIQeiA https://t.co/K4PmsrRgKL
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##### #5. The geometric Burge correspondence and the partition function of polymer replicas
###### Elia Bisi, Neil O'Connell, Nikos Zygouras
We construct a geometric lifting of the Burge correspondence as a composition of local birational maps on generic Young-diagram-shaped arrays. We prove a fundamental link with the geometric Robinson-Schensted-Knuth correspondence and with the geometric Sch\"utzenberger involution. We also show a number of properties of the geometric Burge correspondence, also specializing them to the case of symmetric input arrays. In particular, our construction shows that such a mapping is volume preserving in log-log variables. As an application, we consider a model of two polymer paths of given length constrained to have the same endpoint, known as polymer replica. We prove that the distribution of the polymer replica partition function in a log-gamma random environment is a Whittaker measure, and deduce the corresponding Whittaker integral identity. For a certain choice of the parameters, we notice a distributional identity between our model and the symmetric log-gamma polymer studied by O'Connell, Sepp\"al\"ainen, and Zygouras (2014).
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mathPRb: Elia Bisi, Neil O'Connell, Nikos Zygouras : The geometric Burge correspondence and the partition function of polymer replicas https://t.co/PX9BrATTC4 https://t.co/7TBUsPtlLR
mathMPb: Elia Bisi, Neil O'Connell, Nikos Zygouras : The geometric Burge correspondence and the partition function of polymer replicas https://t.co/XtqKFZfySR https://t.co/LE9uilVK5I
MathPHYPapers: The geometric Burge correspondence and the partition function of polymer replicas. https://t.co/T455S3Wqbj
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##### #6. Sparse Interpolation in Terms of Multivariate Chebyshev Polynomials
###### Evelyne Hubert, Michael F. Singer
Sparse interpolation} refers to the exact recovery of a function as a short linear combination of basis functions from a limited number of evaluations. For multivariate functions, the case of the monomial basis is well studied, as is now the basis of exponential functions. Beyond the multivariate Chebyshev polynomial obtained as tensor products of univariate Chebyshev polynomials, the theory of root systems allows to define a variety of generalized multivariate Chebyshev polynomials that have connections to topics such as Fourier analysis and representations of Lie algebras. We present a deterministic algorithm to recover a function that is the linear combination of at most r such polynomials from the knowledge of r and an explicitly bounded number of evaluations of this function.
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##### #7. On infinite variants of De Morgan law in locale theory
###### Igor Arrieta
A locale, being a complete Heyting algebra, satisfies De Morgan law $(a\vee b)^*=a^*\wedge b^*$ for pseudocomplements. The dual De Morgan law $(a\wedge b)^*={a^* \vee b^*}$ (here referred to as the second De Morgan law) is equivalent to, among other conditions, $(a\vee b)^{**} =a^{**}\vee b^{**}$, and characterizes the class of extremally disconnected locales. This paper presents a study of the subclasses of extremally disconnected locales determined by the infinite versions of the second De Morgan law and its equivalents.
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mathGNb: Igor Arrieta : On infinite variants of De Morgan law in locale theory https://t.co/No7tZjAfkX https://t.co/LGzkNQ7TQ5
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##### #8. Reflex motion in the Milky Way stellar halo resulting from the Large Magellanic Cloud infall
###### Michael S. Petersen, Jorge Peñarrubia
We present the results of N-body models of the Milky Way and Large Magellanic Cloud system and study the kinematic reflex motion in the stellar halo owing to the barycentre displacement of the disc. In agreement with previous studies, we find that the Milky Way disc may be moving at 40 km/s relative to the barycentre prior to the Large Magellanic Cloud infall. The resulting reflex motion is visible in tangential velocities of the stellar halo as a simple dipole. The signal is strongest for stars with long dynamical times, identifiable in position-velocity data as stars with large apocentres, whose dynamical memory is still well-represented by the unperturbed Milky Way potential. The signal varies across the sky depending on the stellar tracer and may be up to the same magnitude as the velocity of the disc centre-of-mass, making reflex motion a source of bias for Milky Way potential determinations based on the modeling of stellar streams and/or smooth halo tracers such as blue horizontal branch or RR Lyrae stars.
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##### #9. Aggregation and Data Driven Identification of Building Thermal Dynamic Model and Unmeasured Disturbance
###### Zhong Guo, Austin R. Coffman, Jeffrey Munk, Piljae Im, Teja Kuruganti, Prabir Barooah
An aggregate model is a single-zone equivalent of a multi-zone building, and is useful for many purposes, including model based control of large heating, ventilation and air conditioning (HVAC) equipment. This paper deals with the problem of simultaneously identifying an aggregate thermal dynamic model and unknown disturbances from input-output data. The unknown disturbance is a key challenge since it is not measurable but non-negligible. We first present a principled method to aggregate a multi-zone building model into a single zone model, and show the aggregation is not as trivial as it has been assumed in the prior art. We then provide a method to identify the parameters of the model and the unknown disturbance for this aggregate (single-zone) model. Finally, we test our proposed identification algorithm to data collected from a multi-zone building testbed in Oak Ridge National Laboratory. A key insight provided by the aggregation method allows us to recognize under what conditions the estimation of the disturbance signal will...
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##### #10. The Orbit of Planet Nine Derived from Engineering Physics
###### Robert Finch, Mattia A. Galiazzo
Several papers have recently suggested the possible presence of a ninth planet (Planet X) that might explain the gravitational perturbations of a number of detached Trans-Neptunian objects. To analyze the possibility further, we have applied celestial mechanics, engineering physics and statistical analysis to develop improved estimates of the planet's primary orbital elements and mass from first engineering principles, using the orbital characteristics of both the original group of 6 objects analyzed and also a second group comprising the original 6 together with 6 additional long-period asteroids selected by the authors. We show that the driving force behind the observed clustering is gravitational torque that arranges the orbits of asteroids in a systematic, orderly manner, and we develop the associated equations of motion. As evidence we show that the expected effects are fully apparent in the orbital characteristics of the correlated bodies involved, including most strikingly regarding their orbital planes, azimuth...
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