The t#-property for integral domains

AbstractGeneralizing work of Gilmer and Heinzer, we define a t#-domain to be a domain R in which ⋂M∈M1RM≠⋂M∈M2RM for any two distinct subsets M1 and M2 of the set of maximal t-ideals of R. We provide characterizations of these domains, and we show that polynomial rings over t#-domains are again t#-domains. Finally, we study overrings of t#-domains

Genetic and Neuroanatomical Support for Functional Brain Network Dynamics in Epilepsy

Focal epilepsy is a devastating neurological disorder that affects an overwhelming number of patients worldwide, many of whom prove resistant to medication. The efficacy of current innovative technologies for the treatment of these patients has been stalled by the lack of accurate and effective methods to fuse multimodal neuroimaging data to map anatomical targets driving seizure dynamics. Here we propose a parsimonious model that explains how large-scale anatomical networks and shared genetic constraints shape inter-regional communication in focal epilepsy. In extensive ECoG recordings acquired from a group of patients with medically refractory focal-onset epilepsy, we find that ictal and preictal functional brain network dynamics can be accurately predicted from features of brain anatomy and geometry, patterns of white matter connectivity, and constraints complicit in patterns of gene coexpression, all of which are conserved across healthy adult populations. Moreover, we uncover evidence that markers of non-conserved architecture, potentially driven by idiosyncratic pathology of single subjects, are most prevalent in high frequency ictal dynamics and low frequency preictal dynamics. Finally, we find that ictal dynamics are better predicted by white matter features and more poorly predicted by geometry and genetic constraints than preictal dynamics, suggesting that the functional brain network dynamics manifest in seizures rely on - and may directly propagate along - underlying white matter structure that is largely conserved across humans. Broadly, our work offers insights into the generic architectural principles of the human brain that impact seizure dynamics, and could be extended to further our understanding, models, and predictions of subject-level pathology and response to intervention

Skolem properties, value-functions, and divisorial ideals

AbstractLet D be the ring of integers of a number field K. It is well known that the ring Int(D) = {f ϵ K[X] ¦ f (D) ⊆ D} of integer-valued polynomials on D is a Prüfer domain. Here we study the divisorial ideals of Int(D) and prove in particular that Int(D) has no divisorial prime ideal.We begin with the local case. We show that, if V is a rank-one discrete valuation domain with finite residue field, then the unitary ideals of Int(V) (that is, the ideals containing nonzero constants) are entirely determined by their values on the completion of V. This improves on the Skolem properties which only deal with finitely generated ideals. We then globalize and consider a Dedekind domain D with finite residue fields. We show that a prime ideal of t(D) is invertible if and only if it is divisorial, and also, in the case where the characteristic of D is 0, if and only if it is an upper to zero which is maximal

Towards an ab initio description of the optical spectra of light-harvesting antennae: application to the CP29 complex of photosystem II.

Only going beyond the static crystal picture through molecular dynamics simulations can a realistic excitonic picture of the light-harvesting complex CP29 be obtained using a multiscale polarizable QM/MM approach

Can lymphangiosarcoma be resurrected? A clinicopathological and immunohistochemical study of lymphatic differentiation in 49 angiosarcomas

Mankey C C, McHugh J B, Thomas D G & Lucas D R (2010) Histopathology 56 , 364–371 Can lymphangiosarcoma be resurrected? A clinicopathological and immunohistochemical study of lymphatic differentiation in 49 angiosarcomas The term lymphangiosarcoma has largely been abandoned in the current classification of endothelial neoplasms. Recently, a number of lymphatic-associated antibodies have been developed for immunohistochemistry, which frequently stain angiosarcomas, implying lymphatic or mixed lymphatic and blood vascular differentiation is common. The aim was to investigate further lymphatic antigen expression, and to explore the relation of immunohistochemistry to morphological and clinical findings.Forty-nine angiosarcomas in tissue microarrays were analysed with D2-40 and antibodies to Prox-1 and vascular endothelial growth factor receptor (VEGFR)-3. D2-40 was positive in 53%, Prox-1 in 76%, and VEGFR-3 in 57%. Tumours with features attributable to lymphatic differentiation such as hobnail and kaposiform morphologies were more often positive with these markers, including a statistical association between D2-40 and hobnailing. Ten tumours had features suggestive of lymphatic differentiation, namely well-differentiated histology, interanastomosing channels devoid of red cells, prominent hobnailing, lymphoid aggregates, and multi-antigen expression of D2-40 (100%), Prox-1 (100%) and VEGFR-3 (60%), which might be deserving of the appellation lymphangiosarcoma. Nine were cutaneous scalp/facial tumours in elderly patients and one arose within chronic lymphoedema.Lymphatic differentiation is common in angiosarcoma, certain subsets show greater lymphatic differentiation than others, and lymphangiosarcoma may be defined pathologically, rather than clinically.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/78689/1/j.1365-2559.2010.03484.x.pd

Deterministic entanglement and tomography of ion spin qubits

We have implemented a universal quantum logic gate between qubits stored in the spin state of a pair of trapped calcium 40 ions. An initial product state was driven to a maximally entangled state deterministically, with 83% fidelity. We present a general approach to quantum state tomography which achieves good robustness to experimental noise and drift, and use it to measure the spin state of the ions. We find the entanglement of formation is 0.54.Comment: 3 figures, 4 pages, footnotes fixe

Long-lived mesoscopic entanglement outside the Lamb-Dicke regime

We create entangled states of the spin and motion of a single $^{40}$Ca$^+$ ion in a linear ion trap. The motional part consists of coherent states of large separation and long coherence time. The states are created by driving the motion using counterpropagating laser beams. We theoretically study and experimentally observe the behaviour outside the Lamb-Dicke regime, where the trajectory in phase space is modified and the coherent states become squeezed. We directly observe the modification of the return time of the trajectory, and infer the squeezing. The mesoscopic entanglement is observed up to $\Delta \alpha = 5.1$ with coherence time 170 microseconds and mean phonon excitation \nbar = 16.Comment: 5 pages, 3 figures. Revised version after editor comment

Radiation Dose and Fluoroscopy Time of Endovascular Treatment in Patients with Intracranial Lateral Dural Arteriovenous Fistulae

Purpose. Intracranial lateral dural arteriovenous fistula (LDAVF) represents a specific subtype of cerebrovascular fistulae, harboring a potentially life-threatening risk of brain hemorrhage. Fluoroscopically guided endovascular embolization is the therapeutic gold standard. We provide detailed dosimetry data to suggest novel diagnostic reference levels (DRL). Methods. Retrospective single-center study of LDAVFs treated between January 2014 and December 2019. Regarding dosimetry, the dose area product (DAP) and fluoroscopy time were analyzed for the following variables: Cognard scale grade, endovascular technique, angiographic outcome, and digital subtraction angiography (DSA) protocol. Results. A total of 70 patients (19 female, median age 65 years) were included. Total median values for DAP and fluoroscopy time were 325 Gy cm2 (25%/75% percentile: 245/414 Gy cm2) and 110 min (68/142min), respectively. Neither median DAP nor fluoroscopy time were significantly different when comparing low-grade with high-grade LDAVF (Cognard I + IIa versus IIb–V; p > 0.05, each). Transvenous coil embolization yielded the lowest dosimetry values, with significantly lower median values when compared to a combined transarterial/transvenous technique (DAP 290 Gy cm2 versus 388 Gy cm2, p = 0.031; fluoroscopy time 85 min versus 170 min, p = 0.016). A significant positive correlation was found between number of arterial feeders treated by liquid embolization and both DAP (rs = 0.367; p = 0.010) and fluoroscopy time (rs = 0.295; p = 0.040). Complete LDAVF occlusion was associated with transvenous coiling (p = 0.001). A low-dose DSA protocol yielded a 20% reduction of DAP (p = 0.021). Conclusion. This LDAVF study suggests several local DRLs which varied substantially dependent on the endovascular technique and DSA protocol