A novel 90xB0; phase shifter for square waves

In the field of electronic instrumentation there are many applications where a circuit is needed to shift the use of square waves by 90xB0;. In this paper a simple and novel scheme to achieve this end is proposed. This circuit, along with a modulo-two-adder, also enables one to obtain the double frequency component of the original input square wave. It is thus possible to have frequency multiplication by powers of two by cascading such circuits in tandem. The entire circuitry, excepting the time averaging capacitors, can be either13; integrated in one chip or fabricated in tins module form

Characterizing the geometrical edges of nonlocal two-qubit gates

Nonlocal two-qubit gates are geometrically represented by tetrahedron known as Weyl chamber within which perfect entanglers form a polyhedron. We identify that all edges of the Weyl chamber and polyhedron are formed by single parametric gates. Nonlocal attributes of these edges are characterized using entangling power and local invariants. In particular, SWAP (power)alpha family of gates constitutes one edge of the Weyl chamber with SWAP-1/2 being the only perfect entangler. Finally, optimal constructions of controlled-NOT using SWAP-1/2 gate and gates belong to three edges of the polyhedron are presented.Comment: 11 pages, 4 figures, Phys. Rev. A 79, 052339 (2009

Logahedra: A new weakly relational domain

Weakly relational numeric domains express restricted classes of linear inequalities that strike a balance between what can be described and what can be efficiently computed. Popular weakly relational domains such as bounded differences and octagons have found application in model checking and abstract interpretation. This paper introduces logahedra, which are more expressiveness than octagons, but less expressive than arbitrary systems of two variable per inequality constraints. Logahedra allow coefficients of inequalities to be powers of two whilst retaining many of the desirable algorithmic properties of octagons

Vere-Jones' Self-Similar Branching Model

Motivated by its potential application to earthquake statistics, we study the exactly self-similar branching process introduced recently by Vere-Jones, which extends the ETAS class of conditional branching point-processes of triggered seismicity. One of the main ingredient of Vere-Jones' model is that the power law distribution of magnitudes m' of daughters of first-generation of a mother of magnitude m has two branches m'm with exponent beta+d, where beta and d are two positive parameters. We predict that the distribution of magnitudes of events triggered by a mother of magnitude $m$ over all generations has also two branches m'm with exponent beta+h, with h= d \sqrt{1-s}, where s is the fraction of triggered events. This corresponds to a renormalization of the exponent d into h by the hierarchy of successive generations of triggered events. The empirical absence of such two-branched distributions implies, if this model is seriously considered, that the earth is close to criticality (s close to 1) so that beta - h \approx \beta + h \approx \beta. We also find that, for a significant part of the parameter space, the distribution of magnitudes over a full catalog summed over an average steady flow of spontaneous sources (immigrants) reproduces the distribution of the spontaneous sources and is blind to the exponents beta, d of the distribution of triggered events.Comment: 13 page + 3 eps figure

Entangling characterization of (SWAP)1/m and Controlled unitary gates

We study the entangling power and perfect entangler nature of (SWAP)1/m, for m>=1, and controlled unitary (CU) gates. It is shown that (SWAP)1/2 is the only perfect entangler in the family. On the other hand, a subset of CU which is locally equivalent to CNOT is identified. It is shown that the subset, which is a perfect entangler, must necessarily possess the maximum entangling power.Comment: 12 pages, 1 figure, One more paragraph added in Introductio

Chaos in a well : Effects of competing length scales

A discontinuous generalization of the standard map, which arises naturally as the dynamics of a periodically kicked particle in a one dimensional infinite square well potential, is examined. Existence of competing length scales, namely the width of the well and the wavelength of the external field, introduce novel dynamical behaviour. Deterministic chaos induced diffusion is observed for weak field strengths as the length scales do not match. This is related to an abrupt breakdown of rotationally invariant curves and in particular KAM tori. An approximate stability theory is derived wherein the usual standard map is a point of ``bifurcation''.Comment: 15 pages, 5 figure

C1q-targeted inhibition of the classical complement pathway prevents injury in a novel mouse model of acute motor axonal neuropathy

Introduction Guillain-Barré syndrome (GBS) is an autoimmune disease that results in acute paralysis through inflammatory attack on peripheral nerves, and currently has limited, non-specific treatment options. The pathogenesis of the acute motor axonal neuropathy (AMAN) variant is mediated by complement-fixing anti-ganglioside antibodies that directly bind and injure the axon at sites of vulnerability such as nodes of Ranvier and nerve terminals. Consequently, the complement cascade is an attractive target to reduce disease severity. Recently, C5 complement component inhibitors that block the formation of the membrane attack complex and subsequent downstream injury have been shown to be efficacious in an in vivo anti-GQ1b antibody-mediated mouse model of the GBS variant Miller Fisher syndrome (MFS). However, since gangliosides are widely expressed in neurons and glial cells, injury in this model was not targeted exclusively to the axon and there are currently no pure mouse models for AMAN. Additionally, C5 inhibition does not prevent the production of early complement fragments such as C3a and C3b that can be deleterious via their known role in immune cell and macrophage recruitment to sites of neuronal damage. Results and Conclusions In this study, we first developed a new in vivo transgenic mouse model of AMAN using mice that express complex gangliosides exclusively in neurons, thereby enabling specific targeting of axons with anti-ganglioside antibodies. Secondly, we have evaluated the efficacy of a novel anti-C1q antibody (M1) that blocks initiation of the classical complement cascade, in both the newly developed anti-GM1 antibody-mediated AMAN model and our established MFS model in vivo. Anti-C1q monoclonal antibody treatment attenuated complement cascade activation and deposition, reduced immune cell recruitment and axonal injury, in both mouse models of GBS, along with improvement in respiratory function. These results demonstrate that neutralising C1q function attenuates injury with a consequent neuroprotective effect in acute GBS models and promises to be a useful new target for human therapy

A Logical Product Approach to Zonotope Intersection

We define and study a new abstract domain which is a fine-grained combination of zonotopes with polyhedric domains such as the interval, octagon, linear templates or polyhedron domain. While abstract transfer functions are still rather inexpensive and accurate even for interpreting non-linear computations, we are able to also interpret tests (i.e. intersections) efficiently. This fixes a known drawback of zonotopic methods, as used for reachability analysis for hybrid sys- tems as well as for invariant generation in abstract interpretation: intersection of zonotopes are not always zonotopes, and there is not even a best zonotopic over-approximation of the intersection. We describe some examples and an im- plementation of our method in the APRON library, and discuss some further in- teresting combinations of zonotopes with non-linear or non-convex domains such as quadratic templates and maxplus polyhedra

Improving Strategies via SMT Solving

We consider the problem of computing numerical invariants of programs by abstract interpretation. Our method eschews two traditional sources of imprecision: (i) the use of widening operators for enforcing convergence within a finite number of iterations (ii) the use of merge operations (often, convex hulls) at the merge points of the control flow graph. It instead computes the least inductive invariant expressible in the domain at a restricted set of program points, and analyzes the rest of the code en bloc. We emphasize that we compute this inductive invariant precisely. For that we extend the strategy improvement algorithm of [Gawlitza and Seidl, 2007]. If we applied their method directly, we would have to solve an exponentially sized system of abstract semantic equations, resulting in memory exhaustion. Instead, we keep the system implicit and discover strategy improvements using SAT modulo real linear arithmetic (SMT). For evaluating strategies we use linear programming. Our algorithm has low polynomial space complexity and performs for contrived examples in the worst case exponentially many strategy improvement steps; this is unsurprising, since we show that the associated abstract reachability problem is Pi-p-2-complete