Oscillation results for Sturm–Liouville problems with an indefinite weight function

AbstractWe prove oscillation results for the real eigenvalues of Sturm–Liouville problems with an indefinite weight function. An essential role is played by the signature of an eigenvalue, which is shown to be related to the signs of the corresponding leading coefficients of the Titchmarsh–Weyl m-function and of the Prüfer angle at this eigenvalue

Local distinguishability of quantum states in infinite dimensional systems

We investigate local distinguishability of quantum states by use of the convex analysis about joint numerical range of operators on a Hilbert space. We show that any two orthogonal pure states are distinguishable by local operations and classical communications, even for infinite dimensional systems. An estimate of the local discrimination probability is also given for some family of more than two pure states

Structure and function of language networks in temporal lobe epilepsy

Individuals with temporal lobe epilepsy (TLE) may have significant language deficits. Language capabilities may further decline following temporal lobe resections. The language network, comprised of dispersed grey matter regions interconnected with white matter fibres, may be atypical in those with TLE. This review explores the structural changes to the language network and the functional reorganisation of language abilities in TLE. We discuss the importance of detailed reporting of patient's characteristics, such as, left- and right-sided focal epilepsies as well as lesional and non-lesional pathological subtypes. These factors can affect the healthy functioning of grey and/or white matter. Dysfunction of white matter and displacement of grey matter function could impact each other's ability, in turn, producing an interactive effect on typical language organisation and function. Surgical intervention can result in impairment of function if the resection includes parts of this structure-function network that are critical to language. Further, impairment may occur if language function has been reorganized and is included in a resection. Conversely, resection of an epileptogenic zone may be associated with recovery of cortical function and thus improvement in language function. We explore the abnormality of functional regions in a clinically applicable framework and highlight the differences in the underlying language network. Avoidance of language decline following surgical intervention may depend on tailored resections to avoid critical areas of grey matter and their white matter connections. Further work is required to elucidate the plasticity of the language network in TLE and to identify sub-types of language representation, both of which will be useful in planning surgery to spare language function

The level set method for the two-sided eigenproblem

We consider the max-plus analogue of the eigenproblem for matrix pencils Ax=lambda Bx. We show that the spectrum of (A,B) (i.e., the set of possible values of lambda), which is a finite union of intervals, can be computed in pseudo-polynomial number of operations, by a (pseudo-polynomial) number of calls to an oracle that computes the value of a mean payoff game. The proof relies on the introduction of a spectral function, which we interpret in terms of the least Chebyshev distance between Ax and lambda Bx. The spectrum is obtained as the zero level set of this function.Comment: 34 pages, 4 figures. Changes with respect to the previous version: we explain relation to mean-payoff games and discrete event systems, and show that the reconstruction of spectrum is pseudopolynomia

Simulations of extensional flow in microrheometric devices

We present a detailed numerical study of the flow of a Newtonian fluid through microrheometric devices featuring a sudden contraction–expansion. This flow configuration is typically used to generate extensional deformations and high strain rates. The excess pressure drop resulting from the converging and diverging flow is an important dynamic measure to quantify if the device is intended to be used as a microfluidic extensional rheometer. To explore this idea, we examine the effect of the contraction length, aspect ratio and Reynolds number on the flow kinematics and resulting pressure field. Analysis of the computed velocity and pressure fields show that, for typical experimental conditions used in microfluidic devices, the steady flow is highly three-dimensional with open spiraling vortical structures in the stagnant corner regions. The numerical simulations of the local kinematics and global pressure drop are in good agreement with experimental results. The device aspect ratio is shown to have a strong impact on the flow and consequently on the excess pressure drop, which is quantified in terms of the dimensionless Couette and Bagley correction factors. We suggest an approach for calculating the Bagley correction which may be especially appropriate for planar microchannels

A functional model, eigenvalues, and finite singular critical points for indefinite Sturm-Liouville operators

Eigenvalues in the essential spectrum of a weighted Sturm-Liouville operator are studied under the assumption that the weight function has one turning point. An abstract approach to the problem is given via a functional model for indefinite Sturm-Liouville operators. Algebraic multiplicities of eigenvalues are obtained. Also, operators with finite singular critical points are considered.Comment: 38 pages, Proposition 2.2 and its proof corrected, Remarks 2.5, 3.4, and 3.12 extended, details added in subsections 2.3 and 4.2, section 6 rearranged, typos corrected, references adde

The Impact of Temporal Lobe Epilepsy Surgery on Picture Naming and its Relationship to Network Metric Change

Background: Anterior temporal lobe resection (ATLR) is a successful treatment for medically-refractory temporal lobe epilepsy (TLE). In the language-dominant hemisphere, 30%- 50% of individuals experience a naming decline which can impact upon daily life. Measures of structural networks are associated with language performance pre-operatively. It is unclear if analysis of network measures may predict post-operative decline. Methods: White matter fibre tractography was performed on preoperative diffusion MRI of 44 left lateralised and left resection individuals with TLE to reconstruct the preoperative structural network. Resection masks, drawn on co-registered pre- and post-operative T1-weighted MRI scans, were used as exclusion regions on pre-operative tractography to estimate the post-operative network. Changes in graph theory metrics, cortical strength, betweenness centrality, and clustering coefficient were generated by comparing the estimated pre- and post-operative networks. These were thresholded based on the presence of the connection in each patient, ranging from 75% to 100% in steps of 5%. The average graph theory metric across thresholds was taken. We incorporated leave-one-out cross-validation with smoothly clipped absolute deviation (SCAD) least absolute shrinkage and selection operator (LASSO) feature selection and a support vector classifier to assess graph theory metrics on picture naming decline. Picture naming was assessed via the Graded Naming Test preoperatively and at 3 and 12 months post-operatively and the outcome was classified using the reliable change index (RCI) to identify clinically significant decline. The best feature combination and model was selected using the area under the curve (AUC). The sensitivity, specificity and F1-score were also reported. Permutation testing was performed to assess the machine learning model and selected regions difference significance. Results: A combination of clinical and graph theory metrics were able to classify outcome of picture naming at 3 months with an AUC of 0.84. At 12 months, change in strength to cortical regions was best able to correctly classify outcome with an AUC of 0.86. Longitudinal analysis revealed that betweenness centrality was the best metric to identify patients who declined at 3 months, who will then continue to experience decline from 3-12 months. Both models were significantly higher AUC values than a random classifier. Conclusion: Our results suggest that inferred changes of network integrity were able to correctly classify picture naming decline after ATLR. These measures may be used to prospectively to identify patients who are at risk of picture naming decline after surgery and could potentially be utilised to assist tailoring the resection in order to prevent this decline

An Electrochemical Study of Frustrated Lewis Pairs: A Metal-free Route to Hydrogen Oxidation

[Image: see text] Frustrated Lewis pairs have found many applications in the heterolytic activation of H(2) and subsequent hydrogenation of small molecules through delivery of the resulting proton and hydride equivalents. Herein, we describe how H(2) can be preactivated using classical frustrated Lewis pair chemistry and combined with in situ nonaqueous electrochemical oxidation of the resulting borohydride. Our approach allows hydrogen to be cleanly converted into two protons and two electrons in situ, and reduces the potential (the required energetic driving force) for nonaqueous H(2) oxidation by 610 mV (117.7 kJ mol(–1)). This significant energy reduction opens routes to the development of nonaqueous hydrogen energy technology

On the oscillation properties of eigenfunctions of Sturm--Liouville problem with singular coefficients

In the paper we consider singular spectral Sturm--Liouville problem $-(py')'+(q-\lambda r)y=0$, $(U-1)y^{\vee}+i(U+1)y^{\wedge}=0$, where function $p\in L_{\infty}[0,1]$ is uniformly positive, generalized functions $q,r\in W_2^{-1}[0,1]$ are real-valued and unitary matrix $U\in\mathbb C^{2\times 2}$ is diagonal. The main goal is to prove that well-known (for smooth case) facts about number and distribution of zeros of eigenfunctions hold in general case.Comment: 7 page