Arbitrarily large families of spaces of the same volume

In any connected non-compact semi-simple Lie group without factors locally isomorphic to SL_2(R), there can be only finitely many lattices (up to isomorphism) of a given covolume. We show that there exist arbitrarily large families of pairwise non-isomorphic arithmetic lattices of the same covolume. We construct these lattices with the help of Bruhat-Tits theory, using Prasad's volume formula to control their covolumes.Comment: 9 pages. Syntax corrected; one reference adde

Multifractal observations of eddies, oil spills and natural slicks in the ocean surface

Natural and man-made distributions of tensioactive substance concentrations in the sea surface features exhibit self-similarity at all radar reflectivity levels when illuminated by SAR. This allows the investigation of the traces produced by vortices and other features in the ocean surface. The man-made oil spills besides often presenting some linear axis of the pollutant concentration produced by moving ships also show their artificial production in the sea surface by the reduced range of scales, which widens as time measured in terms of the local eddy diffusivity distorts the shape of the oil spills. Thanks to this, multifractal analysis of the different backscattered intensity levels in SAR imagery can be used to distinguish between natural and man-made sea surface features due to their distinct self-similar properties. The differences are detected using the multifractal box-counting algorithm on different sets of SAR images giving also information on the age of the spills. Different multifractal algorithms are compared presenting the differences in scaling as a function of some physical generating process such as the locality or the spectral energy cascade

Electrical detection of picosecond acoustic pulses in vertical transport devices with nanowires

Picosecond acoustic pulses, generated in a thin aluminum transducer, are injected into semiconductor vertical transport devices consisting of core-shell GaAsP nanowires. The acoustic pulses induce current pulses in the device with amplitude ∼1 μA. The spectrum of the electrical response is sensitive to the elastic properties of the device and has a frequency cutoff at ∼10 GHz. This work shows the potential of the technique for studies the elastic properties of complex semiconductor nanodevices.Peer reviewe

Signal-averaged P wave analysis for delineation of interatrial conduction – Further validation of the method

<p>Abstract</p> <p>Background</p> <p>The study was designed to investigate the effect of different measuring methodologies on the estimation of P wave duration. The recording length required to ensure reproducibility in unfiltered, signal-averaged P wave analysis was also investigated. An algorithm for automated classification was designed and its reproducibility of manual P wave morphology classification investigated.</p> <p>Methods</p> <p>Twelve-lead ECG recordings (1 kHz sampling frequency, 0.625 <it>μ</it>V resolution) from 131 healthy subjects were used. Orthogonal leads were derived using the inverse Dower transform. Magnification (100 times), baseline filtering (0.5 Hz high-pass and 50 Hz bandstop filters), signal averaging (10 seconds) and bandpass filtering (40–250 Hz) were used to investigate the effect of methodology on the estimated P wave duration. Unfiltered, signal averaged P wave analysis was performed to determine the required recording length (6 minutes to 10 s) and the reproducibility of the P wave morphology classification procedure. Manual classification was carried out by two experts on two separate occasions each. The performance of the automated classification algorithm was evaluated using the joint decision of the two experts (i.e., the consensus of the two experts).</p> <p>Results</p> <p>The estimate of the P wave duration increased in each step as a result of magnification, baseline filtering and averaging (100 ± 18 vs. 131 ± 12 ms; P < 0.0001). The estimate of the duration of the bandpass-filtered P wave was dependent on the noise cut-off value: 119 ± 15 ms (0.2 <it>μ</it>V), 138 ± 13 ms (0.1 <it>μ</it>V) and 143 ± 18 ms (0.05 <it>μ</it>V). (P = 0.01 for all comparisons).</p> <p>The mean errors associated with the P wave morphology parameters were comparable in all segments analysed regardless of recording length (95% limits of agreement within 0 ± 20% (mean ± SD)). The results of the 6-min analyses were comparable to those obtained at the other recording lengths (6 min to 10 s).</p> <p>The intra-rater classification reproducibility was 96%, while the interrater reproducibility was 94%. The automated classification algorithm agreed with the manual classification in 90% of the cases.</p> <p>Conclusion</p> <p>The methodology used has profound effects on the estimation of P wave duration, and the method used must therefore be validated before any inferences can be made about P wave duration. This has implications in the interpretation of multiple studies where P wave duration is assessed, and conclusions with respect to normal values are drawn.</p> <p>P wave morphology and duration assessed using unfiltered, signal-averaged P wave analysis have high reproducibility, which is unaffected by the length of the recording. In the present study, the performance of the proposed automated classification algorithm, providing total reproducibility, showed excellent agreement with manually defined P wave morphologies.</p

There is no "Theory of Everything" inside E8

We analyze certain subgroups of real and complex forms of the Lie group E8, and deduce that any "Theory of Everything" obtained by embedding the gauge groups of gravity and the Standard Model into a real or complex form of E8 lacks certain representation-theoretic properties required by physical reality. The arguments themselves amount to representation theory of Lie algebras in the spirit of Dynkin's classic papers and are written for mathematicians.Comment: Final version, to appear in Communications in Mathematical Physics. The main difference, from the previous version, is the creation of a new section, containing a response to Lisi's objections to our wor

The word and Riemannian metrics on lattices of semisimple groups

Let G be a semisimple Lie group of rank ≥ 2 and Γ an irreducible lattice. Γ has two natural metrics: a metric inherited from a Riemannian metric on the ambient Lie group and a word metric defined with respect to some finite set of generators. Confirming a conjecture of D. Kazhdan (cf. Gromov [Gr2]) we show that these metrics are Lipschitz equivalent. It is shown that a cyclic subgroup of Γ is virtually unipotent if and only if it has exponential growth with respect to the generators of Γ

Invasive meningococcal disease in three siblings with hereditary deficiency of the 8th component of complement: Evidence for the importance of an early diagnosis

Deficiency of the eighth component of complement (C8) is a very rare primary immunodeficiency, associated with invasive, recurrent infections mainly caused by Neisseria species. We report functional and immunochemical C8 deficiency diagnosed in three Albanian siblings who presented with severe meningococcal infections at the age of 15 years, 4 years and 17 months, respectively. The youngest suffered serious complications (necrosis of fingers and toes requiring amputation). METHODS: Functional activity of the classical, alternative and mannose-binding lectin complement pathways was measured in serum from the 3 siblings and their parents (37-year-old woman and 42-year-old man). Forty healthy subjects (20 males and 20 females aged 4-38 years) served as normal controls. Serum complement factors were measured by haemolytic assays and immunoblotting. Sequence DNA analysis of the C8B gene was performed. RESULTS: Analyses of the three complement pathways revealed no haemolytic activity and also absence of C8beta in serum samples from all three siblings. The genetic analysis showed that the three siblings were homozygous for the p.Arg428* mutation in the C8B gene on chromosome 1p32 (MIM 120960). The parents were heterozygous for the mutation and presented normal complement activities. A 2-year follow-up revealed no further infective episodes in the siblings after antibiotic prophylaxis and meningococcal vaccination. CONCLUSIONS: Complement deficiencies are rare and their occurrence is often underestimated. In presence of invasive meningococcal infection, we highlight the importance of complement screening in patients and their relatives in order to discover any genetic defects which would render necessary prophylaxis to prevent recurrent infections and severe complications

Induced Parity Nonconserving Interaction and Enhancement of Two-Nucleon Parity Nonconserving Forces

Two-nucleon parity nonconserving (PNC) interaction induced by the single-particle PNC weak potential and the two-nucleon residual strong interaction is considered. An approximate analytical formula for this Induced PNC Interaction (IPNCI) between proton and neutron is derived ($Q({\bf r} {\bf \sigma}_{p} \times {\bf \sigma}_{n}) \delta({\bf r}_{p}-{\bf r}_{n})$), and the interaction constant is estimated. As a result of coherent contributions from the nucleons to the PNC potential, IPNCI is an order of magnitude stronger ($\sim A^{1/3}$) than the residual weak two-nucleon interaction and has a different coordinate and isotopic structure (e.g., the strongest part of IPNCI does not contribute to the PNC mean field). IPNCI plays an important role in the formation of PNC effects, e.g., in neutron-nucleus reactions. In that case, it is a technical way to take into account the contribution of the distant (small) components of a compound state which dominates the result. The absence of such enhancement ($\sim A^{1/3}$) in the case of T- and P-odd interaction completes the picture.Comment: Phys. Rev. C, to appear; 17 pages, revtex 3, no figure