Experimentally implementable criteria revealing substructures of genuine multipartite entanglement

We present a general framework that reveals substructures of genuine multipartite entanglement. Via simple inequalities it is possible to discriminate different sets of multipartite qubit states. These inequalities are beneficial regarding experimental examinations as only local measurements are required. Furthermore, the number of observables scales favorably with system size. In exemplary cases we demonstrate the noise resistance and discuss implementations.Comment: 14 pages, 4 figure

Package of facts and theorems for efficiently generating entanglement criteria for many qubits

We present a package of mathematical theorems, which allow to construct multipartite entanglement criteria. Importantly, establishing bounds for certain classes of entanglement does not take an optimization over continuous sets of states. These bonds are found from the properties of commutativity graphs of operators used in the criterion. We present two examples of criteria constructed according to our method. One of them detects genuine 5-qubit entanglement without ever referring to correlations between all five qubits.Comment: 5 pages, 4 figure

Mathematical Models of Abstract Systems: Knowing abstract geometric forms

Scientists use models to know the world. It i susually assumed that mathematicians doing pure mathematics do not. Mathematicians doing pure mathematics prove theorems about mathematical entities like sets, numbers, geometric figures, spaces, etc., they compute various functions and solve equations. In this paper, I want to exhibit models build by mathematicians to study the fundamental components of spaces and, more generally, of mathematical forms. I focus on one area of mathematics where models occupy a central role, namely homotopy theory. I argue that mathematicians introduce genuine models and I offer a rough classification of these models

The upcoming New Pact on Migration and Asylum: Will it be up to the challenge? EPC Discussion Paper 29 April 2020

A courageous and ambitious New Pact on Migration and Asylum is one that strengthens the right to asylum; sets the conditions for more equal relationships with third countries when it comes to managing migration; and puts forward a mechanism that can foster genuine solidarity between member states. When the new Commission entered into office in December 2019, it promised a fresh start on migration. President Ursula von der Leyen pledged to deliver a ‘New Pact’ which would break the deadlock between member states on long-awaited reforms, striking a more equitable balance between solidarity and responsibility

On lattices of convex sets in R^n

Properties of several sorts of lattices of convex subsets of R^n are examined. The lattice of convex sets containing the origin turns out, for n>1, to satisfy a set of identities strictly between those of the lattice of all convex subsets of R^n and the lattice of all convex subsets of R^{n-1}. The lattices of arbitrary, of open bounded, and of compact convex sets in R^n all satisfy the same identities, but the last of these is join-semidistributive, while for n>1 the first two are not. The lattice of relatively convex subsets of a fixed set S \subseteq R^n satisfies some, but in general not all of the identities of the lattice of ``genuine'' convex subsets of R^n.Comment: 35 pages, to appear in Algebra Universalis, Ivan Rival memorial issue. See also http://math.berkeley.edu/~gbergman/paper

Minimal 3-loop neutrino mass models and charged lepton flavor violation

We study charged lepton flavor violation for the three most popular 3-loop Majorana neutrino mass models. We call these models "minimal" since their particle content correspond to the minimal sets for which genuine 3-loop models can be constructed. In all the three minimal models the neutrino mass matrix is proportional to some powers of Standard Model lepton masses, providing additional suppression factors on top of the expected loop suppression. To correctly explain neutrino masses, therefore large Yukawa couplings are needed in these models. We calculate charged lepton flavor violating observables and find that the three minimal models survive the current constraints only in very narrow regions of their parameter spaces.Comment: 32+7 pages, 23 figures, 7 table

The student immigration system (Consultation document and consultation response pro-forma)

Includes the consultation document and consultation response pro-forma. Consultation dates: (December 2010 to January 2011) "The government intends to reduce annual net migration to the UK to sustainable levels, in the tens of thousands a year. It expects the student route to make its contribution towards reducing net migration to the UK. Students now represent the largest proportion of net migration from outside Europe. We need to ensure that the number of international students coming to the UK is broadly in balance with the number leaving. The government's policy aim is to ensure that only genuine students who are committed to their academic study come to the UK, with a presumption that upon completion they will leave promptly. This consultation sets out our proposals for achieving this aim." - UKBA website