Real space first-principles derived semiempirical pseudopotentials applied to tunneling magnetoresistance

In this letter we present a real space density functional theory (DFT) localized basis set semi-empirical pseudopotential (SEP) approach. The method is applied to iron and magnesium oxide, where bulk SEP and local spin density approximation (LSDA) band structure calculations are shown to agree within approximately 0.1 eV. Subsequently we investigate the qualitative transferability of bulk derived SEPs to Fe/MgO/Fe tunnel junctions. We find that the SEP method is particularly well suited to address the tight binding transferability problem because the transferability error at the interface can be characterized not only in orbital space (via the interface local density of states) but also in real space (via the system potential). To achieve a quantitative parameterization, we introduce the notion of ghost semi-empirical pseudopotentials extracted from the first-principles calculated Fe/MgO bonding interface. Such interface corrections are shown to be particularly necessary for barrier widths in the range of 1 nm, where interface states on opposite sides of the barrier couple effectively and play a important role in the transmission characteristics. In general the results underscore the need for separate tight binding interface and bulk parameter sets when modeling conduction through thin heterojunctions on the nanoscale.Comment: Submitted to Journal of Applied Physic

On the degree conjecture for separability of multipartite quantum states

We settle the so-called degree conjecture for the separability of multipartite quantum states, which are normalized graph Laplacians, first given by Braunstein {\it et al.} [Phys. Rev. A \textbf{73}, 012320 (2006)]. The conjecture states that a multipartite quantum state is separable if and only if the degree matrix of the graph associated with the state is equal to the degree matrix of the partial transpose of this graph. We call this statement to be the strong form of the conjecture. In its weak version, the conjecture requires only the necessity, that is, if the state is separable, the corresponding degree matrices match. We prove the strong form of the conjecture for {\it pure} multipartite quantum states, using the modified tensor product of graphs defined in [J. Phys. A: Math. Theor. \textbf{40}, 10251 (2007)], as both necessary and sufficient condition for separability. Based on this proof, we give a polynomial-time algorithm for completely factorizing any pure multipartite quantum state. By polynomial-time algorithm we mean that the execution time of this algorithm increases as a polynomial in $m,$ where $m$ is the number of parts of the quantum system. We give a counter-example to show that the conjecture fails, in general, even in its weak form, for multipartite mixed states. Finally, we prove this conjecture, in its weak form, for a class of multipartite mixed states, giving only a necessary condition for separability.Comment: 17 pages, 3 figures. Comments are welcom

Covering Partial Cubes with Zones

A partial cube is a graph having an isometric embedding in a hypercube. Partial cubes are characterized by a natural equivalence relation on the edges, whose classes are called zones. The number of zones determines the minimal dimension of a hypercube in which the graph can be embedded. We consider the problem of covering the vertices of a partial cube with the minimum number of zones. The problem admits several special cases, among which are the problem of covering the cells of a line arrangement with a minimum number of lines, and the problem of finding a minimum-size fibre in a bipartite poset. For several such special cases, we give upper and lower bounds on the minimum size of a covering by zones. We also consider the computational complexity of those problems, and establish some hardness results

Cardiolipin-containing lipid membranes attract the bacterial cell division protein diviva

DivIVA is a protein initially identified as a spatial regulator of cell division in the model organism Bacillus subtilis, but its homologues are present in many other Gram-positive bacteria, including Clostridia species. Besides its role as topological regulator of the Min system during bacterial cell division, DivIVA is involved in chromosome segregation during sporulation, genetic competence, and cell wall synthesis. DivIVA localizes to regions of high membrane curvature, such as the cell poles and cell division site, where it recruits distinct binding partners. Previously, it was suggested that negative curvature sensing is the main mechanism by which DivIVA binds to these specific regions. Here, we show that Clostridioides difficile DivIVA binds preferably to membranes containing negatively charged phospholipids, especially cardiolipin. Strikingly, we observed that upon binding, DivIVA modifies the lipid distribution and induces changes to lipid bilayers containing cardiolipin. Our observations indicate that DivIVA might play a more complex and so far unknown active role during the formation of the cell division septal membrane

Infinite motion and 2-distinguishability of graphs and groups

A group A acting faithfully on a set X is 2-distinguishable if there is a 2-coloring of X that is not preserved by any nonidentity element of A, equivalently, if there is a proper subset of X with trivial setwise stabilizer. The motion of an element a in A is the number of points of X that are moved by a, and the motion of the group A is the minimal motion of its nonidentity elements. When A is finite, the Motion Lemma says that if the motion of A is large enough (specifically at least 2 log_2 |A|), then the action is 2-distinguishable. For many situations where X has a combinatorial or algebraic structure, the Motion Lemma implies that the action of Aut(X) on X is 2-distinguishable in all but finitely many instances. We prove an infinitary version of the Motion Lemma for countably infinite permutation groups, which states that infinite motion is large enough to guarantee 2-distinguishability. From this we deduce a number of results, including the fact that every locally finite, connected graph whose automorphism group is countably infinite is 2-distinguishable. One cannot extend the Motion Lemma to uncountable permutation groups, but nonetheless we prove that (under the permutation topology) every closed permutation group with infinite motion has a dense subgroup which is 2-distinguishable. We conjecture an extension of the Motion Lemma which we expect holds for a restricted class of uncountable permutation groups, and we conclude with a list of open questions. The consequences of our results are drawn for orbit equivalence of infinite permutation groups

The generalized 3-edge-connectivity of lexicographic product graphs

The generalized $k$-edge-connectivity $\lambda_k(G)$ of a graph $G$ is a generalization of the concept of edge-connectivity. The lexicographic product of two graphs $G$ and $H$, denoted by $G\circ H$, is an important graph product. In this paper, we mainly study the generalized 3-edge-connectivity of $G \circ H$, and get upper and lower bounds of $\lambda_3(G \circ H)$. Moreover, all bounds are sharp.Comment: 14 page

Ramified rectilinear polygons: coordinatization by dendrons

Simple rectilinear polygons (i.e. rectilinear polygons without holes or cutpoints) can be regarded as finite rectangular cell complexes coordinatized by two finite dendrons. The intrinsic $l_1$-metric is thus inherited from the product of the two finite dendrons via an isometric embedding. The rectangular cell complexes that share this same embedding property are called ramified rectilinear polygons. The links of vertices in these cell complexes may be arbitrary bipartite graphs, in contrast to simple rectilinear polygons where the links of points are either 4-cycles or paths of length at most 3. Ramified rectilinear polygons are particular instances of rectangular complexes obtained from cube-free median graphs, or equivalently simply connected rectangular complexes with triangle-free links. The underlying graphs of finite ramified rectilinear polygons can be recognized among graphs in linear time by a Lexicographic Breadth-First-Search. Whereas the symmetry of a simple rectilinear polygon is very restricted (with automorphism group being a subgroup of the dihedral group $D_4$), ramified rectilinear polygons are universal: every finite group is the automorphism group of some ramified rectilinear polygon.Comment: 27 pages, 6 figure

Using graph-kernels to represent semantic information in text classification

Most text classification systems use bag-of-words represen- tation of documents to find the classification target function. Linguistic structures such as morphology, syntax and semantic are completely ne- glected in the learning process. This paper proposes a new document representation that, while includ- ing its context independent sentence meaning, is able to be used by a structured kernel function, namely the direct product kernel. The proposal is evaluated using a dataset of articles from a Portuguese daily newspaper and classifiers are built using the SVM algorithm. The results show that this structured representation, while only partially de- scribing document’s significance has the same discriminative power over classes as the traditional bag-of-words approach

Regular graphs of large girth and arbitrary degree

For every integer d > 9, we construct infinite families {G_n}_n of d+1-regular graphs which have a large girth > log_d |G_n|, and for d large enough > 1,33 log_d |G_n|. These are Cayley graphs on PGL_2(q) for a special set of d+1 generators whose choice is related to the arithmetic of integral quaternions. These graphs are inspired by the Ramanujan graphs of Lubotzky-Philips-Sarnak and Margulis, with which they coincide when d is prime. When d is not equal to the power of an odd prime, this improves the previous construction of Imrich in 1984 where he obtained infinite families {I_n}_n of d+1-regular graphs, realized as Cayley graphs on SL_2(q), and which are displaying a girth > 0,48 log_d |I_n|. And when d is equal to a power of 2, this improves a construction by Morgenstern in 1994 where certain families {M_n}_n of 2^k+1-regular graphs were shown to have a girth > 2/3 log_d |M_n|.Comment: (15 pages) Accepted at Combinatorica. Title changed following referee's suggestion. Revised version after reviewing proces

Effects of Nitisinone on Oxidative and Inflammatory Markers in Alkaptonuria: Results from SONIA1 and SONIA2 Studies

Nitisinone (NTBC) was recently approved to treat alkaptonuria (AKU), but there is no information on its impact on oxidative stress and inflammation, which are observed in AKU. Therefore, serum samples collected during the clinical studies SONIA1 (40 AKU patients) and SONIA2 (138 AKU patients) were tested for Serum Amyloid A (SAA), CRP and IL-8 by ELISA; Advanced Oxidation Protein Products (AOPP) by spectrophotometry; and protein carbonyls by Western blot. Our results show that NTBC had no significant effects on the tested markers except for a slight but statistically significant effect for NTBC, but not for the combination of time and NTBC, on SAA levels in SONIA2 patients. Notably, the majority of SONIA2 patients presented with SAA > 10 mg/L, and 30 patients in the control group (43.5%) and 40 patients (58.0%) in the NTBC-treated group showed persistently elevated SAA > 10 mg/L at each visit during SONIA2. Higher serum SAA correlated with lower quality of life and higher morbidity. Despite no quantitative differences in AOPP, the preliminary analysis of protein carbonyls highlighted patterns that deserve further investigation. Overall, our results suggest that NTBC cannot control the sub-clinical inflammation due to increased SAA observed in AKU, which is also a risk factor for developing secondary amyloidosis. © 2022 by the authors