Miracle-dz/UniFAR-FTUs huggingface dataset:
Discovering the roots: Unifying and extending results on multivariate polynomial factoring in algebraic complexity

Multivariate polynomial factoring is one of the most important problems in theoretical computer science with many important applications in various regimes including decoding of Reed-Solomon, Reed-Muller codes [GS98, Sud97], integer factoring [LLMP90], algebra isomorphism [KS06, IKRS12] and primary decomposition of polynomial ideals [GTZ88]. Algebraic circuit is a natural model to represent a multivariate polynomial compactly. Here, an algebraic complexity class contains (multivariate) polynomial families instead of languages. It is a natural question whether an algebraic complexity class is closed under factoring. Famously, Kaltofen [Kal89] showed that VP (Valiant’s P), the class of low degree polynomials with small circuit representation, is uniformly closed under factoring, i.e. for a given d degree n variate polynomial f of circuit size s, there exists a randomized poly(snd)-time algorithm that outputs its factor as a circuit whose size is bounded by poly(snd). This fundamental result has several applications such as ‘hardness versus randomness’ in algebraic complexity [KI03, AV08, DSY09, AGS17], derandomization of Noether Normalization Lemma [Mul17], in the problem of circuit reconstruction [KS09, Sin16], and polynomial equivalence testing [Kay11]. It is still open whether low degree factor of high degree circuits of low complexity has low complexity or not, famously known as Factor Conjecture (due to Peter Bürgisser). In this paper, we show that for an algebraic circuit f (x1, . . . , xn) of size s we prove that each factor has size at most a polynomial in: s and the degree of the squarefree part of f . Consequently, if f1 is a 2Ω(n)-hard polynomial then any nonzero multiple ∏i f ei i is equally hard for arbitrary positive ei’s, assuming that ∑i deg( fi) is at most 2O(n). This result also establishes the fact that when square free degree of the given polynomial is small, factor conjecture is true. It is an old open question whether the class of poly(n)-sized formulas (resp. algebraic branching programs) is closed under factoring. We show that given a polynomial f of degree poly(n) and formula (resp. ABP) size nO(log n) we can find a similar size formula (resp. ABP) factor in randomized poly(nO(log n))-time. Consequently, if determinant requires nΩ(log n) size formula, then the same can be said about any of its nonzero multiples. We also use the same technique to derive the algebraic complexity of gcd of two polynomials. As part of our proofs, we present a general frame work that shows that under random linear transformation, any generic multivariate polynomial can be factored into a power series ring. Hence, we conclude that it is enough to approximate those power series roots. Moreover, the factorization adapts well to circuit complexity analysis. We generalize it to a matrix recurrence (allRootsNI) that approximates all the roots simultaneously. These techniques together help us to make progress towards the old open problems;
Net-Trainer-ST: A Swiss Army Knife for Pentesting, Based on Single Board Computer, for Cybersecurity Professionals and Hobbyists

 Abstract — This article was created as part of the developed master's thesis. It attempts to present a developed device, which will support the work of specialists dealing with broadly understood cybersecurity terms. The device is contrived to automate security tests. In addition, it simulates potential cyberattacks in the most realistic way possible, without causing permanent damage to the network, in order to maximize the quality of the subsequent corrections to the tested network systems. The proposed solution is a fully operational prototype created from commonly available electronic components and a single board computer. The focus of the article is not only put on the hardware part of the device but also on the theoretical and applicatory way in which implemented cybersecurity tests operate and examples of their results.
Evolutionary Origins of ORL Disorders

It is understood that our ancestors gained a strong evolutionary selective advantage in shaping the vocal tract that allowing them speak more intelligibly. However, humans pay heavy prices for the uniqueness of vocal tracts configuration. We precariously swallow our mouthful in exchange for speaking clearly, and the second heavy price humans pay is sleep snoring. Their evolutionary cause is that the respiratory system deriving on the wrong side and too late from the alimentary system. The fact that our nasal septum is usually curved contributes to these disorders. The reason of this is that a few million years ago humans had to compromise from the width of the birth canal with their pelvis in order to stand upright. As for our children’s ears, their development resembles the evolution of hominoids and they are far from smooth.
Trauma and Death in the Emergency Department: A Time to PAUSE (Promoting Acknowledgment, Unity, and Sympathy at the End of Life)

Background: Witnessing death can be difficult and emotionally draining for health care workers and presents a risk factor for burnout. The practice of a ritual pause at patient death to recognize the patient as a person, reflect, and acknowledge the health care team is an emerging intervention that has not been well studied in trauma. Objective: This study aims to explore the effect of a team pause on trauma team member attitudes after emergency department patient death. Methods: This is a pre- and postintervention study of the implementation of a Trauma PAUSE (Promoting Acknowledgment, Unity, and Sympathy at the End of Life) conducted from March 2018 to June 2020. Results: A total of 466 participated in this study. Emergency department employee responses to the pre- (296 of 745 employees contacted responded) and postimplementation surveys (170 of 732 employees contacted responded) were compared. Although not statistically significant, responses to the postsurvey suggested an increased connection to patients and belief in the need for a moment of silence following a death. Employees who had participated in a PAUSE (57/170) reported improvements in internal conflict, feeling of emptiness, resilience, and ability to move on to the next task. Overall, 84.2% (48/57) of Trauma PAUSE participants were satisfied with the Trauma PAUSE. Conclusion: The Trauma PAUSE is a meaningful way to help trauma staff members find peace, maintain resiliency, and readily shift their focus to providing care to other patients.
Super-resolution microscopy of single atoms in optical lattices

We report on image processing techniques and experimental procedures to determine the lattice-site positions of single atoms in an optical lattice with high reliability, even for limited acquisition time or optical resolution. Determining the positions of atoms beyond the diffraction limit relies on parametric deconvolution in close analogy to methods employed in super-resolution microscopy. We develop a deconvolution method that makes effective use of the prior knowledge of the optical transfer function, noise properties, and discreteness of the optical lattice. We show that accurate knowledge of the image formation process enables a dramatic improvement on the localization reliability. This allows us to demonstrate super-resolution of the atoms’ position in closely packed ensembles where the separation between particles cannot be directly optically resolved. Furthermore, we demonstrate experimental methods to precisely reconstruct the point spread function with sub-pixel resolution from fluorescence images of single atoms, and we give a mathematical foundation thereof. We also discuss discretized image sampling in pixel detectors and provide a quantitative model of noise sources in electron multiplying CCD cameras. The techniques developed here are not only beneficial to neutral atom experiments, but could also be employed to improve the localization precision of trapped ions for ultra precise force sensing.
Unveiling the physical conditions of the youngest disks

Context. Protoplanetary disks have been studied extensively, both physically and chemically, to understand the environment in which planets form. However, the first steps of planet formation are likely to occur already when the protostar and disk are still embedded in their natal envelope. The initial conditions for planet formation may thus be provided by these young embedded disks, of which the physical and chemical structure is poorly characterized. Aims. We aim to constrain the midplane temperature structure, one of the critical unknowns, of the embedded disk around L1527. In particular, we set out to determine whether there is an extended cold outer region where CO is frozen out, as is the case for Class II disks. This will show whether young disks are indeed warmer than their more evolved counterparts, as is predicted by physical models. Methods. We used archival ALMA data of 13CO J = 2–1, C18O J = 2–1 and N2D+J = 3–2 to directly observe the midplane of the near edge-on L1527 disk. The optically thick CO isotopologues allowed us to derive a radial temperature profile for the disk midplane, while N2D+, which can only be abundant when CO is frozen out, provides an additional constraint on the temperature. Moreover, the effect of CO freeze-out on the 13CO, C18O and N2D+ emission was investigated using 3D radiative transfer modeling. Results. Optically thick 13CO and C18O emission is observed throughout the disk and inner envelope, while N2D+ is not detected. Both CO isotopologues have brightness temperatures ≳25 K along the midplane. Disk and envelope emission can be disentangled kinematically, because the largest velocities are reached in the disk. A power law radial temperature profile constructed using the highest midplane temperature at these velocities suggest that the temperature is above 20 K out to at least 75 au, and possibly throughout the entire 125 au disk. The radiative transfer models show that a model without CO freeze-out in the disk matches the C18O observations better than a model with the CO snowline at ~70 au. In addition, there is no evidence for a large (order of magnitude) depletion of CO. Conclusions. The disk around L1527 is likely to be warm enough to have CO present in the gas phase throughout the disk, suggesting that young embedded disks can indeed be warmer than the more evolved Class II disks.
On the coherent rotation of diffuse matter in numerical simulations of clusters of galaxies

We present a study on the coherent rotation of the intracluster medium and dark matter components of simulated galaxy clusters extracted from a volume-limited sample of the MUSIC project. The set is re-simulated with three different recipes for the gas physics: $(i)$ non-radiative, $(ii)$ radiative without AGN feedback, and $(iii)$ radiative with AGN feedback. Our analysis is based on the 146 most massive clusters identified as relaxed, 57 per cent of the total sample. We classify these objects as rotating and non-rotating according to the gas spin parameter, a quantity that can be related to cluster observations. We find that 4 per cent of the relaxed sample is rotating according to our criterion. By looking at the radial profiles of their specific angular momentum vector, we find that the solid body model is not a suitable description of rotational motions. The radial profiles of the velocity of the dark matter show a prevalence of the random velocity dispersion. Instead, the intracluster medium profiles are characterized by a comparable contribution from the tangential velocity and the dispersion. In general, the dark matter component dominates the dynamics of the clusters, as suggested by the correlation between its angular momentum and the gas one, and by the lack of relevant differences among the three sets of simulations.
Partial Parsing for Structured Editors

Creating structured editors, which maintain a valid syntax tree at all times rather than allowing to edit program text, is typically a time consuming task. Recent work has investigated the use of existing general-purpose language grammars as a basis for automatically generating structured editors, thus considerably reducing the effort required. However, in these generated editors, input occurs through menu and mouse-based interaction, rather than via keyboard entry that is familiar to most users. In this paper we introduce modifications to a parser of general-purpose programming language grammars to support keyboard-centric interactions with generated structured editors. Specifically, we describe a system we call partial parsing to autocomplete language structures, removing the need for a menu of language constructs in favor of keyboard-based disambiguation. We demonstrate our system's applicability and performance for use in interactive, generated structured editors. Our system thus constitutes a step towards making structured editors generated from language grammars usable with more efficient and familiar keyboard-centric interactions.
Multiferroic materials and magnetoelectric physics: symmetry, entanglement, excitation, and topology

Multiferroics are those materials with more than one ferroic order, and magnetoelectricity refers to the mutual coupling between magnetism (spins and/or magnetic field) and electricity (electric dipoles and/or electric field). In spite of the long research history in the whole twentieth century, the discipline of multiferroicity has never been so highly active as that in the first decade of the twenty-first century, and it has become one of the hottest disciplines of condensed matter physics and materials science. A series of milestones and steady progress in the past decade have enabled our understanding of multiferroic physics substantially comprehensive and profound, which is further pushing forward the research frontier of this exciting area. The availability of more multiferroic materials and improved magnetoelectric performance are approaching to make the applications within reach. While seminal review articles covering the major progress before 2010 are available, an updated review addressing the new achievements since that time becomes imperative. In this review, following a concise outline of the basic knowledge of multiferroicity and magnetoelectricity, we summarize the important research activities on multiferroics, especially magnetoelectricity and related physics in the last six years. We consider not only single-phase multiferroics but also multiferroic heterostructures. We address the physical mechanisms regarding magnetoelectric coupling so that the backbone of this divergent discipline can be highlighted. A series of issues on lattice symmetry, magnetic ordering, ferroelectricity generation, electromagnon excitations, multiferroic domain structure and domain wall dynamics, and interfacial coupling in multiferroic heterostructures, will be revisited in an updated framework of physics. In addition, several emergent phenomena and related physics, including magnetic skyrmions and generic topological structures associated with magnetoelectricity will be discussed. The review is ended with a set of prospectives and forward-looking conclusions, which may inevitably reflect the authors' biased opinions but are certainly critical.
Change of surface critical current in the surface superconductivity and mixed states of superconducting niobium

A systematic study of irreversible magnetization was performed in bulk niobium after different surface treatments. Starting with smooth surfaces and abrading them, a strong increase of the critical current is observed up to an apparent limiting value. An impressive change of the critical current is also observed in the surface superconductivity (SSC) state, reaching values of the same order of magnitude as in the mixed state. We explain also the observation of strong SSC for magnetic fields perpendicular to large facets in terms of nucleation of superconductivity along bumps of a corrugated surface.
Singlet superconductivity in a single-crystal NiBi3 superconductor

Andreev reflection spectroscopy with unpolarized and highly spin-polarized currents has been utilized to study an intermetallic single-crystal superconductor NiBi3. Magnetoresistance at zero bias voltage of point contacts shows the occurrence and suppression of Andreev reflection by unpolarized and polarized current, respectively. The gap value, its symmetry and temperature dependence have been determined using an unpolarized current. The spin state in the NiBi3 sample is determined to be antiparallel using a highly spin-polarized current. The gap value 2Δ/kBT, gap symmetry and its temperature dependence, combined with the antiparallel spin state show that the bulk NiBi3 is a singlet s-wave superconductor.
Reorientation in newly formed fission fragments

The strong quadrupolar component of the Coulomb field between newly formed fission fragments can affect the internal energy of the fragments and their angular momentum. Previous estimates of these effects gave contradictory conclusions about their magnitude. Here we calculate them by solving the time-dependent Hamiltonian equation for the daughter $^{100}$Zr produced in the fission reaction n + $^{235}$U $\rightarrow$ $^{136}$Te + $^{100}$Zr. The Hamiltonian was constructed from the projected angular momentum eigenstates of an aligned deformed mean-field configuration. For typical initial conditions, the average angular momentum of the lighter fragment increases by 1.5 - 3 units.
WHAT ARE THE Omh2 (z1, z2) AND Om (z1, z2) DIAGNOSTICS TELLING US IN LIGHT OF H(z) DATA?

The two-point diagnostics Om(zi, zj) and Omh2(zi, zj) have been introduced as an interesting tool for testing the validity of the Λ cold dark matter (ΛCDM) model. Recently, Sahni et al. combined two independent measurements of H(z) from baryon acoustic oscillation (BAO) data with the value of the Hubble constant H0, and used the second of these diagnostics to test the ΛCDM (a constant equation-of-state parameter for dark energy) model. Their result indicated a considerable tension between observations and predictions of the ΛCDM model. Since reliable data concerning the expansion rates of the universe at different redshifts H(z) are crucial for the successful application of this method, we investigate both two-point diagnostics on the most comprehensive set of N = 36 measurements of H(z) from BAOs and the differential ages (DAs) of passively evolving galaxies. We discuss the uncertainties of the two-point diagnostics and find that they are strongly non-Gaussian and follow the patterns deeply rooted in their very construction. Therefore we propose that non-parametric median statistics is the most appropriate way of treating this problem. Our results support the claims that ΛCDM is in tension with H(z) data according to the two-point diagnostics developed by Shafieloo, Sahni, and Starobinsky. However, other alternatives to the ΛCDM model, such as the wCDM or Chevalier–Polarski–Linder models, perform even worse. We also note that there are serious systematic differences between the BAO and DA methods that ought to be better understood before H(z) measurements can compete with other probes methods.
Extracting information from AGN variability

AGN exhibit rapid, high amplitude stochastic flux variability across the entire electromagnetic spectrum on timescales ranging from hours to years. The cause of this variability is poorly understood. We present a new method for using variability to (1) measure the time-scales on which flux perturbations evolve and (2) characterize the driving flux perturbations. We model the observed light curve of an AGN as a linear differential equation driven by stochastic impulses. Physically, the impulses could be local `hot-spots' in the accretion disk---the linear differential equation then governs how the hot spots evolve and dissipate. The impulse-response function of the accretion disk material is given by the Green's function of the linear differential equation. The timescales on which the hot-spots radiate energy is characterized by the powerspectrum of the driving stochastic impulses. We analyze the light curve of the \Kepler AGN Zw 229-15 and find that the observed variability behavior can be modeled as a damped harmonic oscillator perturbed by a colored noise process. The model powerspectrum turns over on time-scale $385$~d. On shorter time-scales, the log-powerspectrum slope varies between $2$ and $4$, explaining the behavior noted by previous studies. We recover and identify both the $5.6$~d and $67$~d timescales reported by previous work. These timescales represent the time-scale on which flux perturbations grow, and the time-scale on which flux perturbations decay back to the steady-state flux level respectively. We make the software package used to study light curves using our method, \textsc{k\={a}l\={i}}, available to the community.
TeV Cosmic-Ray Anisotropy from the Magnetic Field at the Heliospheric Boundary

We performed numerical calculations to test the suggestion by Desiati and Lazarian that the anisotropies of TeV cosmic rays may arise from their interactions with the heliosphere. For this purpose, we used a magnetic field model of the heliosphere and performed direct numerical calculations of particle trajectories. Unlike earlier papers testing the idea, we did not employ time-reversible techniques that are based on Liouville’s theorem. We showed numerically that for scattering by the heliosphere, the conditions of Liouville’s theorem are not satisfied, and the adiabatic approximation and time-reversibility of the particle trajectories are not valid. Our results indicate sensitivity to the magnetic structure of the heliospheric magnetic field, and we expect that this will be useful for probing this structure in future research.
Electromagnetic waves in the gravitational field of massive dark halos

The propagation of plane electromagnetic waves in the gravitational field inside a rotating cloud of dark matter is analyzed. Formulas for the deflection and absorption of light, and the rotation of the polarization plane are obtained in closed form in terms of the mass density and the angular velocity of the cloud. It is shown that the formulas can be considerably simplified for axisymmetric configurations. As an example, the formalism is applied to a rotating massive cloud described by a Plummer potential.
Non-Markovian effects in electronic and spin transport

We derive a non-Markovian master equation for the evolution of a class of open quantum systems consisting of quadratic fermionic models coupled to wide-band reservoirs. This is done by providing an explicit correspondence between master equations and non-equilibrium Green's functions approaches. Our findings permit to study non-Markovian regimes characterized by negative decoherence rates. We study the real-time dynamics and the steady-state solution of two illustrative models: a tight-binding and an XY-spin chains. The rich set of phases encountered for the non-equilibrium XY model extends previous studies to the non-Markovian regime.