Variation of discrete spectra for non-selfadjoint perturbations of selfadjoint operators

Let B=A+K where A is a bounded selfadjoint operator and K is an element of the von Neumann-Schatten ideal S_p with p>1. Let {\lambda_n} denote an enumeration of the discrete spectrum of B. We show that \sum_n \dist(\lambda_n, \sigma(A))^p is bounded from above by a constant multiple of |K|_p^p. We also derive a unitary analog of this estimate and apply it to obtain new estimates on zero-sets of Cauchy transforms.Comment: Differences to previous version: Extended Introduction, new Section 5, additional references. To appear in Int. Eq. Op. Theor

Quantum correlations and least disturbing local measurements

We examine the evaluation of the minimum information loss due to an unread local measurement in mixed states of bipartite systems, for a general entropic form. Such quantity provides a measure of quantum correlations, reducing for pure states to the generalized entanglement entropy, while in the case of mixed states it vanishes just for classically correlated states with respect to the measured system, as the quantum discord. General stationary conditions are provided, together with their explicit form for general two-qubit states. Closed expressions for the minimum information loss as measured by quadratic and cubic entropies are also derived for general states of two-qubit systems. As application, we analyze the case of states with maximally mixed marginals, where a general evaluation is provided, as well as X states and the mixture of two aligned states.Comment: 10 pages, 3 figure

Slower-than-Light Spin-1/2 Particles Endowed with Negative Mass Squared

Extending in a straightforward way the standard Dirac theory, we study a quantum mechanical wave-equation describing free spinning particles --which we propose to call "Pseudotachyons" (PT's)-- which behave like tachyons in the momentum space, but like subluminal particles (v<c) in the ordinary space. This is allowed since, as it happens in every quantum theory for spin-1/2 particles, the momentum operator (that is conserved) and the velocity operator (that is not) are independent operators, which refer to independent quantities. As a consequence, at variance with ordinary Dirac particles, for PT's the average velocity is not equal to the classical velocity, but actually to the velocity "dual" of the classical velocity. The speed of PT's is therefore smaller than the speed of light. Since a lot of experimental data seems to involve a negative mass squared for neutrinos, we suggest that these particles might be PT's, travelling, because of their very small mass, at subluminal speeds very close to c. The present theory is shown to be separately invariant under the C, P, T transformations; the covariance under Lorentz transformations is also proved. Furthermore, we derive the kinematical constraints linking 4-impulse, 4-velocity and 4-polarization of free PT'sComment: LaTeX; 20 page

Generalized entropic measures of quantum correlations

We propose a general measure of non-classical correlations for bipartite systems based on generalized entropic functions and majorization properties. Defined as the minimum information loss due to a local measurement, in the case of pure states it reduces to the generalized entanglement entropy, i.e., the generalized entropy of the reduced state. However, in the case of mixed states it can be non-zero in separable states, vanishing just for states diagonal in a general product basis, like the Quantum Discord. Simple quadratic measures of quantum correlations arise as a particular case of the present formalism. The minimum information loss due to a joint local measurement is also discussed. The evaluation of these measures in a few simple relevant cases is as well provided, together with comparison with the corresponding entanglement monotones.Comment: 9 pages, 2 figure

Dataset: LoED: The LoRaWAN at the Edge dataset

This paper presents the LoRaWAN at the Edge Dataset (LoED), an open LoRaWAN packet dataset collected at gateways. Real-world LoRaWAN datasets are important for repeatable sensor-network and communications research and evaluation as, if carefully collected, they provide realistic working assumptions. LoED data is collected from nine gateways over a four month period in a dense urban environment. The dataset contains packet header information and all physical layer properties reported by gateways such as the CRC, RSSI, SNR and spreading factor. Files are provided to analyse the data and get aggregated statistics. The dataset is available at: doi.org/10.5281/zenodo.412143

Tremor in motor neuron disease may be central rather than peripheral in origin

BACKGROUND AND PURPOSE: Motor neuron disease (MND) refers to a spectrum of degenerative diseases affecting motor neurons. Recent clinical and post-mortem observations have revealed considerable variability in the phenotype. Rhythmic involuntary oscillations of the hands during action, resembling tremor, can occur in MND, but their pathophysiology has not yet been investigated. METHODS: A total of 120 consecutive patients with MND were screened for tremor. Twelve patients with action tremor and no other movement disorders were found. Ten took part in the study. Tremor was recorded bilaterally using surface electromyography (EMG) and triaxial accelerometer, with and without a variable weight load. Power spectra of rectified EMG and accelerometric signal were calculated. To investigate a possible cerebellar involvement, eyeblink classic conditioning was performed in five patients. RESULTS: Action tremor was present in about 10% of our population. All patients showed distal postural tremor of low amplitude and constant frequency, bilateral with a small degree of asymmetry. Two also showed simple kinetic tremor. A peak at the EMG and accelerometric recordings ranging from 4 to 12 Hz was found in all patients. Loading did not change peak frequency in either the electromyographic or accelerometric power spectra. Compared with healthy volunteers, patients had a smaller number of conditioned responses during eyeblink classic conditioning. CONCLUSIONS: Our data suggest that patients with MND can present with action tremor of a central origin, possibly due to a cerebellar dysfunction. This evidence supports the novel idea of MND as a multisystem neurodegenerative disease and that action tremor can be part of this condition

Entanglement-Saving Channels

The set of Entanglement Saving (ES) quantum channels is introduced and characterized. These are completely positive, trace preserving transformations which when acting locally on a bipartite quantum system initially prepared into a maximally entangled configuration, preserve its entanglement even when applied an arbitrary number of times. In other words, a quantum channel $\psi$ is said to be ES if its powers $\psi^n$ are not entanglement-breaking for all integers $n$. We also characterize the properties of the Asymptotic Entanglement Saving (AES) maps. These form a proper subset of the ES channels that is constituted by those maps which, not only preserve entanglement for all finite $n$, but which also sustain an explicitly not null level of entanglement in the asymptotic limit~$n\rightarrow \infty$. Structure theorems are provided for ES and for AES maps which yield an almost complete characterization of the former and a full characterization of the latter.Comment: 26 page

Highly accurate calculations of the rotationally excited bound states in three-body systems

An effective optimization strategy has been developed to construct highly accurate bound state wave functions in various three-body systems. Our procedure appears to be very effective for computations of weakly bound states and various excited states, including rotationally excited states, i.e. states with $L \ge 1$. The efficiency of our procedure is illustrated by computations of the excited $P^{*}(L = 1)-$states in the $dd\mu, dt\mu$ and $tt\mu$ muonic molecular ions, $P(L = 1)-$states in the non-symmetric $pd\mu, pt\mu$ and $dt\mu$ ions and $2^{1}P(L = 1)-$ and $2^{3}P(L = 1)-$states in He atom(s)

An entropic uncertainty principle for positive operator valued measures

Extending a recent result by Frank and Lieb, we show an entropic uncertainty principle for mixed states in a Hilbert space relatively to pairs of positive operator valued measures that are independent in some sense. This yields spatial-spectral uncertainty principles and log-Sobolev inequalities for invariant operators on homogeneous spaces, which are sharp in the compact case.Comment: 14 pages. v2: a technical assumption removed in main resul

Is Phaseolus vulgaris Leucoagglutinin (PHA-L) a Useful Marker for Labeling Neural Grafts?

The lectin Phaseolus vulgaris leucoagglutinin (PHA-L) has come into wide use as an anterograde neuroanatomical tracer. The ability of this lectin to fill entire neurons and remain in place over long periods suggested it might be an ideal marker for donor cells to be grafted into hosts for long survival periods. We have used the lectin PHA-L to mark fetal rat olfactory bulb (OB) cells prior to grafting into host rat OBs. Hosts were sacrificed at various times up to 9 weeks after grafting, and tissue was immunohistochemically processed for PHA reactivity. After 2 and 4 weeks survival, sparse patterns of labeled cells were observed within the host OBs. However, after 9 weeks survival, few if any labeled cells were visible within host tissue. We conclude that PHA-L may be a less than satisfactory marker for fetal rat cells (other than astrocytes) which are to be identified in host tissue after a period of several weeks