Ultralong-range order in the Fermi-Hubbard model with long-range interactions

We use the dual boson approach to reveal the phase diagram of the Fermi-Hubbard model with long-range dipole-dipole interactions. By using a large-scale finite-temperature calculation on a $64 \times 64$ square lattice we demonstrate the existence of a novel phase, possessing an `ultralong-range' order. The fingerprint of this phase -- the density correlation function -- features a non-trivial behavior on a scale of tens of the lattice sites. We study the properties and the stability of the ultralong-range ordered phase, and show that it is accessible in modern experiments with ultracold polar molecules and magnetic atoms

The rational classification of links of codimension >2

Fix an integer m and a multi-index p = (p_1, ..., p_r) of integers p_i < m-2. The set of links of codimension > 2, with multi-index p, E(p, m), is the set of smooth isotopy classes of smooth embeddings of the disjoint union of the p_i-spheres into the m-sphere. Haefliger showed that E(p, m) is a finitely generated abelian group with respect to embedded connected summation and computed its rank in the case of knots, i.e. r=1. For r > 1 and for restrictions on p the rank of this group can be computed using results of Haefliger or Nezhinsky. Our main result determines the rank of the group E(p, m) in general. In particular we determine precisely when E(p,m) is finite. We also accomplish these tasks for framed links. Our proofs are based on the Haefliger exact sequence for groups of links and the theory of Lie algebras.Comment: 16 page

Astrophysical bounds on supersymmetric dark-matter Q-balls

Stable baryonic Q-balls, which appear in supersymmetric extensions of the Standard Model, could form at the end of cosmological inflation from fragmentation of the Affleck -- Dine condensate. We reconsider astrophysical constraints on such Q-balls as dark matter candidates. Baryonic Q-balls interact with matter by absorbing the baryon number and, effectively, leading to a rapid baryon number non-conservation. We have recently shown that this process can occur at a much faster rate than that used in previous calculations. As a consequence, stability of neutron stars imposes a stringent constraint on the types of Q-balls that can be dark matter. Only the Q-balls that correspond to baryonic flat directions lifted by baryon-number violating operators are allowed as dark-matter candidates.Comment: 10 page

Benford's Law and the Detection of Election Fraud

The proliferation of elections in even those states that are arguably anything but democratic has given rise to a focused interest on developing methods for detecting fraud in the official statistics of a state's election returns. Among these efforts are those that employ Benford's Law, with the most common application being an attempt to proclaim some election or another fraud free or replete with fraud. This essay, however, argues that, despite its apparent utility in looking at other phenomena, Benford's Law is problematical at best as a forensic tool when applied to elections. Looking at simulations designed to model both fair and fraudulent contests as well as data drawn from elections we know, on the basis of other investigations, were either permeated by fraud or unlikely to have experienced any measurable malfeasance, we find that conformity with and deviations from Benford's Law follow no pattern. It is not simply that the Law occasionally judges a fraudulent election fair or a fair election fraudulent. Its "success rate" either way is essentially equivalent to a toss of a coin, thereby rendering it problematical at best as a forensic tool and wholly misleading at worst

Current status of metric reduction of (passive) scanner data

The extraction of metric information from scanner (particularly multispectral) data is presented. Data from both aircraft and spacecraft; singly scanned areas and areas with multiple coverage; various mathematical models used up to the present time; and published numerical results are considered. Future trends are also discussed

Application of Hybrid Fillers for Improving the Through-Plane Heat Transport in Graphite Nanoplatelet-Based Thermal Interface Layers.

The in-plane alignment of graphite nanoplatelets (GNPs) in thin thermal interface material (TIM) layers suppresses the though-plane heat transport thus limiting the performance of GNPs in the geometry normally required for thermal management applications. Here we report a disruption of the GNP in-plane alignment by addition of spherical microparticles. The degree of GNP alignment was monitored by measurement of the anisotropy of electrical conductivity which is extremely sensitive to the orientation of high aspect ratio filler particles. Scanning Electron Microscopy images of TIM layer cross-sections confirmed the suppression of the in-plane alignment. The hybrid filler formulations reported herein resulted in a synergistic enhancement of the through-plane thermal conductivity of GNP/Al2O3 and GNP/Al filled TIM layers confirming that the control of GNP alignment is an important parameter in the development of highly efficient GNP and graphene-based TIMs

Supersymmetric dark-matter Q-balls and their interactions in matter

Supersymmetric extensions of the Standard Model contain non-topological solitons, Q-balls, which can be stable and can be a form of cosmological dark matter. Understanding the interaction of SUSY Q-balls with matter fermions is important for both astrophysical limits and laboratory searches for these dark matter candidates. We show that a baryon scattering off a baryonic SUSY Q-ball can convert into its antiparticle with a high probability, while the baryon number of the Q-ball is increased by two units. For a SUSY Q-ball interacting with matter, this process dominates over those previously discussed in the literature.Comment: 12 page

Boost the Impact of Continuous Formal Verification in Industry

Software model checking has experienced significant progress in the last two decades, however, one of its major bottlenecks for practical applications remains its scalability and adaptability. Here, we describe an approach to integrate software model checking techniques into the DevOps culture by exploiting practices such as continuous integration and regression tests. In particular, our proposed approach looks at the modifications to the software system since its last verification, and submits them to a continuous formal verification process, guided by a set of regression test cases. Our vision is to focus on the developer in order to integrate formal verification techniques into the developer workflow by using their main software development methodologies and tools.Comment: 7 page