Generalised knot groups distinguish the square and granny knots (with an appendix by David Savitt)

Given a knot K we may construct a group G_n(K) from the fundamental group of K by adjoining an nth root of the meridian that commutes with the corresponding longitude. These "generalised knot groups" were introduced independently by Wada and Kelly, and contain the fundamental group as a subgroup. The square knot SK and the granny knot GK are a well known example of a pair of distinct knots with isomorphic fundamental groups. We show that G_n(SK) and G_n(GK) are non-isomorphic for all n>1. This confirms a conjecture of Lin and Nelson, and shows that the isomorphism type of G_n(K), n>1, carries more information about K than the isomorphism type of the fundamental group. An appendix by David Savitt contains some results on representations of the trefoil group in PSL(2,p) that are needed for the proof.Comment: 25 pages, 5 figures, to appear in JKTR. v3: example of the target groups added; slight correction to the construction of the target groups; references updated; some changes to notation. v2: section 4.2 expanded to give overview of proo

Carrier-based sinusoidal pulse-width modulation techniques for flying capacitor modular multi-level cascaded converter

Carrier-based sinusoidal pulse-width modulation (PWM) techniques, such as phase disposoed PWM(PD-PWM) and phase shifted PWM (PS-PWM), are widely applied to control the modular multilevel cascaded converters (MMCC) having full H-bridge as sub-modules. This paper evaluates these PWM techniques when controlling a variant of the H-bridge MMCC, i.e. the MMCC five-level flying capacitor converter as sub-modules. This MMCC poses an extra challenge to PWM schemes; namely maintaining two inner floating capacitor voltage balancing. Two novel PWM techniques known as the swapped carrier PWM techniques are introduced for the control of this converter. The paper compares them with the two conventional ones using a performance metrics composed of voltage waveform performance, capability in natural flying capacitor voltage balancing, converter power loss, and switch utilisation. The results show that the proposed new PWM schemes outperform both conventional methods in both switching and conduction power losses and achieve similar performance like the PS-PWM under the three other metrics

Bipartite entangled stabilizer mutually unbiased bases as maximum cliques of Cayley graphs

We examine the existence and structure of particular sets of mutually unbiased bases (MUBs) in bipartite qudit systems. In contrast to well-known power-of-prime MUB constructions, we restrict ourselves to using maximally entangled stabilizer states as MUB vectors. Consequently, these bipartite entangled stabilizer MUBs (BES MUBs) provide no local information, but are sufficient and minimal for decomposing a wide variety of interesting operators including (mixtures of) Jamiolkowski states, entanglement witnesses and more. The problem of finding such BES MUBs can be mapped, in a natural way, to that of finding maximum cliques in a family of Cayley graphs. Some relationships with known power-of-prime MUB constructions are discussed, and observables for BES MUBs are given explicitly in terms of Pauli operators.Comment: 8 pages, 1 figur

Maximally symmetric stabilizer MUBs in even prime-power dimensions

One way to construct a maximal set of mutually unbiased bases (MUBs) in a prime-power dimensional Hilbert space is by means of finite phase-space methods. MUBs obtained in this way are covariant with respect to some subgroup of the group of all affine symplectic phase-space transformations. However, this construction is not canonical: as a consequence, many different choices of covariance sugroups are possible. In particular, when the Hilbert space is $2^n$ dimensional, it is known that covariance with respect to the full group of affine symplectic phase-space transformations can never be achieved. Here we show that in this case there exist two essentially different choices of maximal subgroups admitting covariant MUBs. For both of them, we explicitly construct a family of $2^n$ covariant MUBs. We thus prove that, contrary to the odd dimensional case, maximally covariant MUBs are very far from being unique.Comment: 22 page

Identification of a surrogate to validate irradiation processing of selected spices

Onion powder and talc were inoculated with one of three groups of Salmonella enterica or a putative surrogate, Enterococcus faecium NRRL B-2354, and the radiation sensitivity of S. enterica was compared to E. faecium. For both inoculated onion powder and inoculated talc, D10-values were greater for E. faecium than any of the three groups of S. enterica. The survival of E. faecium in irradiated talc was used to estimate the potential survival of S. enterica in irradiated spices. Onion powder, dried oregano, whole cumin seeds or peppercorns were mixed with talc inoculated with either S. enterica (previously associated with a foodborne disease outbreak) or E. faecium and irradiated. The D10-values were calculated for each bacterial group and compared between E. faecium and S. enterica within each spice. For each spice, the D10-value for E. faecium was either not statistically different from (P \u3c 0.05) S. entericaor greater than that of S. enterica (onion powder). Quadratic and linear models were developed to allow the estimation of potential surviving populations, and potential decimal reductions of S. enterica, based on surviving populations and decimal reductions determined with E. faecium. The use of E. faecium and these mathematical models would allow a processor to validate an irradiation process by estimating the reduction in S. enterica, based on the population reductions of E. faecium

Similarity classes of 3x3 matrices over a local principal ideal ring

In this paper similarity classes of three by three matrices over a local principal ideal commutative ring are analyzed. When the residue field is finite, a generating function for the number of similarity classes for all finite quotients of the ring is computed explicitly.Comment: 14 pages, final version, to appear in Communications in Algebr