Displacement energy of unit disk cotangent bundles

We give an upper bound of a Hamiltonian displacement energy of a unit disk cotangent bundle $D^*M$ in a cotangent bundle $T^*M$, when the base manifold $M$ is an open Riemannian manifold. Our main result is that the displacement energy is not greater than $C r(M)$, where $r(M)$ is the inner radius of $M$, and $C$ is a dimensional constant. As an immediate application, we study symplectic embedding problems of unit disk cotangent bundles. Moreover, combined with results in symplectic geometry, our main result shows the existence of short periodic billiard trajectories and short geodesic loops.Comment: Title slightly changed. Close to the version published online in Math Zei

Quantum walks on quotient graphs

A discrete-time quantum walk on a graph is the repeated application of a unitary evolution operator to a Hilbert space corresponding to the graph. If this unitary evolution operator has an associated group of symmetries, then for certain initial states the walk will be confined to a subspace of the original Hilbert space. Symmetries of the original graph, given by its automorphism group, can be inherited by the evolution operator. We show that a quantum walk confined to the subspace corresponding to this symmetry group can be seen as a different quantum walk on a smaller quotient graph. We give an explicit construction of the quotient graph for any subgroup of the automorphism group and illustrate it with examples. The automorphisms of the quotient graph which are inherited from the original graph are the original automorphism group modulo the subgroup used to construct it. We then analyze the behavior of hitting times on quotient graphs. Hitting time is the average time it takes a walk to reach a given final vertex from a given initial vertex. It has been shown in earlier work [Phys. Rev. A {\bf 74}, 042334 (2006)] that the hitting time can be infinite. We give a condition which determines whether the quotient graph has infinite hitting times given that they exist in the original graph. We apply this condition for the examples discussed and determine which quotient graphs have infinite hitting times. All known examples of quantum walks with fast hitting times correspond to systems with quotient graphs much smaller than the original graph; we conjecture that the existence of a small quotient graph with finite hitting times is necessary for a walk to exhibit a quantum speed-up.Comment: 18 pages, 7 figures in EPS forma

Bicrossed products for finite groups

We investigate one question regarding bicrossed products of finite groups which we believe has the potential of being approachable for other classes of algebraic objects (algebras, Hopf algebras). The problem is to classify the groups that can be written as bicrossed products between groups of fixed isomorphism types. The groups obtained as bicrossed products of two finite cyclic groups, one being of prime order, are described.Comment: Final version: to appear in Algebras and Representation Theor

Asymptotic Behavior of Ext functors for modules of finite complete intersection dimension

Let $R$ be a local ring, and let $M$ and $N$ be finitely generated $R$-modules such that $M$ has finite complete intersection dimension. In this paper we define and study, under certain conditions, a pairing using the modules \Ext_R^i(M,N) which generalizes Buchweitz's notion of the Herbrand diference. We exploit this pairing to examine the number of consecutive vanishing of \Ext_R^i(M,N) needed to ensure that \Ext_R^i(M,N)=0 for all $i\gg 0$. Our results recover and improve on most of the known bounds in the literature, especially when $R$ has dimension at most two

When and how are lies told? And the role of culture and intentions in intelligence‐gathering interviews

Purpose: Lie‐tellers tend to tell embedded lies within interviews. In the context of intelligence‐gathering interviews, human sources may disclose information about multiple events, some of which may be false. In two studies, we examined when lie‐tellers from low‐ and high‐context cultures start reporting false events in interviews and to what extent they provide a similar amount of detail for the false and truthful events. Study 1 focused on lie‐tellers' intentions, and Study 2 focused on their actual responses. Methods: Participants were asked to think of one false event and three truthful events. Study 1 (N = 100) was an online study in which participants responded to a questionnaire about where they would position the false event when interviewed and they rated the amount of detail they would provide for the events. Study 2 (N = 126) was an experimental study that involved interviewing participants about the events. Results: Although there was no clear preference for lie position, participants seemed to report the false event at the end rather than at the beginning of the interview. Also, participants provided a similar amount of detail across events. Results on intentions (Study 1) partially overlapped with results on actual responses (Study 2). No differences emerged between low‐ and high‐context cultures. Conclusions: This research is a first step towards understanding verbal cues that assist investigative practitioners in saving their cognitive and time resources when detecting deception regardless of interviewees' cultural background. More research on similar cues is encouraged

Magnetron Development

Contains reports on two research projects

Quantum Fourier transform, Heisenberg groups and quasiprobability distributions

This paper aims to explore the inherent connection among Heisenberg groups, quantum Fourier transform and (quasiprobability) distribution functions. Distribution functions for continuous and finite quantum systems are examined first as a semiclassical approach to quantum probability distribution. This leads to studying certain functionals of a pair of "conjugate" observables, connected via the quantum Fourier transform. The Heisenberg groups emerge naturally from this study and we take a rapid look at their representations. The quantum Fourier transform appears as the intertwining operator of two equivalent representation arising out of an automorphism of the group. Distribution functions correspond to certain distinguished sets in the group algebra. The marginal properties of a particular class of distribution functions (Wigner distributions) arise from a class of automorphisms of the group algebra of the Heisenberg group. We then study the reconstruction of Wigner function from the marginal distributions via inverse Radon transform giving explicit formulas. We consider applications of our approach to quantum information processing and quantum process tomography.Comment: 39 page

Magnetron Development

Contains reports on three research projects

Surface code quantum computing by lattice surgery

In recent years, surface codes have become a leading method for quantum error correction in theoretical large scale computational and communications architecture designs. Their comparatively high fault-tolerant thresholds and their natural 2-dimensional nearest neighbour (2DNN) structure make them an obvious choice for large scale designs in experimentally realistic systems. While fundamentally based on the toric code of Kitaev, there are many variants, two of which are the planar- and defect- based codes. Planar codes require fewer qubits to implement (for the same strength of error correction), but are restricted to encoding a single qubit of information. Interactions between encoded qubits are achieved via transversal operations, thus destroying the inherent 2DNN nature of the code. In this paper we introduce a new technique enabling the coupling of two planar codes without transversal operations, maintaining the 2DNN of the encoded computer. Our lattice surgery technique comprises splitting and merging planar code surfaces, and enables us to perform universal quantum computation (including magic state injection) while removing the need for braided logic in a strictly 2DNN design, and hence reduces the overall qubit resources for logic operations. Those resources are further reduced by the use of a rotated lattice for the planar encoding. We show how lattice surgery allows us to distribute encoded GHZ states in a more direct (and overhead friendly) manner, and how a demonstration of an encoded CNOT between two distance 3 logical states is possible with 53 physical qubits, half of that required in any other known construction in 2D.Comment: Published version. 29 pages, 18 figure

Constructing Fluorogenic Bacillus Spores (F-Spores) via Hydrophobic Decoration of Coat Proteins

Background: Bacterial spores are protected by a coat consisting of about 60 different proteins assembled as a biochemically complex structure with intriguing morphological and mechanical properties. Historically, the coat has been considered a static structure providing rigidity and mainly acting as a sieve to exclude exogenous large toxic molecules, such as lytic enzymes. Over recent years, however, new information about the coat’s architecture and function have emerged from experiments using innovative tools such as automated scanning microscopy, and high resolution atomic force microscopy. Principal Findings: Using thin-section electron microscopy, we found that the coat of Bacillus spores has topologically specific proteins forming a layer that is identifiable because it spontaneously becomes decorated with hydrophobic fluorogenic probes from the milieu. Moreover, spores with decorated coat proteins (termed F-spores) have the unexpected attribute of responding to external germination signals by generating intense fluorescence. Fluorescence data from diverse experimental designs, including F-spores constructed from five different Bacilli species, indicated that the fluorogenic ability of F-spores is under control of a putative germination-dependent mechanism. Conclusions: This work uncovers a novel attribute of spore-coat proteins that we exploited to decorate a specific layer imparting germination-dependent fluorogenicity to F-spores. We expect that F-spores will provide a model system to gai